Florida State University Libraries

Transcription

1 Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2004 Synthesis and Characterization of Single- Molecule Magnets: Mn##-Acetate, Fe#Br#, and Analogs Jeremy Micah North Follow this and additional works at the FSU Digital Library. For more information, please contact

2 THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCE Synthesis and Characterization of Single-Molecule Magnets: Mn 12 -Acetate, Fe 8 Br 8, and Analogs By JEREMY MICAH NORTH A dissertation submitted to the Department of Chemistry and Biochemistry in partial fulfillment of the requirements for the degree of Doctorate of Philosophy Degree Awarded: Spring Semester, 2004

3 The members of the Committee approve the thesis of Jeremy Micah North defended on March 19, Naresh Dalal Professor Directing Thesis Alan Marshall Committee Member Oliver Steinbock Committee Member James Brooks Committee Member Approved: Naresh Dalal, Chair, Department of Chemistry and Biochemistry The Office of Graduate Studies has verified and approved the above named committee members. ii

4 TABLE OF CONTENTS List of Tables... vi List of Figures... vii Abstract... ix 1. INTRODUCTION Introduction Overview SYNTHESIS AND EXPERIMENTAL TECHNIQUES Synthesis of Materials Synthesis of Mn 12 -ac Synthesis of Mn 8 Fe Synthesis of Fe 8 Br FeCl 3 tacn Fe 8 Br Synthesis of Fe 8 Br 4 (ClO 4 ) 4 and Fe 8 Br 6.4 (ClO 4 ) Experimental Techniques Conductivity Measurements Photoconductivity Measurements microraman and Infrared Spectroscopy Measurements Single Crystal EPR Measurements ELECTRICAL CONDUCTIVITY MEASUREMENTS OF Mn 12 -ac AND Fe 8 Br iii

5 3.1 Introduction Experimental Setup Electrical Conductivity Measurements of Mn 12 -ac Effect of x-ray irradiation on Mn 12 -ac Photoconductivity Measurements of Mn 12 -ac Conductivity of Fe 8 Br Conduction Pathways Summary RAMAN AND IR CHARACTERIZATION OF THE SMM S Mn 12 -Ac AND Fe 8 Br Overview of Raman and IR experiments Experimental Details Laser Damage of Mn 12 -ac Raman Spectra of Mn 12 -ac and Analogs Fe 8 Br 8 and Analogs Summary and Conclusions ELECTRON PARAMAGNETIC RESONANCE INVESTIGATIONS OF Mn 12 -Ac Introduction Experimental Details α-and β-resonances Angle Dependent EPR Measurements Conclusions...59 iv

6 6. MAIN RESULTS AND CONCLUSIONS Discovery of Semiconducting Behavior in Mn 12 -ac and Fe 8 Br Elucidation of Vibrational Modes EPR Evidence of the Second-Order anisotropy in Mn 12 -ac Summary...67 REFERENCES...68 BIOGRAPHICAL SKETCH...76 v

7 LIST OF TABLES Table 3.1 Optical Band Gap Values of Mn 12 -ac and Fe 8 Br Table 4.1 Comparison of Raman Peak Positions for Mn 12 -ac and analogs...43 Table 4.2 Comparison of Raman Peak Positions for Fe 8 Br 8 and analogs...44 vi

8 LIST OF FIGURES Figure 1.1 Schematic of Mn 12 -ac...6 Figure 1.2 Schematic of Fe 8 Br Figure 1.3 Magnetic Hysteresis Loop of Mn 12 -ac...8 Figure 1.4 Potential energy diagram of Mn 12 -ac in zero magnetic field...9 Figure 2.1 Single crystals of Mn 12 -ac and Fe 8 Br Figure 2.2 Drawing of four-probe technique for conductivity measurements...18 Figure 2.3 Typical setup used for photoconductivity measurements...19 Figure 2.4 Simplified Schematic of the micro-raman spectrometer...20 Figure 2.5 Schematic of system used for EPR measurements...21 Figure 3.1 Temperature dependence of the resistance of Mn 12 -ac...29 Figure 3.2 Conductivity measurements of Mn 12 -ac with constant current...30 Figure 3.3 Photoconductivity measurements of Mn 12 -ac...31 Figure 3.4 Conductivity measurements of Fe 8 Br Figure 3.5 Proposed conduction pathway of Mn 12 -ac...33 Figure 3.6 Proposed conduction pathway of Fe 8 Br Figure 4.1 Raman spectra of undamaged and laser damaged Mn 12 -ac...45 Figure 4.2 Raman spectra of Mn 12 -ac and analogous compounds...46 Figure 4.3 Raman spectra of Mn 12 -ac and model compounds...47 Figure 4.4 Comparison of Raman and IR spectra of Mn 12 -ac...48 vii

9 Figure 4.5 Raman spectra of Fe 8 Br 8 and 17 O-labeled Fe 8 Br Figure 4.6 Raman spectra of Fe 8 Br 8 and the perchlorate analogs...50 Figure 4.7 Raman spectra of Fe 8 Br 8 and model compounds...51 Figure 4.8 Temperature dependence of the Raman spectrum of Fe 8 Br Figure 4.9 Polarized Raman spectra of Fe 8 Br Figure 4.10 Comparison of the Raman and IR spectra of Fe 8 Br Figure 5.1 Schematic of Mn 12 -ac isomers...60 Figure 5.2 Energy level diagram for Mn 12 -ac...61 Figure 5.3 Temperature and Frequency dependence of EPR spectra...62 Figure 5.4 Simulation of angular dependence of EPR spectra at 44 GHz and 15 K..63 Figure 5.5 Angular dependence of experimental EPR spectra at 62 GHz and 15 K...64 Figure 5.6 Simulation of angular dependence of EPR spectra at 62 GHz and 15 K..65 viii

10 ABSTRACT This dissertation describes the synthesis and characterization of two new compounds that are among the most studied materials in solid state chemistry over the past eight or so years. The compounds investigated are [Mn 12 O 12 (CH 3 COO) 16 (H 2 O) 4 ] 2CH 3 COOH 4H 2 O (Mn 12 -ac), [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 7 (H 2 O)Br 8H 2 O (Fe 8 Br 8 ), and several of their analogs. All of these compounds exhibit unusual magnetic ground states, with high electron spin, S = 10, and the novel phenomenon of magnetic quantum tunneling (MQT), whose origin is still not fully understood. We developed methods of growing large, high quality crystals, perhaps the best ones in the literature. We then investigated these materials using electrical conductivity measurements, Raman and infrared spectroscopy, and high-frequency electron paramagnetic resonance (EPR) spectroscopy, and obtained results that should elicit further theoretical and experimental investigations. Chapter 1 provides a general introduction to the field of study here, the topic of single molecule magnets. It summarizes the general properties of these materials and lays the foundation for the studies outlined here. Chapter 2 discusses the synthesis of the materials studied and describes the experimental parameters of each of the techniques used for characterization. Chapter 3 reports our electrical conductivity measurements on Mn 12 -ac, and Fe 8 Br 8, which establish these materials as semiconductors. It also describes measurements that show the photoconductive properties of Mn 12 -ac. Chapter 4 presents Raman and infrared spectroscopy measurements on both materials. Through the use of model compounds and theoretical calculations we were able to assign the majority of the modes in Mn 12 -ac and Fe 8 Br 8. These data report the frequencies of several low-lying vibrations that might be important in the mechanism of MQT. The results of highfrequency single crystal EPR measurements of Mn 12 -ac are reported in Chapter 5. These measurements have shown evidence for a distribution of tilts in the magnetic easy axes of Mn 12 -ac, which could help to explain the mechanism by which magnetic quantum tunneling occurs in this system. Finally, Chapter 6 reports and summarizes the main ix

11 conclusions of this dissertation. Taken together, these results should constitute a significant step in our understanding of the unusual properties of these materials, such as MQT, and should also elicit further theoretical and experimental investigations. x

12 CHAPTER 1 INTRODUCTION 1.1 Introduction The primary focus of this dissertation is the synthesis, spectroscopic, and electrical conductivity investigations of a family of novel compounds that have come to be known as single-molecule magnets (SMMs)[1-3]. The SMMs investigated here, [Mn 12 O 12 (CH 3 COO) 16 (H 2 O) 4 ] 2CH 3 COOH 4H 2 O (abbreviated Mn 12 -ac) [4], and [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 7 (H 2 O)Br 8H 2 O (Fe 8 Br 8 ) [5], were selected because they are among the best characterized of these materials. Both of these compounds contain unpaired electrons which are coupled in a manner that gives rise to a total spin of S = 10. As seen in Figure 1.1, the core of the Mn 12 -ac system consists of 12 mixed-valence Mn ions, which are bound to one another through oxygen bridges. Four Mn 4+ (3d 3, S = 3/2) ions are ferromagnetically coupled to one another in a cubane structure which gives rise to a total spin S = 6. The remaining eight Mn 3+ (3d 4, S = 2) are also ferromagnetically coupled to one another in a crown structure for a total spin of S = 16. The Mn 3+ crown is antiferromagnetically coupled to the inner Mn 4+ cubane, yielding a total net spin of S = 16-6 = 10 for each molecule. Figure 1.2 provides a schematic of the core structure of the Fe 8 Br 8 molecule, which is comprised of eight high spin Fe 3+ (3d 5, S = 5/2) ions. Six of the Fe 3+ ions are ferromagnetically coupled to one another, while the remaining two are antiferromagnetically linked to these six. This gives a net total spin of S = 15 5 = 10, as well. Single-molecule magnets are defined as systems in which a magnetic domain can be reduced to the size of a single molecule below a certain temperature known as the 1

13 blocking temperature, T B [1-3]. The T B for Mn 12 -ac is about 3 K [6], while that for Fe 8 Br 8 is about 1 K [7]. Experimentally, evidence of this criterion is obtained by the presence of magnetic hysteresis in very dilute samples frozen into organic solvents and polymer films [8]. Measurements of dilute samples delineate the effect of any potential coupling between the molecules, indicating the magnetic hysteresis observed can be attributed to properties of each individual molecule as opposed to its observation as a macroscopic domain behavior. Furthermore, the observed magnetic hysteresis loops show sharp steps as seen in Figure 1.3 [6, 7, 9,10]. These quantized steps are an indication of the rare phenomenon known as magnetic quantum tunneling (MQT). In order to understand the phenomenon of MQT, Figure 1.4 presents a brief schematic. SMMs can be visualized in the spin space as being doubly degenerate in the +/- m s spin quantum numbers at zero magnetic field, where the m s levels take the usual (2S+1) values S, -S+1 S-1, S. The + m s and m s values are separated by a barrier (vide infra). To a good approximation, these giant spin systems can be described with the following spin Hamiltonian: Ĥ = µ B B g S + DS z 2 + E(S x 2 - S y 2 ) + B 4 0 O B 4 2 O B 4 4 O Ĥ / (1.1) Here the z-axis is the easy axis of magnetization, and should usually correspond to the highest symmetry axis of the system. The first term is the electron Zeeman interaction, D is the zero-field uniaxial anisotropy parameter, and E is the second order rhombic anisotropy term. The fourth-order terms are given by the spin operator O 0 4 = 35 S 4 z [30S(S +1)-25]S 2 z - 6S(S+1) + 3S 2 (S+1) 2, O 2 4 = 1/4[7S 2 z -S(S + 1)-5](S S 2 - ) + (S S 2 - )[7S 2 z S(S+1) 5], and O 4 4 = 1/2(S S 4 - ) [11]. Ĥ / denotes hyperfine, dipolar and exchange couplings that may be present, and may not commute with the main part of Ĥ. We note that Eq. (1.1) neglects the nuclear Zeeman term and quadrupolar interactions due their small impact. The height of the classical barrier to magnetization reversal is given by ~ DS 2. (For complete accuracy, all diagonal terms in S 4 z, specifically B 0 4, also contribute to the barrier height.) With this scenario in mind, MQT would be defined as the tunneling of the magnetization vector from a level on one side of the barrier to a level on the other side labeled m s. Phonon assisted MQT is defined as when the 2

14 magnetization vector is excited to an m s level closer to the top of the barrier due to thermal excitations and then tunnels through the barrier [12]. Aside from the quantized steps in the magnetic hysteresis loops, MQT also manifests itself in the magnetic relaxation data. Below a certain temperature, the magnetic relaxation becomes essentially temperature independent [9, 10]. This implies the magnetization vector is not being thermally activated across the top of the barrier, but is instead tunneling through the potential barrier (~ DS 2 ). It should be noted that pure quantum tunneling in Mn 12 -ac was first observed by Bokacheva et al. [13]. 1.2 Overview The studies described in this dissertation were initiated in the Fall of At that time Mn 12 -ac and Fe 8 Br 8 had been investigated experimentally by magnetic susceptibility [6, 7, 9,10], nuclear magnetic resonance (NMR) [14-17], electron paramagnetic resonance (EPR) [18-21], neutron scattering [22-25], and heat capacity measurements [26-29]. Both compounds had been investigated theoretically [30-38]. There were however, several significant questions remaining unanswered, which provided the impetus for this undertaking. An important unanswered question about Mn 12 -ac and Fe 8 Br 8 was regarding the electric transport property of these materials. In particular, while the band-gap for Mn 12 - ac had been assessed from optical absorption measurements, there were no data by direct conductivity measurements. During the investigations underway in this dissertation, optical studies of Mn 12 -ac predicted optical band gaps, E g, of about 1.10 and 1.75 ev for the minority and majority spin systems [39]. These data were in only rough agreement with the electronic structure calculations [36, 37], as discussed in Chapter 3. We thus undertook a systematic study to determine the band gap on both Mn 12 -ac and Fe 8 Br 8. One of the most fundamental issues had to deal with understanding and explaining the mechanism of MQT. In order for MQT to occur, there must be a transverse term in the Hamiltonian. This transverse term provides for mixing between the different m s levels. In the Fe 8 Br 8 system, this obligation is met by the presence of a rhombic term (E(S 2 x -S 2 y )). Because Mn 12 -ac has S 4 molecular site symmetry, it has been 3

15 thought that there was no rhombic term in its spin Hamiltonian. Because MQT is known to occur in Mn 12 -ac, there must be some other mechanism which generates a transverse component. The two leading theories to determine the origin of the required symmetry breaking for MQT invoked either (a) nuclear hyperfine terms [32,33,40] or (b) the presence of the higher order terms in the spin Hamiltonian [9, 18]. The presence of a fourth-order terms in the spin Hamiltonian in Mn 12 -ac would provide for mixing between the m s = ±4 levels. Recently, Pederson and co workers at the Naval Research Laboratory had predicted theoretically the frequencies of certain Raman active modes that might be related to the fourth-order anisotropy terms [41] in Mn 12 -ac. There was thus a perceived need for Raman measurements on these SMMs. As will be discussed in Chapter 4, the Raman measurements were complicated because of easy damage by the exciting laser radiation. We thus developed a procedure to minimize the damage and acquire sufficient data. To further add to the debate about the true origin of the transverse terms responsible for MQT in Mn 12 -ac, Cornia et al. recently proposed a model involving disorder of the acetic acids of crystallization [42]. The location and number of acetic acids of crystallization in the structure could potentially break the symmetry of the molecule, thereby providing a direct mechanism for MQT to occur. Therefore, there was a need for angular dependent high frequency EPR measurements to detect and characterize the different isomers observed by Cornia et al. [42]. These measurements led to the discovery of a distribution of tilts of the magnetic easy axes away from the crystallographic c axis of the sample. The results from this study are the subject of Chapter 5. During this undertaking, several significant papers have appeared. These include studies using NMR [43-51], EPR [52-61], optical measurements [62-66], electrical conductivity [67], susceptibility, [68-70], and theoretical studies [71-74]. The relevance of these studies to the present work is brought out in this dissertation. The dissertation is organized as follows: A brief section on the synthesis of both Mn 12 -ac and Fe 8 Br 8, along with the experimental details from each experiment will be provided in Chapter 2. The results from conductivity measurements of both Mn 12 -ac and Fe 8 Br 8 are described in Chapter 3. The Raman and infrared spectroscopy investigations 4

16 of Mn 12 -ac and Fe 8 Br 8 are the subjects of Chapter 4. The focus of Chapter 5 is on the high frequency EPR measurements of Mn 12 -ac, which were performed to probe for possible disorder in the structure that might be responsible for MQT. Finally, Chapter 6 summarizes the major conclusions of this dissertation. 5

17 Schematic of Mn 12 -ac Fig Structure of [Mn 12 O 12 (CH 3 COO) 16 (H 2 O) 4 ] 2CH 3 COOH 4H 2 O (abbreviated Mn 12 -ac) [4]. The arrows indicate the coupling between the different Mn ions. Four Mn 4+ (3d 3, S = 3/2) are ferromagnetically coupled for at total spin of S = 6. The remaining eight Mn 3+ (3d 4, S = 2) are also ferromagnetically coupled to one another in a crown structure for a total spin of S = 16. The Mn 3+ crown is antiferromagnetically coupled to the inner Mn 4+ cubane, yielding a total net spin of S = 16-6 = 10. 6

18 Schematic of Fe 8 Br 8 Fig This schematic shows the structure of [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 7 (H 2 O)Br 8H 2 O (Fe 8 Br 8 ) [5]. Six of the Fe 3+ (3d 5, S = 5/2) ions are ferromagnetically coupled to one another, while the remaining two are antiferromagnetically linked to these six, as highlighted by the arrows. This yields a net total spin of S = 15 5 = 10. 7

19 Mn 12 -Ac T = 2.1 K 50 mt/min (Blue) Classical Loop (Red) Fig The magnetic hysteresis loop of Mn 12 -ac is shown at 2.1 K for B ll easy axis [10]. The steps, which are an indication of the phenomenon of MQT, occur when the m s levels on each side of the classical barrier become degenerate as a result of the applied magnetic field, and the magnetization vector can tunnel across. 8

20 Phonon Assisted MQT Direct MQT Fig Schematic of the degenerate m s levels in zero magnetic field, separated by the classical barrier, whose height is given by ~ DS 2, where D is the zero-field splitting parameter. It should be noted that all of the diagonal terms in S z 4 (B 4 0 ) also contribute to the barrier, not just DS 2. Magnetic quantum tunneling (MQT) is defined as the tunneling of the magnetization vector from a level on one side of the classical energy barrier to a level on the other side. Phonon assisted MQT occurs when the magnetization vector is excited to a higher energy m s level and then tunnels through the barrier. 9

21 CHAPTER 2 SYNTHESIS AND EXPERIMENTAL TECHNIQUES This chapter presents the general experimental details of the studies presented in this dissertation. It begins with the procedures for the syntheses for all the materials studied in this dissertation. In most cases, the compounds were synthesized according to previously reported methods, with slight variations to increase the size and quality of the crystals. The chapter subsequently describes the experimental setup and parameters for each of the techniques utilized herein. 2.1 Synthesis of Materials The syntheses of both of the title compounds in this dissertation [Mn 12 O 12 (CH 3 COO) 16 (H 2 O) 4 ] 2CH 3 COOH 4H 2 O (abbreviated Mn 12 -ac) and [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 7 (H 2 O)Br 8H 2 O (abbreviated Fe 8 Br 8 ) were carried out in similar methods to what was first reported by Lis and Weighardt, respectively [4,5]. The procedure published by Schake et al. [75] was used to synthesize [Mn 8 Fe 4 O 12 (CH 3 COO) 16 (H 2 O) 4 ] 2CH 3 COOH 4H 2 O, (Mn 8 Fe 4 ), which is isostructural to Mn 12 -ac. The original syntheses of two analogs of Fe 8 Br 8, [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 4 (ClO 4 ) 4 8H 2 O and [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 6.4 (ClO 4 ) 1.6 8H 2 O (abbreviated Fe 8 Br 4 (ClO 4 ) 4 and Fe 8 Br 6.4 (ClO 4 ) 1.6, respectively), each containing 20% and 50% perchlorate (ClO - 4 ) [64], are also contained in this section Synthesis of Mn 12 -ac [4] In a typical procedure 4.0 g of Mn(CH 3 CO 2 ) 2 4H 2 O was added to 40 ml of a 60% acetic acid and water solution. The mixture was stirred continually until all of the 10

22 Mn(CH 3 CO 2 ) 2 4H 2 O was completely dissolved. 1.0 g of finely ground KMnO 4 was then added in small amounts over the course of about 2 minutes. The resulting solution was allowed to stir approximately 1 additional minute until all of the KMnO 4 was dissolved. (It should be noted that stirring for periods longer than 1 minute results in the formation of powders, rather than good quality crystals.) The final solution was removed from the stir plate and allowed to sit undisturbed for 3 days, during which time long black rectangular rods crystallized. These Mn 12 -ac crystals typically grew to the dimensions of about 0.5 x 0.5 x 3.0 mm 3. The crystals were filtered in a Buchner funnel and washed with acetone. The collected crystals were then bottled and stored in a refrigerator. A typical crystal of Mn 12 -ac is shown in Figure 2.1. Crystals of deuterated Mn 12 -ac were synthesized in the same manner, using deuterated acetic acid and D 2 O. The deuterated crystals were similar in appearance to the undeuterated ones, but generally of better quality and larger size. Mn 12 -ac crystallizes in the tetragonal space group, with a = b = Å, c = Å, V = 3716 Å 3, and Z = 2 [4]. The molecule itself has S 4 crystallographic symmetry. All of the Mn ions have a distorted octahedral coordination and are bound to one another via triply bridged oxygen atoms. The strong Jahn-Teller distortions in the molecule allow for the identification of Mn 3+ and Mn 4+ atoms. The outer crown of the Mn 12 -ac system is comprised of 8 ferromagnetically coupled Mn 3+ (3d 4, S = 2) atoms. The inner cubane structure contains 4 Mn 4+ (3d 3, S = 3/2), which are also ferromagnetically coupled to one another. The two subsystems are antiferromagnetically coupled to one another yielding a total ground state spin, S = 10 for the molecule. The sample authenticity was routinely verified by x-ray diffraction, with the help of Dr. Khalil Abboud at University of Florida, or Dr. Ronald Clark, here, and SQUID magnetization measurements in our laboratory Synthesis of Mn 8 Fe 4 [75] The isostructural compound [Mn 8 Fe 4 O 12 (CH 3 COO) 16 (H 2 O) 4 ] 2CH 3 COOH 4H 2 O (abbreviated Mn 8 Fe 4 ), in which four of the Mn 3+ in the crown are alternately replaced with Fe 3+, was synthesized by the method first reported by Schake et al.[75]. 11

23 5.0g of Fe(CH 3 CO 2 ) 2 was dissolved in 60 ml of a 60% acetic acid and water solution. Once the Fe(CH 3 CO 2 ) 2 was completely dissolved, 1.77 g of KMnO 4 was slowly added and stirred until dissolved. The solution was removed from the stir plate and heated to 60 o C. The heated solution was set aside and allowed to cool undisturbed. Once cooled, the solution was layered with acetone and again set aside undisturbed. After about 14 to 18 days, small rectangular rods similar in size and shape to Mn 12 -ac formed. The crystals were collected on filter paper and washed with an excess of acetone. The collected crystals were then bottled and stored in a refrigerator. The Mn 8 Fe 4 crystals are tetragonal, with the following unit cell parameters a = b= Å, c = Å, V = Å 3, and Z = 2 [75]. Each molecule has S 4 symmetry. The structure contains a central cubane structure comprised of Mn 4+ and oxygen, as in the Mn 12 -ac case. The outer crown is composed of an alternating arrangement of 4 Mn 3+ and 4 Fe 3+ atoms. As discussed by Schake et al. [75], identification of the Mn 3+ vs. the Fe 3+ was aided by the lack of Jahn-Teller distortion in the Fe 3+ ions. The magnetization data shows Mn 8 Fe 4 has a well-isolated S = 2 ground state [75]. The sample purity was checked through x-ray diffraction and magnetic susceptibility (SQUID) measurements. 2.2 Synthesis of Fe 8 Br 8 [5] The synthesis of Fe 8 Br 8 requires a precursor compound, FeCl 3-1,4,7 triazacyclononane (tacn). A description of the synthesis of the Fe 8 Br 8 precursor, FeCl 3 tacn follows, following Weighardt et al. [5] FeCl 3 tacn [5] Typically, 3.5 g of FeCl 3 6H 2 O was stirred and dissolved in about 100 ml of ethanol. 500 mg of 1,4,7 triazacyclononane (tacn) was dissolved in about 4 ml of ethanol. The tacn ligand was added to a stirred ethanolic solution of FeCl 3 6H 2 O. Immediately, a bright yellow precipitate was formed. The solution was filtered on a sintered glass frit, and the precipitate was washed with an excess of ethanol, as described by Weighardt [5]. 12

24 2.2.2 Fe 8 Br 8 [5] 0.25 g of FeCl 3 tacn was weighed out and added to a 50 ml Erlenmeyer flask. 20 ml of H 2 O and 2 ml of pyridine was added and the solution stirred for approximately 20 minutes. During this time, the color of the solution changed from bright yellow to very dark brown. When the solution reached the desired shade of brown, 5.0 g of NaBr was added to the mixture. This was allowed to stir for an additional 20 minutes until all of the NaBr was totally dissolved. The brown solution was then poured into a crystallization dish and allowed to sit undisturbed for about days. High quality brown orthorhombic crystals of about 4.0 x 6.0 x 0.5 mm 3 formed and were collected by suction filtration in a Buchner funnel outfitted with filter paper. The crystals were then washed with a minimal amount of H 2 O, collected, and stored in a refrigerator. 17 O labeled Fe 8 Br 8 crystals were synthesized in the same manner with 17 O labeled water. A typical crystal of Fe 8 Br 8 is shown in Figure 2.1. The dark brown orthorhombic crystals of Fe 8 Br 8 crystallize in the P1 space group with a = Å, b = Å, c = Å, V = 1956 Å 3, and Z = 1 [5]. Six of the eight Fe 3+ are octahedrally bound to the tacn ligand, while the other two are coordinated in a distorted octahedral symmetry. Six of the Fe 3+ ions, which are bound to the ligand, are ferromagnetically coupled to one another, while the remaining two are antiferromagnetically linked to these six. This gives a net total spin of S = 15 5 = 10. All newly synthesized samples were characterized by x-ray diffraction and magnetic susceptibility Synthesis of Fe 8 Br 4 (ClO 4 ) 4 and Fe 8 Br 6.4 (ClO 4 ) 1.6 [64] The structures of [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 4 (ClO 4 ) 4 8H 2 O and [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 6.4 (ClO 4 ) 1.6 8H 2 O (abbreviated Fe 8 Br 4 (ClO 4 ) 4 and Fe 8 Br 6.4 (ClO 4 ) 1.6, respectively) are very similar to that of Fe 8 Br 8, with the exception of the number of Br - ions [64]. The syntheses of 50% perchlorate (Fe 8 Br 4 (ClO 4 ) 4 ) and 20% perchlorate (Fe 8 Br 6.4 (ClO 4 ) 1.6 ), versions are essentially the same as in the method outlined by Weighardt for Fe 8 Br 8 [5]. Instead of using only NaBr, the appropriate molar amount of NaBr was replaced with the appropriate molar amount of NaClO 4. After sitting 13

25 undisturbed for about 3 or 4 weeks, several crystals formed in each of the dishes. The 20% perchlorate solution yielded reddish brown orthorhombic plates, similar to Fe 8 Br 8. Out of the 50% perchlorate solution, dark brown hexagonal crystals formed. X-ray crystallography confirmed the dark brown hexagonal crystals contained 50% perchlorate (Fe 8 Br 4 (ClO 4 ) 4 ), and the small reddish brown orthorhombic plates contained 20% perchlorate instead of Br - ( i.e. the structure was Fe 8 Br 6.4 (ClO 4 ) 1.6 ). Fe 8 Br 4 (ClO 4 ) 4 crystallizes in the P2 1 /c space group with a = Å, b= , c = , V = Å 3, and Z = 4 [76]. On the other hand, the 20% analogue, Fe 8 Br 6.4 (ClO 4 ) 1.6, crystallizes in the triclinic space group, P1, with a = Å, Å, c = Å, V = Å 3, and Z = 2 [76]. The Fe 8 cores of both molecules are isostructural to the title compound Fe 8 Br Experimental Techniques This subsection gives an overview of the instrumental setup and parameters used for each of the techniques discussed in this dissertation. Specifically, the experiments that will be described are electrical conductivity and photoconductivity measurements, microraman and infrared spectroscopy, and single crystal electron paramagnetic resonance (EPR) measurements Conductivity Measurements dc electrical resistance measurements were carried out in either a constant current or constant voltage setup using a standard four-probe technique [77] as illustrated in Figure 2.2. The voltage drop across the sample was measured by a high impedance (2 X Ohm) electrometer when constant current was applied. The current used was typically in the range of 0.1 to 10 na, and the voltage generally 100 V or less. All measurements were made under vacuum in a temperature-controlled probe, and are described in reference [67]. 14

26 2.3.2 Photoconductivity Measurements A He-Ne laser for red (632.8 nm), and an argon laser for blue (488 nm) and green (514 nm) light in conjunction with a light chopper operating at about 100 Hz, was used to illuminate the sample while direct current was supplied. The dc bias from the sample was measured with an electrometer, and changes in the voltage in response to the chopped light were measured across a 1 M Ω resistor. A lock-in amplifier at 100 Hz was used to detect the resulting ac signal. A schematic of the setup for the photoconductivity measurements is illustrated in Figure 2.3 [78] microraman and Infrared Spectroscopy Measurements Raman spectra were collected using a JY Horiba LabRam HR800. The excitation source was a TUIOptics laser emitting 80 mw of power at a wavelength of 785 nm. A schematic of the microraman setup is provided in Figure 2.4. In order to prevent laser damage to the Mn 12 -ac crystals, a 5 X 0.1 NA low power objective, in conjunction with a 0.6 neutral density filter was used to collect data. Long exposure times of about 2400 seconds, with 4 scans per spectrum were used to collect sufficient signals. Slightly different conditions were used to collect the Fe 8 Br 8 spectra. 480 seconds with 4 scans per spectrum provided a strong enough signal for data analysis. The micro-raman instrument was outfitted with a Linkam THMS 600 cryostat for measurements at temperature in the range of liquid nitrogen. Infrared measurements were taken with a Nicolet 470 Fourier Transform Infrared spectrometer outfitted with a Continuum microscope attachment, using a 15 X objective. 64 scans with a resolution of about 4 cm -1 were collected for both the Mn 12 -ac and Fe 8 Br 8 samples. All of the infrared data were collected at ambient temperature Single Crystal EPR Measurements EPR measurements were made using a cavity perturbation technique in combination with a broadband millimeter-wave vector network analyzer (MVNA) in the laboratory of Professor Steve Hill at the University of Florida. The MVNA system is a phase sensitive, fully sweepable, superheterodyne source detection system capable of frequencies in the range of GHz. This is coupled with a rotating split pair 6.2 T 15

27 horizontal field magnet and a cryostat for measurements at temperatures down to 1.2 K (± 0.01 K). A schematic of the setup used is shown in Figure 2.5. A more detailed description of the MVNA system is provided elsewhere [79,80]. Additional, more specific details for all of the techniques used are presented in the relevant chapters. 16

28 Fe 8 Br 8 Mn 12 -ac Fig Mn 12 -ac crystallizes as black rectangular rods. Crystals of Fe 8 Br 8 form as dark brown orthorhombic plates. Typical crystals of each are shown next to a dime for size comparison. 17

29 Fig This schematic shows the setup for a standard four probe measurement. Current is supplied to the sample on each end, and the voltage is measured across the middle of the sample [77]. 18

30 Fig Schematic of the typical setup used for the photoconductivity measurements, as described in Ref. [78]. 19

31 Fig A simplified schematic of the microraman spectrometer. The laser light travels down through the microscope and is focused on the sample. The reflected light travels back up the microscope and is sent to the CCD detector. 20

32 Figure 2.5. Schematic of the EPR setup used for measurements on single crystals of Mn 12 -ac. A single crystal of Mn 12 -ac is mounted inside the cavity and the solenoid provides a horizontal field of up to 6.2 T. The MVNA system allows for a full range of frequencies between 44 and 200 GHz [79,80]. 21

33 CHAPTER 3 ELECTRICAL CONDUCTIVITY MEASUREMENTS OF Mn 12 -ac AND Fe 8 Br 8 This chapter discusses our investigations of electrical conductivity behavior of the single-molecule magnets (SMMs), [Mn 12 O 12 (CH 3 COO) 16 (H 2 O) 4 ] 2CH 3 COOH 4H 2 O (abbreviated Mn 12 -ac), and [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 7 (H 2 O)Br 8H 2 O (Fe 8 Br 8 ). Our measurements showed that these materials exhibit a semiconductor-like, thermally activated behavior over the K range. These measurements yielded activation energies, E a, which are contrasted with earlier reported absorption edge measurements for Mn 12 -ac [39], and theoretical calculations for both materials [36, 37, 74]. Interestingly, Mn 12 -ac was shown to exhibit photoconductivity in the visible range. Portions of the data presented in this chapter have been reported recently [67]. 3.1 Introduction Because SMMs such as Mn 12 -ac and Fe 8 Br 8 show magnetic hysteresis as a property of individual molecules [1-3], these materials have been proposed as possible candidates for molecular memory devices [3], and as potential candidates for use as quantum computing elements [38]. In order to advance our understanding for possible applications, it is important to understand their electrical conductivity behavior. Prior to these investigations [67], there have been no studies of the electrical conductivity properties of these materials. Another important aspect of the conductivity measurements is the direct determination of the band gap. Through optical absorption measurements, Oppenheimer et al. [39] have deduced optical excitation band gaps, E g, of 1.1 and 1.75 ev for the 22

34 minority (inner tetrahedron) and majority (crown) spin systems in Mn 12 -ac. These results are comparable with the corresponding theoretical estimates of 0.45 and 2.08 ev by Pederson and Khanna [36], and 0.85 and 1.10 ev by Zeng et al. [37]. Although there have been no optical absorption measurements of Fe 8 Br 8, theoretical calculations by Pederson and coworkers have predicted an optical band gap of 0.9 ev for both the majority and minority spin systems [74]. As discussed below, our experiments show that both compounds exhibit fairly clear semiconducting behavior over the K range with distinctly different transport activation energies. It should be noted that in an intrinsic semiconductor, the activation energy, E a, (or band gap) measured via conductivity is related to the previously reported E g values, by assuming 2E a = E g [81]. We also report on photoconductivity experiments performed on Mn 12 -ac over the visible range are reported. The measured photoconductivity exhibits significant wavelength dependence. Furthermore, we also describe x-ray damage investigations to further probe the nature of the electrical transport in these materials Experimental Setup The dc measurements on both samples were carried out using a standard fourprobe technique [77]. The experiments could be setup in either a constant current or constant voltage configuration. Typically the voltages were 100 V or less and the currents were in the range of 0.1 to 1.0 na. All measurements were made under vacuum in a temperature-controlled probe. For the photoconductivity measurements, a He-Ne laser was used for red (632.8 nm) light, and an argon laser for blue (488 nm) and green (514 nm) light. These were used in conjunction with a light chopper operating at 100 Hz. A direct current was supplied to the sample, and changes in the voltage in response to the chopped light were measured across a 1 M Ω resistor. A more detailed description of the photoconductivity setup is given elsewhere [78] Electrical Conductivity Measurements of Mn 12 -ac Figure 3.1 shows the temperature dependence of the resistance, R(T), of a single crystal of Mn 12 -ac in the constant current condition. At room temperature the resistivity values are on the order of 1GΩ cm, and increase rapidly in an activated manner upon 23

35 cooling the sample. The arrows indicate the direction of the temperature change. First, the sample was cooled to 77 K with liquid nitrogen. At these temperatures the resistance became too high to accurately measure. Next, the coolant was allowed to evaporate and resistance measurements were again initiated at about 150 K. As the temperature increased up to about 220 K, the resistance of the sample began to drop until about 300 K. The cause of the irreversibility in the runs with opposite temperature scans is not completely understood. Tentatively, we ascribe this to thermally induced defects in the crystal. In the range of K, the resistances vs. temperature plots for each scan are identical to one another. For this reason, we limited out Arrhenius analysis to temperatures in this region. As shown in the inset of Figure 3.1, ln R exhibits a linear dependence as a function of 1/T over the range of K. This behavior is typical of a semiconducting system with a well defined band gap where R(T) ~exp(e a /k B T). From the slope of the line in the inset, E a is estimated to be about 0.38 ± 0.05 ev. The temperature dependence of the current for the constant voltage (50 V) condition is shown in Figure 3.2. The current through the sample rapidly decreases, as the resistance of the Mn 12 -ac increases, and the temperature is lowered. Below about 210 K, the current becomes too low to accurately measure. The inset of Figure 3.2 shows the corresponding ln R vs. 1/T plot. The slope of the line yields a value of E a = 0.36 ± 0.05 ev. Assuming that E a can be compared with 1/2E g [81], the results from our electrical conductivity measurements on Mn 12 -ac are comparable with earlier absorption edge measurements by Oppenheimer et al. [39], and theoretical calculations by Pederson et al. [36], and Zeng et al. [37]. Our measurements yield E g = 0.74 ± 0.1 ev, while Oppenheimer s absorption measurement gives a value of 1.08 ev for the minority spin system (inner tetrahedron), and 1.75 ev for the majority spin system (crown) [39]. The calculations by Pederson and Khanna give values of 0.45 ev and 2.08 ev for the minority and majority spin systems, respectively [36]. Zeng et al. report an E g of 0.85 ev for the minority spin system and 1.10 ev for the majority spin system [37]. These values of E g are collected in Table

36 3.4. Effect of x-ray irradiation on Mn 12 -ac Hernandez et al. [82] recently observed an increase in the magnetic quantum tunneling (MQT) rate in Mn 12 -ac caused by defects in the lattice as a result of x-ray irradiation and heat treatments. To probe the possible role of defects in the electrical transport properties of this compound, we carried out an x-ray irradiation study as well. As the radiation dose was increased from 2 to 20 hours, the overall resistivity of the system increased, but the plots of ln R vs. 1/T for the different exposure times showed the activation energy remained fairly constant. These data indicate the E a of the Mn 12 -ac system is insensitive to the creation of defects. Hence, the x-ray investigation supports the idea of intrinsic semiconductor-like conduction in Mn 12 -ac, and by inference for Fe 8 Br Photoconductivity measurements of Mn 12 -ac The photoconductivity (PC) of Mn 12 -ac was measured using the ac component of the photocurrent for chopped laser light at several different wavelengths. The dependence of the PC on the dc biasing current at three different wavelengths, nm (red), 514 nm (green), and 488 nm (blue) is shown in Figure 3.3. Clearly, as the photon energy is increased, so does the PC. An increase of about a factor of 8 in the PC is observed when going from to 488 nm. This enhancement must relate to either a creation of charge carriers by the photons, or to an increase in temperature due to light absorption, or a combination of both. However, a simple thermal mechanism can be ruled out by a comparison of the data with that of the UV-visible absorption data on Mn 12 -ac published by Oppenheimer et al. [39]. Over the range of to 488 nm, the absorption data was nearly constant (within a factor of 2), while the photoconductivity measurements show an increase of a factor of 8. Because these considerations argue against a major role of thermal heating, the mechanism of the observed PC enhancement is thus attributed to the creation of charge carriers due to optical absorption Conductivity of Fe 8 Br 8 Temperature dependent conductivity measurements on single crystals of Fe 8 Br 8 were also carried out. Figure 3.4 shows a typical plot of ln R vs. 1/T over the range of 25

37 K. The slope of the line yields a value of E a = 0.73 ± 0.1 ev, which is significantly higher than that of Mn 12 -ac (0.37 ± 0.05 ev). At present there are no optical data available for comparison with conductivity measurements. Assuming the E a is related to the optical gap, E g by E g = 2 E a [81], our electrical conductivity measurements yield a value of E g = 1.46 ± 0.2 ev, which can be compared with the theoretical calculations of Pederson et al. [74] that predict an E g of 0.9 ev. Table 3. 1 provides a comparison of these results, along with the results for Mn 12 -ac. The agreement with theory is thus not very good Conduction Pathways Although we have not been able to arrive at any detailed picture of the conduction pathways in Mn 12 -ac or Fe 8 Br 8, we offer the following possibilities based upon the structure and bonding characteristics of both lattices. The pathway for Mn 12 -ac is based upon the Coulombic interactions between Mn 3+ ions and the polar molecules between two Mn 12 -ac clusters. Figure 3.5 shows a schematic of the proposed pathway for conduction in Mn 12 -ac. A water molecule bound to a Mn 3+ in the outer crown of the molecule, lies 2.7 Å away from an unbound acetate ligand, which is in turn 2.8 Å away from a symmetrically equivalent, unbound acetate ligand adjacent to the closest Mn 12 -ac cluster. The proposed conduction pathway between two Fe 8 Br 8 clusters is illustrated in Figure 3.6. The proposed pathway is through an N-H bond in the 1,4,7- triazacyclononane to water (2.4 Å), to a Br - (2.3 Å), to another water (2.1 Å), and finally to a hydrogen (2.4 Å) directly connected to the 1,4,7-triazacyclononane on the adjacent Fe 8 Br 8 cluster. It should be noted that the total path length between two Mn 12 -ac clusters is about 8.2 Å, while the pathway between two Fe 8 Br 8 clusters is about 9.2 Å. The proposed pathways are consistent with the significantly higher activation energy observed for the Fe 8 Br 8 cluster Summary Through our electrical conductivity investigations, we have determined that both of the SMMs Mn 12 -ac and Fe 8 Br 8 exhibit a semiconductor-like behavior in their electrical transport properties. The E a s were determined to be 0.37 ± 0.05 ev for Mn 12 -ac and 26

38 0.73 ± 0.1 ev for Fe 8 Br 8. Assuming that E a = 1/2E g [81], this leads to E g values of 0.74 ± 0.10 ev, and 1.5 ± 0.2 ev for Mn 12 -ac and Fe 8 Br 8, respectively. The values for Mn 12 -ac are slightly different from the optical band gaps obtained from the absorption measurements [39], and the theoretical estimates by Pederson and Khanna [36], as well as Zeng et al. [37]. Although there have been some theoretical calculations on the optical gap of Fe 8 Br 8 [74], additional optical and theoretical data are needed. It should be noted that calculations only exist for the molecular band gaps, not for the entire lattice. Therefore we can only speculate the importance of intercluster ligand bridges in the mechanism of electrical conduction. 27

39 Table 3.1. Comparison of E g from conductivity and optical data, and theoretical calculations [67]. a Present work, assuming E g = 2E a [81]. b Oppenheimer et al. [39], minority spin cluster. c Pederson et al. [36], minority spin cluster. d Oppenheimer et al. [39], majority spin cluster. e Pederson et al. [36], majority spin cluster. f Zeng et al. [37], minority spin cluster. g Zeng et al. [37], majority spin cluster. h Pederson et al. [74], minority spin cluster. i Pederson et al. [74], majority spin cluster. 28

40 Fig Temperature dependence of the resistance R of Mn 12 -ac measured under a constant current condition. The arrows indicate the direction of the temperature change. The inset shows a plot of ln R vs. 1/T. The slope of this line shown in green yields an activation energy, E a = 0.38 ± 0.05 ev. 29

41 Fig Temperature dependence of the measured current under a constant voltage bias (50 V). As the temperature decreases and the resistance of the sample increases, the current though the sample goes towards zero, and becomes immeasurable. The arrow shows the direction of the temperature sweep. The inset shows a plot of ln R vs. 1/T, which yields E a = 0.36 ± 0.05 ev. 30

42 Fig The induced photocurrent is shown as a function of the applied direct current. The light intensity of the red (632.8 nm), green (514 nm), and blue (488 nm) is about 1 mw. A factor of about 8 increase in the photocurrents as the wavelength is decreased from to 488 nm is observed. 31

43 Fig Plot of ln R vs. 1/T for Fe 8 Br 8. The solid blue line yields a value of E a = 0.73 ± 0.1 ev. 32

44 Mn Å Mn Å Mn 3+ -H 2 O acetate acetate H 2 O-Mn 3+ Fig Schematic of the proposed conduction pathway between two Mn 12 -ac clusters. The path (outlined in blue) goes from a water molecule bound to a Mn 3+, to an unbound acetate, and then to a symmetrically equivalent unbound acetate, which is adjacent to a bound water on the neighboring Mn 12 -ac cluster. 33

45 2.3 Å 2.4 Å Br - H 2 O H 2 O 2.4 Å 2.1 Å Fe-N-H H 2 O Br - H 2 O H-N-Fe Fig Proposed conduction pathway between two Fe 8 Br 8 molecules. The pathway (outlined in purple) extends from a hydrogen bound to 1,4,7-triazacyclononane on the Fe 8 Br 8 cluster, to an unbound water, to a bromine ion, through an adjacent water, and through another hydrogen bound to a 1,4,7-triazacyclononane of the neighboring Fe 8 Br 8 cluster. 34

46 CHAPTER 4 RAMAN AND IR CHARACTERIZATION OF THE SMM S Mn 12 -Ac AND Fe 8 Br 8 This chapter presents our Raman and infrared (IR) measurements of the SMM s [Mn 12 O 12 (CH 3 COO) 16 (H 2 O) 4 ] 2CH 3 COOH 4H 2 O (abbreviated Mn 12 -ac), [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 7 (H 2 O)Br 8H 2 O (abbreviated Fe 8 Br 8 ), and their analogs in the range of cm -1. These constitute the first such measurements on any SMM. Through the use of model compounds and previously reported theoretical calculations, the majority of the modes have been assigned. Portions of these data have been previously reported in our recent publications [64-66]. 4.1 Overview of Raman and IR experiments One of the most sought after answers in the field of SMMs has been to better understand the mechanism by which magnetic quantum tunneling (MQT) occurs [1-3]. As was previously described, MQT is the phenomenon by which the magnetization vector tunnels from one side of the potential energy barrier to the other. In order for MQT to occur there must be a source of transverse anisotropy. These transverse fields allow for the m s levels to mix. In Fe 8 Br 8, this criterion is met by the two-fold symmetry of the molecule, which provides a nonzero E term (E(S 2 x -S 2 y ) in the spin Hamiltonian (Eq. 1.1). As discussed earlier in Chapter 1, due to the high symmetry of Mn 12 -ac (S 4 ), there is no E term or immediately apparent source of transverse anisotropy. For this reason, the exact mechanism that provides the transverse terms in Mn 12 -ac has remained controversial [9,18,32,33,40]. The actual process of MQT involves both pure quantum tunneling and phonon-assisted tunneling. Although a number of different experiments 35

47 have been performed to better understand the mechanism of MQT in Mn 12 -ac and Fe 8 Br 8, there has been a scarcity of data on the phonon modes of each. Sushkov et al. [62] made an important step in this direction, when it was discovered that some of the infrared modes of Mn 12 -ac exhibited significant line shape changes when measured under an externally applied magnetic field at liquid helium temperatures. Following this observation, Pederson et al. [41] carried out electronic structure density functional theory calculations on Mn 12 -ac, and suggested that some of the low frequency Mn-O modes might be the origin of the necessary transverse terms, specifically a term which provides for a fourth-order magnetic anisotropy energy. This term 1/2(S S 4 - ) in the spin Hamiltonian contributes to m s = ± 4 transitions involved in the mechanism of the phonon-assisted tunneling of the magnetization vector. It was thus of interest to conduct detailed Raman and IR experiments to determine and characterize the phonon modes of these compounds. Although there are currently no DFT calculations on the vibrational properties of Fe 8 Br 8, the Raman and IR experimental spectra are reported in hopes of laying out the groundwork for future endeavors. In a general way, comparison of the Mn 12 -ac results with the theoretical calculations supports the predicted role of these transitions in the MQT phenomenon. 4.2 Experimental Details All Raman measurements were made using a JY Horiba LabRam HR 800 with a TUIOptics laser emitting 80 mw of power at 785 nm as described in Chapter 2. Because of the sensitivity of some of the materials to laser damage, a 5 X 0.1NA low power objective coupled with 0.6 neutral density filter was used to collect Raman data. In order to collect a sufficient signal for the Mn 12 -ac sample and analogs, we used long exposure times of about 2400 s per scan with 4 scans per spectrum. For the Fe 8 Br 8 sample and analogs, 480 s per scan with 4 scans per spectrum provided a reasonable signal for data analysis. Infrared data were collected for both Mn 12 -ac and Fe 8 Br 8 with a Nicolet 470 Fourier Transform Infrared spectrometer outfitted with a Continuum microscope attachment, using a 15 X objective. Sufficient signal to noise ratio was obtained with 64 scans for each sample. 36

48 Due to the large size and complexity of both Mn 12 -ac and Fe 8 Br 8, group theoretical analyses were not a reasonable approach for assigning the Raman modes of these compounds. Therefore, the Raman spectra of several model compounds, which contained similar structural features as the title compounds, were used to identify the origin of various vibrational modes in the spectra. Specifically, the spectra of KMnO 4, Mn(CO 2 CH 3 ) 2, and MnO 2, were used to characterize peaks in Mn 12 -ac, while the molecules 1,4,7-triazacyclononane (tacn), FeCl 3 tacn, and Fe 2 O 3 were utilized as an aid in the mode assignment of Fe 8 Br Laser Damage of Mn 12 -ac Figure 4.1 shows both the spectrum of laser damaged Mn 12 -ac and undamaged Mn 12 -ac. In the spectrum of the crystal damaged by the laser, the peaks were broadened out and lost spectral resolution, as compared with the spectrum of the undamaged sample. In order to acquire spectra of undamaged Mn 12 -ac, it was necessary to use a 0.6 neutral density filter to prevent damage by the laser. Because a neutral density filter was used, longer collection times were needed to collect a spectrum with a sufficient signal to noise ratio. 4.4 Raman Spectra of Mn 12 -ac and Analogs Our initial impetus for undertaking the Raman measurements arose from an infrared study by Sushkov et al. on Mn 12 -ac [62]. As noted therein several of the infrared modes in Mn 12 -ac display noticeable spectral broadening under an externally applied magnetic field at liquid helium temperatures. These results suggest that these and perhaps other bands involve interactions with the magnetic moment. We surmised in particular that the Raman bands might provide a higher resolution, and even additional information on the spin-vibron interactions. Meanwhile Pederson and coworkers reported DFT calculations on Mn 12 -ac, and proposed that several of the low-frequency Mn-O modes might play an important role in the overall mechanism of MQT [41]. Agreement between the experimentally and theoretically predicted modes should in a general way support the mechanism outlined previously [41]. The work described in this 37

49 section of the dissertation and reported elsewhere [64-66] should serve as the underpinnings for future Raman experiments in the presence of an applied magnetic field. Figure 4.2 shows a typical Raman spectrum of Mn 12 -ac in comparison to spectra from the analogous compounds, deuterated Mn 12 -ac and Mn 8 Fe 4. The spectra are all very similar to one another and contain several sharp peaks. Due to the relative size of the Mn 12 -ac cluster as compared with the slight mass increase upon the replacement of hydrogen with deuterium, there are only very slight differences in the two spectra. Similarly, replacement of four of the Mn 3+ in the outer crown, with Fe 3+ also only slightly changes the spectra. Because Fe is only one atomic mass unit larger than Mn, it is not unexpected that this slight mass difference has only a neglible effect on its Raman spectrum. On the other hand, this result implies that Raman spectroscopy could be used as an analytical technique to identify potential Mn 12 -ac SMM analogs (vide infra). A comparison of the observed modes along with the theoretical predictions [41] is shown in Table 4.1. Pederson and coworkers predicted several low frequency Raman modes in Mn 12 - ac and suggested that they should be relevant to the fourth-order anisotropy term in the spin Hamiltonian [41]. Our observed modes at 287 and 536 cm -1 compare well with those predicted peaks at 281 and 465 cm -1. Pederson et al. attributed these peaks to Mn- O stretches in the molecule. Peaks predicted at 630 and 670 cm -1 can be attributed to the experimentally observed modes at 646 and 684 cm -1. Additionally, the broad peak in the Raman spectrum of Mn 12 -ac is related to the mode that is calculated at 1496 cm -1. Table 4.1 reports the experimental peak positions along with the DFT predictions by Pederson et al. [41]. Additional assignments were made using model compounds. Figure 4.3 contains spectra from the model compounds Mn(CH 3 CO 2 ) 2, MnO 2, and KMnO 4. These compounds were chosen because they contain Mn-O bonds with some bonding similarities. There are several similarities between the spectra of Mn(CH 3 CO 2 ) 2, and Mn 12 -ac. For example, the semi-broad peak which is observed at 209 cm -1 in Mn 12 -ac is also evident at 222 cm -1 in Mn(CH 3 CO 2 ) 2. Additionally, the broad mode in Mn 12 -ac which is centered around 1399 cm -1, is also present in Mn(CH 3 CO 2 ) 2. Specifically, we have assigned this as belonging to a symmetric COO stretch in the acetate ligand based 38

50 upon literature data [83]. A peak at 1576 cm -1, which is present in both compounds is assigned as the asymmetric COO stretch following Nakamoto [83]. A vibrational mode, which is present at 646 cm -1 in Mn 12 -ac, is related to the Mn-O vibration at 656 cm -1 in MnO 2. The shift in the values is attributed to the large bulk of the Mn 12 O 12 core in Mn 12 - ac. The peak at 403 cm -1 in the model compound KMnO 4 is also present in Mn 12 -ac at the same frequency. Thus, this mode has been assigned as belonging to a Mn-O vibration. Several peaks in the previously reported infrared (IR) spectroscopy data [62,63], which match very well those observed in the Raman data of Mn 12 -ac. The Raman bands at 287 and 403 cm -1 compare well with the IR modes observed at 284 and 408 cm -1 [62]. In addition to the previously reported IR data [62,63], we felt it necessary to acquire IR data at higher frequencies. Our measurements are shown in Figure 4.4. As can be seen therein, the mode at 601 cm -1 in the Raman spectrum corresponds to a mode at the same frequency in the IR spectrum. Peaks at 1399 and 1576 cm -1, which are attributed to vibrations in the acetate ligands, are also evident in the IR data at 1385 and 1567 cm -1, respectively. 4.5 Fe 8 Br 8 and Analogs The success of the Raman study on Mn 12 -ac encouraged us to extend it to Fe 8 Br 8, and its analogs. The spectra obtained are presented in Figs and summarized below. We start with Fe 8 Br 8 enriched with the 17 O isotope. The Raman spectra of Fe 8 Br 8 and its 17 O-enriched analogue can be seen in Figure 4.5. Because the isotope effect is so small in comparison to the large bulk of the Fe 8 Br 8 molecule, there are only a few very minor differences in the two spectra. A comparison of the peak positions for the Fe 8 Br 8 and 17 O-labeled Fe 8 Br 8 is shown in Table 4.2. As was the case for Mn 12 -ac, the Raman spectrum of Fe 8 Br 8 can be used as a fingerprint for the core structure of the molecule. This allows for Raman spectroscopy to become an analytical tool for identifying various analogs of Fe 8 Br 8, which maintain the core structure. An example of this can be seen in Figure 4.6, which shows Fe 8 Br 8 in comparison to the 20% and 50% perchlorate analogs, Fe 8 Br 6.4 (ClO 4 ) 1.6, and Fe 8 Br 4 (ClO 4 ) 4. Many of the peaks are of similar size, shape, and intensity, albeit with minor frequency shifts. The sharp strong peak, which is located at 39

51 956 cm -1 in the NaClO 4, is assigned as a totally symmetric (A) Cl-O vibration [83]. This peak is slightly shifted in the 20% and 50% perchlorate samples to a value of 933 cm -1. Therefore this peak was assigned as belonging to ionic perchlorate in the cluster. Furthermore, the relative intensity of the mode at 933 cm -1 increases as the percentage of perchlorate in the molecule also increases. A full comparison of the perchlorate analogs is presented in Table 4.2. Similar to the experiments for Mn 12 -ac, a series of model compounds were utilized in the assignment of the Fe 8 Br 8 modes. Figure 4.7 shows a comparison of the model compounds with Fe 8 Br 8. A quick comparison of the spectrum of the unbound ligand tacn, with that of the Fe 8 Br 8 cluster, shows that most of the peaks above 800 cm -1 are due mostly to vibrations in the organic ligand. The peak that is present at 575 cm -1 in the Fe 8 Br 8 is present in the FeCl 3 tacn, and tacn at 578 cm -1, thus the peak is assignable to the ligand. A similar argument can be made that the peak observed at 348 cm -1 in the Fe 8 Br 8, is also assignable to vibrations in the tacn ligand. The peak at 193 cm -1 in the title compound is observed in the FeCl 3 tacn, but not in the unbound tacn ligand. Therefore, this peak is assigned to a Fe-N stretch. The mode at 500 cm -1 in the Fe 8 Br 8 appears to be a superposition of the peak at 502 cm -1 in FeCl 3 tacn and the A 1g peak at 498 cm -1 in Fe 2 O 3 [84]. This is also the case for the mode at 417 cm -1 in the Fe 8 Br 8. Oxygen is only slightly heavier than nitrogen, so it is not surprising that the Fe-N and Fe-O vibrations occur at very close frequencies in FeCl 3 tacn and Fe 2 O 3. Therefore, the peaks at 417 and 500 cm -1 are assigned to a superposition of Fe-N and Fe-O stretches. Assignments of the majority of peaks in Fe 8 Br 8 are reported in Table 4.2. Slight shifts in some of the low-frequency Raman modes were observed in temperature dependence experiments from 300 to 78 K, as can be seen in Figure 4.8. The mode that is observed at 151 cm -1 at 300 K shifts to the slightly higher frequency of 154 cm -1 as the temperature is lowered to 78 K. On the other hand, it is interesting to note that the mode at 127 cm -1 stays relatively constant, seeming to be relatively temperature independent. This provides further evidence that the peak at 151 cm -1 can be attributed to a Fe-N vibration. The Fe-N bonds to the ligand would be more affected than the Fe-O bonds in the core of the cluster. As the temperature is lowered even further, it is anticipated there will be more spectral changes as the blocking temperature of the sample 40

52 is approached. At present we have no facilities to carry out Raman measurements at such low temperatures (below 1 K for Fe 8 Br 8 ). By examining the Raman spectra when the scattering is polarized parallel and perpendicular to the incident light, it is possible to assign the various vibrations as symmetric or asymmetric [85]. When the scattering is polarized parallel to the incident light, it is possible to see all of the peaks. When the scattering is polarized perpendicular to the incident light, the symmetric peaks are of lower relative intensity. As can be seen in Figure 4.9, the two intense peaks at 127 and 151 cm -1 have a much weaker intensity when the scattering is polarized perpendicular. Therefore, we have assigned these peaks as symmetric vibrations. The modes at 417, 459, and 499 cm -1 are also assigned to symmetric vibrations. The majority of the modes in the ligand correspond to asymmetric stretches such as the peaks at 611 and 955 cm -1, which are also assigned as asymmetric vibrations. As for Mn 12 -ac, it was clearly of interest to find a comparison between the Raman and the IR spectra. Figure 4.10 shows a comparison of the Raman data and infrared (IR) data for Fe 8 Br 8. The size, shape, and position of several of the peaks in the Raman spectrum correspond well with modes present in the IR spectrum. The Raman peaks that appear at 1358 and 1375 cm -1 are almost identically reproduced in the IR data at 1357 and 1359 cm -1. As has been reported for Mn 12 -ac [62], higher resolution infrared studies under the influence of an externally applied magnetic field at liquid helium temperatures should give a better understanding of the nature of the observed modes. 4.6 Summary and Conclusions Through the use of model compounds and theoretical predictions, we have been able to assign most of Raman modes of both Mn 12 -ac and Fe 8 Br 8. Due to the large size of the SMMs studies, there is a collective behavior of the vibrational modes, and thus a breakdown of the traditional selection rules for Raman and IR spectroscopy. Therefore we have utilized the "functional group" approach for the mode assignment even though the vibrational modes in SMMs (especially the lowest energy ones) are collective and involve the entire molecule. One significant advantage of the functional group analysis is that the vibrations can be easily visualized and are appropriate for describing the motion 41

53 of ligands. The experimental data reported for Mn 12 -ac show good agreement with the theoretically predicted Raman spectrum [41] and previously reported infrared data [62], however there have been no previously reported infrared or theoretical calculations on the vibrational properties of Fe 8 Br 8 for comparison. The Raman measurements on both materials presented in this chapter are the first such measurements of any SMM. The data reported here should serve as the foundation for additional studies utilizing much lower temperatures and applied magnetic fields, which might provide more insight into the exact nature of the observed modes and their possible implications on the mechanism of MQT as proposed by Pederson and coworkers [41]. 42

54 Table 4.1. The Raman modes (cm -1 ) [64] and theoretical calculations [41] of the vibrational modes of Mn 12 -ac and its analogs. It should be noted that in all cases, the theoretical predictions by Pederson and coworkers are at a higher frequency. [41] 43

55 Table 4.2. Vibrational modes of Fe 8 Br 8 and its analogs. The Raman peak positions of Fe 8 Br 8 and its analogs (cm -1 ) are very similar to one another. The mode assignments were made with the aid of model compounds [64]. w = weak, s = strong. 44

56 Laser Damage in Raman Spectra Figure 4.1. Spectra exhibiting laser damage and loss of spectral resolution due to the exciting laser radiation. Care was taken to minimize this damage by using a series of neutral density filters. See text and Ref. [64]. 45

57 Mn-O -CO 2 CH 3 Figure 4.2. Typical Raman spectra of Mn 12 -ac, deuterated Mn 12 -ac, and the isostructural compound Mn 8 Fe 4. The numbers with the arrows indicate the mode frequencies in cm

58 Mn-O -CO 2 CH 3 Figure 4.3. Raman spectrum of Mn 12 -ac in comparison to Raman spectra of the model compounds, Mn(CH 3 CO 2 ) 2, MnO 2, and KMnO 4. The origin of several of the modes in Mn 12 - ac can be directly assigned with the help of the model compounds. The numbers with arrows are the mode frequencies in cm

59 Mn-O -CO 2 CH 3 Figure 4.4. The IR spectrum of Mn 12 -ac is shown in comparison to its Raman spectrum. The numbers and arrows indicate the peak positions in cm -1. As can be seen in the figure, there are several common peaks in the Raman and IR spectra. 48

60 Fe-O Fe-O and Fe-N tacn Figure 4.5. Raman spectrum of Fe 8 Br 8 in comparison to the spectrum of 17 O-labeled Fe 8 Br 8. The small effect of the isotopic substitution on the overall mass of the cluster, leads to only very minor perturbations in the spectrum. The numbers and arrows indicate the peak positions in cm

61 933 cm -1 Figure 4.6. The 20% and 50% perchlorate analogs, Fe 8 Br 6.4 (ClO 4 ) 1.6, and Fe 8 Br 4 (ClO 4 ) 4 are shown in comparison to NaClO 4 and Fe 8 Br 8. The strong peaks indicated with the arrows are attributed to ionic ClO 4 - in the molecule. 50

62 tacn tacn Fig The Raman spectra of the model compounds FeCl 3 tacn, tacn, and Fe 2 O 3 are shown in comparison to the spectrum of Fe 8 Br 8. The model compounds help to characterize the origin of several of the observed modes. The numbers and arrows indicate the frequencies of the peaks in cm

63 Fig The temperature dependence of the low-frequency modes of Fe 8 Br 8 is shown above. It should be noted that the peak at 151 cm -1 at 300 K shifts to 154 cm -1 as the temperature is lowered to 78 K, but the peak at 127 cm -1 remains relatively temperature independent. 52

64 Fe-N Fe-O and Fe-N Fe-O tacn Fig The Raman spectra of Fe 8 Br 8 with the scattering polarized parallel and perpendicular to the incident radiation gives information about the whether the observed mode is a symmetric or asymmetric vibration. The numbers indicate the peak positions in cm

65 tacn tacn Fig The Raman spectrum of Fe 8 Br 8 is shown in comparison to the IR spectrum. Several of the common modes are highlighted with numbers and arrows in cm

66 CHAPTER 5 ELECTRON PARAMAGNETIC RESONANCE INVESTIGATIONS OF Mn 12 -Ac This chapter presents our electron paramagnetic resonance measurements of the single-molecule magnet (SMM) [Mn 12 O 12 (CH 3 COO) 16 (H 2 O) 4 ] 2CH 3 COOH 4H 2 O (abbreviated Mn 12 -ac), which relate to a recently proposed model by Cornia et al. [42] where disorder associated with the acetic acids of crystallization induces tilts in the magnetic easy axes away from the crystallographic axis of the crystal. The results provide direct evidence for the disorder, something not observable by other techniques. These tilts may be the source of transverse anisotropy in the system, which allows for the phenomenon of magnetic quantum tunneling (MQT) occurring in Mn 12 -ac. Portions of this data have been reported in our recent papers [58, 59, 86] Introduction In order for MQT to occur there must be a source of transverse magnetic fields, which serves to mix the different m s levels in the system. In the SMM, [(C 6 H 15 N 3 ) 6 Fe 8 O 2 (OH) 12 ]Br 7 (H 2 O)Br 8H 2 O (abbreviated Fe 8 Br 8 ), this condition is met by the two-fold symmetry of the molecule. The lack of tetragonal symmetry in the Fe 8 Br 8 lattice provides a non-zero term, E(S 2 x -S 2 y ), in the spin Hamiltonian of the system. Therefore, MQT can occur in Fe 8 Br 8 due to this transverse term, leading to a mixing of the levels differing by m s = ±2. On the other hand, each molecule of the SMM Mn 12 -ac has S 4 symmetry. Because of the high symmetry of the molecule, there is no immediately evident source of the transverse anisotropy required for MQT to occur. Different groups have attributed the source of the necessary symmetry breaking to dipolar 55

67 and nuclear hyperfine fields [32,33,40], low frequency Mn-O vibrations [41], and most recently to disorder of the acetic acids of crystallization in the molecule [42]. Recent detailed x-ray crystallography studies by Cornia et al. [42] have noted additional diffraction spots, suggesting that most of the Mn 12 -ac molecules in the crystal do not actually possess the four-fold symmetry as was previously thought. Acetic acids of crystallization in the structure break the symmetry of the molecule. This is because there are only four acetic acid molecules and there are eight possible sites for hydrogen bonding. This symmetry breaking gives rise to six different types of Mn 12 -ac clusters that can be present in each crystal, as illustrated in Figure 5.1 [42]. Assuming a statistical distribution (n = the number of acetic acids), the n = 0 and n = 4 isomers should represent about 12.5 % (6.25 % each) of the total possible combinations. Because of the S 4 symmetry of these isomers, they should not contribute to the transverse anisotropy of system in the proposed model. The remaining n = 1 isomers, n = 2 cis and trans isomers, and n = 3 isomers, which comprise about 82.5% of the total possible combinations, have less than S 4 symmetry and would thus provide a mechanism for MQT to occur. Cornia et al. predict the n = 1, and n = 3 isomers will have about a 0.3 o tilt from the crystallographic axis, and the n = 2 cis isomers will have the greatest tilt at 0.4 o away. Additionally, the n = 0, n = 4, and n= 2 trans isomers, which represent about 25% of the total population, should exhibit no tilt, i.e. their magnetic easy axes should lie completely parallel the crystallographic c axis of Mn 12 -ac [42]. With the aid of x-ray crystallography, Cornia et al. [42] suggested the easy magnetization axis, z, of the different isomers should deviate from the crystallographic c axis by no more than about 0.4 o. Until now, there has been no direct evidence of the predicted tilts in a single crystal of Mn 12 -ac, and it is not clear that this is possible by any technique other than EPR spectroscopy using single crystals. Here we report EPR measurements on a single crystal of Mn 12 -ac under applied transverse fields that provide direct evidence of such tilts. These conclusions provide an explanation for several previously reported EPR transitions that cannot be explained in the context of the standard giant spin Hamiltonian [57, 58]. 56

68 5.2. Experimental Details As previously outlined in Chapter 2, the EPR measurements were carried with a broadband Millimeter-wave Vector Network Analyzer (MVNA), coupled with a 6.2 T split pair horizontal field magnet. This system allows for measurements from 44 to 200 GHz. For the measurements, the Mn 12 -ac sample was placed on the endplate of an oversized cylindrical cavity (details in Fig. 5.3). For fields higher than those available with the split pair magnet, a cavity was constructed to enable in situ rotation of the end plate with an angle resolution of 0.18 o to be used in a standard 9 T superconducting magnet [87]. In all cases, the temperature of the sample was controlled using a combination of heaters and cold helium gas. A more detailed description of the experimental setup and the MVNA system can be found in Reference [78,79,87]. 5.3 α-and β-resonances In order to provide the background for the studies related to the tilts, it seems worthwhile starting with the earlier work on the so-called β-resonances [21]. In the high field limit (gµ B B > D S), when the magnetic field is applied along the hard axis of Mn 12 - ac, there should be a total of 20 EPR transitions between the 21 (2S + 1) spin-states in the S = 10 system. Figure 5.2 (a) shows an energy level diagram for several of the low-lying states with the magnetic field applied on the hard axis. In the high field limit, the levels are labeled by m x, which is the projection of the total spin along the applied field axis obtained with the SIM EPR program [88]. The transitions at high fields consist of excitations between the adjacent levels, i.e. m x = ±1. The EPR transitions are labeled as alpha, α, for transitions between even to odd m s levels, and as beta, β, for odd to even levels. In Figure 5.2(a), the α-resonances are shown as sticks and the β-resonances as solid circles. Additionally, the transitions are labeled by the absolute value of the m x level from which the transition was excited. For example, the highest field stick seen in Figure 5.2 (a) corresponds to the α10 resonance. As illustrated in Figure 5.2 (b), the α-resonance transition frequencies should smoothly decrease down to zero as the transverse field is reduced. However for the β- resonances there is minimum frequency required for a transition from the odd to even m x levels. This implies that below a certain frequency (about 90 GHz) the β-resonances 57

69 should not continue to be present in the spectrum. However, experiments show the β- resonances, continue to appear well below this cutoff frequency. Figure 5.3 contains three typical spectra at 44.3, 77.4, and GHz showing that the β9 resonance is present at each of the frequencies. This requires that there must be a different explanation for these peaks. In order to try to explain the odd to even resonances, computer simulations were performed using the software package SIM [88] and the accepted values of D = cm -1, B 0 4 = -2.0 x 10-5 cm -1, and B 4 4 = ±3.2 x 10-5 cm -1 from earlier EPR measurements [57, 58]. Figure 5.4 shows the simulation at a frequency of 44 GHz at 15 K, and the magnetic field aligned perpendicular to the easy axis of the crystal (θ = 90 o ). These simulations predict only the α-resonances and no β-resonances at all. However, with only one degree away from the hard axis the α-resonances do not appear, and the β-resonances are present. Because the experimental spectrum at 44.3 GHz shows both α-and β- resonances (Fig. 5.3), we therefore propose a distribution of molecular easy axes centered around the four-fold crystallographic c axis of the sample. 5.4 Angle Dependent EPR Measurements In order to further confirm the above conjecture and to determine the magnitudes of the tilts, we carried out precise angle-dependent measurements in order to confirm the above hypothesis. Figure 5.5 shows angle dependent measurements recorded at a frequency of 61.9 GHz at 15 K. The angle was varied about 3.5 o on both sides of the hard axis, i.e. θ = 86.5 o 93.5 o in 0.18 o degree increments. As in the 44 GHz measurements, both the α- and β-resonances are present at θ = 90.0 o. Furthermore, the α- and β-peaks overlap one another over a substantial range of about 2 o. This is in direct contrast to Figure 5.6, which shows angle dependent simulations at a frequency of 62 GHz, and a temperature of 15 K. It is immediately obvious that at θ = 90.0 o there should be no over lap between the α- and β-resonances. In Figure 5.5, at θ = 90.0 o the β9 resonance appears as a small shoulder, however the simulations in Figure 5.6 do not predict this peak to appear until about 1.5 o away from the hard axis. All of these data suggest that the molecular easy axes of some of the molecules in the crystal are tilted by up ± 1.5 o away from the crystallographic c axis. The observed 58

70 tilts represent a factor of 4 or 5 increase in the deduced values from the x-ray crystallography experiments by Cornia et al. [42]. It seems worth reiterating that the EPR measurements should yield a more accurate description of the tilts in Mn 12 -ac than the previous x-ray measurements, due to the fact that x-ray measurements cannot probe the magnetic structure of the material in the manner that EPR can. 5.5 Conclusions Our angle-resolved single-crystal high-frequency EPR measurements have demonstrated that some of the molecular easy axes of SMM Mn 12 -ac are tilted with respect to crystallographic c axis of the sample. These results thus directly support the acetic acid induced easy axis tilt model of Cornia et al. [42]. However the tilts of about 1.5 o observed with our EPR measurements are significantly larger than the values predicted by the x-ray measurements of Cornia et al. [42]. This distribution of tilts, around what was previously thought to be the only easy magnetization axis of the crystal (i.e. the crystallographic c axis) could be the missing source of transverse anisotropy in the Mn 12 -ac system, and could help to explain the mechanism by which MQT occurs. Thus, there is urgent need for theoretical calculations of such an effect of the acetic acids of hydration. 59

71 Fig Schematic of the six different isomers of Mn 12 -ac observed by Cornia et al. [42]. The n = 0, and n = 4 isomers, which contribute about 12.5% of the molecules, both have S 4 symmetry and therefore do not have an E term to contribute to the phenomenon of MQT. 60

72 Fig (a) Energy level diagram for Mn 12 -ac with the field applied in the hard plane (θ = 90 o ). The labels on the left of the figure correspond to the spin projection along the z (lowfield m z basis) axis, while those on the right hand side correspond to the spin projection along the applied field direction (high field m x basis). The blue sticks represent even to odd (α) transitions, while the red circles represent odd to even (β) transitions. (b) Plot of the α- and β-transition frequencies as a function of applied magnetic field. It should be noted that the frequency of the α-transitions continues smoothly to zero, while the β-transitions go through a minimum. 61

73 Fig Temperature and frequency dependence of the EPR spectra of Mn 12 -ac with the magnetic field applied approximately along the hard axis of the crystal. As is evident in this figure, the β-resonances continue to appear down to at least 44.3 GHz, contrary to the simulations in Fig

74 15 K Fig Simulations of EPR spectra at 44 GHz and 15 K, as a function of field orientation in 0.2 o increments. The main point of this figure is to point out the alternate appearance and disappearance of the α- and β-resonances. This is in contrast to the 44 GHz measurements shown in Fig. 5.3, which clearly show α- and β-resonances at the same angle. 63

75 62 GHz 15 K Fig Experimental spectra of Mn 12 -ac taken at 62 GHz, and 15 K as a function of field orientation in 0.18 o increments. In this figure, both α- and β-resonances are clearly evident at many of the same angles. The experimental spectra in this figure can be directly compared with the simulations shown in Fig

76 62 GHz 15 K Fig EPR spectra of Mn 12 -ac simulated with 62 GHz at 15 K as a function of the applied magnetic field orientation in increments of 0.2 o. In contrast to the experimental spectra shown in Fig. 5.5, the α- and β-resonances appear in alternating increments. A comparison of these spectra with the experimental spectra provides the strongest support for a distribution of tilts of the magnetic easy axes around the four-fold crystallographic axis. 65