Joris van Slageren. stuttgart.de

Transcription

1 Joris van Slageren 1. Physikalisches Institut, Universität Stuttgart stuttgart.de

2 Introduction 2 Low temperature properties of molecular magnets usually described in the ground state multiplet. In that case the zero field splitting of the ground state is a linear combination of the single ion zerofield splittings and anisotropic spin-spin interaction. Anisotropic spin-spin interaction can be divided in anisotropic exchange due to spin-orbit coupling and dipolar interactions. D = d D + d D S S S i i ij ij i i< j D = 3 D /2 zz E = D D /2 xx yy

3 Introduction ˆ = D S ) z S S + /3] + B4 O4 + E( S S ) + B x y 4O4 H [ ˆ ( 1 ˆ ˆ ˆ ˆ 3 Axial ZFS creates the energy barrier : E = DS 2. Transverse terms allow quantum tunneling. Energy (cm 1 ) Coefficient Mc -10 ψ = c M i i S Energy (cm 1 ) Coefficient Mc M S M S

4 Introduction 4 The three commandments of Single Molecule Magnets 1. Thou shalt have a high spin ground state. 2. Thou shalt have a large negative axial zero-field splitting. 3. Thou shalt not have transverse zero-field splitting.

5 Magnetic Resonance Spectroscopy 5 E m s = ½ m s = -½ B 10 M = -1 M = EPR Field necessary: B 0 FDMRS No field necessary: B = 0 Frequency Domain Magnetic Resonance Spectroscopy

6 Aims 6 Transmission S = 1 I D -E I +1> -1> I D + E I 0> Frequency (cm -1 ) H Sˆ Sˆ Sˆ ˆ [ 2 ( 1)/3] ( 2 2 = D ) z S S + + E x y FDMRS can determine energy splittings accurately Aims Characterize new, interesting materials. Origin of zero-field splitting: origin or higher order parameters, accuracy of giant spin model. Study of magnetization dynamics: quantum tunnelling of the magnetization. Study of intermolecular interactions: dipolar, exchange.

7 7 Frequency Domain Magnetic Resonance Spectroscopy The Stuttgart Terahertz Setup microwaves terahertz infrared 3 GHz 100 GHz 1 THz 12 THz 0.1 cm cm cm cm -1 Backward Wave Oscillators: tunable terahertz sources

8 8 Frequency Domain Magnetic Resonance Spectroscopy The Stuttgart Terahertz Setup Phase and transmission: two independent experimental parameters Transmission Phase/freq. (cm) µ' µ" Frequency (GHz)

9 9 Frequency Domain Magnetic Resonance Spectroscopy The Stuttgart Terahertz Setup Current experimental parameters: H = 0-8 T T = K ν = 1-40 cm -1 ( GHz) Faraday geometry: H ext // q Voigt geometry: H ext q parallel mode: H ext // h ac perpendicular mode: H ext h ac Linearly/circularly polarized radiation

10 10 Frequency Domain Magnetic Resonance Spectroscopy The Stuttgart Terahertz Setup

11 Contents Zero-Field Splittings in single ion complexes 2. Single Molecule Magnets in Solution 3. Faraday Effect in Mn 12 ac 1.0 Transmission Faraday angle θ F ( ) Frequency (cm -1 ) Frequency (cm -1 )

12 Contents Zero-Field Splittings in single ion complexes 2. Single Molecule Magnets in Solution 3. Faraday Effect in Mn 12 ac Dr. Suriyakan Vongtragool Nadeschda Kirchner Dr. Marc Durán

13 ZFS in single ion complexes 13 [Ni(HIM2-py)2NO3](NO3) NiHimpy HIM2-py: 2-(2-pyridyl)-4,4,5,5-tetramethyl- 4,5-dihydro-1H-imidazolyl-1-hydroxy Ni II has a d 8 configuration In octahedral surroundings this gives an S = 1 spin state. This triplet state is split. H ˆ ˆ ˆ = DSz + E( Sx - S y) HO N N d x 2 -y 2 d z 2 z N HIM2-py I D -E I I D + E I d xy d xz d yz G. Rogez, J.-N. Rebilly, A.-L. Barra, L. Sorace, N. Kirchner, M. Duran, J. van Slageren, S. Parsons, L. Ricard, A. Marvilliers, T. Mallah, Angew. Chem. Int. Ed., 44, (2005) y x

14 ZFS in single ion complexes NiHimpy 14 Transmission T = 60 K T = 15.0 K T = 1.80 K Frequency (cm -1 ) Resonance lines at 9.7 and 10.3 cm -1. D = ± 0.1 cm -1 E = 0.3 ± 0.1 cm -1 Transmission ratio H ˆ ˆ ˆ = DSz + E( Sx - S y) Frequency (cm -1 )

15 ZFS in single ion complexes NiHimpy 15 µ (x 10 3 ) Experiment Calc. (D < 0) Calc. (D > 0) Temperature (K) Absolute intensities show that D is negative Transmission is determined by magnetic permeability Magnetic permeability is determined by transition intensity and lineshape function Transition intensity is given by number of molecules, transition probability, Boltzmann factor, transition energy and partition function µ = 1+ µ ( ω) i, f if R g µ ˆ B f Sα i 8π N A α = xyz,, if pi p f 3 Mr Z ω fi µ = ρ ( )

16 ZFS in single ion complexes 16 [Fe(H 2 O) 6 ] 2+ HS Fe II has a d 6 configuration: S = 2 Considering FeO 6 coordination geometry: Idealized O h symmetry Considering H 2 O ligands: much lower symmetry H ˆ ˆ ˆ = DSz + E( Sx - S y) d xy d xz d yz J. Telser, J. van Slageren, S. Vongtragool, M. Dressel, W.M. Reiff, S.A. Zvyagin, A. Ozarowski, J. Krzystek "High-Frequency and -Field EPR Spectroscopy of the High-Spin Ferrous Ion in Hexaaqua Complexes" Magn. Res. Chem., 43, S130 S139 (2005).

17 ZFS in single ion complexes Transmission T = 5 K Frequency (cm -1 ) [Fe(H 2 O) 6 ](ClO 4 ) 2 Oscillation in baseline: interference, determined by ε and d. Four transitions observed

18 ZFS in single ion complexes 18 Intensity (arb. u.) 225 GHz [Fe(H 2 O) 6 ](ClO 4 ) 2 D = (4), E = +0.69(1) cm 1 g = 2.18(1) and g = 2.023(6) H ˆ ˆ ˆ = DSz + E( Sx - S y)

19 ZFS in single ion complexes Transmission Signal (V) GHz = 23 cm Wavenumber (cm -1 ) Field (T) (NH 4 ) 2 [Fe(H 2 O) 6 ](SO 4 ) 2 D = (2), E = (2) cm 1 Compare [Fe(H 2 O) 6 ](ClO 4 ) 2 D = (4), E = +0.69(1) cm 1 H ˆ ˆ ˆ = DSz + E( Sx - S y)

20 ZFS in single ion complexes Transmission K 10 K 20 K 30 K 40 K 60 K 80 K 100 K Frequency (cm -1 ) [Fe(H 2 O) 6 ](SO 4 ) D = , E = cm 1 D = , E = cm 1 Transmission H ˆ ˆ ˆ = DSz + E( Sx - S y) Frequency (cm -1 )

21 ZFS in single ion complexes 21 H 10 0 T µ dm dt h ac = µγ 0 M H H = H + h 0 ac Transmission B ac _ _ c B ac // c Frequency (cm -1 ) In EPR, radiation field B ac is usually perpendicular to external field IN FDMRS, the external field is replaced by the ZFS unique axis Transmission Frequency (cm -1 )

22 Contents Zero-Field Splittings in single ion complexes 2. Single Molecule Magnets in Solution 3. Faraday Effect in Mn 12 ac Fadi El Hallak

23 Mn 12 piv Mn 12 [Mn 12 O 12 (O 2 CC(CH 3 ) 3 ) 16 (H 2 O) 4 ]: Mn 12 piv [Mn 12 O 12 (O 2 CCH 3 ) 16 (H 2 O) 4 ]: Mn 12 ac 23 To what extent are the molecules really independent in the crystal? Exchange interactions are possible, dipolar interactions always exist. Increasing the size of the carboxylate ligand does not change the dipolar interaction much. Dispersion in matrix: solution

24 Mn 12 piv Mn 12 [Mn 12 O 12 (O 2 CC(CH 3 ) 3 ) 16 (H 2 O) 4 ]: Mn 12 piv 24 Concentration decrease R av

25 Mn 12 piv Mn 12 [Mn 12 O 12 (O 2 CC(CH 3 ) 3 ) 16 (H 2 O) 4 ]: Mn 12 piv 25 Heater 2 Temperature Sensor Heater 1 Solution insert

26 Mn 12 piv Mn 12 [Mn 12 O 12 (O 2 CC(CH 3 ) 3 ) 16 (H 2 O) 4 ]: Mn 12 piv 26 toluene:dcm=1:1. AC susceptibility measurements show that molecule stays intact. small amount of fast relaxing species. χ" χ' Hz 10 Hz 100 Hz 1000 Hz T / K χ' χ" Hz T / K Mn 12 piv in solution Mn 12 ac crystal

27 Mn 12 piv Mn 12 [Mn 12 O 12 (O 2 CC(CH 3 ) 3 ) 16 (H 2 O) 4 ]: Mn 12 piv K 27 Spin Hamiltonian Parameters D = cm -1 B 40 = -2.0 x 10-5 cm -1 B 44 = -7.2 x 10-5 cm -1 S. Hill : [Mn 12 O 12 (O 2 CCH 2 C(CH 3 ) 3 ) 16 (H 2 O) 4 ]: Mn 12 tbuac D = cm -1 B 40 = -2.5 x 10-5 cm -1 B 44 = ±4.3 x 10-5 cm -1 Gaussian lineshape: Linewidth determined by in the sample: D-strain dipolar fields Transmission Transmission Experiment Lorentz Fit Gauss Fit 2.0 K Wavenumber (cm -1 ) T=20K Wavenumber (cm -1 )

28 28 Mn12piv [Mn12O12(O2CC(CH3)3)16(H2O)4]: Mn12piv Transmission mg/ml 23.5 mg/ml 54.0 mg/ml Wavenumber (cm ) Transmission Unquenched Quenched Wavenumber (cm ) FDMRS spectra show two species Concentration dependence shows: 1. microcrystalline precipitate 2. solvated molecules Field domain measurements and analysis in progress. Signal [a.u.] ν = 303 GHz T=25K T=20K T=15K T=10K T=5K c = 2.75mM 0 Field (T) 1 2

29 Contents Zero-Field Splittings in single ion complexes 2. Single Molecule Magnets in Solution 3. Faraday Effect in Mn 12 ac Dr. Suriyakan Vongtragool

30 Magnetic Relaxation in Mn 12 ac [Mn 12 O 12 (O 2 CCH 3 ) 16 (H 2 O) 4 ] 2 CH 3 COOH 3 H 2 O: Mn 12 ac 30 All measurements performed on single crystal mosaics in Faraday geometry c plane H = DS ˆ + D S ˆ + C( S ˆ - S ˆ ) + g µ SH ˆ z 4 z x y B D = cm -1, D 4 = x 10-4 cm -1, C = 2 x 10-5 cm -1 J. van Slageren, S. Vongtragool, A. Mukhin, B. Gorshunov, M. Dressel, "Terahertz Faraday Effect in Single Molecule Magnets", Phys. Rev. B, 72, (R) (2005).

31 Faraday Effect in Mn 12 ac Circularly polarized light wire grid Wire grid: Tungsten wires (20 µm) aligned close together (80 µm) e wires is reflected. e wires is transmitted. 31 Linearly polarized (45 ) light falls on wire grid/mirror combination. component is reflected at wire grid. component is transmitted at wire grid and reflected at mirror For path length difference ¼λ circular polarization. wire grid mirror

32 Faraday Effect in Mn 12 ac 32 Circularly polarized light 10 0 R.H.C. For M +q, resonance line only for left handed light, in accordance with EPR selection rule T fc Selective excitations on either side of potential double well possible Relaxation studies in zero field possible. Transmission L.H.C. L.H.C. Energy (cm 1 ) M = -1 M = T fc R.H.C Frequency (cm) -1

33 Faraday Effect in Mn 12 ac 33 Linearly polarized light 10 0 Nonmagnetized sample: single resonance line Magnetized sample: two minima These minima are dependent on the analyser angle. Effect of the rotation of the polarization Transmission T=1.76 K H=0 M=M s α A =0 o α A =45 o α A =-45 o H c α sample polarizer analyzer q 10 0 α A =90 o T = 1.76 K H = 0 T Frequency (cm -1 )

34 Faraday Effect in Mn 12 ac 34 Linearly polarized light 10 0 At resonance: one circular component completely absorbed circularly polarized radiation θ F Outside of resonance: no light is absorbed linearly polarized light Transmission cm cm cm cm -1 At resonance edge: one component slightly absorbed phase shift induced rotation of the polarization T=1.76 K H=0 M=M s α A =0 o y 9.8 cm -1 x 10 cm cm Freqency (cm-1)

35 Faraday Effect in Mn 12 ac Linearly polarized light Efficient Faraday rotation Rotation angle up to 150 / mm. Ellipticity changes accordingly. Frequency tunable by magnetic field Faraday angle θ F ( ) Ellipticity Frequency (cm -1 )

36 Faraday Effect in Mn 12 ac Linearly polarized light Zero-Field Cooled sample Equal populations in ±10> states Resonance line splits up in small external fields No magnetization relaxation Faraday rotation effect observed in nonmagnetized sample (lineshape) Transmission ν -10 ν +10 H = 0 T H = 0.5 T H = 1 T Frequency (GHz) E ν +10 ν -10 H -9> -10> +9> +10>

37 Faraday Effect in Mn 12 ac Linearly polarized light At higher T magnetization relaxes Faraday rotation effect is time-dependent Relaxation can be studied using zero-field magnetic resonance Transmission min 4 min 13 min 34 min T = 3.3 K Frequency (cm -1 )

38 Conclusions 38 Frequency Domain Magnetic Resonance Spectroscopy is a very powerful technique to study magnetic anisotropy in molecular magnets. Zero-Field Splittings can be determined accurately. FDMRS spectra of SMM in solution were recorded. It was shown that single molecule magnets act as efficient Faraday rotators of terahertz radiation Magnetization dynamics can be explained. Quantum Tunneling of the Magnetization was observed spectroscopically.

39 Acknowledgments 39 Universität Stuttgart Dr. Suriyakan Vongtragool Nadeschda Kirchner Dr. Marc Duran Fadi El Hallak Christoph Schlegel Prof. Martin Dressel Russian Academy of Sciences, Moscow Prof. Alexander Mukhin Dr. Boris Gorshunov Roosevelt University Prof. Joshua Telser NHMFL, Tallahassee Dr. Jurek Krzystek Université Paris Sud Prof. Tallal Mallah, Dr. Guillaume Rogez Jean-Noel Rebilly Universität Bielefeld Prof. Achim Müller Alice Merca, Ana Maria Todea University of Edinburgh Dr. Euan Brechin Universität Bern Prof. Hans-Ulrich Güdel Dr. Colette Boskovic Dr. Andreas Sieber Dr. Oliver Waldmann MPI Bioanorganische Chemie, Mülheim / Ruhr Prof. Karl Wieghardt Kallol Ray, Ruta Kapre Universität Karlsruhe Prof. Annie Powell, Ian Hewitt University of the Negev, Israel Prof. Boris Tsukerblat ICMB, Barcelona Dr. Daniel Ruiz Molina, Jordi Gomez Deutsche Forschungsgemeinschaft (GRK 448, SPP 1137, SFB/TR 21)

40 Publications 40 A.A. Mukhin, B. Gorshunov, M. Dressel, C. Sangregorio, D. Gatteschi Phys. Rev. B 63, (2001) M. Dressel, B. Gorshunov, K. Rajagopal, S. Vongtragool, A.A. Mukhin Phys. Rev. B 67, (R) (2003) S. Vongtragool, B. Gorshunov, A.A. Mukhin, J. van Slageren, M. Dressel, A. Müller Phys. Chem. Chem. Phys. 5, 2778 (2003) J. van Slageren, S. Vongtragool, B. Gorshunov, A.A. Mukhin, N. Karl, J. Krzystek, J. Telser, A. Müller, C. Sangregorio, D. Gatteschi, M. Dressel Phys. Chem. Chem. Phys. 5, 3837 (2003) S. Vongtragool, B. Gorshunov, M. Dressel, J. Krzystek, D.M. Eichhorn, J. Telser Inorg. Chem. 42, 1788 (2003) S. Vongtragool, A. Mukhin, B. Gorshunov, M. Dressel Phys. Rev. B 69, (2004) G. Rogez, J.-N. Rebilly, A.-L. Barra, L. Sorace, N. Kirchner, M. Duran, J. van Slageren, S. Parsons, L. Ricard, A. Marvilliers, T. Mallah, Angew. Chem. Int. Ed., 44, (2005) K. Ray, A. Begum, T. Weyhermüller, S. Piligkos, J. van Slageren, F. Neese, K. Wieghardt, J. Am. Chem. Soc.,127, (2005). S. Piligkos, G. Rajaraman, M. Soler, N. Kirchner, J. van Slageren, R. Bircher, J. Davidson, S. Parsons, H.-U. Güdel, J. Kortus, W. Wernsdorfer, G. Christou, and E.K. Brechin, J. Am. Chem. Soc., 127, (2005). A. Sieber, C. Boskovic, R. Bircher, O. Waldmann, S.T. Ochsenbein, H.U. Güdel, N. Kirchner, J. van Slageren, W. Wernsdorfer, A. Neels,. H. Stoeckli-Evans, S. Janssen, F. Juranyi, H. Mutka, Inorg. Chem., 44, (2005) J. van Slageren, S. Vongtragool, A. Mukhin, B. Gorshunov, M. Dressel, Phys. Rev. B, 72, (R) (2005). J. Telser, J. van Slageren, S. Vongtragool, M. Dressel, W.M. Reiff, S.A. Zvyagin, A. Ozarowski, J. Krzystek, Magn. Res. Chem., 43, S130 S139 (2005).

41 Torque: Effective Magnetic Permeability Equation of motion: Application of ac (radiation field): M = χh T= M H µ 0 dm dt From eq. of motion magnetic permeability tensor is derived: = µγ 0 M H H = H + h 0 ac M = M + m µ κ 0 = µ 0 κ µ ac µ 0 From Maxwell's equations the effective magnetic permeability is derived. H T z M 0 41 ωω 0 m µ = 1+ χxx, yy = ω ω ωωm κ = iχxy = iχyx = 2 2 ω ω 0 Faraday geometry (M // q): Voigt geometry (M q): µ eff = µ ± κ µ eff 2 2 µ κ = µ ± depending on circular polarization The transmission of a plane parallel sample is a function of this effective magnetic permeability. D.M. Pozar, Microwave Engineering, Wiley; B. Lax, K.J. Button, Microwave Ferrites and Ferrimagnetics, McGraw-Hill