Modeling the crystal-field splitting of energy levels of Er 3+ 4f 11 in charge-compensated sites of KPb 2 Cl 5

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1 JOURNAL OF APPLIED PHYSICS 100, Modeling the crystal-field splitting of energy levels of Er 3+ 4f 11 in charge-compensated sites of KPb 2 Cl 5 John B. Gruber, a Raylon M. Yow, Anmol S. Nijjar, Charles C. Russell III, and Dhiraj K. Sardar Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, Texas Bahram Zandi Army Research Laboratories (ARL)/Adelphi Laboratory Center, 2800 Powder Mill Road, Adelphi, Maryland Arnold Burger and Utpal N. Roy Centre for Photonic Materials and Devices, Department of Physics, Fisk University, Nashville, Tennessee Received 6 September 2005; accepted 28 June 2006; published online 22 August 2006 A point-charge lattice-sum model corrected for induced multipoles is used to investigate the crystal-field splitting of the 2S+1 L J energy levels of Er 3+ 4f 11 ions that occupy charge-compensated sites in the laser host crystal KPb 2 Cl 5. Spectroscopic data are reported and analyzed for Er 3+ between 1550 and 440 nm at cryogenic temperatures. The crystal-field Stark splitting of the ground-state manifold 4 I 15/2 and the splitting of individual excited manifolds of Er 3+ are established from analyses of temperature-dependent hot band absorption spectra. The analyses confirm the Stark splitting of the 4 I J and 4 F 9/2 manifolds that are reported in the literature. From an analysis of the data, it appears that only one of the two possible Pb 2+ sites serving as a charge-compensated site for Er 3+ is involved in the optical activity of the Er 3+ ions. From an examination of the crystallographic data of KPb 2 Cl 5, we identify a possible site for the optically active Er 3+ ion in the lattice and calculate the lattice-sum components for that site. These components are used to evaluate the crystal-field splitting of the energy levels of Er 3+ at that site. The charge-compensation model assumes that Er 3+ substitutes for Pb 2+ in the Pb 2 site with a vacancy in a nearby K + site. To obtain the best overall agreement between calculated and experimental levels, the position of the Er 3+ ion is treated as an adjustable parameter along the quantization axis. Individual manifold centroids of the Er 3+ ion are also varied. From a least-squares fitting analysis, we obtain a rms deviation of 10 cm 1 between 48 calculated-to-observed Stark levels American Institute of Physics. DOI: / I. INTRODUCTION In the ongoing search for laser host materials, especially for use in the eye-safe region and in the midinfrared wavelength range between 4 and 10 m, the crystal host known as potassium lead chloride KPb 2 Cl 5 has many of the spectroscopic and mechanical properties required for efficient use in device applications associated with remote sensing, infrared counter measures, and communication networking. 1 6 The phonon spectrum in this material is represented by lower phonon frequencies that are found in the more popular oxide hosts. 7 Consequently, quenching of luminescence by means of multiphonon decay is reduced so that fluorescent lifetimes are more optimal for stimulated emission at desired wavelengths appropriate for emerging technological applications. Indeed, single crystals of potassium lead halides have proven to be the low-phonon-energy host for solid-state infrared lasers that possibly represent the next generation of diodepumped light sources for important biomedical and biochemical applications. 8,9 Several groups have already found a Author to whom correspondence should be addressed; FAX: ; electronic mail: john.gruber@utsa.edu that the lifetimes of many of the emitting excited states of rare-earth ions such as Pr 3+,Nd 3+,Dy 3+, and Er 3+ in these halides are sufficiently long to induce upconversion to states in the visible and ultraviolet by excitation originating from intense near infrared laser diodes. 4 6,10 As a result, there is current interest in learning more about the local environment surrounding the R 3+ ion and the dynamics of energy transfer in charge-compensated sites in KPb 2 Cl 5. A comprehensive investigation of the crystal structure, crystal growth, and optical properties of ternary alkali lead chlorides has been carried out by Nitsch et al. a decade ago. 11 More recently, a material characterization of Er 3+ - doped KPb 2 Cl 5 has been reported by Roy et al. 12 and by Jenkins et al. 6 In the latter publication, they report the Starklevel splitting of the Er 3+ 4f 11 multiplet manifolds, 4 I J and 4 F 9/2, along with the observation that the low temperature spectra indicate that the Er 3+ ions appear to replace only one of the two low-symmetry nonequivalent divalent lead sites. We have examined the crystal structure for KPb 2 Cl 5 reported by Nitsch et al. 11 and found that at least one chargecompensation model may explain their findings. The model assumes that the divalent Pb 2 ion and the nearest-neighbor /2006/100 4 /043108/6/$ , American Institute of Physics

2 Gruber et al. J. Appl. Phys. 100, A nm components can be expressed as crystal-field splitting parameters B nm that determine a set of Stark levels that are compared to the experimental levels reported in the present study. Previous experience in calculating the crystal-field splitting of rare-earth ions in charge-compensated sites in other laser host crystals has proven useful in setting up the calculations II. EXPERIMENTAL DETAILS FIG. 1. The local coordination of the Pb 2 and K sites in KPb 2 Cl 5. The assumption is made that trivalent erbium replaces divalent lead Pb 2 along the low-symmetry axis connecting the Pb 2 site with a K + vacancy. K ion serving as a vacancy site may avail a suitable environment to attract the Er 3+ ion during crystal growth. In the present study, a point-charge model corrected for induced multipoles is used to investigate the crystal-field splitting of the energy levels of Er 3+ in a charge-compensated site along a low-symmetry axis of quantization that connects the Pb 2 site with the K site, as shown in Fig. 1. From the comprehensive crystallographic data on monoclinic KPb 2 Cl 5 reported by Nitsch et al., 11 we find the Pb 2 site at the top of a distorted polyhedron with the K site at the bottom. By adjusting the relative position of the Er ion along the axis between the Pb 2 and the K sites to accommodate both for the size of the Er and to satisfy energy minimization conditions for the Er within the lattice, we have calculated a set of lattice-sum components A nm at the designated Er site. The Many of the details concerning the synthesis of KPb 2 Cl 5 are described in the work of Roy et al., 12 who also point out the difficulties associated with growing crystals of laser optical quality. An examination of the phase diagrams of PbCl 2 and KCl given by Nitsch et al. 11 sheds light on the problem. In the Pb K Cl system, a congruent compound of KPb 2 Cl 5 is found with a melting temperature of 434 C. Phase transitions are reported at 251 or 270 C. 16,17 Our spectroscopic studies made at cryogenic temperatures over the past year show no change in spectroscopic structure due to a phase change as a result of repeated cycles of temperature change between 8 K and room temperature. We suspect that the same phase remained stable throughout our spectroscopic measurements. The crystals were cut and polished parallel to the c axis and had dimensions of mm 3. They are optically clear of defects and have the pale red color characteristic of the Er 3+ ion. In growing the erbium-doped crystal, high purity anhydrous ErCl 3 was used as the dopant, which was added to zone-refined KPb 2 Cl 5, sealed under vacuum in an ampoule, and placed inside a vertical Bridgman furnace for crystal growth. Unfortunately, little is known about the segregation coefficient, and so we can only report that the crystal contained 5.0 mol % of ErCl 3 that was mixed with the KPb 2 Cl 5 prior to melting the mixture and growing the crystal. A Cary model 14R spectrophotometer controlled by a desktop computer was used to obtain the absorption spectra of Er 3+ in KPb 2 Cl 5 between 1550 and 440 nm at nominal cryogenic temperatures as low as 8 K. The sample was mounted on the cold finger of a closed-cycle helium cryogenic refrigerator, CTI model 22. Spectra were taken at 0.1 nm intervals, and the spectral bandwidth had a lower limit of 0.5 nm over the wavelength investigated. The absorption spectrum observed at approximately 20 K between 1550 and 440 nm is tabulated in Table I and represents multiplet manifolds 4 I 13/2, 4 I 11/2, 4 I 9/2, 4 F 9/2, 4 S 3/2, 2 H 11/2, 4 F 7/2, 4 F 5/2, and 4 F 3/2. Temperature-dependent hot band spectra are designated by an asterisk in column 2. From an analysis of the hot-band absorption spectra representing transitions from Stark levels in the ground-state manifold to Stark levels in excited manifolds, we have determined a Stark-level splitting of the 4 I 15/2 manifold that is listed in Table II. The results are compared to those of Jenkins et al. 6 in the table. Spectra representing transitions from the ground-state Stark level Z 1 and nearby first excited Stark level Z 2 are not fully resolved in the spectra shown in Figs The absorption spectrum of the 4 F 9/2 Fig. 3 best shows the unresolved structure involving transitions from these two

3 Gruber et al. J. Appl. Phys. 100, TABLE I. Absorption spectrum of Er 3+ in KPb 2 Cl 5. Spectrum obtained at approximately 20 K; hot bands denoted by an asterisk in column 2 confirmed by 80 K and higher temperature spectra. 2S+1 L J a nm b cm 1 c E cm 1 d e Z n N n Transition Expt. f E cm 1 Calc. g Percent free-ion state h 4 I 13/ * Z 3 Y Z 1,2 Y I 13/ I 11/ Z 1,2 Y I 13/ I 11/ Z 1,2 Y I 13/ I 11/ I 15/ * Z 3 Y Z 1,2 Y I 13/ I 11/ I 15/ * Z 3 Y Z 1,2 Y I 13/ I 11/ I 15/ * Z 3 Y Z 1,2 Y I 13/ I 11/ I 15/ Z 1,2 Y I 13/ I 11/ I 15/2 4 I 11/ * Z 3 X s * Z 3 X Z 1,2 X I 11/ I 9/ I 13/ Z 1,2 X I 11/ I 9/ F 9/ * Z 4 X s * Z 4 X Z 1,2 X I 11/ I 13/ I 9/2 977 s Z 1,2 X I 11/ I 9/ I 13/ Z 1,2 X I 11/ I 9/ I 13/2 973 s Z 1,2 X I 11/ I 9/ I 13/2 4 I 9/ * Z 2 W Z 1 W I 9/ I 11/ I 13/ * Z 3 W * Z 2 W Z 1 W I 9/ I 11/ F 3/ * Z 2 W Z 1 W I 9/ I 11/ S 3/ * Z 2 W Z 1 W I 9/ I 11/ S 3/ Z 1,2 W I 9/ I 11/ F 9/2 4 F 9/ * Z 3 V * Z 2 V Z 1 V F 9/ H 11/ I 13/ * Z 2 V Z 1 V F 9/ H 11/ F 5/ * Z 3 V * Z 2 V Z 1 V F 9/ H 11/ I 11/ * Z 3 V * Z 2 V Z 1 V F 9/ F 5/ I 9/ * Z 4 V Z 1,2 V F 9/ F 5/ I 11/2 4 S 3/ * Z 5 U * Z 4 U * Z 3 U Z 1,2 U S 3/ H 11/ G 11/ * Z 3 U Z 1,2 U S 3/ H 11/ I 9/2 2 H 11/ * Z 3 T * Z 3 T Z 1,2 T H 11/ S 3/ F 7/ Z 1,2 T H 11/ S 3/ F 7/2

4 Gruber et al. J. Appl. Phys. 100, TABLE I. Continued. 2S+1 L J a nm b cm 1 c E cm 1 d e Z n N n Transition Expt. f E cm 1 Calc. g Percent free-ion state h Z 1,2 T H 11/ S 3/ F 7/ * Z 3 T Z 1,2 T H 11/ S 3/ F 5/ * Z 3 T Z 1,2 T H 11/ S 3/ F 7/ Z 1,2 T H 11/ S 3/ F 7/2 4 F 7/ * Z 3 S Z 1,2 S F 7/ H 11/ F 5/ * Z 4 S Z 1,2 S F 7/ H 11/ F 3/ * Z 3 S Z 1,2 S F 7/ F 5/ H 11/ Z 1,2 S F 7/ F 5/ F 3/2 4 F 5/ * Z 4 R * Z 3 R Z 1,2 R F 5/ F 3/ F 7/ Z 1,2 R F 5/ F 3/ F 7/ Z 1,2 R F 5/ F 3/ F 7/2 4 F 3/ * Z 3 Q * Z 4 Q Z 1 Q F 3/ F 5/ F 7/ * Z 3 Q s Z 1,2 Q F 3/ F 5/ F 7/2 a Multiplet Manifold of Er 3+ 4f 11 ; number in parentheses is the calculated centroid for the manifold. b Wavelength in nanometers. c Absorption coefficient in cm 1. d Energy of transition in vacuum wave numbers. e Transition from Stark levels Z n 4 I 15/2 to excited Stark levels N n. f Experimental Stark level in vacuum wave numbers. g Calculated Stark levels using B nm listed in Table II. h Percent mixing of 2S+1 L J states in designated manifold. levels. In this figure the main peak in the band, usually to the right and at lower energy than the shoulder, is usually more intense and is temperature dependent, reflecting the changes in population between Z 1 and Z 2 with temperature. The changes in relative intensity are easiest to follow in the spectra recorded between 8 and 15 K. Jenkins et al. 6 report a splitting between Z 1 and Z 2 as 5 cm 1. By deconvoluting the temperature-dependent spectra, we approximate a splitting similar to that reported. 6 The value we obtain is listed in Table II. Transitions from unresolved spectra representing transitions from Z 1 and Z 2 are represented as Z 1,2 to excited Stark levels N n and are listed in Table I. Hot bands representing transitions from Z 3 through Z 8 to excited Stark levels in other manifolds are generally well resolved as shown in Figs There appears to be no evidence for a second Er site. The average value for Z 3 through Z 8 is listed in Table II. TABLE II. Splitting of 4 I 15/2 and crystal-field parameters B nm. 2S+1 L J a Stark levels b Energy cm 1 c 4 l 15/2 Experimental Stark levels from Ref. 6 0, 5, 20, 38, 63, 159, 200, Experimental Stark levels from absorption data, present 0, 6, 23, 38, 65, 153, 197, 247 study Calculated Stark levels using B nm listed below 4, 9, 30, 42, 51, 149, 198, 236 B nm d C s symmetry B 20 = 131, B 22 =184, B 40 =93.2, B 42 = 754, IB 42 = 70.7, B 44 = 470, IB 44 =343, B 60 = 55.6, B 62 =1.2, IB 62 =143, B 64 =57.2, IB 64 =10.4, B 66 = 139, IB 66 =136 all in cm 1 a Manifold of the ground-state of Er 3+ 4f 11 ; number in parentheses is the calculated centroid. b Experimental Stark levels from Jenkins et al. Ref. 6 ; levels obtained from this study based on analyses of hot-band absorption spectra. c Energy levels reported in vacuum wave numbers. d Imaginary crystal-field parameters are designated as IB nm.

5 Gruber et al. J. Appl. Phys. 100, FIG. 2. Absorption spectrum of the 4 I 13/2 manifold obtained at approximately 15 K. III. CRYSTAL STRUCTURE AND MODELING RESULTS The crystal structure of KPb 2 Cl 5 can be understood by first examining the structure of PbCl 2, which is constructed from mutually bound irregular coordination polyhedra as shown by Nitsch et al. 11 in Figs. 4 and 5 of their publication. The polyhedra are represented as distorted trigonal prisms where six chlorine atoms are found at the apexes and the remaining three chlorines appear above the centers of the oblong faces. The lead atom is in the center of this cage of nine chlorine atoms see Fig. 1. When KPb 2 Cl 5 is formed, the geometry of the original sublattice of Pb remains unchanged except for the distortion by KCl. The planes occupied by K and Pb alternate and are mutually shifted when viewed along the quantization axis. There are two symmetry-independent lead ion sites, Pb 1 and Pb 2, that Nitsch et al. 11 show in Figs. 8 and 9 of their paper. We have made use of the data from these figures to model the Pb 2 and K vacancy positions in the present study. Based on size and energy considerations, the most likely substitution of Er appears to take place around the FIG. 4. Absorption spectrum of the 2 H 11/2 manifold obtained at approximately 15 K. Pb 2 site along an axis with a nearest-neighbor K vacancy in the K sublattice as shown in Fig. 1. Any model involving Er located away from either Pb sites will involve low symmetry in any case. When checking the possibility that the optically active site may involve the Pb 1 site instead of the Pb 2 site, we found that the experimental splitting reported in Tables I and II is in better agreement with the calculated splitting if we chose the Pb 2 site instead of the Pb 1 site. A point-charge lattice-sum model corrected for induced multipoles was used to investigate the plausibility of these assumptions. Separations between ions in the crystal are reported in the literature. Nitsch et al. 11 report KPb 2 Cl 5 as monoclinic, with a Å = , b Å = , c Å = ,, =90, = , Z=4, and space group P2 1 /C. Separation between sublattices can be determined from their data as well. By adjusting the position of the Er ion along the axis separating the Pb 2 and K vacancy sites as shown in Fig. 1, we obtain a set of lattice-sum components A nm that gives the best agreement with the observed splitting when Er is placed 0.2 Å from the Pb 2 site along the axis separating the Pb 2 and K vacancy sites. This value FIG. 3. Absorption spectrum of the 4 I 9/2 manifold at approximately 15 K showing the splitting between the ground-state Stark level Z 1 and the first excited level Z 2. FIG. 5. Absorption spectrum of the 4 F 7/2 manifold obtained at approximately 12 K.

6 Gruber et al. J. Appl. Phys. 100, is determined by making a systematic comparison between the experimental splitting and the calculated splitting as based on changing the position of the erbium along the axis in increments of 0.05 Å from the Pb 2 origin. To calculate the effect of the vacancy at the K site, we set a negative charge at this site, leaving an effective charge on all other ions in their lattice sites and then adding the contribution to the A nm at the site representing Er along the quantization axis. The calculated splitting given in Tables I and II is based on the chosen set of A nm at the Er site in terms of the crystalfield splitting parameters B nm that are related to the A nm as B nm = n A nm n=2,4,6. Values for n for Er 3+ 4f 11 are given by Morrison and Leavitt. 18 We chose a crystal-field Hamiltonian reflecting the low symmetry of the Er 3+ ion in the charge-compensated site C s. The crystal-field Hamiltonian is expressed in the notation of Morrison and Leavitt 18 equivalent to the Wybourne 19 notation, H CEF = n 11 B * nm n=even m= n i=1 C nm i, 1 where the B nm are the crystal-field parameters and the C nm are defined as C nm i = 4 2n +1 Y nm i, i, 2 with C n m = 1 m * C nm and where Y nm are the ordinary spherical harmonics In C s symmetry, values of m are restricted by n+m=0,2,4 with m n and n=2, 4, and 6. The number of A nm for C s symmetry is 14, with the A 22 real and positive and obtained by a rotation about the quantization axis. Advances in crystal-field splitting theory have appeared since the model used in the present study was first developed. A recent review by Newman and Ng summarizes some of these contributions. 21 A very recent study by Rudowicz and Qin 22 points out the need to clarify inconsistencies between the crystal-field parameters reported in the literature for different rare ions in low-symmetry sites. This issue becomes an even more difficult problem when axes are chosen in charge-compensated systems where axes are selected based on the particular model. The present investigation was inspired by the analysis of symmetry-preserving charge compensation and vacancies in laser host crystals by Morrison 23 and subsequent work by some of the authors who worked with him In the present study, the lattice-sum components are expressed as A nm = e 2 q j C nm Rˆ j /R n+1 j, 3 j where q j is the formal charge on the ion at the vector distance R J. The sum is taken over all ions in the lattice. 23 The simplicity and consistency within the model make it useful as an initial step in establishing crystal-field parameters. The crystal-field Hamiltonian given in Eq. 1 together with the free-ion Hamiltonian for Er 3+ 4f 11 described by Wybourne 19 and Judd 20 are combined to form a total Hamiltonian that is diagonalized over the lowest-energy 13 multiplets of the Er 3+ 4f 11 configuration that involve a total of 60 energy Stark levels. The calculated Stark levels for the ten lowest-energy manifolds reported in Table I column 7 can be compared to the experimental Stark levels given in column 6. Only the calculated centroids given in column 1 were adjusted to give the best agreement to the observed manifold centroids. The calculated centroids for each manifold were adjusted by a least-squares fitting routine so as to obtain a rms of 10 cm 1 between 48 calculated-to-experimental Stark levels in ten lowest-energy multiplet manifolds of Er 3+ 4f 11 in KPb 2 Cl 5. In summary, we have modeled the crystal-field splitting of the energy levels of Er 3+ in the host crystal KPb 2 Cl 5 by assuming that Er 3+ replaces Pb 2+ in one of the two nonequivalent sites in the lattice. The model assumes that the Er 3+ substitutes along an axis between the Pb 2 site and a K + vacancy. We obtain a rms deviation of 10 cm 1 between 48 calculated and experimental Stark levels within the ten lowest-energy multiplet manifolds of Er 3+ 4f 11 in KPb 2 Cl 5. ACKNOWLEDGMENT This research was partially supported by the NSF Center for Biophotonics Science and Technology, managed by U.C. Davis, CA, No. PHY N. W. Jenkins, S. R. Bowman, L. B. Shaw, and J. R. Lindle, J. Lumin. 97, M. C. Nostrand, R. H. Page, S. A. Payne, L. I. Isaenko, and A. P. Yelisseyen, J. Opt. Soc. Am. B 18, R. Balda, M. Voda, M. Al-Saleh, and J. Fernandez, J. Lumin. 97, M. C. Nostrand, R. H. Page, S. A. Payne, W. F. Krupke, P. G. Schunemann, and L. I. Isaenko, OSA Trends Opt. Photonics Ser. 26, S. R. 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