Gadolinium in lutetium fluoride—an electron paramagnetic resonance study

Journal of Physics and Chemistry of Solids 62 (2001) 485±489

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Gadolinium in lutetium ¯uorideÐan electron paramagnetic resonance study K.J. Guedes a, K. Krambrock a,*, J.Y. Gesland b a UFMG, Departamento de FõÂsica, ICEx, CP 702, 30.123-970 Belo Horizonte, Brazil Equipe de Physique de l'Etat CondenseÂ, CNRS URA no 807 Avenue Messiaen BP, 535 72017 Le Mans Cedex, France

b

Received 15 May 2000; accepted 19 May 2000

Abstract Gadolinium (Gd 31) in Czochralski-grown lutetium ¯uoride (LuF3) has been investigated by electron paramagnetic resonance (EPR). Detailed analysis of the EPR angular dependencies reveals that Gd 31 entered substitutionally for Lu 31 in monoclinic Cs site symmetry. The Lu site seems to be more distorted by the Gd ion as compared to the Y site in YF3. The zero-®eld splitting of the ground state b20 is 21.8372 GHz which is more than twice compared to that of Gd 31 in host crystals of LaF3, in which gadolinium has the same co-ordination number. The results of the ®ne structure analysis are compared to a similar study in the iso-structural host YF3. The obtained results seem to be in contrast to the superposition model. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: D. Electron paramagnetic resonance

1. Introduction From a theoretical point of view, it is interesting to investigate the interaction of Gd 31 with its crystalline environment, because the zero-®eld splittings of Gd31 with a pure S ground state have not been understood so far. It is clear that the pointcharge model cannot give a satisfactory solution to the problem. However, the superposition model[1], which was used successfully to explain the interaction of Gd31 in the LaF3 iso-structural hosts[2], seems to be in contrast to our observations of the ®ne structure parameters of Gd31 in the iso-structural hosts, YF3 [3] and LuF3, presented in this paper. From a technological point of view, it is interesting to study ¯uoride materials since they can be used as active media for tunable solid state lasers or as fast scintillator materials. The lanthanide tri-¯uorides LnF3 with Ln ˆ Sm, Eu, Gd, Tb, Ho, Er, Tm, Yb and Lu are particularly interesting in such applications because their room temperature space group is orthorhombic Pnma …D16 2h † which favours applications in non-linear optics. As examples, LuF3 doped by Ce 31 ions has been shown to have very fast scintillating * Corresponding author. Tel.: 155-31-499-5625; fax: 155-31499-5600. E-mail address: klaus@®scia.ufmg.br (K. Krambrock).

properties [4] and GdF3 doped by Nd 31 has interesting laser properties in the near infrared[5]. Like YF3 and GdF3, single crystal growth of lutetium ¯uoride by the Czochralski method is dif®cult because of a high temperature phase transition from rhombohedral to orthorhombic structure[6]. However, we succeeded to grow large single crystals of LuF3 directly in the orthorhombic phase by using a mixture of LiF (0.45) and LuF3 (0.55) in the melt. The crystals are colourless and non-hygroscopic, which is important for their use as active media in laser or scintillator technology. For the electron paramagnetic resonance (EPR) measurements samples with dimensions of 3 £ 2 £ 5 mm3 were cut with faces normal to the crystallographic axes using the cleavage plane (010). The orientation of the samples was con®rmed by Laue X-ray analysis. EPR spectra were obtained at low and room temperature and X-band frequencies with the usual 100 kHz ®eld modulation. EPR angular dependencies were recorded for rotations of the crystal in all three orthorhombic planes ab, ac and bc or alternatively (001), (010) and (100).

2. Experimental results and discussion Fig. 1 shows the EPR spectra of Gd 31 in LuF3 single

0022-3697/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0022-369 7(00)00190-6

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K.J. Guedes et al. / Journal of Physics and Chemistry of Solids 62 (2001) 485±489

Fig. 1. EPR spectra of Gd 31 in a single crystal LuF3 (solid line) obtained for Bib measured at 300 K (curve a) and 50 K (curve b) with a microwave frequency of 9.38 GHz.

crystal for Bib measured at 300 K (curve a) and 50 K (curve b) with a microwave frequency of 9.38 GHz. The spectra consist of seven EPR lines with unequal intensities consistent with the ®ne structure spectrum expected for Gd 31 with ground state (4f 7) 8S7/2. The EPR lines correspond to DMS ˆ ^1 transitions. The EPR linewidths are about 10 G. In crystal ®eld, the eight-fold degeneracy is partly removed owing to the admixture with higher states resulting in a set of four two-fold levels [7,8]. For a low-symmetry case like LuF3 the degeneracy is totally removed, leading to seven ®ne structure EPR lines. Gadolinium impurities enter in LuF3 from traces in the raw material LuF3, which had a purity of 99.99%. From our EPR measurements in comparison with a standard sample we estimate the Gd concentration to be about 10 17 cm 23. The angular variation of the EPR spectra for the magnetic ®eld in the ac plane is shown in Fig. 2. Fig. 3 shows the angular variation with the magnetic ®eld in the ab plane. In Figs. 2 and 3, the dots correspond to EPR line positions and the solid and dotted lines to a computer ®t using the following spin Hamiltonian for the monoclinic lutetium site symmetry[9]: X X 1 m m 1 m m ~ ! g´S~ 1 H ˆ bH´ 3 b2 O2 1 60 b4 O4 mˆ0;^ 1;^ 2

1

X mˆ0;^ 2;^ 4;^ 6

mˆ0;^ 2;^ 4

1 1260

m bm 6 O6

…1† with spin S ˆ 7=2 and b is the Bohr magneton. The ®rst term in the right-hand side of Eq. (1) is the Zeeman term which describes the interaction between the electron spin S and the applied external magnetic ®eld H. The remaining terms are related to the splitting of the electronic levels in zero

magnetic ®eld. The spin operators Om l are functions of degree l of the angular momentum operator SZ, S1 and S2. They are called the Stevens operators [10] and transform according to the symmetry operations of the point symmetry of the site in consideration. The bm l are empirical coef®cients determined from the experiment. The parameters of the spin Hamiltonian were evaluated by ®tting simultaneously the line positions of all clearly resolved lines, in the ab, ac and bc planes. The process consists in an exact diagonalization in combination with a least-squares-®tting procedure in which all resonant EPR line positions, obtained for several orientations of the external magnetic ®eld, were ®tted. We have performed three m types of ®ttings: with (I) all bm l ; l ˆ 2; 4; 6; (II) bl ; l ˆ m 2; 4; (III) bl ; l ˆ 2: This was done in order to see how critical are the higher-order parameters bm l …l ˆ 4; 6† for the EPR analysis. From the analysis, we conclude that the bm l with l ˆ 4 signi®cantly improve the root mean square deviation (RMSD), however, effect of bm l with l ˆ 6 is negligible. The values of the g-tensor and the parameters for all bm l …l ˆ 2 and 4, umu # l† at 300 K are shown in Table 1 together with the ®ne structure parameters of Gd 31 in YF3[3]. From these values it is clear that the shape of the EPR angular dependence is dominated by the electronic quadrupole tensor. The absolute signs of b02 and b04 were found in the usual way by observing the relative intensities of the EPR lines as a function of temperature[11]. From the measurements at 50 K we found that b02 is negative. However, the analysis was dif®cult because of superposition of lines from other rare earth elements seen at low temperatures for HiZ. The bm l values we found are unique for monoclinic site symmetry (see for example the discussion by McGavin, Table 4 of Ref. [12]). The values do not change

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Fig. 2. Angular variation of the X-band EPR spectra in the ac plane for Gd 31 in a LuF3 single crystal at room temperature, u ˆ 08 corresponds to c and u ˆ 908 to a. The solid lines are ®tted curves that connect data points from the same transition DMS ˆ ^1 for two set of magnetically inequivalent ions. They are related by a rotation of 508 in this plane. The dotted lines belong to the forbidden transitions of type uDMS u $ 2:

when using another axis system, only the sign of the bm 4 values are inverted. In Fig. 2, the two spectra (solid lines) correspond to two magnetically inequivalent Gd-sites and belong to transitions of type DMS ˆ ^1: The dotted lines are related to forbidden transitions of type uDMS u $ 2: When rotating the crystal in the ab plane, the seven ®ne structure lines split into doublets. The EPR spectra indicate that the Gd 31 enters substitutionally into the lutetium site, which has monoclinic point symmetry Cs. Fig. 4 shows the projection of the LuF3 crystal structure on the ac plane. The principal axes X and Z of the electronic quadrupole tensor, which is the dominant interaction, are rotated by 258 in relation with the crystallo-

graphic axes a and c, respectively. From the EPR angular dependence (Fig. 2), the principal axis Z of one of the two magnetically inequivalent Gd-sites is found at u ˆ 258; where the splitting of the EPR lines is the largest. The Xaxis is chosen perpendicular to Z in the mirror plane ac. Consequently, the Y-axis is coincident with the crystallographic axis b. The principal axis Z 0 of the other magnetically inequivalent Gd ion is found simply by rotation of 508 about the b-axis. The g tensor is nearly isotropic. For monoclinic point symmetry, we expect two independent values for the electronic quadrupole tensor, D and E or b02 and b22 ; respectively, in its principal axes system. However, in our experiment we have rotated the crystal

Fig. 3. Angular variation of the X-band EPR spectra in the ab plane for Gd 31 in a LuF3 single crystal at room temperature. The magnetic ®eld is in fact off the ab plane by about 100. This small misalignment was taken into account in our calculations and it does not affect the results presented here. The solid lines are ®tted curves that connect data points from the same transition DMS ˆ ^1 for two set of equivalent ions. The angles u ˆ 08 and u ˆ 908 correspond to b and a axes, respectively. The dotted lines belong to the forbidden transitions of type uDMS u $ 2:

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K.J. Guedes et al. / Journal of Physics and Chemistry of Solids 62 (2001) 485±489

Fig. 4. Projection of the structure of LuF3 on the ac plane showing the principal axes Z and X of the electronic quadrupole tensor which are rotated by 258 about the b axis. The principal axes (Z and Z 0 ) of the two magnetically inequivalent gadolinium ions are rotated by about 508 about the b axis in the ac plane.

about the crystallographic axes, which are not coincident with the principal axes of the electronic quadrupole tensor. Therefore, off-diagonal elements like b12 and b21 are 2 22 24 present[12]. The terms b22 2 ; b4 and b4 are also expected. However, their values are small as shown in Table 1. From the EPR angular dependence in the ab plane (Fig. 3), we observe seven lines for B parallel to the b-axis. The lines split in doublets when rotating the crystal in the ab plane because two of the four physically equivalent ions are magnetically inequivalent in pairs in this plane. The results of the spin Hamiltonian parameters for Gd31 in LuF3 and YF3 [3] can be compared to EPR studies of Gd31 in similar host crystals of the type LaF3. Misra et al. [2]have made an EPR study of Gd31 doped single crystals of CeF3, LaF3, PrF3 and NdF3. They have used Newman's superposition model [1] for the explanation of the spin Hamiltonian parameters in these iso-structural hosts with hexagonal structure (LaF3). In this model, the ®ne structure parameters are related to intrinsic parameters of crystal structure and ionic radii. The main conclusion is that the b02 ®ne structure parameter is inversely proportional to the ionic radii. If we compare the data for Gd in LuF3 with that in YF3, Ê and Y 0.893 A Ê [13] or taking as the ionic radii of Lu 0.85 A alternatively 1.03 and 1.07 for coordination number nine[14], respectively, we ®nd that the b02 parameter is proportional to the ionic radii. This result is in contrast to the prediction of the superposition model. This does not

mean, of course, that the superposition model is not valid in general. However, this result does show the need of more experimental data for Gd 31 in different host crystals in order to test the validity of the superposition model. Table 1 Values of room temperature spin Hamiltonian parameters for Gd 31 in YF3 [3] and LuF3. All bm l and their root mean square deviations (RMSD) are expressed in GHz. Here, n is the number of data points used in the analysis Parameters

YF3

LuF3

gxx gyy gzz b02 b12 b22 b21 2 b22 2 b04 b24 b44 b22 4 b24 4 RMSD n

1.9874 ^ 0.0007 1.9846 ^ 0.0005 1.9906 ^ 0.0009 21.978 ^ 0.001 0.370 ^ 0.004 0.103 ^ 0.001 0.263 ^ 0.006 20.010 ^ 0.002 0.0015 ^ 0.0005 20.055 ^ 0.001 0.054 ^ 0.002 20.012 ^ 0.003 0.005 ^ 0.003 0.05 715

1.9929 ^ 0.0005 1.9828 ^ 0.0004 1.9915 ^ 0.0005 21.8372 ^ 0.0008 20.190 ^ 0.003 0.107 ^ 0.001 0.024 ^ 0.004 20.013 ^ 0.001 0.0092 ^ 0.0003 20.068 ^ 0.001 0.068 ^ 0.001 0.002 ^ 0.002 20.006 ^ 0.001 0.04 1165

K.J. Guedes et al. / Journal of Physics and Chemistry of Solids 62 (2001) 485±489

b02

The value we have found is about three times larger than that for the LaF3 hosts studied by Misra et al.[1]. The co-ordination number of the gadolinium site is nine for both series; nevertheless, the mean distance to nearest-neighbour ligands of the paramagnetic ion is only about ®ve percent smaller in the LuF3 and YF3. Therefore, the b02 value is unexpectedly high. Further, theoretical analysis is under way to understand the interaction of the Gd 31 ion with its environment. The appearance of the b12 and b21 Stevens 2 parameters can be explained by the fact that the rotation of the crystal was done in the crystallographic crystal system which is not coincident with the principal axes system. However, a small local distortion cannot be ruled out. Speci®cally, the Gd ion should distort the Lu site in LuF3 more than the Y site in YF3 because of the smaller ionic radii of the Lu ion.

3. Conclusions Detailed analysis of the EPR spectra of Gd 31 in LuF3 allowed us to determine the ®ne structure parameters for monoclinic Cs symmetry. The b02 parameter found for Gd 31 in LuF3 is unexpectedly high when compared to Gd 31 in the LaF3 structure and is of the same order as that for Gd 31 in YF3. However, the distortion introduced by Gd in the Lu site is stronger as in the Y site in YF3. From the high b02 value we conclude that both host crystal systems, YF3 and LuF3, are promising laser host systems. Our results suggest that more measurements are needed in other crystal systems to test the validity of the superposition model, particularly on its predictions about the b02 parameter.

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Acknowledgements We are grateful to Prof. Paulo SeÂrgio Soares GuimaraÄes for fruitful discussions. One of us, K.J.G. acknowledge ®nancial support form the Brazilian agency FAPEMIG. References [1] S.K. Misra, P. Mikolajczak, N.R. Lewis, Phys. Rev. B 24 (1981) 3729. [2] S.K. Misra, P. Mikolajczak, S. Korczak, J. Chem. Phys. 74 (1981) 922. [3] K.J. Guedes, K. Krambrock, J.Y. Gesland, J. Phys. C 11 (1999) 7211. [4] B. Moine, C. Dujardin, H. Lautesse, C. Pedrini, P. Martin, J.Y. Gesland, Mater. Sci. Forum 239±241 (1997) 245. [5] J.M. Breteau, J.Y. Gesland, Opt. Mater. 5 (1996) 267. [6] K. Rotereau, J.Y. Gesland, P. Daniel, A. Bulou, Mater. Res. Bull. 28 (1993) 813. [7] H.A. Buckmaster, Y.H. Shing, Phys. Stat. Sol. (a) 12 (1972) 325. [8] G. Feher, H.E.D. Scovil, Phys. Rev. 105 (1957) 760. [9] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Clarendon, Oxford, 1970 (chap. 5, p. 335). [10] A. Zalkin, D.H. Templeton, J. Am. Chem. Soc. 75 (1953) 2453. [11] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Clarendon, Oxford, 1970 (chap. 3, p. 161). [12] D.G. McGavin, J. Magn. Reson. 74 (1987) 19. [13] A. Iandelli, A. Palenzona, in: K.A. Gschneidner Jr., L.R. Eyring (Eds.), Alloys and intermetallics, Handbook on the Physics and Chemistry of Rare Earths, vol. 2, North-Holland, Amsterdam, 1982, p. 22 (chap. 13). [14] R.D. Shannon, Acta Cryst. A32 (1976) 751.