Crystal field effects on the magnetic susceptibility of rare earth tellurium oxides

1. Phys. C&-m. Solids Vol. 54, No. I I, pp. 1471-1474, Printed in Great Britain.

1993

002s3697/93 s6.00 + 0.00 0 1993 Rrgamon Press Ltd

CRYSTAL FIELD EFFECTS ON THE MAGNETIC SUSCEPTIBILITY OF RARE EARTH TELLURIUM OXIDES C. CASCALES,~$ P. PORCHER~ and R. Shz-PUCHE)( tInstituto de Ciencia de Materiales, CSIC, Serrano 113, E-28006 Madrid, Spain §Laboratoire de Chimie MCtallurgique et de Spectroscopic des Terres Rares, UPR 209 du CNRS, 1, pl. A. Briand, F-92195 Meudon, France [[Departamento de Quimica Inorganica, Facultad de Ciencias Quimicas, Universidad Complutense, E-28040 Madrid, Spain (Received

5 Match

1993; accepted in revised form 29 July 1993)

Abatrnet--The magnetic susceptibilities of the rare earth tellurates RErTe,O,, (where RE is a trivalent rare earth ion, Pr, Nd or Eu) have been measured, on polycrystalline powders, in the temperature range 4.2-300 K. In every case, an expression of the wavefunctions associated to each energy level in the corresponding 4f *, 4f’ and 4f 6 configurations, previously obtained from spectroscopic measurements and crystal field effects analysis (considering approximate Cr, and/or C, RE site symmetries), was used in the simulation of the magnetic susceptibilities and its evolution vs temperature. Satisfactory agreements between the experimental and calculated magnetic susceptibilities have been obtained. Keywords:

Rare earth tellurates, crystal fields, magnetic susceptibility.

1.INTRODUCTION The crystallographic description of the isostructural family of rare earth tellurates RE2Te40,, have received considerable attention in recent years [l-3]. These compounds, isomorphic through the whole lanthanide series, crystallize in the monoclinic system, space group C2/c (No. 15), Z = 4. The RE atoms occupy only one kind of 8fcrystallographic position, with very low C, point symmetry. The eight-fold coordination polyhedron of the RE is a distorted square antiprism of oxygens, REOr, connected by sharing edges, which creates bidimensional chains. The link between these and the corresponding link to the TeO, polyhedra give rise to the tridimensional structure. Our preliminary studies [4-51 of the optical properties of Pr3+, Nd3+ and Eu3+ tellurates, pure and doped-Gd compounds, show the high quality of the spectroscopic data: complete experimental information that involves many electronic transitions from different emitting levels, shows that the emission from upper excited levels is not quenched, and narrow lines mean high crystallinity of materials. The electronic spectra were analyzed according to the crystal field (CF) theory and very good correlations were obtained between the experimental and simulated energy level schemes, the approximate C,, and/or C, site symmetries were supposed. The accurate description

#Author to whom correspondence should be addressed.

of the spectroscopic properties of these materials is the first step in magnetic properties calculations, like the effective moment or the paramagnetic susceptibility (in this case due exclusively to the RE ions) and its variation vs temperature. For f electrons, the application of the magnetic tensor L +g,S on the obtained wavefunction associated with a given energy level leads to a good simulation of the data. In the present work we study the influence of the CF on the magnetic susceptibility of the triply ionized Pr, Nd and Eu tellurates, RE2Te40,, , and we report the comparison between experimental and calculated susceptibles vs temperature. This magnetic characteristic can be understood in terms of the crystal field model. 2. EXPERIMENTAL DETAILS

Preparation of samples Polycrystalline light-coloured rare-earth tellurium oxides were synthesized as indicated in [3]. Sample purity and crystal structure were checked by routine X-ray diffraction powder analysis, which showed only the expected phase. Additional experimental conditions and more crystallographic details have been described elsewhere [2].

Magnetic susceptibility measurements The magnetic susceptibility measurements were performed by the Faraday method in applied fields of 12 kG from liquid helium temperature to 300 K,

1471

C. CASCALES et al.

1472

using a DMSS susceptometer. The setup was calibrated with HgCo(SCN), and Gd,(SO.,), . 8HrO as standards. The diamagnetic correction was calculated using the values, in lob6 emu mol-‘, of - 16, - 12, and -20 for 02- Te4+ and RE3+, respectively [6]. The magnetic suskptibilities were found to be independent of the magnetic field in the temperature range of measurements. 3. MAGNETIC SUSCEPTIBILITY AND THE CRYSTAL FIELD LEVELS

According to the work of Van Vleck [7], the susceptibility corresponding to a principal axis i( =x,y, z) is calculated by the formula:

in which N is the Avogadro’s number, b the Bohr magneton, k the Boltzmann constant, E and (b the non-perturbed eigenvalues and wavefunctions, respectively, described on the SLJM, basis and H is the magnetic tensor operator L + g,S. The different values of the tensor components (or combinations of them) destroy the isotropy observed for the free ion or even for an ion in cubic symmetry. The anisotropy components are called x1 (component 0 of the tensor) and x,, (components f 1 of the tensor). The sums run over thermally populated levels, according to the Boltzmann population, Ba = exp(-E$‘)/kT)/

1 exp( - E’,O)/kT). a

In that expression, the matrix elements are calculated using the Racah algebra rules. The formula is the sum of a temperature-dependent diagonal term and a temperature-independent off-diagonal term, which is reminiscent of the classical Curie-Weiss law. The off-diagonal term, a result of the second-order perturbation, usually has little importance, with the exception of the ground states with J = 0. The sum runs over all other states (b # a). In rare earths, 4f” configurations, the calculation agrees fairly closely with experiment, mainly for neodymium (S-101 and erbium [l l] compounds. The application to Eu’+ is more tedious: due to the high degeneracy of the 4f 6 configuration the exact composition of the Eu3+ eigenfunctions is difficult to handle. The complete CF calculation would need a low symmetry to diagonalize a 3003-dimensioned secular determinant, and even when the problem is reduced to 2, 3 or 4 submatrices, if the symmetry allows it, the calculation is not very feasible. On the other hand, Et? presents

a particularity: the ‘F. ground level is non-magnetic, with a vanishing value for the first order magnetic interaction E $?. . Only the second order element E \& is non-zero, which underlines the extreme sensitivity of the paramagnetic susceptibility to the value of this element, itself strongly dependent on the CF strength. As a consequence of the ‘F, energy position, the thermal population of these levels starts to be taken into account for temperatures higher than about S&100 K. This double particularity explains why the Curie-Weiss law is not obeyed at low temperature. Anyway, very good predictions of x vs T are obtained, with the plateau at low temperature perfectly reproduced [12-l 31. In order to calculate 1 from the Van Vleck equation, we had obtained the CF levels and their corresponding eigenfunctions from diagonalization of the CF Hamiltonian, whose expression, following Wyboume’s formalism is a sum of products of spherical harmonics and CF parameters:

For the rare earth tellurium oxides, the lanthanide ion occupies a crystallographic position with the low C, point symmetry. The serial development of the CF potential keep non-zero all of the 27 CF parameters, which constitutes non-realistic conditions of simulation. Instead of C,, the approximate C, (or C, as well) point symmetry was used for the simulation involving 14 non-zero CF parameters among which five imaginary S i (S i is set to zero by an appropriate choice of the reference axis system). Moreover, if the imaginary part of CF parameters is cancelled, the symmetry increases up to C,, , involving only nine CF parameters. These approximations have been used previously [45]. For the 4f 2 and 4f 3 configurations of Pr3+ and Nd3+, respectively, the full secular determinant including free ion as well as CF parameters has been considered. For the 4f6 configuration of Eu3+ the crystal field simulation can be performed accurately on the very reduced basis of the ‘F lo!SLJM) states. When magnetic susceptibility calculations were performed all configuration states were involved, inducing two submatrices whose size are approximately 1500 x 1500, in C, (or C,) symmetry. Diagonalization of such sized matrices required about 30 MO RAM and 20 h cpu on a 80486-66 PC (NDP FORTRAN compiler). Instead of that, the C,, symmetry lowering reduces by a factor of two the requested RAM and by a factor of four the computing time. Calculations in a higher point symmetry seem to be more confident than the configuration truncations used previously [14]. They have been performed using the Fortran routines REEL and IMAGE [15].

Rare earth tellurium oxides

1473

Table 1. Magnetic moments (BM), calculated (Pa) by using Van Vleck’s formula, and observed (k) at room temperature, and paramagnetic Curie temperatures t$,, (K), for RErTe,O,, compounds

0

ido

z&l

Fig. 1. Temperature dependence of the reciprocal magnetic susceptibility for Pr,Te,O,, . Open circles are the experimental data, and the solid line is the calculated average reciprocal susceptibility. 4. RESULTS AND DISCUSSION

The comparison between experimental and calculated average value of temperature dependence of the reciprocal molar magnetic susceptibilities are plotted in Figs 1 and 2, circles for experimental and solid lines from CF parameters data results, respectively. For Pr and Nd compounds experimental values of the effective paramagnetics moments (p,,) and paramagnetic Curie temperature (0,) were obtained by least square fits of the linear part of the reciprocal susceptibility curves at higher temperatures and are given in Table 1. The effective paramagnetic moments are close to the values for the free ions. The deviations from Curie-Weiss behaviour, evident in Figs 1 and 2, at low temperature, reflect the splitting of the ground state associated with these cations under the influence of the CF. The negative values obtained for the Weiss constants, Or,,are also entirely due to CF effects, since antiferromagnetic interactions are not operative. Or values are higher for Nd,Te,O,,, which presents stronger field effects. Figure 3 shows the characteristic magnetic behaviour of Eu,Te,O,, . Below x 50 K PrrTe,O,, both the experimental

T (K) Fig. 2. Temperature dependence of the reciprocal magnetic susceptibility for Nd,Te,O,, . Open circles are the experimental data and the solid line is the calculated average reciprocal susceptibility.

RE

4f”

J

Pr Nd Eu

2 3 6

4 912 0

g

k-drn

415 8/l 1

3.58 3.62

PC

PO

3.41 3.38 3.61 3.58 3.28 3.24

ep

-34.1 -38.0

and the calculated curves of the reciprocal susceptibility bend upward to level off. The material shows above z 200 K experimental reciprocal susceptibilities are larger than those calculated, but below this temperature the situation is reversed. The same type of mismatch has been observed on PrVO, [16], PrWO,Cl, Pr,WO,Cl, and Na,Pr(MoO,), [17]. The situation is significantly different in our previous study about Pr, Sb,O,r , where a very good agreement was found between experiment and calculation [13]. It is clear that the discrepancy has nothing to do with an approximate calculation induced by the symmetry lowering, because PrVO, and Na,Pr(MoO,), have higher point symmetries (& and S,) as well as Pr,Sb50n (S,). An accidental lifting of the E irreducible representation of the ground state is excluded for PrWO,Cl and Pr, WOBCl, (low point symmetry). The only simple explanation lies in the large anisotropy found in the calculation of the paramagnetic susceptibility at low temperature, Table 2, decreasing with increasing temperature. It is then possible that preferred orientations could be operative on the magnetic susceptibility measurement of the polycrystalline powder. In a similar way, calculations of magnetic susceptibility from optical data on REF, matrices, RE = P?+ and Nd3+ [18], also show highly anisotropic behaviour at low temperatures for the PrF, compound. The problem will be solved by measurements on single crystals. In fact, these anisotropic effects have been fully reproduced in some

l&O

2dO

T (K)'

la

Fig. 3. Temperature variation of the magnetic susceptibility for Eu,Te,O,, Open circles are the experimental data, and solid line is the theoretical average magnetic susceptibility.

C. CAScxws

1474 Table 2. Calculated

T(K) 2 4 6 8 10 12 14 16 18 20 40 60 80 100 120 140 160 180 200 250 300 350 400 450

xx 0.562 0.562 0.562 0.562 0.562 0.562 0.562 0.562 0.561 0.561 0.557 0.545 0.531 0.519 0.508 0.497 0.485 0.472 0.460 0.421 0.385 0.352 0.323 0.297

temperature

G 1.173 1.173 1.173 1.173 1.173 1.173 1.173 1.173 1.173 1.173 1.160 1.116 1.047 0.970 0.894 0.825 0.762 0.706 0.657 0.557 0.481 0.423 0.377 0.339

et al.

dependent paramagnetic Values in 102 emu units

X1 2.685 2.685 2.685 2.685 2.685 2.685 2.685 2.684 2.682 2.680 2.532 2.229 1.916 1.646 1.427 1.250 1.106 0.989 0.892 0.711 0.588 0.500 0.435 0.383

studies [ 191on crystals of dilute alloys of Pr in Y and LU. The experimental and calculated curves for Ndr Te,O, I agree well, over all the measured temperature range, especially at low temperature: the deviation from the Curie-Weiss law below x40 K, as a consequence of the CF splitting, is very well reproduced. The magnetic susceptibility of Eu,Te,O,, increased with decreasing temperatures down to 100 K; below this temperature it flattens out. At very low temperature (< 10 K) it increases again. This last feature indicates a small quantity (< 0.1%) of highly paramagnetic Eu*+ ion, always present in europium mixed oxides. Below 100 K only the non-magnetic ‘F, ground level is populated, the susceptibility plateau is only due to the temperature-independent term of the Van Vleck formula, and its value strongly depends on the position of the ‘F, crystal field levels, i.e. 304, 380 and 419cm-’ above ‘F,, on one side and on the wavefunction composition on the other side. It is clear that the measured susceptibility is well reproduced by the Van Vleck formula. REFERENCES 1. Redman M. J., Binnie W. P. and Carter J. R., J. LessCommon Met. 16, 407 (1968). 2. Parada C., Alonso J. A. and Rasines I., Inorg. Chim. Acra 111, 197 (1986).

XS” I .473

1.473 1.473 1.473

1.473 1.473 1.473 1.473 1.472 1.471 1.416 1.297 1.165 1.045 0.943 0.857 0.784 0.722 0.669 0.563 0.485 0.425 0.378 0.340

susceptibility

1;’ 11,530.7 11,530.7 11,530.7 1L530.7 1L530.7 11.530.7 11;530.7 11.531.4 111531.4 lL531.4 11646.9 12,038.g 12,670.3 13,429.l 14,261.3 15,135.5 16,042.4 16,942.4 17,938.g 20445.7 23,076.O 25,799.g 28,591.9 3L431.7

XL’ 3724.1 3724.1 3724.1 3734.1 3734.1 3734.1 3734.1 3725.8 3727.9 3727.9 3949.9 4485.9 5220.0 6073.7 7007.5 8000.0 9037.8 10,111.4 1L213.7 14,061.4 16997.0 19,986.l 23,009.l 26,054.6

for Pr2Te40,,

.

-I x 8” 6788.0 6788.0 6788.0 6788.0 6788.0 6788.1 6788.6 6789.8 6792.4 6797.2 7059.9 7710.8 8584.8 9567.1 10602.7 11666.8 12,748.g 13.843.9 14,950.2 17,758.5 20,618.l 23,518.6 26,450.9 29408.3

3. Castro A., Enjalbert R., Lloyd D., Rasines I. and Galy J., J. Solid Stare Chem. 85, 100 (1990). E., Lemaitre-Bhtise M. and 4. Cascales C., Antic-Fidancev Percher P., J. Alloys Camp. 180, 11 I (1992). E., Lemaitre-Blaise M. and 5 Cascales C., Antic-Fidancev Percher P., J. Phys. Condens. Matter 4, 2721 (1992). 6. Mulay L. N., Magnetic Susceptibility, p. 1782. Wiley, New York (1963). 7. Van Vleck J. V.,‘J. appl. Phys. 39, 365 (1968). 8. Caro P., Derouet J., Beaury L. and Soulie E., J. Chem. Phys. 70, 2542 (1975). 9. Caro P., Derouet J., Beaury L., Teste de Sagey G., Chaminade J. P., Aride J. and Pouchard M. J. Chem. Phys. 74, 2698 (1981). 10. Beaury L. and Caro P., J. Phys. France 51,471 (1990). and Puri S. P.,.J. Phys. C7, 2077 (1974); 11. Vishwamittar Phvs. Rev. B9, 4673 (1974). j. Magn. Magn. Mat. 58, 61 12. Care P. and Porcher‘P., (1986). E., Lemaitre-Blaise M., 13. Saez-Puche R., Antic-Fidancev Percher P., Cascales C. and Rasines I., J. Less Common Met. 148, 369 (1989). 14. Teste de Sagey G., Percher P., Garon G. and Caro P., Rare Earth in Modern Science and Technology (Edited by J. G. McCarthy and J. J. Rhyne). Plenum, New York (1982). programs REEL and IMAGE 15. Percher P., Computer for simulation of d” and f’ configuration involving real and complex crystal field parameters. (Unpublished, 1989.) 16. Guo M. D., Aldred A. T. and Chan S. K., J. Phys. Chem. Solids 48, 229 (1987). C., Percher P., Saez-Puche P., to be 17. Cascales published. C.. Ph.D. Thesis, Universitt de Paris18. Levcuras-Coulon Suh, Orsay (1984). 19. Touborg P., Nevald R. and Johansson T., Phys. Rev. B 17, 4454 (1978).