PHYSICAL REVIEW B VOLUME 22, NUMBER 1 1 JULY 19&0 Magnetic properties in some holmium compounds M. Saha and D. Ghosh Magnetisrn Department, Indian Association for the Cultivation of'Science, Calcutta 700 032, India (Received 26 June 1979) In continuation of our previous studies on the magnetic susceptibilities in Tb(OH)3 and Dy(OH)3, this work reports the results of a study of the isomorphous Ho(OH)3 crystalline com- plex. Using the crystal-field parameters (CFP) reported from earlier optical studies, calculations were made for the principal magnetic susceptibilities K»» and K&, their anisotropies (K»» — K&), ' and their average values K, g values, the crystal-field splitting of the ground Is term, and the Schottky specific heat C, for Ho(OH)3, Ho(ES)3, and HoC13 between 300 and 80 K. The study showed that the anisotropy (K»» — K&) was much more sensitive than K or g values to the values of the CFP. The effect of variation of CFP on (K»» — K&) was studied, and interesting limiting values for some of the CFP were obtained; this is applicable to any crystalline com- plexes of Ho + in a C31, field. I. INTRODUCTION We reported earlier the results of our studies on magnetic susceptibilities in single crystals of Tb(OH) 3 (Ref. I) and Dy(OH)3. The principal susceptibilities K»» and Kz were obtained from the simultaneous measurements of magnetic anisotropies (K~~ — Kq) 1 and the average susceptibilities K = 3 (K~~+2Kq) in the temperature range 300 — 80 K. Using these exper- imental results, we estimated the corresponding crystal-field parameters (CFP) by varying them indi- vidually to get the best fit in this temperature range. We observed that the values of CFP thus obtained differed from those reported from earlier optical studies, the deviation being prominent in Dy(OH)3. Such a type of discrepancy between the CFP values as obtained from the optical and magnetic data was also reported in Dy(ES)3. It is to be mentioned that for these rare-earth complexes the spectra are very complicated, especially at higher energies. Conse- quently, assignments of the levels and the determina- tion of the CFP from such studies are not always reli- able. Furthermore, it is found that in many instances the crystal-field splitting is markedly improved if dif- ferent sets of CFP are used for different multiplets. We have noted' that the magnetic anisotropy, in particular, and its thermal variations are very sensi- tive to the values of CFP chosen. Consequently, this property can be studied to determine accurately the CFP for the ground term. As a continuation of pre- vious work, " we have calculated (K~~ — Kq), K, g values, and the Schottky specific heat C, of Ho(OH)3. Since experimental data on the magnetic anisotropies at high temperatures are not available for this crystal, we studied here the effect of variations of CFP on (K~~ — Kq) in the temperature range 300-80 K. II. THEORY The ground multiplet of the Ho3+ ion (4f'o) is 518, and the first excited term is about 5030 cm ' higher. ' The point-group symmetry at the rare- earth-ion site of the Ho'+ complexes considered is C3t, . A C3I, crystalline field splits the ground term into singlets and non-Kramers doublets. In the static-crystal-field model the Hamiltonian has the familiar form Hc 82 V2 +84 V4 +86 V6 +8 V The matrix elements of the crystal-field operators under different J manifolds in the intermediate cou- pling scheme have been worked out and tabulated by Dieke. " The resulting matrices were diagonalized to obtain the related eigenvalues and eigenfunctions. The energy-level schemes for the three Ho'+ com- pounds are shown in Table I (p, is the crystal quan- tum number). The magnetic-field matrix elements were then cal- culated using the Hamiltonian H„=gopH J (2) where go=1.241. ' The gram ionic or molar suscepti- CFP are also reported from optical spectra on Ho'+ in LaC13 (Refs. 5 and 6) and Ho(ES)3. ' We have calculated the principal magnetic susceptibilities, g values, and specific heat C, for these complexes also. Similar type of calculations have been reported9 for several rare-earth hydroxides; however, the effect of CFP variation has not been considered therein. Since the CFP in these three Ho'+ compounds differ wide- ly, it was expected that the magnetic and thermal properties would differ. 22 308 O1980 The American Physical Society