Phys Chem Minerals (1990) 17:157-160 PHYSICS [ GHEMISTRY ]MIHKRALS 9 Springer-Verlag 1990 Ligand Field Analysis of the Magnetic Susceptibilities and Miissbauer Spectra of Ilvaite, a Mixed Valence Iron Mineral T. Kundu and D. Ghosh Solid State Physics Department, Indian Association for the Cultivation of Science, Calcutta-700032, India Received May 7, 1989 Abstract, The thermal characteristics of magnetic susceptibi- lities and their anisotropies of single crystal of ilvaite, a mixed valence iron sorosilicate, have been analysed in the light of Ligand Field (LF) theory using a minimum number of approximations. The electronic energy pattern and the corresponding wavefunctions were obtained from best fit- ting of these experimental results with the corresponding theoretical values. These results were next used to calculate the thermal characteristic of the quadrupole splitting A EQ in ilvaite. It was found that the values of A E e are reasonably close to those reported from M6ssbauer studies. The present analysis suggest appreciable molecular overlap between the orbits of the ligand electrons and those of the Fe 2+ atoms, the overlap being prominent along the chain direction as also observed from electrical conductivity measurements. Burns 1970) and making a minimum number of approxima- tions. It may be mentioned that in LF theory, the basic 3 d orbitals of the Crystal Field theory are modified to include overlap of the electron charge clouds of the ligands with those of the central ion as in Molecular Orbital (MO) theory. LF theory is therefore capable of describing bond polarities from total covalency to total ionic by considering appro- priate reduction factors, which occur during calculation of matrix elements for the orbital angular momentum opera- tors and spin angular momentum operators. Thus the ex- pressions for the susceptibilities KII and Kl and the quadru- polar splitting of the Fe z+ are derived in terms of the LF parameters, which are to be determined from best fitting of the experimental results. Introduction llvaite is a silicate mineral, containing appreciable iron in two different oxidation states, viz., ferrous and ferric, and as a result accurate determination of the magnetic character of the mineral becomes particularly interesting. The present work is a continuation of our earlier work (Ghosh et al. 1987) on the study of the thermal characteristic of the mag- netic susceptibilities and their anisotropies in different crys- tallographic planes of a single crystal of ilvaite from Elba (Italy) in the temperature range of 400-21 K. The molar susceptibility Krr in the ab plane was found to rotate on cooling below 343 + 1 K till 90 + 2 K, the crystal being para- magnetic at these temperatures, and the symmetry of the magnetic ellipsoid was found to remain unchanged. The sign of magnetic anisotropy AK=(KII-K• was found to be negative which essentially suggested a singlet ground state 5.4 for the Fe 2+ ions in agreement with previous M6ssbauer studies (Coey et al. 1984). Even though magnetic susceptibility and M6ssbauer ex- periments on ilvaite have been reported earlier (Yamanaka and Tak6uchi 1979; Beran and Bittner 1979; Coey et al. 1984; Amthauer and Rossman 1984), yet no attempt has been made so far to correlate these results from a theoretical point of view. The present study was therefore undertaken to analyse the observed results of M6ssbauer spectra (MS) and magnetic susceptibilities, both being localised phenom- ena, using the Ligand Field (LF) theory (Van Vleck 1935; Theoretical Theoretical expressions for molar magnetic susceptibilities, Kpl and Kz, of Fe 2+ have been worked out on the basis of Abragam and Pryce's method (1951). From earlier studies on MS and magnetic susceptibilities, a pseudotetragonal symmetry was detected at the Fe 2 + sites in ilvaite. Hence the appropriate effective Hamiltonian Haf, operating on the orbital ground triplet state S T2g for 3 d 6 Fe 2+ ion, is defined as: Heff =A (1-12)-~rr ~ lzsz--2ze'(l + s_ +l_ s +)/2, where A is the tetragonal splitting of the ground 5 T2g state, 20 and 21 are the spin-orbit coupling coefficients of Fe 2+ in crystals rendered anisotropic by anisotropic overlap of ligand s and p charge clouds with 3 d electrons of Fe 2§ and Land6 factors e and c( are related with admixture co- efficients. For Fe 2+, ct~c(~l (Abragam and Pryce 1951). Solving for the secular matrices the nine energy eigenvalues (El) and the corresponding eigenfunctions (~ were derived. On application of the magnetic perturbation on these states, the expressions for K H and K• (emu/mole/atom) were ob- tained using the Van Vleck's (1932) formula: Kj - g~ N f12 Z ~ [(E! ~3)2/kT - 2 E~ 2)] e x p ( - E!~ T). i The expressions for susceptibilities KIj and K• are thus functions of A, ~ott , ~o• ktt and k• where q)[[ andq~• are.