Magnetism and exchange in the layered transition metal thiophosphates and their solid solutions

Abstract

It was mentioned in the Introductory Chapter that changes in the magnetic behaviour of the intercalation compounds of the transition metal thiophosphates depend crucially on the magnetism of the host lattice. Hence an adequate description of magnetism in the host lattice is a prerequisite to understanding magnetism in the intercalated compounds. The anisotropic magnetic susceptibilities of the layered antiferromagnet NiPS? (T? = 155 K) were measured between 30 K – 675 K. The susceptibilities showed a weak XY anisotropy in the high?temperature paramagnetic phase with ?? > ??, where ?? is the susceptibility when the external field is along the trigonal axis (? to the layer). The system may be described by the effective spin Hamiltonian H = ????? J?? S?·S?, with the quadratic single?ion anisotropy term introducing anisotropy in an otherwise isotropic situation. The exchange J and single?ion anisotropy parameter D were determined from an analysis of the high?temperature anisotropic susceptibility data for two different models: (i) the Oguchi Model in which a pair of spins chosen at random is treated exactly while their interactions with the rest of the crystal are approximated by a mean field, and (ii) the Correlated Effective Field (CEF) approximation developed by Lines which reduces the many?body problem to a single?particle, non?interacting ensemble form by the introduction of static temperature?dependent correlation parameters evaluated by forcing consistency with the fluctuation?dissipation theorem. Analytical expressions of the anisotropic susceptibilities were derived for the Oguchi model. It was found that the CEF approximation was superior to the Oguchi model in being able to account for short?range antiferromagnetic correlations and hence gave a better description of the susceptibility in NiPS?. The exchange and crystal?field parameters for the CEF approximation were: J/k = ?58.0 K; D/k = 16.1 K; g? = 2.05 and g? = 2.13. The anisotropic magnetic susceptibility of the two?dimensional orbitally unquenched Ising antiferromagnet FePS? was analysed in the CEF approximation. The formalism introduces spin correlations in the simplest possible manner while also accounting for the excited states of the orbitally unquenched transition?metal ion, the energies of which are comparable to exchange and thermal energies. In FePS? the degeneracy of the ?T? state is completely lifted by the combination of trigonal distortion of the FeSe octahedra, spin?orbit coupling and Zeeman splitting. In the calculation of the susceptibilities in the CEF approximation, the entire 15?level structure of the ?T? state was retained. Good agreement with experiment was obtained for ?/k = 215.5 K; ??/k = 166.5 K; Jnn/k = 27.7 K; Jnnn/k = ?2.3 K. Using these values, the CEF predicted a T? = 123 K for FePS? which was identical to the observed value. The accuracy of the CEF approximation was also ascertained by comparison with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS?, for which high?temperature series expansion data is available. This comparison established the effectiveness of the special?k point scheme in providing Brillouin?zone averages in the computation of susceptibilities in the CEF approximation. The results show that the CEF approximation provides a simple and elegant way to analyse the susceptibilities of exchange?coupled systems in which the individual ion possesses a complicated level structure. It successfully accounts for both the complex energy?level structure arising from crystal field, spin?orbit coupling, etc., as well as spin correlations that manifest at temperatures much higher than T? in these low?dimensional systems. Since the bonding nature of the magnetic ion in MPS? is essentially ionic, it was expected that homogeneous solid solutions of the transition?metal thiophosphates would form over the entire concentration range. It was therefore worthwhile to investigate the mixed?metal thiophosphates of the formula M???M??PS? (M, M? = Mn, Fe, Ni) to synthesise interesting host lattices for future intercalation studies. Before tackling these complicated multi?component systems in which M and M? have different energy?level structures, the simpler diamagnetically diluted zinc analogues of the MPS? compounds of the formula Zn???M?PS? were investigated. The powder susceptibilities of Zn???M?PS? were measured over the entire concentration range between 30 K – 300 K. Transitions were observed below the percolation threshold (x = 0.7) for nearest?neighbour interactions on a honeycomb lattice. The plots of the molar Curie constant C? vs. concentration x showed a linear variation. Crystals for some compositions were obtained and their anisotropic magnetic susceptibilities reported between 30 K – 300 K. An adequate description of magnetism in the diluted phases was obtained in the framework of CEF for the high?temperature regime. No variable parameters were used; the microscopic parameters were maintained as in the pure compounds, and x was determined by AAS. The calculated susceptibilities compared favourably with experimental data, especially below the percolation threshold. The calculated anisotropic susceptibilities were also in good agreement with experimental values for the crystals. The decrease in anisotropy for low concentrations of the magnetic ion agreed extremely well with those obtained from CEF. The preparation and characterisation of the M???M??PS? (M, M? = Mn, Ni, Fe) phases were successfully carried out. Magnetic susceptibility measurements in the temperature range 30 K – 350 K were performed. Crystals for some compositions were obtained. The CEF was further developed to account for magnetism in the mixed?metal thiophosphates. The microscopic parameters considered in the calculations were the same as for the pure phases; x was obtained from AAS measurements. The only floating variable was J????. It was found to be 2.0 K for J???Fe throughout the range of x. Neutron diffraction has determined the magnetic ordering in NiPS? and FePS? to be the same. Based on the susceptibility fits and on T? vs. x trends, a single type of magnetic ordering was predicted throughout the concentration range for Fe???Ni?PS?. In Mn???Ni?PS?, good fits were obtained for the high?temperature paramagnetic regime for J???Mn = ?26 K. Again, a single magnetic ordering was proposed. For Mn???Fe?PS?, good fits were obtained for JFe?Mn = +0.7 K (iron?rich phases) and JFe?Mn = ?2.0 K (manganese?rich phases). Neutron diffraction shows that the extreme members of this series (FePS? and MnPS?) have different magnetic orderings. The predicted T? vs. x trends reveal a tetracritical point in the composition range 0.7 > x > 0.3. The phase diagram obtained was attributed to competing magnetic orderings. The present work has established a theoretical base for future intercalation studies in the mixed transition?metal thiophosphates.