Phase Transitions and Spin Waves in Cerium

Abstract

In the Gamma-Alpha phase transition in Cerium, the magnetic properties change from a temperature-dependent Curie-Weiss susceptibility in the high temperature gamma phase to a temperature-independent paramagnetic susceptibility in the low temperature alpha phase. Taking into account the crystal-field split Hamiltonian, the energy eigenvalues and eigenfunctions are calculated for the doublet and the quartet ground states which are then used to determine the Kondo temperature for different crystal field splittings. The susceptibility and B-T phase diagrams are obtained for both the ground states and it is concluded that the doublet ground state is in better agreement with the experimental results. The P-T phase diagram is obtained using the Anderson model and the Non-Crossing Approximation. This numerical method determines the free energy for a given hybridization and subsequently the susceptibility, specific heat and the Fermi-liquid temperature. Using these, the P-V phase diagram is first obtained and then the P-T phase diagram derived from it using Maxwell's equal area construction. CePdSb is one of the few ternary compounds which exhibit Kondo lattice behavior along with a ferromagnetic ground state. The competitions between the RKKY interaction and the Kondo interactions are consistent with expectations based on the Doniach phase diagram. The susceptibility in the high temperature regime calculated using the linear response theory concurs well with the experimental results. At low temperatures, the exchange interaction dominates the magnetic behavior of the system. Taking into consideration the single-ion anisotropy and the Heisenberg interaction, the spin-wave dispersion spectrum is obtained using the Holstein-Primakoff transformation and renormalized Stevens coefficients. The spin-spin correlation function is obtained and found to agree very well with the inelastic neutron scattering data.