Theory of Magnetic—Moment-Jump Phase Transition with Application to UP

The simple Heisenberg exchange Hamiltonian $H_{12}=J{\overrightarrow{\mathrm{S}}}_1·{\overrightarrow{\mathrm{S}}}_2$ may not represent the interaction between magnetic ions in a crystal well enough to permit a prediction of even the qualitative features of the magnetic properties. When the electric charge densities of the magnetic ions are nonspherical because of crystal field and spin-orbit interactions, the magnetic ions are coupled by electrostatic multipole interactions (EMI). When the temperature is such that there are states of different multipole moments being thermally populated, EMI can have a qualitative effect on the temperature dependence of the magnetic properties. In this paper, we show that in the molecular-field approximation, the Hamiltonian consisting of only the crystal-field potential and the Heisenberg exchange energy cannot account for the moment-jump phase transition observed in antiferromagnetic uranium monophosphide (UP). We develop a molecular-field theory including the quadrupole-quadrupole interaction term of the EMI and show how this theory can predict the moment-jump phase transition. Finally, we describe a calculation based on this theory and obtain the low-temperature behavior of the sublattice magnetization including the moment jump observed in UP.