Hybrid excitations due to crystal field, spin-orbit coupling, and spin waves in LiFePO₄

We report on the spinwaves and crystal field excitations in single crystal LiFePO₄ by inelastic neutron scattering over a wide range of temperatures, below and above the antiferromagnetic transition of this system. In particular, we find extra excitations below T_N = 50 K that are nearly dispersionless and are most intense around magnetic zone centers. We show that these excitations correspond to transitions between thermally occupied excited states of Fe²⁺ due to splitting of the S = 2 levels that arise from the crystal field and spin-orbit interactions. These excitations are further amplified by the highly distorted nature of the oxygen octahedron surrounding the iron atoms. Above T_N, magnetic fluctuations are observed up to at least 720 K, with an additional inelastic excitation around 4 meV, which we attribute to single-ion effects, as its intensity weakens slightly at 720 K compared to 100 K, which is consistent with the calculated cross sections using a single-ion model. Our theoretical analysis, using the MF-RPA model, provides both detailed spectra of the Fe d shell and estimates of the average ordered magnetic moment and T_N. By applying the MF-RPA model to a number of existing spin-wave results from other LiMPO₄ (M = Mn, Co, and Ni), we are able to obtain reasonable predictions for the moment sizes and transition temperatures.