We report on the spin waves and crystal field excitations in single crystal ${\mathrm{LiFePO}}_4$ 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 ${\mathrm{Fe}}^{2+}$ 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 $\mathrm{Li}M{\mathrm{PO}}_4$ ($M=\mathrm{Mn}$, Co, and Ni), we are able to obtain reasonable predictions for the moment sizes and transition temperatures.

• Received 31 August 2016
• Revised 6 February 2017
• Corrected 30 March 2017

DOI:https://doi.org/10.1103/PhysRevB.95.104409