Temperature-Dependent Interplay of Dzyaloshinskii-Moriya Interaction and   Single-Ion Anisotropy in Multiferroic BiFeO$_3$
  Low-energy magnon excitations in multiferroic BiFeO$_3$ were measured in detail as a function of temperature around several Brillouin zone centers by inelastic neutron scattering experiments on single crystals. Unique features around 1 meV are directly associated with the interplay of the Dzyaloshinskii-Moriya interaction and a small single-ion anisotropy. The temperature dependence of these and the exchange interactions were determined by fitting the measured magnon dispersion with spin-wave calculations. The spectra best fits an easy-axis type magnetic anisotropy and the deduced exchange and anisotropy parameters enable us to determine the anharmonicity of the magnetic cycloid. We then draw a direct connection between the changes in the parameters of spin Hamiltonian with temperature and the physical properties and structural deformations of BiFeO$_3$. 
Jaehong Jeong, Manh Duc Le, P. Bourges, S. Petit, S. Furukawa, Shin-Ae   Kim, Seongsu Lee, S-W. Cheong, and Je-Geun Park
cond-mat.mtrl-sci cond-mat.str-el