Temperature-Dependent Interplay of Dzyaloshinskii-Moriya Interaction and Single-Ion Anisotropy in Multiferroic ${\mathrm{BiFeO}}_3$

Low-energy magnon excitations in multiferroic ${\mathrm{BiFeO}}_3$ 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 fit 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 ${\mathrm{BiFeO}}_3$.

Figure 1

(a)–(c) Experimental $\mathrm{Im}[\chi (\mathbf{q},\omega )]$ along the [$h$, 0, 0] direction at different temperatures and Brillouin zone centers with $k_f=1.55{\AA }^{-1}$. (d) Energy scans at three different $\mathrm{\Gamma }$ points with $k_f=1.55{\AA }^{-1}$. (e) Higher-resolution $q\text{−}E$ map at $\mathbf{q}=(1,0,-1)$ and $T=270\mathrm{K}$ with $k_f=1.2{\AA }^{-1}$. (f) $E$ scans along dashed lines in (e) with $k_f=1.2{\AA }^{-1}$. In (a) and (e), $q$ scans are shown for three representative low energies.

Figure 2

(a) Calculated magnon dispersion curves and simulated $\mathrm{Im}[\chi (\mathbf{q},\omega )]$ convoluted with the instrumental resolution function along [$h$, 0, 0] centered on $\mathbf{q}=(1,0,-1)$ for different model parameters. (b) Schematic view of the $q\text{−}E$ plane along [$h$, 0, 0] and resolution ellipsoid (orange). (c) Simulated $E$ scan at (1, 0, $-1$) is shown for five different models.

Figure 3

Simulation results for different (a) $J/J_0$, (b) $D_u$, and (c) $K$. Best fit results with $k_f=1.55{\AA }^{-1}$ at (d) 16 K, (e) 50 K, and (f) with $k_f=1.2{\AA }^{-1}$ at 270 K.

Figure 4

(a) Temperature dependence of $\mathrm{Im}[\chi (\mathbf{q},\omega )]$ at $\mathbf{q}=(1,0,-1)$ with best fit curves. (b) Temperature dependence of $J\tilde{S}$, $D_u\tilde{S}$, $K\tilde{S}$, and a period of the magnetic cycloid with the arrows representing typical error bars. We estimated the temperature dependence of the moment $\tilde{S}$ (dashed line) and the electric polarization ($P$) using the structural data taken from Ref. [20] while the open symbol of $\lambda$ is taken from Ref. [19].