Spin Wave Measurements over the Full Brillouin Zone of Multiferroic ${\mathrm{BiFeO}}_3$

Using the inelastic neutron scattering technique, we measured the spin wave dispersion over the entire Brillouin zone of room temperature multiferroic ${\mathrm{BiFeO}}_3$ single crystals with magnetic excitations extending to as high as 72.5 meV. The full spin waves can be explained by a simple Heisenberg Hamiltonian with a nearest-neighbor exchange interaction ($J=4.38\mathrm{meV}$), a next-nearest-neighbor exchange interaction ($J^{\prime }=0.15\mathrm{meV}$), and a Dzyaloshinskii-Moriya-like term ($D=0.107\mathrm{meV}$). This simple Hamiltonian determined, for the first time, for ${\mathrm{BiFeO}}_3$ provides a fundamental ingredient for understanding the novel magnetic properties of ${\mathrm{BiFeO}}_3$.

Figure 1

(a) The crystal structure of the $R3c$ space group with the magnetic unit cell (dashed line) for a simple $G$-type structure. The horizontal arrow denoted by $\mathbf{D}$ indicates the direction of the Dzyaloshinskii-Moriya-like vector. (b) A photo of ten crystals coaligned within 3° of one another, and (c) Brillouin zone of the hexagonal symmetry with the thick lines indicating some of the high symmetry directions, along which the data are presented and discussed in the text.

Figure 2

(a) Theoretical spin waves calculated with three different Hamiltonians as discussed in the text. The two inserts are for the blown-up figures of the low energy parts to illustrate the effects of the Dzyaloshinskii-Moriya-like term ($D$) on the spin waves along the $\Gamma \mathrm{\text{−}}M$ and $\Gamma \mathrm{\text{−}}A$ directions, respectively. (b) Experimental spin waves measured at AMATERAS beamline (circles) and MERLIN beamline (contour plot) together with the theoretical spin waves (solid line) calculated with $J=4.38$ and $J^{\prime }=0.15\mathrm{meV}$: the dashed line is for the theoretical spin waves calculated with the Hamiltonian having the NN interaction alone. Inserts are for the momentum cut at the $M$ and $A$ points.

Figure 3

A contour plot of the spin waves is shown along the [0 0 $l$] direction ($L\mathrm{\text{−}}M\mathrm{\text{−}}L$) with lines for theoretical curves as discussed in the text.