Terahertz Spectroscopy of Spin Waves in Multiferroic ${\mathrm{BiFeO}}_3$ in High Magnetic Fields

We have studied the magnetic field dependence of far-infrared active magnetic modes in a single ferroelectric domain ${\mathrm{BiFeO}}_3$ crystal at low temperature. The modes soften close to the critical field of 18.8 T along the [001] (pseudocubic) axis, where the cycloidal structure changes to the homogeneous canted antiferromagnetic state and a new strong mode with linear field dependence appears that persists at least up to 31 T. A microscopic model that includes two Dzyaloshinskii-Moriya interactions and easy-axis anisotropy describes closely both the zero-field spectroscopic modes as well as their splitting and evolution in a magnetic field. The good agreement of theory with experiment suggests that the proposed model provides the foundation for future technological applications of this multiferroic material.

Figure 1

Pseudocubic unit cell of ${\mathrm{BiFeO}}_3$ showing the positions of Fe ions, the ferroelectric polarization $\mathbf{P}$, three equivalent directions of the cycloidal ordering vector ${\mathbf{q}}_k$, the applied static magnetic field ${\mathbf{B}}_0\parallel [001]$, and the wave vector of incident light $\mathbf{k}$ together with the electric field ($\mathbf{e}$) component of light in two orthogonal polarizations that were used in the experiment. $J_1$ and $J_2$ are the nearest- and next-nearest-neighbor exchange interactions.

Figure 2

Absorbance spectra of spin wave modes in zero field in $\mathbf{e}\parallel [110]$ polarization (a) and in $\mathbf{e}\parallel [1\overline{1}0]$ polarization (b). Solid curves ${\alpha }_F$ were measured after applying the high field ${\mathbf{B}}_0\ge 21\mathrm{T}$. Dotted curves are initial absorbance spectra ${\alpha }_I$ of the zero field cooled sample.

Figure 3

Magnetic field dependence of spin wave modes in the terahertz absorption spectrum of ${\mathrm{BiFeO}}_3$ at low temperature. The areas of triangles and circles are proportional to the absorption line areas. The vertical dashed line at $B_c=18.8\mathrm{T}$ marks the metamagnetic transition. Green dashed lines are the fit of our data and ESR data [38] (squares) above 19 T to a model from Ref. [38]. Blue solid lines are calculated modes of cycloid $q_1$. Dotted blue lines are calculated modes of cycloids $q_2$ and $q_3$, shown only below 6 T where corresponding excitations are observed in measured spectra; the lowest energy mode is shown also for higher fields since there is a matching excitation in ESR data. The theoretically predicted metamagnetic transition is at 20 T for cycloid ${\mathbf{q}}_1$ and at 16.5 T for cycloids ${\mathbf{q}}_2$ and ${\mathbf{q}}_3$.