Optical properties and magnetochromism in multiferroic ${\text{BiFeO}}_3$

In order to investigate spin-charge coupling in multiferroic oxides, we measured the optical properties of ${\text{BiFeO}}_3$. Although the direct 300 K charge gap is observed at 2.67 eV, absorption onset actually occurs at much lower energy with ${\text{Fe}}^{3+}$ excitations at 1.41 and 1.90 eV. Temperature and magnetic-field-induced spectral changes reveal complex interactions between on-site crystal-field and magnetic excitations in the form of magnon sidebands. We employ the sensitivity of these magnon sidebands to map out the magnetic-field-temperature phase diagram which demonstrates optical evidence for spin spiral quenching above 20 T and suggests a spin domain reorientation near 10 T.

Figure 1

(Color online) 300 K absorption coefficient $\alpha \left(E\right)$ as a function of energy. Inset: closeup view of $\alpha \left(E\right)$ below 2.2 eV. Although this data was collected from a series of samples, $\alpha \left(E\right)$ is an optical constant of the material.

Figure 2

(Color online) (a) Variable temperature absorption spectra in the range of the ${\text{Fe}}^{3+}$ $d-d$ excitations. (b) Oscillator strength (1–1.62 eV) as a function of temperature. Analysis of the 1.9 eV peak shows the same trends, but reliability is reduced due to overlap with the nearby charge transfer edge.

Figure 3

(Color online) (a) $\Delta \alpha \left(E,H\right)$ for different magnetic fields at 4 K ($\vec{H}\perp {\left(012\right)}_{\text{hex}}$ face). Dips and peaks highlight magnon sideband displacements with field. Thin lines show proposed magnon peaks in $\alpha \left(E\right)$ that shift to generate the observed shape of $\Delta \alpha \left(E,H\right)$. Similar results are observed at higher temperatures. (b) Schematic illustration of magnon sidebands. The exciton and magnon are created together to satisfy selection rules. (c) Integrated absorption intensity (see text). (d) Simulated total intensity change $I_{\Delta \alpha }^{\text{sim}}\left(H\right)\propto -\sum {\vec{S}}_i\cdot {\vec{S}}_j$ and displacement $I_{\left|\Delta \alpha \right|}^{\text{sim}}\left(H\right)\propto \sum {\vec{S}}_i\cdot \vec{H}$ of magnon sidebands. (e) $\Delta \alpha$ as a function of magnetic field for $D_1$ at various temperatures. (f) $\Delta \alpha$ as a function of magnetic field for $P_1$ at various temperatures.

Figure 4

(Color online) $H-T$ phase diagram of ${\text{BiFeO}}_3$ constructed using $\Delta \alpha \left(E,H\right)$ data like that in Figs. 3e, 3f.