Resonant x-ray magnetoelectric effect in a centrosymmetric spinel oxide

We show clear evidence that the local magnetoelectric (ME) effect arising from the noncentrosymmetric magnetic sites can be element-specifically detected by using the resonant x-ray ME scattering (XMES), even in systems where the space-inversion $\left(I\right)$ or the time-reversal $\left(R\right)$ symmetry is globally restored. At the (222) reflection in a centrosymmetric spinel oxide ${\text{MnCr}}_2{\text{O}}_4$, where the conventional Mn-resonant x-ray magnetic scattering is forbidden, we have observed a resonant magnetic signal at the intra-atomic $1s\text{−}3d$ absorption edge of Mn ions on tetrahedral sites, which is uniquely attributed to the XMES. This unique x-ray scattering is caused by a transfer of the spectral weight between the electric dipole $\left(E1\right)$ and electric quadrupole $\left(E2\right)$ transitions through the spin-orbit coupling. The possibility of the important application utilizing the ME scattering technique is discussed as well.

Figure 1

(Color online) [(a) and (b)] ME effect of a magnetic ion surrounded by a tetrahedral oxygen ligand. An electric dipole $\left(p\right)$ can be induced by an application of an external magnetic field $\left(H\right)$ via the ME effect. The direction of $p$ becomes reversed under (c) the space-inversion $\left(I\right)$ or (d) the time-reversal $\left(R\right)$ operations.

Figure 2

(Color online) (a) The crystal structure of spinel ${\text{MnCr}}_2{\text{O}}_4$ and the electronic configurations of the ${\text{Mn}}^{2+}$ and the ${\text{Cr}}^{3+}$ ions, which occupy the tetrahedral $A$ sites $\left(T_d\right)$ and the octahedral $B$ sites $\left(O_h\right)$, respectively. (b) $A$ sites in the unit cell of spinel structure. (c) The alignments of the $A$ sites along the [111] direction. The signs of the ME scattering at the (0,0,0) and $\left(\frac{1}{4},\frac{1}{4},\frac{1}{4}\right)$ positions are opposite.

Figure 3

(Color online) (a) X-ray absorption spectrum at room temperature; (b) x-ray scattering spectrum; and (c) magnetic field modulated x-ray scattering spectrum $\Delta I_s/I_s$ at 20 K at the (222) reflection for $E^{\omega }\parallel H\parallel \left[11\overline{2}\right]$ in the vicinity of the $\text{Mn}K$-absorption edge in ${\text{MnCr}}_2{\text{O}}_4$. The solid line in (c) is merely the guide for the eyes. In (c), the spectrum of the second-harmonic $\left(2f\right)$ component of the magnetic modulation is also shown by open circles. The experimental configuration of the magnetic field modulated x-ray scattering is shown in the inset of (c).

Figure 4

(Color online) (a) Temperature dependence of the resonant (peak-to-peak) and nonresonant (background) intensities in $\Delta I_s/I_s$ at the (222) reflection around the $\text{Mn}K$-absorption edge. The solid and dotted lines show the magnetization in a magnetic field of 800 Oe applied along the $\left[11\overline{2}\right]$ direction. (b) The optical ME effect arising from a ${\text{Mn}}^{2+}$ ion in the noncentrosymmetric $A$ site in the configuration of $E^{\omega }\parallel H\parallel \left[11\overline{2}\right]$. (c) Microscopic origin of the XMES in ${\text{MnCr}}_2{\text{O}}_4$ (see text).