Full magnetoelectric response of Cr${}_2$O${}_3$ from first principles

The linear magnetoelectric response of Cr${}_2$O${}_3$ at zero temperature is calculated from first principles by tracking the change in magnetization under a macroscopic electric field. Both the spin and the orbital contributions to the induced magnetization are computed, and in each case the response is decomposed into lattice and electronic parts. We find that the transverse response is dominated by the spin-lattice and spin-electronic contributions, whose calculated values are consistent with static and optical magnetoelectric measurements. In the case of the longitudinal response, orbital contributions dominate over spin contributions, but the net calculated longitudinal response remains much smaller than the experimentally measured one at low temperatures. We also discuss the absolute sign of the magnetoelectric coupling in the two time-reversed magnetic domains of Cr${}_2$O${}_3$.

Figure 1

Rhombohedral primitive cell of Cr${}_2$O${}_3$. The arrows indicate the orientations of the magnetic moments on the Cr ions (the spins on the ions point opposite to the arrows). The center of the cell is a center of inversion symmetry coupled with time reversal.