Quadratic optical responses in a chiral magnet

Chiral magnets, which break both spatial inversion and time reversal symmetries, carry a potential for quadratic optical responses. Despite the possibility of enhanced and controlled responses through the magnetic degree of freedom, the systematic understanding remains yet to be developed. We here study nonlinear optical responses in a prototypical chiral magnetic state with a one-dimensional conical order by using the second-order response theory. We show that the photovoltaic effect and the second harmonic generation are induced by asymmetric modulation of the electronic band structure under the conical magnetic order, and the coefficients, including the sign, change drastically depending on the frequency of incident lights, the external magnetic field, and the strength of spin-charge coupling. We find that both effects can be enormously large compared to those in the conventional nonmagnetic materials. Our results would pave the way for next-generation optical electronic devices, such as unconventional solar cells and optical sensors, based on chiral magnets.

Figure 1

Schematic pictures of (a) a chiral helimagnetic state (CHM) at $m=0$, (b) a chiral conical magnetic state (CCM) at $0<m<1$, and (c) a forced ferromagnetic state (FFM) at $m=1$, where $m$ is the magnetization parallel to the $z$ axis. The blue and green wavy arrows represent incoming linearly polarized lights oscillating in the $z$ direction with frequency ${\omega }_1$ and ${\omega }_2$, respectively. The cyan arrow represents a nonlinear electric current generated in the CCM with frequency ${\omega }_1+{\omega }_2$ along the $z$ axis.

Figure 2

(a) Energy dispersions of itinerant electrons, ${\varepsilon }_{\pm }$, and (b) the coefficient in Eq. (8), $|J_{\pm }^z{|}^2(J_{--}^z-J_{++}^z)$, as functions of $k^{\prime }$ for several values of $m$. The data are calculated for the strongly coupled case with $J=8.0$, $t_2=-0.1$, $D=0.12$, and $n=0.7$. (c) and (d) Contour plots of the photovoltaic coefficient ${\sigma }_{\mathrm{PVE}}^{zzz}$ in Eq. (6) and the intensity of the SHG $|{\sigma }_{\mathrm{SHG}}^{zzz}|$ in Eq. (7), respectively, as functions of $\omega$ and $m$. The lower panels show the $\omega$ dependences for several $m$.

Figure 3

Similar plots to Fig. 2 for the weakly coupled case with $J=0.2$, $t_2=-0.2$, $D=0.02$, and $n=0.3$.