Figure 1

(a) Crystal structure of ${\mathrm{G}\mathrm{a}\mathrm{F}\mathrm{e}\mathrm{O}}_3$. Black, gray, and white balls indicate iron, gallium, and oxygen ions, respectively. Orthorhombic unit cell with the lattice constants $a=8.72$, $b=9.37$, and $c=5.07\AA$, and the space group $Pc{2}_{1}n$ is shown by black lines [8, 9]. (b) Temperature dependence of magnetization curves. The magnetic field is applied along the $c$ (50 and 150 K) and $a$ axes (50 K).Reuse & Permissions

Figure 2

(a) Experimental configuration for the measurement of the Kerr rotation of SH light in a ${\mathrm{G}\mathrm{a}\mathrm{F}\mathrm{e}\mathrm{O}}_3$ crystal. (b) Square root of SH intensity $\sqrt{I(2\omega )}$ in $S_{\mathrm{i}\mathrm{n}}{S}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ (solid circles) and $S_{\mathrm{i}\mathrm{n}}{P}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ (open circles) configurations as a function of temperature. A solid line represents the magnetization in a magnetic field of 0.35 T applied parallel to the $c$ axis (magnetic easy axis). A dotted line is merely the guide for the eyes. (c) Analyzer-angle dependence of SH intensity at 100 K, 180 K ($T<T_C$), and 250 K ($T>T_C$). Analyzer angles $\theta$ of $0°$ and $90°$ stand for $p$- and $s$-polarized SH light, respectively. Solid and open circles indicate the SH intensity for $+z$ and $-z$ directions of the magnetic field, respectively.Reuse & Permissions

Figure 3

(a) Topographic image of the $ac$ surface of the crystal as taken by the SH light in the nonmagnetic configuration, i.e., $P_{\mathrm{i}\mathrm{n}}\mathrm{\text{−}}{P}_{\mathrm{o}\mathrm{u}\mathrm{t}}$. Magnetic domains aligned along the $c$ axis were observed by reflected SH intensity in (b) $S_{\mathrm{i}\mathrm{n}}(S+P{)}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ and (c) $S_{\mathrm{i}\mathrm{n}}(S-P{)}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ configurations. With the former (latter) configuration, SHG intensity from domains which are magnetized along the $-z$ ($+z$) direction is much larger than from $+z$ ($-z$) magnetized domains. (d) Composition of images (b) and (c) which are colored blue and red to show magnetic domains with the magnetization direction of $-z$ and $+z$, respectively. In external magnetic fields of (e) $-0.05\mathrm{T}$ and (f) $+0.05\mathrm{T}$ along the $c$ axis, the multidomain structure disappeared and the magnetization is aligned uniformly over the whole part of the crystal.Reuse & Permissions

Figure 4

Upper panel: energy levels of ${\mathrm{F}\mathrm{e}}^{3+}$ ions in free space and in an ${\mathrm{O}}_h$ octahedral crystal field. Middle panel: MSH and OPA processes. The observed (calculated) level energies are shown in units of eV. (See the text.) Lower panel: spectrum of MSHG (magnetization-induced $S_{\mathrm{i}\mathrm{n}}{S}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ component) on the ${\mathrm{G}\mathrm{a}\mathrm{F}\mathrm{e}\mathrm{O}}_3$ $ac$ surface at 10 K (solid line) and 220 K (dotted line) and the OPA optical density of the $40\mathrm{\text{−}}\mu \mathrm{m}$-thick crystal at 10 K (dash-dotted line). The SH spectrum is plotted for two-photon energy, i.e., photon energy of SH light.Reuse & Permissions