Polar magneto-optical Kerr effect for low-symmetric ferromagnets

The polar magneto-optical Kerr effect (MOKE) for low-symmetric ferromagnetic crystals is investigated theoretically based on first-principles calculations of optical conductivities and a transfer matrix approach for the electrodynamics part of the problem. Exact average magneto-optical properties of polycrystals are described, taking into account realistic models for the distribution of domain orientations. It is shown that for low-symmetric ferromagnetic single crystals the MOKE is determined by an interplay of crystallographic birefringence and magnetic effects. Calculations for a single crystal and bicrystal of hcp $⟨11\overline{2}0⟩$ Co and for a polycrystal of $\mathrm{Cr}{\mathrm{O}}_2$ are performed, with results being in good agreement with experimental data.

Figure 1

Crystal structures of (a) $⟨11\overline{2}0⟩$ ferromagnetic hcp Co and (b) ⟨010⟩ ferromagnetic $\mathrm{Cr}{\mathrm{O}}_2$. Coordinate systems are as used in magneto-optics calculations.

Figure 2

Calculated optical conductivity tensor of hcp Co with magnetization direction $⟨11\overline{2}0⟩$. Quantities are shown in a range where only direct interband tranzition are important.

Figure 3

Calculated optical response of $⟨11\overline{2}0⟩$ hcp Co in polar MOKE geometry. The polarization vector is parallel to the crystallographic $x$ axis at zero angle. Curves shifted to higher values just below $5\mathrm{eV}$ correspond to positive angles.

Figure 4

Calculated optical response of bicrystalline hcp $⟨11\overline{2}0⟩$ Co. At 0° the polarization vector is along a main crystal axis of one of the domains.

Figure 5

Optical response of hcp $⟨11\overline{2}0⟩$ Co in polar MOKE geometry. Theoretical data are for special cases of the direction of the polarization vector. Experimental data are due to Weller et al. Results for hcp ⟨0001⟩ are shown for comparison.

Figure 6

Calculated optical conductivity tensor of ⟨010⟩ $\mathrm{Cr}{\mathrm{O}}_2$.

Figure 7

Calculated optical response of $a$-axis-textured sixfold symmetrically ordered $\mathrm{Cr}{\mathrm{O}}_2$. The solid line shows the rotation $\psi$ of the polarization ellipse. The dashed line shows its ellipticity $\chi$.