Cubic magneto-optic Kerr effect in Co(111) thin films

Abstract

The magneto-optic Kerr effect (MOKE) is often applied as a tool for the magnetic characterization of thin films. Here, the change in polarization upon reflection from the magnetized sample is mainly regarded as being linearly proportional to the magnetization $\mathbf{M}$ (LinMOKE). MOKE contributions of second order in $\mathbf{M}$, also known as quadratic MOKE (QMOKE), which are proportional to $\mathbf{M}^2$, have also been studied in the past and used in thin film characterization. Recently, we reported on a systematic investigation of third-order MOKE contributions, named cubic MOKE (CMOKE) in Ni(111) thin films. This CMOKE manifests itself as an anisotropic contribution to the MOKE signal (with regard to the crystallographic orientation) measured in longitudinal or transversal configuration in full magnetic saturation. While LinMOKE (odd in $\mathbf{M}$) and QMOKE (even in $\mathbf{M}$) can easily be separated by methods based on magnetization parity, this no longer holds true for LinMOKE and CMOKE (odd in $\mathbf{M}$). It is therefore crucial to be aware of CMOKE contributions in order to correctly interpret MOKE data. Here, we report on the observation of CMOKE in thin film heterostructures with structurally twinned and untwinned Co(111) layers, demonstrating that a large CMOKE is not only present in Ni thin films. Additionally, we show that the observed anisotropic contributions cannot stem from LinMOKE by analyzing their dependence on the angle of incidence (AoI) of light. While the QMOKE is almost vanishing in Co(111) using light with wavelengths of 635\,nm and 406\,nm, the CMOKE contributions reach up to about 30\% of the LinMOKE contribution at an AoI of 45 degrees and become even more dominant towards normal AoI, which emphasizes the importance of higher-order MOKE effects in magneto-optic experiments.

Figures (4)

• Figure 1: (a,d) Specular XRD with insets showing the respective layer stacks, (b,e) off-specular texture maps of the CoO{002} (inner ring) and Co{002} (outer ring) diffraction peaks and (c,f) corresponding off-specular $\theta$-2$\theta$ scans for samples 1 and 2, respectively. Insets in (c,f) show the Co{002} peaks at $\alpha$=0$^\circ$,60$^\circ$ after baseline subtraction. The inset in (e) shows the experimental geometry for off-specular measurements.
• Figure 2: (a,e) MOKE curves at sample positions of $\alpha$=210$^\circ$ and $\alpha$=270$^\circ$, (b,f) coercive field and (c,g) remanent magnetization depending on $\alpha$, (d,h) MOKE in magnetic saturation at $B_0$=230 mT depending on $\alpha$ for samples 1 and 2, respectively.
• Figure 3: Results of the eight-directional measurements for (a) sample 1 and (b) sample 2 including fits of the numerical simulations. The finite offset of $\Phi _{M_T^3}$ cannot be simulated. Therefore, the fits of $\Phi _{M_T^3}$ and $\Phi _{M_T^2-M_L^2}$ overlap for sample 2. The inset shows the experimental geometry. Magnetic field directions $\mu = 90^\circ /270^\circ$ are parallel to the plane of incidence.
• Figure 4: Measurement of sample 1 (circles) and simulations (solid black lines) of (a) the angular dependence of $\Phi _{M_L,M_L^3}$ with varying AoI, (b) offsets and (c) amplitudes of $\Phi _{M_L,M_L^3}$ and $\Phi _{M_T^3}$ depending on the AoI.