Anisotropic x-ray magnetic linear dichroism and spectromicroscopy of interfacial Co/NiO(001)

Abstract

Photoemission electron microscopy (PEEM) with linearly polarized x rays is used to determine the orientation of antiferromagnetic domains by monitoring the relative peak intensities at the $3d$ transition metal ${L}_{2}$ absorption edge. In such an analysis it is necessary to take into account the orientations of the x-ray polarization $\mathbf{E\ifmmode \hat{}\else \^{}\fi{}}$ and magnetization $\mathbf{H\ifmmode \hat{}\else \^{}\fi{}}$ with respect to the crystalline axes. We address this problem by presenting a general expression of the angular dependence for both x-ray absorption (XA) spectroscopy and x-ray magnetic linear dichroism (XMLD) for arbitrary directions of $\mathbf{E\ifmmode \hat{}\else \^{}\fi{}}$ and $\mathbf{H\ifmmode \hat{}\else \^{}\fi{}}$ in the (001) cubic plane. In cubic symmetry the angular-dependent XMLD is a linear combination of two spectra with different photon energy dependencies. As a result the intensity maxima of the XA and XMLD are no longer found for $\mathbf{E\ifmmode \hat{}\else \^{}\fi{}}$ parallel to $\mathbf{H\ifmmode \hat{}\else \^{}\fi{}}$ and their directions will vary with photon energy. When $\mathbf{E\ifmmode \hat{}\else \^{}\fi{}}$ or $\mathbf{H\ifmmode \hat{}\else \^{}\fi{}}$ is along a high-symmetry axis there is only one spectrum. The angular-dependent XMLD can be separated into an isotropic part, which is symmetric around $\mathbf{H\ifmmode \hat{}\else \^{}\fi{}}$, and an anisotropic part, which depends on the orientation of the crystal axes. The anisotropic part has maximal intensity when $\mathbf{E\ifmmode \hat{}\else \^{}\fi{}}$ and $\mathbf{H\ifmmode \hat{}\else \^{}\fi{}}$ have equal but opposite angles with respect to the [100] direction. The Ni${}^{2+}$ ${L}_{2}$ edge has the peculiarity that the isotropic part vanishes, which has the interesting consequence that the maximum in the XMLD intensity is obtained not only for $\mathbf{E\ifmmode \hat{}\else \^{}\fi{}}\ensuremath{\parallel}\mathbf{H\ifmmode \hat{}\else \^{}\fi{}}\ensuremath{\parallel}$ [100] but also for ($\mathbf{E\ifmmode \hat{}\else \^{}\fi{}}\ensuremath{\parallel}$ [110], $\mathbf{H\ifmmode \hat{}\else \^{}\fi{}}\ensuremath{\parallel}$ [1$\mathrm{1\ifmmode \bar{}\else \={}\fi{}}$0]). We apply the angular-dependent theory to determine the spin orientation near the Co/NiO(100) interface. The PEEM images show that the ferromagnetic Co spins and antiferromagnetic NiO spins are aligned perpendicular to each other. By rotating the sample with respect to the linear x-ray polarization we furthermore find that the perpendicular coupling with the ferromagnetic Co layer at the interface causes a canting of the antiferromagnetic Ni moments. This shows that taking into account the angular dependence of the XMLD in the detailed analysis of PEEM images can lead to an accurate retrieval of the spin axes of the antiferromagnetic domains.