Field-Induced Magnetic Circular X-Ray Dichroism in Paramagnetic Solids: A New Magneto-Optical Effect

It is demonstrated that for paramagnetic solids an external magnetic field—in analogy to the magneto-optical Kerr effect in the visible regime of light—gives rise to a magnetic circular dichroism in x-ray absorption (MCXD). A detailed description of this new field-induced magneto-optical phenomenon is given. In particular it is shown that the resulting dichroic spectra may be used to deduce the spin and orbital susceptibility in a component resolved way by making use of a modified form of the MCXD sum rules.

Figure 1

Absorption coefficient ${\mu }_{M_{2,3}}$ and induced MCXD spectrum $\Delta {\mu }_{M_{2,3}}$ for the $M_{2,3}$ edges of Rh in fcc-Rh. An external field of 10 T was assumed for the calculation of $\Delta {\mu }_{M_{2,3}}$.

Figure 2

Derivation of the partial susceptibilities ${\chi }_{ss}$, ${\chi }_{os}$, and ${\chi }_{oo}$ with respect to the energy for fcc-Pd as obtained from direct linear response calculations. The dashed lines give their spectroscopic counterparts $d{\tilde{\chi }}_{ss}/dE$, $d{\tilde{\chi }}_{os}/dE$, and $d{\tilde{\chi }}_{oo}/dE$, respectively, that have been obtained by application of the sum rules [Eqs. (5, 6)] in their differential form.

Figure 3

Results of an application of the sum rules [Eqs. (5, 6)] for Pt in ${\mathrm{A}\mathrm{g}}_x{\mathrm{P}\mathrm{t}}_{1-x}$. The upper and lower panels give the spin and orbital susceptibility, ${\chi }_{\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}}^{\mathrm{P}\mathrm{t}}$ and ${\chi }_{\mathrm{o}\mathrm{r}\mathrm{b}}^{\mathrm{P}\mathrm{t}}$, respectively, as obtained from direct linear response calculations (full symbols) and the field-induced MCXD for the $M_{2,3}$ spectra (open symbols). The triangles in the upper panel represent results obtained ignoring the Stoner exchange enhancement of ${\chi }_{\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}}$.