First-principles calculations of steady-state voltage-controlled magnetism: Application to x-ray absorption spectroscopy experiments

Recent x-ray absorption experiments have demonstrated the possibility to accurately monitor the magnetism of metallic heterostructures controlled via a time-independent perturbation caused, for example, by a static electric field. Using a first-principles, nonequilibrium Green's function scheme, we show how the measured dichroic signal for the corresponding steady-state situation can be related to the underlying electronic structure and its response to the external stimulus. The suggested approach works from the infinitesimal limit of linear response to the regime of strong electric field effects, which is realized in present experimental high-sensitivity investigations.

Figure 1

Sketch of the layered system considered: A Co/Pd layer system is connected to the left and to the right to Cu leads. The Co and Pd layers, together with a few neighboring Cu layers, form the central so-called interaction zone.

Figure 2

(a) Layer- ($n$-) resolved profile of the spin magnetic moment $m_{\mathrm{\Phi }}^n$ (in ${\mu }_B$) for the investigated Co/Pd bilayer system for three applied voltages: $\mathrm{\Phi }=-0.34$ (red bars), 0 (black bars), and $+0.34$ V (blue bars). (b) Electric-field-induced contribution to the profile $\mathrm{\Delta }{m}_{\mathrm{\Phi }}^n=m_{\mathrm{\Phi }}^n-m_0^n$ (solid bars) for the voltage drop $\mathrm{\Phi }=+0.34$ V with $\mathrm{\Delta }{m}_{\mathrm{\Phi }}^{dn}$ its part due to the $d$ electrons (shaded bars).

Figure 3

Layer-$n$-resolved Edelstein coefficient $p_{\mathrm{zz}}^n$ (solid bars) together with its part $p_{\mathrm{zz}}^{d,n}$ due to the $d$ electrons (shaded bars). In addition, the layer-resolved charge conductivity ${\sigma }_{\mathrm{zz}}^n$ (orange circles) is shown.

Figure 4

Electric-field-induced change in the spin magnetic moment of the $d$ states of Pd, as a function of the applied voltage $\mathrm{\Phi }$, averaged over the Pd layers: $\langle \mathrm{\Delta }{m}_{\mathrm{\Phi }}^d\rangle$ calculated directly from the lesser Green's function $G_{\mathrm{\Phi }}^{<}\left(E\right)$ via Eq. (2) (open diamonds) and $\langle \mathrm{\Delta }{m}_{\mathrm{\Phi }}^{\mathrm{XMCD}d}\rangle$ deduced from the XMCD spectra at the $L_{2,3}$ edges via the modified sum rules [see Eq. (4)] (solid circles).