Electric field control and effect of Pd capping on magnetocrystalline anisotropy in FePd thin films: A first-principles study

Using ab initio electronic structure calculations, we have investigated the effect of an electric field and of a heavy-metal cap of Pd on the magnetocrystalline anisotropy (MCA) of FePd ultrathin film. Analysis of the energy- and $k$-resolved distribution of the orbital character of the minority-spin band reveals that the perpendicular MCA of the uncapped film mainly arises from the spin-orbit coupling (SOC) between unoccupied Fe $d_{xy}$ and occupied Fe $d_{x^2-y^2}$ states. On the other hand, the SOC between the Pd- and Fe-derived $d$ states yields negative contributions to the MCA. We find that the sensitivity of the surface anisotropy energy to the applied electric field is 18 fJ/(Vm) and is due to changes in the occupation of the surface Fe atoms $d_{x^2-y^2}$ and ($d_{xz},d_{yz}$) orbitals. We demonstrate that the thickness of the Pd cap has a dramatic effect on the MCA and can even switch the magnetization from out-of- to in-plane orientation. The underlying origin is the change of the position and orbital character of the spin-polarized quantum well states induced in the Pd cap by varying its thickness. These results have important implications for exploiting heavy metals with large spin-orbit coupling (Ru, Pd, Ta, Pt, or Au) as contacts with ferromagnetic thin films to tailor the magnetic switching of spintronic devices by tuning the cap thickness.

Figure 1

Schematic models for the calculation of the MCA of FePd thin films (a) with and (b) without Pd capping. The arrow indicates the positive direction of the E-field.

Figure 2

(a) Total magnetic moment on the surface Fe in the 9-ML-thick FePd film vs the E-field, with the moment along the [100] and [001] direction, respectively. (b) Difference in orbital moment of the surface Fe between the [001] and [100] orientation (left scale) and the MCA of the thin film (right scale) as a function of the E-field.

Figure 3

The $k$-resolved MCA along the high-symmetry directions in the two-dimensional Brillouin zone.

Figure 4

Energy- and $k$-resolved distribution of the orbital character of the minority-spin band of the 9 ML FePd film for the Fe $d_{xy}$ (upper panel) and $d_{x^2-y^2}$ (lower panel) states. The color denotes the amplitude of the $d$-orbital character. The horizontal line denotes the Fermi level.

Figure 5

Energy-level diagram of the minority-spin states of the 9 ML FePd film at the $\overline{\Gamma }$ and $\overline{M}$ points relative to the Fermi energy (horizontal dashed line). The red (blue) horizontal lines denote the Fe- (Pd-)derived bands and the green line denotes the Fe-$d_{z^2}$/Pd-$d_{z^2}$ hybridized bands, where the thickness of the lines is proportional to the specific $d$-orbital character. The solid (dashed) vertical arrows indicate the SOC between various occupied and unoccupied states which give positive (negative) contribution to the MCA.

Figure 6

Difference in $k$-resolved MCA induced by the E-field of (a) $-0.5$ V/Å and (b) 0.5 V/Å relative to the zero-field case for the 9 ML FePd film. The arrows indicate the MCA peak that is strongly affected by the E-field reversal.

Figure 7

Energy- and $k$-resolved distribution of the orbital character of the minority-spin band of the 9 ML FePd film for the surface Fe $d_{xy}$ (upper panel) and $d_{x^2-y^2}$ (lower panel), respectively. The color denotes the amplitude of the $d$-orbital character.

Figure 8

(a), (b) Surface charge densities of $d_{x^2-y^2}$ and $(d_{xz},d_{yz})$ states, respectively, under zero field within an energy range of 0.6 eV below the Fermi level in the $\overline{\Gamma M}$ region. (c), (d) Charge density differences induced by an E-field of 0.5 V/Å. The unit of contour values is $e/{\AA }^3$.

Figure 9

(a) Difference between the total orbital moment along the [001] and [100] directions and (b) the MCA of the 3-ML-FePd/$n$-ML-Pd system as a function of the Pd cap thickness. The horizontal dashed line in (b) denotes the MCA value of the uncapped FePd film.

Figure 10

Total Pd $d$-derived DOS projected on and averaged over all MLs in the Pd cap for different Pd cap thickness. The arrows indicate the spin-polarized QWS near the Fermi level.

Figure 11

Energy- and $k$-resolved distribution of the Pd-cap-derived $d_{xz}$ (top panel) and $d_{yz}$ (bottom panel) orbitals of the minority-spin band along $\overline{\Gamma X}$ for the 3 ML FePd film capped with 3 ML (left panels) and 4 ML (right panels) of Pd, respectively. The various bands near the Fermi level are labeled by numbers.

Figure 12

Energy- and $k$-resolved distribution of the Pd-cap-derived $d_{xz}$, $d_{yz}$, $d_{z^2}$, and $d_{x^2-y^2}$ orbitals along the $\overline{MX}$ direction, with 3-ML-thick FePd films capped by 9 ML Pd.