Tailoring magnetic properties of metallic thin films with quantum well states and external electric fields

Thickness dependence of magnetic anisotropy energy (MAE) and spin polarization in Fe and Co multilayers on a Pt(001) substrate are investigated with ab initio techniques. As the thickness of the thin films is increased, an oscillatory behavior of the MAE of the systems is observed. For Fe multilayers, this even results in the periodic switching of the easy axis from out of plane to in plane. Capping the multilayers with Pt, in most cases, leads to a strong enhancement of the MAE. Our calculations give clear evidence that such oscillatory behavior of MAE can be attributed to spin-polarized quantum well states (QWS) existing in thicker multilayers. The spin polarization of the QWS is also shown to have a profound thickness dependence. Finally, we show that both MAE and spin polarization of the QWS are sensitive to external electric field and can be tailored therewith.

Figure 1

Magnetic anisotropy energy (circles) in meV, for ${\mathrm{Fe}}_N/$Pt(001) multilayers as a function of the Fe thickness for 1 $\le$ $N$ $\le$ 9, $N$ being the number of Fe layers, is shown. A positive (negative) sign in MAE indicates an out-of-plane (in-plane) axis of magnetization (easy axis), respectively. Thickness dependence of the orbital moment anisotropy (OMA) of the multilayers (rectangles) in ${\mu }_{\mathrm{B}}$ is also presented.

Figure 2

Majority (minority) density of states (DOS) (solid lines) for ${\mathrm{Fe}}_N/$Pt(001) with 3 $\le$ $N$ $\le$ 8, close to the $\Gamma$ is plotted. The dotted lines represent the contribution from both the $d_{xz}$ and $d_{yz}$ orbitals and the projection on $d_{x^2-y^2}$ orbital is assigned by the dotted-dashed line. The triangle and rectangle arrows guide the shift in DOS as the Fe-film thickness is increased.

Figure 3

Magnetic anisotropy energy (MAE) in meV for Pt$/{\mathrm{Fe}}_N/$Pt(001) multilayers as a function of the Fe thickness, 1 $\le$ $N$ $\le$ 9, where $N$ is the number of Fe layers plotted. A positive (negative) sign in MAE stands for a positive (negative) magnetization axis, respectively. The orbital magnetic moment difference versus the thickness of the film is also shown.

Figure 4

The average spin polarization of QWS, close to the $E$${}_f$ in ${\mathrm{Fe}}_N/$Pt(001) (rectangles) and Pt$/{\mathrm{Fe}}_N/$Pt(001) (circles) as a function of Fe thickness is drawn. The SP is averaged from the value of SP at $E_f+$ 0.1 eV, $E_f$ and $E_f-$ 0.1 eV.

Figure 5

Magnetic anisotropy energy (circles) of (a) ${\mathrm{Co}}_N/$Pt(001) and (b) $\text{Pt}/{\mathrm{Co}}_N/$Pt(001) multilayers as a function of the Co thickness for 1 $\le N\le$ 9 is shown, where $N$ is assigned for the number of Co layers. A positive (negative) sign in MAE indicates an out-of plane (in-plane) easy axis, respectively. Thickness dependence of the orbital moment anisotropy (OMA) of the multilayers (rectangles) in ${\mu }_{\mathrm{B}}$ is also presented.

Figure 6

Majority and minority DOS of Pt-capped Co multilayer on Pt(001), close to the $\Gamma$ point, are plotted. The DOS are plotted for Co multilayers in the range $3\le N\le 8$. The dashed, dashed-dotted, and dotted lines represent the contribution from $d_{xz\left(yz\right)}$, $d_{z^2}$, and $d_{x^2-y^2}$ orbitals, respectively. The triangle arrows guide the shift in the DOS.

Figure 7

The average spin polarization of QWS, close to the Fermi energy, in ${\mathrm{Co}}_N/$Pt(001) (rectangles) and Pt$/{\mathrm{Co}}_N/$Pt(001) (circles) as a function of Co thickness is drawn. The SP is averaged from the value of SP at $E_f+$ 0.1 eV, $E_f$ and $E_f-$ 0.1 eV.

Figure 8

(a) The MAE as function of external electric field for Pt$/{\mathrm{Fe}}_4/$Pt(001) supercell. (b) The rate of change of the MAE ($\Delta$MAE), in percents per V/Å, as a result of an external electric field normalized by the MAE of the neutral system, for a different number of Fe layers of Pt$/{\mathrm{Fe}}_N/$Pt(001) system. The $\Delta$MAE is evaluated for $E_{+}=0.4$ and $E_{-}=-0.4$ [see Eq. (2)].

Figure 9

The Kohn-Sham eigenenergies close to the $\Gamma$ point for which the $s+p$, $d_{xz}$, and $d_{x^2-y^2}$ orbitals of four layers of Fe [Pt$/{\mathrm{Fe}}_4/$Pt(001)] have high contribution. The energy of the electronic levels (relative to the Fermi energy) is presented for an electric field of 0.4 V/Å (dashed lines) and $-0.4$ V/Å (full lines), and two $k$ points, $\Gamma$ and $\Gamma +\delta$ points, have been considered ($\delta =0.03$ $\AA {}^{-1}$).