Enhanced perpendicular magnetocrystalline anisotropy energy in an artificial magnetic material with bulk spin-momentum coupling

We systematically investigate the perpendicular magnetocrystalline anisotropy (MCA) in $\mathrm{Co}-\mathrm{Pt}/\mathrm{Pd}$-based multilayers. Our magnetic measurement data show that the asymmetric Co/Pd/Pt multilayer has a significantly larger perpendicular magnetic anisotropy (PMA) energy compared to the symmetric Co/Pt and Co/Pd multilayer samples. We further support this experiment by first-principles calculations on ${\mathrm{CoPt}}_2, {\mathrm{CoPd}}_2$, and CoPtPd, which are composite bulk materials that consist of three atomic layers in a unit cell, Pt/Co/Pt, Pd/Co/Pd, and Pt/Co/Pd, respectively. By estimating the contribution of bulk spin-momentum coupling to the MCA energy, we show that the CoPtPd multilayer with symmetry breaking has a significantly larger PMA energy than the other multilayers that are otherwise similar but lack symmetry breaking. This observation thus provides evidence of the PMA enhancement due to the structural inversion symmetry breaking and highlights the asymmetric CoPtPd as an artificial magnetic material with bulk spin-momentum coupling, which opens a pathway toward the design of materials with strong PMA.

Figure 1

(a) $M-H$ loops of ${[\mathrm{Co}\left(0.2\mathrm{nm}\right)/\mathrm{Pt}\left(0.2\mathrm{nm}\right)]}_{10}, {[\mathrm{Co}\left(0.2\mathrm{nm}\right)/\mathrm{Pd}\left(0.2\mathrm{nm}\right)]}_{10}$, and ${[\mathrm{Co}\left(0.2\mathrm{nm}\right)/\mathrm{Pd}\left(0.2\mathrm{nm}\right)/\mathrm{Pt}\left(0.2\mathrm{nm}\right)]}_{10}$ films. The op and ip denote $M-H$ loops with out-of-plane and in-plane magnetic fields, respectively. (b) High- resolution transmission electron microscopy (TEM) image for the full stack of the ${[\mathrm{Co}\left(0.2\mathrm{nm}\right)/\mathrm{Pd}\left(0.2\mathrm{nm}\right)/\mathrm{Pt}\left(0.2\mathrm{nm}\right)]}_{10}$ film.

Figure 2

Band structure along the $k_x=k_z=0$, i.e. along the $\left(0,-\frac{1}{2},0\right)\to \left(0,\frac{1}{2},0\right)$ path, (a) and (b) without spin-orbit coupling, and (c) and (d) with SOC, and (e) and (f) the two dimensional $(k_x,k_y)$ in-plane Fermi surface, i.e., at $k_z=0$, together with the contour map of $k$-dependent MCA energy within this surface. Left and right panels show the plots for ${\mathrm{CoPt}}_2$ and CoPtPd, respectively. The $m_{+x}$ and $m_{-x}$ labels indicate the magnetization along, respectively, the $+x$ and $-x$ directions. Likewise, $E\left(m_{\alpha }\right)$ indicates the energy of $\alpha$ direction-imposed magnetization.