Ferroelectric-driven tunable magnetism in ultrathin platinum films

Electric control of magnetism in magnetoelectric (ME) multiferroics is expected to have a significant impact on a wide range of technological applications. Here, we predict the modulation of magnetism in ultrathin platinum films due to the ferroelectric polarization of the ${\mathrm{BaTiO}}_3$ substrate, which along with biaxial strain changes the density of states at the Fermi energy. We demonstrate that both the magnitude and direction of the magnetization depend strongly on the polarization direction and/or strain. This leads to an unprecedented ME effect involving a giant change of magnetocrystalline anisotropy under polarization switching due to the large spin-orbit coupling of Pt. These findings pave the way of an alternative strategy for the design of nonvolatile and ultralow power spintronics and magnetic memory storage devices.

Figure 1

(a) Atomic structures of the (001) 3Pt/BTO bilayer. The top (bottom) panel shows the interface in which the direction of polarization (gray arrow) $P_{\uparrow }$ ($P_{\downarrow }$) is pointing towards (away from) the Pt layer. (b) Average magnetic moment per atom of the 3 and 5 ML freestanding Pt films as a function of in-plane lattice constant. The orange dashed vertical lines denote the experimental lattice constant of bulk BTO (3.992 Å) and Pt (3.920 Å), respectively.

Figure 2

Layer-resolved magnetic spin moments of the Pt atoms in (a) 3Pt/BTO and (c) 5Pt/BTO for $P_{\downarrow }$ (single-hatched bar) and $P_{\uparrow }$ (double-hatched bar) polarizations, and for $a_{\parallel }=3.920$ (blue bars) and 3.992 Å (red bars), respectively. The subscripts I, C, and S refer to interface, central, and surface Pt layers, respectively. (b) Variation of the layer-resolved Pt spin moments in the 3Pt/BTO heterostructure with $P_{\downarrow }$, $P_{\uparrow }$ and no polarization, $P_0$. The gray bars show the total spin moment of the 3ML Pt film. (d) Non-spin-polarized layer (Pt)-resolved density of states at the Fermi energy $\left[N\left(E_F\right)\right]$ versus $a_{\parallel }$ for the freestanding 3 ML Pt (black squares) and for the 3Pt/BTO bilayer (triangles) for $P_{\uparrow }$ ($P_{\downarrow }$) polarization indicated with the up (down) triangles. The vertical lines denote the experimental lattice constant of bulk BTO (3.992 Å) and Pt (3.920 Å), respectively.

Figure 3

MCA energy as a function of Fermi level position ($\mu -E_F$) for the Pt/BTO bilayers with $a_{\parallel }=$ (a) 3.920 and (b) 3.992 Å. Blue and green curves denote the MCA with up and down polarization, respectively. Black arrows show the shift of chemical potential, $\mathrm{\Delta }$, upon polarization switching.

Figure 4

Energy- and k-resolved distribution of the minority-spin bands of the surface Pt-derived $d_{yz}$, $d_{xz}$, and $d_{x^2-y^2}$ states along the symmetry directions of the 2D BZ for $P_{\uparrow }$ and $P_{\downarrow }$ and for $a_{\parallel }=$ (a) 3.920 and (b) 3.992 Å, respectively. The Fermi level is set at zero energy.