Giant Modification of the Magnetocrystalline Anisotropy in Transition-Metal Monolayers by an External Electric Field

Controlling and designing quantum magnetic properties by an external electric field is a key challenge in modern magnetic physics. Here, from first principles, the effects of an external electric field on the magnetocrystalline anisotropy (MCA) in ferromagnetic transition-metal monolayers are demonstrated which show that the MCA in an Fe(001) monolayer [but not in Co(001) and Ni(001) monolayers] can be controlled by the electric field through a change in band structure, in which small components of the $p$ orbitals near the Fermi level, which are coupled to the $d$ states by the electric field, play a key role. This prediction obtained opens a way to control the MCA by the electric field and invites experiments.

Figure 1

Calculated MCA energy, $E_{\mathrm{MCA}}$, and the anisotropy of orbital moments, $\Delta m^{\mathrm{orbit}}=m_{001}\mathrm{\text{−}}{m}_{100}$, as a function of the external electric field, $F_{\mathrm{ext}}$, for the Fe(001) monolayer.

Figure 2

Calculated MCA energy, $E_{\mathrm{MCA}}$, as a function of the number of valence electrons, $N$, for the Fe(001) and Co(001) monolayers. Dashed and solid lines represent results for an external electric field of zero and $1\mathrm{eV}/\AA$ values, respectively. The point at $N=8$ (9) corresponds to the number of valence electrons in the present Fe (Co) system.

Figure 3

(a) Calculated minority-spin band structure along high-symmetry directions for an Fe(001) monolayer in an external electric field of zero (dotted lines) and $1\mathrm{eV}/\AA$ (solid lines). The reference energy ($E=0$) places the Fermi energy, $E_F$. Arrows indicate band gaps induced by the electric field. Bands 1, 3, and 4 stand for $d_{z^2}$, $d_{x^2\mathrm{\text{−}}{y}^2}$, and $d_{xy}$ states, respectively, and bands 5 and $5^{*}$ are weakly bonding and antibonding $d_{xz,yz}$ states. (b) MCA energy contribution, $E_{\mathrm{MCA}}(\mathbf{k})$ [19] in zero field (dotted line) and at $1\mathrm{eV}/\AA$ (solid line). (c) Results when the number of valence electrons, $N$, is set to 8.4 within the rigid band.

Figure 4

Calculated band structure in zero field along high-symmetry directions for an Fe(001) monolayer. Open circles and triangles represent bands having small components (possessing more than 1% in the Fe muffin-tin sphere) of $p_z$ and $p_{x,y}$ orbitals, respectively.

Figure 5

Calculated minority-spin band structure and MCA energy contribution, $E_{\mathrm{MCA}}(\mathbf{k})$ [19], along high-symmetry directions for a Co(001) monolayer in an external electric field of zero (dotted lines) and $1\mathrm{eV}/\AA$(solid lines). Notation, the same as in Fig. 3.