Electric field control of magnons in magnetic thin films: Ab initio predictions for two-dimensional metallic heterostructures

We explore possibilities for control of magnons in two-dimensional heterostructures by an external electric field acting across a dielectric barrier. By performing ab initio calculations for a Fe monolayer and Fe bilayer, both suspended in vacuum and deposited on Cu(001), we demonstrate that external electric field can significantly modify magnon lifetimes and that these changes can be related to field-induced changes in layer-resolved Bloch spectral functions. For systems with more magnon dispersion branches, the gap between high- and low-energy eigenmodes varies with the external field. These effects are strongly influenced by the substrate. Considerable variability in how the magnon spectra are sensitive to the external electric field can be expected, depending on the substrate and on the thickness of the magnetic layer.

Figure 1

Schematic device layout. Precessing magnetic moments (red arrows) that compose a magnon mode (blue wave) are studied as a function of an external electric field acting along the stacking direction across a dielectric barrier (green region) which prevents charge transport.

Figure 2

DOS of a Fe monolayer suspended in vacuum for different values of ${\mathrm{E}}_{\text{field}}$. All the curves fall essentially on top of each other, with no discernible effects from the electric field.

Figure 3

Difference between the DOS projected on individual layers of a Fe bilayer as a function of ${\mathrm{E}}_{\text{field}}$.

Figure 4

Adiabatic magnon spectrum for the Fe bilayer suspended in vacuum with ${\mathrm{E}}_{\text{field}}=0$. The ${\omega }_2\left(\mathit{q}\right)$ solution is plotted with an artificial offset of $+10$ meV to allow visualization where energy degenerate. The color coding represents the magnitude of the corresponding complex eigenvectors, projected on the ${\mathrm{Fe}}_2$ layer.

Figure 5

Energy gap between the high- and low-energy magnon branches at $\mathit{q}=\overline{\mathrm{\Gamma }}$ for an iron bilayer suspended in vacuum (cf. Fig. 4) evaluated as a function of ${\mathrm{E}}_{\text{field}}$.

Figure 6

Spin-polarized Fe-projected DOS for a Fe monolayer on Cu(001) for different intensities and polarities of the external electric field.

Figure 7

Dependence of the magnetic moments at Fe sites on the external electric field for a Fe monolayer on Cu(001).

Figure 8

Fe-projected Bloch spectral function for a Fe monolayer on Cu(001), color coded to indicate the predominantly down-spin polarization of electronic states at the Fermi level. From top to bottom: Results for ${\mathrm{E}}_{\text{field}}=-5.2$, 0, or $+5.2$ (V/nm).

Figure 9

Adiabatic magnon spectrum of a Fe monolayer on Cu(001) for selected values of ${\mathrm{E}}_{\text{field}}=-5.2$, 0, and $+5.2$ (V/nm).

Figure 10

Top panel: Magnon spectrum for a Fe monolayer on Cu(001) for ${\mathrm{E}}_{\text{field}}=0$, depicting eigenvalues according to Eq. (2) (darker line) together with the corresponding intensity of Stoner excitations obtained by evaluating Eq. (7) (lighter shaded area, in arbitrary units). Bottom panel: Relative change of the magnon lifetime (obtained as the inverse of the Stoner intensity) with ${\mathrm{E}}_{\text{field}}$, for three choices of the $\mathit{q}$-vector indicated in the top graph by differently dashed vertical lines of matching colors.

Figure 11

Spin magnetic moment versus ${\mathrm{E}}_{\text{field}}$ for the exposed ${\mathrm{Fe}}_2$ (brown full circles, left scale) and subsurface ${\mathrm{Fe}}_1$ (blue empty circles, right scale) for an iron bilayer over Cu(001) substrate.

Figure 12

Adiabatic magnon spectrum for a Fe bilayer on Cu(001) and with ${\mathrm{E}}_{\text{field}}=0$. The color coding represents the magnitude of the corresponding complex eigenvectors, projected on the ${\mathrm{Fe}}_2$ layer (as in Fig. 4).

Figure 13

Energy gap between the high- and low-energy magnon branches at $\mathit{q}=\overline{\mathrm{\Gamma }}$ for an iron bilayer on Cu(001) (cf. Fig. 12) evaluated as a function of ${\mathrm{E}}_{\text{field}}$.

Figure 14

Inter-layer Heisenberg exchange couplings $J_{IJ}^{12}$ for a Fe bilayer on Cu(001) plotted as a function of the $|{\mathit{R}}_I-{\mathit{R}}_J|$ distance, for ${\mathrm{E}}_{\text{field}}$= $-5.2$, 0, and $+5.2$ (V/nm).