Anisotropic carrier dynamics in a laser-excited ${\mathrm{Fe}}_1/({\mathrm{MgO})}_3\left(001\right)$ heterostructure from real-time time-dependent density functional theory

The interaction of a femtosecond optical pulse with a ${\mathrm{Fe}}_1/({\mathrm{MgO})}_3$(001) metal/oxide heterostructure is investigated using time-dependent density functional theory calculations in the real-time domain. We systematically study electronic excitations as a function of laser frequency, peak power density, and polarization direction. While spin-orbit coupling is found to result in only a small time-dependent reduction of magnetization (less than 10%), we find a marked anisotropy in the response to in-plane and out-of-plane polarized light, which changes its character qualitatively depending on the excitation energy: the Fe layer is efficiently addressed at low frequencies by in-plane polarized light, whereas for frequencies higher than the MgO band gap, we find a particularly strong response of the central MgO layer for cross-plane polarized light. For laser excitations between the charge transfer gap and the MgO band gap, the interface plays the most important role, as it mediates concerted transitions from the valence band of MgO into the $3d$ states of Fe closely above the Fermi level and from the Fe states below the Fermi level into the conduction band of MgO. As these transitions can occur simultaneously without altering the charge balance of the layers, they could potentially lead to an efficient transfer of excited carriers into the MgO bulk, where the corresponding electron and hole states can be separated by an energy which is significantly larger than the photon energy.

Figure 1

Layer-resolved electronic density of states indicating the main orbital character of the states in the vicinity of the gap. The colored areas (orange for $\hslash \omega =2.25\mathrm{eV}$, blue for $\hslash \omega =4.5\mathrm{eV}$, green for $\hslash \omega =7.75\mathrm{eV}$) mark the maximum energy range in which direct resonant excitations can be expected (i.e., from the occupied states at $-\hslash \omega$ to the Fermi level and from the Fermi level up to the unoccupied states at $\hslash \omega$). The horizontal arrow in the lowest panel denotes the position of the MgO band gap, obtained from the comparison of the bulk LDA band structure with the bands originating from the center layer of MgO [42]. Inset: Side view of the minimal heterostructure ${\mathrm{Fe}}_1$/(MgO)${}_3$(001). The oscillating arrows illustrate the two orientations of the propagation direction of the applied laser pulses and the corresponding polarization of the electric field with respect to the layer stacking.

Figure 2

Time-dependent vector potentials of laser pulses with different frequencies of $\hslash \omega$ = 2.25 eV, $\hslash \omega$ = 4.5 eV, and $\hslash \omega$ = 7.75 eV (left) and Fourier transform of the time-dependent electric field for these laser pulses (right).

Figure 3

Change of the total magnetic moment in the simulation cell as a function of time for in-plane and out-of-plane laser pulses with different laser frequencies.

Figure 4

Changes in the charge distribution $\mathrm{\Delta }\rho (\mathbf{r},t)=\rho (\mathbf{r},t)-\rho (\mathbf{r},0)$ at $t=20.2\mathrm{fs}$ after illumination with an in-plane polarized laser pulse with $S_{\mathrm{peak}}\approx 5\times {10}^{12}\mathrm{W}/{\mathrm{cm}}^2$ for (a) $\hslash \omega$ = 2.25 eV, (b) $\hslash \omega$ = 4.5 eV, and (c) $\hslash \omega$ = 7.75 eV. Red/blue isosurfaces indicate regions with a depletion/accumulation of charge with an isosurface level of $\pm 2\times {10}^{-3}{e}_0/a_B^3$.

Figure 5

Time-dependent changes in the layer-resolved $\mathrm{\Delta }\mathrm{TDDOS}$ for three in-plane laser pulses with frequencies (a)–(c) $\hslash \omega$ = 2.25 eV, (d)–(f) $\hslash \omega$ = 4.5 eV, (g)–(i) $\hslash \omega$ = 7.75 eV, and a peak power density of $S_{\mathrm{peak}}\approx 5\times {10}^{12}$ W/${\mathrm{cm}}^2$. The three columns show the partial $\mathrm{\Delta }{D}_{\sigma }(E,t)$ of the Fe, the IF-MgO, and the center-MgO layers, respectively. The energy $E$ is given relative to the Fermi level. Note that the color scale differs between the columns. Purple arrows mark particular transitions and hybridizations, which are discussed in the text. The green area at the left edge of each panel shows the static ground-state partial density of states for the respective layer. For better visibility, the static DOS of the MgO layers in the center and right column is scaled by a factor 4 compared to Fe in the left column.

Figure 6

Snapshot of the evolution of the charge distribution $\mathrm{\Delta }\rho (\mathbf{r},t)$ for out-of-plane polarized pulses at $t=20.2\mathrm{fs}$ for (a) $\hslash \omega =4.5\mathrm{eV}$ and (b) $\hslash \omega =7.75\mathrm{eV}$. Same colors and isolevels as in Fig. 4. The positions of the atoms in the cell in (a) and (b) are the same as in Fig. 1 with Fe in the center. In (c), we shift the differential charge distribution shown in (b) by one half lattice vector in each direction, in order to better visualize the features at the edges of the original unit cell. As a result, O(C) is now located in the center, while Fe is placed at the edges of the cell.

Figure 7

(a) Change of the electronic charge inside the muffin-tin spheres around the ions relative to the initial state, $\mathrm{\Delta }Q\left(t\right)=Q\left(t\right)-Q\left(0\right)$, during and after the application of in-plane (ip) and out-of-plane (oop) polarized laser pulses with $\hslash \omega$ = 4.5 eV and $\hslash \omega$ = 7.75 eV. The initial charges $Q\left(0\right)$ within the muffin-tin spheres for Fe, Mg(IF), O(IF), Mg(C), and O(C) are $24.42e_0, 10.67e_0, 7.24e_0, 10.72e_0$, and $7.24e_0$, respectively. (b),(c) Fourier transform of $\mathrm{\Delta }Q\left(t\right)$ shown in (a) for $\hslash \omega$ = 4.5 eV and $\hslash \omega$ = 7.75 eV, respectively.

Figure 8

Time-dependent changes in the layer-resolved $\mathrm{\Delta }\mathrm{TDDOS}$ for out-of-plane laser pulses with frequencies (a)–(c) $\hslash \omega =4.5\mathrm{eV}$ and (d)–(f) $\hslash \omega =7.75\mathrm{eV}$ and a peak power density of $S_{\mathrm{peak}}\approx 5\times {10}^{12}$ W/${\mathrm{cm}}^2$. The three columns show the partial $\mathrm{\Delta }{D}_{\sigma }(E,t)$ for the Fe, MgO(IF), and MgO (C) layers, respectively. The energy $E$ is given relative to the Fermi level. Note that the color scale differs between the columns. Purple arrows mark particular transitions and hybridizations, which are discussed in the text. The green areas again refer to the static partial DOS, scaled as in Fig. 5.

Figure 9

Schematic illustration of the concerted excitation mechanism mediated by interface states involving two simultaneous, but independent excitations across the charge transfer gap. This leads to the accumulation of excited carriers with a small energy separation in the metallic layer and a significantly larger separation than $\hslash \omega$ in the MgO part. In this way, an efficient repopulation of carriers from valence band (red frame) to conduction band states (blue frame) is possible even for photon energies below the band gap of the insulator. The colored areas refer to the electronic bands. Green: valence and conduction bands of the (bulk) insulator; blue: $d$ states of the (bulk) metal and interface states.