Concerted Mechanism of Carrier Dynamics in Laser‐Excited Fen/(MgO)m(001) Heterostructures from Real‐Time Time‐Dependent DFT

Using real‐time time‐dependent density functional theory (RT‐TDDFT), the electronic response of a Fen/(MgO)m(001) (n=1,3,5 and m=3,5,7) metal/insulator heterostructure to an optical excitation is calculated, considering laser frequencies below, near, and above the bandgap of the insulator and two directions of polarization. The spatial redistribution of electronic charge after illumination shows a strong dependence on the frequency and polarization direction of the laser pulse with a similar pattern for all thicknesses. The comparison of the layer‐resolved changes in occupation of the ground‐state orbitals after optical excitation obtained for Fen/(MgO)m(001) and bulk Fe reveals the origin of excited carriers in the heterostructures: In the central and interface Fe layers carriers are excited from states in the vicinity of the Fermi‐level to the conduction band of MgO. Simultaneously, excitations take place from the valence band of MgO to Fe states above the Fermi‐level. This concerted mechanism allows for an effective bidirectional relocation of excited carriers between the metallic and insulating subsystems in heterostructures with a thickness of several nanometers, providing an effective accumulation of hot carriers in the insulating layers, even at photon energies in the vicinity and below the bandgap of bulk MgO.


Introduction
The microscopic understanding of non-equilibrium states created e.g., through femtosecond laser pulses has developed into a central topic in condensed matter research.Such nonequilibrium states can be very different from the ground state and encompass the realization of transient phases, which cannot be reached by conventional equilibrium methods, [1][2][3] some as evidenced by a correlation between the time-resolved changes in tr-XAS at the O-K edge and ultrafast electron diffraction experiments sensitive to the Fe-subsystem.However, the potential mechanisms allowing for a direct transfer of hot carriers between the Fe and MgO systems remain elusive.In this context, real-time time-dependent density functional theory (RT-TDDFT) calculations can render detailed insight into the redistribution of electronic charge and changes in occupation numbers in the heterostucture after photoexcitation and thus enable a thorough understanding of the excitation processes and the transfer of carriers in metal/oxide heterostructures.Recently, this approach was used to simulate the carrier dynamics in a minimal model Fe 1 /(MgO) 3 (001) heterostructure, containing a single Fe layer and three MgO layers, excited by an ultrashort laser pulse. [24,25]he results indicate a strong dependence of the excitation on the laser frequency and the polarization direction of the electric field.While the Fe layer is most efficiently addressed for frequencies below the bandgap of bulk MgO, the main excitation shifts to the MgO part for higher frequencies and out-of-plane polarization.Moreover, hybridized states at the interface play an essential role to mediate the energy transfer from Fe to MgO and vice versa.A concerted excitation mechanism was proposed, involving two simultaneous excitations via interface states: one from occupied states of the metal to the conduction band of the insulator and simultaneously, another from the top of the valence band of MgO into Fe states above the Fermi level. [25]This interfacebased mechanism allows reaching energy levels for the hot carriers that are separated by nearly twice the photon energy.Since Fe 1 /(MgO) 3 (001) contains only a single metal layer, the question arises about the robustness of this mechanism in more realistic heterostructures with an extended number of layers of both the metal and the insulator.
Here, we focus on the role of Fe and MgO thickness on the propagation of excitations through the Fe/MgO(001) interface, induced by a laser pulse.To assess this effect, we simulate the explicit time evolution of Fe 3 /(MgO) 5 (001) and Fe 5 /(MgO) 7 (001) heterostructures using RT-TDDFT and compare the excitation pattern to the one in Fe 1 /(MgO) 3 (001), [24,25] as well as bulk Fe.We consider different laser frequencies below, around and higher than the bulk MgO bandgap and both in-and out-of-plane polarization.
The paper is structured as follows: The computational details are presented in Section 2. Section 3.1 comprises a brief discussion of the ground-state geometry and electronic structure of the Fe 3 /(MgO) 5 (001) and Fe 5 /(MgO) 7 (001) heterostructures.In Section 3.2, we discuss the absorption spectra from the random phase approximation (RPA).The results of the TDDFT calculations in the real-time domain are presented in Section 3.3, which focuses on the time evolution of the charge density redistribution, and Section 3.4, where the excitation patterns extracted from the time-dependent occupation numbers in Fe n /(MgO) m (001) heterostructures are compared to the one in bulk Fe.Finally, Section 4 summarizes the results.

Computational Details
The structural optimization of the heterostructures (lattice parameters and internal positions) was performed with the VASP plane wave code (version 5.4.4), [26,27] using the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) [28] for the exchange and correlation functional with a plane wave cutoff of 500 eV and a k-point grid of 16 × 16 × 6.The electonic structure, optical absorption spectra, and time-dependent properties were calculated with the ELK code, [29] using the previously optimized geometry.The ELK code is based on the all-electron full-potential linearized augmented-plane wave (FLAPW) method and implements timedependent DFT (TDDFT) in the real-time (RT) domain.For the exchange-correlation functional we have chosen the local (spin) density approximation, L(S)DA, in the parametrization of Perdew and Wang (PW92). [30]To model Fe 3 /(MgO) 5 (001) and Fe 5 /(MgO) 7 (001) heterostructures, we used muffin tin radii of 1.139, 1.164, and 0.855 Å for Fe, Mg, and O, respectively.To keep the numerical efforts tractable for the RT-TDDFT part, the plane wave cut-off parameter, RK max , was set to 7.This proved sufficient to obtain an electronic density of states (DOS) in good agreement with the VASP results.A 8 × 8 × 3k-mesh was used for the reciprocal space sampling, leading to a convergence of the total energy within 11 meV compared to a 22 × 22 × 10 mesh, while the magnetic moments of the Fe atoms converged within 0.016  B ∕ion and the charge within the corresponding muffintin (MT) spheres to 10 −3 e − ∕MT-sphere, which is significantly smaller than the time-dependent variation of this quantity.The convergence criterion for the electronic self-consistency cycle was a root-mean-square change of 10 −7 a.u. in the Kohn-Sham potential.The presented results are within the scalar-relativistic approximation, as calculations with explicit inclusion of spin-orbit coupling (SOC) did not lead to notable changes in the occupation numbers.
For comparison to the RT-TDDFT results, the frequencydependent dielectric function was calculated in the framework of the random phase approximation in the limit of q → 0. For the RPA calculations, the reciprocal space is sampled by a 16 × 16 × 6 k-mesh.In the RT-TDDFT investigation, we simulate laser pulses with different laser frequencies but the same peak power density of S peak ≈ 5 × 10 12 Wcm −2 and constant duration.The monochromatic electromagnetic wave is folded with a Gaussian envelope with a constant full-width at half-maximum (FWHM) of 5.81 fs.The peak of the pulse is reached at t = 11.6 fs after the start of the simulation.
[33][34][35] The electric field of the laser pulse, expressed by the vector potential, A ext (t), enters the KS equation as a velocity gauge.
By solving the TDKS equations, we can obtain the timedependent electronic properties of a system such as timeresolved DOS (TDDOS), D  (E, t), which maps the transient occupation numbers of the Kohn-Sham orbitals onto the ground-state DOS using the following scheme, see ref. [33]: where g ik (t) are the time-dependent and spin-resolved occupation numbers, defined as: Adv. Theory Simul.2024, 7, 2300319 here, n jk is the occupation number of the j th orbital and Φ i are the ground-state Kohn-Sham orbitals. [32]

Geometry and Electronic Structure in the Ground State
Before turning to the optical excitations in Fe 3 /(MgO) 5 (001) and Fe 5 /(MgO) 7 (001) heterostructures, we discuss shortly the ground state properties and compare them to Fe 1 /(MgO) 3 (001). [24,25]As shown in Figure 1, the layers of bcc Fe are rotated by 45 • with respect to the MgO lattice to achieve best lattice match where O is located apically to Fe.The structural properties are discussed in the Supporting Information [36] , see Table S1 (Supporting Information).
The impact of the layer thickness on the electronic structure is assessed based on the layer-resolved density of states (LDOS) of Fe 1 /(MgO) 3 (001), Fe 3 /(MgO) 5 (001), and Fe 5 /(MgO) 7 (001), shown in Figure 2, using a Gaussian-type smearing of  = 0.05 eV for all curves.A central observation is the narrowing of the Fe 3d band at the interface.The effect is most pronounced for Fe 1 /(MgO) 3 (001), while the bandwidth increases for the thicker heterostructures and the shape resembles the one of Fe bulk for the Fe layers further away from the interface toward the central layer.The smaller bandwidth leads to sharper features, for instance the peaks observed in the minority spin channel of Fe(IF) close to E F at about −0.5 and +0.2 eV in Fe 1 /(MgO) 3 (001), which exhibit a considerable hybridization with O 2p states of MgO(IF).These peaks split up further and broaden for Fe 3 /(MgO) 5 (001) and Fe 5 /(MgO) 7 (001).While the majority spin Fe 3d band is nearly fully occupied, the minority 3d band extends to +2.6 eV.As will be discussed below, this has a significant effect on the excitation pattern.Within the MgO part, the band offset between the MgO valence band and Fe 3d band is reduced with increasing thickness of MgO.The MgO valence band edge is shifted toward the Fermi level, from −3.7 eV for Fe 1 /(MgO) 3 (001) to about −3.1 eV for Fe 5 /(MgO) 7 (001).A common characteristic of all systems is the significant hybridization between d 3z 2 −r 2 orbitals of Fe(IF) with the p z orbitals of the apical O(IF), leading to a noticeable DOS in MgO(IF) e.g., at +0.8 eV in the majority spin channel (for a discussion of the orbital character of the respective states, see refs.[24, 25]).Important interface related features in the LDOS of MgO(IF) are observed around −2 eV in the majority channel and at +0.2 eV in the minority channel.These arise from the hybridization of d xz and d yz orbitals of Fe with p x and p y orbitals of apical O.As displayed in the insets showing the magnified LDOS in the MgO layers around the Fermi level, the interface states fade out exponentially in the deeper MgO layers away from the interface, as the thickness of MgO is increased, with the central layers approaching bulk MgO behavior.

Absorption Spectra from RPA
The imaginary part of the frequency-dependent dielectric tensor Im[()] characterizes the optical absorption properties of the heterostructure.In Figure 3, the in-plane ( xx () =  yy (), upper panel) and out-of-plane ( zz (), lower panel) components of the imaginary part of the dielectric tensor calculated in the random phase approximation for Fe 1 /(MgO) 3 (001), Fe 3 /(MgO) 5 (001), and Fe 5 /(MgO) 7 (001) are compared to bulk Fe and MgO.
A striking feature of Fe 1 /(MgO) 3 ( 001) is that the in-plane components are dominated by the metallic Fe layer with a large absorption in the low-energy region.On the contrary, the outof-plane components are determined by the insulating MgO part with significantly reduced absorption for frequencies below the bandgap of bulk MgO. [24]Here only some contributions from the hybridized states in the gap from the interface MgO layer are visible.Increasing the thickness of the Fe-slab to 3 and 5 layers adds significant weight to  xx () for ℏ < 4eV compared to Fe 1 /(MgO) 3 (001) and also introduces a sizable outof-plane absorption in  zz () in the same energy range.These differences in the absorption behavior of Fe 3 /(MgO) 5 (001) and Fe 5 /(MgO) 7 (001) w.r.t.Fe 1 /(MgO) 3 (001) -in particular, the reduced anisotropy -imply that also the time-resolved evolution will be impacted by the increasing thickness of Fe and MgO in the heterostructure.

Real-Time Evolution of the Charge Distribution
To understand the dynamics of carrier excitation and their transfer across the interface we analyze the electron density redistribution upon laser excitation obtained from RT-TDDFT.For a direct comparision with the minimum model system Fe 1 /(MgO) 3 (001), we applied laser pulses with the same photon energies and a constant peak power density of S peak ≈ 5 × 10 12 Wcm −2 as in our previous work. [24,25]The pulse duration is limited due to folding with a Gaussian envelope with a full-width at half-maximum (FWHM) of 5.81 fs, which results in a finite width of about 0.6 eV (FWHM) in the frequency domain.Different photon energies were considered ranging from below (ℏ = 1.63 eV and ℏ = 3.27 eV), in the order of (ℏ = 4.5 eV) and above (ℏ = 7.75 eV) the LDA bandgap of bulk MgO (4.64 eV [37,38] ).Pulses with electric field oriented along the x-(in-plane) or z-axis (out-of-plane) were taken into account.We concentrate here on the thickest Fe 5 /(MgO) 7 (001) heterostructure, the electron density redistribution for Fe 3 /(MgO) 5 (001) is presented in Figure S1 of the Supporting Information [36] and exhibits a qualitatively similar picture.Still smaller deformations of the charge clouds persist, which are also subject to small oscillating fluctuations.Figures S2 and S3 (Supporting Information [36] ) provide further detail on the magnitude of these fluctuations.
In-plane polarized pulses with photon energies of ℏ = 1.63 eV and ℏ = 3.27 eV -both lower than the bulk MgO bandgap -deform mainly the charge clouds in the Fe layers with a weaker impact on the apical oxygen in MgO(IF), see Figure 4a,b.The largest charge redistribution is observed in the Fe(IF) and Fe(IF+1) layers, indicating a transfer from in-plane to out-ofplane 3d orbitals, whereas the excitation within Fe(C) appears to be smaller.At larger photon energies close to (4.5 eV) and beyond (7.75 eV) the bandgap of bulk MgO the charge redistribution around the Fe atoms decreases, whereas a notable charge depletion at the O sites throughout the MgO part emerges for 7.75 eV.
For out-of-plane pulses with energies of ℏ = 1.63 eV and ℏ = 3.27 eV in Figure 4e,f the excitation is again mainly in The vertical lines denote the laser frequencies used in our RT-TDDFT calculations.For comparison, we also show respective spectra calculated for cubic bulk Fe and MgO. [24]e Fe part as for in-plane polarization, but significantly weaker, consistent with strong anisotropy in response observed for Fe 1 /(MgO) 3 (001). [24]In contrast, for ℏ = 7.75 eV (Figure 4h), which lies well beyond the bulk MgO bandgap, a qualitatively different picture of the excitation emerges with a strong depletion of charge from the Fe slab, especially at Fe(IF) and accumulation in the interstitial part and a particularly strong excitation throughout the MgO region with depletion at the oxygen sites and accumulation at the Mg sites, which were not involved in the preceding cases.
In conclusion, the results for the thicker heterostructures Fe 3 /(MgO) 5 (001) (cf. [36]) and Fe 5 /(MgO) 7 (001) confirm the previously reported trends for Fe 1 /(MgO) 3 (001) concerning the frequency and polarization-dependent response of the system, [25] despite the qualitative changes in Im[()] for the thicker systems: Laser pulses with lower energy excite primarily the Fe slab, in particular for in-plane polarization of light.In turn, the MgO part is more efficiently addressed by photons with energies above the MgO bulk bandgap with out-of-plane polarization.In both cases, the central Fe layers exhibit a smaller excitation than the layers closer to the IF.

Frequency-Dependence of the Excitation Pattern
In a further step, we disentangle the role of different energy-, spin-, and layer-resolved excitation processes in promoting excited carriers through the heterostructure.For this, we calculated the change of spin-and layer-resolved TDDOS D  (E, t) of Fe 3 /(MgO) 5 (001) and Fe 5 /(MgO) 7 (001) as a function of time t before, during and after the laser pulse.As reported previously for the minimal system Fe 1 /(MgO) 3 (001), the energy variation of ΔD  (E, t) remains essentially constant in time after the decay of the laser pulse. [24,25]This is also the case for more realistic heterostructures, as demonstrated for Fe 5 /(MgO) 7 (001) in the Supporting Information. [36]For brevity, we therefore discuss in the following only changes in the partial TDDOS of Fe 5 /(MgO) 7 (001) at time t 1 = 20.2fs relative to its initial distribution at time t 0 = 0, i.e., ΔD  (E) = ΔD  (E, t 1 ) − ΔD  (E, t 0 ).For better visibility, we plot the absolute value of ΔD  (E) and distinguish depletion and accumulation of occupation of the corresponding orbitals by red and blue colors, as we did for the charge densities.

Excitation Pattern of Bulk Fe
While the minimal system Fe 1 /(MgO) 3 (001) [24,25] harbors only a single ultrathin Fe-layer, a bulk-like coordination of Fe is restored in thicker heterostructures, and we expect, in accordance with the previous sections, that the properties of the inner Fe layers approach bulk behavior.Therefore, we discuss briefly the response of bulk Fe to the same laser pulses as applied to Fe n /(MgO) m (001).Due to the cubic symmetry of -Fe no difference is expected for in-and out-of-plane polarization.Figure 5a shows a relatively broad excitation pattern in both spin channels for ℏ = 1.63 eV.In contrast to the nearly filled majority band, the minority spin 3d band is approximately half-filled and is thus more susceptible to excitations, due to the large number of initial and final states below and above the Fermi level.The energy range of the excitations spans from −5 to +4 eV, which is large compared to the energy of the pulse (1.63 eV).Even considering its relatively broad FWHM of 0.6 eV, one would expect that the excitation would not exceed substantially an interval of ±2 eV around the Fermi level.We ascribe the extended energy range to the particularly large absorption taking place at low energies, consistent with the steep rise in the imaginary part of the dielectric function in Figure 3.For the electric field strength of the applied pulses, this may induce visible non-linear effects in the absorption.
With increasing photon energies, such non-linear features in the excitation pattern beyond ±ℏ around E F decrease substantially.In Figure 5b,c In Figure 5d, ℏ = 7.75 eV, we can identify once again distinct features in ΔD  (E), which are separated by ℏ: In the majority channel at −0.5 and +7.3 eV, as well as around ±4 eV; in the minority channel small features at −6 and +2 eV, as well as around More importantly, we can observe extended energy intervals with a vanishing change in occupation and these are obviously -due to the metallic character of bcc-Fe -not related to regions with a vanishing static DOS.In particular, we can identify several regions where essentially no or little excitations take place (cf.orange arrows in Figure 5d): in the majority channel the interval between E F and 2 eV, as well as around −2 eV and a strong reduction around +6 eV.In the minority channel, we also find three extended regions with vanishing excitations: Between −5 and −3.5 eV, between ±1 eV and between +2 and +4 eV.For all photon energies, a region of low excitations in an interval around E F is observed, which is related to a deep minimum in the static minority spin DOS of bulk bcc Fe.Its width increases with increasing photon energy and becomes a complete gap for the largest photon energy.Such features are important for the later comparison to the excitations in the heterostructure.For bulk MgO, essentially no impact is expected for laser pulses below the bandgap.In our previous study [25] we also showed that even photon energies in the vicinity of the LDA bandgap of bulk MgO do not lead to a substantial redistribution in the occupation of states between the valence and the conduction band.However, an excitation with ℏ = 7.75 eV leads to one comparatively sharp transition, which removes carriers from the upper valence band edge to states located approximately 3 eV above the conduction band minimum.

Excitations in Fe/MgO(001) Heterostructures Illuminated with In-Plane-Polarized Laser Light
Having understood the excitation pattern in the bulk materials, we now turn to ΔD  (E) in the heterostructures.In contrast to the cubic bulk systems, the polarization direction of the electric field introduces a significant anisotropy in the carrier dynamics. [24,25]e start with the in-plane polarized case, i. e., the orientation of the electric field vector parallel to the interface.
Figure 6 displays the comparison of the layer-and spinresolved changes ΔD  (E) for Fe 5 /(MgO) 7 (001) after illumination with ℏ = 1.63 eV, ℏ = 3.27 eV, ℏ = 4.5 eV, and ℏ = 7.75 eV.The majority of excitations are encountered in a window of ±ℏ around E F .Maxima in the static DOS provide an enhanced density of initial or final states for a direct excitation between occupied and unoccupied states, separated by ℏ.Therefore, the patterns in the panels correlate essentially with the features (peaks and valleys) in the respective static layer-resolved DOS in Figure 2. Changes in occupation substantially outside the window of ±ℏ around E F cannot be reached by a direct excitation process.These are particularly prominent for ℏ = 1.63 eV where we observe significant occupation of states at +3 eV and above as well as a depletion at and below −3 eV in both spin channels in Figure 6a.These should be be regarded as nonlinear effects such as multi-photon excitations or the temporary renormalization of the energies of initial and final states as a consequence of the changed interactions within the excited charge cloud, arising from a combination of large field strength and large absorption, in particular for low frequencies (cf. Figure 3).Such non-linear patterns are still present for ℏ = 3.27 eV in Figure 6b but decrease substantially for larger photon energies.
A direct excitation (vertical black arrows in Figure 6a) is observed in the majority channel of the Fe layer from initial states below E F to the remainder of the unoccupied d-states at around +0.8 eV.This is still below the charge transfer gap, thus the propagation of these excitations into the MgO conduction band cannot be expected.However, due to the presence of interface states, we encounter a considerable population in MgO(IF), which decreases quickly with the distance from the interface, while a corresponding depletion of carriers below E F is not encountered in the MgO part.A full comparison of the excitation processes in Fe n /(MgO) m (001) is presented in the Supporting Information. [36]t suggests that the population at +0.8 eV becomes larger with increasing thickness, which indicates a transfer of excited carriers from the deeper Fe layers towards MgO(IF) and MgO(IF-1).A population of states in MgO(IF) directly above E F occurs also in the minority channel, but here it goes hand in hand with the depopulation of interface states below E F .
Increasing the frequency to ℏ = 3.27 eV allows for excitations in the Fe subsystem to reach across the charge transfer gap: Fi-nal states between 2.5 and 3 eV (vertical black arrows) hybridize with the sp-orbitals of the MgO conduction band, see the vertical arrows in Figure 6b.We observe the transfer of carriers into MgO(IF) that does not decay toward MgO(C).Since direct excitations in bulk-like MgO are not possible for this photon energy, this indicates the propagation of carriers excited in the Fe subsystem or MgO(IF) into the conduction band of MgO.
With increasing photon energies the picture becomes more defined.Excitations with ℏ = 4.5 eV are of particular interest since they correspond to the setup of recent optical-pump-x-ray-probe experiments on Fe/MgO heterostructures [23,39] and we expect to capture essential aspects of the experimental pump process in our modeling.
We first concentrate on the minority channel of Fe 5 /(MgO) 7 (001), shown in the lower panels of Figure 6c.The photon energy is in the vicinity but still below the LDA bandgap of bulk MgO and thus, as we have shown earlier, [25] the direct excitations across the bulk MgO LDA bandgap is negligible.Therefore, the significant deoccupation seen at the top of the valence band in the MgO(C) layers in Figure 6c between −4 and −4.5 eV, which extends through all the MgO layers (horizontal purple arrows), can be associated with direct excitations to states slightly above E F in MgO(IF) and the Fe layers.Furthermore, the comparison with Figure 5c reveals that in bulk Fe excitations with final states up to 1 eV above E F are sparse and there is a sharp decrease in generated carriers below −4 eV.In contrast, we find in the minority channel of Fe(C) in Figure 6c a large occupation directly above the Fermi level, while the depletion below -4 eV is small.This indicates, that the carriers above E F do not result from a direct excitation within the Fe-layers with a bulk-like DOS.It rather suggests a dominating role of the interface layers MgO(IF) and Fe(IF) in the effective transfer of carriers from states below −4 eV in MgO(C) to states just above E F in Fe(C), as depicted by the diagonal purple arrows in Figure 6c.In the majority channel (upper panels), a similar process can be identified.Here, however, the excitation via hybridized states (diagonal purple arrow) stands in competition with direct excitations from the Fe-d band in all Fe layers (vertical black arrows), because we encounter for bulk Fe in Figure 5c, as well as for Fe(C) in Figure 6(c) that the amount of carrier depletion around -4 eV is of similar magnitude as the occupation at +1 eV.
As indicated by the green arrows, we also observe the reverse process: Carriers slightly below the Fermi level in the Fe-subsystem are excited across the charge transfer gap to MgO conduction band states between +4 and +4.5 eV into the central layers of MgO.This allows the transfer of carriers from states in Fe(C) just below E F to conduction band states in MgO(C).As the photon energy is below the bandgap of MgO, the additional carriers in MgO cannot result from a direct excitation within the insulator.However, following the same argument given above, we cannot safely distinguish in this case, whether the excitation generating these carriers takes place in the bulk-like layers of Fe or at the interface.The comparison to ℏ = 3.27 eV reveals, that the MgO valence and conduction band states at −4 and +4 eV, respectively, are of particular importance for the transfer of carriers in both directions: For the lower photon energy in Figure 6b, the transfer between the subsystems is reduced since the relevant levels at ±4 eV cannot be reached by a direct excitation in the linear regime.As the changes in occupation for these transitions are consistent with resonant excitations and rather large, we may safely exclude a significant non-linear contribution here.Non-linear contributions are of higher order, i. e., of lower magnitude compared to direct resonant excitations (interface and bulk), in particular for the frequencies in the order and above the MgO bandgap as corroborated by our previous analysis of the dependence of the excitation pattern on the pulse intensity in the Supporting Information of ref. [25] (Figures S6 and S7).
For ℏ = 4.5 eV the transfer of carriers thus works efficiently in both directions simultaneously.This avoids a significant net accumulation of charge in one of the subsystems, which would come with a penalty from Coulomb interaction.A similar concerted process has been proposed previously for the minimal het-erostructure Fe 1 /(MgO) 3 (001). [25]Our present work thus proves, that this simultaneous bi-directional relocation of carriers is active also in heterostructures with thicker slabs of Fe and MgO, which are easier to realize in experiment.The significant spinsplitting of the Fe-d states affects the hybridization with the MgO conduction band states, which are relevant for the propagation of the carriers.The hybridization is enhanced here for the majority spin channel, leading to a substantial depletion of states in the valence band of MgO(C) compared to the minority channel and thus to spin-dependent changes in |ΔD  (E)| even for the (nonmagnetic) insulating component.
For laser pulses, which are above the bulk MgO LDA bandgap and in the order of or beyond the bandwidth of the Fe-d band, direct excitations in the Fe-subsystem are diminished compared to  001) heterostructure.Same colors for positive and negative signs as in Figure 6.The upper panels refer to the majority spin channels and the lower panels to the minority spin channels.Black, purple, and green arrows refer to particular transitions, which are discussed in the text.
the lower photon energies, since now either initial or final states lie outside the range of the Fe-d band.On the other hand, the bidirectional transfer of carriers is still effective for ℏ = 7.75 eV as shown in Figure 6d.Here, transitions take place from −5.5 and −7 eV in MgO to +2.0 eV in the majority spin channel of Fe, as indicated by the diagonal purple arrows.It is important to note, that for this process, there is no corresponding excitation in bulk-Fe, cf.orange arrows in Figure 5d, and therefore this excitation must involve interface states.In the reverse direction (green arrows in Figure 6) carriers from below E F down to −2 eV are excited to unoccupied states around +6 eV and above.This may take place entirely in the metallic subsystem, but the occupation of the final states extends deeply into the conduction band of the MgO subsystem.Similarly, in the majority spin channel carriers are transferred from MgO states at −7 eV to Fe states up to +1 eV (purple arrows).Simultaneously, Fe-states from −2 or −1 eV below E F are depleted in favor of MgO states between +5.5 and +7 eV, as illustrated by the green arrows.Overall, the difference in excitation pattern between the two spin channels is significantly reduced at this energy.Additionally, we observe direct excitations in the MgO layers from states below the Fermi level at −3.5 to −4.0 eV to conduction band states around +4 eV, indicated by the black vertical arrows in Figure 6d.
It is important to note that the above-sketched mechanisms are essentially independent of the thickness of the layers; the qualitative picture, which was already obtained for the smallest system size turns out to be effective also in systems with much larger layer thicknesses.This is corroborated by a detailed comparison of the excitation pattern of Fe 1 /(MgO) 3 (001), Fe 3 /(MgO) 5 (001), and Fe 5 /(MgO) 7 (001) heterostructures for all frequencies presented in the Supporting Information. [36]

Excitations in Fe/MgO(001) for Out-of-Plane Polarization of the Electric Field
Some important distinctions occur in ΔD  (E) for polarization of the electric field perpendicular to the interface planes, that are consistent with the conclusions drawn from the dielectric constants presented in Section 3.2 and the transient changes in the charge distribution discussed in Section 3.3: A particularly strong reduction of the scale of ΔD  (E) with respect to in-plane polarized light occurs for the lowest frequencies, whereas the picture reverses for photon energies above the bandgap of bulk MgO.The latter is demonstrated in Figure 7b, where the amplitude of the features in ΔD  (E) increases by more than a factor of two for ℏ = 7.75 eV.On the other hand, the magnitude of the light induced changes in occupation are rather similar for ℏ = 4.5 eV for both orientations of the electric field, see Figure 7a.In contrast to the in-plane polarization shown in Figure 6c, for ℏ = 4.5 eV we observe in Figure 7a, a significant occupation of minority states after the pulse between +2 and +5.5 eV in the MgO conduction band, similar to the majority channel.This is accompanied by an enhanced depletion of states at the upper valence band edge of the central MgO layer in both spin channels.Besides the direct excitations for ℏ = 7.75 eV in Figure 7b, we find in the minority spin channel a depletion around −7 eV in the valence band of MgO concomitant with accumulation of states right above E F in the Fe subsystem (purple arrows).This process is significantly enhanced as compared to Figure 6d.Furthermore, we see in Figure 7b an enhanced excitation of MgO conduction band states around +5 eV in combination with an enhanced depletion in the Fe subsystem at −2.5 eV (green arrows), which is clearly above the valence band edge of MgO.

Conclusion
We systematically explored carrier dynamics and excitation patterns in Fe n /(MgO) m (001) metal-insulator heterostructures (n = 3, 5 and m = 5, 7) excited by a laser pulse in the optical to ultraviolet range corresponding to photon energies below, around, and above the bandgap of bulk MgO.The polarization of the electric field was selected in-and out-of-plane with respect to the stacking of the heterostructures.The response to optical excitations was characterized in terms of the dielectric tensor calculated in the random phase approximation.We found that cross-plane components of the dielectric tensor increase below the DFT bandgap of bulk MgO with increasing thickness of the metallic Fe part, which diminishes the anisotropic response to pulses with in-plane and cross-plane polarization of the electric field, observed previously in Fe 1 /(MgO) 3 (001). [25]ubsequent real-time TDDFT simulations provided insight into the transfer of carriers within and between the Fe and MgO subsystems.The analysis was carried out in terms of the electron density redistribution and layer-resolved changes in the occupation numbers before and after the laser pulse.The redistribution of electronic charge shows a significant anisotropy and a qualitatively similar picture for both Fe 3 /(MgO) 5 (001), and Fe 5 /(MgO) 7 (001): The Fe-layer is efficiently addressed at low frequencies by in-plane polarized light, whereas for frequencies higher than the bulk MgO bandgap, we found a particularly large response of the MgO layers to cross-plane polarized light.
The time-resolved changes in the energy-resolved occupation numbers of the Kohn-Sham orbitals are consistent with the predictions from the dielectric function, but yield additional insight into the spatial resolution with respect to the layer and the energy of the involved orbitals.For frequencies in the order of and above the LDA bulk MgO bandgap, we observed a simultaneous charge transfer from the valence band of MgO to Fe states above E F and from Fe d-states below the Fermi level to the conduction band of MgO.This concerted process is relevant for both polarization directions and occurs in all investigated heterostructures.It results in the accumulation of hot carriers in the conduction band of the MgO subsystem, which are not encountered in the bulk of the insulator after photo-excitation.In contrast to the excitation in the bulk systems, which is confined to particular energy ranges, a much richer pattern of redistributed occupation is observed in the heterostructures, which is largely independent of the layer thickness.Since changes in the occupation are present in the central (bulk) layers of the heterostructures, but not observed in the (separate) bulk systems, we can conclude that in the heterostructure, the hybridized interface states play the dominant role in the relocation of charge carriers between the subsystems.These findings confirm that the concerted mechanism of heat transfer initially sketched in ref. [25] for a minimum model system remains robust in realistic heterostructures involving several layers of both Fe and MgO, away from the interface.Our findings suggest furthermore that a careful tuning of the photon energy and polarization direction may allow to select the transfer between favorably oriented orbitals via particular interface states even in extended heterostructures with a layer thickness in the range of one or several nanometers.
Hot carriers generated by optical absorption processes play an important role in photocatalysis or harvesting of solar energy (e. g., refs.[40, 41]).Such applications often require the separation of positive and negative charge carriers.The concerted mechanism, presented here, results in the simultaneous transfer of both carrier types and thus the charge remains balanced.On the other hand, the energy of these carriers is substantially different in the two subsystems.This implies a transfer of energyor rather heat, as the energy may dissipate very quickly within a few 10-100 fs.The excited carriers may, in principle, be detected in state-of the art optical pump, x-ray probe experiments as presented in Rothenbach et al. [23], which requires further improvements with respect to time-and energy-resolution.Nevertheless, the comprehensive understanding of the conditions under which optically excited carriers propagate into and possibly through the interface might open further opportunities to achieve control of the transfer of excitations in other classes of metal-insulator heterostructures.

Figure 4
illustrates the change Δ(r, t) = (r, t) − (r, 0) in the spatially and time-resolved charge density (r, t) at t = 20.2fs, i. e., after the application of the laser pulse, w.r.t.t = 0 in the Fe 5 /(MgO) 7 (001) heterostructure for different frequencies and polarization directions.Animations of the full temporal evolution of Δ(r, t) indicate horizontal/vertical fluctuations of the elec-tronic clouds around the atomic positions for the in-plane/outof-plane polarization of the electric field during the pulse.At t = 20.2fs (and beyond), the electric field has decayed completely.

Figure 3 .
Figure 3. Imaginary part of the dielectric tensor Im[ ij ()] of Fe 1 /(MgO) 3 (001), Fe 3 /(MgO) 5 (001), and Fe 5 /(MgO) 7 (001) as well as the bulk materials as a function of energy: a) in-plane (Im[ xx ()]=Im[ yy ()]) and b) out-of-plane Im[ zz ()] components, respectively, calculated within RPA.The spectra are shifted vertically by a constant value of 5 for clarity.The vertical lines denote the laser frequencies used in our RT-TDDFT calculations.For comparison, we also show respective spectra calculated for cubic bulk Fe and MgO.[24] , majority channel features are located close to E F and around ±2.5 eV for both photon energies, ℏ = 3.27 and 4.5 eV.For ℏ = 4.5 eV additional features are found at +4 and −4.5 eV.In the minority channel in Figure 5b features showing depletion at −2.5 and −1.5 eV and accumulation at +0.8 and +1.8 eV occur.For the larger frequency in Figure 5c, we can identify an analogous relation between features centered around −2.8 and −1 eV below E F and +1.8 and +3.5 eV above.

Figure 5 .
Figure 5. Spin-resolved changes in the time-dependent DOS of bulk Fe at t = 20.2fs (after the decay of the laser pulse) w.r.t.t = 0, i. e., ΔD  (E) = D  (E, 20.2fs) − D  (E, 0), for laser pulses with frequencies of ℏ = 1.63 eV, ℏ = 3.27 eV, ℏ = 4.5 eV, and ℏ = 7.75 eV and a peak power density of S peak ≈ 5 × 10 12 Wcm −2 .For better visibility, we plot the absolute value, the sign is indicated by the color.Blue: positive sign, accumulation of occupation; red: negative sign, depletion of occupation.The upper panels refer to the majority spin channels and the lower panels to the minority spin channels.The orange arrows denote features discussed in the text.

Figure 6 .
Figure 6.Spin-and layer-resolved changes in the TDDOS at t = 20.2fs (after the decay of the laser pulse) w.r.t.t = 0, ΔD  (E) = D  (E, 20.2fs) − D  (E, 0), for in-plane polarized laser pulses with frequency of a) ℏ = 1.63 eV, b) ℏ = 3.27 eV, c) ℏ = 4.5 eV, and d) ℏ = 7.75 eV applied to the Fe 5 /(MgO) 7 (001) heterostructure.For better visibility we plot the absolute value |ΔD  (E)|, the sign is indicated by the color.Blue: positive sign, accumulation of occupation; Red: negative sign, depletion of occupation.The upper panels refer to the majority spin channels and the lower panels to the minority spin channels.Black, purple, and green arrows refer to particular transitions, which are discussed in the text.

Figure 7 .
Figure 7.The difference ΔD  (E) of the layer-resolved TDDOS between t = 0 and t = 20.2fs (after the decay of the laser pulse), for out-of-plane laser pulses with frequencies of a) ℏ = 4.5 eV and b) ℏ = 7.75 eV applyed to the Fe 5 /(MgO) 7 (001) heterostructure.Same colors for positive and negative signs as in Figure6.The upper panels refer to the majority spin channels and the lower panels to the minority spin channels.Black, purple, and green arrows refer to particular transitions, which are discussed in the text.