Minority-spin impurity band in $\mathrm{n}$-type (In,Fe)As: A materials perspective for ferromagnetic semiconductors

Fully understanding the properties of n-type ferromagnetic semiconductors (FMSs), complementary to the mainstream $\mathrm{p}$-type ones, is a challenging goal in semiconductor spintronics because ferromagnetism in $\mathrm{n}$-type FMSs is theoretically nontrivial. Soft-x-ray angle-resolved photoemission spectroscopy (SX-ARPES) is a powerful approach to examine the mechanism of carrier-induced ferromagnetism in FMSs. Here our SX-ARPES study on the prototypical $\mathrm{n}$-type FMS (In,Fe)As reveals the entire band structure, including the Fe-$3d$ impurity bands (IBs) and the host InAs ones, and provides direct evidence for electron occupation of the InAs-derived conduction band (CB). A minority-spin Fe-$3d$ IB is found to be located just below the conduction-band minimum (CBM). The IB is formed by the hybridization of the unoccupied Fe $3d$ states with the occupied CBM of InAs in a spin-dependent way, resulting in the large spin polarization of CB. The band structure with the IB is varied with band filling, which cannot be explained by the rigid-band picture, suggesting a unified picture for realization of carrier-induced ferromagnetism in FMS materials.

Figure 1

SX-ARPES spectra of (In,Fe)As:Be. (a) Fermi surface mapping (FMS) in the $k_z\text{−}{k}_x$ plane. $k_x$ indicates the momentum along the Γ-K-X ([110]) direction. The solid curves are $\mathit{k}$-space cuts for fixed hν. (b) Enlarged plot near the Γ point $\left[k_z=15\left(2\pi /c\right)\right]$. The top and right plots are momentum distribution curves along the $k_x$ and $k_z$ cuts across the Γ point (dashed lines), respectively. (c) ARPES intensity along the Γ-K-X line obtained at $h\nu =908$ eV. The inset is a blowup of the EP. (d) Energy distribution curves (EDCs) around the Γ point.

Figure 2

Resonant ARPES spectra of (In,Fe)As:Be. (a) Fe $L_3$ XAS spectrum. The constant-initial-state (CIS) spectrum at $E_B=0.25$ eV corresponding to the α-IB is also plotted. The arrows denote the excitation energies for rARPES. (b) Fe $L_3$ rARPES spectra. The left and right panels are the off- and on-resonance spectra, respectively. α- and β-IBs are Fe $3d$-derived impurity bands. (c) EDCs of the rARPES spectra. (Top) On- and off-resonance EDCs at $k_x=-1.0$. (Bottom) Differences of the EDCs corresponding to the Fe-$3d$ PDOS at various $k_x$. The vertical bars indicate a dispersive peak.

Figure 3

Comparison of band structures of (In,Fe)As with and without doping. (a) Band dispersions along the Γ-K-X ([110]) line in (In,Fe)As:Be. The IB intensity obtained by rARPES is superimposed in the positive $k_x$ region. The dispersions of the LH (circle), HH (square), and SO (rhombus) bands are also plotted. (Right) EDC at Γ (thin line) and Fe-$3d$ PDOS (thick line). The colored areas denote the energy ranges of the Fe-$3d$ IBs. (b) Band dispersion near $E_{\mathrm{F}}$ in InAs:Be, with the EDC at Γ on the right. (c) Band dispersion in (In,Fe)As as well as (In,Fe)As:Be (Fig. 3).

Figure 4

Band diagram of (In,Fe)As. (a, b) Schematic DOS for ferromagnetic (In,Fe)As:Be and paramagnetic (In,Fe)As, respectively. DOS including the Fe $3d$-derived IBs embedded in the VB and CB of the host InAs. The expected unoccupied Fe $3d_{\downarrow }$ states are also shown. (c, d) Band diagrams for (In,Fe)As:Be and (In,Fe)As, respectively. Hybridization between Fe $3d{e}_{\downarrow }$ and CB leads to the formation of α-IB and hybridization between Fe $3d{t}_{2\downarrow }$ and VB to the formation of β-IB. Dash-dotted lines are the InAs-derived band dispersion without the hybridization. Electron occupation of CB pushes down the partially filled α-IB to be located below CBM, leading to the large spin-splitting ${\mathrm{\Delta }}_{ex}$ of the CB.

Figure 5

APRES spectrum of (In,Fe)As:Be obtained along the Γ-K-X line with $s$ polarization. (a) APRES intensity along the Γ-K-X line obtained at $h\nu =908$ eV. HH is the heavy-hole band of the host InAs. The incident photon energy for this measurement is of 908 eV as well as the ARPES spectrum taken with $p$ polarization shown in Fig. 2. (b) EDCs around the Γ point.

Figure 6

Fe $L_3$ resonant ARPES spectra of (In,Fe)As:Be taken with $s$ polarization. The left and right panels are the off- and on-resonance spectra, respectively. IB is the Fe $3d$-derived impurity band.

Figure 7

Spin-density functional theory calculation for an ${\mathrm{In}}_{31}{\mathrm{Fe}}_1{\mathrm{As}}_{32}$ supercell. (a, b) Spin-resolved band structure. The weight of Fe $3d$ is indicated by the size of red circles. The blue dash-dotted line is the energy position of $E_{\mathrm{F}}$ in the Be-doped samples as observed experimentally. Note that as $E_{\mathrm{F}}$ is shifted upwards, the Fe $3d{t}_{2\downarrow }$ and $e_{\downarrow }$ bands are also shifted upwards and remain located above $E_{\mathrm{F}}$ due to Coulomb interaction, as denoted by red arrows. The impurity band near $E_{\mathrm{F}}$ (α-IB) observed in the present work is considered to result from hybridization between the Fe $e_{\downarrow }$ bands and the CBM. (c) DOS for the up-spin (upper curve) and down-spin states (lower curve). (d) Partial density of states for Fe $3d$.

Figure 8

Fermi surface mapping of an InAs:Be thin film. (a, b) In-plane and out-of-plane FSM, respectively. The top right plots are momentum distribution curves (MDCs) along the $k_x$ and $k_y$ or $k_z$ cuts across the Γ point (dashed lines), respectively.

Figure 9

Band dispersions of InAs:Be. (a) ARPES image plot along the Γ-K-X line obtained with $p$ polarization. LH and SO denote the light-hole and split-off bands, respectively. (b) Energy distribution curves (EDCs) of the spectrum taken with $p$ polarization. (c) ARPES image plot along the Γ-K-X line obtained with $s$ polarization. HH denotes the heavy-hole band. (d) EDCs of the spectrum taken with $s$ polarization. The ARPES images are second derivatives of the ARPES intensities.

Figure 10

Band dispersions of paramagnetic (In,Fe)As. (a) ARPES image plot along the Γ-K-X line obtained with $p$ polarization. (b) EDCs of the spectrum taken with $p$ polarization. (c) ARPES image plot along the Γ-K-X line obtained with $s$ polarization. HH denotes the heavy-hole band. (d) EDCs of the spectrum taken with $s$ polarization. The ARPES images are second derivatives of the ARPES intensities.

Figure 11

Fe $L_3$ resonant ARPES spectra of paramagnetic (In,Fe)As. (a, b) rARPES spectra taken with $p$ and $s$ polarizations, respectively. The left and right panels are the off- and on-resonance spectra, respectively. IB denotes the impurity band.