Unveiling the impurity band induced ferromagnetism in the magnetic semiconductor (Ga,Mn)As

(Ga,Mn)As is a paradigm of a diluted magnetic semiconductor which shows ferromagnetism induced by doped hole carriers. With a few controversial models emerging from numerous experimental and theoretical studies, the mechanism of the ferromagnetism in (Ga,Mn)As still remains a puzzling enigma. In this article, we use soft x-ray angle-resolved photoemission spectroscopy to positively identify the ferromagnetic Mn $3d$-derived impurity band (IB) in (Ga,Mn)As. The band appears dispersionless and hybridized with the light-hole band of the host GaAs. These findings conclude the picture of the valence-band structure of (Ga,Mn)As disputed for more than a decade. The nondispersive character of the IB and its location in vicinity of the valence-band maximum indicate that the Mn $3d$-derived IB is formed as a split-off Mn-impurity state predicted by the Anderson impurity model. Responsible for the ferromagnetism is predominantly the transport of hole carriers in the IB.

Figure 1

Band dispersion near the $\Gamma$ point in the Ga${}_{0.975}$Mn${}_{0.025}$As thin film. The incident photon energy is $h\nu =890$ eV. (a, b) ARPES images along the $\Gamma$-K-$\mathrm{X}$ line measured with $p$ and $s$ polarizations, respectively. The light-hole (LH) and split-off (SO) bands are clearly seen with the $p$ polarization, while the heavy-hole (HH) band is active with the $s$ polarization. (c) ARPES image along the $\Gamma$-$\mathrm{X}$-$\Gamma$ line. (d)–(f) Energy-distribution curves (EDCs) around the $\Gamma$ point corresponding to (a)–(c). The vertical bars are guides for the eyes tracing the spectra structures. The Fermi-level position has been measured with Au foil in electrical contact with the sample. These results identify the textbook manifold of LH, HH, and SO bands of GaAs.

Figure 2

Comparison of EDCs in vicinity of the $\Gamma$ point taken at $h\nu =890$ eV between Ga${}_{0.975}$Mn${}_{0.025}$As and GaAs thin films. The EDCs of GaAs are shifted to match the band dispersion to that of Ga${}_{0.975}$Mn${}_{0.025}$As. The momentum $k_{\parallel }$ is along the $\Gamma$-K-$\mathrm{X}$ direction and its unit is $2\sqrt{2}\pi /a$, where $a$ is the in-plane lattice constant. (Ga,Mn)As shows additional spectral weight at $E_{\mathrm{F}}$ consistent with its metallic conductivity.

Figure 3

Comparison of the band dispersions between different BZs across $k_z$. The momentum $k_{\parallel }$ is along the $\Gamma$-K-$\mathrm{X}$ direction. The band dispersions taken at $h\nu =650$ eV are determined by fitting the experimental MDCs with the Lorentzian function. The identity of the dispersions measured with different probing depths excludes any significant band bending.

Figure 4

Resonant angle-resolved photoemission spectroscopy (r-ARPES) spectra at the Mn $L_{2,3}$ edge in Ga${}_{0.975}$Mn${}_{0.025}$As. (a) Mn $L_{2,3}$ XAS spectrum. The red and blue vertical dashed lines correspond to the resonant $h\nu$ for the ferromagnetic and paramagnetic components, respectively. (b) Constant-initial-state (CIS) spectra taken at $E_B=0.25$ and 4.0 eV with $s$ polarization. (c)–(f), (g)–(j) r-ARPES images taken in a series of at $h\nu$ from 638 to 642 eV with $s$ and $p$ polarization, respectively, with the $h\nu$ points shown as rhombi in the inset of (a). All the images are represented in second derivative along $E_B$ (positive values of $-d^{2}I/d{E}^2$ [42]) and plotted in logarithmic scale to emphasize the resonance enhancements. (k, l) Resonant EDCs around the $\Gamma$ and at the $X$ points taken with $p$ and $s$ polarizations, respectively. The red curves are the EDCs for $h\nu =640$ eV, the blue ones for $h\nu =640.5$ eV. The green areas denote differences between the red and blue curves. These linear dichroism results identify the IB hybridization with the LH band of GaAs but not with the HH band.

Figure 5

Valence-band structure of (Ga,Mn)As. (a) Band dispersion around the $\Gamma$ point near $E_{\mathrm{F}}$ along the $\Gamma$-K-$\mathrm{X}$ line. IB is the Mn $3d$-derived impurity band on top of the LH, HH, and SO bands of GaAs. Open and closed symbols are the MDC and EDC peak positions, respectively, for the GaAs bands fitted with a quadratic polynomial. The solid curves are their fit with a quadratic polynomial function centered at the $\Gamma$ point to the band dispersion. (b) The experimental band diagram as densities of states of the Mn $3d$-derived IB embedded into the VB in host GaAs. Dash-dotted line denotes anticipated unoccupied density of states.

Figure 6

Bound magnetic polarion picture of FM in (Ga,Mn)As. (a) Zhang-Rice singlet-like bound magnetic polaron around the doped Mn ion. (b) Schematic image of overlap among the magnetic polarons in (Ga,Mn)As.

Figure 7

One-electron levels of AIM for the Mn ion in (Ga,Mn)As showing a split-off state above the VBM. Left: Strength of the $p$-$d$ hybridization $|t_{{\varepsilon }^{\prime }\gamma }{|}^2$. Right: The right side and left side of the integral equation (A9) as a function of $\varepsilon$. The crossing point indicated by the black circle gives the solution for the discrete level (split-off state) occupied by the doped hole.