Local structure of Mn in hydrogenated ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$

In this paper we investigate the incorporation of hydrogen in ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ for samples with $x\approx 0.005$ grown by metal-organic vapor-phase epitaxy and with $0.03<x<0.05$ grown by low-temperature molecular-beam epitaxy. The anisotropic electron-paramagnetic-resonance (EPR) signal observed for the paramagnetic ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ samples with $x\approx 0.005$ after hydrogenation is characteristic for ${\text{Mn}}^{2+}$ substitutional on the Ga site. Contributions of crystal fields to the EPR signal indicative of Mn-H complexes with H atoms near the Mn are negligibly small. The relative volume increase in a single ${\text{Mn}}_{\text{Ga}}\text{-As}$ atom pair upon hydrogenation $\Delta V_{\text{H}}/V_{\text{Mn-As}}\approx 0.14\pm 0.07$ as deduced from a comparison of the high-resolution x-ray diffraction $2\Theta /\Omega$ scans of as-grown and hydrogenated samples with $0.03<x<0.05$ is expected for Mn-H complex formation. However, the accuracy of this measurement is not sufficient to draw unambiguous conclusions about the specific nature of the Mn-H configuration. Extended x-ray absorption fine-structure (EXAFS) analysis and x-ray absorption near-edge spectroscopy (XANES) on samples with $0.03<x<0.05$ show no indication for bond-centered Mn-H complexes as determined from a detailed comparison of the EXAFS Fourier transforms and the XANES spectra with the simulations. The overwhelming structural evidence of these techniques therefore points to comparatively large distances between the Mn and the H atoms at least in ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ films with Mn concentrations above 0.005, which would be the case for either complexes with the hydrogen atom in the antibonding position or for compensation via isolated interstitial hydrogen.

Figure 1

(a) Ferromagnetic resonance spectra of the as-grown, the annealed, and the hydrogenated sample 1 investigated via XAFS in Sec. 5 for the external magnetic field oriented perpendicular to the film plane at 5 K. Hydrogenation leads to a strong suppression of the ferromagnetic resonance signal. The hydrogenated sample features a broad paramagnetic resonance at $g=2.0$ scaled up in (b).

Figure 2

The upper diagram shows the anisotropy of the EPR resonance fields ${\mu }_0{H}_{\text{res}}$ simulated using $g=2$, $A=-5.75\text{mT}\times g{\mu }_B$, $D_{001}=-0.1\text{mT}\times g{\mu }_B$, $D_{111}=0.1\text{mT}\times g{\mu }_B$, and $a=-1.55\text{mT}\times g{\mu }_B$. The size of the dots corresponds to the expected intensity of the respective resonance line. The lower diagram shows the angular dependence of the EPR of the hydrogenated MOVPE-grown sample with $x\approx 0.005$ (full lines). The spectra have been simulated (dashed line) with the same parameters as in the upper diagram.

Figure 3

Breit-Rabi diagram for $\text{GaAs}:{\text{Mn}}^{2+}$ with the magnetic field oriented normal to the ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ layer. The vertical lines indicate the allowed magnetic-dipole transitions with $\Delta m_s=\pm 1$ and $\Delta m_i=0$ for a transition energy of $39\mu \text{eV}$ corresponding to a microwave frequency of 9.3 GHz.

Figure 4

(Color online) (a) Schematic picture of the ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ crystal illustrating the origin of the uniaxial crystal-field anisotropy contributions $D_{001}$ and $D_{111}$ in ${\mathcal{H}}_{\mathcal{S}}$. (b) $D_{001}$ is caused by the uniaxial epitaxial strain $\left(c>a_{\text{GaAs}}\right)$, while the change in local symmetry due to the incorporation of hydrogen is accounted for by $D_{111}$ [(c) and (d)]. In (c) the hydrogen atom is shown in the bond-centered position, denoted as ${\text{Mn}}_{\text{Ga}}{\text{-H}}_{\text{bc}}$ in Ref. 17 corresponding to bcAs(Mn) in Ref. 16. In (d) the hydrogen atom is shown in the antibonding position, denoted as ${\text{Mn}}_{\text{Ga}}{\text{-H}}_{\text{ab}\left(\text{As}\right)}$ in Ref. 17 corresponding to abAs(Mn) in Ref. 16. The arrows indicate a slight shift of the As and the ${\text{Mn}}_{\text{Ga}}$ atoms from the substitutional lattice sites.

Figure 5

Reciprocal space map of the asymmetric (404) reflex of a ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ layer with nominal Mn concentration $x=0.039$ (a) before and (b) after hydrogenation.

Figure 6

$2\Theta /\Omega$ scans of the symmetric (004) reflex of ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ layers with varying Mn concentration $x$ before (solid circles) and after (open circles) hydrogenation. For clarity curves are shifted vertically. The angle $2\Theta =66.058°$ marked by the vertical dashed line corresponds to the (004) reflex of the GaAs substrate.

Figure 7

(a) Relaxed lattice parameter as a function of Mn concentration $x$ before (solid symbols) and after (open symbols) hydrogenation. The circles correspond to the samples investigated in Fig. 6 and the triangles to the samples further characterized via XAFS below. The error bars are deduced from the full width at half maximum of the (004) reflex of the (Ga,Mn)As layer in Fig. 6. (b) Increase in relaxed lattice parameter upon hydrogenation $\Delta a_{\text{H}}$. The notation is the same as in (a).

Figure 8

(Color online) (a) Off-axis bond-centered configuration $\left({\text{Mn}}_{\text{Mn}}{\text{-H}}_{\text{bc}}^{\ast }\right)$, and (b) antibonding configuration $\left({\text{Mn}}_{\text{Mn}}{\text{-H}}_{\text{ab}\left(\text{As}\right)}\right)$ of the ${\text{Mn}}_{\text{Ga}}\text{-H}$ complex with the bond lengths calculated by Goss and Briddon (Ref. 17). Similar values have been obtained by Bonapasta et al. (Ref. 16). (c) Expected radial distribution function for the off-axis bond-centered configuration $\left({\text{Mn}}_{\text{Ga}}{\text{-H}}_{\text{bc}}^{\ast }\right)$. (d) Expected radial distribution function for the antibonding configuration $\left({\text{Mn}}_{\text{Ga}}{\text{-H}}_{\text{ab}\left(\text{As}\right)}\right)$. To estimate these radial distribution functions we used the bond lengths to the neighboring As atoms from Ref. 17 depicted in (a) and (b) and broadened the distribution function by Lorentzians with a full width at half maximum (FWHM) of $0.2\text{Å}$.

Figure 9

XAFS absorption coefficient $\mu \left(E\right)$ of an as-grown ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ sample with $x=0.039$. The dashed curve is a smooth background function representing the absorption of an isolated Mn atom ${\mu }_0\left(E\right)$. Inset shows the extracted $k\chi \left(k\right)$ spectrum described in the text.

Figure 10

Comparison of the Fourier transforms of the $\text{Mn}K$-edge EXAFS $\chi$ functions of an as-grown, a hydrogenated, and an annealed reference sample. Inset shows the $k$-weighted $\text{Mn}K$-edge EXAFS $\chi$ functions. The dashed curves are fits to the measured data. For clarity the curves are shifted vertically.

Figure 11

(a) Nearest As-neighbor bond length $R_{\text{As}}$, (b) nearest Ga-neighbor bond length $R_{\text{Ga}}$, and (c) second-nearest As-neighbor bond length $R_{\text{As}2}$, as well as (d) nearest As-neighbor Debye-Waller factor ${\sigma }_{\text{As}}^2$, (e) nearest Ga-neighbor Debye-Waller factor ${\sigma }_{\text{Ga}}^2$, and (f) second-nearest As-neighbor Debye-Waller factor ${\sigma }_{\text{As}2}^2$ as a function of sample treatment ($\text{H}=\text{hydrogenation}$, $\text{A}=\text{annealing}$) determined from the fits to the spectra on sample 1 in Fig. 10 and on sample 2.

Figure 12

(Color online) Comparison of the XANES spectra of a hydrogenated and as-grown piece of sample 2 (the two lowest spectra) with ab initio simulations performed in the FMS approach for different Mn-H complexes: single Mn (sMn), bond-center (bc), and antibonding (ab) complexes with H linked to either Mn or As, and two more complexes (abAsGa, bcAsGa) where the distance between Mn and H is bigger.

Figure 13

(Color online) (a) Zoom on the pre-edge region of Fig. 12; the vertical lines delimitate the pre-edge peak/shoulder. (b) Comparison of the experimental XANES spectra with the FMS simulations that give the best agreement, i.e., sMn for the as-grown sample and abAsGa for the hydrogenated one, respectively.