Magnetic Properties and Electronic Configurations of Mn Ions in the Diluted Magnetic Semiconductor Ba_1−xK_x(Zn_1−yMn_y)₂As₂ Studied by X-ray Magnetic Circular Dichroism and Resonant Inelastic X-ray Scattering

Figure 1(a) shows the Mn \(L_{2,3}\)-edge XAS spectra of Mn-BaZn₂As₂. Magnetic fields of \(\pm 1\) T were applied along the c-axis. The single peak structure of the \(L_{3}\) main peak evidences that Mn-BaZn₂As₂ does not contain extrinsic Mn components such as oxidized Mn atoms at the surface unlike in the case of GaMnAs.²²⁾ The XMCD spectrum is shown in Fig. 1(b). The XMCD lineshape is consistent with a previous report for samples with slightly different doping levels.²³⁾ From the experimental XMCD spectra, we have determined the spin and orbital magnetic moments separately by applying the XMCD sum rules.^24,25) The \(3d\) electron occupation number appearing in the sum rule was set to 5. The estimated spin and orbital magnetic moments per Mn ion are \(m_{\text{spin}} = 0.45\pm 0.03\) \(\mu_{\text{B}}\) and \(\mu_{\text{orb}} = 0.05\pm 0.01\) \(\mu_{\text{B}}\), respectively. We attribute the small spin moment compared with 5 \(\mu_{\text{B}}\), the value expected for Mn²⁺ (\(d^{5}\)), to a competition between the antiferromagnetic (AFM) superexchange interaction for the nearest-neighbor Mn atoms and ferromagnetic (FM) interaction through long-range coupling mediated by the itinerant carriers. A theoretical work predicts that the effective exchange coupling \(J_{\mathrm{H}}^{\text{eff}}\) between Mn pairs changes sign from AFM to FM when they are separated by more than 3 Å for hole-doped cases, \(x=0.2\) and 0.4.¹⁶⁾ Indeed, the end compound BaMn₂As₂ is a local-moment AFM insulator with the extraordinarily high Néel temperature of \(T_{\mathrm{N}}=625\) K, and the AFM order remains robust in the hole-doped system Ba\(_{1-x}\)K_xMn₂As₂ up to \(x=0.40\).^26,27) The XMCD magnetic moments are consistent with the total magnetization estimated from SQUID magnetometry.²⁰⁾ The small orbital magnetic moment is in line with GaMnAs,²²⁾ reaffirming the \(S=5/2\) high spin configuration of Mn \(3d\) electrons. The nonzero value reflects the finite contribution from the charge-transferred states in the ground state.

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Figure 1. (Color online) (a) X-ray absorption spectra of Ba_0.7K_0.3(Zn_0.85Mn_0.15)₂As₂ single crystals at the Mn \(L_{2,3}\) edge taken in the total-electron-yield mode. Magnetic fields of \(\pm 1\) T were applied along the c axis, and x-rays were incident 30° from the c-axis. (b) X-ray magnetic circular dichroism at the Mn \(L_{2,3}\) edge. The spin and orbital moments per Mn ion are deduced to be \(0.45\pm 0.03\) and \(0.05\pm 0.01\) \(\mu_{\text{B}}\), respectively.

Having established the magnetic properties of the Mn ions in the ground state, we study the electronic configurations via the excitation spectra. Figure 2(a) shows the scattering geometry of the RIXS experiment. The detector angle \(2\theta\) was fixed at 90° throughout this work, and the polarization of incident photons was kept either within or perpendicular to the scattering plane (referred to as π and σ scattering geometries, respectively). The momentum transfer \(\boldsymbol{q}\) in the Brillouin zone of Ba\(_{1-x}\)K_x(Zn\(_{1-y}\)Mn_y)₂As₂ is shown in panel (b). At the Mn \(L_{3}\) edge with \(2\theta=90\)° geometry, the magnitude of \(\boldsymbol{q}\) was \(0.602\,\pi/a\) or \(0.993\,2\pi/c\), where \(a=4.12\) Å and \(c=13.58\) Å are in-plane and out-of-plane lattice constants, respectively. The incident angle \(\theta_{i}\) with respect to the a–b plane can be varied by rotating the sample on the rotation axis perpendicular to the scattering plane. In the momentum space, this corresponds to rotating the \(\boldsymbol{q}\) vector within the Γ–XZ plane as illustrated in the figure. In the specular scattering geometry (\(\theta_{i}=45\)°), the \(\boldsymbol{q}\) vector approximately corresponds to the Γ–Z distance (\(2\pi/c=0.606\,\pi/a\)).

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Figure 2. (Color online) (a) Scattering geometry of the RIXS experiment. (b) Momentum transfer \(\boldsymbol{q}\) in the Brillouin zone of Ba\(_{1-x}\)K_x(Zn\(_{1-y}\)Mn_y)₂As₂. (c) XAS spectra taken in the total-fluorescence-yield mode. The incident photon energies employed for RIXS measurements are indicated by arrows. (d) Incident energy dependence of the RIXS spectra taken with the σ polarization. Vertical bars indicate fluorescent-like emission that has a constant x-ray energy.

Figure 2(c) shows XAS spectra in the Mn \(L_{2,3}\)-edge region of Mn-BaZn₂As₂ collected in the total-fluorescence-yield mode. The Mn \(L_{3}\) peak is located at 639 eV and the photon energies used in the following RIXS measurements are indicated by black arrows. Figure 2(d) shows RIXS spectra taken with various incident photon energies (\(h\nu\)) across the \(L_{3}\) peak with the σ polarization. At the \(L_{3}\) peak, we observed a broad feature between 1 and 6 eV energy loss. This broad feature originates from the d–d excitation of the Mn ion. Upon detuning the photon energy from the \(L_{3}\) peak toward higher energies, we observe broad continuous excitations that exhibit fluorescent behavior. These excitations originate from emission from the intermediate states where electrons in the As \(4p\) valence band screen the Mn \(2p\) core holes through the As \(4p\)–Mn \(3d\) hybridization.

In Fig. 3, we compare the RIXS spectrum taken at the Mn \(L_{3}\) peak with the π polarization and that for Ga_0.96Mn_0.04As from Kobayashi et al.²⁸⁾ In both systems, the d–d excitation profiles are much broader than the experimental energy resolution of 80 meV. As an origin of the broadening, we consider the fast decay of the final states into electron–hole pairs in the As \(4p\) valence and conduction bands, as theoretically proposed for Mn impurity in Ag.²⁹⁾ In Ga_0.96Mn_0.04As, the small band gap of the host GaAs opens a decay channel for the d–d excitations into the continuum of electron–hole pairs in the GaAs host.²⁸⁾ The same decay mechanism is expected in Mn-BaZn₂As₂, as the narrower band gap of 0.23 eV of BaZn₂As₂³⁰⁾ than that of GaAs (1.42 eV) makes the electron–hole pair creation more efficient. Regarding the peak positions of the d–d excitations, the main peak of Ga_0.96Mn_0.04As is located at 3 eV (green triangle), which corresponds to the peak in the calculated spectra for the Mn³⁺ state. Kobayashi et al. concluded that the charge-transferred \(3d^{5}\underline{L}\) state is more appropriate for the description of the Mn impurity state in GaMnAs. For Mn-BaZn₂As₂, on the other hand, peak structures are also present around 2 and 4 eV (open triangles), which correspond to the peaks in the calculated spectra for the Mn²⁺ state. In addition, the intensity between 2 and 4 eV (black triangle) is also high, which is attributed to emission from the Mn³⁺ configuration as in GaMnAs. Based on this consideration, we conclude that both the pure acceptor \(3d^{5}\) electron configuration with free holes and the \(3d^{5}\underline{L}\) electron configuration with bound holes contribute to the ground state of Mn ions in Mn-BaZn₂As₂.

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Figure 3. (Color online) Comparison of RIXS spectra for Ba_0.7K_0.3(Zn_0.85Mn_0.15)₂As₂ and Ga_0.96Mn_0.04As.²⁸⁾ The spectra are taken with π-polarized photons at the Mn \(L_{3}\) peak. Filled triangles indicate the peak originating from the Mn³⁺ configuration, and open triangles indicate those from the Mn²⁺ configuration.

The coexistence of the Mn²⁺ and Mn³⁺ states is a natural consequence of the energy level of the Mn impurity band with respect to the VBM of the host material. In GaMnAs, the Mn impurity band is formed slightly above the VBM of the host semiconductor GaAs.³¹⁾ All the doped holes occupy the Mn impurity level which is formed by hybridization with the As \(4p\) orbitals. This situation realizes the \(3d^{5}\underline{L}\) electron configuration for every doped hole. In Mn-BaZn₂As₂, on the other hand, the Mn impurity levels are located below the VBM.¹⁸⁾ The hole carriers, introduced independently by K doping, predominantly occupy the top of the valence band consisting of the As \(4p\) orbitals. The majority of Mn ions may thus remain in the pure \(3d^{5}\) configuration without strong influence of hole carriers. At the same time, part of the hole carriers, twice as many as Mn ions, can also enter the Mn impurity level slightly below the Fermi energy. This realizes the \(3d^{5}\underline{L}\) state with a bound hole.

In addition to the d–d excitation of relatively high energies primarily localized on the Mn ion, it is important to study low-energy magnetic excitations. In order to investigate such excitations, the excitations in the lower energy region were measured with π polarization for incident angles \(\theta_{i}=45\) and 65°, as shown in Fig. 4(a). In the scattering geometry with \(2\theta=90\)°, the π polarization vector of the incident photons is always orthogonal to the two polarization vectors of the scattered photons. This condition suppresses elastic charge scattering³²⁾ and prevents the high-energy tail of the elastic peak from obscuring low-energy excitations. Instead, the RIXS response is dominated by the magnetic excitations. The broad d–d peaks do not show significant change between \(\theta_{i}=45\) and 65°, as expected for the local excitations. Figure 4(b) shows an expanded plot of the low-energy region. In addition to the elastic peak and the d–d excitations, we observe weak and broad peaks around 0.35 eV as indicated by open circles. Theoretical studies based on the p–d exchange model predict that ferromagnetic DMSs can support collective acoustic and optical spin-wave modes, and a continuum of Stoner excitations.^33–35) Their energy scales are determined by the zero-temperature spin-splitting gap \(\Delta=cJ_{pd}S\) for the itinerant carriers, where c is the magnetic ion density, \(J_{pd}\) is the p–d exchange and \(S=5/2\) is the local spin. As typical parameters for GaMnAs, König et al.³⁴⁾ take \(c=1\) nm⁻³ and \(J_{pd}=0.15\) eV nm³. Then the energy scale of the acoustic spin wave becomes \(0.02\Delta\sim 10\) meV, which is difficult to detect with the present energy resolution. On the other hand, the optical spin waves and Stoner excitations occur at much higher energy scales Δ (\(\sim 0.4\) eV) because the energy scales are determined by the flipping of a single spin in the ferromagnetic itinerant carriers. This energy scale matches that of the weak peak at 0.35 eV. The direct observation of the acoustic spin wave requires further RIXS measurements of the low energy region with higher resolution.

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Figure 4. (a) RIXS spectra taken at the Mn \(L_{3}\) edge with π polarizations for incident angles \(\theta_{i}=45\) and 65°. (b) Enlarged plot of the low energy-loss region. Circles indicate broad peaks originating from the Stoner excitations.