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Valence, exchange interaction, and location of Mn in polycrystalline Mn(x)Ga(1-x)N (x<0.04)

We present an experimental study for polycrystalline samples of the diluted magnetic semiconductor Mn(x)Ga(1-x)N (x<0.04) in order to address some of the existing controversial issues. Different techniques were used to characterize the electronic, magnetic, and structural properties of the samples, and inelastic neutron scattering was employed to determine the magnetic excitations associated with Mn monomers and dimers. Our main conclusions are as follows: (i) The valence of the Mn ions is 2+. (ii) The Mn(2+) ions experience a substantial single-ion axial anisotropy with parameter D=0.027(3) meV. (iii) Nearest-neighbor Mn(2+) ions are coupled antiferromagnetically. The exchange parameter J= 0.140(7) meV is independent of the Mn content x, i.e., there is no evidence for hole-induced modifications of J towards a potentially high Curie temperature postulated in the literature.

There is an ongoing debate on the physical properties of the compound Mn x Ga 1-x N, a diluted magnetic semiconductor (DMS) with potential applications in spintronics and blue-LED technologies [1,2]. The interest in Mn x Ga 1-x N is driven by the prediction of Mn-induced ferromagnetism with Curie temperatures T C exceeding room temperature [3], which is required for a technological breakthrough in the field of DMSs. Up to the present, myriads of experiments have been performed for Mn x Ga 1-x N compounds, but the conclusions still remain highly controversial as recently summarized by Nelson et al. [4]. A basic problem with Mn x Ga 1-x N is the low solubility of Mn ions in the host compound GaN, so that the investigated samples are often contaminated by Mn clusters or other phases which are ferromagnetic in nature, e.g., MnGa (T C >600 K) and Mn 4 N (ferrimagnetic, T C =738 K). For this reason, the observation of ferromagnetism above room temperature reported in the literature has to be considered with caution, especially as none of these findings has resulted in a device working at room temperature. There are some other important questions associated with Mn x Ga 1-x N for which so far no common agreement has been obtained, namely: (i) What is the valence of the Mn ions Based on the procedure outlined by Szyszko et al. [5], polycrystalline Mn x Ga 1-x N samples were synthesized with manganese concentrations up to x=0.08. The Mn content x was determined by energy dispersive X-ray (EDX) spectroscopy. Analyses by X-ray and neutron diffraction showed that Mn x Ga 1-x N crystallizes in the hexagonal space group P6 3 mc, but even for low values of x an impurity phase of type MnN y (y<1) with tetragonal space group I4/mmm was always present. We concentrated our experimental study on detailed investigations of two samples with x 1 =0.024(3) and x 2 =0.072 (2) [7]. The diffraction data taken at T=293 K were analyzed both for the main phase Mn x Ga 1-x N and for the impurity phase MnN y . In model I the dopant Mn ions were treated as substitutional ions at the Ga-site with position (2/3,1/3,0). However, the refinement provided an occupation number of Mn close to zero. Consequently, in further data refinements we allowed the zcoordinate of the Mn position (1/3,2/3,z) to be varied, resulting in a zdisplacement of about 0.3 Å from the regular Ga site for model II. Model III was triggered by the results of a Fourier analysis, based on the difference between the observed and the calculated structure factors, which gave evidence for additional scattering from Mn at the interstitial site (2/3,1/3,z) with z=0.18 (3). The structure parameters obtained for the three models are summarized in Table I. Models I and III are based on fixed z-coordinates of the Mn ions. If we start the refinement with the initial parameters of models I and III by releasing the z-constraint of the Mn position, the fitting procedure converges to the parameters of model II. We therefore feel that model II provides the most probable solution for the structure of Mn x Ga 1-x N. Another argument for model II (and against model III) is the fact that in principle there is no room for placing ions at interstitial sites in the densely packed Wurtzite crystal structure of Mn x Ga 1-x N, unless either N or Ga vacancies are created in order to comply with the interatomic distances. This is in contrast to the related DMS Mn x Ga 1-x As, where the dopant Mn ions can occupy interstitial sites commensurate with the zinc-blende crystal structure [8]. Due to the small differences of the reliability factors listed in Table I for the three models, there remains some uncertainty concerning the z-coordinate of the Mn ions.
However, it is important to realize that the local symmetry of Mn ions being either at the sites (2/3,1/3,z) or at regular Ga sites (2/3,1/3,0) is identical with tetrahedral coordination, which is an important aspect for the analysis of both the X-ray absorption near-edge structure (XANES) and the INS experiments Electron paramagnetic resonance (EPR) experiments performed with a microwave frequency of 9.39 GHz gave rise to a resonance at a magnetic field of 0.33 T, similar to the results described by Zajac et al. [12], which agrees with the field-induced splitting of the m=|±1/2> ground state of Mn 2+ ions for g=2. In addition, analyses of magnetic susceptibility and magnetization data also favor Mn 2+ .
INS experiments were carried out with use of the high-resolution time-offlight spectrometer CNCS [13] at the spallation neutron source (SNS) at Oak Ridge National Laboratory. The samples were enclosed in aluminum cylinders of 8 mm diameter and placed into a He cryostat to achieve temperatures T≥1.7 K. Additional experiments were performed for vanadium to allow the correction of the raw data with respect to background, detector efficiency, and absorption according to standard procedures. We searched for magnetic excitations over a wide energy range, but we did not observe magnetic intensity for energy transfers >0.6 meV. Energy spectra taken for Mn x Ga 1-x N with x=0.04 in the neutron energy-gain configuration are shown in Fig. 2(a) for moduli of the scattering vector Q in the range 0.5≤Q≤1.5 Å -1 . The energy of the incoming neutrons was 1.55 meV, with instrumental energy resolutions of Gaussian shape increasing from 20 μeV to 29 μeV for energy transfers from 0 meV to 0.5 meV, respectively. We observe an increase of the intensity upon raising the temperature from 1.7 K to 6.0 K. This becomes more clear by plotting the difference of the energy spectra as shown in Fig. 2(b), which has the advantage that uncertainties about the background are automatically eliminated. Taking intensity differences has proven to be an extremely powerful procedure to analyze INS data [14].
The data of Fig. 2 where D is the axial single-ion anisotropy parameter, and s z denotes the zcomponent of the spin operator s of the Mn ions. The corresponding neutron cross-section for monomer transitions |m>→|m'> is defined by [17] where F(Q) is the magnetic form factor, n m (T) the Boltzmann population factor of the initial state |m>, and -s z ≤m≤s z . The transition matrix element gives rise to the selection rules The spin Hamiltonian of Mn dimers is given by where J is the bilinear exchange parameter. It is convenient to base the where R is the distance between the two dimer spins.
Mn 3+ : D=0.108(5) meV, J=-0.139(10) meV, i.e., the Mn dimers are antiferromagnetically coupled. Similar values J=-0.16 (3) meV [19] and J=-0.136 meV [20] were derived from magnetization and magnetic susceptibility data, respectively. INS experiments were also performed for Mn x Ga 1-x N with x=0.02 as shown in Fig. 2(c). The resulting energy spectra turned out to be very similar to those for x=0.04 displayed in Fig. 2 a hole-mediated mechanism such as Zener's kinetic exchange interaction [21].
In fact, the concentration of mobile holes was measured to be <10 18 cm -3 for crystalline Mn x Ga 1-x N (x<0.1) [19]. A similar number was reported for the DMS compound Mn x Zn 1-x Te (x≤0.05) where the exchange coupling determined by INS experiments experienced a marginal shift of not more than 1% due to the hole-mediated interaction [22].
The analysis of the neutron diffraction data did not provide a definite answer concerning the location of the dopant Mn 2+ ions in Mn x Ga 1-x N, although model II (see Table I) is favored for reasons given above. In order to arrive at a conclusive solution of the structure, investigations on single crystals or further neutron diffraction experiments extended to a larger Q-range (by using neutrons with wavelength of typically 0.5 Å) are highly desirable, which are expected to provide an improved discrimination of the models in terms of the χ 2 test.
In conclusion, the realization of ferromagnetic DMSs with high Curie