Antiferromagnetism in Nanofilms of Mn-Doped GaN - American

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Antiferromagnetism in Nanofilms of Mn-Doped GaN C. Echeverría-Arrondo,†,‡ J. Pérez-Conde,§ and A. Ayuela*,‡,∥ †

Departamento de Química Física, Universidad del País Vasco, E-48080 Bilbao, Spain Donostia International Physics Center, E-20018 San Sebastián, Spain § Departamento de Física, Universidad Pública de Navarra, E-31006 Pamplona, Spain ∥ Centro de Física de Materiales CFM-MPC Centro Mixto CSIC-UPV/EHU, Departamento de Física de Materiales, E-20018 San Sebastián, Spain ‡

ABSTRACT: We theoretically study the role of surfaces in the electronic and magnetic properties of nanofilms made of wurtzite and zinc-blende (Ga,Mn)N. The studied doping reactions suggest that Mn impurities replacing Ga cations preferably stay just below the unsaturated surface rather than near the substrate. The hole-mediated ferromagnetism, typical of (Ga,Mn)N bulk, is absent from these films, and Mn moments for the most stable cationic positions become antiferromagnetically coupled. The holes ascribed to dopants in (Ga,Mn)N semiconductors are here occupied by electrons from dangling bonds. In other less-stable sites, Mn atoms are ferromagnetic; the surface moment can be then parallel to them and small, as in the wurtzite and zinc-blende (111) geometries, or antiparallel and large, as in zinc-blende (001). Hence, the magnetic interplay between surfaces and Mn impurities depends on the surface orientation, which could be useful for the design of magnetic nanodevices.

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INTRODUCTION Group-III-nitride semiconductors are vastly employed in optoelectronics because of their wide band gap.1 Magnetic dopants, such as Mn atoms, opened the field of spintronics several years ago,2 since they can convert these nitrides into magnetic semiconductors,3,4 wherein they can also act as efficient luminescence centers. These magnetic nitrides present large Zeeman effects that allow improving devices, such as random access memories.5,6 Concerning nanostructures, small clusters of (Ga,Mn)N contain Mn atoms antiferromagnetically coupled when increasing surface-to-volume ratios due to the prominent role of crystal fields.7 However, more promising nanostructures using (Ga,Mn)N focus on thin films grown on substrates. Although they experimentally show mixed ferromagnetic8−10 and paramagnetic8,11−13 behaviors, we explore here the (Ga,Mn)N nanostructures that besides become antiferromagnetic by decreasing the layer thickness. As this prospect has not yet been observed, it is now timely to investigate the spin coupling trends in (Ga,Mn)N nanofilms, in order to get insights into the magnetism of nitrides.

can be up to 10% before phase segregation between GaN and Mn nitrides.20,21 We take 3% as a typical doping content within this range.10,21−24 The chosen film thickness of 1 nm makes relevant the determinant role of surfaces in this shallow region. We perform spin-polarized calculations with the projector augmented-wave method,25 as implemented in the VASP code26−28 within density functional theory. The exchangecorrelation potential29 follows the generalized-gradient approximation GGA+U, where U = 4 eV and J = 0.8 eV are suitable parameters 30 for an accurate description of magnetic (Ga,Mn)N. The number of plane waves in the basis set is given by a cutoff energy of 500 eV. We use a converged grid of 3 × 3 × 1 k points to sample the Brillouin zone of a 4 × 4 supercell with 12 Å of empty space between neighbor slabs. This sampling corresponds to a grid of 12 × 12 × 1 k points per formula unit in the plane. The input geometries are WZ(0001),13 ZB(111),16 and ZB(001),17 all of them with the same tetrahedral symmetry up to first neighbors. The epilayers are grown on GaN templates with the same crystal structure and orientation. The atomic misfit and strain at the interface (Ga,Mn)N−GaN are hence small and, to some extent, reproduced during the atomic relaxation of the unit cells. Following previous work in ref 7, the substrate is accounted for by attaching pseudohydrogens of fractional charge 3e/4 to the bottom N atoms, which do not affect the electronic and magnetic properties of the studied films.31 The input crystals are depicted in Figure 1: panel (a) shows wurtzite and panels

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COMPUTATIONAL DETAILS In this paper, we study Ga1−xMnxN unsaturated slabs of 1 nm thickness with wurtzite (WZ)8−14 and zinc-blende (ZB)15−18 crystal structures. We consider the epitaxial growth on a GaN template that, in turn, lies on a substrate typically made of either sapphire, Si, or SiC.19,20 These layers are then doped with two substitutional Mn impurities per unit cell of 128 GaN atoms, the Mn concentration thus being x = 2/64 ≃ 0.03. When doped layers are grown with molecular beam epitaxy using nitrogen−hydrogen plasma, the impurity concentration © 2014 American Chemical Society

Received: February 8, 2014 Revised: June 30, 2014 Published: July 7, 2014 18064

dx.doi.org/10.1021/jp501387c | J. Phys. Chem. C 2014, 118, 18064−18068

The Journal of Physical Chemistry C

Article

grown by molecular beam epitaxy (MBE) in a reactor chamber. Gallium and manganese atoms are provided by effusion cells, whereas nitrogen reactive species are produced by an electroncyclotron resonance (ECR) plasma source.21 The oxidation state of Mn in (Ga,Mn)N is +2, as confirmed by X-ray absorption spectra measurements.23 Doping reactions involve the adsorption and diffusion of Mn atoms34 until they get fixed at the cationic positions of the films. In order to determine the energy cost to reach this final stage in the doping process, we focus on the following reaction among Ga, N, and Mn atoms GaN + 2Mn+2 → (Ga,Mn)N + 2Ga +2

(1)

where ions Mn2+ could come from the precursor bis(methylcyclopentadienyl)manganese (MCp2Mn), also present in colloidal samples.13 The energy for this substitutional doping, ER, is defined as the usual diference between products and reactants, and it is obtained from the total energies of the ions Mn2+ and Ga2+, following the same procedure as that in ref 7. The computed substitutional energies ER are obtained using fully relaxed structures and are given in Figure 2a−c. From

Figure 1. Cross sections of (Ga,Mn)N unit cells with (a) WZ(0001), (b) ZB(111), and (c) ZB(001) crystal structures and orientations, which are lying on an interface (Ga,Mn)N−GaN simulated by pseudohydrogens of fractional charge 3e/4 attached to the bottom N atoms. These artificial atoms do not affect the electronic and magnetic properties of the films more than real GaN templates in experiments do.31 The Ga cations are drawn with light blue and the N anions with red. The cationic positions considered for the Mn impurities are labeled with capital letters: sites A, B, F, and H are on a shallow plane; sites C, D, and G are on a bulklike plane; site E is far deep, near the substrate.

Figure 2. Doping reaction energy ER as a function of Mn sites following the same labels as in Figure 1. Triangles refer to the ferromagnetic coupling and rhombuses to the antiferromagnetic one. The given exchange energies are indicated in meV for the most stable pairs of Mn spins, antiferromagnetic and placed below the surface. Note the huge exchange energy obtained for dopants in WZ films, 730 meV.

(b) and (c) show two orientations in zinc blende. Lattice constants have been optimized for bulk GaN: in wurtzite, a = 3.24 Å and c = 5.29 Å; in zinc blende, a = 4.59 Å. The atomic positions in the films are fully relaxed until forces become smaller than 0.02 eV/Å.

these data, manganese doping results to be energetically more favorable for the crystal geometry and orientation ZB(001) in Figure 2c. Note that the (001) direction has the smallest elastic constant and, as a consequence, it can accommodate more structural deformation with little energy cost. The most stable positions for Mn dopants are shallow: AB first-neighbor sites in WZ and ZB(001), AF second-neighbor sites in ZB(111). Thus, Mn impurities occupy the Ga cations just below the surface, where they are antiferromagnetically aligned. The corresponding ferromagnetic states are above in energy by the magnetic energy differences of 730, 122, and 3 meV, respectively, as indicated in panels (a), (c), and (b) of Figure 2. From the same figure, we realize that, for the nearest-neighbor dopants, the ferromagnetic−antiferromagnetic energy difference decreases following this order: WZ, ZB(111), and ZB(001). Because of this decreasing trend, the ground magnetic state is reversed into ferromagnetic for some Mn positions, such as CD and CE in

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RESULTS AND DISCUSSION When these films are grown by plasma-assisted molecular beam epitaxy, Mn atoms substitute the inner cations and get fixed at approximately random positions.32 The distribution of dopants is described as homogeneous from secondary ion mass spectrometry measurements.20,24 The surface termination of the layers is pure Ga-like, because it is energetically favored.33 We consider first- and second-neighbor cationic positions for the impurities: the latter are indicated in Figure 1 with labels AB, AD, CD, and CE; the former are AF, CG, AE, and HE. The order of preference for such sites is obtained by analyzing the doping reactions. The studied thin films can be experimentally 18065



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ZB(001); see Figure 2c. We explain this finding below based on the unsaturated surface. Surface electrons play a role in the magnetic configuration of Mn spins. Before doping and atomic reconstruction, dangling bonds are occupied by unpaired electrons, which are sketched in the upper part of Figure 3a. During relaxation of the

The importance of Mn holes is highlighted by means of the density of states, as plotted in Figure 4. We consider two

Figure 4. Spin-resolved total and local densities of states (DOSs) for the ferromagnetic arrangement of dopants in two cases of significance: (a) AB sites in WZ slabs, with an antiferromagnetic ground state (see Figure 2); and (b) CE sites in the ZB(001) slabs, with a ferromagnetic ground state. The given total DOSs, plotted in cyan, are 1/10 of the calculated values. The local DOSs, drawn with solid and dotted blue lines, are the projections onto the 3d orbitals of both Mn impurities. The vertical dotted line marks the occupied states. Note that Mn holes are only present in the band gap of ZB(001) (panel (b)).

different doping and crystal situations, AB sites in WZ (Figure 4a), and CE sites in ZB(001) (Figure 4b). From Figure 2, the ground states are antiferromagnetic and ferromagnetic, respectively. This difference can be ascribed to Mn holes around the Fermi energy. In the WZ case, they are missing; note their absence in the spectrum of Figure 4a. However, in the ZB(001) case, Mn holes are present, spatially far from the surface, but close to the Fermi energy; note them in Figure 4b. These holes activate the hole-mediated mechanism of ferromagnetism, whereby Mn dopants replacing the CE and also the CD Ga atoms within the ZB(001) films are more stable in the ferromagnetic configuration, already seen in Figure 2c. We focus next on the rich surface magnetism. When Mn spins are antiferromagnetically aligned, the surface polarization decreases almost down to zero, because there is no preferred orientation for the surface spins; see left scheme of Figure 5a. Nevertheless, when Mn spins are ferromagnetic (right scheme), the surface polarization from the unpaired electrons is either added to the Mn moments or subtracted from them; the total moment is either 10 or 8 μB, respectively. There are thus two possible configurations for the surface magnetism, parallel and antiparallel to Mn spins, with values in between 0.1 and −1.1 μB; these values are given in Figure 5b−d by the size of the drawn squares. Note the difference between Ga−N atomic arrangements on the substrate, which yield two distinct atomic projections: hexagonal on top of WZ and ZB(111) films, but square on ZB(001) films. In WZ and ZB(111) slabs, the surface moments for Mn at the Ga sites of lowest substitutional energy are about 0.1 μB. In contrast, for high-energy substitutional Ga positions, they are large, around −1.1 μB. The surface moment is smaller when parallel to Mn spins because it is in the same spin channel than they are and can thereby contribute to their ferromagnetic coupling. The ZB(001) films with a square pattern on top yield a different behavior of the surface magnetism compared to the layers with hexagonal termination. In fact, the surface moment in ZB(001) films is antiparallel and large, −0.9 μB, for the ground-state positions, AB; see Figure

Figure 3. (a) Clean wurtzite unit cell before and after the atomic reconstruction. The dangling bonds on top of the outermost Ga atoms, initially as shown in the upper part, arrange in alternate rows represented in the lower part by surfaces of constant spin-up density (in gray). (b) Because of the doping, Mn holes are now available in the spectrum to be filled by unpaired electrons, following this scheme.

undoped unit cell, these electrons can either gather and form bonds between neighboring Ga atoms (see panel (b)) or remain unpaired and contribute to the surface polarization; see the same panel (b) and the isosurfaces of constant spin density in Figure 3a. These isosurfaces are arranged in lines on top of the outermost Ga atoms, on half of them. When films are doped with manganese, the unpaired electrons can also move inward to fill the Mn holes, following the scheme given in panel (b) of Figure 3; in the WZ symmetry, Mn impurities at AB sites become antiferromagnetic for this reason. Unlike in ref 7, where the antiferromagnetic coupling of dopants is induced by the saturated surface, here, we center on the dangling bonds and their interplay with the Mn−Mn spin ordering. In nanofilms, of course, the effect of a large volume-to-surface ratio, although less relevant, is still present. 18066



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Moreover, for both types of (111) and (001) ZB slabs, it is almost null at CD and CE sites, which are more bulklike, but above 200 meV at the extreme positions AE and HE. From the previous data, we realize that, for the cases when ΔE is negative, the surface moment could be turned parallel by increasing the applied magnetic field, and this flip would be seen as a jump in the magnetization curve. These cases correspond to Ga positions of high substitutional energy, including, as an exception, the ground state in ZB(001) films, sites AB. Therefore, when considering a sample with a uniform spreading of Mn dopants, an experimental magnetization curve is expected to be rich featured with a fine structure.

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CONCLUSIONS

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AUTHOR INFORMATION

In summary, we investigate 1 nm thick layers of wurtzite and zinc-blende (Ga,Mn)N, a key nitride of the group III-V, with density functional theory. The energetic analysis of doping reactions reveals that substitutional Mn atoms are placed by the surface, where dangling electrons are available to occupy the empty states contributed by the dopants to the clean spectrum in GaN. Thereby, the hole-mediated ferromagnetism, which is typical in bulk, gets blocked as an effective mechanism, and Mn impurities align antiferromagnetically. We also show that surface moments may be either parallel or antiparallel to the Mn spins when arranged in the ferromagnetic configuration. This unusual behavior of magnetic impurities in nanometric thin films is also expected to occur in nanoclusters of (Ga,Mn)N. We note, however, that crystal fields in quantum dots play a major role and may modify results.7 The reported antiferromagnetic order in (Ga,Mn)N nanostructures encourages further investigations on diluted magnetic nitrides.

Figure 5. (a) Scheme of the surface and Mn−Mn moments. When the Mn−Mn coupling is antiferromagnetic, the surface local moment is zero (left), but when it is ferromagnetic, the surface moment can be either parallel or antiparallel to the Mn spins (right). (b−d) Magnitudes and exchange energies of surface moments for Mn spins aligned ferromagnetically. Panels (b) and (c) are for WZ and ZB(111), respectively. Panel (d) is for ZB(001) with a square terminated surface. Square sizes are proportional to the magnitude of the surface moment. The smallest squares indicate 0.1 μB, and the largest ones correspond to 1.1 μB. Colors denote the alignment of the surface moment with respect to the ferromagnetic Mn spins: red when parallel and blue when antiparallel.

5d. In addition, the scattering of square sizes in the ZB(001) case reveals the larger variety of surface moments present in these slabs. The random deposition of dopants, as it is actually performed in many experiments, leads to Mn impurities spreading over all cationic positions.32 We can hence assume that all Ga atoms are replaced with the same probability. We now sum the magnetically most stable surface moments for all the equally probable spreadings of impurities considered here, grouped in Mn−Mn pairs. We remember that these moments are positive when parallel, negative when antiparallel, and zero for the antiferromagnetic Mn spins. Surfaces contribute in average by −0.28 μB in the WZ case, −0.34 μB in ZB(111), and −0.28 μB in ZB(001). We next sum the moduli of the two surface moments corresponding to every Mn−Mn pair, parallel and antiparallel. Irrespective of Mn location and crystal symmetry, this sum is found approximately constant, 1.2 μB. As for the local Mn magnetic moments, they are in a narrow range for WZ, [4.42−4.47] μB, in a wider range for ZB(111), [4.24−4.46] μB, and in an even broader range for ZB(001), [4.16−4.50] μB. These detailed differences over the distribution of Mn moments are correlated to the scattering of surface ones and are related, in the last instance, to the different arrangements of Ga−N atoms on the substrate and resulting patterns on top. Finally, we calculate the exchange energy required to reverse the surface local moment from parallel to antiparallel, ΔE per Mn−Mn pair, as given in Figure 5. For the most-stable sites in WZ and ZB(111), AB and AF, respectively, this energy is about 50 meV in both cases; however, it is larger than 200 meV and negative for the ground-state positions in ZB(001), AB.

Corresponding Author

*E-mail: [email protected]. Phone: +34 943 01 8416. Fax: +34 943 01 5800. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the Basque Government through the NANOMATERIALS project (Grant No. IE05151) under the ETORTEK Program (iNanogune), the Spanish MCyT (FIS2010-19609-C02-02), and the UPV (Grant No. IT366-07). We gratefully acknowledge the computing resources from DIPC and SGI-SGIKerUPV.

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Antiferromagnetism in Nanofilms of Mn-Doped GaN - American

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