Research Letter  Open Access
Structural and Magnetic Properties of MnBased Diluted Magnetic Semiconductors and Alloys
Abstract
Direct supercell approach calculations of the magnetic exchange interactions in Mndoped ScN was carried out in the local spin density approximation by using the muffintinorbital Green's function method. We found that magnetic interactions are long range interactions and affected by the randomness, band gap corrections, and carrier concentrations. Using total energy minimization approach we found that the global energy minimum of MnN is obtained for zincblende structure. If the compound is compressed by 6%, the energy minimum corresponds to the rocksalt structure in disagreement with the experimentally observed tetragonal distorted rocksalt structure, known as phase. An isostructural phase transition for alloys from MnN phase to ScN phase was found to occur at a hydrostatic pressure of 18โGPa. We predict above room temperature for Mn concentrations of about 10% in ScNโ:โMn system.
1. Introduction
The undergoing intensive research and the current industrial and technological interests in the field of spintronics stimulate the search for highCurietemperature diluted magnetic semiconductors (DMSs). The typical zinc blende IIIV semiconductors doped with magnetic impurities suffer from low solubility manifested in the formation of secondary phases. Clearly, there is an interest in finding an alternative semiconductor host and magnetic dopants like Mn with T_{c} above room temperature. One limitation of the traditional semiconductors tried up to now is the small solubility of magnetic dopants like Mn in them. To conquer this problem we, alternatively, propose the less known rocksalt structure ScN semiconductors, because it shares a common crystal structure with magnetic (or antiferromagnetic) transition metal nitrides [1]. The growth of mixed MSN alloys using molecular beam epitaxial growth technique has been reported [2]. In our study, the exchange magnetic interactions were investigated by fitting the total energies of nearestneighbor pairs of parallel and antiparallel Mn spins to a Heisenberg Hamiltonian. The interactions with near and distant cells were considered. The nearest neighbor exchange interactions can be written as We found that exchange magnetic interactions are long range and drastically affected by the randomness of the cell as was observed in other DMSs [3, 4]. The search for magnetic semiconductors with a curie temperature T_{c} above room temperature (RT) is currently one of the major issues in semiconductor spintronics [5]. For MnN, three different phases, including RS, ZB, and WZ are considered. Both ferromagnetic (FM) and antiferromagnetic (AFM) states are calculated for each compound in the three phases. The binary ScN is an RS semiconductor with inplane lattice constant ranging between 4.50 and 4.503โร , indirect band gap from X of approximately 1โeV, and a direct transition at X point of 2.1โ2.4โeV [6]. In addition, experimental studies and theoretical calculations have confirmed that ScN stabilizes in a fivefold coordinated structure called hScN [7]. On the other hand, Mn is an early transition metal and has slightly tetragonal distorted rocksalt, known as phase [8]. Thus, it is of great interest to combine MnN with ScN to yield Mndoped ScN DMSs and ferromagnetic MSN alloys. Within mean field theory, the Curie temperature has been estimated to be above 400โK for 3% Mn.
2. Methodology
Firstprinciple calculations within the framework of the density functional theory [9, 10] and spin local density approximation (SLDA) [11, 12] are performed. We employed the fullpotential linearizedaugmented planewave (FPLAPW) method as well as linearized muffintin orbital (LMTO) both in the atomic sphere approximation (ASA) and in a full potential (FP) as used in the Wien2k code [13] and WIEN97 code [14] applied to a 2atom unit cell because they allow a shift in the diagonal elements of the Hamiltonian in a straightforward manner. Therefore, they allow us to correct the LDA underestimate of the band gap. The muffintin radius adopted were 1.75โa.โu. for Mn and 1.44โa.โu. for N in MnN. The total energy and eigen values were converged to 10^{5}โeV and 10^{4}โeV, respectively. The calculations were performed with spinpolarized potentials in order to analyze the ferromagnetic phases of MnN. A โโkpoint mesh was used to ensure the convergence of Brillouin zone integrations. To study the exchange magnetic interactions as a function of MnMn pairs and the effects of carrier concentration and doping on Curie temperature, we used a 64 supercell with cutoff energy of 25โRy to ensure full convergence.
3. Results
3.1. Magnetic Stability, Magnetic Moment, and the Phase Transition in MnDoped ScN DMS and MSN Alloys
Our total energy calculations of MnN as a function of lattice constant a in RS, WZ, and ZB in Ferromagnetic (FM) and antiferromagnetic (AFM) states indicate that the global energy minimum is obtained for ZB structure. If the compound is compressed by 6%, the energy minimum corresponds to the RS structure. This result disagrees with a slightly tetragonal distorted RS structure, known as phase experimentally found for MnN binary. From the curvature of total energy as a function of a for the AFM state, we deduce a bulk modulus โGPa (see Table 1). Next, we consider the different magnetic configurations of MnN. Our results are summarized in Table 2. The energy difference between FM and AFM is โeV/atom. Previous analysis of the partial density of states has concluded that majority states are filled with three electrons and lead to localized spins [1]. This is consistent with our value for the magnetic moment of MnN (see Table 2). Having confirmed that ScNโ:โMn can behave as a DMS, we turn our attention to study the structural properties of MSN alloys. Previously, we found that ScN/GaN and ScN/InN superlattices can exhibit isostructural phase transitions (IPTs) at certain values of hydrostatic pressure (see [15] and references therein). We found that IPTs were associated with anomalies optical and piezoelectric properties. In this work, we examine the possibility of IPTs in MSN alloys. Figure 1 shows the lattice constant a of the MSN alloys as a function of the hydrostatic pressure. We started with the theoretical lattice constant of ZB MnN and experimental lattice constant of MnN, and we studied the variation of lattice constant with hydrostatic pressure. Figure 1 shows a remarkable phenomenon: from 5 to 18โGPa the lattice parameter increases by 15% indicating drastic continuous structural transformations in this pressure range. Thus, anomalous optical, piezoelectric, and magnetic properties are expected. It also indicates that this alloy undergoes a sharp prerssureinduced isostructural phase transition at a critical hydrostatic pressure of 18โGPa from the tetragonal distorted RS phase into the fivefold coordinated hScN. Since the synthesis of MSN alloys has been achieved for a wide range of Mn concentrations, we would suggest that concern experimental groups should study temperature dependence of magnetization, resistivity, and spceific heat of MSN alloys as a function of hydrostatic pressure.


3.2. Exchange Magnetic Interactions, Critical Temperatures, and the Effects of Carrier Concentration
We next focus on Mndoped ScN DMS. Figure 2 plots the nearest neighbor MnMn exchange interactions as a function of the distance in ScNโ:โMn. We found that FM configurations have lower energy than AFM state. This ferromagnetic coupling is somehow surprising when keeping in mind that the coupling in MnN is antiferromagnetic. We explain this by the fact that the larger MnMn distance will lead to less overlap between the Mn t_{2} orbitals, which favors ferromagnetic coupling, and also the nearest neighbor exchange interactions in ScNโ:โMn are much less than in the MnN binary. In order to account for the effect of randomness, we construct relatively large supercell consists of 128 atoms. Our (SLDA) results indicate that exchange magnetic interactions follow RudermanKittelKasuyaYosida (RKKY) [16, 17]. Figure 2 also indicates that strong second nearest neighbor interactions are suppressed by large exchange magnetic interactions that can be correlated with the critical temperature T_{c} by averaging J_{ij} over the various atoms in the cell. A good estimate for T_{c} can be obtained using a meanfield approximation (MF) and even a better estimate of T_{c} is obtained using the cluster variation method (CVM). For Mn concentrations up to 30%, the exchange interactions of up to four nearestneighbors are significant. The MF and CVM Curie temperatures and as functions of Mn concentration for Mndoped ScN are shown in Figure 3. It indicates that T_{c} increases with Mn concentrations and saturates above Mn concentration of 28% at a maximum T_{c} of 670โK. T_{c} above room temperatures is predicted for Mn concentration larger than 12%. Thus, ferromagnetic behavior above room temperature is possible in Mndoped ScN. It should be noted that for small concentration of Mn (6.25%) (a cell of 64 atoms) with Mn located only at first nearest neighbors with no second nearest neighbor pair had โK and โK. However, large supercells (128 atoms) with all Mn are located at second nearest neighbors with no Mn on first nearest neighbors exhibit lower values of โK and โK, respectively. Next, we consider the effects of defects affecting the carrier concentration. We can account for the effect of additional doping by simply shifting the Fermi level. Figure 4 shows as a function of electron concentration. We consider both type and type doping. Negative electron concentrations correspond to type doping, and positive values correspond to type doping. The increases and remains high up to โcm^{3} but then drops to about zero for about โcm^{3}. Such electron concentrations are rather typical for Mndoped ScN samples. At least one sample with 3% Mn was reported to show a ferromagnetic behavior up to 50โK [18]. The type doping in ScN is generated from nitrogen vacancies. Consequently, we carried out some calculations with about 10% Mn and 3% nitrogen vacancy corresponding to two per cell. The 3% corresponds to doping by about โe/cm^{3}. We found that drops by approximately 11%.
4. Conclusions
In summary, our direct supercell simulations show that Mndoped ScN is promising DMS systems with extraordinary optical, structural, and magnetic properties. By using total energy calculations, we found that global energy minimum of MnN is obtained for ZB structure. As the compound is slightly compressed, the energy minimum corresponds to the RS structure exhibiting a magnetic moment of a value of 2.52โ in disagreement with the experimental distorted RS phase found for Mn. Our calculations for the magnetic exchange interactions indicate the possibility of above room temperature T_{c} for Mn concentrations of about 10%. Our results on the effects of doping indicate that room temperature ferromagnetism is achieved by maintaining the type carrier concentration below 10^{20}โcm^{3}. Thus, the Mndoped ScN DMS is expected to be the key candidate component for life time spintronic devices. In addition, we found that MSN alloys undergo an isostructural phase transition from MnN phase to hScN at a critical hydrostatic pressure of 18โGPa. Such a transition could be associated with several anomalous properties.
Acknowledgments
The author acknowledges E. Sigmund and his research team at Brandenburg Technical University in (BTU), CottbusGermany, for useful discussions. Computational support has been provided by the Theoretical physics institute at BTU in Germany.
References
 A. Herwadkar and W. R. L. Lambrecht, โMndoped ScN: a dilute ferromagnetic semiconductor with local exchange coupling,โ Physical Review B, vol. 72, no. 23, Article ID 235207, 6 pages, 2005. View at: Publisher Site  Google Scholar
 H. A. AlBrithen, H. Yang, and A. R. Smith, โIncorporation of manganese into semiconducting ScN using radio frequency molecular beam epitaxy,โ Journal of Applied Physics, vol. 96, no. 7, pp. 3787โ3792, 2004. View at: Publisher Site  Google Scholar
 J. L. Xu, M. van Schilfgaarde, and G. D. Samolyuk, โRole of disorder in Mn:GaAs, Cr:GaAs, and Cr:GaN,โ Physical Review Letters, vol. 94, no. 9, Article ID 097201, 4 pages, 2005. View at: Publisher Site  Google Scholar
 L. Bergqvist, O. Eriksson, J. Kudrnovsky, V. Drchal, P. Korzhavyi, and I. Turek, โMagnetic percolation in diluted magnetic semiconductors,โ Physical Review Letters, vol. 93, no. 13, Article ID 137202, 4 pages, 2004. View at: Publisher Site  Google Scholar
 I. Zutic, J. Fabian, and S. D. Sarma, โSpintronics: fundamentals and applications,โ Reviews of Modern Physics, vol. 76, no. 2, pp. 323โ410, 2004. View at: Publisher Site  Google Scholar
 P. Dismukes, W. M. Yim, and V. S. Ban, โEpitaxial growth and properties of semiconducting ScN,โ Journal of Crystal Growth, vol. 1314, pp. 365โ370, 1972. View at: Google Scholar
 N. Farrer and L. Bellaiche, โProperties of hexagonal ScN versus wurtzite GaN and InN,โ Physical Review B, vol. 66, no. 20, Article ID 201203, 4 pages, 2002. View at: Publisher Site  Google Scholar
 A. Leineweber, R. Niewa, H. Jacobs, and W. Kockelmann, โThe manganese nitrides $\eta $${\text{Mn}}_{3}{\text{N}}_{2}$ and $\theta $${\text{Mn}}_{6}{\text{N}}_{5+x}$: nuclear and magnetic structures,โ Journal of Materials Chemistry, vol. 10, no. 12, pp. 2827โ2834, 2000. View at: Publisher Site  Google Scholar
 P. Hohenberg and W. Kohn, โInhomogeneous electron gas,โ Physical Review, vol. 136, no. 3B, pp. B864โB871, 1964. View at: Publisher Site  Google Scholar
 W. Kohn and L. J. Sham, โSelfconsistent equations including exchange and correlation effects,โ Physical Review, vol. 140, no. 4A, pp. A1133โA1138, 1965. View at: Publisher Site  Google Scholar
 A. D. Becke, โDensityfunctional exchangeenergy approximation with correct asymptotic behavior,โ Physical Review A, vol. 38, no. 6, pp. 3098โ3100, 1988. View at: Publisher Site  Google Scholar
 J. P. Perdew, K. Burke, and Y. Wang, โGeneralized gradient approximation for the exchangecorrelation hole of a manyelectron system,โ Physical Review B, vol. 54, no. 23, pp. 16533โ16539, 1996. View at: Google Scholar
 P. Blaha, K. Schwarz, G. K. H Madsen, D. Kvasnicka, and J. Luitz, Crystal Properties, Technische Universität, Wien, Austria, 2001.
 P. Blaha, K. Schwarz, and J. Luitz, WIEN97: A Full Potential Linearized Augmented Plane Wave Package for Calculating Crystal Properties, Karlheinz Schwarz, Technische Universität, Wien, Austria, 1999.
 V. Ranjan, S. BinOmran, L. Bellaiche, and A. Alsaad, โIsostructural phase transitions in GaN/ScN and InN/ScN superlattices,โ Physical Review B, vol. 71, no. 19, Article ID 195302, 6 pages, 2005. View at: Publisher Site  Google Scholar
 M. A. Ruderman and C. Kittel, โIndirect exchange coupling of nuclear magnetic moments by conduction electrons,โ Physical Review, vol. 96, no. 1, pp. 99โ102, 1954. View at: Publisher Site  Google Scholar
 T. Kasuya, โA Theory of Metallic Ferro and Antiferromagnetism on Zener's Model,โ Program on Number Theory and Physics, vol. 16, p. 45, 1956. View at: Google Scholar
 C. Constantin, โGrowth, Structural, Electronic and Optical Characterization of Nitride Semiconductors Grown by rfPlasma Molecular Beam Epitaxy,โ , Ph.D. thesis, Ohio University, Athens, Ohio, USA, 2005. View at: Google Scholar
Copyright
Copyright © 2009 A. Alsaad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.