A first-principles study of magnetic properties of Zn0.94Mg0.01Mn0.05O

The structural and magnetic properties of Mg/Mn-doped ZnO were investigated by the first-principles study and Monte Carlo methods (MCs). Applying magnetic force theorem (MFT) and using Kohn-Sham orbitals in the GGA-PBE scheme, the exchange coupling parameters (J) were calculated to figure out the magnetic interactions between atomic sites. Mn-Mg volume clustered (C1) ferromagnetic (FM) state was preferred; herewith, the calculated magnetic moment of Mn was 4.19μB and Mg has the highest moment value when clustered with Mn ions. Nearest Mn ions interacted antiferromagnetic (AFM) despite the increasing distance lead them to be in FM. However, AFM/FM wasoriginated from the p-d hybridization, superexchange interaction and direct exchange between distant Mn ions. In addition, the Curie temperature (Tc) was calculated as 311K using averaged magnetization and magnetic susceptibility via MC.


Introduction
Zinc oxide (ZnO) has become an important semiconductor material with a wide direct band gap of 3.37 eV and a large exciton binding energy of 60 meV at room temperature [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. ZnO crystal with wurtzite geometry is an II-VI compound semiconductor [18,19]. These features make it broadly useful in optoelectronic devicesand photoelectric applications, namely,gas sensors, transparent conductive oxides, and light-emitting devices [19][20][21][22]. In this perspective, metal oxides are particularly favorable materials used in primary technologies such as photovoltaics or solar fuel production as well as in energy storage technologies (e.g. batteries) [6,13]. Besides, ZnO can be turned into a diluted magnetic semiconductor (DMS) via doping certain concentrations of impurity atoms, especially transition metals, and gain significant magnetic properties. Ferromagnetism (FM) at room temperature (RT) provides a wide area for device applications [11,12,14,15,[23][24][25]. Since FM behavior almost induced by structural and electronic properties of a material (also ZnO), previous and latest theoretical studies focused on these features to investigate the origin of magnetism and interested properties. Xue et al found that Ni-3d and O-2p states had a strong hybridization near Fermi level in Ni-doped zinc blende (ZB) ZnO and magnetic moments mainly originated from the unpaired Ni 3d orbitals, and the O 2p orbitals contribute a little to the magnetic moments [26]. Khalid et al [11] observed shifting of Fermi level in the conduction band with increasing metal concentrations and metal-doped ZnO having ferromagnetic naturevia DFT with generalized gradient approximation (GGA). Moreover, Fedorov et al [12] reported ferromagnetism induced by intrinsic defects in ZnO (DFT-GGA). Mamamouni et al [14] focused on the electronic structure of the V-doped ZnO system using DFT resulting in Ruderman-Kittel-Kasuya-Yosida (RKKY)interaction and the atomic spin polarization of V were the key factors for the presence of ferromagnetism in V-doped ZnO system. However, at room temperature, particle size sensitive ferromagnetism was observed for ZnO nanoparticlesand oxygen vacancies playedacrucial role inthe size of the nanoparticles [15]. Cao et al [23] interested inthe electronic and magnetic properties of (Mn,Fe)co-doped ZnO within the GGA and GGA+U schemes resulting in aground state ferromagnetic ordering, which was mediated by double exchange mechanism. Electronic and magnetic properties of the Mn-doped ZnO semiconductor were calculated by the full-potential linearized augmented plane wave (FP-LAPW) method with the local spin density approximation (LSDA) and the modified Becke-Johnson (mBJ) potentialconsidering magnetic interaction between the Mn atoms, both the near and far positions exist [24]. Recently, El Haimeur et al [25] investigated the optical, electronic, and magnetic properties (Curie temperature, magnetic moment) of Zn 1-x M x O (M=Fe 5%, Co 1%, Cr 5%, and Mn 5%) by KKR method and deduced that TM impurities induce ferromagnetism with the Curie temperature closer to roomtemperature. In contrast, Liu et al [27] reported that Mn-doped ZnO exhibited antiferromagnetism, only Co-Mnco-dopedZnO possessed high Tc of better ferromagnetism rather than Co or Mn-doped ZnO. Gallegos et al [28] showed that magnetic moment lowered by the presence of oxygen vacancies, which could lead to a phase transition from FM to AFM. According to Goumrhar et al [29], 6% Mn doping caused ferromagnetic behavior, which was originated from double exchange interaction, p-d hybridization. On the other hand, Mg doping to ZnO increased bandgap [30][31][32]. Singh and Chae [33] showed that nanoparticles of MgO exhibited ferromagnetism and improved optical and dielectric behavior. Chen et al [34] showed that under external electric field, was used to tune magnitude of band gap and band dispersion, ZnMgO monolayer isa direct band gap semiconductor [30]. Özgür et al [4] calculated the band gap of ZnMgO as 3.37 eV and showed that their results were consistent with the experimental results.
Present work presents a relatively wide content focused on the magnetic properties through structural analysis of Zn 0.94 Mg 0.01 Mn 0.05 O based on the experimental data. Structural information and magnetic moments of four distinct distributions of dopants (Mg/Mn) as surface cluster (L1)/surface non-cluster (L2), volume cluster (C1), and volume non-cluster (C2) were obtained by performing density functional theory calculations (DFT) with the generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) scheme. The magnetic force theorem (MFT) was used to calculate exchange couplings J, between atoms in lattice sites. Thus, the most favored magnetic state was determined and the origin of magnetism was revealed. Finally, a fastened procedure was applied to calculate the Curie temperature (T c ) by Monte Carlo methods based on the Metropolis algorithm since RT ferromagnetism was demanded materials.

Computational details
The effects of dopant concentration and site positioning of impurity ions to magnetic behavior were determined by performing first-principles calculations using the OpenMx 3.8 package [35]. Two main modes, namely, volume and surface cases, were devised to modestly specify the most preferable formation of doped structure. Such an exertion would provide essential information about the distribution tendency of the impurity atoms either layered or cubed. Besides, the nearest neighboring of Mn ions as clusters point out the Mn-O-Mn bonding while only Zn-O-Mn bonding should be apparent for the parted Mn ions. Previous studies showed that clustering of doped atom is preferable in contrast to unclustered/randomly distributions (for ZnNiO [36][37][38][39][40][41]; for ZnMnO [24,[27][28][29][42][43][44][45][46][47]; for ZnMgO [4, 30-34, 40, 48]; for ZnCrO [25,49]; for ZnCoO [27,29,37,47,50]  GGA was used in the Perdew-Burke-Ernzerhof (PBE) [55] scheme for exchange-correlation function assigning SCF criteria as 1.0E-7 Ha and k-points has been set to 12×12×4 for Monkhorst-Pack grid [56] restricting the energy range of density of states between −20 and 20 eV. However, AFM and FM phases were investigated dealing with collinear spins along c direction neglecting spin-orbit interaction due to its trivial contribution to the current structure. We determined exchange coupling constants, J ij , between strongly localized moments of different atomic sites by a magnetic force theorem [57] since total energy could not be known in advance. For a better magnetic characterization of many-particle systems, Heisenberg model can be used with predetermined exchange coupling constants which can be obtained via DFT calculations. Lack of direct experimental measurement, in particular, to determine these parameters, several approaches took place [58][59][60][61][62] and one of them was based on LDA through magnetic phase states (MTS) which were detailed by Zeng et al [58] in a theoretical manner. Boukhvalov et al [59] reported a Hubbard correction (U) included the LDA method, namely, LDA+U to handle Heisenberg exchange coupling parameters (J) more realistic. They calculated effective J parameters for Mn clusters. A Green's function formalism was developed in order to be applicable to a non-orthogonal basis set, on account of a better estimation of exchange couplings. Equation (1), which was arisen from rigid spin approximation (RSA) applied to DFT ground state [42][43][44][45], was used to calculate J ij between i and j sites where Gij denotes the Kohn-Sham orbital states related spin-dependent single-particle Green's function, and V ij is the exchange interaction potential [63].

Results and discussions
ZnMgMnO supercell (P6 3 mc space group) was constructed based on experimental lattice parameters (given in table 1) via packaging 5×5×2 of the ZnO unit cell having totally 200 atoms. Mn and Mg concentrations were fixed to 5% and 1%, respectively during simulations. Composition with optimized Mn/Mg positions in hexagonalstructure to total energies was also given in table 1 and figure 1. L1, L2, C1, and C2 are labels set to represent cluster/non-cluster surface layers and cubed volume distributions. Only Mn cluster with Mg cluster/ non-cluster distribution was adequately built to investigate the electronic and magnetic properties due to a common assent, which suggested that the behavior of dopant ions was clustering in a host material. The energy difference ΔE=E AFM -E FM of these structures indicates that the favorable magnetic phases are either ferromagnetic (FM) or antiferromagnetic (AFM). (ΔE) L1 =1.947 meV and (ΔE) L2 =4.60 meV refer to an FM ground state for both surface layered distributions; herewith, non-clustered Mg possessed a bigger energy difference. In C1 and C2 cases, (ΔE) C1 and (ΔE) C2 were found to be 11.6 meV and 6.5 meV, respectively. Note that ΔE of volume distributions was higher than surface ones; in fact, volume clustering had the highest value comparing with the rest of the studied distributions. In addition, since physical properties are mostly related to structural content, bond angles and bond lengths were calculated by a self-coded script importing geometry optimized L1, L2, C1, and C2 crystallographic data (see tables 2 and 3). Bond angles and standard deviation of optimized geometries were calculated by averaging angles for each species existing in ZnMgMnO the structure including standard deviation per means of bond angles. The interdependency of these angles and lengths determines the variety of the exchange interactions, both directly and indirectly, due to the electronic occupancy of atomic orbitals. Thus, the hybridizing of certain ones (p-d) should control the atomic magnetic behavior of the system that is induced by the structural properties of materials like bond angles. According to table 3, label (2) and label (8) bond angles did not exist in the L2 and C2 distributions due to the distant position. Even though, one does not have a piece of exact information, in which atoms make certain bonds to dramatically contribute tothe magnetic phase of the system. Indirect exchange mechanisms, in particular, superexchange and double exchange determining magnetic behavior, ferromagnetic or antiferromagnetic, naturally occurred through A-O-B like triple bounded via oxygen (A and B should be the different ion of the same atom or totally different atoms) [65][66][67].
Averaged bond angles were shown in figure 2 Figure 3 illustrates the A-C bond length corresponding to the A-B-C bond angle with a linear fit. Note that variation in bond angle may not affect the bond length of any third-part atom which is bounded to B. As shown in figure 3, one can deduce that existence of Mn ions distinguishably reduces not only reduce bond angles and bond lengths but also lead to Mn-Mn direct coupling (see Mn-O-Mn and O-Mn-O data). However, other couplings and bonds including also Mg can be seen as a part of a fingerprint-like distribution that forms the 'spinal' of the system; besides, L1, C1 and L2, C2 resemble each other.
Orbital and total magnetic moments were obtained in terms of μB from spin-polarized DFT calculations point out the effect of clustering and non-clustering configurations even surface and volume type. In case of C1, the magnetic moment of Mn, Mg, Zn, and O were found to be 4.197248666 μB, 0.020923716 μB, 0.003242702 μB, and 0.017441612 μB, where Mn is the main contributor mostly from all five d-orbitals that almost possessed equal values. Similar results were obtained from other configurations. Mg of C1 or L1  4).  Further magnetic properties were investigated via calculating J exchange coupling constants between host and guest atoms to reveal direct and indirect exchange interactions, especially superexchange, double-exchange, and orbital hybridizations which lead the material gain ferromagnetic (including ferrimagnetism) behavior because of impurity atoms. Since C1 possessed the most stable ferromagnetism, we calculated J values only for this state. Bond lengths, the sign of exchange interaction (AFM/FM), and J values aregiven in table 4. Besides, detailed information on distance and neighboring oxygen type reveals the correlation between structural property and magnetic behavior; in fact, orbital hybridizations and indirect mechanisms should be appropriately explained. One can remember that there are 5 Mn atoms in which 4 of them were located around an Mn atom in cubed volume configuration. 2.99412 Å and 2.98579 Å distant Mn-Mn pairs showed strong AFM  The bond length of Mg-Mn neighboring oxygen couple is evidently longer than Mg-Zn neighboring oxygen couple and AFM interaction exists between Mg-O even Mn mediated a more energetic exchange value relative to Zn. However, Mn-O has an FM type interaction whose strength decreases in direct proportion with increasing distance between these atoms. FM interaction shows dominancy against AFM(10 times larger) when only MgO and MnO couples are compared. On the other hand, when the bond angle of Mn-O-Mn was increased, AFM interaction weakened up to nearly 7 times except fordistant Mn ions in which FM interaction exists. However, magnetic strengths of Mg-Mn couples were found to be high as distant Mn-Mn pairs. Mg which was bonded to Zn oxygen (Mg-O b,c ) and Mg-Zn, slightly contributed to the exchange mechanism of the whole system as AFM and FM state, respectively.
The intriguing nature of DMS materials, which are constructed by doping 3d or 4f TM elements forming impurities or pioneering vacancies, provided many question marks about the origin of magnetism. Several models such as p-d hybridization, superexchange, double exchange, Zener-RKKY, were suggested to make clear the origin of ferromagnetism, especially in TM doped semiconductors [1,[69][70][71][72] including nanowires [73,74].   table 4). The abovementioned interactions commonly formed the magnetic behavior of the system, FM was preferred; however, several magnetic states exactly existed in the same system. In the light of obtained magnetic moment (μ B ) and exchange couplings (J) from DFT, magnetic susceptibility (to determine T c ) of nanoparticles which are built on geometry optimized ZnMgMnO supercell, were calculated via Markov Chain Monte Carlo (MCMC) methods based on the Metropolis algorithm detailed in Duru et al [41]. Thus, transition temperature as a primary parameter for the application of magnetic materials in the device world, namely daily life, was determined by Heisenberg Hamiltonian expressed in equation (2).
where S i and S j represent the nearest neighboring spins interacting with each other with J ij (r ij ) exchange energy and B is the applied field. |S α |was set to 1 and calculated J values (calculated by MFT) were used during the simulation. The thermal equilibrium process took 40% of total MC steps and elapsed time for expectation values was 60% at temperature (T). As shown in figure 6, magnetization versus temperature (M-T) and susceptibility measurements were taken starting from 1 K to 800 K andthe Curie temperature of Zn 0.94 Mg 0.01 Mn 0.05 O was found as 311 K, and it is a meaningful value, which is close to room temperature. It is obvious that nanoparticle shows FM behavior directly related to calculated exchange couplings between site atoms below 311 K. Note that distant Mn-Mn pairs (>5.8) contributed to FM while AFM behavior started to show up when they come closer. Thus, relatively big nanoparticles would possess FM like behavior in contrast to slightly small ones. Note that, in a previous study, a non-linear intriguing relation between size and magnetic behavior was found [41]. Mg-O pairs contributed to AFM state whereas Mg-Mn pairs interacted FM. This was the reason that why clustered Mg with Mn structure (C1) was preferred to be in FM state.

Conclusion
The structural and magnetic properties of Mg/Mn-doped ZnO were investigated by the first-principles study and Monte Carlo methods (MCs). Applying magnetic force theorem (MFT) and using Kohn-Sham orbitals in the GGA-PBE scheme, the exchange coupling parameters (J) were calculated to figure out the magnetic interactions between atomic sites one by one. According to geometry optimization of four different configurations as surface/volume clustered Mn and clustered/non-clustered Mg  determine T c of Mg/Mn-doped ZnO nanoparticle via measuring averaged magnetization and magnetic susceptibility. The Curie temperature T c was found as 311 K, which is absolutely above the room temperature.