Low-temperature ferromagnetism in (Ga, Mn)N: Ab initiocalculations

Abstract

The magnetic properties of dilute magnetic semiconductors (DMSs) are calculated from first-principles by mapping the ab initio results on a classical Heisenberg model. By using the Korringa-Kohn-Rostoker coherent-potential approximation (KKR-CPA) method within the local-density approximation, the electronic structure of (Ga, Mn)N and (Ga, Mn)As is calculated. Effective exchange coupling constants J ij 's are determined by embedding two Mn impurities at sites i and j in the CPA medium and using the J ij formula of Liechtenstein et al. [J. Magn. Magn. Mater. 67, 65 (1987)]. It is found that the range of the exchange interaction in (Ga, Mn)N, being dominated by the double exchange mechanism, is very short ranged due to the exponential decay of the impurity wave function in the gap. On the other hand, in (Ga, Mn)As, where p-d exchange mechanism dominates, the interaction range is weaker but long ranged, because the extended valence hole states mediate the ferromagnetic interaction. Curie temperatures (T C 's) of DMSs are calculated by using the mean-field approximation (MFA), the random-phase approximation, and the, in principle exact, Monte Carlo method. It is found that the T C values of (Ga, Mn)N are very low since, due to the short-ranged interaction, percolation of the ferromagnetic coupling is difficult to achieve for small concentrations. The MFA strongly overestimates T C . Even in (Ga, Mn)As, where the exchange interaction is longer ranged, the percolation effect is still important and the MFA overestimates T C by about 50%-100%. Dilute magnetic semiconductors (DMSs), such as (In, Mn)As and (Ga, Mn)As discovered by Munekata et al. and Ohno et al., have been well investigated as hopeful materials for spintronics. 1 Curie temperatures (T C 's) of these DMSs are well established 1-3 and some prototypes of spintronics devices have been produced based on these DMSs. The magnetism in these DMSs are theoretically investigated and it is known that the ferromagnetism in these systems, as well as (Ga, Mn)Sb, can be well described by Zener's p-d exchange interaction, due to the fact that the majority of d states lies energetically in the lower part of the valence band.4 Dietl et al. 5 and MacDonald et al. 6 explained many physical properties of (Ga, Mn)As based on the p-d exchange model, and first-principles calculations by Sato et al. showed that the concentration dependence of T C in (Ga, Mn)As was well understood by the p-d exchange interaction if a correction to the local-density approximation (LDA) is simulated by the LDA+ U method with U = 4 eV. 4 While these p-d exchange systems, in which the d states of Mn impurities are practically localized, are well understood, there exist an even larger class of systems where the d levels lie in the gap exhibiting impurity bands for sufficiently large concentrations. To these impurity band systems belong (Ga, Mn)N, (Ga, Cr)N, (Ga, Cr)As, (Zn, Cr)Te, (Zn, Cr)Se, and many others, as shown by first-principles calculations. 7Most of these systems are controversially discussed ...

Ferromagnetism in nitrogen-doped MgO: Density-functional calculations

“…We confirmed this by calculations ͑not shown here in detail͒ of the total energy of the ferromagnetic state, E ferro , versus the disordered-localmoment state energy, E DLM ; the latter is represented in the CPA by an alloy of the type MgO 1−x N 0.5x ↑ N 0.5x ↓ , where N ↑ and N ↓ are impurities with magnetic moment pointing "up" and "down." 22 As is typical for double-exchange DMS systems, 16 we found that the energy gain of the ferromagnetic state, E DLM − E ferro , scales with the square root of the concentration. Further confirmation on the ferromagnetic nature of the ground state comes from calculations of the exchange constants, to be presented in the next section.…”

“…[16][17][18] The scope of this paper is to investigate the appearance and stability of the ferromagnetic state, including calculations for the Curie temperature, in MgO 1−x N x compounds for x Ͻ 15%, in view of recent experimental activities with respect to the particular system. 19 Our focus is on the solution provided by local density-functional theory ͑DFT͒, presented in Sec.…”

Disorder and the effectiveMn−Mnexchange interaction inGa1−xSilva1, Fazzio2, Santos3 et al. 2005Phys. Rev. B15150View full textAdd to dashboardCite

“…18,19,20,21,22,23,24,25,26 Some predict an alternating sign for the exchange coupling, but these predictions should be taken with extreme care, since these theoretical calculations are based on non-fullpotential muffin-tin-type potentials which are not reliable to treat the electronic structure of covalent semiconductor systems such as (Ga,Mn)As DMS. Also, disorder quite certainly is not adequately taken into account within simple effective-medium approaches such as VCA or CPA, as fluctuations in the Mn positions essentially lead to variations in the Mn-Mn exchange-coupling parameters, as apparent from Fig.…”

“…In a series of theoretical studies, in which the effect of randomness/disorder is described by the coherent-potential approximation (CPA), Kudrnovský et al 19,20 and Bergqvist et al 21 have used a tight-binding linear muffin-tin orbital method, together with the magnetic force theorem, to study the dependence of the Mn-Mn exchange couplings and critical temperatures with the concentration of Mn impurities in III-V and group IV DMS. Also, Sato et al 22,23 have used muffin-tin type potentials together with a KKR-CPA approach to study Curie temperatures and exchange interactions in III-V DMS. Moreover, Sandratskii and Bruno 24,25,26 have used the augmentedspherical-wave method within the local-density approxi-mation to investigate exchange interactions, Curie temperatures and the influence of the clustering of Mn impurities in (Ga,Mn)As.…”

Role of conduction electrons in mediating exchange interactions in Mn-based Heusler alloys

“…Indeed, a large number of first-principles calculations showed that these materials have very high Curie temperatures. [87][88][89][90][91][92][93] As mentioned in preceding part, the direction of the conduction electron spin polarization with respect to the local moment and its amplitude are important in classifying ferromagnets. From the obtained results, the full-Heusler alloys can be characterized as weak ferromagnets since the spin polarization is negative for all Z constituents, i.e., sp-d mixing is dominating.…”