Calculating the Curie temperature reliably in diluted III-V ferromagnetic semiconductors

Abstract

We present a semi-analytic theory for the Curie temperature in diluted magnetic semi-conductors that treats disorder effects exactly in the effective Heisenberg Hamiltonian, and spin fluctuations within a local RPA. The exchange couplings are taken from concentration dependentab initio estimates. The theory gives very good agreement with published data for wellannealed samples of Mn x Ga 1−x As. We predict the critical temperatures for Mn x Ga 1−x N lower than in doped GaAs, despite the stronger nearestneighbour ferromagnetic coupling. We also predict the dependence on the hole concentration.Search for diluted magnetic semiconductors with ferromagnetism stable to high temperatures has been hampered by the many physical parameters that may determine magnetic properties. These include the choice of host semiconductor, that of the doping magnetic impurity, the degree of compensation, and methods of preparation and treatment of the sample [1]. The underlying mechanism of interaction between dopant spins has without doubt been correctly identified: Ruderman-Kittel-Kasuya-Yosida(RKKY)-like effective interactions mediated by both the host [2,3] and the doping band [4-6]. Despite this, the theory has not lead to reliable quantitative predictions. Comparison of calculations has been complicated by difficulties of full characterizing the samples. In samples of GaAs doped with Mn, extensive experimental studies [1] have now allowed for greater control over sample parameters and there is now apparently convergence to reliable experimental values of the critical temperature of different groups [7-10]. An important factor was that the carrier densities were measured simultaneously by magneto-transport. There is now the possibility of testing calculations against experiments and determining the origin of past discrepancies.Ab initio calculations using the Local Density Approximation and the magnetic force theorem can be used [5] to derive realistic values of magnetic exchange interactions between classical impurity spins. These calculations also take into account the effect on the effective exchange of disorder of the carriers, within a Coherent Potential Approximation (CPA). Similar calculations based on supercells [12,13] lead to comparable results at low concentration. It has become apparent that the difficulty is not in deriving the effective magnetic Hamiltonian correctly but in treating its thermodynamics accurately. As we will demonstrate explicitly here, treating the magnetic correlations by over-simplified mean field theories [14,15] has lead to overstatement , by a wide margin, of the critical temperature T c . The disorder in the effective magnetic model also plays an important role that cannot be simply treated by an effective medium theory of the style of the Virtual Crystal Approximation (VCA) [16]. This suggests that the discrepancy with experiment is largely due to approximations made to the effective Hamiltonian, not the values of the couplings themselves. Thus by improving the treatment of the effective Hamilt...

Exchange interactions, spin waves, and transition temperatures in itinerant magnets

“…The calculated exchange interactions for two Fe impurities in an fcc Au host are shown in figure 6 (inset in the left panel). The values of J RR for impurities along the nearest-neighbour direction [110] (which gives the dominating contribution to exchange interactions in this case) were multiplied by the cube of the interatomic distance in order to illustrate the RKKY asymptotics for large distances (figure 6, inset in the right panel). However, it takes a few oscillations (a preasymptotic regime) before the asymptotic value of the oscillation amplitudes is reached.…”

“…Both formulations are rather complicated which allowed to perform numerical calculations for environmental disorder limited to nearest neighbours only, but they seem promising for future studies with true long-range interactions. The disorder can be taken into account exactly by Monte Carlo simulations using large simulation cells which can describe fluctuations beyond any effective-medium approach [24]; the combined effect of magnetic and chemical fluctuations can also be included within a real-space RPA [110].…”

Compensation, interstitial defects, and ferromagnetism in diluted ferromagnetic semiconductors

“…The new element we are bringing here, is a quantitative theory for the Curie temperature, which as we shall explain below, is much more accurate than Zener mean-field theory. We note that in ref [9] we anticipated the fact that the changes in the carrier density due solely to anti-sites were insufficient to explain the reduction of T C .…”

Spin diffusion in bulk GaN measured with MnAs spin injector

“…The wide-band-gap III-V semiconductor GaN, which generally crystallizes in the hexagonal wurtzite (w) structure, has gathered much interest as a promising material for spintronics due to its room temperature ferromagnetism when doped with rare-earth metals (e.g., manganese), 1 and also its weak spin-orbit coupling (SOC) which results in long spin-relaxation times. GaN also shows attractive optoelectronic properties in the visible spectrum range, making it suitable for spin-light emitting diodes (spinLEDs) and lasers.…”