Three-dimensional Heisenberg critical behavior in the highly disordered dilute ferromagnetic semiconductor (Ga,Mn)As - Wang, Mu; Marshall, Robin Alexander; Edmonds, Kevin W.; Rushforth, A.W.; Campion, R.P.; Gallagher, B.L. (American Physical Society, 2016)
We present detailed studies of critical behavior in the strongly site-disordered dilute ferromagnetic semiconductor (Ga,Mn)As. (Ga,Mn)As has a low saturation magnetization and relatively strong magnetocrystalline anisotropy. This combination of properties inhibits domain formation, thus removing a principal experimental difficulty in determining the critical coefficients β and γ. We find that there are still a large number of problems to overcome in terms of measurement procedures and methods of analysis. In particular, the combined effects of disorder and inhomogeneity limit the accessible critical region. However, we find that accurate and reproducible values of the critical exponents β and γ can be obtained from Kouvel-Fisher plots of remanent magnetization and magnetic susceptibility for our (Ga,Mn)As samples. The values of β and γ obtained are consistent with those of the three-dimensional Heisenberg class, despite the very strong disorder present in this system, and they are inconsistent with mean field behavior. Log-log plots of M(H) data for our samples are consistent with the three-dimensional Heisenberg value of the critical exponent δ, but accurate values of δ could not be obtained for our samples from these plots. We also find that accurate values of the critical exponent α could not be obtained by fitting to the measured temperature derivative of resistivity for our samples.We find that modified Arrott plots and scaling plots are not a practical way to determine the universality class or critical exponents, though they are found to be in better agreement with three-dimensional Heisenberg values than mean field values. Below the critical temperature range, we find that the magnetization shows power-law behavior down to a reduced temperature of t ∼ 0.5, with a critical exponent β ∼ 0.4, a value appreciably lower than the mean field value of β = 0.5. At lower temperatures, Bloch 3/2 law behavior is observed due to magnons.