We present a theory of magnetic anisotropy in III 1Ϫx Mn x V-diluted magnetic semiconductors with carrierinduced ferromagnetism. The theory is based on four-and six-band envelope function models for the valenceband holes and a mean-field treatment of their exchange interactions with Mn ϩϩ ions. We find that easy-axis reorientations can occur as a function of temperature, carrier density p, and strain. The magnetic anisotropy in strain-free samples is predicted to have a p 5/3 hole-density dependence at small p, a p Ϫ1 dependence at large p, and remarkably large values at intermediate densities. An explicit expression, valid at small p, is given for the uniaxial contribution to the magnetic anisotropy due to unrelaxed epitaxial growth lattice-matching strains. Results of our numerical simulations are in agreement with magnetic anisotropy measurements on samples with both compressive and tensile strains. We predict that decreasing the hole density in current samples will lower the ferromagnetic transition temperature, but will increase the magnetic anisotropy energy and the coercivity.
We report on a theoretical study of dc transport coefficients in (Ga,Mn)As diluted magnetic semiconductor ferromagnets that accounts for quasiparticle scattering from ionized Mn 2+ acceptors with a local moment S = 5/2 and from non-magnetic compensating defects. In metallic samples Boltzmann transport theory with Golden rule scattering rates accounts for the principle trends of the measured difference between resistances for magnetizations parallel and perpendicular to the current. We predict that the sign and magnitude of the anisotropic magnetoresistance can be changed by strain engineering or by altering chemical composition.
We apply the theory of elasticity to study the effects of Skyrmion mass on lattice dynamics in quantum Hall systems. We find that massive Skyrme lattices behave like a Wigner crystal in the presence of a uniform perpendicular magnetic field. We make a comparison with the microscopic Hartree-Fock results to characterize the mass of quantum Hall skyrmions at ϭ1 and investigate how the low temperature phase of Skyrme lattices may be affected by the Skyrmion mass.
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