Journal of Magnetism and Magnetic Materials 272–276 (2004) 351–352 Effect of spin-polarized subbands in the inhomogeneous hole gas providing the indirect exchange in GaMnAs bilayers M.A. Boselli a, *, I.C. da Cunha Lima a , A. Ghazali b a Instituto de F! ısica, Universidade do Estado do Rio de Janeiro Rua S * ao Francisco Xavier 524, 20.500-013 Rio de Janeiro, R.J., Brazil b Groupe de Physique des Solides, CNRS, Universit ! es Paris 6 et Paris 7, F-75 251 Paris Cedex 05, France Abstract The magnetic order resulting from the indirect exchange in the metallic phase of a (Ga,Mn)As/GaAs double layer structure is studied via Monte Carlo simulation. The polarization of the hole gas is taken into account, establishing a self-consistency between the magnetic order and the electronic structure. The Curie–Weiss temperatures calculated for these low-dimensional systems are in the range of 50–80 K; and the dependence of the transition temperature with the GaAs separation layer is established. r 2003 Published by Elsevier B.V. PACS: 75.50.Pp; 75.10.Nr; 75.70.Cn Keywords: Diluted magnetic semiconductor; (Ga, Mn)As; Spintronics The ferromagnetic order in the metallic phase of (Ga,Mn)As [1] is understood as resulting from the indirect exchange between the Mn ions due to the local spin polarization in the hole gas. Here, a Monte Carlo simulation is performed to determine the resulting magnetic phases in a structure consisting of two thin layers of metallic (Ga,Mn)As imbedded in a GaAs host. A confinement-adapted RKKY-like exchange is as- sumed, provided by the interaction of the localized magnetic moments of the Mn ions with a spin-polarized hole gas through a Kondo-like sp–d interaction [2]. A bilinear interaction term, taking into account the polarization of hole gas can be obtained in a second-order perturbation expansion as an effective Hamiltonian H eff ¼ X i;j ðC mm ij þ C kk ij ÞS z i S z j þðC mk ij þ C km ij ÞðS x i S x j þ S y i S y j Þ: ð1Þ The upper and lower indices denote spin components and positions, respectively, and the vertical arrows the spin states. The exchange coefficients C mn ij are expressed in terms of the eigenenergies e n;k and z-eigenfunctions f n ðzÞ at the Mn sites ðz i ; R i Þ: C mn ij ¼ X nAm X n 0 An X q I 2A   2 f à n 0 ðz i Þf n ðz i Þ  f à n ðz j Þf n 0 ðz j Þw n;n 0 ðR ij Þ ð2Þ with w n;n 0 ðR ij Þ being the real space Fourier transform of the Lindhard function. The heavy hole single band electronic structure is obtained self-consistently, assuming that holes interact with a uniform magnetization (identified with the average magnetization of the DMS layers). The model Hamiltonian contains the kinetic energy, the Hartree term and the interaction with the magnetic layers through a configurational averaged Kondo term [3]. According to the Metropolis algorithm at a given temperature, the energy of the system of Mn ions is calculated, and the equilibrium state for a given temperature is sought by changing the individual magnetic moment orientation. A slow cooling stepwise process is accomplished, making sure that the thermal equilibrium is reached at every temperature. Whenever the magnetization reaches thresholds of multiples of ARTICLE IN PRESS *Corresponding author. Instituto de F! ısica, Universidade de S * ao Paulo, CP 66318, 05315-970 S * ao Paulo, SP, Brazil. E-mail address: boselli@uerj.br (M.A. Boselli). 0304-8853/$ - see front matter r 2003 Published by Elsevier B.V. doi:10.1016/j.jmmm.2003.11.383