Session K19: Focus Session: III-V Magnetic Semiconductors III

Exchange interactions of DMS alloys in the GW approximation

Dilute Magnetic semiconductors are a new but little understood class of materials, and in particular the origin of ferromagnetism in these materials. As we will show, the LSDA combined with the rigid-spin approximation fails to predict the observed magnetism in many of these materials, and a key question is whether the failing is due to the approximations made, or is something else going on? The best understood of DMS is zincblende Mn$_x$Ga$_{1-x}$As, with $x\tilde{<}0.1$. Optimally grown thin films have been recently shown to exhibit conventional temperature-dependent magnetization behavior with $T_c\sim{}170$K. Using a standard LDA linear-response technique the LSDA total energy is mapped analytically onto a Heisenberg hamiltonian, which is analyzed for random and partially ordered structures. Temperature-dependent properties were investigated using a form of the Cluster Variation method for the Heisenberg model. The calculated $T_c$ is predicted to increase with $x$ to $x$=15\%, reaching $T_c\sim$250K. For still larger $x$, $T_c$ is predicted to fall and turn antiferromagnetic when $x${}$>$50\%. Clustering and spin-orbit coupling are both found to reduce $T_c$. Thus in this case the theory falls in good agreement with observed values for low concentration. An analysis shows the Mn $e_g$ levels are responsible for the antiferromagnetic contribution. We show that suitable short-period superlattices can minimize this contribution, thus signficantly enhancing $T_c$. Many other less well studied DMS alloys--particularly nitride and oxide compounds--have now been reported with $T_c$ exceeding 300K. Several of these cases were investigated, and the LSDA linear-response predicts low $T_c$, typically $T_c<100$K. Moreover, the LDA results for Mn$_x$Ga$_{1-x}$As at large $x$ are at variance, with observed ferromagnetism in a quantum dot of MnAs in the zincblende phase[1]. To address validity of the LSDA+rigid approximation, a we present results from a recent implementation of self-consistent {\em GW} calculation of the spin susceptibility. As will be described {\em GW} alters the exchange parameters in even in elemental transition metals, and the changes in transition metal compounds can be dramatic. $^1$K. Ono et al, J. Appl. Phys. {\bf 91}, 8088 (2002).   

Combinatorial design of high-temperature ferromagnetic semiconductors from first principles

The Curie temperature $T_C$ of Mn-doped GaAs depends strongly on the arrangement of the substitutional Mn dopants. For example, the highest $T_C$ reported so far was attained in thin GaMnAs layers embedded in GaAs. However, an exhaustive search of all possible configurations to find those that maximize $T_C$ is difficult, due to the astronomically large number of possibilities. Here we address this problem by parametrizing the Curie temperature of a set of $\sim$ 50 input configurations, calculated from first principles using linear-response theory and Monte Carlo simulations, in terms of configuration variables (“cluster expansion”). Once established, this expansion allows us to search almost effortlessly the Curie temperature of arbitrary configurations of Mn dopants in GaAs. We find that the highest $T_C$ ($>$350K) is achieved for (GaAs)$_m$/(MnAs)$_n$ superlattices in the (201) crystallographic orientation, with (m,n)=(4,1). Our general approach of cluster expanding {\it electronic or magnetic properties} of complex systems opens the way to first-principles combinatorial design of materials with prescribed transition temperatures. This work was supported by DARPA, under NREL contract No. DEAC36-98-GO10337.   

First-principles study of the effects on ferromagnetic coupling in Mn/GaAs digital ferromagnetic heterostructure by free holes Injection and Be co-dopant

We use density functional theory to study the effect of free holes injection and Be co-dopant on the ferromagnetic coupling in Mn/GaAs digital ferromagnetic heterostructure (DFH). The injection of free holes is simulated by assigning a range of concentrations of missing electrons in unit cell. The $\delta$-layer doping of Mn atoms in GaAs introduces three spin-polarized hole bands which are the consequence of hybridization between the $d$-states of the Mn atoms and the $p$-states of the nearest neighboring As atoms. The distribution of hole charge density shows that these spin-polarized holes are confined to the vicinity of the Mn $\delta$-layer. After the injection of free holes, the Fermi energy E$_{F}$ is lowered, then the number of spin-polarized holes in the layer of MnAs is increased monotonously. We characterize the ferromagnetic coupling by the total energy difference between the ferromagnetic and the antiferromagnetic phases , E$_{FA}$, per one pair of Mn atoms. The results of E$_{FA}$, E$_{F}$, and the projected spin-polarized holes at Mn and the nearest neighboring As atoms are shown as a function of concentration of the injected free holes. We demonstrate the enhancement of the ferromagnetic coupling, which is in agreement with the experimental results of Nazmul et al.$^{[1]}$. In contract, after the Be co-dopant in Mn/GaAs-DFH, the ferromagnetic coupling is deteriorated. We will give the explanation. [1] A. M. Nazmul et at. Phys. Rev. B67, 241308(R) (2003).   

Mn doped InP nanowires: An ab initio study

We investigated the electronic and magnetic properties of Mn doped InP nanowires. Our study was based on total energy density functional calculations. The Mn dopants were placed substitutionally in In atom sites. We have found that the most energetically favorable position for the Mn atom is near the surface. However, a small amount of Mn atoms will be located at ``bulk-like'' positions in the wire. When the Mn atoms are in ``bulk-like'' positions, the Mn-3d majority-spin-orbitals appear in two different regions of the valence band (VB): about 2.0 eV below the top of the VB and resonant with the top of the VB. In these cases there is also an empty orbital in the gap whit p-character. The total valence spin-densities ($\rho_{\uparrow} - \rho_{\downarrow}$), for a single Mn atom in any of the configurations studied here, show a strong localized magnetic moment around the Mn atom site. In order to study the magnetic coupling we also did calculations with two Mn atoms in each cell. For several configurations studied, we concluded that if both Mn atoms are in ``bulk-like'' positions the system presents ferromagnetic ordering. On the other hand, if at least one of the Mn atoms is located near the surface, there is no magnetic ordering or the system is antiferromagnetic.   

Ab-initio Prediction of Conduction Band Spin Splitting in Zincblende Semiconductors

We use a recently developed self-consistent $GW$ approximation to present systematic \emph{ab initio} calculations of the conduction band spin splitting in III-V and II-V zincblende semiconductors. The spin orbit interaction is taken into account as a perturbation to the scalar relativistic Kohn-Sham hamiltonian. These are the first calculations of conduction band spin splittings based on a quasiparticle approach. We show that the self-consistent $GW$ scheme accurately reproduces the relevant band parameters, and is therefore expected to be a reliable predictor of spin splittings. The results are compared to the few available experimental data and a previous calculation based on a model one-particle potential. We show that the commonly used ${\bf{}k}\cdot{\bf{}p}$ hamiltonian is missing contributions, and cannot reliably reproduce the splittings.   

Microscopic Hamiltonian for dilute magnetic semiconductors

We formulated a real space Hamiltonian to study the effect of dilute magnetic doping of III-V semiconductors. A p-type valence band is considered and nearest neighbor hopping of holes in a diamond lattice is allowed. The relevant hopping parameters between orbitals are obtained using the Slater technique. Considering the effects of the spin-orbit interactions the number of degrees of freedom per site is reduced from 6 (3 orbitals and two spin orientations for the p bands) to 4 (the four projections corresponding to j=3/2 which is the quantum number of the heavy and light hole bands). The ferromagnetic interaction between the doped magnetic impurities and the spin of the mobile holes is written in the appropriated base. The numerical values of the hopping parameters and Hund interaction are obtained from the literature for the different compounds and, thus, there are no free parameters. The properties of the materials are calculated using numerical techniques. The newly developed TPEM method allows us to consider lattices as big as 6x6x6 cubes containing 8 ions each. Finite size effects are very small when systems larger than 3x3x3 cubes are considered. For Mn doped GaAs we reproduce the experimentally observed Curie temperatures for all the studied values of effective hole dopings. For Mn doped GaN our results predict above room temperature Tc's.   

Electron-mediated ferromagnetism and negative $s-d$ exchange splitting in semiconductors

Magnetic semiconductors have many unique physical properties that can be used for magneto-optical and spintronic applications. Currently, most of the studies on magnetic semiconductors are focused on hole-mediated FM systems. In this work we discuss several approaches that can enhance the spin- splitting at the conduction band edge and consequently induce electron-mediated stabilization of ferromagnetic semiconductors. We show that kinetic $s-d$ coupling can be introduced through chemical ordering and/or strain. We find that quantum confinement has a large effect on the spin- splitting at the conduction band edge. It can effectively reverse the sign of the conduction band splitting, thus, sheding light on the recent puzzling experimental observation that $s-d$ exchange splitting is negative in semiconductor superlattices. Finally, we show that, using rare-earth elements as magnetic dopants, the symmetry-allowed $s-f$ coupling can lead to a large splitting at the conduction band edge.   

Theory of magnetic circular dichroism in GaMnAs

We present a newly developed theoretical approach to calculate the magnetic circular dichroism in diluted magnetic semiconductors. Our approach uses the tight-binding method to incorporate the spin-orbit coupling and to obtain the electronic structure over a sufficiently wide energy range. The optical transitions from the valence band to the impurity band that can not be treated in the effective mass theories are included in our calculations. We consider GaMnAs, in which the Mn dopants interact with the GaAs host through the p-d exchange interaction. Our calculations show spin-polarized acceptor states, and resonances within the valence bands. The local density of states near the valence band edge is significantly enhanced by these resonances and qualitatively different from what is obtained from models based on rigid-band shift. We find that the optical transition from deep in the valence band to the impurity band can be stronger than the transition from the valence band edge to the conduction band edge, and can account for the broad positive peak in the magnetic circular dichroism data.   

Electrical conductivity in disordered spin-dependent media: application to diluted magnetic semiconductors

Most theoretical calculations of the electrical conductivity and optical response in diluted magnetic semiconductors (DMSs) treat disorder in relaxation time approximation, using phenomenological relaxation times. However, the role of disorder in III-V DMS materials, particularly the non-trivial effects of spin-dependent scattering from magnetic impurities, requires more careful consideration. In this work we go beyond the relaxation time approximation and derive the electrical conductivity in spin-dependent disordered systems based on the equation of motion for the paramagnetic current-current response function. The general expression relates the full current response function to the set of full system spin-density response functions and is valid for any strength of disorder. We present numerical results for conductivities and dielectric functions in the weak disorder limit, treating carriers with a simple parabolic band model and electron interactions within RPA. For various system parameters we study the relative importance of Coulomb and spin-dependent scattering processes. Special attention is paid to the effects of spatially correlated versus random scattering centers.   

Ferromagnetism of Ga$_{1-x}$Mn$_x$As and Weiss theory of Curie temperature in the coherent potential approximation

Using spin-$\frac{1}{2}$ description of valence holes and Kondo coupling between local spins and carriers, the zinc-blende GaAs-based III-V diluted magnetic semiconductors (DMS) are studied in the coherent potential approximation (CPA). We use the exact Hilbert transformation of the face-centered cubic (fcc) density of states (DOS). Our calculated relation of ground-state energy and impurity magnetization shows that ferromagnetism is always favorable at low temperatures. For very weak Kondo coupling, the density of states (DOS) of the host semiconductor is modified slightly. Impurity band can be generated at the host band bottom only when Kondo coupling is strong enough. Using Weiss molecular theory, we predict a nonlinear relation of Curie temperature with respect to Kondo coupling. Our calculated $T_{\rm C}$ agrees with measured values very well.   

The ($T=0$) Phase Diagram of the RKKY model

We consider magnetic moments (e.g. Mn ions in Ga$_{1-x}$Mn$_{x}$As) coupled via the indirect exchange RKKY interaction. We obtain via Monte Carlo the $T=0$ phase diagram as a function of Mn density $n_{i}$ and the relative carrier (hole) concentration $n_{c}/n_{i}$. As evidenced by a diverging correlation length and the magnetic susceptibility, the boundary between the ferromagnetic (FM) and paramagnetic (PM) phases constitutes a line of zero temperature critical points with behavior very similar to that of a percolation transition. In particular, ferromagnetic clusters increase in size and ultimately coalesce to span the system as the phase boundary is approached from the PM side. In the dilute limit, we find that bulk ferromagnetism vanishes for $n_{c}/n_{i} > 0.1$. We also incorporate the local antiferromagnetic super-exchange coupling between nearest neighbor magnetic impurities, eliminating ferromagnetism above a Mn density threshold $n_{i}^{\mathrm{crit}}$. We discuss the impact of a finite carrier mean free path $l$, which we include as a damping factor in the RKKY range function. Among our findings for an $l$ on the order of the lattice constant $a$ is an expansion of the ferromagnetic region in the phase diagram, though with a suppression of the Curie Temperature $T_{c}$. We determine the values of $n_{i}$,$n_{c}$, and $l$ which maximize $T_{c}$.   

Photo-induced ferromagnetism in dilute magnetic semiconductors through Bogoliubov-Valatin transformation

The dilute magnetic semiconductor is an emerging area of interest because of their possible applications in spintronics. One can control ferromagnetism in these materials by shining light on the sample. The incident light creates extra carriers (electrons and holes) across the band gap, thereby enhancing the carrier-mediated ferromagnetism between the localized Mn moments. The effect is studied by a model Hamiltonian that includes the kinetic energy and Columb interaction terms and the coupling of carriers to light. The Hamiltonian is solved by B-V transformation and then minimizing the ground-state energy by a variational method. We study how the critical temperature varies with light frequency and coupling of light to the carrieres.   

Intrinsic Resistance of Magnetic Topological Defects

We show that magnetic topological defects in zincblende magnetic semiconductors have an intrinsic resistance against ballistic transport of holes with spin-orbit coupling. The intrinsic resistance is independent of the real space size and detailed shape of the defects, provided that their spatial variations are sufficiently smooth. Rather, it depends on the shape of the defects in the magnetic orderparameter space. For typical parameters, the intrinsic resistance of a domain wall defect is as large as the geometrical resistance and should therefore be experimentally measurable.