Session N12: Focus Session: Diluted Magnetic Semiconductors I

Effects of co-doping on ferromagnetism in (Zn,Cr)Te.

Room-temperature ferromagnetism in semiconductors has emerged as one of the most challenging topics in today's materials science and technology. Indeed, enormous research activities have so far been directed towards developing ferromagnetic semiconductors with high transition temperatures. Despite many reports claiming high-temperature ferromagnetism for a broad class of diluted magnetic semiconductors, their intrinsic nature has sometimes been controversial[1], with a lack of elaborated analysis of structural and electronic properties. Among them, Cr-doped ZnTe has been regarded as one of the promising materials of room-temperature ferromagnetism because its intrinsic nature was confirmed through magnetic circular dichroism (MCD) measurement[2]. In this presentation, we report the effect of co-doping of charge impurities on ferromagnetic properties in this material. It was found that ferromagnetism was suppressed in (Zn,Cr)Te co-doped with nitrogen (N) as an acceptor impurity[3] and was enhanced in a crystal co-doped with iodine (I) as a donor impurity[4]. In particular, the apparent Curie temperature $T_{C}$ of Zn$_{1-x}$Cr$_{x}$Te with a Cr composition of $x$ = 0.05 increased up to 300K at maximum due to I-doping, compared to $T_{C}\sim $30K in the undoped crystal. In the structural and compositional analysis using TEM/EDS, it was revealed that the origin of this remarkable effect of the co-doping was the variation of Cr distribution in the crystals; the Cr distribution was strongly inhomogeneous in I-doped crystals with higher $T_{C}$, in contrast to an almost uniform distribution in undoped or N-doped crystals with lower $T_{C}$ or being paramagnetic. In the crystals of inhomogeneous distribution, Cr-rich regions with a typical size of several ten nanometers formed in the Cr-poor matrix act as ferromagnetic nanoclusters, resulting in an apparent ferromagnetic behavior of the whole crystal. These variation of the Cr uniformity can be linked to a change in the Cr charge state due to the co-doping, which is considered to affect the aggregation energy of Cr ions in the host compound ZnTe[5]. These findings will open a new way to control the formation of magnetic nanoclusters in the semiconductor matrix and ferromagnetic properties by manipulating the charge state of magnetic impurities. \newline [1] see, $e.g.$ C. Liu \textit{et al.}, J. Mater. Sci.: Mater. Electron. \textbf{16}, 555 (2005), S. A. Chambers \textit{et al.}, Mater. Today \textbf{9}, 28 (2006). \newline [2] H. Saito \textit{et al.}, Phys. Rev. Lett. \textbf{90}, 207202 (2003). \newline [3] N. Ozaki \textit{et al.}, Appl. Phys. Lett. \textbf{87}, 192116 (2005). \newline [4] N. Ozaki\textit{ et al.}, Phys. Rev. Lett. \textbf{97}, 037201 (2006). \newline [5] T. Dietl, Nature Mater. \textbf{5}, 673 (2006).   

Reentrant ferromagnetism and its stability in magnetic semiconductors

The magnetization of a ferromagnetic material normally decays monotonically with increasing temperature. Here we demonstrate theoretically the possibility of quite different behavior: reentrant ferromagnetism in semiconductors [1]. Reentrant magnetism can arise in semiconductors because as the temperature rises, the resulting higher concentration of thermally excited carriers can enhance the exchange coupling between magnetic impurities. This opens the possibility of materials exhibiting a transition from the low-temperature paramagnetic phase, in which carriers are frozen out, to a ferromagnetic phase at higher temperature. Thus, in the absence of other ferromagnetic mechanisms there will be two critical temperatures, T$_{c1}$ $<$ T$_{c2}$, describing para-to-ferromagnetic and ferro-to-paramagnetic transitions, respectively. Here we determine the phase diagram and the stability of reentrant ferromagnetism within a self-consistent description in which the spin-splitting in both carrier bands is included [2]. We discuss the implications of our findings for transport measurements in magnetic semiconductors, and suggest several candidate materials in which reentrant ferromagnetism might be observable. [1] I. \v{Z}uti\'c, A. Petukhov, S. C. Erwin, preprint. [2] I. \v{Z}uti\'c, J. Fabian, S. C. Erwin, Phys. Rev. Lett. 97, 026602 (2006).   

Ferromagnetic transition temperature of a two-band model for diluted magnetic semiconductors

Within dynamical-mean field theory we investigate the ferromagnetic transition temperature ($T_{c}$) of a two-band model for diluted magnetic semiconductors in a large range of coupling constants, hopping parameters, and carrier densities [1]. We reveal that $T_{c}$ is optimized at all fillings when both impurity bands fully overlap in the same energy interval, namely when the exchange couplings and bandwidths are equal. The optimal $T_{c}$ is found to be about twice larger than the maximal value obtained in the one-band model. Within a one-band model we also discuss the influence of the Coulomb attractive potential by acceptors on the critical ferromagnetic temperature [2]. \newline [1]. F. Popescu, Y. Yildirim, G. Alvarez, A. Moreo, and E. Dagotto, Phys. Rev. B, 73 (2006), 075206. \newline [2]. F. Popescu, C. Sen, E. Dagotto, and A. Moreo, in preparation.   

Magnetic properties of the two-impurity Anderson model for a semiconductor host

We study the nature of the magnetic correlations in the two-impurity Anderson model for a semiconductor host using the quantum Monte Carlo technique and the Hartree-Fock approximation. We find that the impurity spins exhibit ferromagnetic correlations with a range which can be much more enhanced than in a half-filled metallic band. In particular, the range is longest when the Fermi level is located above the top of the valence band and decreases as the impurity bound state becomes occupied. In addition, we investigate the magnetic correlations between the impurity moments and the host electronic spins. Comparisons with the photoemission and optical absorption experiments suggest that this model captures the basic electronic structure of Ga$_{1-x} $Mn$_x$As, the prototypical dilute magnetic semiconductor (DMS). These numerical results might also be useful for synthesizing DMS or dilute-oxide ferromagnets with higher Curie temperatures.   

Phase Diagram of the Disordered RKKY Model in Dilute Magnetic Semiconductors

We consider ferromagnetism in spatially randomly located magnetic moments, as in a diluted magnetic semiconductor, coupled via the carrier-mediated indirect exchange RKKY interaction. We obtain, via Monte Carlo calculations, the magnetic phase diagram as a function of the impurity moment density $n_{i}$ and the relative carrier concentration $n_{c}/n_{i}$. As evidenced by the diverging ferromagnetic correlation length and magnetic susceptibility, the boundary between ferromagnetic and nonferromagnetic phases constitutes a line of zero temperature critical points which can be viewed as a magnetic percolation transition. In the dilute limit, we find that bulk ferromagnetism vanishes for $n_{c}/n_{i} > 0.1$. We also incorporate the local antiferromagnetic direct superexchange interaction between nearest neighbor impurities and examine the impact of a damping factor in the RKKY range function. This work has been done in collaboration with Sankar Das Sarma at the University of Maryland and supported by the US-ONR and NSF. \newline \newline [1] D.J. Priour, Jr. and S. Das Sarma, Phys. Rev. Lett., {\bf 97}, 127201 (2006). \newline [2] D.J. Priour, Jr. and S. Das Sarma, Phys. Rev. B, {\bf 73}, 165203 (2006). \newline [3] D.J. Priour, Jr., E.H. Hwang, and S. Das Sarma, Phys. Rev. Lett. {\bf 95}, 037201 (2005). \newline [4] S. Das Sarma, E.H. Hwang, and D.J. Priour, Jr., Phys. Rev. B {\bf 70}, 161203 (2004). \newline [5] D.J. Priour, Jr., E.H. Hwang, and S. Das Sarma, Phys. Rev. Lett. {\bf 92}, 117201 (2004).   

Absence of Self-Averaging in Disordered Heisenberg Models

With the aid of direct large-scale Monte Carlo simulations, we find a lack of self-averaging near the Curie temperature $T_ {c}$ for classical ferromagnetic Heisenberg models on disordered three dimensional lattices. Our calculations encompass a wide range of system sizes, generally systems with between $10^{3}$ and $10^{5}$ magnetic moments, and we have in general found the extent of the violation of self-averaging to be very stable throughout this range of sizes. In contradiction to the Harris Criterion, which predicts self-averaging to be intact for disordered Heisenberg models, we find the degree of violation of self-averaging (as extrapolated to the bulk limit) to rise monotonically with increasing disorder strength; even small amounts of disorder yield a nonzero, albeit weak, violation of self- averaging. We examine various bond and site disordered Heisenberg models, and we also consider strongly disordered RKKY models for dilute magnetic semiconductors, where we find a marked violation of self-averaging. This work has been supported by the US-ONR and NSF.   

The Mobility Edge in Disordered Ferromagnetic Doped Semiconductors

While the clearest example of ferromagnetism in doped semiconductors is seen in diluted magnetic semiconductors such as Ga$_{1-x}$Mn$_x$As,\footnote{H. Ohno, Science 281, 951 (1998)} under certain conditions, semiconductors doped with non-magnetic impurities may also exhibit ferromagnetic ground states.\footnote{Erik Nielsen and R. N. Bhatt, APS March Meeting 2006.} We present numerical results of the nature of single particle states in such a positionally disordered three-dimensional system with a maximally spin-polarized ground state using a realistic potential for hydrogenic centers.\footnote{R. N. Bhatt and T. M. Rice, Physical Review B 23, 1920 (1981).} In particular, we identify the mobility edges, which mark the energies at which single particle states become delocalized, and whose location relative to the Fermi energy determine electronic transport in the system. We describe the dependence of the mobility edges on impurity density and potential, and discuss the variation of conductivity with impurity and carrier density.   

Exchange interactions in Mn-doped ScN

We present a computational study of the exchange interactions in Mn-doped ScN. First, we test to what extent the Heisenberg Hamiltonian applies to large spin rotations. We calculate them instead from a non-collinear calculation with a small rotation. This shows that the exchange interactions obtained from a collinear energy difference (antiferromagnetic- ferromagnetic) would be overestimated by about 30\%. Next, we calculate the exchange interactions using the linear response multiple scattering theory approach of Liechtenstein et al. We find $\sum_j J_{0j}$ for a nearest neighbor pair is the same as before, but we now find this to be a sum over many long-range interactions. The actual near neighbor interactions are an order of magnitude smaller. Finally, we study various special quasirandom structures with 256 and 432 atoms per cell with concentrations of 3-10 \%. These calculations indicate that with randomness, many of the long-range interactions become negative and thus lead us to believe that Mn-doped ScN is not a ferromagnetic semiconductor but a spin-glass. These calculations do not yet include the effects of n-type doping,which might add ferromagnetic couplings for long-range neighbors.   

Coulomb attraction and defects in dilute magnetic semiconductors

Employing the dynamical mean-field approximation we study the phase diagram of a double-exchange model that includes interactions between the holes and the local magnetic moments and also the negatively charged ions. We calculate the ferromagnetic transition temperature, magnetization and susceptibility for a range of parameters and compare the results of a single band model with a four-band model which properly includes the heavy and light bands. The inclusion of the Coulomb attraction allows a better comparison with experiments by reducing the values of the exchange coupling needed to support a ferromagnetic transition. For small or intermediate exchange couplings the Coulomb attraction increases the transition temperature. We will also study a model where additional non-magnetic defects are included in the Hamiltonian. In the presence of these defects the ferromagnetic transition is expected to be rapidly suppressed.   

Numerical Study of Magnetically doped III-V Zinc-Blende-Type Semiconductors

Using a newly developed real-space Hamiltonian for zinc-blende dilute magnetic III-V semiconductors we study the properties of a variety of materials. The hopping parameters are functions of the tabulated Luttinger parameters of the III-V parent compounds, and the dispersion of the heavy-hole, light-hole, and split-off bands is reproduced next to the top of the valence band in the undoped case. The exchange interaction parameter $J$ is obtained from measurements; thus, there are no free parameters in the model. The spin-orbit interaction is considered as well as the randomness in the doping. Unbiased Monte Carlo techniques are applied to clusters containing about 300 III-type ions. After successfully reproducing experimental results for (Ga,Mn)As [1], here we present a comprehensive study of the magnetization vs. temperature, the density of states, and the charge distribution for Mn doped GaSb, GaP, GaN, AlP, and InAs. We also present the calculated Curie temperatures for a variety of Mn concentrations and hole compensations. \newline \newline [1] Y. Yildirim, G. Alvarez, A. Moreo, and E. Dagotto, preprint October 2006   

Complexities in diluted magnetic semiconductors-a theoretical perspective from ab-initio electronic structure calculations

Diluted magnetic semiconductors (DMS), the essential materials for semiconductor spintronics, show a variety of complex properties, e.g., defect-mediated (ferro/antiferro)magnetic interactions and the disorder leading to magnetic percolation effects. Using the ab-initio Korringa-Kohn-Rostoker-Coherent-Potential-Approximation, the magnetic pair exchange parameters of a Heisenberg model have been calculated for Mn doped ZnO and half-Heusler NiTiSn hosts followed by the calculation of transition temperatures using Monte-Carlo simulations. Zinc vacancies and nitrogen substituting oxygen atoms lead to ferromagnetic interactions in Mn doped ZNO while in a defect free case, the interaction between Mn atoms is antiferromagnetic. The calculated critical temperatures are low ($\sim $35 K) due to the short-ranged exchange interactions and low defect concentration. In the other case, Mn doped NiTiSn shows a high critical temperature ($\sim $300 K) for 22 {\%} Mn concentration. Below 3{\%} Mn, there is no magnetic long range order as the magnetic percolation is not established. The results are in good agreement with experiments.