No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Carrier-mediated ferromagnetic interactions in structures of magnetic semiconductors
Abstract
Various mechanisms that control the magnitude of the ferromagnetic interaction in semiconductors and their quantum structures are described. Two alternative approaches, the Ruderman–Kittel–Kasuya–Yosida (RKKY) and self-consistent models are recalled and their equivalence is demonstrated in the mean field approximation (MFA). It is shown how the long-range nature of the RKKY interactions in semiconductors, by making the thermal fluctuations of magnetization irrelevant, stabilizes an ordered phase and results in the validity of the MFA, even in the disordered magnetic systems of reduced dimensionality. The role of confinement and of the associated modifications in the density-of-states is examined and shown to be important. It is pointed out that disorder and carrier–carrier interactions may have a profound influence on the spin–spin coupling, particularly near the metal-to-insulator transition (MIT). The corresponding effects are analyzed in terms of the disordered Fermiliquid and Hubbard models, developed for the description of doped semiconductors on the metallic side of the MIT. Outstanding properties of 1D systems, resulting from peculiarities of their DOS, tendency toward spin-density formation and possible charge-spin separation are mentioned. The question concerning the role of non-scalar spin–spin interactions driven by spin-orbit coupling, notably in strained systems, is addressed. Finally, the important issue of control of magnetic properties by electrostatic gate potentials or illumination is presented.
... Here m * denotes the in-plane effective mass andL W is an effective width of the region occupied by carriers relevant to ferromagnetism given by (Dietl et al., 1999;Haury et al., 1997),L ...
... The formation of spin-density waves is expected in the case of carrier-mediated ferromagnetism in 1D systems (Dietl et al., 1999). ...
... An increase of T C with P , of the magnitude corroborating the p-d Zener model, was Haury et al., 1997;empty circles, Boukari et al., 2002). The dashed line represents the 2D (Dietl et al., 1999) and 3D p-d Zener model . Solid line is theoretical for the 3D case, taking into account the antiferromagnetic portion of the RKKY interaction . ...
This review compiles results of experimental and theoretical studies on thin
films and quantum structures of semiconductors with randomly distributed Mn
ions, which exhibit spintronic functionalities associated with collective
ferromagnetic spin ordering. Properties of p-type Mn-containing III-V as well
as II-VI, III-VI, IV-VI, I-II-V, and elemental group IV semiconductors are
described paying particular attention to the most thoroughly investigated
system (Ga,Mn)As that supports the hole-mediated ferromagnetic order up to 190
K for the net concentration of Mn spins below 10%. Multilayer structures
showing efficient spin injection and spin-related magnetotransport properties
as well as enabling magnetization manipulation by strain, light, electric
fields, and spin currents are presented together with their impact on metal
spintronics. The challenging interplay between magnetic and electronic
properties in topologically trivial and non-trivial systems is described,
emphasizing the entangled roles of disorder and correlation at the carrier
localization boundary. Finally, the case of dilute magnetic insulators is
considered, such as (Ga,Mn)N, where low temperature spin ordering is driven by
short-ranged superexchange that is ferromagnetic for certain charge states of
magnetic impurities.
... In addition, oxygen vacancies also act as donors in ZnO, so it is possible that the mechanism of ferromagnetism in this system is a carrier-induced model. 36 Therefore, we plan to examine and compare the saturation magnetization in a system in which a different donor density is intentionally doped. Nevertheless, our present results show a strong possibility of fabricating DMS materials with a controllable process. ...
In the reported study, thin films of ZnO doped with 10 wt. % Co were fabricated by pulsed laser deposition under different oxygen partial pressures. The results of x-ray photoelectron spectroscopy show that the valence state of the Co ions is 2+ and that the number of oxygen vacancies is increased by lowering the oxygen partial pressure during deposition. The results of UV–visible absorption spectroscopy show that the Co ²⁺ ions substitute for the Zn sites in the ZnO lattice. Ferromagnetism in the Co-doped ZnO thin films is observed up to 300 K. Furthermore, the saturation magnetization increases as the oxygen partial pressure decreases, indicating a strong correlation between the number of oxygen vacancies and the saturation magnetization. This suggests that ferromagnetism in Co-doped ZnO can be enhanced by simply controlling the oxygen partial pressure that causes oxygen vacancies. Furthermore, how the mechanism for the expression of ferromagnetism can be explained by the bound magnetic polaron model is discussed.
... To establish conditions allowing for carriers'-mediated ferromagnetic ordering and to evaluate the magnitudes of Curie temperature T C and of various thermodynamic quantities, I made use of all that broad knowledge gathered over decades for the mainstream semiconductor compounds, i.e., III-V and II-VI tetrahedrally bonded semiconductors with carriers residing at the Brillouin zone center b [134][135][136]. While in Grenoble (altogether 7 months in 1994-1997), stimulated by Yves Merle d'Aubigné , I demonstrated the equivalence of the RKKY and Zener models, and predicted T C s for various dimensionality structures of II-VI compounds in the mean-field approximation [134,137]. Zener's model (Phys. Rev. B 81, 440 (1951)) in this context means competition between spin entropy and carrier energy lowering coming from exchange splitting of the band. ...
... To establish conditions allowing for carriers'-mediated ferromagnetic ordering and to evaluate the magnitudes of Curie temperature T C and of various thermodynamic quantities, I made use of all that broad knowledge gathered over decades for the mainstream semiconductor compounds, i.e., III-V and II-VI tetrahedrally bonded semiconductors with carriers residing at the Briilouin zone center [134][135][136]. While in Grenoble (altogether 7 months in 1994-1997), stimulated by Yves Merle d'Aubigné , I demonstrated the equivalence of the RKKY and Zener models, and predicted T C s for various dimensionality structures of II-VI compounds in the mean-field approximation [134,137]. Zener's model [Phys. Rev. B 81, 440 (1951)] in this context means competition between spin entropy and carrier energy lowering coming from exchange splitting of the band). ...
The abundance of semiconductors in our smartphones, computers, fiber optic junctions, cars, light sources, photovoltaic and thermoelectric cells results from the possibilities of controlling their properties through doping, lighting, and applying various fields. This paper, a part of the volume celebrating 100 years of the Polish Physical Society, presents a biased selection of worthwhile results obtained by researchers at the Institute of Physics, Polish Academy of Sciences relevant, as seen today, to topological matter and spintronics. Comprehensive studies, combining materials development, experimental investigations, and theoretical description of narrow-gap and dilute-magnetic semiconductors have been especially significant in this context. This survey also emphasizes, in an autobiographical tone, a half of a century of the author's intellectual emotions accompanying the rise of ideas and quantitative theories, allowing identifying the physics behind ongoing and future observations.
... Moreover, coupling to Mn spins may stabilize ferromagnetic order or spindensity waves formed by Peierls instability in the 1D case at temperatures much higher than bulk T Curie (ref. 31), ...
As qubits resistant to local decoherence, Majorana bound states (MBSs) open prospects for fault-tolerant quantum computation. These zero-energy excitations are predicted to emerge at one-dimensional (1D) junctions of nonconventional superconductors and topologically trivial systems, i.e., at the terminations of relevant 1D quantum wires or at boundaries, such as vortices, of 2D counterparts. Here we show, by using soft point-contact spectroscopy, that an electron-hole gap with a broad zero-bias conductance maximum develops at the topological surfaces of diamagnetic, paramagnetic, and ferromagnetic Pb1-y-xSnyMnxTe, where y > 0.67 and 0 < x < 0.10. The temperature dependence of the gap shows a critical behaviour with Tc up to 4.5 K, which however is not accompanied by a global superconductivity. We assign these findings to the presence of 1D topological states adjacent to surface atomic steps in topological crystalline insulators of IV-VI compounds. Within this scenario, the interplay of carrier-carrier interactions, spin exchange with Mn ions, and pairing coupling within the at 1D channels results in MBSs with lifted Kramers degeneracy, which are immune to the ferromagnetic ordering in the sample interior.
... It is worth noting that a simple adaption of this formula to (Ga,Mn)As by replacing r nn with (xN 0 ) −1/3 resulted in an overestimation of the p-d exchange integral by an order of magnitude [211]. Allowing for spatially modulated structures, the magnetic ordering temperature T C for a carrier-controlled ferromagnet is given by a solution of the mean-field equation [65,220], ...
My doctoral thesis. The work was awarded with distinctions and (parts) International Union of Pure and Applied Physics' Young Authors Best Paper Award and supported by the scholarship of the President of Polish Academy of Sciences.
... We determine p(z) and then m Sat (V G ) and T C (V G ) in a self consistent way adopting the hole density-of-states effective mass from the 6×6 In order to determine T C (V G ) we note that the channel width is narrower than the phase coherence length of the holes 21 , which implies a collective two-dimensional behaviour of the Mn spins across the channel. In this case, in terms of the sheet hole density p s = ∫dz p(z) and the corresponding thermodynamic density of states at the Fermi level ρ s (E F ) = ∂p s /∂E F , T C according to the p-d Zener model 2,22 can be written in the form, ...
The question of whether the Anderson-Mott localization enhances or reduces magnetic correlations is central to the physics of magnetic alloys. Particularly intriguing is the case of (Ga, Mn)As and related magnetic semiconductors, for which diverging theoretical scenarios have been proposed. Here, by direct magnetization measurements we demonstrate how magnetism evolves when the density of carriers mediating the spin-spin coupling is diminished by the gate electric field in metal-insulator-semiconductor structures of (Ga, Mn)As. Our findings show that the channel depletion results in a monotonic decrease of the Curie temperature, with no evidence for the maximum expected within the impurity-band models. We find that the transition from the ferromagnetic to the paramagnetic state proceeds by means of the emergence of a superparamagnetic-like spin arrangement. This implies that carrier localization leads to a phase separation into ferromagnetic and non-magnetic regions, which we attribute to critical fluctuations in the local density of states, specific to the Anderson-Mott quantum transition.
We present a theory of collective spin excitations in diluted-magnetic-semiconductor quantum wells in which local magnetic moments are coupled via a quasi-two-dimensional gas of electrons or holes. In the case of a ferromagnetic state with partly spin-polarized electrons, we find that the Goldstone collective mode has anomalous k 4 dispersion and that for symmetric quantum wells odd parity modes do not disperse at all. We discuss the gap in the collective excitation spectrum which appears when spin-orbit interactions are included.
A mean-field model of ferromagnetism mediated by delocalized or weakly localized holes in zinc-blende and wurzite diluted magnetic semiconductors is presented. The model takes into account strong spin-orbit and k⋅p couplings in the valence band as well as the influence of strain upon the hole density of states. Possible effects of disorder and carrier-carrier interactions, particularly near the metal-to-insulator transition, are discussed. A quantitative comparison between experimental and theoretical results for (Ga,Mn)As demonstrates that the theory describes the values of the Curie temperatures observed in the studied systems as well as explaining the directions of the easy axes and the magnitudes of the corresponding anisotropy fields as a function of biaxial strain. Furthermore, the model reproduces the unusual sign, magnitude, and temperature dependence of the magnetic circular dichroism in the spectral region of the fundamental absorption edge. Chemical trends and various suggestions concerning design of ferromagnetic semiconductor systems are described.
We examine the effects of positional disorder of the magnetic ion in III-V Diluted Magnetic Semiconductors such as (Ga,Mn)As at low carrier densities on the nature of the low-temperature ordered magnetic state, using numerical mean field and Monte Carlo methods. We find that positional disorder leads to a highly inhomogeneous ferromagnetic order in the low carrier density limit, with unusual thermodynamic and magnetic behavior. Spin-orbit coupling presented in the valence band leads to frustration in the hole-doped system, but does not significantly affect the low temperature magnetization.
The present status of research and prospects for device applications of ferromagnetic (diluted magnetic) semiconductors (DMS) is presented. We review the nature of the electronic states and the mechanisms of the carrier-mediated exchange interactions (mean-field Zener model) in p-type Mn-based III-V and II-VI compounds, highlighting a good correspondence of experimental findings and theoretical predictions. An account of the latest progress on the road of increasing the Currie point to above the room temperature is given for both families of compounds. We comment on a possibility of obtaining ferromagnetism in n-type materials, taking (Zn,Mn)O:Al as the example. Concerning technologically important issue of easy axis and domain engineering, we present theoretical predictions and experimental results on the temperature and carrier concentration driven change of magnetic anisotropy in (Ga,Mn)As.
In this paper the present understanding of the origin of ferromagnetic response that has been detected in a number of diluted magnetic semiconductors and diluted magnetic oxides at room temperature is outlined. It is argued that in these systems, owing to a typically small solubility of magnetic ions, crystallographic or chemical phase separation into regions with a large and a small concentration of magnetic component takes place. The ferromagnetic signatures then come from the regions with a large concentration of magnetic ions, which show non-zero spontaneous magnetization up to the blocking temperature, whose magnitude is proportional to the nanocrystal volume and magnetic anisotropy. Novel methods enabling a control of nano-assembling of magnetic nanocrystals in non-conducting matrices as well as possible functionalities of these spatially modulated magnetic systems are described. We also discuss phase separations into paramagnetic and ferromagnetic regions, which are driven by the Anderson-Mott localization and/or competing ferromagnetic and antiferromagnetic interactions. Finally, the question whether the high temperature ferromagnetism is possible in materials without magnetic ions is addressed.
A robust long-range antiferromagnetic coupling between ferromagnetic Ga0.97Mn0.03As layers has previously been realized via insertion of nonmagnetic Be-doped GaAs spacers between the magnetic layers. In this paper we report the observation of weak antiferromagnetic coupling between Ga0.97Mn0.03As layers through undoped GaAs spacers with thicknesses as large as 25 monolayers. The field and the temperature dependences of the sample magnetization suggest that the interlayer coupling in these systems substantially deviates from typical ferromagnetic behavior. Polarized neutron reflectivity measurements reveal antiferromagnetic alignment between Ga0.97Mn0.03As layers when a weak field is applied perpendicular to the magnetic easy axis during cooling below TC. The strength of the observed coupling between the magnetic layers is estimated to be weaker than 0.05 mT.
Modem information technology utilizes the charge degree of freedom of electrons in semiconductors to process the information and the spin degree of freedom in magnetic materials to store the information. In semiconductor devices, the spin of carriers has played a minor role so far because well-established semiconductor devices based on Si and GaAs are non-magnetic and show only negligible effects of spin. On the other hand, from the physical points of view, the enhanced spin-related phenomena due to the coexistence of the magnetism and semiconductor properties have been recognized in magnetic semiconductors and diluted magnetic semiconductors (DMS). DMS are based on non-magnetic semiconductors, and are obtained by alloying them with a sizable amount (a few percents or more) of magnetic elements, such as Mn.
We study a model thin film containing diluted bilayer structure with the RKKY
long-range interaction. The magnetic subsystem is composed of two magnetically
doped layers, separated by an undoped nonmagnetic spacer and placed inside a
wider film modelled by a quantum well of infinite depth. We focus our study on
the range of parameters for which the antiferromagnetic coupling between the
magnetic layers can be expected. The critical temperatures for such system are
found and their dependence on magnetic layer thickness and charge carriers
concentration is discussed. The magnetization distribution within each magnetic
layer is calculated as a function of layer thickness. The external field
required to switch the mutual orientation of layer magnetizations from
antiferromagnetic to ferromagnetic state is also discussed.
We show that in ferromagnetic semimetals, in which the Ruderman-Kittel-Kasuya-Yosida indirect exchange predominates, the magnetically ordered state is unstable against inhomogeneous fluctuations. At a temperature slightly lower than the Curie temperature, the system enters into a state in which both the carrier density and the magnetization are modulated. The modulation scale is fixed by the Coulomb screening of the carriers, and can be tuned by changing the ratio of the electron and hole concentrations. At much lower temperatures a reentrant transition into a uniformly ordered state occurs. The modulated state is strongly suppressed by an external magnetic field. The results explain qualitatively the magnetic properties of EuB6.
Recent advances in the theory and experimental realization of ferromagnetic semiconductors give hope that a new generation of microelectronic devices based on the spin degree of freedom of the electron can be developed. This review focuses primarily on promising candidate materials (such as GaN, GaP and ZnO) in which there is already a technology base and a fairly good understanding of the basic electrical and optical properties. The introduction of Mn into these and other materials under the right conditions is found to produce ferromagnetism near or above room temperature. There are a number of other potential dopant ions that could be employed (such as Fe, Ni, Co, Cr) as suggested by theory [see, for example, Sato and Katayama-Yoshida, Jpn. J. Appl. Phys., Part 2 39, L555 (2000)]. Growth of these ferromagnetic materials by thin film techniques, such as molecular beam epitaxy or pulsed laser deposition, provides excellent control of the dopant concentration and the ability to grow single-phase layers. The mechanism for the observed magnetic behavior is complex and appears to depend on a number of factors, including Mn–Mn spacing, and carrier density and type. For example, in a simple Ruderman–Kittel–Kasuya–Yosida carrier-mediated exchange mechanism, the free-carrier/Mn ion interaction can be either ferromagnetic or antiferromagnetic depending on the separation of the Mn ions. Potential applications for ferromagnetic semiconductors and oxides include electrically controlled magnetic sensors and actuators, high-density ultralow-power memory and logic, spin-polarized light emitters for optical encoding, advanced optical switches and modulators and devices with integrated magnetic, electronic and optical functionality. © 2003 American Institute of Physics.
In order to single out dominant phenomena that account for carrier-controlled magnetism in p-Cd1−xMnxTe
quantum wells we have carried out magneto-optical measurements and Monte Carlo simulations of time dependent magnetization. The experimental results show that magnetization relaxation is faster than 20 ns in the paramagnetic state. Decreasing temperature below the Curie temperature TC results in an increase of the relaxation time but to less than 10 �s. This fast relaxation may explain why the spontaneous spin splitting of electronic states is not accompanied by the presence of nonzero macroscopic magnetization below TC. Our Monte Carlo results reproduce the relative change of the relaxation time on decreasing temperature. At the same time, the numerical calculations demonstrate that antiferromagnetic spin-spin interactions, which compete with the hole-mediated long-range ferromagnetic coupling, play an important role in magnetization relaxation of the system. We find, in particular, that magnetization dynamics is largely accelerated by the presence of antiferromagnetic couplings to the Mn spins located outside the region, where the holes reside. This suggests that macroscopic spontaneous magnetization should be observable if the thickness of the layer containing localized spins will be smaller than the extension of the hole wave function. Furthermore, we study how a spin-independent part of the Mn potential affects TC. Our findings show that the alloy disorder potential tends to reduce TC, the effect being particularly strong for the attractive potential that leads to hole localization.
In order to explain the absence of hysteresis in ferromagnetic p-type (Cd,Mn)Te quantum wells (QWs), spin dynamics was previously investigated by Monte Carlo simulations combining the Metropolis
algorithm with the determination of hole eigenfunctions at each Monte Carlo sweep. Short-range
antiferromagnetic superexchange interactions between Mn spins- which compete with the hole-
mediated long-range ferromagnetic coupling- were found to accelerate magnetization dynamics if the
layer containing Mn spins is wider than the vertical range of the hole wavefunction.Employing this
approach it is shown here that appreciate magnitudes of remanence and coercivity can be obtained if
Mn ions are introduced to the quantum well in a delta-like fashion.
The solid solution of the ternary transition metal Zintl phase Ca14-xEuxMnSb11 (0 < x < 14) has been prepared by heating a mixture of stoichiometric amounts of the elements in a two-zone furnace with Thigh = 1100 °C and Tlow = 1050 °C. The ternary transition metal compounds crystallize in the tetragonal space group I41/acd and are isostructural with the Zintl compound Ca14AlSb11. The lattice parameters of the Ca14-xEuxMnSb11 compounds linearly increase with increasing Eu substitution for Ca. The Eu atoms preferentially occupy the Ca(2) site first and subsequently occupy Ca(4), Ca(1), and Ca(3), in order, among the four crystallographically inequivalent Ca sites. Temperature-dependent magnetic susceptibility measurements of the solid solution reveal that Eu replacement for Ca induces complex magnetic interactions in the compound, from simple ferromagnetic interactions for Ca14MnSb11 to ferrimagnetic interactions for Eu14MnSb11, because of the Eu2+(4f 7) magnetic moment. The paramagnetic Curie temperature of the Ca14-xEuxMnSb11 compounds shows an interesting change with varying x, and the magnetic easy axis gradually changes in the solid solution from perpendicular (for Ca14MnSb11) to parallel (for Eu14MnSb11) to the crystal c axis. The electrical transport properties of the Ca14-xEuxMnSb11 (x = 0, 3, 11) compounds show a close relation to their magnetic properties and are compared to the previous results for Ca14-xEuxMnSb11 (x = 13, 14). The influence of Eu doping on the structural and physical property of Ca14-xEuxMnSb11 is discussed in terms of the site preferences of Eu for the four different Ca sites.
The spin-dependent interactions in diluted magnetic semiconductors are reviewed. The non-trivial dependence of the p-d and the d-d exchange interactions, which rule the magnetic properties of these materials, on the electronic configuration of the magnetic ions is presented. Depending on the occupation numbers in the ionic d shell and the position of the d level with respect to the bands, both the kinetic exchange and the superexchange can lead to antiferromagnetic, ferromagnetic Kondo-like interactions or even orbital dependent, sensitive to Jahn-Teller distortion couplings. Finally, the interactions explaining the ferromagnetism in III-V and p-II-VI with Mn ions, the magnetic properties in semiconductor quantum wells and the interlayer spin correlations in magnetic/non-magnetic semiconductor superlattices are discussed.
The exchange interactions and nanoscale phase separations in magnetically doped semiconductors are discussed along with substitutional magnetic impurities. The chapter also discusses the coupling of effective mass carriers to the localized spins, emphasizing non-perturbative effects, which appear when the coupling gets strong, and presents the origin and consequences of carrier-mediated ferromagnetic spin–spin interactions. The chapter explains why the disorder-free p–d Zener model captures the relevant physics as long as the holes stay delocalized or weakly localized. The dominant effect that shows up on crossing the insulator-to-metal transition is the appearance of large spatial fluctuations in the carrier density, which lead to the corresponding highly nonuniform texture of transition metal (TM) spin polarization. The chapter discusses why the assumption about a random distribution of magnetic ions has to be abandoned in many cases and the methods that allow controlling the magnetic ion aggregation and indicating a number of applications proposed for these multicomponent and multifunctional systems.
This chapter reviews theoretical understanding of ferromagnetic response that has been detected in diluted magnetic semiconductors (DMS). Particular attention is paid to those ferromagnetic DMS in which no precipitation of other crystallographic phases has been observed. It is argued that these materials can be divided into three categories. The first consists of (Ga,Mn)As, heavily doped p-(Zn,Mn)Te, and related compounds. In these solid solutions, the theory built on p–d Zener's model of hole-mediated ferromagnetism and on either the Kohn-Luttinger kp theory or the multiorbital tight-binding approach describes qualitatively, and often quantitatively, thermodynamic, micromagnetic, optical, and transport properties. Moreover, the understanding of these materials has provided a basis for the development of novel methods enabling magnetization manipulation and switching. To the second group, belong compounds in which a competition between long-range ferromagnetic and short-range antiferromagnetic interactions and/or the proximity of the localization boundary lead to an electronic nanoscale phase separation that results in characteristics similar to colossal magnetoresistance oxides. Finally, in a number of compounds a chemical nanoscale phase separation into the regions with small and large concentrations of the magnetic constituent is present. Methods of controlling the spinodal decomposition and possible functionalities of these systems are outlined.
This paper reviews various origins of ferromagnetic response that has been detected in diluted magnetic semiconductors (DMS). Particular attention is paid to those ferromagnetic DMS in which no precipitation of other crystallographic phases has been observed. It is argued that these materials can be divided into three categories. The first consists of (Ga,Mn)As and related compounds. In these solid solutions the theory built on p–d Zener's model of hole-mediated ferromagnetism and the Kohn–Luttinger kp theory of semiconductors describes quantitatively thermodynamic, micromagnetic, optical, and transport properties. Moreover, the understanding of these materials has provided a basis for the development of novel methods enabling magnetisation manipulation and switching. To the second group belong compounds, in which a competition between long-range ferromagnetic and short-range antiferromagnetic interactions and/or the proximity of the localisation boundary lead to an electronic nano-scale phase separation that results in characteristics similar to colossal magnetoresistance oxides. Finally, in a number of compounds a chemical nano-scale phase separation into the regions with small and large concentrations of the magnetic constituent is present. It has recently been suggested that this spinodal decomposition can be controlled by the charge state of relevant magnetic impurities. This constitutes a new perspective method for 3D self-organised growth of coherent magnetic nanocrystals embedded by the semiconductor matrix.
This paper reviews the current status and prospects of research on ferromagnetism in tetrahedrally coordinated magnetic semiconductors and their nanostructures. Results of a quantitative comparison between experimental and theoretical results, notably for Mn-based III–V and II–VI thin films and heterostructures, are presented. This comparison demonstrates that the current theory of the hole-mediated exchange interactions describes correctly the values of Curie temperatures TC, magnetic anisotropy, and magnetic circular dichroism. On this basis, chemical trends are examined and show to lead to the prediction of semiconductor systems with TC that may exceed room temperature. Furthermore, the important issue of tailoring magnetic properties by electrostatic or ferromagnetic gates, by confinement or illumination, by exchange bias or strain are discussed. The interesting question of designing spatially modulated magnetic structures in quantum structures is addressed, too. Finally, hopes associated with materials containing magnetic ions other than Mn are mentioned.
The current status of research on the carrier-mediated ferromagnetism in tetrahedrally coordinated semiconductors is briefly reviewed. The experimental results for III–V semiconductors, where Mn atoms introduce both spins and holes, are compared to the case of II–VI compounds, in which the ferromagnetism has been observed for the modulation-doped p-type Cd1−xMnxTe/Cd1−y−zMgyZnzTe:N heterostructures, and more recently, in Zn1−xMnxTe:N epilayers. On the theoretical side, a model is presented, which takes into account: (i) strong spin–orbit and kp couplings in the valence band; (ii) the effect of confinement and strain upon the hole density-of-states and response function, and (iii) the influence of disorder and carrier–carrier interactions, particularly near the metal-to-insulator transition. A comparison between the experimental and theoretical results demonstrates that the model can describe the magnetic circular dichroism, the values of TC observed in the studied systems as well as explain the directions of the easy axis and the magnitudes of the corresponding anisotropy fields as a function of confinement and biaxial strain. Various suggestions concerning design of novel ferromagnetic semiconductor systems are described.
The effect of binary alloy disorder on the ferromagnetic phases of f-electron materials is studied within the periodic Anderson model. We find that disorder in the conduction band can drastically enhance the Curie temperature T{c} due to an increase of the local f moment. The effect may be explained qualitatively and even quantitatively by a simple theoretical ansatz. The emergence of an alloy Kondo insulator at noninteger filling is also pointed out.
The collective behavior of spins in a dilute magnetic semiconductor is determined by their mutual interactions and influenced by the underlying crystal structure. Hence, we begin with the atomic quantum-mechanical description of this system using the proposed variational-perturbation calculus, and then turn to the emerging macroscopic picture employing phenomenological constants. Within this framework we study spin waves and exchange stiffness in the p-d Zener model of (Ga,Mn)As, its thin layers and bulk crystals described by the spds* tight-binding approximation. Analyzing the anisotropic part of exchange, we find that the Dzyaloshinskii-Moriya interaction may lead to the cycloidal spin arrangement and uniaxial in-plane anisotropy in thin layers, resulting in a surface-like anisotropy in thicker films. We also derive and discuss the spin-wave contribution to magnetization and Curie temperature. Our theory reconstructs the values of stiffness determined from the temperature dependence of magnetization, but reproduces only partly those obtained from analyzing precession modes in (Ga,Mn)As thin films. Comment: 17 pages, 12 figures (added Eq. 36, replaced Fig. 10)
The Curie temperature TC is investigated as a function of the hole
concentration p in thin films of ferromagnetic semiconductor (Ga,Mn)As. The
magnetic properties are probed by transport measurements and p is varied by the
application of an external electric field in a field-effect transistor
configuration. It is found that TC is proportional to p^{\gamma}, where the
exponent \gamma = 0.19 \pm 0.02 over a wide range of Mn compositions and
channel thicknesses. The magnitude of gamma is reproduced by a p-d Zener model
taking into account nonuniform hole distribution along the growth direction,
determined by interface states and the applied gate electric fields.
This paper reviews the present understanding of the origin of ferromagnetic response of diluted magnetic semiconductors and diluted magnetic oxides as well as in some nominally magnetically undoped materials. It is argued that these systems can be grouped into four classes. To the first belong composite materials in which precipitations of a known ferromagnetic, ferrimagnetic or antiferromagnetic compound account for magnetic characteristics at high temperatures. The second class forms alloys showing chemical nano-scale phase separation into the regions with small and large concentrations of the magnetic constituent. To the third class belong (Ga,Mn)As, heavily doped p-(Zn,Mn)Te, and related semiconductors. In these solid solutions the theory built on p-d Zener's model of hole-mediated ferromagnetism and on either the Kohn-Luttinger kp theory or the multi-orbital tight-binding approach describes qualitatively, and often quantitatively many relevant properties. Finally, in a number of carrier-doped DMS and DMO a competition between long-range ferromagnetic and short-range antiferromagnetic interactions and/or the proximity of the localisation boundary lead to an electronic nano-scale phase separation. Comment: review, 19 pages, 4 figures
Motivated by the recent suggestion of anisotropic effective exchange interactions between Mn spins in Ga$_{1-x}$Mn$_x$As (arising as a result of spin-orbit coupling), we study their effects in diluted Heisenberg spin systems. We perform Monte Carlo simulations on several phenomenological model spin Hamiltonians, and investigate the extent to which frustration induced by anisotropic exchanges can reduce the low temperature magnetization in these models and the interplay of this effect with disorder in the exchange. In a model with low coordination number and purely ferromagnetic (FM) exchanges, we find that the low temperature magnetization is gradually reduced as exchange anisotropy is turned on. However, as the connectivity of the model is increased, the effect of small-to-moderate anisotropy is suppressed, and the magnetization regains its maximum saturation value at low temperatures unless the distribution of exchanges is very wide. To obtain significant suppression of the low temperature magnetization in a model with high connectivity, as is found for long-range interactions, we find it necessary to have both ferromagnetic and antiferromagnetic (AFM) exchanges (e.g. as in the RKKY interaction). This implies that disorder in the sign of the exchange interaction is much more effective in suppressing magnetization at low temperatures than exchange anisotropy.
The current status and prospects of research on ferromagnetism in semiconductors are reviewed. The question of the origin of ferromagnetism in europium chalcogenides, chromium spinels and, particularly, in diluted magnetic semiconductors is addressed. The nature of electronic states derived from 3d of magnetic impurities is discussed in some details. Results of a quantitative comparison between experimental and theoretical results, notably for Mn-based III-V and II-VI compounds, are presented. This comparison demonstrates that the current theory of the exchange interactions mediated by holes in the valence band describes correctly the values of Curie temperatures T_C magnetic anisotropy, domain structure, and magnetic circular dichroism. On this basis, chemical trends are examined and show to lead to the prediction of semiconductor systems with T_C that may exceed room temperature, an expectation that are being confirmed by recent findings. Results for materials containing magnetic ions other than Mn are also presented emphasizing that the double exchange involving hoping through d states may operate in those systems. Comment: 18 pages, 8 figures; special issue of Semicon. Sci. Technol. on semiconductor spintronics
We present a systematic study of the ferromagnetic transition induced by the holes in nitrogen doped Zn1-xMnxTe epitaxial layers, with particular emphasis on the values of the Curie-Weiss temperature as a function of the carrier and spin concentrations. The data are obtained from thorough analyses of the results of magnetization, magnetoresistance and spin-dependent Hall effect measurements. The experimental findings compare favorably, without adjustable parameters, with the prediction of the Rudermann-Kittel-Kasuya-Yosida (RKKY) model or its continuous-medium limit, that is, the Zener model, provided that the presence of the competing antiferromagnetic spin-spin superexchange interaction is taken into account, and the complex structure of the valence band is properly incorporated into the calculation of the spin susceptibility of the hole liquid. In general terms, the findings demonstrate how the interplay between the ferromagnetic RKKY interaction, carrier localization, and intrinsic antiferromagnetic superexchange affects the ordering temperature and the saturation value of magnetization in magnetically and electrostatically disordered systems. Comment: 14 pages, 10 figures
Magnetotransport properties of p-type ferromagnetic (Ga,Mn)As, a diluted magnetic semiconductor based on III-V semiconductors, are measured and the p-d exchange between holes and Mn 3d spins is determined. The ferromagnetic transition temperatures calculated based on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction using the exchange reproduce remarkably well the observed ferromagnetic transition temperatures, demonstrating that ferromagnetism of (Ga,Mn)As has its origin in the RKKY interaction mediated by holes.
Signatures of spin-glass freezing such as the appearance of 1/f conductance noise, the recovery of universal conductance fluctuations, aging, as well as magnetic and thermal irreversibilities, are detected in mesoscopic wires of Cd1-xMnxTe:I at millikelvin temperatures. Spectral characteristics of conductance time series are consistent with the droplet model of short-range spin glasses.
We report on the growth and basic characterization of new quantum well structures made of diluted magnetic semiconductors. The novelty of the structures has two aspects. First, by molecular beam epitaxy we attempted to grow diluted magnetic semiconductor materials containing chromium ions as the magnetic component. We succeeded in obtaining materials containing up to 3 atomic percent of Cr in ZnTe and CdTe hosts. The structural quality of these materials grown in a form of relatively thick (1–4 μm) epitaxial layers, as evidenced by X-ray double rocking curves, degrades quickly with an increasing molar fraction of Cr. The lattice parameter of the cubic, zinc-blende phase is found to increase with the Cr contents. On the other hand, the optical quality of the structures containing Cr ions only in the quantum wells regions is quite satisfactory. The second aspect of the novelty of the reported structures is related to a precise composition profiling. The digital growth method in MBE is used to fabricate parabolic, half-parabolic and triangular quantum wells. Such structures are more effective in confining electron and hole motions than the usual rectangular quantum wells, as evidenced by large exciton binding energy values.
Using doped semiconductors as a paradigm, the low-temperature magnetic and thermodynamic behaviour of a disordered system undergoing a metal-insulator transition is described, and compared with various theoretical approaches from the metallic and insulating phases. Issues addressed include universal behaviour in the insulating phase, local moments in the metallic phase, and effects of compensation.
Incorporation of diluted magnetic semiconductors as the barrier material in heterostructures is of great interest since it allows one to induce magnetically large variations of the conduction- and valence-band offsets which, in turn, give rise to large variations of the carrier confinement energies observed by optical spectroscopy. This Zeeman effect is now well understood for a field applied along the heterostructure growth axis. Then both the heavy- and light-hole-related lines split approximately symmetrically into two circularly polarized components. In this paper we analyze the Zeeman splitting observed for a magnetic field applied in the plane of the layers. Then at low field the heavy-hole splitting is vanishingly small. At larger fields, very strongly asymmetric splittings are observed, reflecting the change of the ``best'' quantization axis, from the growth axis to the field direction. The theoretical analysis accounts well for both the Zeeman splittings and the change in the intensities of the linearly polarized lines.
Light-induced persistent change in the concentration of occupied shallow donors (photomemory effect) in Cd1-xMnxTe1-ySey:In has been used for determining the contribution of donor-bound magnetic polarons to the total magnetization of the crystal. This contribution must be taken into account in any precise description of low temperature properties of diluted magnetic semiconductors containing shallow donors. The observed agreement between experimental data and the theory of bound magnetic polarons provides additional support for the negative-U model of DX-like centers in II-VI semiconductors.
High-quality iodine-doped ZnSe layers have been grown by MOVPE using alkyliodide sources (ethyliodide and n-butyliodide). The carrier concentration at room temperature, n, can be widely controlled from 1×1016 to 3×1019 cm-3 by varying the dopant flow rate. The lowest resistivity of 1.3×10-3 ω cm has been obtained at the highest doping level. The I-doped layers exhibit strong blue photoluminescence at room temperature. The emission intensity from the layers with n=(2-3)×1018 cm-3 is several handred times stronger than that from undoped ZnSe.
The carrier states are considered in disordered or in not-fully-ordered nometallic systems under conditions when the internal parameters of the medium change relatively rapidly. In a definite region of temperatures and electron-medium interaction constants, there can be produced in these systems fluctuons, i.e., large-radius formations in which the electron is autolocalized near the change of the fluctuation, concentration, or internal parameter of the medium, and maintains the fluctuations stationary through its field. The characteristics of fluctuons are investigated in solutions, in para- and ferromagnetic semiconductors, in systems near the critical point in a solution, or in a gas-liquid system, and also near a first-order phase transition point. The mechanism of fluctuon mobility is discussed. A transition of electrons into fluctuonic states can have the character of a smeared first-order transition and can alter strongly different electronic properties of the system, as well as some other system properties. The possibility of spontaneous dispersion of a system with easily-alterable internal parameters is considered at a relatively high carrier density.
We report on growth and characterization of modulation doped CdTe/Cd
1- yMg yTe quantum well structures. Well resolved
Shubnikov—de Haas oscillations and quantum Hall effect have been
observed. In the best CdTe/Cd 1- yMg yTe
structures the modulation doping enabled fabrication of a
two-dimensional electron gas with mobility exceeding 10 5 cm
2/V s. This is the highest mobility reported in wide-gap
II-VI materials.
Magnetotransport is investigated in a new class of heterostructures wherein a two-dimensional electron gas (2DEG) is exchange coupled to a 2D distribution of local moments. Quantum transport in these “magnetic” 2DEGs is strongly influenced by the s-d exchange-enhanced spin splitting, resulting in a highly spin polarized gas beginning at large Landau level filling factors. Diffusive transport in low magnetic fields is dominated by modifications of the Hartree corrections to the conductivity arising from the giant spin splitting. An anomalous negative magnetoresistance at higher magnetic fields suggests the suppression of spin-disorder scattering.
Critical exponents for a d-dimensional system with an isotropic n-component order parameter and long-range attractive interactions decaying as 1/rd+?? (??>0) are derived, using the renormalization group approach, as power series in ??=2??-d>0 (?????2, fixed) or ????=??-1/2d>0 (d fixed) and, separately, to order 1/n for all d and ?????2. For ??<0 the exponents have fixed ("classical") values; when ??=????=0 fractional powers of ln(??T/Tc) appear; when ??>2 the exponents assume their short-range values.
Transport properties of 2% Gd‐doped EuO with Tc≈123°K have been investigated. The resistivity anomaly in the neighborhood of Tc can be explained satisfactorily by critical scattering theory. Estimates of the exchange interaction between conduction electrons and localized spins are found to vary from 4.9×10−2 eV in Gd :EuO to 4.3×10−2 eV in Gd :EuS.
Cyclotron resonance of electron and holes have been optically detected at 70 GHz and at 1.8 K in n-type CdTe. The bare effective masses, in unit of the free electron mass, are found to be: m* = 0.088 ± 0.004, m*lh = 0.12 ± 0.01, m* = 0.60 ± for H // <100>, and m*e = 0.089 0.004, m*lh = 0.11 ± 0.01, m*hh = 0.69 ± 0.02 for H // <111>. The Luttinger valence band parameters deduced from these measurements are: γ1 = 5.3 ± 0.5, γ2 = 1.7 ± 0.3 and γ3 = 2.0 ± 0.3, in fair agreement with the calculations of Lawaetz.
The carrier states are considered in disordered or in not-fully-ordered nometallic systems under conditions when the internal parameters of the medium change relatively rapidly. In a definite region of temperatures and electron-medium interaction constants, there can be produced in these systems fluctuons, i.e., large-radius formations in which the electron is autolocalized near the change of the fluctuation, concentration, or internal parameter of the medium, and maintains the fluctuations stationary through its field. The characteristics of fluctuons are investigated in solutions, in para- and ferromagnetic semiconductors, in systems near the critical point in a solution, or in a gas-liquid system, and also near a first-order phase transition point. The mechanism of fluctuon mobility is discussed. A transition of electrons into fluctuonic states can have the character of a smeared first-order transition and can alter strongly different electronic properties of the system, as well as some other system properties. The possibility of spontaneous dispersion of a system with easily-alterable internal parameters is considered at a relatively high carrier density.
The presence of a ferromagnetic transition in single, modulation-doped, 8 nm quantum well of ${\mathrm{Cd}}_{0.976}{\mathrm{Mn}}_{0.024}\mathrm{Te}/{\mathrm{Cd}}_{0.66}{\mathrm{Mg}}_{0.27}{\mathrm{Zn}}_{0.07}\mathrm{T}\mathrm{e}:\mathrm{N}$ is evidenced by photoluminescence magnetospectroscopy. The transition is driven by long range Ruderman-Kittel-Kasuya-Yosida interactions between Mn spins, mediated by $2\ifmmode\times\else\texttimes\fi{}{10}^{11}$ holes per ${\mathrm{cm}}^{2}$. It occurs at 1.8 K, in agreement with a mean-field model.
We report the inducement of a ferromagnetic order by photogenerated carriers in a novel III-V\char21{}based magnetic semiconductor heterostructure $p$-(In,Mn)As/GaSb grown by molecular beam epitaxy. At low temperatures $(<35\mathrm{K})$, samples preserve ferromagnetic order even after the light is switched off, whereas they recover their original paramagnetic condition above 35 K. The results are explained in terms of hole transfer from GaSb to InMnAs in the heterostructure, which enhances a ferromagnetic spin exchange among Mn ions in the InMnAs layer.
Resistivity and Hall-effect measurements in Eu0.95Gd0.05S give evidence for the onset of a well defined conduction band with critical scattering coexisting with magnetic impurity states.
Ruderman-Kittel-Kasuya-Yosida interaction between localized spins is considered for various dimensionality structures of doped diluted magnetic semiconductors. The influence of this interaction on the temperature and magnetic-field dependencies of magnetization and spin splitting of the bands are evaluated in the mean-field approximation. The results show that the hole densities that can presently be achieved are sufficiently high to drive a paramagnetic-ferromagnetic phase transition in bulk and modulation-doped structures of II-VI diluted magnetic semiconductors.
Results of millikelvin resistance studies of barely metallic n-Cd1-xMnxSe, n-Cd1-xFexSe, and n-Cd1-xZnxSe, doped with In or Sc, are presented and discussed in terms of the formation of bound magnetic polarons at the localization boundary.
Thermal properties of large magnetic polarons localized on donors in a magnetic semiconductor are studied theoretically with the effect of thermodynamic fluctuations of magnetization taken into account. The model quantitatively describes recent spin-flip Raman scattering data for Cd0.95Mn0.05Se.
The growth conditions and the electrical properties of modulation-doped Cd1-xMnxTe/Cd1-y-zZnzMgyTe : N (0 less than or equal to x less than or equal to 0.05) quantum well structures, in which a ferromagnetic transition has been observed, are presented. The growth temperature, the design of the structure and the composition of layers must be controlled with a greater care than in undoped samples. Ohmic contacts have been realised on a single quantum well structure by growing a composition graded layer at the surface.
Spin dynamics of electrons in n-type Cd0.95Mn0.05Se near the metal-to-insulator transition are probed by means of inelastic-light-scattering measurements as a function of magnetic field up to 8 T and temperature down to 0.25 K. The observed Raman spin-flip scattering line is demonstrated to arise from itinerant (diffusive) electrons. The spin-split energies (Stokes shifts), being determined by the s-d exchange interaction, increase strongly as the temperature is lowered, and at 0.25 K attain values that correspond to an effective Landé factor as large as 500. Variations of the spin-split energy with the magnetic field follow a modified Brillouin function suitable for this diluted magnetic semiconductor in a paramagnetic phase. A better description of experimental results is obtained, however, assuming the existence of an additional magnetization that depends only weakly on the external magnetic field. Such magnetization could be induced by bound magnetic polarons, and, therefore, its appearance points indirectly to the presence of local s spins on the metallic side of the metal-to-insulator transition. Studies of the linewidth in forward- and backscattering geometries provide information on the spin-relaxation time T2 and spin-diffusion coefficient Ds of itinerant electrons. The magnitude of T2 is shown to be primarily determined by (i) spin-flip scattering of electrons by magnetic ions and (ii) motionally narrowed inhomogeneous broadening caused by compositional fluctuations of magnetization. It is demonstrated that, in agreement with theoretical expectations, both T2 and Ds are strongly affected by electron-electron interactions and localization corrections.
We consider the magnetic field and temperature dependences of the spin splitting for an electron localized on a shallow donor, taking into account the s-d coupling with the surrounding magnetic ions. We calculate the probability distribution of the spin splitting Δ with the thermodynamic fluctuations of magnetization included. They are responsible for persistence of the spin splitting at ambient temperature in the absence of the field. The probability distribution of the spin splitting is the main factor determining the energy and the shape of the optical transition line between the spin-split states. We compare our results with recent experimental results on spin-flip Raman scattering in Cd1-xMnxSe. Our theory provides a satisfactory quantitative description of the donor electron accompanied by a nonuniform cloud of magnetization in that material.
A new GaAs‐based diluted magnetic semiconductor, (Ga,Mn)As, was prepared by molecular beam epitaxy. The lattice constant of (Ga,Mn)As films was determined by x‐ray diffraction and shown to increase with the increase of Mn composition, x. Well‐aligned in‐plane ferromagnetic order was observed by magnetization measurements. Magnetotransport measurements revealed the occurrence of anomalous Hall effect in the (Ga,Mn)As layer. © 1996 American Institute of Physics.
Magnetism has been a topic of study since the ancient times of science. Judging by the number of papers appearing each year, the group of scientists concerned with the properties of magnetic materials is vastly expanding. The reason for the great interest in this field is not only the wide application which these materials have found in technology, but also the chance to contribute to the understanding of basic physics. The term “magnetic material” in this article refers to a substance which spontaneously exhibits magnetic order below a certain temperature. This magnetic order can be of the ferro-, ferri-, antiferro-, or metamagnetic kind. However, within these magnetic structures ferromagnetism appears to be the most important one. Ferromagnetism is defined by the spontaneous parallel alignment of atomic magnetic moments over relatively large regions of a solid. Magnetic order is limited to compounds which contain elements with incompletely filled electron shells, as for example, the transition elements.
Symmetrically strained Si/SiGe superlattices (25 Å wells/14 Å barriers) with homogeneous Sb doping concentrations of 4.5 and show low-temperature magnetoconductivity effects which can be explained by single-electron backscattering and disorder-induced electron - electron interaction for an anisotropic three-dimensional case. The insulating phase of two lower doped samples (2.0 and ) is documented by the observation of variable range hopping conductivity. In addition, the extrapolated zero-temperature conductivities for in different magnetic fields show a magnetic-field-induced metal-to-insulator transition, demonstrating a three-dimensional behaviour of this superlattice with respect to localization.
The influence of a system of magnetic-field-aligned paramagnetic ions on the conduction and valence band electron states is studied. A model applicable to large-gap semiconductors is presented, in which the direct influence of a magnetic field on the band electron states is neglected. This assumption allows to calculate the E(k) dependence in the presence of a magnetic field. The calculations are performed in the Kohn-Luttinger model producing a strongly anisotropic and nonparabolic structure. As an illustration of the obtained results measurements of the exciton reflection structure in a magnetic field are presented on the ternary semiconductor CdMnTe. The ratio of the exchange integrals of conduction band electrons and valence band electrons to manganese ions is estimated to α/β = −0.25.Es wird der Einfluß eines Systems von im Magnetfeld ausgerichteten paramagnetischen Ionen auf die Leitungs- und Valenzbandelektronenzustände untersucht. Vorgeschlagen wird ein auf breitbandige Halbleiter anwendbares Modell, in dem der direkte Einfluß des Magnetfeldes auf die Bandelektronenzustände vernachlässigt wird. Diese Voraussetzung ermöglicht die Berechnung der E(k)-Abhängigkeit bei Vorhandensein eines Magnetfeldes. Die Bcrechnungen werden ausgeführt im Kohn-Luttinger-Modell, welches eine stark anisotrope und nichtparobolische Struktur ergibt. Zur Illustration der erhaltenen Ergebnisse werden Messungen der Exzitonen-Reflexions-struktur im Magnetfeld für CdMnTe-Halbleiter angeführt. Das Verhältnis der Austauschintegrale von Leitungsbandelektronen und Valenzbandelektronen mit Mangan-Ionen wird zu α/β = −0,25 geschätzt.
The stability of free magnetic polarons (FMP) is studied as a function of dimensionality in the mean-field approximation. The non-linear Schrödinger equation is solved numerically in a self-consistent manner. Realistic properties of the magnetic medium (here diluted magnetic semiconductors) are included. Hole FMP stability in quantum wells or quantum wires with finite barrier is treated, the magnetic medium being either in the barrier or in the well (or wire). Qualitative extension to exciton FMP is given: the stability of exciton FMP in CdMnTe/CdTe/CdMnTe quantum wells seems unlikely.
La stabilité des polarons magnétiques libres est étudiée en fonction de la dimensionnalité dans une approximation de champ moyen. L'équation de Schrödinger non-linéaire est résolue numériquement de facon self-consistante. Les propriétés du milieu magnétique (ici les semiconducteurs magnétiques dilués) sont prises en compte de facon réaliste. La stabilité des polarons libres de trou est traitée dans les puits ou fils quantiques avec barrière de hauteur finie, le matériau magnétique étant, soit dans la barrière, soit dans le puits (ou le fil). Une extension qualitative aux excitons est proposée: la stabilité des polarons libres de type exciton paraǐt improbable dans les puits quantiques CdMnTe/CdTe/CdMnTe.
We report on the doping properties of the II–VI Te-related compounds, ZnTe, CdTe and CdZnTe, CdMgTe and ZnMgTe, using two different nitrogen plasma sources. High doping levels are measured for ZnTe, slightly lower for CdTe (8 × 1017cm−3). Following the comparative study of nitrogen doping in these materials, we invoke the possible formation of nitride compounds as responsible for the large nitrogen amount incorporated in Mg-containing alloys. The formation of such compounds might be reduced by using appropriate growth conditions and doping levels in the 4 × 1017cm−3 range are obtained in ternary and quaternary alloys containing Mg. Such doping levels allow the growth and the study of high-quality modulation-doped heterostructures.
Magnetic susceptibility and Hall effect in Pb1−x−ySnyMnx semimagnetic semiconductor with 0.03 ⩽ x ⩽ 0.12 were investigated as a function of carrier concentration. At low temperatures a ferromagnetic phase was observed in the samples with a high carrier concentration. The dependence of the Curie temperature Tc on the carrier concentration p has a threshold-like character for all investigated samples. The threshold hole concentration depends on the Mn content and decreases with increasing concentration of manganese ions. The results are summarized in the form of Tc(x,p) magnetic phase diagram.
Magnetization measurements down to 10 mK of Cd 1-x Mn x Te for Mn concentrations 0.01≤x≤0.15 show spin glass behavior. Such behavior is attibuted to short‐range exchange and dipolar interactions. Both interactions are used to explain the concentration dependence of the spin freezing temperatures for 0.01≤x≤0.6, the short‐range exchange dominating at high concentrations, and the dipolar interaction at low concentrations.
We review the physical properties of diluted magnetic semiconductors (DMS) of the type A<sup>II</sup> 1-x Mn x B<sup>VI</sup> (e.g., Cd 1-x Mn x Se, Hg 1-x Mn x Te). Crystallographic properties are discussed first, with emphasis on the common structural features which these materials have as a result of tetrahedral bonding. We then describe the band structure of the A<sup>II</sup> 1-x Mn x B<sup>VI</sup> alloys in the absence of an external magnetic field, stressing the close relationship of the sp electron bands in these materials to the band structure of the nonmagnetic A<sup>II</sup>B<sup>VI</sup> ‘‘parent’’ semiconductors. In addition, the characteristics of the narrow (nearly localized) band arising from the half‐filled Mn 3d<sup>5</sup> shells are described, along with their profound effect on the optical properties of DMS. We then describe our present understanding of the magnetic properties of the A<sup>II</sup> 1-x Mn x B<sup>VI</sup> alloys. In particular, we discuss the mechanism of the Mn<sup>+</sup><sup>+</sup>‐Mn<sup>+</sup><sup>+</sup> exchange, which underlies the magnetism of these materials; we present an analytic formulation for the magnetic susceptibility of DMS in the paramagnetic range; we describe a somewhat empirical picture of the spin‐glasslike freezing in the A<sup>II</sup> 1-x Mn x B<sup>VI</sup> alloys, and its relationship to the short range antiferromagnetic order revealed by neutron scattering; and we point out some not yet fully understood questions concerning spin dynamics in DMS revealed by electron paramagnetic resonance. We then discuss the sp‐d exchange interaction between the sp band electrons of the A<sup>II</sup> 1-x Mn x B<sup>VI</sup> alloy and the 3d<sup>5</sup> electrons associated with the Mn atoms. Here we present a general formulati-
on of the exchange problem, followed by the most representative examples of its physical consequences, such as the giant Faraday rotation, the magnetic‐field‐induced metal‐to‐insulator transition in DMS, and the properties of the bound magnetic polaron. Next, we give considerable attention to the extremely exciting physics of quantum wells and superlattices involving DMS. We begin by describing the properties of the two‐dimensional gas existing at a DMS interface. We then briefly describe the current status of the A<sup>II</sup> 1-x Mn x B<sup>VI</sup> layers and superlattices (systems already successfully grown; methods of preparation; and basic nonmagnetic properties of the layered structures). We then describe new features observed in the magnetic behavior of the quasi‐two‐dimensional ultrathin DMS layers; and we discuss the exciting possibilities which the sp‐d exchange interaction offers in the quantum‐well situation. Finally, we list a number of topics which involve DMS but which have not been explicitly covered in this review such as elastic properties of DMS, DMS‐based devices, and the emerging work on diluted magnetic semiconductors other than the A<sup>II</sup> 1-x Mn x B<sup>VI</sup> alloys—and we provide relevant literature references to these omitted topics.
We demonstrate the introduction of high carrier densities into two and three‐dimensional magnetic semiconductor heterostructures that contain large local concentrations of magnetic moments. The use of (ZnSe) m-f (MnSe) f digital alloys readily allows the fabrication of epilayer samples of moderate Mn composition with carrier concentrations up to ∼10<sup>19</sup> cm<sup>-3</sup>. Modulation doping of ZnSe/Zn 1-x-y Cd y Mn x Se quantum wells enables the fabrication of a 2‐D electron gas confined within the magnetic region with sheet concentrations up to ∼6×10<sup>11</sup> cm<sup>-2</sup>. © 1996 American Institute of Physics.
The p‐type doping of ZnTe, CdTe, and Cd 1-x Zn x Te (CZT) using a nitrogen dc plasma source during growth by molecular beam epitaxy is demonstrated. For ZnTe, doping levels as high as 10<sup>20</sup> cm<sup>-3</sup> were achieved. In CZT alloys, a progressive decrease of the maximum doping level is observed for decreasing Zn content. Using pulse doping methods, a doping level of p≊3×10<sup>18</sup> cm<sup>-3</sup> is obtained for a 12% Zn CZT layer. For CdTe layers, the highest level achieved is p≊10<sup>17</sup> cm<sup>-3</sup>. The progressive acceptor compensation phenomenon is discussed with emphasis on the role of the lattice distortion on the nitrogen incorporation mechanisms.
For the first time clear evidence for two‐dimensional Shubnikov–de Haas oscillations in modulation‐doped CdTe/CdMnTe quantum‐well structures is reported. The structures were grown by molecular‐beam epitaxy using ZnBr 2 as a novel source material for the n‐type doping of II‐VI epitaxial layers. From an analysis of the Shubnikov–de Haas oscillations a carrier density of 9×10<sup>11</sup> cm<sup>-2</sup> and an effective mass of 0.1 m 0 could be deduced. Due to band filling the Fermi energy in the subbands is shifted above the conduction‐band edge. This can be detected as a Stokes shift of absorption compared to photoluminescence recombination. From the Fermi energy shift the carrier concentration can be estimated, which agrees well with values determined by Hall‐effect measurements.
The study of Cd0.9Mn0.1Te/Cd0.6Mg0.4Te quantum wells with semimagnetic well layers in inplane and perpendicular magnetic fields enables us to develop a general picture of the anisotropic Zeeman splitting in semimagnetic quantum wells. Due to quantum confinement and strain a two-dimensional spin quantization occurs, which gives rise to a vanishing spin splitting of heavy-hole states and a twice larger spin splitting of light-hole states for inplane magnetic fields. With increasing magnetic fields a reorientation of hole spins towards the magnetic field direction occurs due to the huge exchange splitting in semimagnetic layers. Investigating different width (CdMn)Te/(CdMg)Te quantum wells with thicknesses ranging from 100Å down to 18Å a significant dependence of the inplane Zeeman pattern on the well thickness is found. We demonstrate that the competition between initial quantization due to quantum confinement and the magnetic field induced exchange splitting defines the complex Zeeman pattern in inplane magnetic fields.
A review is given on the effects of the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between localized spins in various dimensionality systems of doped diluted magnetic semiconductors (DMS). Since this interaction is long-range, its influence on the temperature and magnetic field dependencies of magnetization and spin splitting of the bands is evaluated in the mean-field approximation, but by taking into considerations disorder-modified carrier–carrier interactions. The results show that the hole densities, which can presently be achieved, are sufficiently high to drive a paramagnetic–ferromagnetic phase transition in bulk and modulation-doped structures of II–VI DMS. Our recent photoluminescence studies on MBE-grown samples, containing a single, modulation-doped, 8 nm quantum well of Cd1−xMnxTe/Cd1−y−zMgyZnzTe:N are discussed. These studies reveal the presence of a ferromagnetic transition induced by the two-dimensional hole gas. The transition occurs between 1.8 and 2.5 K, depending on the Mn concentration x, in agreement with the theoretical model.
This paper reviews the progress made in the last several years in understanding the properties of disordered electronic systems. Even in the metallic limit, serious deviations from the Boltzmann transport theory and Fermi-liquid theory have been predicted and observed experimentally. There are two important ingredients in this new understanding: the concept of Anderson localization and the effects of interaction between electrons in a disordered medium. This paper emphasizes the theoretical aspect, even though some of the relevant experiments are also examined. The bulk of the paper focuses on the metallic side, but the authors also discuss the metal-to-insulator transition and comment on problems associated with the insulator.
A calculation is given of the indirect exchange Ii·Ij type coupling
of nuclear magnetic moments in a metal by means of the hyperfine
interaction with the conduction electrons. The interaction appears
to account qualitatively for the broad nuclear spin resonance lines
observed in natural metallic silver. It is expected that the interaction
may sharpen the resonances in pure isotopic specimens. The line shape
of the minority isotope in a binary mixture may tend to be Gaussian,
while that of the majority isotope may tend to be Lorentzian, if
the indirect exchange interaction is dominant.
The charge (or spin) polarisation induced in its vicinity by an impurity A at point B in an alloy is calculated with inclusion of possible scattering effects by other impurities distributed at random between A and B. Possible applications of the calculation include: 1) The question of the form factors of magnetic impurities (these being necessarily measured at relatively high concentrations. 2) Order disorder transformations : in an alloy undergoing such a transformation, the mean free path varies strongly with temperature and the effective interaction between atoms becomes also temperature dependent. 3) Magnetic order in the rare earth metals : the observed change of pitch of the spirals with temperature having possibly the same origin. 4) The suppression of the Kohn anomaly in phonon spectra due to impurity (or thermal) scattering of the electrons. On calcule la polarisation de charge (ou de spin) induite en un point B dans un alliage au voisinage d'une impureté A en tenant compte de la diffusion des électrons par d'autres impuretés (réparties au hasard) entre A et B. Les applications possibles de ce calcul comprennent : 1) La discussion des facteurs de forme magnétiques d'impuretés (ceux-ci étant nécessairement mesurés à des concentrations relativement élevées). 2) L'étude des transformations ordre désordre : dans un alliage subissant une telle transformation, le libre parcours moyen varie fortement avec la température, et l'interaction effective entre atomes également. 3) L'étude des configurations magnétiques des métaux de terres rares, où le même mécanisme pourrait expliquer la variation du pas des hélices avec la température. 4) La disparition de l'anomalie de Kohn dans les spectres de phonons en présence de diffusion par des impuretés ou par les vibrarions de réseau.
REVIEW
Semiconductor devices generally take advantage of the charge of electrons, whereas magnetic materials are used for recording information involving electron spin. To make use of both charge and spin of electrons in semiconductors, a high concentration of magnetic elements can be introduced in nonmagnetic III-V semiconductors currently in use for devices. Low solubility of magnetic elements was overcome by low-temperature nonequilibrium molecular beam epitaxial growth, and ferromagnetic (Ga,Mn)As was realized. Magnetotransport measurements revealed that the magnetic transition temperature can be as high as 110 kelvin. The origin of the ferromagnetic interaction is discussed. Multilayer heterostructures including resonant tunneling diodes (RTDs) have also successfully been fabricated. The magnetic coupling between two ferromagnetic (Ga,Mn)As films separated by a nonmagnetic layer indicated the critical role of the holes in the magnetic coupling. The magnetic coupling in all semiconductor ferromagnetic/nonmagnetic layered structures, together with the possibility of spin filtering in RTDs, shows the potential of the present material system for exploring new physics and for developing new functionality toward future electronics.
The dependence of the calculated Ruderman-Kittel-Kasuya-Yosida range function of a one-dimensional free-electron metal on the order of the integrations over the occupied states, and over the Fourier components of the perturbation is discussed and clarified. The correct result is derived. The range function of a magnetized layer (e.g., a magnetic layer in a multilayer material) is also calculated and compared with the range functions of point sources in the one-dimensional and in the three-dimensional cases.
We consider the indirect exchange between magnetic moments placed in a metallic environment that is weakly disordered due to the presence of randomly distributed nonmagnetic impurities. We find that the even moments of the exchange interactions are long-ranged, falling off as a power law in the spin separation distance just as in the pure metal. Depending on the experimental quantity of interest, the effective coupling between spins is given by either the first or the second moment of the distribution of exchange couplings in the system. The effect of spin-orbit scattering on the interaction between local moments is considered. In the case of isotropic spin-orbit scattering in both bulk materials and thin films, the isotropic exchange interactions are exponentially suppressed at large distances. In strictly two dimensions, however, there are long-range anisotropic spin-exchange couplings that fall off inversely with the square of the distance. In this case the interaction becomes effectively Ising at large distances. The distribution of couplings is seen to be broad, reflecting the sensitivity of the interactions to changes in the impurity configuration. Correlations of the couplings between sites are also found to have power-law fall-off with distance; however, these are higher order in the perturbation expansion. The relevance to experiments is discussed.
We present in detail a quantitatibe description of Zeeman splittings of exciton states in a nonmagnetic quantum well with diluted-magnetic-semiconductor barriers which takes interface mixing into account. For structures with high Mn concentration in the barrier we show that this effect leads to a dramatic increase of the Zeeman splitting even to a value exceeding the barrier splitting. We describe a method of interface characterization based on Zeeman-effect measurements. It enables one to study the shape of the interface profile, the influence of the growth conditions on the interface, and provides a perspective to decouple the influence of interface mixing from truly two-dimensional magnetic effects in studies of ultrathin magnetic layers. The influence of the parameters of the model on the results obtained and the practical applicability of the method are discussed. In particular, we show that the quantum well profile is strongly asymmetric in relation to the growth direction and we demonstrate the small influence of the intrinsic effect in relation to interface magnetism.
A theory of superexchange in Cr-based ${\mathit{A}}_{\mathrm{II}}$${\mathit{B}}_{\mathrm{VI}}$ diluted magnetic semiconductors (DMS's) is presented. The spin interaction between ${\mathrm{Cr}}^{2+}$ ions, calculated numerically for zinc chalcogenides, exhibits properties unique in DMS's, it is ferromagnetic, and depends on the relative orientations of the ionic Jahn-Teller distortions. We explain the origin of this unusual behavior and predict a ferromagnetic character of the superexchange in other Cr-based ${\mathit{A}}_{\mathrm{II}}$${\mathit{B}}_{\mathrm{VI}}$ DMS's. \textcopyright{} 1996 The American Physical Society.
The magnetoresistance (MR) and Hall coefficient of n-type Cd0.95Mn0.05Te samples with carrier concentrations 1.2×1017≤n≤6.6×1017 cm-3 were measured at 1.2≤T≤4.2 K in fields up to 200 kOe. The results at zero magnetic field show that the carrier concentration at the metal-insulator transition is nc≃2×1017 cm-3, in rough agreement with Mott’s prediction. In fields H≲80 kOe the resistivity ρ first increases with H, then passes through a maximum, and finally decreases. The increase of ρ at low fields is accompanied by an increase in the magnitude of the Hall coefficient, while the decrease of ρ above the maximum is accompanied by an increase in the Hall mobility. The MR below ∼80 kOe is attributed to mechanisms associated with the giant spin splitting of the conduction band. The increase of ρ at low fields follows the behavior expected from quantum corrections to the conductivity arising from the electron-electron interaction. The decrease of ρ above the maximum is attributed to the rise of the Fermi energy in the majority-spin subband. Above ∼80 kOe the qualitative behavior of the MR depends on the carrier concentration. Samples with n<nc exhibit an upturn in the resistivity at high fields. This effect is attributed to the squeezing of the donor-electron wave function. In addition, the MR of these samples shows an anomaly near the first magnetization step. In metallic samples (n>nc) the MR and Hall coefficient exhibit oscillations at high fields. The oscillations are interpreted as Shubnikov–de Haas oscillations arising from the majority-spin subband. This interpretation is supported by model calculations.
A strong temperature and magnetic field dependence of conductivity has been found in Cd0.95Mn0.05Se. The effect appears to result from the influence of magnetic polarons and of the exchange-induced spin splitting on the quantum corrections to the conductivity of disordered magnetic metals.
We present an analytical method which enables one to find the exact spatial dependence of the indirect RKKY interaction between the localized moments via the conduction electrons for the arbitrary dimensionality $n$. The corresponding momentum dependence of the Lindhard function is exactly found for any $n$ as well. Demonstrating the capability of the method we find the RKKY interaction in a system of metallic layers weakly hybridized to each other. Along with usual $2k_F$ in-plane oscillations the RKKY interaction has the sign-reversal character in a direction perpendicular to layers, thus favoring the antiferromagnetic type of layers' stacking. Comment: 3 pages, REVTEX, accepted to Phys.Rev. B
- Jaroszyński