III–V Based Magnetic Semiconductors

Jungwirth, T.

doi:10.1007/978-94-007-6892-5_20

T. Jungwirth^4,5

7483 Accesses

Abstract

(Ga,Mn)As and related (III,Mn)V compounds are at the forefront of spintronics research exploring the synergy of ferromagnetism with the physics and the technology of semiconductors. Over the past 20 years, the research of (Ga,Mn)As has led to a deeper understanding of previously known spintronics phenomena, to discoveries of new effects, and to demonstrations of unprecedented functionalities of experimental spintronics devices with general applicability to a wide range of magnetic materials. In this chapter we review some of the basic structural, magnetic, electronic, and optical properties of the ferromagnetic (III,Mn)V semiconductors, as well as the devices fabricated from these model spintronics materials.

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III–V Based Magnetic Semiconductors

Magnetic III–V Semiconductor-Based Hybrid Structures

Room Temperature Ferromagnetism: Nonmagnetic Semiconductor Oxides and Nonmagnetic Dopants

Article 20 February 2021

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Introduction

(Ga,Mn)As has been the most extensively studied member of the Mn-doped III–V family of magnetic semiconductors. It becomes ferromagnetic for doping above 1 % of the Mn local moments and acceptors. For semiconductor hosts this is a very high doping level which in case of (Ga,Mn)As and some related (III,Mn)V compounds can be achieved by the nonequilibrium, low-temperature molecular-beam-epitaxy (LT-MBE) technique [1–6].

Magnetic properties of the material can be modified by the means common in semiconductors, such as doping, electric fields, or light. For example, several experiments have verified that changes in the carrier density and distribution in thin (III,Mn)As films due to an applied gate voltage can induce reversible changes of the Curie temperature T _c, as illustrated in Fig. 1, and of other magnetic and magneto-transport properties [7–16]. The interplay between optical and magnetic properties was demonstrated in experiments in which ferromagnetism in a (III,Mn)As system is turned on and off optically or in which recombination of spin-polarized carriers injected from the ferromagnetic semiconductor yields emission of circularly polarized light [17–19].

The tunability of magnetic properties and compatibility with established heterostructure growth and microfabrication techniques in semiconductors have made (Ga,Mn)As an ideal test-bed material for spintronics research. High-quality magnetic tunnel junctions have been demonstrated showing large tunneling magnetoresistances [20–23]. In the studies of spin–transfer torques in tunnel junctions [24] and domain walls [25–31], the dilute-moment p-type (Ga,Mn)As is unique for its low saturation magnetization and strong spin–orbit coupled valence band [32–34]. This implies low currents required to excite magnetization dynamics and the leading role of magnetocrystalline anisotropies over the dipolar shape anisotropy fields, which allows for unprecedented control of the magneto-transport phenomena ex situ by microfabrication [27, 35] or in situ by piezoelectric gating [31, 36–38].

Besides the more conventional spintronics effects such as the tunneling magnetoresistance and spin–transfer torque, (Ga,Mn)As studies have particularly important contributions to the research of spintronics phenomena based on the relativistic spin–orbit coupling. Here among the new effects discovered in (Ga,Mn)As, and subsequently observed in other systems including conventional metal magnets, are the anisotropic magnetoresistance effects in nanostructures [39–44] and the current-induced spin–orbit torques observed in uniform magnetic structures [45, 46]. The optical activity of (Ga,Mn)As, characteristic of direct-gap semiconductors, has led to the discovery of the optical counterparts of the current-induced torques [47, 48].

In this chapter we provide an overview of the magnetic and electronic properties of (Ga,Mn)As and of the spintronics phenomena and devices that have been explored using this model material system. For more detailed discussions, we refer to other comprehensive review articles on ferromagnetic semiconductors [49–54].

Electronic Structure and Magnetic Coupling

The most stable position of Mn in the GaAs host lattice up to a certain level of Mn doping is on the Ga site. The isolated Mn_Ga substitutional impurity has the character of a local moment with zero orbital angular momentum and with spin S = 5/2 (Landé g-factor g = 2) due to the five 3d electrons and a moderately bound hole. The experimental acceptor binding energy of Mn_Ga is $ {E}_a^0\approx 0.1 $ eV [55–59].

At concentrations ≪ 1 % of Mn_Ga, (Ga,Mn)As is insulating and paramagnetic. Experimentally, ferromagnetism in (Ga,Mn)As is observed when Mn doping reaches approximately 1 %, and the system is still below but near the insulator-to-metal transition [60–63]. At these Min concentrations, the localization length of the holes is extended to a degree that allows them to mediate, via the sp − d hybridization, ferromagnetic exchange interaction between Min local moments, even though the moments are dilute. Beyond 1.5 % Mn doping, (Ga,Mn)As becomes a degenerate semiconductor with a metallic-like conduction [49, 51, 63]. In the metallic regime, Mn provides delocalized holes with a density comparable to Mn density [64–66].

Unlike the metal–insulator phase transition, which is sharply defined in terms of the temperature T = 0 limit of the conductivity, the crossover in the character of states near the Fermi level in semiconductors with increased doping is gradual [51, 67–71]. At very weak doping, the Fermi level resides inside a narrow impurity band separated from the valence band by an energy gap of magnitude close to the impurity binding energy. At high doping when (Ga,Mn)As is ferromagnetic and metallic, the basic electronic structure and origin of magnetism have been a subject of some controversies. Here it is important to separate the physics and terminology sides of the debate.

We start with the character of the electronic structure. Physics: Based on a resonant tunneling study, it was concluded [72] that the effect of Mn impurities in ferromagnetic metallic (Ga,Mn)As is condensed within a narrow (~10’s meV) detached impurity band, leaving the host GaAs valence band virtually unaffected. The photoemission studies [73, 74], on the other hand, showed that there is no gap between the Mn-induced impurity band and the GaAs valence bands and that Mn introduces changes throughout the entire valence band. Impurity and valence bands are merged in ferromagnetic (Ga,Mn)As, according to photoemission. While in the resonant tunneling experiments the detached impurity band is not measured directly and its presence if inferred indirectly from electrical transport measurement through a heterostructure containing (Ga,Mn)As, the merged impurity and valence bands are observed directly in the photoemission spectroscopy of bare (Ga,Mn)As films. Terminology: For merged impurity and valence bands, assigning the Fermi level states to an impurity band or to a valence band if ambiguous and, therefore, only a matter of the choice of a preferred language.

A related but separate side of the debate concerns the nature of the magnetic coupling in the ferromagnetic metallic (Ga,Mn)As. Physics: Density functional theory calculations of the band structure of (Ga,Mn)As are in agreement with the photoemission measurements [73, 74]. Microscopic calculations of the (Ga,Mn)As band structure based on the multiorbital tight-binding-approximation (TBA) Anderson model [75], which are in broad agreement with the density functional theory, provide a direct link between microscopic electronic structure calculations and effective models of magnetic coupling mechanisms. In (Ga,Mn)As, a smaller part of the spectral weight near the Fermi energy is formed by Mn d-orbitals and a larger part by the host GaAs sp-orbitals [73–75], as shown in Fig. 2. The states near the Fermi energy are formed by sp-orbitals with moderately hybridized Mn d states. Zener’s effective sp − d kinetic-exchange model is derived by performing the Schrieffer–Wolff transformation of the sp − d hybridization (and Coulomb interaction) into an effective exchange coupling between magnetic moments and carrier spins [51]. In the transformation, the sp − d hybridization is treated perturbatively so the model accuracy increases with decreasing hybridization strength. For the moderate sp − d hybridization in (Ga,Mn)As, one can expect sizable corrections beyond the weak sp − d hybridization limit of the kinetic-exchange model. Simultaneously, the Fermi level states in (Ga,Mn)As are not characterized by occupying a narrow detached impurity band with a dominant Mn d-orbital composition. The material is, therefore, far from the corresponding Zener’s d − d hopping double-exchange model when viewed from the perspective of the orbital-resolved electronic structure.

The weak sp − d hybridization kinetic-exchange model predicts a linear dependence of the mean-field Curie temperature T _c on the Mn moment density, and the d − d hopping double-exchange model predicts a square-root dependence on the Mn moment density [52]. In both models the mean-field T _c increases monotonously with the Mn moment density, and calculations based on the density functional theory band structure show a sublinear dependence for (Ga,Mn)As [52]. Strongly distinct predictions of the two models are for the carrier-density dependence of the mean-field T _c. While the kinetic-exchange model predicts a weak monotonous increase of T _c with increasing density (to power 1/3 approximately), the double-exchange model predicts maximum T _c at half filling and zero T _c for zero carrier compensation (filled or empty d − d hopping impurity band). Microscopic tight-binding Anderson [66] and density functional [52] calculations show initially an increasing T _c trend with increasing carrier density followed by a saturation near zero carrier compensation. The microscopic theories are consistent with experiments in Ref. [66] and [76]. On the other hand, the experimental work in Ref. [77] and [78] concluded that T _c collapses at zero carrier compensation. In Ref. [66] and [76], T _cs reach ~ 190 K while in Ref. [77] and [78] T _cs reach only ~ 90 K. Measurements in Ref. [66] and [76] were performed on (Ga,Mn)As materials prepared under carefully optimized synthesis conditions. The essential importance of optimized material synthesis for elucidating experimental doping trends in micromagnetic parameters of (Ga,Mn)As is thoroughly discussed in Ref. [79].

Terminology: It is only a matter of a preferred terminology how the mutually fully consistent physical results, as obtained among others in Refs. [52, 66, 73–76], are linked to Zener’s magnetic exchange models. One may emphasize the presence of contributions beyond the weak hybridization limit in (Ga,Mn)As by using a term “moderate sp − d hybridization kinetic exchange” [75], and others might prefer using a term “kinetic exchange with admixed double exchange” [52, 73].

In Fig. 3 we show density of states (DOS) over the entire Mn_Ga doping range obtained from the generalized gradient approximation (GGA) + U density functional calculations [52, 75]. The GGA + U, the TBA-Anderson, and the kinetic-exchange Zener theories all provide a consistent picture of the band structure of ferromagnetic (Ga,Mn)As. Simultaneously, it is important to keep in mind that the moderate acceptor binding energy of Mn_Ga shifts the insulator-to-metal transition to orders of magnitude higher doping densities than in the case of common shallow nonmagnetic acceptors, as mentioned above [63, 75]. Disorder and correlation effect, therefore, play a comparatively more significant role in (Ga,Mn)As than in degenerate semiconductors with common shallow dopants, and any simplified one-particle band picture of ferromagnetic (Ga,Mn)As can only represent a proxy to the electronic structure of the material.

To illustrate the role of strong intrinsic disorder in ferromagnetic (Ga,Mn)As, we show in Fig. 4 the local DOS along one of the directions inside the simulation cells illustrated in Fig. 5 for 5 % Mn doping. In the model, the band structure and disorder effects are treated at an equal level by using exact diagonalization supercell simulation method [80]. There is an extensive weight of the density of states in the mid-gap region which arises from the deep bonding states created by neighboring Mn impurities. The higher energy tail of the disordered valance band comprises localized states as highlighted in Fig. 4b. On the other hand, the Fermi energy is located deep in the delocalized region away from the mobility edge. The spatial inhomogeneity of the distribution of states in the gap region and the peaks formed by bonding states in the gap region are consistent with scanning tunneling microscopy (STM) experiments [81]. The effect of strong disorder on the wave functions is illustrated in Fig. 5 which compares the probability distributions of a localized state near the disordered valance band edge, a delocalized state near the Fermi energy, and a state near the mobility edge.

Curie Temperature and Doping Trends

As seen in Fig. 3, the bands evolve continuously from the intrinsic nonmagnetic semiconductor GaAs, via the degenerate ferromagnetic semiconductor (Ga,Mn)As to the ferromagnetic metal MnAs. From this it can be expected that T _c of MnAs, with the value close to room temperature (350 K for cubic MnAs inclusions in (Ga,Mn)As [82, 83]), sets the upper theoretical bound of achievable T _cs in (Ga,Mn)As across the entire doping range. In experiment, the Mn_Ga doping is limited to approximately 10 % with corresponding T _c reaching 190 K in uniform thin-film crystals prepared by optimized LT-MBE synthesis and post-growth annealing. In these samples the hole density is in the ~ 10²⁰ − 10²¹ cm⁻³ range, i.e., several orders of magnitude higher than densities in commonly used nonmagnetic semiconductors but also one to two orders of magnitude lower than is typical for metals.

A detailed measurement of the Curie temperature in a high-quality (Ga,Mn)As material is illustrated in Fig. 6 [84]. Figure 6a shows magnetization M(T) measured along the easy axis in this material over the whole studied temperature range. The remanence vanishes sharply at $ T\to {T}_c^{-} $. Figure 6b shows results of corresponding measurements of the resistivity ρ(T). A useful insight into the physics of the shoulder in ρ(T) near T _c is obtained by first removing the nonmagnetic part in the temperature dependence, c _nm T, which is approximated by linearly extrapolating from the high-temperature ρ(T) data (see the straight dotted line in Fig. 6b). The measured M(T) then allows to subtract the contribution from uncorrelated scattering, assuming a M ² expansion dependence [5, 85–87]. On the ferromagnetic side, a very close fitting is achieved by ρ _fit(T) = c ₀ + c _nm T + c _m2 M ²(T) + c _m4 M ⁴(T). On the paramagnetic side, the nose dive of the remaining magnetic contribution to ρ(T) suggests that the shoulder in the measured resistivity originates from a singular behavior at $ T\to {T}_c^{+} $ rather than from disorder broadening effects. The singularity is revealed by numerically differentiating the experimental zero-field ρ(T) curve, as shown in Fig. 6c. The position of the sharp peak in dρ/dT coincides with the Curie temperature determined from M(T).

The dρ/dT singularity described in Fig. 6 is a generic characteristic of optimized (Ga,Mn)As films spanning a wide range of Mn dopings. This is illustrated in Fig. 7c together with the other doping characteristics of the optimized materials shown in Fig. 7. From the doping trends seen in Fig. 7, the uniform (Ga,Mn)As materials with minimized extrinsic disorder can be divided into the following groups: At nominal dopings below ~ 0.1 %, the (Ga,Mn)As materials are paramagnetic, strongly insulating, showing signatures of the activated transport corresponding to valence band−impurity band transitions at intermediate temperatures and valence band−conduction band transitions at high temperatures (see Fig. 7a) [63, 79]. For higher nominal dopings, 0.5 ≲ x ≲ 1.5 %, no clear signatures of activation from the valence band to the impurity band are seen in the dc transport, indicating that the bands start to overlap and mix, yet the materials remain insulating. At x ≈ 1.5 %, the low-temperature conductivity of the film increases abruptly by several orders of magnitude (see Fig. 7b), and the system turns into a degenerate semiconductor. The onset of ferromagnetism occurs already on the insulating side of the transition at x ≈ 1 %. All ferromagnetic samples over a broad nominal Mn-doping range can have sharp Curie point singularities when synthesized under individually optimized growth and post-growth annealing conditions (see Fig. 7c).

The hole concentration p can be measured by the slope of the Hall curve at high fields with an error bar due to the multi-band nature estimated to ~ 20 % [66]. Within this uncertainty, the overall trend shows increasing p with increasing doping in the optimized materials, as shown in Fig. 7d. Similarly, the saturation moment and T _c steadily increase with increasing nominal doping up to x ≈ 13 %, as shown in Fig. 7e, f. Assuming 4.5 μ _B per Mn atom [88], the density N _Mn of uncompensated Mn_Ga moments can be inferred from the magnetization data (see left y-axis in Fig. 7e). Since there is no apparent deficit of p compared to N _Mn and since the interstitial Mn impurity [89–91] compensates one local moment but two holes, it can be concluded that interstitial Mn, which is the key contributor to extrinsic disorder, is removed in the optimally grown and annealed epilayers. Hence, a broad series of optimized (Ga,Mn)As materials can be prepared with reproducible characteristics, showing an overall trend of increasing saturation moment with increasing x, increasing T _c (reaching ~ 190 K), and increasing hole density. The materials have no measurable charge or moment compensation of the substitutional Mn_Ga impurities and have a large degree of uniformity.

Magnetic Anisotropy Effects in Films and Devices

Micromagnetic Parameters

The magnetic anisotropy relates to the dependence of the total energy of the magnetic material on the direction of the magnetization vector. In magnetic memories it is the key parameter that determines the retention of the stored information. In the optimized (Ga,Mn)As epilayers grown on GaAs, the internal magnetic anisotropy fields are dominated by three components. The out-of-plane component K _out is a sum of the thin-film shape anisotropy and the relativistic magnetocrystalline anisotropy due to the compressive growth strain in (Ga,Mn)As deposited on the GaAs substrate. The cubic magnetocrystalline anisotropy K _c reflects the zinc-blended crystal structure of the host semiconductor. The additional uniaxial anisotropy component K _u along the in-plane diagonal is not associated with any measurable macroscopic strain in the epilayer, and its origin is still debated.

In a ferromagnetic resonance experiment, the precession frequency is given by

$$ \begin{array}{l}f=\frac{g{\mu}_B}{h}\Big[{H}_{ext} \cos \left(\varphi -{\varphi}_H\right)-2{K}_{out}\\ {}+{K}_c\left(3+ \cos 4\varphi \right)/2+2{K}_u{ \sin}^2\left(\varphi -\pi /4\right)+\Delta {H}_n\Big]{}^{1/2}\\ {}\ \times \Big[{H}_{ext} \cos \left(\varphi -{\varphi}_H\right)\\ {}+2{K}_c \cos 4\varphi -2{K}_u \sin 2\varphi +\Delta {H}_n\Big]{}^{1/2},\end{array} $$

(1)

where g is the Landé g-factor of Mn moments, μ _B is the Bohr magneton, φ and φ _H are the in-plane magnetization and external magnetic-field angles measured from the [100] crystal axis, and ΔH _n is the shift of the resonant field for the higher-index n spin wave modes with respect to the n = 0 uniform precession mode. In order to uniquely determine the anisotropy constants, field-dependent precession frequency measurements were performed on the optimized films by a magneto-optical pump-and-probe technique and complemented by the superconducting quantum interference device (SQUID) measurements [79].

The values of K _out and K _c for the given Mn doping are well reproducible in materials whose synthesis yields the same optimized values of the basic structural, magnetic, and transport properties. For the K _u constant, variations in the width of the optimized thin (Ga,Mn)As films or of other otherwise insignificant changes of the growth or annealing conditions may yield sizable changes of K _u. This indicates a more subtle, extrinsic nature of this magnetic anisotropy component.

The sign of K _out implies that the (Ga,Mn)As/GaAs materials are in-plane ferromagnets. The competing magnitudes of K _c and K _u and the different doping trends of these two in-plane magnetic anisotropy constants (see Fig. 8a) are therefore crucial for the micromagnetics of the materials. The biaxial anisotropy K _c dominates at very low dopings, and the easy axis aligns with the main crystal axis [100] or [010]. At intermediate dopings, the uniaxial anisotropy K _u is still weaker but comparable in magnitude to K _c. In these samples the two equilibrium easy axes are tilted toward the $ \left[1\overline{1}0\right] $ direction, and their angle is sensitive to small changes of temperature or externally applied electrostatic or piezo voltages [7, 8, 11–14, 31, 36–38].

The origin of the magnetocrystalline anisotropies is in the spin–orbit coupling of the valence band holes mediating the ferromagnetic Mn–Mn coupling, as described on a qualitative or semiquantitative level by the model, kinetic-exchange Hamiltonian theory [92–94].

For completeness we show in Fig. 8b the Gilbert damping constants and spin stiffnesses inferred from the same set of measurements as for the magnetic anisotropy constants. Their values are also consistent with theory predictions for the spin–orbit coupled disordered valence band of (Ga,Mn)As [32, 95–98].

Resistors

Resistors, capacitors, and transistors are among the key elements of electronic circuits. Here and in sections “Tunnel Junctions,” “Capacitors,” and “Transistors,” we review how research in (Ga,Mn)As has contributed to studies of the relativistic magnetic anisotropy phenomena reflected in functionalities of these electronic devices.

In general, magnetic effects on transport properties of conductors can be ascribed to three different categories: ordinary (orbital), due to the Lorentz force; spin-dependent, due to spin splitting of bands through ferromagnetism or the Zeeman effect; and extraordinary, relativistic in origin through the spin–orbit interaction. Well-known examples of these effects are Lorentz magnetoresistance, giant magnetoresistance (GMR) [99], and anisotropic magnetoresistance (AMR) [100], respectively. (Ga,Mn)As represents a favorable model system for understanding the phenomenology and detailed microscopic origin of the AMR in ohmic resistors [101–108].

AMR is the symmetric magnetoresistance coefficient with the longitudinal and transverse resistivities obeying, ρ _L(M) = ρ _L(−M) and ρ _T(M) = ρ _T(−M), where M has an arbitrary orientation. AMR was discovered by Lord Kelvin in transition metal ferromagnets [109] and was used in the first generation of hard drive read heads and magnetoresistive random access memories (MRAMs) [110].

Among the remarkable AMR features of (Ga,Mn)As ferromagnetic semiconductors are the opposite sign of the noncrystalline component, compared to most metal ferromagnets, and the crystalline terms reflecting the rich magnetocrystalline anisotropies [101–107]. In Fig. 9 we show an example of AMR data replotted from Ref. [107] which reports a systematic experimental and phenomenological study of the AMR coefficients in (Ga,Mn)As films, grown on (001)- and (113)A-oriented GaAs substrates.

Microscopic numerical simulations [102, 111] consistently describe the sign and magnitudes of the noncrystalline AMR in the standard (Ga,Mn)As materials with metallic conductivities and capture the presence of the more subtle crystalline terms associated with, e.g., growth-induced strain [104, 111]. In the following paragraphs, we describe some of the rich AMR phenomenology in (Ga,Mn)As in more detail and explain the basic microscopic physics of the AMR in dilute-moment ferromagnets. For simplicity we discuss only AMR in saturating magnetic fields, i.e., for M fully aligned with the external field, and the pure AMR geometry with zero (antisymmetric) Hall signal, i.e., for M oriented in the plane of the device. (Ga,Mn)As films grown on the (001)-GaAs substrate will be considered.

The phenomenological decomposition of the AMR of (Ga,Mn)As into various terms allowed by symmetry is obtained by extending the standard phenomenology [112], to systems with the cubic [100] plus the uniaxial [110] anisotropy. With this the longitudinal AMR is written as [108]

$$ \begin{array}{c}\hfill \frac{\Delta {\rho}_{xx}}{\rho_{av}}={C}_I \cos 2\phi +{C}_U \cos 2\psi +{C}_C \cos 4\psi \hfill \\ {}\hfill +{C}_{I,C} \cos \left(4\psi -2\phi \right),\hfill \end{array} $$

(2)

where Δρ _xx = ρ _xx–ρ _av, ρ _av is the ρ _xx averaged over 360° in the plane of the film, ϕ is the angle between the magnetization unit vector $ \widehat{\mathbf{M}} $ and the current I, and ψ is the angle between $ \widehat{\mathbf{M}} $ and the [110] crystal direction. The four contributions are the noncrystalline term, the lowest order uniaxial and cubic crystalline terms, and a crossed noncrystalline/crystalline term. The purely crystalline terms are excluded by symmetry for the transverse AMR, and one obtains

$$ \frac{\Delta {\rho}_{xy}}{\rho_{av}}={C}_I \sin 2\phi -{C}_{I,C} \sin \left(4\psi -2\phi \right). $$

(3)

In the dilute-moment systems like (Ga,Mn)As ferromagnets, two distinct microscopic mechanisms lead to anisotropic carrier lifetimes. One combines the spin–orbit coupling in the carrier band with polarization of randomly distributed magnetic scatterers and the other with polarization of the carrier band itself resulting in an asymmetric band-spin texture. Although acting simultaneously in real systems, theoretically both mechanisms can be turned on and off independently. Since the former mechanism clearly dominates in (Ga,Mn)As, the spin splitting of the valence band is neglected in the following qualitative discussion. This is further simplified by focusing on the noncrystalline AMR in the heavy-hole Fermi surfaces in the spherical, s ∥ k, spin-texture approximation [113] and considering scattering off a δ-function potential $ \propto \left(r+\widehat{\mathbf{M}}\cdot \mathbf{s}\right) $. Here s and k are the carrier spin operator and wave vector, and r represents the ratio of nonmagnetic and magnetic parts of the Mn impurity potential. Assuming a proportionality between conductivity and lifetimes of carriers with k||I gives the following qualitative analytical expression for the AMR in this class of materials [108],

$$ \frac{\sigma \left(\widehat{\mathbf{M}}\parallel \mathbf{I}\right)}{\sigma \left(\widehat{\mathbf{M}}\perp \mathbf{I}\right)}=\left({r}^2+\frac{1}{4}\right) \left({r}^2+\frac{1}{12}\right) {\left({r}^2-\frac{1}{4}\right)}^{-2}. $$

(4)

Therefore, when r ≪ 1, one expects $ \sigma \left(\widehat{\mathbf{M}}\parallel \mathbf{I}\right)<\sigma \left(\widehat{\mathbf{M}}\perp \mathbf{I}\right) $ (as is usually observed in metallic ferromagnets). However, the sign of the noncrystalline AMR reverses at a relatively weak nonmagnetic potential ($ r=/\sqrt{20} $ in the model), its magnitude is then maximized when the two terms are comparable (r = 1/2), and, for this mechanism, it vanishes when the magnetic term is much weaker than the nonmagnetic term (r → ∞).

Physically, carriers moving along $ \widehat{\mathbf{M}} $, i.e., with s parallel or antiparallel to $ \widehat{\mathbf{M}} $, experience the strongest scattering potential among all Fermi surface states when r = 0, giving $ \sigma \left(\widehat{\mathbf{M}}\parallel \mathrm{I}\right)<\sigma \left(\widehat{\mathbf{M}}\perp \mathrm{I}\right) $. When the nonmagnetic potential is present, however, it can more efficiently cancel the magnetic term for carriers moving along $ \widehat{\mathbf{M}} $ and for relatively small r, the sign of AMR flips. Since $ r<1/\sqrt{20} $ is unrealistic for the magnetic acceptor Mn in GaAs [51, 111], one obtains $ \sigma \left(\widehat{\mathbf{M}}\parallel \mathrm{I}\right)<\sigma \left(\widehat{\mathbf{M}}\perp \mathrm{I}\right) $, consistent with experiment.

Differences among experimental AMRs for current along the [100], [110], and $ \left[1\overline{1}0\right] $ directions show that cubic and uniaxial crystalline terms are also sizable. This phenomenology is systematically observed in experimental AMRs of weakly or moderately compensated metallic (Ga,Mn)As films. Typical data for such systems [108], represented by the 25 nm Ga_0.95Mn_0.05As film with 3.6% AMR, are shown in Fig. 10 for the Hall bars patterned along the [100], [010], [110], and $ \left[1\overline{1}0\right] $ directions.

The high crystalline quality metallic (Ga,Mn)As samples allow to produce low contact resistant Hall bars accurately orientated along the principle crystallographic axes, from which it is possible to extract the independent contributions to the AMR. It is also possible to fabricate low contact resistance Corbino disk samples for which the averaging over the radial current lines eliminates all effects originating from a specific direction of the current [108]. Corbino measurements are possible in these materials because they are near-perfect single crystals but with low carrier density and mobility (compared with single-crystal metals) and so can have large source-drain resistances compared with the contact resistances.

Measured results for a Corbino device fabricated from the same 25 nm Ga_0.95Mn_0.05As film as used for the Hall bars are shown in Fig. 11 [108]. The AMR signal is an order of magnitude weaker than in the Hall bars and is clearly composed of a uniaxial and a cubic contribution. Figure 11 also shows the crystalline components of the AMR extracted by fitting the Hall bar data to the phenomenological longitudinal and transverse AMR expressions. Figure 11d shows the consistency for the coefficients C _I,C, C_U, and C_C when extracted from the Hall bar and Corbino disk data over the whole range up to the Curie temperature (80 K). The uniaxial crystalline term, C _U, becomes the dominant term for T ≥ 30 K. This correlates with the uniaxial component of the magnetic anisotropy which dominates for T ≥ 30 K as observed by SQUID magnetometry measurements [108, 114].

A unique AMR phenomenology has been observed on ultrathin (5 nm) Ga_0.95Mn_0.05As films [108]. The crystalline terms dominate the AMR with the uniaxial crystalline term being the largest. SQUID magnetometry on 5 nm Ga_0.95Mn_0.05As films consistently shows that the uniaxial component of the magnetic anisotropy dominates over the whole temperature range [115]. The 5 nm films have lower Curie temperatures (T _C ≈ 30 K) than the 25 nm films and become highly resistive at low temperature, indicating that they are close to the metal–insulator transition. The strength of the effect in the 5 nm films is remarkable, and it is not captured by theory simulations assuming weakly disordered, fully delocalized (Ga,Mn)As valence bands. It might be related to the expectation that magnetic interactions become more anisotropic with increasing localization of the holes near their parent Mn ions as the metal–insulator transition is approached [51].

Tunnel Junctions

The tunneling magnetoresistance (TMR) represents the difference between resistivities in configurations with parallel and antiparallel polarizations of ferromagnetic layers separated by a nonmagnetic barrier in magnetic tunnel junctions [99, 116–119]. The TMR in tunnel junctions can be much larger than the AMR of simple ohmic resistors and is the key effect utilized for readout in modern MRAMs [120].

In (Ga,Mn)As, functional magnetic tunnel junction devices can be built, as demonstrated by the measured large TMR effects [20–24, 121–125]. Here we focus on the physics of the tunneling anisotropic magnetoresistance (TAMR) which was discovered in (Ga,Mn)As-based tunnel devices [22, 39, 121, 122, 125–128]. TAMR, like AMR, arises from spin–orbit coupling and reflects the dependence of the tunneling density of states of the ferromagnetic layer on the orientation of the magnetization. The effect does not rely on spin coherence in the tunneling process and requires only one ferromagnetic contact.

In Fig. 12 we show the TAMR signal which was measured in a (Ga,Mn)As/AlO_x/Au vertical tunnel junction [39, 129]. For the in-plane magnetic field applied at an angle 50° off the [100]-axis, the magnetoresistance is reminiscent of the conventional spin-valve signal with hysteretic high-resistance states at low fields and low-resistance states at saturation. Unlike the TMR, however, the sign changes when the field is applied along the [100]-axis. Complementary SQUID magnetization measurements confirmed that for the sample measured in Fig. 12, the high-resistance state corresponds to magnetization in the (Ga,Mn)As contact aligned along the [100]-direction and the low-resistance state along the [010]-direction and that this TAMR effect reflects the underlying magnetocrystalline anisotropy between the M || [100] and M || [010] magnetic states of the specific (Ga,Mn)As material used in the study. Since the field is rotated in the plane perpendicular to the current, the Lorentz force effects on the tunnel transport can be ruled out. Microscopic calculations consistently showed that the spin–orbit coupling-induced density-of-state anisotropies with respect to the magnetization orientation can produce TAMR effects in (Ga,Mn)As of the order ~1 % to ~10 % [39, 129].

At very low temperatures and bias voltages, huge TAMR signals were observed [129] in a (Ga,Mn)As/GaAs/(Ga,Mn)As tunnel junction (see Fig. 13) which are not described by the one-body theories of anisotropic tunneling transmission coefficients. The observation was interpreted as a consequence of electron–electron correlation effects near the metal–insulator transition [130]. Large anisotropic magnetoresistance effects were also measured in lateral nano-constriction devices fabricated in ultrathin (Ga,Mn)As materials [131–133]. The comparison of the anisotropic magnetoresistance signals in the unstructured part of the device and in the nano-constriction showed a significant enhancement of the signal in the constriction [131]. Subsequent studies of these nano-constrictions with an additional side gate patterned along the constriction, discussed in detail in section “Transistors” [10, 42, 134, 135], indicated that single-electron charging effects were responsible for the observed large anisotropic magnetoresistance signals.

Capacitors

Classifying magnetocapacitance along similar lines as magnetoresistance, both ordinary and spin-dependent effects have been observed in various systems. Changes in capacitance as a function of in-plane magnetic field were measured in two-dimensional electron gases and attributed to combined Lorentz force and quantum confinement effects [136, 137]; spin-dependent effects were measured due to the Zeeman splitting in Pd plate capacitors [138], and in magnetic tunnel junctions, several measurements have shown changes in capacitance as a function of relative magnetization orientation [139–141]. Research in (Ga,Mn)As has led to the discovery of the third class, the anisotropic magnetocapacitance whose origin is in the spin–orbit interaction [142].

Figure 14 shows the capacitor stack with one of the electrodes made of (Ga,Mn)As, the equivalent circuit, and the measured complex admittance of the capacitor. In Fig. 15 the capacitance is plotted as a function of in-plane (a) and out-of-plane (b) magnetic-field orientation. There is a clear cubic in-plane symmetry and uniaxial out-of-plane symmetry to the change in capacitance. This is the symmetry that might be expected due to the bulk cubic crystal symmetry in the plane and uniaxial out-of-plane anisotropy due to the compressive strain on the (Ga,Mn)As epilayer grown on the GaAs substrate.

Based on the Thomas–Fermi screening length, one can formulate an effective “kinetic” capacitance, in series to the conventional geometric capacitance, with a dependence on the DOS [143]:

$$ {C}_k/A=\sqrt{e^2{\upepsilon}_0{\upepsilon}_{eff}{\rho}_{3\mathrm{D}}} $$

(5)

where ρ _3D is the DO, ϵ ₀ ϵ _eff is the effective dielectric constant of the constant material, and A is the area of the plate. Taking ρ _3D ≈ 10⁴⁶ J⁻¹m⁻³ from independent DOS measurements in (Ga,Mn)As [144], $ {C}_k/A\approx 50{\mathrm{fF}\upmu \mathrm{m}}^{-2} $. The change in the total capacitance of the device C _T can be related to the change in the kinetic capacitance by

$$ \frac{\Delta {C}_T}{C_T}=\frac{C_T}{C_k}\;\frac{\Delta {C}_k}{C_k}. $$

(6)

It can be seen from this equation that increasing the ratio of total to kinetic capacitance would increase the size of the modulation when rotating the magnetization vector in the ferromagnet. The total capacitance per area of the studied device is ≈ 2fF μm⁻². From these values a ≈ 5% change in the DOS would be needed to explain the 0.1 % anisotropic magnetocapacitance measured for the out-of-plane field rotation, a value which is reasonable in the studied (Ga,Mn)As material.

Transistors

Magnetically induced changes in the position of the chemical potential can be used to construct field-effect transistors whose channel conductance is controlled by spin-dependent effects in the electrodes. Shifts in the chemical potential associated with the magnetic-field-induced Zeeman splitting of the ferromagnetic bands were observed in single-electron transistor (SET) devices as spin-dependent magneto-Coulomb oscillations [145, 146]. Research in (Ga,Mn)As-based SETs has led to the discovery of the relativistic Coulomb-blockade (CB) AMR [10, 42, 44, 134, 135].

Ferromagnetic SETs with (Ga,Mn)As in the transport channel of the transistor [42, 135] were fabricated by trench-isolating a side-gated narrow channel in a thin-film (Ga,Mn)As epilayer (see Fig. 16). The nonuniform carrier concentration produces differences between chemical potentials Δμ of the lead and of the island in the constriction. There are two mechanisms through which Δμ depends on the magnetic field. One is caused by the direct Zeeman coupling of the external magnetic field and leads to a CB magnetoresistance previously observed in ferromagnetic metal SETs [147].

The CB-AMR effect, discovered in the (Ga,Mn)As SETs, is attributed to the spin–orbit coupling-induced anisotropy of the carrier chemical potential, i.e., to magnetization orientation-dependent differences Δμ(M) between chemical potentials of the lead and of the island in the constriction [42]. A marked shift in the CB oscillation pattern is observed when |Δμ(M)| is of the order of the island single-electron charging energy. The fact that CB-AMR occurs when the anisotropy in a band structure-derived parameter is comparable to an independent scale (single-electron charging energy) makes the effect distinct and potentially much larger in magnitude as compared to the AMR and TAMR. Indeed, resistance variations by more than three orders of magnitude were observed in the (Ga,Mn)As SETs.

The sensitivity of the magnetoresistance to the orientation of the applied magnetic field is an indication of the anisotropic magnetoresistance origin of the effect. This is confirmed by the observation of comparably large and gate-controlled magnetoresistance in a field-sweep experiment and when the saturation magnetization is rotated with respect to the crystallographic axes. The field-sweep and rotation measurements are shown in Fig. 17c, d and compared with analogous measurements of the ohmic AMR in the unstructured part of the (Ga,Mn)As bar, plotted in Fig. 17a, b [42]. In the unstructured bar, higher or lower resistance states correspond to magnetization along or perpendicular to the current direction. Similar behavior is seen in the SET part of the device at, for example, V _G = −0.4 V, but the anisotropic magnetoresistance is now hugely increased and depends strongly on the gate voltage.

The huge magnetoresistance signals can be also hysteretic which shows that CB-AMR SETs can act as a nonvolatile memory/transistor element. In nonmagnetic SETs, the CB “on” (low resistance) and “off” (high resistance) states can represent logical “1” and “0,” and the switching between the two states can be realized by applying a gate voltage, in analogy with a standard field-effect transistor. The CB-AMR SET can be addressed also magnetically with comparable “on” to “off” resistance ratios in the electric and magnetic modes.

Anther type of a (Ga,Mn)As SET device [44] is shown in Fig. 18. Here the SET has a micron-scale Al island separated by aluminum oxide tunnel junctions from Al source and drain leads (Fig. 18a). It is fabricated on top of a (Ga,Mn)As layer, which is electrically insulated from the SET by an alumina dielectric, and acts as a spin back gate to the Al SET. By sweeping the externally applied potential to the SET gate (Vg), one obtains the conductance oscillations that characterize the CB, as shown in Fig. 18b. Due to the magnetic gate, a shift is observed in these oscillations by an applied saturating magnetic field which rotates the magnetization in the (Ga,Mn)As gate. Figure 18b shows measurements for the in-plane (Φ = 90°) and for the perpendicular-to-plane (Φ = 0°) directions of magnetization. Alternatively, Fig. 18c shows the channel conductance as a function of the magnetization angle Φ for a fixed external potential V _g applied to the gate. The oscillations in Φ seen in Fig. 18c are of comparable amplitude as the oscillations in V _g in Fig. 18b.

Since the (Ga,Mn)As back gate is attached to a charge reservoir, any change in the internal chemical potential of the gate induced by the rotating magnetization vector causes an inward, or outward, flow of charge in the gate, as illustrated in Fig. 18e. This change in back-gate charge offsets the Coulomb oscillations (Fig. 18b) and changes the conductance of the nonmagnetic transistor channel for a fixed external potential applied to the gate (Fig. 18c).

The device clearly derives its functionality from the oldest among spintronics phenomena, namely, from the AMR. Simultaneously it appears to violate the established definition of spintronics as a portmanteau meaning “spin transport electronics.” In the device shown in Fig. 18, the transport channel is nonmagnetic, and all the spin action is encoded in the capacitively coupled magnetic gate electrode.

Spin-Hall Magnetoresistance

We have mentioned in section “Resistors” that the first generation of magnetic random access memories (MRAMs) was based on the AMR. These MRAMs relied on magnetic fields not only for writing but also for reading the information in a uniaxial ferromagnet [110]. The Oersted field was employed for partially tilting the moments during readout and by this for breaking the symmetry between the opposite magnetization orientation states. Without the tilt, i.e., for moments flipped strictly by 180°, the AMR vanishes by symmetry. In modern MRAMs based on the TMR, the auxiliary Oersted field is removed from the readout scheme [148]. Instead, the symmetry breaking is provided by interfacing the storing free ferromagnet with a reference fixed ferromagnet.

Research in (Ga,Mn)As has led to the discovery [149] of a reading scheme for the 180° magnetization reversal which does not require a symmetry-breaking magnetic field or a reference ferromagnet [149, 150]. It is due to the so-called linear spin-Hall magnetoresistance (LSMR) [149] with the maximum and minimum resistance values corresponding to the opposite magnetization directions in the ferromagnet. In the studied structure, the ferromagnet is represented by a Ga_0.91Mn_0.09As film with Curie temperature T _c1 = 155 K. It is grown on top of a Ga_0.97Mn_0.03As which remains paramagnetic down to T _c2 = 95 K, has a similar conductivity as the top, higher Mn-doped film, and for which one expects a sizable spin-Hall effect (SHE) [151, 152]. This bilayer geometry implies that for the given in-plane current polarity, the SHE generates a fixed in-plane, perpendicular-to-current spin polarization at the interface with the ferromagnetic (Ga,Mn)As. When the axis of the in-plane magnetization of the ferromagnet is also transverse to the current, as illustrated in Fig. 19a, then flipping the sign of the magnetization results in the LSMR. The phenomenology can be viewed as analogous to the ferromagnetic bilayer structure operated in the in-plane current GMR geometry and with the fixed reference ferromagnet replaced in the structure with the paramagnetic SHE polarizer.

The measurement setup is shown in Fig. 19b and the magnetoresistances detected at 130 K are plotted in Fig. 19c, d. At a probe current of amplitude 5 μA, corresponding to current density of 1.25 × 10⁴ Acm⁻², a negligible change in the longitudinal resistance R _xx is observed for the magnetic field swept along the easy axis, as shown in Fig. 19c. On the other hand, at 150 and 300 μA, a magnetoresistance signal is observed which increases with increasing current and is an odd function when reversing magnetization by 180°. The hysteretic R _xx jumps whose sign flips when flipping the field-sweep direction or the polarity of the probe current occur at ±0.2 mT which is the easy-axis coercive field. Figure 19d shows the difference between resistance states for opposite magnetizations set by sweeping the magnetic field from negative or positive values to the zero field. The difference increases linearly with the applied probe current and change sign for the opposite current polarity.

We note that the LSMR effect [149, 150] is related to another spin-Hall magnetoresistance which is quadratic in the spin-Hall angle [153]. In the latter effect, a spin current generated by the SHE is either absorbed at the interface with a ferromagnet when the SHE polarization is transverse to the magnetization or, in the parallel configuration, it is reflected. The reflected spin current generates an additional voltage via the inverse SHE which renormalizes the resistance of the device. Unlike the LSMR and like the AMR, this quadratic-in-SHE phenomenon is independent of the sign of the magnetization.

Current-Induced Torques

When spin-polarized carriers are injected into a magnetic region whose moments are misaligned with the injected spin polarization of the carriers, spin–transfer torques (STTs) can act on the magnetization of the ferromagnet [154]. The phenomena belong to an important area of spintronics research focusing on the means for manipulating magnetic moments by electric fields and are the basis of the emerging technologies for scalable MRAMs [120].

Theoretical description of STTs is simplified when the nonequilibrium spin density of carriers s and magnetization M of the ferromagnet are treated as separate degrees of freedom and when the timescales for the coupled dynamics of s and M are very different. Dilute-moment ferromagnetic semiconductors, and (Ga,Mn)As in particular, are model systems in which the first assumption is well justified microscopically. Saturation magnetization of the ferromagnet M is primarily due to Mn d-orbital local moments, while the carrier states near the top of the valence band (or bottom of the conduction band) are dominated by As p-orbitals (or Ga s-orbitals) [49, 51].

The timescale for the precession of the nonequilibrium carrier spin polarization in the exchange field of local moments, described by

$$ \frac{d\mathbf{s}}{dt}=\frac{J_{\mathrm{ex}}cS}{\hslash}\mathbf{s}+\widehat{\mathbf{M}}, $$

(7)

is $ {\tau}_{\mathrm{ex}}=\hslash /{J}_{\mathrm{ex}}cS $, where J _ex is the carrier-local moment exchange coupling and cS ≡ |M|. The timescale for the precession of local moments in the exchange field of the nonequilibrium carrier spin polarization, described by

$$ cS\frac{d\widehat{\mathbf{M}}}{dt}=cS\frac{J_{\mathrm{ex}}\left|\mathbf{s}\right|}{\hslash}\widehat{\mathbf{M}}\times \widehat{\mathbf{s}}, $$

(8)

is $ \hslash /{J}_{\mathrm{ex}}\left|\mathbf{s}\right| $. Since cS ≫ |s| is common in the STT experiments, the local moment dynamics is typically much slower than the nonequilibrium carrier spin dynamics [47, 154–157]. This allows one to phenomenologically describe STTs in two steps. In the first step, the fast dynamics of s is considered, and one looks for a steady-state component of the nonequilibrium carrier spin density, δ s. In the second step, δ s is introduced into Eq. 8 in order to infer STTs acting on the magnetization M of the ferromagnet.

Phenomenologically, the nonequilibrium carrier spin dynamics in the presence of the exchange field of local moments and steady injection rate P of carriers with spin polarization vector $ \widehat{\mathbf{n}} $ misaligned with M is given by

$$ \frac{d\mathbf{s}}{dt}=\frac{J_{\mathrm{ex}}cS}{\hslash}\mathbf{s}\times \widehat{\mathbf{M}}+P\widehat{\mathbf{n}}-\frac{\mathbf{s}}{\tau_{\mathrm{s}}}, $$

(9)

where the last term reflects a finite spin lifetime of the nonequilibrium carriers in the ferromagnet. Two components of STT can be distinguished when considering two limiting cases of Eq. 9 [47, 154–157]. One limit is when carrier spin lifetime τ _s is much larger than the precession time τ _ex. In this case, and assuming for simplicity $ \widehat{\mathbf{n}}\perp $ $ \widehat{\mathbf{M}} $, the steady-state component of the nonequilibrium carrier spin polarization in the ferromagnet is oriented perpendicular to both $ \widehat{\mathbf{n}} $ and $ \widehat{\mathbf{M}} $ and |δ _S|/τ _ex = P. This follows from the steady-state solution of Eq. 9 (d s/dt = 0) in which the last term on the right-hand side is neglected, and the rate of tilt of the nonequilibrium carrier spin polarization due to precession in the exchange field of local moments (first term in Eq. 9) is canceled by the rate of the incoming carrier spin polarization (second term in Eq. 9). The steady-state carrier polarization δ s produces STT acting on the magnetization,

$$ cS\frac{d\widehat{\mathbf{M}}}{dt}=P\widehat{\mathbf{M}}\times \left(\widehat{\mathbf{n}}\times \widehat{\mathbf{M}}\right). $$

(10)

In this adiabatic STT the entire spin-angular momentum of the injected carriers is transferred to the magnetization, independent of τ _s, τ _ex, and other parameters of the system. The adiabatic STT has been considered since the seminal theory works [158, 159] on carrier-induced magnetization dynamics which opened a large field ranging from metal magnetic tunnel junctions switched by current to tunable oscillators [154] and ultrafast photomagnetic laser excitations of ferromagnetic semiconductors [47, 157].

In the opposite limit of τ _s ≪ τ _ex, δ s remains parallel to the injected spin polarization $ \widehat{\mathbf{n}} $, and its magnitude is a product of the spin injection rate and spin lifetime, |δ _s| = Pτ _s. This follows from Eq. 9 in which the first term on the right-hand side is neglected. The resulting nonadiabatic STT [155],

$$ cS\frac{d\widehat{\mathbf{M}}}{dt}=\frac{\tau_{\mathrm{s}}}{\tau_{\mathrm{ex}}}P\left(\widehat{\mathbf{M}}\times \widehat{\mathbf{n}}\right), $$

(11)

is perpendicular to the adiabatic STT and has a magnitude |s|/τ_ex = Pτ _s /τ_ex. For intermediate ratios τ _ex /τ _s, both the nonadiabatic and adiabatic torques can be present, and the ratio of their magnitudes (nonadiabatic to adiabatic) is given by β = τ _ex /τ _s [155–157]. The nonadiabatic STT plays a crucial role in current-induced domain-wall (DW) motion [155, 156]. It allows for a nonzero mobility of DW in the low-current steady-flow regime, with the DW mobility proportional to β/α where α is the damping parameter [155, 156, 160, 161].

One of the sources of small τ _s, i.e., large nonadiabatic STT, is spin–orbit coupling. Remarkably, a related spin–orbit torque (SOT) produced by spin–orbit coupling and electrical current can occur even in uniformly magnetized systems [45, 46, 162–166]. The presence of SOT in uniform ferromagnets can be illustrated by considering linear-response transport theory in which the occupied states on the Fermi surface are redistributed by the applied electrical current. The redistribution combined with microscopic non-collinearity of spin expectation values on the spin–orbit coupled Fermi surface produces a nonequilibrium steady-state component of the carrier spin polarization in systems with broken inversion symmetry. When misaligned with the equilibrium magnetization, SOT acts on the magnetic moments [163, 164, 167]. SOT has been employed in current-assisted magnetization reversal experiments in uniformly magnetized ferromagnetic semiconductor and metal thin films [45, 165] and in all-electrical ferromagnetic resonance measurements of uniformly magnetized ferromagnetic semiconductor nanodevices [46], and recent studies of thin-film metal ferromagnets have proposed that SOT can enhance the mobility of current-driven DWs [168].

Ferromagnetic (III,Mn)V semiconductors represent an ideal experimental realization of the above model picture of the STT [169], as well as of SOT [45, 46, 163–166] phenomena. The strong exchange interaction is accompanied in these materials by a strong spin–orbit coupling, resulting in τ _s ~ τ _ex and, therefore, in the expectation of significant contributions of both adiabatic and nonadiabatic STTs [28, 30, 33, 34] and of SOT. Another favorable feature of dilute-moment (III,Mn)V ferromagnets is their low saturation moment, as compared to conventional dense-moment metal ferromagnets. Together with the high degree of spin polarization of carriers, it implies that electrical currents required to excite magnetization by STT in ferromagnetic semiconductors are also comparatively low [24–27, 32]. The combination of low saturation moment and strong spin–orbit coupling has yet another key advantage which is the dominant role of magnetocrystalline anisotropy fields over the demagnetizing anisotropy fields [27]. It allows to control the stability of the internal DW structure in situ by a piezoelectric stressor attached to the ferromagnetic semiconductor sample [31]. Similarly, the inversion symmetry-breaking terms in the spin–orbit coupled band structure of (Ga,Mn)As, responsible for SOT, can be controlled by the lattice-matching growth strain or strains introduced post-growth by microfabrication or piezoelectric stressors [46, 94].

Tunnel Junctions and Domain Walls

In magnetic tunnel junctions with (Ga,Mn)As electrode, STT-induced switching was observed [24] at current densities of the order 10⁴ − 10⁵ Acm⁻², as shown in Fig. 20. This is consistent with theory expectations [32] predicting one to two orders of magnitude lower current densities than in the STT experiments in common dense-moment metal ferromagnets.

Critical currents of the order 10⁵ Acm⁻² for the DW motion in the creep regime have been reported and the effect thoroughly explored in perpendicularly magnetized (Ga,Mn)As thin-film devices [25, 26, 170]. The perpendicular magnetization geometry was achieved by growing the films under a tensile strain on a (In,Ga)As substrate and is particularly useful for the direct magneto-optical Kerr-effect imaging of the domains, as illustrated in Fig. 21.

The viscous-flow regime over a wide current range was achieved in high crystal quality (Ga,Mn)(As,P)/GaAs epilayers grown under tensile strain, resulting again in the out-of-plane easy axis [29–31]. The idea behind experiments shown in Fig. 22 is based on predictions of a simplified 1D model in which a Bloch (or Néel) DW in an out-of-plane magnetized system is assumed and in which the viscous-flow DW motion in a low-current steady regime is separated from a high-current precessional regime by the Walker breakdown (WB) [160, 161, 171]. The mobility (velocity divided by current) is larger below WB when the nonadiabatic STT is strong enough that β/α > 1. For β/α < 1, on the other hand, the DW mobility is larger above the WB threshold current.

The important property of the ferromagnetic semiconductor sample is that the position of the WB is governed by the uniaxial magnetocrystalline anisotropy field parallel to the magnetic epilayer plane and the rotation plane of the DW, whose magnitude can be tuned in a controlled way by applying bias voltage to an attached piezostressor [31, 36, 94, 172]. As a result, one can tune in situ the WB threshold current j _WB and the DW mobility and infer the β/α ratio which characterizes the strengths of adiabatic and nonadiabatic STTs in the studied magnet. The experimental realization of this proposal [172] is shown in Fig. 22c, d [31]. By comparing Fig. 22b, c, it can be concluded that both adiabatic and nonadiabatic STTs act in the current-driven DW motion experiments and that the characteristic ratio β/α < 1. Figure 22d shows that by shifting the WB position one can control DW mobilities. Up to 500 % mobility variation, for an electrical-current-driven domain wall, have been observed in these piezoelectrically controlled DW STT experiments in (Ga,Mn)(As,P).

Uniform Magnets

The experimental discovery of SOT was reported in a (Ga,Mn)As sample whose image is shown in Fig. 23c [45]. The device was patterned into a circular island with eight nonmagnetic ohmic contacts (Fig. 23a). In the presence of a strong external magnetic field H, the magnetization of the ferromagnetic island is aligned with the field. For weak fields, however, the direction of magnetization is primarily determined by magnetic anisotropy. As a small field (5 < H < 20 mT) is rotated in the plane of the sample, the magnetization is realigned along the easy axis closest to the field direction. Such rotation of magnetization by an external field is demonstrated in Fig. 24. For the current $ \mathbf{I}\parallel \left[1\overline{1}0\right] $, the measured transverse AMR (R _xy) is positive for M || [100] and negative for M || [010]. The switching angles where R _xy changes sign are denoted as φ ⁽ⁱ⁾_H on the plot. The data can be qualitatively understood if one considers an extra current-induced effective magnetic field H _eff, as shown schematically in Fig. 23b. The symmetry of the measured H _eff with respect to I coincides with the unique symmetry of the strain-related SOT field (Fig. 23c).

A form of ferromagnetic resonance (FMR) has been demonstrated based on SOT in which an electric current oscillating at microwave frequencies is used to create an effective SOT field in the magnetic material being probed, which makes it possible to characterize individual nanoscale samples with uniform magnetization profile [46]. Lithographically patterned (Ga,Mn)As and (Ga,Mn)(As,P) nanoscale bars were characterized, including broadband measurements of resonant damping as a function of frequency and measurements of anisotropy fields as a function of bar width and strain. In addition, vector magnetometry of these driving SOT fields revealed contributions with the symmetry of both the strain-related Dresselhaus SOT and of an additional Rashba-symmetry SOT.

The principle of the SOT-FMR technique is illustrated in Fig. 25a [46]. To drive the FMR, a microwave-frequency current was passed through the nanobar (Fig. 25b). For detection, a frequency mixing effect based on AMR was used. When magnetization precession is driven, there is a time-dependent change ΔR(t) in longitudinal resistance from the equilibrium value R (owing to AMR). The resistance oscillates with the same frequency as the microwave current, thus causing frequency mixing, and a directly measurable d.c. voltage V _dc is generated. This voltage provides a direct probe of the amplitude and phase of magnetization procession with respect to microwave current.

Figure 26 presents measurements on an 80 nm wide nanobar patterned in the $ \left[1\overline{1}0\right] $ direction from the (Ga,Mn)(As,P) epilayer. The magnetic-field dependence of V _dc is measured at different microwave frequencies. The frequency of the incident current is fixed while an external d.c. magnetic field H ₀ is swept, and a well-defined resonance peak appears (Fig. 26a). The peak is well fitted by the solution of the Landau–Lifshitz–Gilbert (LLG) equation , which describes the dynamics of precessional motion of the magnetization.

Figure 26b plots the frequency dependence of the resonance field H _res. The FMR linewidth $ \left(\Delta H=\Delta {H}_{inhomo}+\alpha \omega /\gamma \right) $ describes the damping in the ferromagnetic system. The broadband nature of the setup allows to determine the inhomogeneous contribution to the damping (Fig. 26c), and the Gilbert damping constant α (Fig. 26d) presents the data from an in-plane scan of the magnetic field, showing that there is a strong uniaxial anisotropy perpendicular to the bar direction. By analyzing the peak positions (Fig. 26e), the SOT-FMR allows to quantify the anisotropy fields in the studied micro- or nanoscale magnet.

Studies of the SOT in (Ga,Mn)As have also identified an additional anti-damping SOT contribution which has a common microscopic origin with the intrinsic anomalous and spin-Hall effects [173]. Unlike the above scattering-related field-like SOT, described within the semiclassical Boltzmann theory, the presence of an anti-damping SOT with a scattering-independent origin is captured by the time-dependent quantum-mechanical perturbation theory. Here the linear-response theory considers the equilibrium distribution function, and the applied electric field perturbs the carrier wave functions.

The anti-damping like SOT with the theoretically predicted symmetries was identified in measurements in (Ga,Mn)As, as shown in Fig. 27 [173]. The all-electrical broadband SOT-FMR technique [46] was applied which allowed to perform 3D vector magnetometry on the driving SOT fields and showed that the anti-damping SOT plays an important role in driving the magnetization dynamics in (Ga,Mn)As.

Magnonic Charge Pumping

In the STT, spin-angular momentum is transferred from the carriers to the magnet where it excites magnetization dynamics. A reciprocal effect to the STT is the spin pumping in which pure spin current is generated from magnetization precession [174, 175]. Spin pumping can be used not only for probing magnetization dynamics in ferromagnets but also spin physics in paramagnets, e.g., for measuring the SHE angles. Magnetization dynamics also produces electrical signals in the ferromagnetic layer through galvanomagnetic effects. Experiments in a (Ga,Mn)As/p-GaAs model system, where sizable galvanomagnetic effects are present, have demonstrated that neglecting the galvanomagnetic effects in the ferromagnet can lead to a large overestimate of the SHE angle in the paramagnet. The study has also shown a method to separate voltages of these different origins in the spin-pumping experiments in the ferromagnet/paramagnet bilayers [151].

The Onsager reciprocity relations imply that there is also a reciprocal phenomenon of the SOT in which electrical signal is generated from magnetization precession in a uniform, spin–orbit coupled magnetic system with broken space inversion symmetry (see Fig. 28) [176, 177]. In this reciprocal SOT effect, no secondary spin–charge conversion element is required, and, as for the SOT, (Ga,Mn)As with broken inversion symmetry in its bulk crystal structure and strong spin–orbit coupled holes represents a favorable model system to explore this phenomenon. The effect was observed in (Ga,Mn)As and was termed a magnonic charge pumping [178].

Light-Induced Torques

Circularly Polarized Light

As discussed in the previous section, current-induced STT is a phenomenon in which angular momentum of a spin-polarized electrical current entering a ferromagnet is transferred to the magnetization. The effect has opened a new research field of electrically driven magnetization dynamics in magnetic nanostructures and plays an important role in the development of a new generation of memory devices and tunable oscillators. Optical excitations of magnetic systems by laser pulses have been a separate research field whose aims are to explore magnetization dynamics at short time scales and enable ultrafast spintronics devices. The observation in (Ga,Mn)As [47] of the optical spin–transfer torque (OSTT) [157, 179] has built the bridge between these two fields of spintronics research. In a pump-and-probe optical experiment, a coherent spin precession in a (Ga,Mn)As ferromagnetic semiconductor was excited by circularly polarized laser pulses. During the pump pulse, the spin-angular momentum of photo-carriers generated by the absorbed light is transferred to the collective magnetization of the ferromagnet.

(Ga,Mn)As is a favorable candidate for observing OSTT [157, 179]. The direct-gap GaAs host allows the generation of a high density of photo-carriers, optical selection rules for circularly polarized light yield high degree of spin polarization of photo-carriers in the direction of the light propagation, and the carrier spins interact with ferromagnetic moments on Mn via exchange coupling. When the ferromagnetic Mn moments are excited, this can be sensitively detected by probe laser pulses due to strong magneto-optical signals in (Ga,Mn)As [180–189].

Coupled precession dynamics of the magnetization orientation and the nonequilibrium photo-carrier spin density is governed by the analogous equations to Eqs. 8 and 9, where the carrier–Mn moment exchange coupling constant is J _ex ≈ 50 meVnm³ for holes and J _ex ≈ 10 meVnm³ for electrons in (Ga,Mn)As. In the optical experiments, P in Eq. 9 is the rate per unit volume at which carrier spins with orientation $ \widehat{\mathbf{n}} $ are optically injected into the ferromagnet. In the studied experimental geometry with normal incidence of the laser pulse and in-plane easy axis of (Ga,Mn)As, the equilibrium $ \widehat{\mathbf{M}} $ is perpendicular to $ \widehat{\mathbf{n}} $. The sign of $ \widehat{\mathbf{n}} $ is given by the helicity of the circularly polarized laser pulse.

The timescale of photoelectron precession due to the exchange field produced by the high-density ferromagnetic Mn moments is τ _ex ~ 100 fs. The major source of spin decoherence of the photoelectrons in (Ga,Mn)As is the exchange interaction with fluctuating Mn moments. Microscopic calculations of the corresponding relaxation time give a typical scale of 10’s ps [157]. The other factor that limits τ _s introduced in Eq. 9 is the photoelectron decay time which is also ~10’s ps, as inferred from reflectivity measurements of the (Ga,Mn)As samples [47]. Within the spin lifetime, the photoelectron spins therefore precess many times around the exchange field of ferromagnetic moments. In the corresponding regime of τ _s ≫ τ _ex, the OSTT has the form of the adiabatic STT given by Eq. 10 and is illustrated in Fig. 29a. The precession time of holes in (Ga,Mn)As is ~10’s fs, and the spin lifetime of holes, dominated by the strong spin–orbit coupling, is estimated to ~1–10 f. [157]. Since τ _s ≲ τ _ex for holes, their contribution is better approximated by the weaker torque which has the form of nonadiabatic STT given by Eq. 11 and is neglected in the discussion below.

The experimental observation of the magnetization precession in (Ga,Mn)As excited by OSTT, with tire characteristic in opposite phases of the oscillations excited by pump pulses of opposite helicities, is presented in Fig. 30a. In the experiment, the output of a femtosecond laser is divided into a strong, 300 f. long pump pulse and a weak delayed probe pulse that are focused to the same spot on the measured sample. To observe the OSTT, a circularly polarized pump laser beam is used. The pump-induced change of the magneto-optical response of the sample is measured by a time-delayed linearly polarized probe pulse. The magneto-optical signals shown in Fig. 30a represent the rotation of the polarization plane of the reflected probe beam. Figure 30b shows the calculated time evolution of the polar angle φ _M and the azimuthal angle θ _M of the magnetization corresponding to the measured data in Fig. 30a for the σ ⁺ helicity.

Since the period of the oscillations seen in Fig. 30 is much larger than tine pump-pulse duration, the action of OSTT is reflected only in the initial phase and amplitude of the free precession of the magnetization. The opposite phase of the measured magneto-optical signals triggered by pump pulses with opposite helicities highlights that the OSTT is not accompanied by any polarization-independent excitation mechanism. Indeed, a linearly polarized pump pulse with any orientation of the polarization is not exciting the magnetization precession. Polarization-independent excitations of magnetization precession in (Ga,Mn)As have been reported prior to the discovery of OSTT [180–189]. The experiments were interpreted in terms of changes of the magnetocrystalline anisotropy induced by the laser pulse [180–189]. The samples studied in Fig. 30a could be also excited by the magnetic anisotropy-related mechanism. In the measurements shown in Fig. 30a, this mechanism was intentionally suppressed in order to highlight the observation of OSTT. This was done by attaching a piezostressor to the (Ga,Mn)As sample which modifies the magnetic anisotropy of the ferromagnetic film due to the differential thermal contraction and allows for an additional in situ electrical control of the in-plane magnetocrystalline anisotropy.

Spin-polarized photo-carriers were also demonstrated to exert an OSTT on the DWs [190]. The resulting optical manipulation of the position of DWs was observed in a perpendicularly magnetized ferromagnetic semiconductor (Ga,Mn)(As,P). The direction of the domain-wall motion was controlled via the OSTT using the helicity of the laser, as illustrated in Fig. 31. Unlike current- or magnetic-field-driven DWs, the OSTT mechanism provides an optical tweezer-like ability to position and locally probe domain walls and to study DW dynamics on ultrashort timescales.

Linearly Polarized Light

As discussed in section “Uniform Magnets,” carriers in a magnet under applied electric field can develop a nonequilibrium spin polarization due to the relativistic spin–orbit coupling even in the absence of an external polarizer. This results in the current-induced SOT acting on the magnetization. In this section we review the observation of the optical counterpart of SOT in (Ga,Mn)As [48].

In OSTT discussed above, the external source for injecting spin-polarized carriers is provided by circularly polarized light at normal incidence which yields high degree of out-of-plane spin polarization of injected photo-carriers due to the optical selection rules in GaAs. Since large OSTT requires large spin lifetime of injected carriers, i.e., spin–orbit coupling is detrimental for OSTT, the weakly spin–orbit coupled photoelectrons play the key role in this case. In OSOT, on the other hand, the absence of an external polarizer corresponds to photo-carrier excitations which are independent of the polarization of the pump laser pulses. Since the phenomenon relies on spin–orbit coupling, the nonequilibrium photo holes are essential in this case. Because of the lack of external polarizer and because of strong spin–orbit coupling, precession of carriers in the exchange field of magnetic moments is not the origin of the torque in this case, in close analogy to the current-induced SOT and reminiscent of the nonadiabatic STT.

The model physical picture of the OSOT is as follows: The optically injected photo holes relax toward the hole Fermi energy of the p-type (Ga,Mn)As on a short (~100 fs) timescale, creating a nonequilibrium excess hole density in the valence band. The change in the occupation of the hole states, as compared to the equilibrium state in dark, and the spin–orbit coupling can generate a nonequilibrium hole spin polarization which is misaligned with the equilibrium orientation of Mn moments. This nonequilibrium photo-hole polarization persists over the timescale of the hole recombination (~ps) during which it exerts a torque on the Mn local moments via the kinetic-exchange coupling. The three key characteristic features, i.e., the nonequilibrium occupation of carrier states, spin–orbit coupling in carrier bands, and the resulting nonequilibrium carrier polarization acting on the magnetic moments via exchange coupling, make OSOT the direct optical counterpart of the current-induced SOT. Since the applied electrical drift (and relaxation) yields a nonequilibrium carrier occupation in the form of asymmetric redistribution on the Fermi surface, the current-induced SOT is observed in systems with broken inversion symmetry in the crystal. OSOT is caused by optical generation (and relaxation) of photo-carriers without an applied drift, and, therefore, the broken inversion symmetry in the crystal is not required. It is replaced by the broken time reversal symmetry, i.e., by a nonzero spin polarization of carrier bands in equilibrium. This is another reason why holes in the strong exchange-split valence band in (Ga,Mn)As govern OSOT.

The schematic illustration and the experimental observation of OSOT are shown in Fig. 32. Apart from the physically more intriguing nature of relativistic OSOT, as compared to OSTT, its experimental identification is complicated by the presence of thermal excitation mechanisms of magnetization dynamics in the case of pump-polarization-independent signals [191, 192]. The absorption of the pump laser pulse leads to photo-injection of electron–hole pairs. The non-radiative recombination of photoelectrons produces a transient increase of lattice temperature which builds up on the timescale of ~ 10 ps and persists over ~ 1000 ps. This results in a quasi-equilibrium easy-axis orientation which is tilted from the equilibrium easy axis. Consequently, Mn moments in (Ga,Mn)As start to precess around quasi-equilibrium easy axis, as illustrated in Fig. 32a, with a typical precession time of ~ 100 ps given by the magnetic anisotropy fields in (Ga,Mn)As. The easy axis stays in-plane and the sense of rotation within the plane of the (Ga,Mn)As film with increasing temperature is uniquely defined. In the notation introduced in Fig. 32c, the change of the in-plane angle δφ of magnetization during the thermally excited precession can be only positive.

OSOT, illustrated in Fig. 32b, acts during the laser pulse (with a duration of 200 fs) and fades away within the hole recombination time (~ ps). It causes an impulse tilt of the magnetization which allows one to clearly distinguish OSOT from the considerably slower thermal excitation mechanism. Moreover, the initial OSOT-induced tilt of magnetization can yield precession angles that are inaccessible in the thermally induced magnetization dynamics. This provides another evidence for OSOT. Examples of the direct observation of the thermally governed excitation of magnetization at a lower pump-pulse intensity and of the OSOT-governed excitation at a higher intensity are shown in Fig. 32d. These dynamical magneto-optical signals are completely independent of the polarization of pump pulses, i.e., they are the same for any orientation of the polarization plane of linearly polarized pump laser pulses. The distinct features of OSOT, described in the previous paragraph, are clearly visible when comparing the two measured trajectories of magnetization angles.

A full quantitative theory of OSOT is a challenging problem compared to the theory of OSTT [47, 157, 179]. In the latter case, the nonequilibrium spin density of weakly spin–orbit coupled photoelectrons, producing the OSTT, is directly determined by the external polarizer, i.e., by the intensity, propagation axis, and helicity of the circularly polarized pump laser beam. The relation between the nonequilibrium density of photo holes and the transverse component of their spin polarization, producing OSOT in the case of light-polarization-independent excitations, results from a more complex interplay of spin–orbit coupling and photo-generation and relaxation processes in the spin–split valence band of the ferromagnetic semiconductor [193]. The effective field due to the nonequilibrium spin density of the photo holes, J _ex s, generating OSOT can be related in a simplified picture [48] to the hole-density-dependent magnetocrystalline anisotropy field. This can be illustrated using the model kinetic-exchange Hamiltonian $ H={H}_{host}+{J}_{ex}cS\widehat{\mathbf{M}}\cdot \boldsymbol{\sigma} $ [51, 94], where H _host is the host Hamiltonian semiconductor and σ is the hole spin operator. The anisotropy field can then be written as [164]

$$ \begin{array}{c}\hfill {\mathbf{H}}_{an}=-\frac{1}{cS}\;\frac{\partial }{\partial \widehat{\mathbf{M}}}{\displaystyle \sum_a{\displaystyle \int d\mathbf{k}{\upepsilon}_{a,\mathbf{k}}{f}_{a,\mathbf{k}}}}\hfill \\ {}\hfill =-\frac{1}{cS}{\displaystyle \sum_a{\displaystyle \int d\mathbf{k}\left\langle a,\mathbf{k}\left|\frac{\partial H}{\partial \widehat{\mathbf{M}}}\right|a,\mathbf{k}\right\rangle {f}_{a,\mathbf{k}}}}\hfill \\ {}\hfill =-{\displaystyle \sum_a{\displaystyle \int d\mathbf{k}\left\langle a,\mathbf{k}\left|{J}_{ex}\boldsymbol{\sigma} \right|a,\mathbf{k}\right\rangle {f}_{a,\mathbf{k}}}}\hfill \\ {}\hfill =-{J}_{ex}\mathbf{s}\hfill \end{array} $$

(12)

Here ϵ _a,k and f _a,k are the eigenenergy of H and Fermi distribution function, respectively, labeled by the band and wave vector index. Since the easy-axis orientation is sensitive to the hole density, H _an and the corresponding OSOT field J _ex s can change when the hole density is increased by, e.g., the photoexcitation.

Summary

We have reviewed the electronic and magnetic properties of (III,Mn)V ferromagnetic semiconductors and devices fabricated in these materials, focusing on the most extensively explored and exploited (Ga,Mn)As. Over the two decades of research in (Ga,Mn)As, its material properties have been extensively debated from the basic physics perspective in order to elucidate the role of the high density of magnetic and electrical Mn impurities in the semiconductor host and the implications of the Mn doping on the Curie temperature, conductivity, and other hybrid magneto-semiconducting characteristics of the material. This material research side of (Ga,Mn)As now seems to have reached a rather mature stage. Where (Ga,Mn)As and the related (III,Mn)V materials continue to bring new surprises and inspiration is primarily in the research of relativistic spintronics phenomena and device functionalities. A number of effects that continuously expand the portfolio of spintronics fundamentals have been initially observed in (Ga,Mn)As and subsequently rediscovered or transferred to other magnetic systems, including high Curie temperature ferromagnets relevant for applications. This trend is likely to continue in the future since (Ga,Mn)As encompasses a range of unique and favorable structural, magnetic, electronic, and optical properties rendering this ferromagnetic semiconductor an ideal model system for research in spintronics phenomena and devices.

Abbreviations

AMR:: Anisotropic magnetoresistance
CB:: Coulomb blockade
DOS:: Density of states
DW:: Domain wall
FMR:: Ferromagnetic resonance
GGA:: Generalized gradient approximations
GMR:: Giant magnetoresistance
LSMR:: Linear spin-Hall magnetoresistance
LT-MBE:: Low-temperature molecular-beam epitaxy
MRAM:: Magnetic random access memory
OSOT:: Optical spin–orbit torque
OSTT:: Optical spin–transfer torque
SET:: Single-electron transistor
SHE:: Spin-Hall effect
SOT:: Spin–orbit torque
SQUID:: Superconducting quantum interference device
STM:: Scanning tunneling microscopy
STT:: Spin–transfer torque
TAMR:: Tunneling anisotropic magnetoresistance
TBA:: Tight-binding approximation
TMR:: Tunneling magnetoresistance
WB:: Walker breakdown

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Acknowledgments

This review is based on numerous helpful discussions with our colleagues. In particular we acknowledge discussions with Richard Campion, Tomasz Dietl, Kevin Edmonds, Andrew Ferguson,Tom Foxon, Bryan Gallagher, Allan MacDonald, Jan Mašek, Petr Němec, Vít Novák, Hideo Ohno, Kamil Olejník, Andrev Rushforth, Jairo Sinova, Karel Výborný, Dieter Weiss, Jorg Wunderlich, and Jan Zemen. We also acknowledge support from the ERC Advanced Grant No. 268066, from the Ministry of Education of the Czech Republic Grant No. LM2011026, and from the Czech Science Foundation Grant No. 14-37427G

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Authors and Affiliations

Institute of Physics ASCR, v.v.i., Praha 6, Czech Republic
T. Jungwirth
School of Physics and Astronomy, University of Nottingham, Nottingham, UK
T. Jungwirth

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T. Jungwirth
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York-Nanjing International Center of Spintronics, Nanjing University, Nanjing, China
Yongbing Xu
Institute for Molecular Engineering, University of Chicago, Chicago, Illinois, USA
David D. Awschalom
Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai, Japan
Junsaku Nitta

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Jungwirth, T. (2016). III–V Based Magnetic Semiconductors. In: Xu, Y., Awschalom, D., Nitta, J. (eds) Handbook of Spintronics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6892-5_20

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DOI: https://doi.org/10.1007/978-94-007-6892-5_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-6891-8
Online ISBN: 978-94-007-6892-5
eBook Packages: Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

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III–V Based Magnetic Semiconductors

Abstract

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III–V Based Magnetic Semiconductors

Magnetic III–V Semiconductor-Based Hybrid Structures

Room Temperature Ferromagnetism: Nonmagnetic Semiconductor Oxides and Nonmagnetic Dopants

Keywords

Introduction

Electronic Structure and Magnetic Coupling

Curie Temperature and Doping Trends

Magnetic Anisotropy Effects in Films and Devices

Micromagnetic Parameters

Resistors

Tunnel Junctions

Capacitors

Transistors

Spin-Hall Magnetoresistance

Current-Induced Torques

Tunnel Junctions and Domain Walls

Uniform Magnets

Magnonic Charge Pumping

Light-Induced Torques

Circularly Polarized Light

Linearly Polarized Light

Summary

Abbreviations

References

Acknowledgments

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III–V Based Magnetic Semiconductors

Abstract

Similar content being viewed by others

III–V Based Magnetic Semiconductors

Magnetic III–V Semiconductor-Based Hybrid Structures

Room Temperature Ferromagnetism: Nonmagnetic Semiconductor Oxides and Nonmagnetic Dopants

Keywords

Introduction

Electronic Structure and Magnetic Coupling

Curie Temperature and Doping Trends

Magnetic Anisotropy Effects in Films and Devices

Micromagnetic Parameters

Resistors

Tunnel Junctions

Capacitors

Transistors

Spin-Hall Magnetoresistance

Current-Induced Torques

Tunnel Junctions and Domain Walls

Uniform Magnets

Magnonic Charge Pumping

Light-Induced Torques

Circularly Polarized Light

Linearly Polarized Light

Summary

Abbreviations

References

Acknowledgments

Author information

Authors and Affiliations

Corresponding author

Editor information

Editors and Affiliations

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Copyright information

About this entry

Cite this entry

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