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To gain insight into the spin-glass state of diluted magnetic semiconductors, we have examined the magnetic and electronic properties of ${\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$ using density-functional theory as well as performed magnetization measurements on the $x=0.43$ and 0.55 systems to demonstrate a clear spin-glass transition consistent with previous literature. Using a generalized gradient approximation, we investigate the electronic and magnetic properties for $x=0$, 0.075, 0.15, 0.25, and 0.50 doping levels using the magnetic moment of ${\mathrm{Mn}}^{2+}$ as guide for the dependence of the Hubbard onsite potential on the electronic structure. Simulations on both ferromagnetic (FM) and antiferromagnetic (AFM) configurations yield a distinct AFM ground-state preference, which is consistent with a zero-magnetic-moment spin-glass state. Here an onsite potential of up to 8 eV on the Mn $3d$ orbitals is needed to harden the magnetic moment toward $S=5/2$. From our analysis of the electronic structure evolution with doping and onsite potential, we confirm the semiconducting state of the Mn-doped ZnTe as well as show that the presence of Mn incorporated into the ZnTe matrix at the Zn lattice site produces magnetic interactions through the Te ions with a distinct Te-Mn $pd$-orbital hybridization. Furthermore, we show that this hybridization is activated with the Mn doping above 0.25 concentration, which corresponds to the doping level in which the spin-glass transition begins to rise. Therefore, it is likely that the coupling of $pd$-orbital hybridization of the Mn and Te $p$ orbitals is a precursor to the enhancement of the spin-glass transition temperature.

We study a new diluted magnetic semiconductor system based on the spin of the ionized acceptor Cr$^+$. We show that the negatively charged Cr$^+$ ion, an excited state of the Cr in II-VI semiconductor, can be stable when inserted in a CdTe quantum dot (QD). The Cr$^+$ attracts a heavy-hole in the QD and form a stable hole-Cr$^+$ complex. Optical probing of this system reveals a ferromagnetic coupling between heavy-holes and Cr$^+$ spins. At low temperature, the thermalization on the ground state of the hole-Cr$^+$ system with parallel spins prevents the optical recombination of the excess electron on the 3$d$ shell of the atom. We study the dynamics of the nano-magnet formed by the hole-Cr$^+$ exchange interaction. The ferromagnetic ground states with M$_z$=$\pm$4 can be controlled by resonant optical pumping and a spin relaxation time in the 20 $\mu$s range is obtained at T=4.2 K. This spin memory at zero magnetic field is limited by the interaction with phonons.

Calculations suggest that ordered Heusler alloys with 18 valance electrons could exhibit a variety of unusual electronic and magnetic states that are absent in the constituent elements. They include magnetic semiconductors, spin gapless semiconductors, compensated ferrimagnetic half-metals, and metallic antiferromagnets. Magnetic order has been predicted at exceptionally high temperature. Any of this would be of interest for spin electronics. Here, we investigate the magnetic properties of bulk, single-phase ${\mathrm{V}}_{3}\mathrm{Al}$, CrVTiAl and the corresponding Ga compounds, with and without $^{57}\mathrm{Fe}$ doping. Results are compared with data on the constituent elements. We conclude that all the as-cast alloys show some degree of B2-type ordering, but all of them are Pauli paramagnets with dimensionless susceptibilities close to the average of the atomic constituents. Prolonged annealing of the single-phase as-cast alloys leads to phase segregation. Density functional theory calculations on ${\mathrm{V}}_{3}X$ and $\text{CrVTi}X$ with $X=B$, Al, Ga, and In confirm that different atomic arrangements on the four interpenetrating face-centered cubic sublattices of the Heusler structure could indeed lead to unusual magnetic properties, but both magnetism and semiconductivity are destroyed by disorder. The energy and entropy differences between different ordered magnetic phases preclude the stabilization of any single one of them. All are metastable and inaccessible in alloys prepared from the melt.

The discovery of two-dimensional (2D) van der Waals (vdW) intrinsic magnets has opened a promising avenue to design high-performance magnetic tunnel junctions (MTJs) based on 2D materials. In this work, using first-principles calculations, it is demonstrated that bilayer $\mathrm{Co}{\mathrm{Br}}_{2}$ is intrinsically a magnetic semiconductor with intralayer ferromagnetic (FM) and interlayer antiferromagnetic (AFM) couplings and the interlayer AFM coupling in bilayer $\mathrm{Co}{\mathrm{Br}}_{2}$ is independent on the stacking orders. Moreover, using the nonequilibrium Green's function combined with density functional theory, it is found that due to the large difference between interlayer AFM and FM states of the $\mathrm{Co}{\mathrm{Br}}_{2}$ barrier, the conductance of spin filter (SF) vdW MTJs based on the graphene/bilayer $\mathrm{Co}{\mathrm{Br}}_{2}$/graphene heterostructure for the interlayer FM state of the $\mathrm{Co}{\mathrm{Br}}_{2}$ barrier is about 25 times that for the interlayer AFM state of the $\mathrm{Co}{\mathrm{Br}}_{2}$ barrier. Consequently, a high tunneling magnetoresistance (TMR) ratio of $2420%$ is achieved in this SF-vdW MTJ at zero bias. In particular, because the current for the interlayer FM state of the $\mathrm{Co}{\mathrm{Br}}_{2}$ barrier rapidly increases with the increase of bias voltage, a giant TMR ratio of up to about $38\phantom{\rule{0.16em}{0ex}}000%$ can be achieved in this SF-vdW MTJ at 0.2-V bias. Our results suggest that SF-vdW MTJs formed by the interlayer AFM barrier with variable conductivity hold great potential for developing vdW MTJs with a high TMR ratio.

Exchange coupling between localized spins and band or topological states accounts for giant magnetotransport and magnetooptical effects as well as determines spin-spin interactions in magnetic insulators and semiconductors. However, even in archetypical dilute magnetic semiconductors such as Cd$_{1-x}$Mn$_x$Te and Hg$_{1-x}$Mn$_x$Te the evolution of this coupling with the wave vector is not understood. A series of experiments have demonstrated that exchange-induced splitting of magnetooptical spectra of Cd$_{1-x}$Mn$_x$Te and Zn$_{1-x}$Mn$_x$Te at the L points of the Brillouin zone is, in contradiction to the existing theories, more than one order of magnitude smaller compared to its value at the zone center and can show an unexpected sign of the effective Land\'e factors. The origin of these findings we elucidate quantitatively by combining: (i) relativistic first-principles density functional calculations; (ii) a tight-binding approach that takes carefully into account k-dependence of the potential and kinetic sp-d exchange interactions; (iii) a theory of magnetic circular dichroism (MCD) for $E_1$ and $E_1$ + $\Delta_1$ optical transitions, developed here within the envelope function $kp$ formalism for the L point of the Brillouin zone in zinc-blende crystals. This combination of methods leads to the conclusion that the physics of MCD at the boundary of the Brillouin zone is strongly affected by the strength of two relativistic effects in particular compounds: (i) the mass-velocity term that controls the distance of the conduction band at the L point to the upper Hubbard band of Mn ions and, thus, a relative magnitude and sign of the exchange splittings in the conduction and valence bands; (ii) the spin-momentum locking by spin-orbit coupling that reduces exchange splitting depending on the orientation of particular L valleys with respect to the magnetization direction., Comment: 20 pages, 6 figures

One primary concern in diluted magnetic semiconductors (DMSs) is how to establish a long-range magnetic order with a low magnetic doping concentration to maintain the gate tunability of the host semiconductor, as well as to increase Curie temperature. Two-dimensional van der Waals semiconductors have been recently investigated to demonstrate the magnetic order in DMSs; however, a comprehensive understanding of the mechanism responsible for the gate-tunable long-range magnetic order in DMSs has not been achieved yet. Here, we introduce a monolayer tungsten diselenide (WSe2) semiconductor with V dopants to demonstrate the long-range magnetic order through itinerant spin-polarized holes. The V atoms are sparsely located in the host lattice by substituting W atoms, which is confirmed by scanning tunneling microscopy and high-resolution transmission electron microscopy. The V impurity states and the valence band edge states are overlapped, which is congruent with density functional theory calculations. The field-effect transistor characteristics reveal the itinerant holes within the hybridized band; this clearly resembles the Zener model. Our study gives an insight into the mechanism of the long-range magnetic order in V-doped WSe2, which can also be used for other magnetically doped semiconducting transition metal dichalcogenides., 19 pages, 4 figures

Graphene is favorable to realize topological nontrivial state by introducing spin-orbit coupling and exchange field through the proximity effect. The recent discovery of van der Waals magnets allows great proximitized modulation on graphene by building atomically clean heterostructures. Here, we realize anomalous Hall effect in graphene coupling with a layered magnetic material, ${\mathrm{Fe}}_{x}{\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{S}}_{2}$. The anomalous Hall resistance and the carrier density show a nonmonotonous dependence on the back-gate voltage, indicating emergence of band-structure transformation. Furthermore, low-field quantum interference measurement shows the enhancement of spin-orbit coupling (SOC) in the heterostructure. Our findings confirm that graphene coupling to ${\mathrm{Fe}}_{x}{\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{S}}_{2}$ is an ideal platform that is likely to introduce a strong exchange field and SOC simultaneously, which has outstanding potential in realizing topological nontrivial states and spintronics.

The magneto-optical (MO) effects are a powerful probe of magnetism and electronic structure of magnetic solids but also have valuable applications in high-density data-storage technology. Yttrium iron garnet (${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$) (YIG) and bismuth iron garnet (${\mathrm{Bi}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$) (BIG) are two widely used magnetic semiconductors with significant magneto-optical effects. In this paper, we present a thorough theoretical investigation on magnetism, electronic, optical, and MO properties of YIG and BIG, based on the density functional theory with the generalized gradient approximation plus on-site Coulomb repulsion. We find that YIG exhibits significant MO Kerr and Faraday effects in UV frequency range that are comparable to ferromagnetic iron. Moreover, BIG shows gigantic MO effects in visible frequency region that are several times larger than YIG. This is because the calculated MO conductivity (${\ensuremath{\sigma}}_{xy}$) of BIG is nearly ten times larger than that of YIG. Interestingly, the calculated band structures reveal that BIG is a single spin semiconductor. They also show that in YIG, Y $sd$ orbitals mix mainly with the high-lying conduction bands, leaving Fe $d$ orbital dominated lower conduction bands almost unaffected by the spin-orbit coupling (SOC) on the Y atom. In contrast, Bi $p$ orbitals in BIG hybridize significantly with Fe $d$ orbitals in the lower conduction bands, leading to large SOC-induced band splitting in the bands. Consequently, the MO transitions between the upper valence bands and lower conduction bands are greatly enhanced when Y is replaced by heavier Bi. Our calculated Kerr and Faraday rotation angles of YIG as well as Faraday rotation angles for BIG agree well with the available experimental values. Thus, we believe that our predicted giant MO Kerr effect in BIG will stimulate further MOKE experiments on high-quality BIG crystals. This work thus shows that the iron garnets not only offer a useful platform for exploring the interplay of spin current, magnetism, and optics degrees of freedom, but also have promising applications in high-density MO data-storage and low-power consumption spintronic nanodevices.

In intrinsic magnetic semiconductors, the absorption of a single photon can generate a spin polaron, whose magnetic moment reaches many thousands of Bohr magnetons [1.2]. Here we investigate photoinduced spin polarons, using Monte Carlo simulations. In antiferromagnetic semiconductors, photoinduced spin polarons are most efficiently generated in the whole temperature interval up to the phase transition, whereas in ferromagnetic semiconductors much larger spin polarons can be photoinduced, but only around the phase transition temperature. Because Monte Carlo simulations are computationally expensive, we developed an analytical model, based on the Weiss field theory. Although the Weiss model does not provide as much information as a Monte Carlo simulation, such as spin texture and fluctuations, it yields formulas that can be used to estimate instantly the expected photoinduced spin polaron size in many intrinsic magnetic semiconductors., Comment: Accepted for publication in Phys. Rev. B

Magneto-optical control of optical absorption spectra is theoretically investigated in two-dimensional (2D) dilute magnetic semiconductors such as monolayer transition metal dichalcogenides (TMDs) doped with magnetic ions. The underlying mechanism relies on efficient spin transfer between spin-polarized photoexcited carriers and localized magnetic ions via exchange scattering, and subsequent shifts in the electronic band structure induced by the resulting time-reversal symmetry breaking. A self-consistent model based on a rate equation is developed to analyze dynamical polarization of itinerant carrier spins and localized magnetic moments under circularly polarized optical excitation and the corresponding band modifications. The results illustrate that nonlinear effects such as optical bistability and self-opacity can indeed be achieved efficiently for a range of excitation power and frequency. In particular, the addition of magnetic dopants is shown to reduce the optical power required for the necessary band shifts by four orders of magnitude compared to that via the optical Stark effect in a nonmagnetic counterpart. Further investigation in a multidimensional parameter space elucidates the conditions for practical realization of the desired nonlinear effects in 2D TMD monolayers.

The magnetic long-range ordering states of van der Waals magnets at low temperatures have gained much interest, yet their high-temperature paramagnetic states remain largely unexplored. In this paper, we apply the disordered local moment picture for describing the paramagnetic states of two-dimensional magnetic semiconductors. We calculate the electronic structure of paramagnetic phases of ${\mathrm{CrI}}_{3},\phantom{\rule{0.28em}{0ex}}{\mathrm{CrSiTe}}_{3}$, and ${\mathrm{NiPS}}_{3}$ using the density functional theory with static Hubbard corrections. The semiconducting electronic structures are successfully reproduced without any inclusion of dynamical correlation effects. The local electronic structure of magnetic ions in the paramagnetic phase resembles those in the magnetically ordered phase. The band structures of the paramagnetic phases are also analyzed. The itinerant ferromagnet ${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ is also briefly discussed where the disordered local moment picture is not applicable due to the coexistence of itinerant and local magnetism.

Being a wide band gap system GaMnN attracted considerable interest after the discovery of highest reported ferromagnetic transition temperature $T_C$ $\sim$ 940 K among all diluted magnetic semiconductors. Later it become a debate due to the observation of either a ferromagnetic state with very low $T_C$ $\sim$ 8 K or sometimes no ferromagnetic state at all. We address these issues by calculating the ferromagnetic window, $T_C$ Vs $p$, within a $t-t'$ Kondo lattice model using a spin-fermion Monte-Carlo method on a simple cubic lattice. We exploit the next-nearest-neighbor hopping $t'$ to tune the degree of delocalization of the free carriers and show that carrier localization (delocalization) significantly widen (shrunken) the ferromagnetic window with a reduction (enhancement) of the optimum $T_C$. We connect our results with the experimental findings and try to understand the ambiguities in ferromagnetism in GaMnN., 10 pages, 7 figures

In two-dimensional (2D) magnetic systems, large magnetic anisotropy is needed to stabilize the magnetic order according to Mermin-Wagner theorem. Based on density functional theory (DFT) calculations, we propose that the magnetic anisotropic energy (MAE) of 2D ferromagnetic (FM) semiconductors can be strongly enhanced in van der Waals heterostructures by attaching a nonmagnetic semiconductor monolayer with large spin-orbit coupling. We studied Cr2Ge2Te6/PtSe2 bilayer heterostructures, where each layer has been realized in recent experiments. The DFT calculations show that the MAE of Cr2Ge2Te6/PtSe2 is enhanced by 70%, and the Curie temperature TC is increased far beyond room temperature. A model Hamiltonian is suggested to analyze the DFT results, showing that both the Dzyaloshinskii-Moriya interaction and the single-ion anisotropy contribute to the enhancement of the MAE. Based on the superexchange picture, we find that the decreased energy difference between 3d orbitals of Cr and 5p orbitals of Te contributes partially to the increase of TC. Our present work indicates a promising way to enhance the MAE and TC by constructing van der Waals semiconductor heterostructures, which will inspire further studies on the 2D magnetic semiconductor systems., Comment: 10 pages, 5 figures

In recent experiments, high Curie temperatures ${T}_{c}$ above room temperature were reported in ferromagnetic semiconductors Fe-doped GaSb and InSb, while low ${T}_{c}$ between 20 K to 90 K were observed in some other semiconductors with the same crystal structure, including Fe-doped InAs and Mn-doped GaSb, InSb, and InAs. Here we study systematically the origin of high temperature ferromagnetism in Fe, Mn, Cr-doped GaSb, InSb, and InAs magnetic semiconductors by combining the methods of density functional theory and quantum Monte Carlo. In the diluted impurity limit, the calculations show that the impurities Fe, Mn, and Cr have similar magnetic correlations in the same semiconductors. Our results suggest that high (low) ${T}_{c}$ obtained in these experiments mainly comes from high (low) impurity concentrations. In addition, our calculations predict the ferromagnetic semiconductors of Cr-doped InSb, InAs, and GaSb that may have possibly high ${T}_{c}$. Our results show that the origin of high ${T}_{c}$ in (Ga,Fe)Sb and (In,Fe)Sb is not due to the carrier induced mechanism because ${\mathrm{Fe}}^{3+}$ does not introduce carriers.

The antiferromagnetic-ferromagnetic competition in a diluted magnetic semiconductor is discussed. In a virtual-crystal approximation, the active magnetic ions in the system are assumed to distribute homogeneously, and the quantum magnetic correlations are described in the Kondo lattice model involving local disorder. In the framework of the dynamical mean-field theory, we deliver the signatures of the static magnetic susceptibility function and the ${B}_{1g}$ channel Raman response adapting to the model. At low temperatures, one finds the antiferromagnetic instability against the ferromagnetic state when the impurity band is nearly filled. For a completely filled impurity band system, the antiferromagnetic state is stabilized in the case of sufficiently large magnetic exchanges. The effect of the thermal fluctuations on the phase competition is also discussed. Analyzing the ${B}_{1g}$ channel Raman spectrum attributes a competition between the short-range magnetic order and the short-wavelength excitation in the filled impurity band paramagnetic state.

Quantized spin-wave known as magnon, a bosonic quasiparticle, can drag electrons or holes via s-d exchange interaction and boost the thermopower over the conventional diffusive thermopower. P-type magnon-drag thermopower has been observed in both ferromagnetic and antiferromagnetic metallic and degenerate semiconductors. However, it has been less reported for intrinsic or $n$-type magnetic semiconductors; therefore, the impact of magnon-bipolar carrier drag on thermopower has remained unexplored. Here, a theoretical model for magnon-bipolar carrier drag thermopower is derived based on the magnon-carrier interaction lifetimes. The model predicts that the bipolar carrier drag thermopower becomes independent of both the carrier and magnon relaxation times. A proof of concept experiment is presented that confirms this prediction. We also report the observation of magnon-carrier drag thermopower in n-type and intrinsic ferromagnetic semiconductors experimentally. The p-type antiferromagnetic MnTe is doped with different amounts of Cr to produce nondegenerate and n-type semiconductors of various carrier concentrations. Cr dopants have a donor nature and create ferromagnetic-antiferromagnetic clusters due to the $\mathrm{C}{\mathrm{r}}^{3+}$ oxidation state. Heat capacity measurements confirm the presence of magnons in Cr-doped MnTe. It is shown that the magnon-drag thermopower is significantly reduced for 3%--5% Cr-doped samples due to bipolar drag effects and becomes negative for 14% and 20% Cr-doped MnTe due to dominant magnon-electron drag thermopower.

We report the observation of tens of minor lines of the combinational spin-flip Raman scattering in a CdTe:Mn quantum well by means of the high-resolution optical spectroscopy. Classification of this manifold leads to four characteristic values of energy, that correspond to four different types of pair clusters of Mn ions: the nearest, second, third, etc., neighbors. All the four energies show up in a single experiment with a very high precision, providing experimental grounds for a deeper understanding of the $d\ensuremath{-}d$ exchange interactions in a diluted magnetic semiconductor and demonstrating the capacity of the employed method. The major (nearest-neighbor) exchange constant ${J}_{1}=6.15\ifmmode\pm\else\textpm\fi{}0.05$ K was found to consent with its previously reported value. Other detected characteristic energies are as follows ($\ifmmode\pm\else\textpm\fi{}0.05$ K): ${J}_{(2)}=1.80$ K, ${J}_{(3)}=1.39$ K, ${J}_{(4)}=0.81$ K.

The quantum anomalous Hall effect (QAHE) has been experimentally observed in magnetically doped topological insulators at ultralow temperatures. Inhomogeneous ferromagnetism is considered to be one of the main factors that lead to the unexpected low QAHE observation temperature. Dopant-induced disorder is usually the origin of the inhomogeneous ferromagnetism. Here, our systematic first-principles calculations demonstrate that inhomogeneous mixing of Bi and Sb in a ${(\mathrm{Bi},\mathrm{Sb})}_{2}{\mathrm{Te}}_{3}$ system is the intrinsic origin of inhomogeneous ferromagnetism. Different from diluted magnetic semiconductors, the mixing energy of Cr and V in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$, and ${(\mathrm{Bi},\mathrm{Sb})}_{2}{\mathrm{Te}}_{3}$ topological insulators clearly show that magnetic dopants are homogeneously distributed even in the presence of naturally formed crystalline defects. Surprisingly, our study shows that the mixing energies of Sb and Bi in a ${(\mathrm{Bi},\mathrm{Sb})}_{2}{\mathrm{Te}}_{3}$ system are all positive in the whole range of doping concentration, indicating that Bi elements in a ${(\mathrm{Bi},\mathrm{Sb})}_{2}{\mathrm{Te}}_{3}$ system are inhomogeneously distributed. Moreover, the formation energies of Cr and V suggest that they are relatively easy to substitute Bi sites in Bi inhomogeneously distributed ${(\mathrm{Bi},\mathrm{Sb})}_{2}{\mathrm{Te}}_{3}$ systems, which leads to inhomogeneous ferromagnetism of the experimental QAHE system. The influence of the inhomogeneous distribution of Bi on the electronic structures of bulk ${(\mathrm{Bi},\mathrm{Sb})}_{2}{\mathrm{Te}}_{3}$ systems is also analyzed. We believe that our finding of the intrinsic origin of magnetic inhomogeneity should be beneficial for the experimental enhancement of the QAHE observation temperature in magnetically doped topological insulators.

Our analysis based on the results of hybrid and semilocal density-functional calculations with and without Hubbard $U$ correction for on-site Coulomb interactions reveals the true magnetic ground states of three transition-metal dichalcogenide monolayers, viz., ${\mathrm{FeTe}}_{2},{\mathrm{VS}}_{2}$, and ${\mathrm{NiTe}}_{2}$, which comprise inhomogeneous magnetic moment configurations. In contrast to earlier studies considering only the magnetic moments of transition-metal atoms, the chalcogen atoms by themselves have significant, antiparallel magnetic moments owing to the spin polarization through $p\text{\ensuremath{-}}d$ hybridization. The latter is found to be true for both $H$ and $T$ phases of ${\mathrm{FeTe}}_{2},{\mathrm{VS}}_{2}$, and ${\mathrm{NiTe}}_{2}$ monolayers. Our predictions show that the ${\mathrm{FeTe}}_{2}$ monolayer in its lowest-energy structure is a half metal, which prevails under both compressive and tensile strains. Half metallicity occurs also in the ${\mathrm{FeTe}}_{2}$ bilayer but disappears in thicker multilayers. The ${\mathrm{VS}}_{2}$ monolayer is a magnetic semiconductor; it has two different band gaps of different character and widths for different spin polarization. The ${\mathrm{NiTe}}_{2}$ monolayer, which used to be known as a nonmagnetic metal, is indeed a magnetic metal with a small magnetic moment. These monolayers with intriguing electronic and magnetic properties can attain new functionalities for spintronic applications.

We illustrate an approach based on itinerant magnetism for finding ferromagnetic semiconductors that can be gate tuned to study quantum critical points. We show that $p$-type ${\mathrm{FeAs}}_{2}$ is an example. The complex nonparabolic band structure of this material leads to a ferromagnetic instability when doped, while at the same time allowing for a modest transport effective mass. This leads to an analogy between magnetic semiconductors and thermoelectric materials.

We perform systematic first-principles calculations to investigate the spin-phonon coupling (SPC) of $\mathrm{C}{\mathrm{r}}_{2}\mathrm{G}{\mathrm{e}}_{2}\mathrm{T}{\mathrm{e}}_{6}$ (CGT) monolayer (ML). It is found that the ${E}_{\mathrm{g}}$ phonon mode at $211.8\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$ may have a SPC as large as $3.19\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$, as it alters the direct exchange interaction across Cr-Cr pairs. The strength of SPC of the CGT ML can be decreased by an in-plane lattice stretch. These results provide useful insights for the understanding of SPC in two-dimensional magnetic semiconductors and may guide the design of spintronic and spin Seebeck materials and devices.

A detailed account of the local atomic structure and disorder at 5 K across the phase diagram of the high-temperature superconductor ${\mathrm{K}}_{x}{\mathrm{Fe}}_{2\ensuremath{-}y}{\mathrm{Se}}_{2\ensuremath{-}z}{\mathrm{S}}_{z}$ $(0\ensuremath{\le}z\ensuremath{\le}2)$ is obtained from neutron total scattering and associated atomic pair distribution function (PDF) approaches. Various model-independent and model-dependent aspects of the analysis reveal a high level of structural complexity on the nanometer length scale. Evidence is found for considerable disorder in the $c$-axis stacking of the ${\mathrm{FeSe}}_{1\ensuremath{-}x}{\mathrm{S}}_{x}$ slabs without observable signs of turbostratic character of the disorder. In contrast to the related FeCh (Ch = S, Se)-type superconductors, substantial Fe-vacancies are present in ${\mathrm{K}}_{x}{\mathrm{Fe}}_{2\ensuremath{-}y}{\mathrm{Se}}_{2\ensuremath{-}z}{\mathrm{S}}_{z}$, deemed detrimental for superconductivity when ordered. Our study suggests that the distribution of vacancies significantly modifies the iron-chalcogen bond-length distribution, in agreement with observed evolution of the PDF signal. A crossoverlike transition is observed at a composition of $z\ensuremath{\approx}1$, from a correlated disorder state at the selenium end to a more vacancy-ordered (VO) state closer to the sulfur end of the phase diagram. The S-content-dependent measures of the local structure are found to exhibit distinct behavior on either side of this crossover, correlating well with the evolution of the superconducting state to that of a magnetic semiconductor toward the $z\ensuremath{\approx}2$ end. The behavior reinforces the idea of the intimate relationship of correlated Fe-vacancy order in the local structure and the emergent electronic properties.

$\mathrm{B}{\mathrm{i}}_{2}{\mathrm{O}}_{2}\mathrm{Se}$ is a novel layer-structured material with high electron mobility, while its efficiency could be greatly improved by doping different elements to introduce a magnetic spin order. We investigated the electronic and magnetic properties of various transition metal (TM) ($\mathrm{TM}=\mathrm{Mn}$, Cr, Fe, Co, and Ni) doped $\mathrm{B}{\mathrm{i}}_{2}{\mathrm{O}}_{2}\mathrm{Se}$ within a framework of density functional theory (DFT), and discovered that $\mathrm{B}{\mathrm{i}}_{2\ensuremath{-}n}{\mathrm{X}}_{n}{\mathrm{O}}_{2}\mathrm{Se}$ exhibits long-range magnetic ordered structure via competition among double-exchange, p-d exchange, and superexchange interaction. The magnetic order of the bulk phase in which the magnetic atoms form interlayer coupling would vary with the type and concentration of doped atoms, but all the layered phases in which the magnetic atoms are in-plane coupled show ferromagnetic order. By combing DFT calculations with the Monte Carlo scheme, we solve the exchange interaction constants for the Heisenberg model and further evaluate the Curie temperatures of $\mathrm{B}{\mathrm{i}}_{2\ensuremath{-}n}{\mathrm{X}}_{n}{\mathrm{O}}_{2}\mathrm{Se}$. Ferromagnetic order for most doped systems exhibit to be robust with high Curie temperature, some of which overcomes room temperature (for 12.5% Co-doped layer $\mathrm{B}{\mathrm{i}}_{2}{\mathrm{O}}_{2}\mathrm{Se}$). It is also worth mentioning that the appearance of impurity energy levels narrows the band gap and enhances the spin-orbit coupling of $d$ orbitals and therefore increase large magnetic anisotropy energy. Our study demonstrates a potential pathway to design new dilute magnetic semiconductors through doping of $\mathrm{B}{\mathrm{i}}_{2\ensuremath{-}n}{\mathrm{X}}_{n}{\mathrm{O}}_{2}\mathrm{Se}$ by magnetic transitional elements.

We explore the impact of a Rashba-type spin-orbit interaction in the conduction band on the spin dynamics of hot excitons in diluted magnetic semiconductor quantum wells. In materials with strong spin-orbit coupling, we identify parameter regimes where spin-orbit effects greatly accelerate the spin decay and even change the dynamics qualitatively in the form of damped oscillations. Furthermore, we show that the application of a small external magnetic field can be used to either mitigate the influence of spin-orbit coupling or entirely remove its effects for fields above a material-dependent threshold., 9 pages, 5 figures

Phonons are well known to be the main mechanism for the coupling between bright and dark excitons in nonmagnetic semiconductors. Here, we investigate diluted magnetic semiconductors where this process is in direct competition with the scattering at localized magnetic impurities. To this end, a recently developed quantum kinetic description of the exciton spin dynamics in diluted magnetic semiconductor quantum wells is extended by the scattering with longitudinal acoustic phonons. A strong phonon impact is found in the redistribution of exciton momenta on the exciton parabola that becomes especially prominent for high temperatures and exciton distributions further away from the exciton resonance which are optically dark. Despite their impact on the energetic redistribution, acoustic phonons virtually do not affected the exciton spin dynamics as the exciton-impurity interaction always dominates. Furthermore, it turns out that the exciton spin lifetime increases by roughly one order of magnitude for nonequilibrium hot exciton distributions and, in addition, pronounced quantum kinetic signatures in the exciton spin dynamics appearing after resonant optical excitation are drastically reduced., Comment: 13 pages, 6 figures

The magnetic properties over a wide range of temperatures in diluted magnetic semiconductors (DMSs) are discussed in the framework of the Kondo lattice model with magnetic impurity disorder. In the approach of dynamical mean-field theory, a set of self-consistent equations has been derived to specify single-particle Green functions. Analytical expressions of the static magnetic susceptibility and the ${B}_{1g}$ channel Raman response are then delivered. Inspecting for signatures of an itinerant carrier density of states and magnetization, we have identified a stable ferromagnetic (FM) state at low temperature. With increasing temperature, thermal fluctuations diminish the ordered state and the system favors a paramagnetic (PM) phase. Tracking and tracing different model parameters, the FM-PM transition phase diagram has been constructed. Spin fluctuations in the PM state have been pointed out in the behaviors of the self-energies, the static magnetic susceptibility, and the Raman scattering. Analyzing the properties of the ${B}_{1g}$ channel Raman response, we have attributed a formation of magnetic polarons in the PM state. The magnetic polaron scenario in a wide range of temperatures has been then intensively discussed. For the first time, both the static magnetic susceptibility and the ${B}_{1g}$ Raman response have been combined together to discuss the magnetic properties in DMSs compactly based on the dynamical mean-field approach.

The transport through a domain wall pinned at a nanoconstriction in (Ga,Mn)As wires is investigated theoretically using the Landauer-B\"uttiker approach by considering the Rashba and Dresselhaus spin-orbit interactions. The local nonequilibrium spin densities produced by electrical spin injection at the nanoconstriction are calculated numerically along the nanowire. The adiabatic and nonadiabatic components of the spin-transfer torque, expressed in terms of the gradient of the spin current density, are also computed. An oscillatory behavior in the spin-transfer torque is observed for the systems containing atomically sharp domain walls, due to the strong reflections at the domain wall caused by the large magnetization gradient. It is demonstrated that the strength of the oscillations for nonadiabatic spin torque increases by the negative Rashba parameter ${\ensuremath{\alpha}}_{x}$, while it decreases with increasing positive values of ${\ensuremath{\alpha}}_{x}$. However, the nonadiabatic spin torque increases with $\left|{\ensuremath{\alpha}}_{y}\right|$, regardless of its sign. Furthermore, it is shown that the Dresselhaus coupling $\ensuremath{\beta}$ does not considerably alter the $z$ component of the spin torque, while the other two components are effectively changed by the Dresselhaus spin-orbit interaction.

Structure-property relationships have always been guiding principles for materials discovery. Here we explore the relationships to discover two-dimensional (2D) materials with the goal of identifying 2D magnetic semiconductors for spintronics applications. In particular, we report a density functional theory + $U$ study of single-layer antiferromagnetic (AFM) semiconductor ${\mathrm{CoS}}_{2}$ with the pentagonal structure forming the so-called Cairo tessellation. We find that this single-layer magnet exhibits an indirect band gap of 1.06 eV with electron and hole effective masses of 0.52 and 1.93 ${m}_{0}$, respectively, which may lead to relatively high electron mobility. The hybrid density functional theory calculations correct the band gap to 2.24 eV. We also compute the magnetocrystalline anisotropy energy (MAE), showing that the easy axis of the AFM ordering is along the $b$ axis with a sizable MAE of 153 $\ensuremath{\mu}\mathrm{eV}$ per Co ion. We further calculate the magnon frequencies at different spin-spiral vectors, based on which we estimate the $\mathrm{N}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\text{e}}\mathrm{el}$ temperatures to be 20.4 and 13.3 K using the mean field and random phase approximations, respectively. We then apply biaxial strains to tune the band gap of single-layer pentagonal ${\mathrm{CoS}}_{2}$. We find that the energy difference between the ferromagnetic and AFM structures strongly depends on the biaxial strain, but the ground state remains the AFM ordering. Although the low critical temperature prohibits the magnetic applications of single-layer pentagonal ${\mathrm{CoS}}_{2}$ at room temperature, the excellent electrical properties may find single-layer semiconductor applications in optoelectronic nanodevices.

We report on the magnetic and electronic properties of single-crystalline ${\mathrm{Ga}}_{0.91}{\mathrm{Mn}}_{0.09}\mathrm{S}$, which is a quasi-two-dimensional diluted magnetic semiconductor (DMS). Through an analysis of magnetization data, we show the existence of an anomalously high spin-glass transition temperature at 11.2 K. Using density functional theory (DFT), we characterize the properties contributing to the spin-glass transition through an examination of the electronic and magnetic properties for ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{S}$ with $x$ varying from 0.00 to 0.18 by randomly substituting Mn atoms into the gallium (Ga) lattice sites. We show that the presence of magnetic atoms produces impurity bands in the electronic structure, where an analysis of the density of states shows an increase in magnetic impurity bands at the Fermi level that lowers the semiconducting gap and is consistent with diluted magnetic semiconductors. Furthermore, this indicates that the spin-glass transition in ${\mathrm{Ga}}_{0.91}{\mathrm{Mn}}_{0.09}\mathrm{S}$ is similar to other DMS materials, where the primary mechanism is likely through magnetic exchange. However, the increased electron density in the system with Mn doping could explain the anomalously higher spin-glass transition temperature in ${\mathrm{Ga}}_{0.91}{\mathrm{Mn}}_{0.09}\mathrm{S}$. In comparison with the substantially lower transition temperatures in related II-VI based systems (i.e., ${\mathrm{Zn}}_{1\ensuremath{-}x}\mathrm{Mn}{}_{x}\mathrm{Te}$), the high transition temperature is associated with more metallic spin-glass systems that interact through RKKY exchange, which leads to the conclusion that there may be a combination of interactions occurring in these systems. Further measurements on the other substitution percentages will hopefully clarify these interactions.

Magnetoreflection (MR) and magnetophotoluminescence (MPL) are studied in the diluted magnetic semiconductor ${\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$. The use of both methods in parallel allows us to follow features resulting from the mean-field exchange behavior as well as individual characteristics of ${\mathrm{Mn}}^{2+}$ paramagnetic ions. Resonance linewidths observed in MR are analyzed and shown to depend on spin-dependent scattering of excitons. A striking feature of the MPL spectrum is an enhancement of all spin-polarized luminescence structures in an external magnetic field. Relations between the Zeeman energy shift of exciton transitions due to exchange interaction of Mn ions with mobile carriers and circular polarization of MPL due to internal recombination in ${\mathrm{Mn}}^{2+}$ are revealed. Mixing of left and right circular light polarizations is demonstrated in excitonic and donor-acceptor pair (DAP) structures of MPL peaks. An enhancement of binding energy with increasing magnetic field for excitons localized by potential fluctuations is demonstrated and explained. It is observed that the energy of MPL peaks related to DAPs is only weakly sensitive to magnetic field. This relative stability is caused by a suppression of the mean-field Zeeman shift due to the two-component form of impurity wave functions. The simultaneous presence of paramagnetic ions and residual nonmagnetic impurities in our ${\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$ samples provides for a rich physical picture.

Interlayer coupling is of vital importance for manipulating physical properties, e.g., electronic band gap, in two-dimensional materials. However, tuning magnetic properties in these materials is yet to be addressed. Here, we found the in-plane magnetic orders of $\mathrm{Cr}{\mathrm{S}}_{2}$ mono and few layers are tunable between striped antiferromagnetic (sAFM) and ferromagnetic (FM) orders by manipulating charge transfer between Cr ${t}_{2g}$ and ${e}_{g}$ orbitals. Such charge transfer is realizable through interlayer coupling, direct charge doping, or substituting S with Cl atoms. In particular, the transferred charge effectively reduces a portion of ${\mathrm{Cr}}^{4+}$ to ${\mathrm{Cr}}^{3+}$, which, together with delocalized S $p$ orbitals and their resulting direct S-S interlayer hopping, enhances the double-exchange mechanism favoring the FM rather than sAFM order. An exceptional interlayer spin-exchange parameter was revealed over $\ensuremath{-}10\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$, an order of magnitude stronger than available results of interlayer magnetic coupling. It addition, the charge doping could tune $\mathrm{Cr}{\mathrm{S}}_{2}$ between $p$- and $n$-doped magnetic semiconductors. Given these results, several prototype devices were proposed for manipulating magnetic orders using external electric fields or mechanical motion. These results manifest the role of interlayer coupling in modifying magnetic properties of layered materials and shed considerable light on manipulating magnetism in these materials.

Through density functional theory simulations with the generalized gradient approximation, confirmed by the more sophisticated hybrid functional, we predict the triggering of ${d}^{0}$ ferromagnetism in C doped ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ at a hole density of $3.36\ifmmode\times\else\texttimes\fi{}{10}^{21}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$ (one order less than the critical hole density of ZnO) having magnetic moment of $2.0\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}$ per defect with ferromagnetic coupling large enough to promote room-temperature ferromagnetism. The persistence of ferromagnetism at room temperature is established through computation of the Curie temperature by the mean field approximation and ab initio molecular dynamics simulations. The induced magnetic moment is mainly contributed by the $2p$ orbital of the impurity C and the $2p$ orbital of O and we quantitatively and extensively demonstrate through the analysis of density of states and ferromagnetic coupling that the Stoner criterion is satisfied to activate room-temperature ferromagnetism. As the system is stable at room temperature, C doped ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ has feasible defect formation energy and ferromagnetism survives for the choice of hybrid exchange functional, and at room temperature we strongly believe that C doped ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ can be tailored as a room-temperature diluted magnetic semiconductor for spintronic applications.

We have investigated the electronic structure of the dilute magnetic semiconductor (DMS) Ga0.98Mn0.02P and compared it to that of an undoped GaP reference sample, using hard x-ray photoelectron spectroscopy (HXPS) and hard x-ray angle-resolved photoemission spectroscopy (HARPES) at energies of about 3 keV. We present experimentaldata,aswellastheoreticalcalculations,tounderstandtheroleoftheMndopantintheemergenceof ferromagnetism in this material. Both core-level spectra and angle-resolved or angle-integrated valence spectra are discussed. In particular, the HARPES experimental data are compared to free-electron final-state model calculations and to more accurate one-step photoemission theory. The experimental results show differences between Ga0.98Mn0.02P and GaP in both angle-resolved and angle-integrated valence spectra. The Ga0.98Mn0.02P bands are broadened due to the presence of Mn impurities that disturb the long-range translational order of the host GaP crystal. Mn-induced changes of the electronic structure are observed over the entire valence band range, including the presence of a distinct impurity band close to the valence-band maximum of the DMS. These experimental results are in good agreement with the one-step photoemission calculations and a prior HARPES study of Ga0.97Mn0.03As and GaAs [Gray et al., Nat. Mater. 11, 957 (2012)], demonstrating the strong similarity between these two materials. The Mn 2p and 3s core-level spectra also reveal an essentially identical state in doping both GaAs and GaP.

We present an experimental study for polycrystalline samples of the diluted magnetic semiconductor MnxGa1−xN (x 0.04) in order to address some of the existing controversial issues. X-ray and neutron diffraction, x-ray absorption near-edge structure, and electron paramagnetic resonance experiments were used to characterize the structural, electronic, and magnetic properties of the samples, and inelastic neutron scattering was employed to determine the magnetic excitations associated with Mn monomers and dimers. Our main conclusions are as follows: (i) The valence of the Mn ions is 2+. (ii) The Mn2+ ions experience a substantial single-ion axial anisotropy with parameter D = 0.027(3) meV. (iii) Nearest-neighbor Mn2+ ions are coupled antiferromagnetically. The exchange parameter J = −0.140(7) meV is independent of the Mn content x; i.e., there is no evidence for hole-induced modifications of J towards a potentially high Curie temperature postulated in the literature.

Magneto-optical effects have been investigated over the infrared visible spectral range in $A{\mathrm{Cr}}_{2}{\mathrm{O}}_{4}$ ($A=\text{Fe},\text{Co}$) spinel oxides with noncollinear spin orders in their ground states. We found large magneto-optical Kerr rotation and ellipticity at the on-site $d\ensuremath{-}d$ transitions of the ${A}^{2+}$ ions located within the charge gap. The magneto-optical Kerr rotation of ${\ensuremath{\vartheta}}_{\mathrm{Kerr}}\ensuremath{\approx}{12}^{\ensuremath{\circ}}$ observed in ${\mathrm{CoCr}}_{2}{\mathrm{O}}_{4}$ is unprecedentedly large among magnetic semiconductors and points toward the uniqueness of tetrahedrally coordinated ${\mathrm{Co}}^{2+}$ ions in generating strong magneto-optical response. Criteria of strong magneto-optical effects emerging at on-site $d\ensuremath{-}d$ transitions of transition metal ions are discussed.

Dilute magnetic semiconductors (DMS) are nonmagnetic semiconductors doped with magnetic transition metals. The recently discovered DMS material (Ba$_{1-x}$K$_{x}$)(Zn$_{1-y}$Mn$_{y}$)$_{2}$As$_{2}$ offers a unique and versatile control of the Curie temperature, $T_{\mathrm{C}}$, by decoupling the spin (Mn$^{2+}$, $S=5/2$) and charge (K$^{+}$) doping in different crystallographic layers. In an attempt to describe from first-principles calculations the role of hole doping in stabilizing ferromagnetic order, it was recently suggested that the antiferromagnetic exchange coupling $J$ between the nearest-neighbor Mn ions would experience a nearly twofold suppression upon doping 20\% of holes by potassium substitution. At the same time, further-neighbor interactions become increasingly ferromagnetic upon doping, leading to a rapid increase of $T_{\mathrm{C}}$. Using inelastic neutron scattering, we have observed a localized magnetic excitation at about 13 meV, associated with the destruction of the nearest-neighbor Mn-Mn singlet ground state. Hole doping results in a notable broadening of this peak, evidencing significant particle-hole damping, but with only a minor change in the peak position. We argue that this unexpected result can be explained by a combined effect of superexchange and double-exchange interactions.

We have studied the structural, electronic, and magnetic properties of spinel ${\mathrm{Co}}_{3}{\mathrm{O}}_{4}$(111) surfaces and their interfaces with ZnO(0001) using density functional theory within the generalized gradient approximation with the on-site Coulomb repulsion term. Two possible forms of spinel surface, containing ${\mathrm{Co}}^{2+}$ or ${\mathrm{Co}}^{3+}$ ions and terminated with either cobalt or oxygen ions, were considered, as well as their interface with zinc oxide. Our calculations demonstrate that ${\mathrm{Co}}^{3+}$ ions attain nonzero magnetic moments at the surface and interface, in contrast to the bulk, where they are not magnetic, leading to the ferromagnetic ordering. Since heavily Co doped ZnO samples can contain a ${\mathrm{Co}}_{3}{\mathrm{O}}_{4}$ secondary phase, such magnetic ordering at the interface might explain the origin of the magnetism in such diluted magnetic semiconductors.

We present systematic temperature-dependent resistance noise measurements on a series of ferromagnetic ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ epitaxial thin films covering a large parameter space in terms of the Mn content $x$ and other variations regarding sample fabrication. We infer that the electronic noise is dominated by switching processes related to impurities in the entire temperature range. While metallic compounds with $xg2%$ do not exhibit any significant change in the low-frequency resistance noise around the Curie temperature ${T}_{\mathrm{C}}$, we find indications for an electronic phase separation in films with $xl2%$ in the vicinity of ${T}_{\mathrm{C}}$, manifesting itself in a maximum in the noise power spectral density. These results are compared with noise measurements on an insulating ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{P}$ reference sample, for which the evidence for an electronic phase separation is even stronger and a possible percolation of bound magnetic polarons is discussed. Another aspect addressed in this work is the effect of ion-irradiation-induced disorder on the electronic properties of ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ films and, in particular, whether any electronic inhomogeneities can be observed in this case. Finally, we put our findings into the context of the ongoing debate on the electronic structure and the development of spontaneous magnetization in these materials.

The magnetoresistance of a material conveys various dynamic information about charge and spin carriers, inspiring both fundamental studies in physics and practical applications such as magnetic sensors, data storage, and spintronic devices. Magnetic impurities play a crucial role in the magnetoresistance as they induce exotic states of matter such as the quantum anomalous Hall effect in topological insulators and tunable ferromagnetic phases in dilute magnetic semiconductors. However, magnetically doped topological Dirac semimetals are hitherto lacking. Here, we report a systematic study of Cr-doped $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$ thin films grown by molecular-beam epitaxy. With the Cr doping, $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$ thin films exhibit unexpected negative transverse magnetoresistance and strong quantum oscillations, bearing a trivial Berry's phase and an enhanced effective mass. More importantly, with ionic gating the magnetoresistance of Cr-doped $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$ thin films can be drastically tuned from negative to positive, demonstrating the strong correlation between electrons and the localized spins of the Cr impurities, which we interpret through the formation of magnetic polarons. Such a negative magnetoresistance under perpendicular magnetic field and its gate tunability have not been observed previously in the Dirac semimetal $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$. The Cr-induced topological phase transition and the formation of magnetic polarons in $\mathrm{C}{\mathrm{d}}_{3}\mathrm{A}{\mathrm{s}}_{2}$ provide insights into the magnetic interaction in Dirac semimetals as well as their potential applications in spintronics.

We investigate theoretically the influence of an external magnetic field on the spin dynamics of excitons in diluted magnetic semiconductor quantum wells. To this end, we apply a quantum kinetic theory beyond the Markov approximation which reveals that non-Markovian effects can significantly influence the exciton spin dynamics. If the magnetic field is oriented parallel to the growth direction of the well, the Markovian spin-transfer rate decreases monotonically with increasing field as predicted by Fermi's golden rule. The quantum kinetic theory follows this result qualitatively but predicts pronounced quantitative differences in the spin-transfer rate as well as in the long-time spin polarization. However, for an in-plane magnetic field, where the Markovian spin-transfer rate first drops and then increases again, quantum kinetic effects become so pronounced that the Markovian trend is completely reversed. This is made evident by a distinct maximum of the rate followed by a monotonic decrease. The deviations can be traced back to a redistribution of carriers in energy space caused by correlations between excitons and magnetic dopants. The same effect leads to a finite electron-spin polarization at long times in longitudinal as well as transverse fields which is much larger than the corresponding Markovian prediction., Comment: 17 pages, 7 figures

We consider a condensate of exciton polaritons in a diluted magnetic semiconductor microcavity. Such a system may exhibit magnetic self-trapping in the case of sufficiently strong coupling between polaritons and magnetic ions embedded in the semiconductor. We investigate the effect of the nonequilibrium nature of exciton polaritons on the physics of the resulting self-trapped magnetic polarons. We find that multiple polarons can exist at the same time, and we derive a critical condition for self-trapping that is different from the one predicted previously in the equilibrium case. Using the Bogoliubov--de Gennes approximation, we calculate the excitation spectrum and provide a physical explanation in terms of the effective magnetic attraction between polaritons, mediated by the ion subsystem.

Many researchers have shown an interest in Ge-based dilute magnetic semiconductors (DMSs) due to potential advantages for semiconductor spintronics applications. There has been great discussion about mechanisms of experimentally observed ferromagnetism in (Ge,Fe) and (Ge,Mn). We investigate the electronic structures, structural stabilities, magnetic exchange coupling constants, and Curie temperature of Ge-based DMSs, and clarify origins of the ferromagnetism, on the basis of density functional theory calculations. In both the (Ge,Fe) and (Ge,Mn) cases, the inhomogeneous distribution of the magnetic impurities plays an important role to determine the magnetic states; however, physical mechanisms of the ferromagnetism in these two materials are completely different. By the spinodal nanodecomposition, the Fe impurities in Ge gather together with keeping the diamond structure, so that the number of the first-nearest-neighbor Fe pairs with strong ferromagnetic interaction increases. Therefore, the Curie temperature drastically increases with the progress of the annealing. Our cluster expansion method clearly reveals that the other ordered compounds with different crystal structures such as ${\mathrm{Ge}}_{3}{\mathrm{Mn}}_{5}$ and ${\mathrm{Ge}}_{8}{\mathrm{Mn}}_{11}$ are easily generated in the (Ge,Mn) system. The estimated Curie temperature of ${\mathrm{Ge}}_{3}{\mathrm{Mn}}_{5}$ is in agreement with the observed Curie temperature in experiments. It should be considered that the precipitation of the ferromagnetic ${\mathrm{Ge}}_{3}{\mathrm{Mn}}_{5}$ clusters is an origin of high Curie temperature in (Ge,Mn).

$\mathrm{Ti}{\mathrm{O}}_{2}$ in the rutile phase is known to be an incipient ferroelectric. Considering Nb-Cr codoping we examine if ferroelectricity can be induced at the low doping limit in $\mathrm{T}{\mathrm{i}}_{(1\text{\ensuremath{-}}x)}{(\mathrm{N}{\mathrm{b}}_{0.5}\mathrm{C}{\mathrm{r}}_{0.5})}_{x}{\mathrm{O}}_{2}$ ($x=0.05%$, 1%, 5%, and 10%). A relaxor behavior is found in the temperature range 20--120 K which obeys the Vogel-Fulcher relation while pyrocurrent measurements confirm switching of the electric polarization. The spontaneous net polarization is doping dependent with a maximum at 1% and for doping concentrations above 5% is found to be paraelectric. Ab initio density functional theory based calculations suggest that the Nb-Cr pair behaves like a dipole and polarizes the neighboring $\mathrm{Ti}{\mathrm{O}}_{6}$ octahedra, stabilizing a ferroelectric ground state akin to magnetic impurities in dilute magnetic semiconductors. At larger doping concentrations one finds that Nb-Cr clusters result in a vanishing polarization.

The correlation between magnetic properties and microscopic structural aspects in the diluted magnetic semiconductor Ge$_{1-x}$Mn$_{x}$Te is investigated by x-ray diffraction and magnetization as a function of the Mn concentration $x$. The occurrence of high ferromagnetic-transition temperatures in the rhombohedrally distorted phase of slowly-cooled Ge$_{1-x}$Mn$_{x}$Te is shown to be directly correlated with the formation and coexistence of strongly-distorted Mn-poor and weakly-distorted Mn-rich regions. It is demonstrated that the weakly-distorted phase fraction is responsible for the occurrence of high-transition temperatures in Ge$_{1-x}$Mn$_{x}$Te. When the Mn concentration becomes larger, the Mn-rich regions start to switch into the undistorted cubic structure, and the transition temperature is suppressed concurrently. By identifying suitable annealing conditions, we successfully increased the transition temperature to above 200 K for Mn concentrations close to the cubic phase. Structural data indicate that the weakly-distorted phase fraction can be restored at the expense of the cubic regions upon the enhancement of the transition temperature, clearly establishing the direct link between high-transition temperatures and the weakly-distorted Mn-rich phase fraction.

Among the known transition metal dichalcogenides, monolayer ${\mathrm{VS}}_{2}$ has attracted particular attention because of its intrinsic ferromagnetism and great application potential as a high-performance functional nanomaterial. Here, using first-principles calculations, we study the structural and electronic phase transitions in monolayer ${\mathrm{VS}}_{2}$ induced by charge doping. We show that without electron or hole doping, ${\mathrm{VS}}_{2}$ stabilizes in the 2H phase and is a bipolar magnetic semiconductor (BMS) whose valence and conduction states near the Fermi level carry opposite spin polarization. With the increase of hole doping concentration, ${\mathrm{VS}}_{2}$ will first experience an electronic phase transition from a BMS to a half metal, followed by a 2H-to-1T structural phase transition (SPT) which concomitantly results in another electronic phase transition from the half metal to a normal metal. Moreover, the reduced reaction barrier from the 2H to 1T phases by hole doping can make the occurrence of the SPT easier. However, electron doping can only induce the BMS-to-half metal electronic phase transition but will not trigger the SPT within the experimentally accessible doping regime. The different effects of hole and electron dopings on the SPT are further explained by the energy band diagram of ${\mathrm{VS}}_{2}$. These results establish the potential for ${\mathrm{VS}}_{2}$ utilization in innovative phase-change electronic and spintronic devices.

We investigate doping- and pressure-induced changes in the electronic state of Mn $3d$ and As $4p$ orbitals in II-II-V-based diluted magnetic semiconductor $(\mathrm{B}{\mathrm{a}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}){(\mathrm{Z}{\mathrm{n}}_{1\ensuremath{-}y}\mathrm{M}{\mathrm{n}}_{y})}_{2}\mathrm{A}{\mathrm{s}}_{2}$ to shed light into the mechanism of indirect exchange interactions leading to high ferromagnetic ordering temperature ($T\mathrm{c}=230\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ in optimally doped samples). A suite of x-ray spectroscopy experiments (emission, absorption, and dichroism) show that the emergence and further enhancement of ferromagnetic interactions with increased hole doping into the As $4p$ band is accompanied by a decrease in local $3d$ spin density at Mn sites. This is a result of increasing Mn $3d--\mathrm{As} 4p$ hybridization with hole doping, which enhances indirect exchange interactions between Mn dopants and gives rise to induced magnetic polarization in As $4p$ states. On the contrary, application of pressure suppresses exchange interactions. While Mn K $\ensuremath{\beta}$ emission spectra show a weak response of $3d$ states to pressure, clear As $4p$ band broadening (hole delocalization) is observed under pressure, ultimately leading to loss of ferromagnetism concomitant with a semiconductor to metal transition. The pressure response of As $4p$ and Mn $3d$ states is intimately connected with the evolution of the As-As interlayer distance and the geometry of the $\mathrm{MnA}{\mathrm{s}}_{4}$ tetrahedral units, which we probed with x-ray diffraction. Our results indicate that hole doping increases the degree of covalency between the anion (As) $p$ states and cation (Mn) $d$ states in the $\mathrm{MnA}{\mathrm{s}}_{4}$ tetrahedron, a crucial ingredient to promote indirect exchange interactions between Mn dopants and high $T\mathrm{c}$ ferromagnetism. The instability of ferromagnetism and semiconducting states against pressure is mainly dictated by delocalization of anion $p$ states.

The doping of semiconductors with magnetic impurities gives rise not only to a spin-spin interaction between quasifree carriers and magnetic impurities but also to a local spin-independent disorder potential for the carriers. Based on a quantum kinetic theory for the carrier and impurity density matrices as well as the magnetic and nonmagnetic carrier-impurity correlations, the influence of the nonmagnetic scattering potential on the spin dynamics in DMS after optical excitation with circularly polarized light is investigated using the example of Mn-doped CdTe. It is shown that non-Markovian effects, which are predicted in calculations where only the magnetic carrier-impurity interaction is accounted for, can be strongly suppressed in the presence of nonmagnetic impurity scattering. This effect can be traced back to a significant redistribution of carriers in k-space which is enabled by the build-up of large carrier-impurity correlation energies. A comparison with the Markov limit of the quantum kinetic theory shows that, in the presence of an external magnetic field parallel to the initial carrier polarization, the asymptotic value of the spin polarization at long times is significantly different in the quantum kinetic and the Markovian calculations. This effect can also be attributed to the formation of strong correlations, which invalidates the semiclassical Markovian picture and it is stronger when the nonmagnetic carrier-impurity interaction is accounted for. In an external magnetic field perpendicular to the initial carrier spin, the correlations are also responsible for a renormalization of the carrier spin precession frequency. Considering only the magnetic carrier-impurity interaction, a significant renormalization is predicted for a very limited set of material parameters and excitation conditions. Accounting also for the nonmagnetic interaction, a relevant renormalization of the precession frequency is found to be more ubiquitous. Fil: Cygorek, M.. University of Bayreuth; Alemania Fil: Ungar, F.. University of Bayreuth; Alemania Fil: Tamborenea, Pablo Ignacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Ecología, Genética y Evolución. Buenos Aires; Argentina Fil: Axt, V.M.. University of Bayreuth; Alemania

We generalize the multiband typical medium dynamical cluster approximation and the formalism introduced by Blackman, Esterling and Berk so that it can deal with localization in multiband disordered systems with both diagonal and off-diagonal disorder with complicated potentials. We also introduce a new ansatz for the angle resolved typical density of states that greatly improves the numerical stability of the method while preserving the independence of scattering events at different frequencies. Starting from the first-principles effective Hamiltonian, we apply this method to the diluted magnetic semiconductor Ga$_{1-x}$Mn$_x$N, and find the impurity band is completely localized for Mn concentrations $x, Comment: 9 pages, 5 figures