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Altermagnetic (AM) materials exhibit non-relativistic, momentum-dependent spin-split states, ushering in new opportunities for spin electronic devices. While the characteristics of spin-splitting have been documented within the framework of the non-relativistic spin group symmetry, there has been limited exploration of the inclusion of relativistic symmetry and its impact on the emergence of a novel spin-splitting in the band structure. This study delves into the intricate relativistic electronic structure of an AM material, alpha-MnTe. Employing temperature-dependent angle-resolved photoelectron spectroscopy across the AM phase transition, we elucidate the emergence of a relativistic valence band splitting concurrent with the establishment of magnetic order. This discovery is validated through disordered local moment calculations, modeling the influence of magnetic order on the electronic structure and confirming the magnetic origin of the observed splitting. The temperature-dependent splitting is ascribed to the advent of relativistic spin-splitting resulting from the strengthening of AM order in alpha-MnTe as the temperature decreases. This sheds light on a previously unexplored facet of this intriguing material.

Anomalous Hall effect (AHE) plays important role in the rapidly developing field of antiferromagnetic spintronics. It has been recently discussed that it can be a feature of not only uncompensated magnetic systems but also in altermagnetic materials. Hexagonal MnTe belongs to this appealing group of compounds exhibiting AHE and is commonly perceived as magnetically compensated. Here, we demonstrate that bulk form of MnTe exhibits small but detectable magnetic moment correlating with hysteretic behaviour of the AHE. We formulate a phenomenological model which explains how this feature allows to create a disbalance between states with opposite N\'eel vector and prevent the AHE signal from averaging out to zero. Moreover, we show how the dependence of AHE on the N\'eel vector arises on microscopical level and highlight the differences in Berry curvature between magnetically compensated and uncompensated systems.

Altermagnetism is a recently identified magnetic symmetry class combining characteristics of conventional collinear ferromagnets and antiferromagnets, that were regarded as mutually exclusive, and enabling phenomena and functionalities unparalleled in either of the two traditional elementary magnetic classes. In this work we use symmetry and ab initio theory to explore X-ray magnetic circular dichroism (XMCD) in the altermagnetic class. Our results highlight the distinct phenomenology in altermagnets of this time-reversal symmetry breaking response, and its potential utility for element-specific spectroscopy and microscopy in altermagnets. As a representative material for our XMCD study we choose $\alpha$-MnTe with the compensated antiparallel magnetic order in which an anomalous Hall effect has been already demonstrated both in theory and experiment. The predicted magnitude of XMCD lies well within the resolution of existing experimental techniques., Comment: Experimental data added

We report synthesis of single crystalline NaMnAs, confirm its antiferromagnetic order and characterise the sample by photoemission spectroscopy. The electronic structure was studied using optical transmittance, x-ray and ultraviolet spectroscopy and by theoretical modeling using local density approximation (LDA) extended to LDA+U when Heisenberg model parameters were determined. Optical transmittance measurement have confirmed the theoretical predictions that NaMnAs is a semiconductor. Also the N\'eel temperature was closer determined for the first time from temperature dependence of magnetization, in agreement with our Monte Carlo simulations., Comment: 11 pages, 11 figures

Temperature-dependent resistivity and magnetoresistance are measured in bulk tetragonal phase of antiferromagnetic CuMnAs and the latter is found to be anisotropic both due to structure and magnetic order. We compare these findings to model calculations with chemical disorder and finite-temperature phenomena included. The finite-temperature ab initio calculations are based on the alloy analogy model implemented within the coherent potential approximation and the results are in fair agreement with experimental data. Regarding the anisotropic magnetoresistance (AMR) which reaches a modest magnitude of 0.12%, we phenomenologically employ the Stoner-Wohlfarth model to identify temperature-dependent magnetic anisotropy of our samples and conclude that the field-dependence of AMR is more similar to that of antiferromagnets than ferromagnets, suggesting that the origin of AMR is not related to isolated Mn magnetic moments., Comment: 10+ pages, few minor issues corrected

Magnetotransport constitutes a useful probe to understand the interplay between electronic band topology and magnetism in spintronics devices based on topological materials. A recent theory of Lu and Shen [Phys. Rev. Lett. 112, 146601 (2014)] on magnetically doped topological insulators predicts that quantum corrections $\Delta\kappa$ to the temperature-dependence of the conductivity can change sign during the Curie transition. This phenomenon has been attributed to a suppression of the Berry phase of the topological surface states at the Fermi level, caused by a magnetic energy gap. Here, we demonstrate experimentally that $\Delta\kappa$ can reverse its sign even when the Berry phase at the Fermi level remains unchanged, provided that the inelastic scattering length decreases with temperature below the Curie transition.

Tetragonal phase of CuMnAs progressively appears as one of the key materials for antiferromagnetic spintronics due to efficient current-induced spin-orbit torques whose existence can be directly inferred from crystal symmetry. Theoretical understanding of spintronic phenomena in this material, however, relies on the detailed knowledge of electronic structure (band structure and corresponding wave functions) which has so far been tested only to a limited extent. We show that AC permittivity (obtained from ellipsometry) and UV photoelectron spectra agree with density functional calculations. Together with the x-ray diffraction and precession electron diffraction tomography, our analysis confirms recent theoretical claim [Phys.Rev.B 96, 094406 (2017)] that copper atoms occupy lattice positions in the basal plane of the tetragonal unit cell., Comment: 5 pages, 5 figures + Supplementary Information

Antiferromagnetic hexagonal MnTe is a promising material for spintronic devices relying on the control of antiferromagnetic domain orientations. Here we report on neutron diffraction, magnetotransport, and magnetometry experiments on semiconducting epitaxial MnTe thin films together with density functional theory (DFT) calculations of the magnetic anisotropies. The easy axes of the magnetic moments within the hexagonal basal plane are determined to be along $\left<1\bar100\right>$ directions. The spin-flop transition and concomitant repopulation of domains in strong magnetic fields is observed. Using epitaxially induced strain the onset of the spin-flop transition changes from $\sim2$~T to $\sim0.5$~T for films grown on InP and SrF$_2$ substrates, respectively., Comment: 9 pages, 7 figures

Magneto-structural phase transition in FeRh epitaxial layers was studied optically. It is shown that the transition between the low-temperature antiferromagnetic phase and the high-temperature ferromagnetic phase is accompanied by a rather large change of the optical response in the visible and near infrared spectral ranges. This phenomenon was used to measure the phase transition temperature in FeRh films with thicknesses from 6 to 100 nm and it was observed that the hysteretic transition region broadens significantly in the thinner films., Comment: 7 pages, 4 figures

A common perception assumes that magnetic memories require ferromagnetic materials with a non-zero net magnetic moment. However, it has been recently proposed that compensated antiferromagnets with a zero net moment may represent a viable alternative to ferromagnets. So far, experimental research has focused on bistable memories in antiferromagnetic metals. In the present work we demonstrate a multiple-stable memory device in epitaxial manganese telluride (MnTe) which is an antiferromagnetic counterpart of common II-VI semiconductors. Favorable micromagnetic characteristics of MnTe allow us to demonstrate a smoothly varying antiferromagnetic anisotropic magnetoresistance (AMR) with a harmonic angular dependence on the applied magnetic field, analogous to ferromagnets. The continuously varying AMR provides means for the electrical read-out of multiple-stable antiferromagnetic memory states which we set by heat-assisted magneto-recording and by changing the angle of the writing field. We explore the dependence of the magnitude of the zero-field read-out signal on the strength of the writing field and demonstrate the robustness of the antiferromagnetic memory states against strong magnetic field perturbations. We ascribe the multiple-stability in our antiferromagnetic memory to different distributions of domains with the N\'eel vector aligned along one of the three $c$-plane magnetic easy axes in the hexagonal MnTe film. The domain redistribution is controlled during the heat-assisted recording by the strength and angle of the writing field and freezes when sufficiently below the N\'eel temperature.

Intraband and interband contributions to the current-driven spin-orbit torque in magnetic materials lacking inversion symmetry are theoretically studied using Kubo formula. In addition to the current-driven field-like torque ${\bf T}_{\rm FL}= \tau_{\rm FL}{\bf m}\times{\bf u}_{\rm so}$ (${\bf u}_{\rm so}$ being a unit vector determined by the symmetry of the spin-orbit coupling), we explore the intrinsic contribution arising from impurity-independent interband transitions and producing an anti-damping-like torque of the form ${\bf T}_{\rm DL}= \tau_{\rm DL}{\bf m}\times({\bf u}_{\rm so}\times{\bf m})$. Analytical expressions are obtained in the model case of a magnetic Rashba two-dimensional electron gas, while numerical calculations have been performed on a dilute magnetic semiconductor (Ga,Mn)As modeled by the Kohn-Luttinger Hamiltonian exchanged coupled to the Mn moments. Parametric dependences of the different torque components and similarities to the analytical results of the Rashba two-dimensional electron gas in the weak disorder limit are described., Comment: 10 pages, 5 figures

We predict that a lateral electrical current in antiferromagnets can induce non-equilibrium N\'eel order fields, i.e. fields whose sign alternates between the spin sublattices, which can trigger ultra-fast spin-axis reorientation. Based on microscopic transport theory calculations we identify staggered current-induced fields analogous to the intra-band and to the intrinsic inter-band spin-orbit fields previously reported in ferromagnets with a broken inversion-symmetry crystal. To illustrate their rich physics and utility, we considered bulk Mn2Au with the two spin sublattices forming inversion partners, and a 2D square-lattice antiferromagnet with broken structural inversion symmetry modelled by a Rashba spin-orbit coupling. We propose an AFM memory device with electrical writing and reading., Comment: 5 pages, 4 figures

Magnetic linear dichroism and birefringence in (Ga,Mn)As epitaxial layers is investigated by measuring the polarization plane rotation of reflected linearly polarized light when magnetization lies in the plane of the sample. We report on the spectral dependence of the rotation and ellipticity angles in a broad energy range of 0.12-2.7 eV for a series of optimized samples covering a wide range on Mn-dopings and Curie temperatures and find a clear blue shift of the dominant peak at energy exceeding the host material band gap. These results are discussed in the general context of the GaAs host band structure and also within the framework of the k.p and mean-field kinetic-exchange model of the (Ga,Mn)As band structure. We find a semi-quantitative agreement between experiment and theory and discuss the role of disorder-induced non-direct transitions on magneto-optical properties of (Ga,Mn)As., Comment: 18 pages

Recent observations of current-induced magnetization switching at ferromagnet/normal-conductor interfaces have important consequences for future magnetic memory technology. In one interpretation, the switching originates from carriers with spin-dependent scattering giving rise to a relativistic anti-damping spin-orbit torque (SOT) in structures with broken space-inversion symmetry. The alternative interpretation combines the relativistic spin Hall effect (SHE), making the normal-conductor an injector of a spin-current, with the non-relativistic spin-transfer torque (STT) in the ferromagnet. Remarkably, the SHE in these experiments originates from the Berry phase effect in the band structure of a clean crystal and the anti-damping STT is also based on a disorder-independent transfer of spin from carriers to magnetization. Here we report the observation of an anti-damping SOT stemming from an analogous Berry phase effect to the SHE. The SOT alone can therefore induce magnetization dynamics based on a scattering-independent principle. The ferromagnetic semiconductor (Ga,Mn)As we use has a broken space-inversion symmetry in the crystal. This allows us to consider a bare ferromagnetic element which eliminates by design any SHE related contribution to the spin torque. We provide an intuitive picture of the Berry phase origin of the anti-damping SOT and a microscopic modeling of measured data., Comment: Send to: ajf1006@cam.ac.uk

Cyclotron resonance has been measured in far-infrared transmission of GaAs/Al$_x$Ga$_{1-x}$As heterostructures with an etched hexagonal lateral superlattice. Non-linear dependence of the resonance position on magnetic field was observed as well as its splitting into several modes. Our explanation, based on a perturbative calculation, describes the observed phenomena as a weak effect of the lateral potential on the two-dimensional electron gas. Using this approach, we found a correlation between parameters of the lateral patterning and the created effective potential and obtain thus insights on how the electronic miniband structure has been tuned. The miniband dispersion was calculated using a simplified model and allowed us to formulate four basic criteria that have to be satisfied to reach graphene-like physics in such systems.

We demonstrate a scalable new ferromagnetic resonance (FMR) technique based on the spin-orbit interaction. An alternating current drives FMR in uniform ferromagnetic structures patterned from the dilute magnetic semiconductors (Ga,Mn)As and (Ga,Mn)(As,P). This allows the direct measurement of magnetic anisotropy coefficients and damping parameters for individual nano-bars. By analysing the ferromagnetic resonance lineshape, we perform vector magnetometry on the current-induced driving field, observing contributions with symmetries of both the Dresselhaus and Rashba spin-orbit interactions., Comment: 4 figures

We investigate the spin-polarization of the ferromagnetic semiconductor (Ga,Mn)As by point contact Andreev reflection spectroscopy. The conductance spectra are analyzed using a recent theoretical model that accounts for momentum- and spin-dependent scattering at the interface. This allows us to fit the data without resorting, as in the case of the standard spin-dependent Blonder-Tinkham-Klapwijk (BTK) model, to an effective temperature or a statistical distribution of superconducting gaps. We find a transport polarization PC{\approx}57%, in considerably better agreement with the k{\cdot}p kinetic-exchange model of (Ga,Mn)As, than the significantly larger estimates inferred from the BTK model. The temperature dependence of the conductance spectra is fully analyzed., Comment: 4 pages, 3 figures

The concept of low-voltage depletion and accumulation of electron charge in semiconductors, utilized in field-effect transistors (FETs), is one of the cornerstones of current information processing technologies. Spintronics which is based on manipulating the collective state of electron spins in a ferromagnet provides complementary technologies for reading magnetic bits or for the solid-state memories. The integration of these two distinct areas of microelectronics in one physical element, with a potentially major impact on the power consumption and scalability of future devices, requires to find efficient means for controlling magnetization electrically. Current induced magnetization switching phenomena represent a promising step towards this goal, however, they relay on relatively large current densities. The direct approach of controlling the magnetization by low-voltage charge depletion effects is seemingly unfeasible as the two worlds of semiconductors and metal ferromagnets are separated by many orders of magnitude in their typical carrier concentrations. Here we demonstrate that this concept is viable by reporting persistent magnetization switchings induced by short electrical pulses of a few volts in an all-semiconductor, ferromagnetic p-n junction., Comment: 11 pages, 4 figures

We observe a singularity in the temperature derivative $d\rho/dT$ of resistivity at the Curie point of high-quality (Ga,Mn)As ferromagnetic semiconductors with $T_c$'s ranging from approximately 80 to 185 K. The character of the anomaly is sharply distinct from the critical contribution to transport in conventional dense-moment magnetic semiconductors and is reminiscent of the $d\rho/dT$ singularity in transition metal ferromagnets. Within the critical region accessible in our experiments, the temperature dependence on the ferromagnetic side can be explained by dominant scattering from uncorrelated spin fluctuations. The singular behavior of $d\rho/dT$ on the paramagnetic side points to the important role of short-range correlated spin fluctuations., Comment: 4 pages, 3 figures

It has been demonstrated that magnetocrystalline anisotropies in (Ga,Mn)As are sensitive to lattice strains as small as 10^-4 and that strain can be controlled by lattice parameter engineering during growth, through post growth lithography, and electrically by bonding the (Ga,Mn)As sample to a piezoelectric transducer. In this work we show that analogous effects are observed in crystalline components of the anisotropic magnetoresistance (AMR). Lithographically or electrically induced strain variations can produce crystalline AMR components which are larger than the crystalline AMR and a significant fraction of the total AMR of the unprocessed (Ga,Mn)As material. In these experiments we also observe new higher order terms in the phenomenological AMR expressions and find that strain variation effects can play important role in the micromagnetic and magnetotransport characteristics of (Ga,Mn)As lateral nanoconstrictions., Comment: 11 pages, 4 figures, references fixed

We demonstrate dynamic voltage control of the magnetic anisotropy of a (Ga,Mn)As device bonded to a piezoelectric transducer. The application of a uniaxial strain leads to a large reorientation of the magnetic easy axis which is detected by measuring longitudinal and transverse anisotropic magnetoresistance coefficients. Calculations based on the mean-field kinetic-exchange model of (Ga,Mn)As provide microscopic understanding of the measured effect. Electrically induced magnetization switching and detection of unconventional crystalline components of the anisotropic magnetoresistance are presented, illustrating the generic utility of the piezo voltage control to provide new device functionalities and in the research of micromagnetic and magnetotransport phenomena in diluted magnetic semiconductors., Comment: Submitted to Physical Review Letters. Updates version 1 to include a more detailed discussion of the effect of strain on the anisotropic magnetoresistance

We present details of our experimental and theoretical study of the components of the anisotropic magnetoresistance (AMR) in (Ga,Mn)As. We develop experimental methods to yield directly the non-crystalline and crystalline AMR components which are then independently analyzed. These methods are used to explore the unusual phenomenology of the AMR in ultra thin (5nm) (Ga,Mn)As layers and to demonstrate how the components of the AMR can be engineered through lithography induced local lattice relaxations. We expand on our previous [Phys. Rev. Lett. \textbf{99}, 147207 (2007)] theoretical analysis and numerical calculations to present a simplified analytical model for the origin of the non-crystalline AMR. We find that the sign of the non-crystalline AMR is determined by the form of spin-orbit coupling in the host band and by the relative strengths of the non-magnetic and magnetic contributions to the impurity potential., Comment: Submitted to JMMM for conference proceedings of WUN-SPIN 2007 (York, UK)

The large saturation magnetization in conventional dense moment ferromagnets offers flexible means of manipulating the ordered state through demagnetizing shape anisotropy fields but these dipolar fields, in turn, limit the integrability of magnetic elements in information storage devices. We show that in a (Ga,Mn)As dilute moment ferromagnet, with comparatively weaker magnetic dipole interactions, locally tunable magnetocrystalline anisotropy can take the role of the internal field which determines the magnetic configuration. Experiments and theoretical modeling are presented for lithographically patterned microchannels and the phenomenon is attributed to lattice relaxations across the channels. The utility of locally controlled magnetic anisotropies is demonstrated in current induced switching experiments. We report structure sensitive, current induced in-plane magnetization switchings well below the Curie temperature at critical current densities 10^5 Acm^-2. The observed phenomenology shows signatures of a contribution from domain-wall spin-transfer-torque effects., Comment: 9 pages, 9 figures, Phys. Rev. B in press

Our experimental and theoretical study of the non-crystalline and crystalline components of the anisotropic magnetoresistance (AMR) in (Ga,Mn)As is aimed at exploring the basic physical aspects of this relativistic transport effect. The non-crystalline AMR reflects anisotropic lifetimes of the holes due to polarized Mn impurities while the crystalline AMR is associated with valence band warping. We find that the sign of the non-crystalline AMR is determined by the form of spin-orbit coupling in the host band and by the relative strengths of the non-magnetic and magnetic contributions to the impurity potential. We develop experimental methods directly yielding the non-crystalline and crystalline AMR components which are then independently analyzed. We report the observation of an AMR dominated by a large uniaxial crystalline component and show that AMR can be modified by local strain relaxation. We discuss generic implications of our experimental and theoretical findings including predictions for non-crystalline AMR sign reversals in dilute moment systems., Comment: 4 pages, 3 figures. Phys. Rev. Lett. in press

We compare quantum Hall systems at filling factor 2 to those at filling factors 2/3 and 2/5, corresponding to the exact filling of two lowest electron or composite fermion (CF) Landau levels. The two fractional states are examples of CF liquids with spin dynamics. There is a close analogy between the ferromagnetic (spin polarization P=1) and paramagnetic (P=0) incompressible ground states that occur in all three systems in the limits of large and small Zeeman spin splitting. However, the excitation spectra are different. At filling factor 2, we find spin domains at half-polarization (P=1/2), while antiferromagnetic order seems most favorable in the CF systems. The transition between P=0 and 1, as seen when e.g. the magnetic field is tilted, is also studied by exact diagonalization in toroidal and spherical geometries. The essential role of an effective CF-CF interaction is discussed, and the experimentally observed incompresible half-polarized state is found in some models.

The dependence of the activated gap on magnetic field is studied for the fractional filling factor~1/3. By comparing the experimental results with results from exact diagonalization calculations we are able to identify the excitation of a small antiskyrmion in the low-field regime and a cross-over to spinless excitations at higher magnetic fields. The effect of sample quality is studied. On the side of the theory, comparison between different geometries (torus and sphere) and different sizes is carried out. Under inclusion of Landau level mixing and finite thickness, we obtain a good agreement between calculated energies and experimental results., Comment: submitted to PRB

Full quantum-mechanical description of electrons moving in 3D structures with unidirectional periodic modulation subject to tilted magnetic fields requires an extensive numerical calculation. To understand magneto-oscillations in such systems it is in many cases sufficient to use the quasi-classical approach, in which the zero-magnetic-field Fermi surface is considered as a magnetic-field-independent rigid body in k-space and periods of oscillations are related to extremal cross-sections of the Fermi surface cut by planes perpendicular to the magnetic-field direction. We point out cases where the quasi-classical treatment fails and propose a simple tight-binding fully-quantum-mechanical model of the superlattice electronic structure., Comment: 8 pages, 7 figures, RevTex, submitted to Phys. Rev. B