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The Pauli exclusion principle combined with interactions between fermions is a unifying basic mechanism that can give rise to quantum phases with spin order in diverse physical systems. Transition-metal ferromagnets, with isotropic ordering respecting crystallographic rotation symmetries and with a net magnetization, are a relatively common manifestation of this mechanism, leading to numerous practical applications, e.g., in spintronic information technologies. In contrast, superfluid $^3$He has been a unique and fragile manifestation, in which the spin-ordered phase is anisotropic, breaking the real-space rotation symmetries, and has zero net magnetization. The recently discovered altermagnets share the spin-ordered anisotropic zero-magnetization nature of superfluid $^3$He. Yet, altermagnets appear to be even more abundant than ferromagnets, can be robust, and are projected to offer superior scalability for spintronics compared to ferromagnets. Our Perspective revisits the decades of research of the spin-ordered anisotropic zero-magnetization phases including, besides superfluid $^3$He, also theoretically conceived counterparts in nematic electronic liquid-crystal phases. While all sharing the same extraordinary character of symmetry breaking, we highlight the distinctions in microscopic physics which set altermagnets apart and enable their robust and abundant material realizations., Comment: 12 pages, 4 figures

Nanoscale detection and control of the magnetic order underpins a broad spectrum of fundamental research and practical device applications. The key principle involved is the breaking of time-reversal ($\cal{T}$) symmetry, which in ferromagnets is generated by an internal magnetization. However, the presence of a net-magnetization also imposes severe limitations on compatibility with other prominent phases ranging from superconductors to topological insulators, as well as on spintronic device scalability. Recently, altermagnetism has been proposed as a solution to this restriction, since it shares the enabling $\cal{T}$-symmetry breaking characteristic of ferromagnetism, combined with the antiferromagnetic-like vanishing net-magnetization. To date, altermagnetic ordering has been inferred from spatially averaged probes. Here, we demonstrate nanoscale imaging and control of altermagnetic ordering ranging from nanoscale vortices to domain walls to microscale single-domain states in MnTe. We combine the $\cal{T}$-symmetry breaking sensitivity of X-ray magnetic circular dichroism with magnetic linear dichroism and photoemission electron microscopy, to achieve detailed imaging of the local altermagnetic ordering vector. A rich variety of spin configurations can be imposed using microstructure patterning or thermal cycling in magnetic fields. The demonstrated detection and control of altermagnetism paves the way for future research ranging from ultra-scalable digital and neuromorphic spintronic devices, to the interplay of altermagnetism with non-dissipative superconducting or topological phases., Comment: 17 pages, 3 figures

We present a phenomenological theory of altermagnets, that captures their unique magnetization dynamics and allows modelling magnetic textures in this new magnetic phase. Focusing on the prototypical d-wave altermagnets, e.g. RuO$_2$, we can explain intuitively the characteristic lifted degeneracy of their magnon spectra, by the emergence of an effective sublattice-dependent anisotropic spin stiffness arising naturally from the phenomenological theory. We show that as a consequence the altermagnetic domain walls, in contrast to antiferromagnets, have a finite gradient of the magnetization, with its strength and gradient direction connected to the altermagnetic anisotropy, even for 180$^\circ$ domain walls. This gradient generates a ponderomotive force in the domain wall in the presence of a strongly inhomogeneous external magnetic field, which may be achieved through magnetic force microscopy techniques. The motion of these altermagentic domain walls is also characterized by an anisotropic Walker breakdown, with much higher speed limits of propagation than ferromagnets but lower than antiferromagnets.

Previous experiments in compensated magnets have demonstrated a potential for approaching the limit of fastest and least-dissipative operation of digital memory bits. However, the analog route has been virtually unexplored at (sub)ps time scales. In this paper, we report on experimental separation of heat-related and quench-switching-related resistance signal dynamics induced at room temperature by a single femtosecond-laser-pulse in memory devices from metallic antiferromagnetic CuMnAs. We show that the heat-related dynamics, on picosecond to hundreds of nanoseconds time scales, can be used as a short-term memory where information about input stimuli, represented by laser-pulses, is stored temporarily. When the quench-switching threshold is reached, information is transferred to the device variable resistance, serving as a long-term memory, with time components of 10 ms and 10 s. We also deduced 10 ps time scale as an upper estimate for a conversion of the short-lived transient temperature increase to the quench-switched metastable states., Comment: 19 pages, 4 figures

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.

Lifted Kramers spin-degeneracy has been among the central topics of condensed-matter physics since the dawn of the band theory of solids. It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology to topological quantum matter. Traditionally, lifted Kramers spin-degeneracy has been considered to originate from two possible internal symmetry-breaking mechanisms. The first one refers to time-reversal symmetry breaking by magnetization of ferromagnets, and tends to be strong due to the non-relativistic exchange-coupling origin. The second mechanism applies to crystals with broken inversion symmetry, and tends to be comparatively weaker as it originates from the relativistic spin-orbit coupling. A recent theory work based on spin-symmetry classification has identified an unconventional magnetic phase, dubbed altermagnetic, that allows for lifting the Kramers spin degeneracy without net magnetization and inversion-symmetry breaking. Here we provide the confirmation using photoemission spectroscopy and ab initio calculations. We identify two distinct unconventional mechanisms of lifted Kramers spin degeneracy generated by the altermagnetic phase of centrosymmetric MnTe with vanishing net magnetization. Our observation of the altermagnetic lifting of the Kramers spin degeneracy can have broad consequences in magnetism. It motivates exploration and exploitation of the unconventional nature of this magnetic phase in an extended family of materials, ranging from insulators and semiconductors to metals and superconductors, that have been either identified recently or perceived for many decades as conventional antiferromagnets.

Altermagnets are an emerging third elementary class of magnets. Unlike ferromagnets, their distinct crystal symmetries inhibit magnetization while, unlike antiferromagnets, they promote strong spin polarization in the band structure. The corresponding unconventional mechanism of timereversal symmetry breaking without magnetization in the electronic spectra has been regarded as a primary signature of altermagnetism, but has not been experimentally visualized to date. We directly observe strong time-reversal symmetry breaking in the band structure of altermagnetic RuO$_2$ by detecting magnetic circular dichroism in angle-resolved photoemission spectra. Our experimental results, supported by ab initio calculations, establish the microscopic electronic-structure basis for a family of novel phenomena and functionalities in fields ranging from topological matter to spintronics, that are based on the unconventional time-reversal symmetry breaking in altermagnets.

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

Topologically protected magnetic textures, such as skyrmions, half-skyrmions (merons) and their antiparticles, constitute tiny whirls in the magnetic order. They are promising candidates for information carriers in next-generation memory devices, as they can be efficiently propelled at very high velocities using current-induced spin torques. Antiferromagnets have been shown to host versions of these textures, which have gained significant attention because of their potential for terahertz dynamics, deflection free motion, and improved size scaling due to the absence of stray field. Here we show that topological spin textures, merons and antimerons, can be generated at room temperature and reversibly moved using electrical pulses in thin film CuMnAs, a semimetallic antiferromagnet that is a testbed system for spintronic applications. The electrical generation and manipulation of antiferromagnetic merons is a crucial step towards realizing the full potential of antiferromagnetic thin films as active components in high density, high speed magnetic memory devices., Comment: 11 pages, 4 figures

The anomalous Hall effect, commonly observed in metallic magnets, has been established to originate from the time-reversal symmetry breaking by an internal macroscopic magnetization in ferromagnets or by a non-collinear magnetic order. Here we observe a spontaneous anomalous Hall signal in the absence of an external magnetic field in an epitaxial film of MnTe, which is a semiconductor with a collinear antiparallel magnetic ordering of Mn moments and a vanishing net magnetization. The anomalous Hall effect arises from an unconventional phase with strong time-reversal symmetry breaking and alternating spin polarization in real-space crystal structure and momentum-space electronic structure. The anisotropic crystal environment of magnetic Mn atoms due to the non-magnetic Te atoms is essential for establishing the unconventional phase and generating the anomalous Hall effect., Comment: 34 pages, 14 figures

We show scalable and complete suppression of the recently reported terahertz-pulse-induced switching between different resistance states of antiferromagnetic CuMnAs thin films by ultrafast gating. The gating functionality is achieved by an optically generated transiently conductive parallel channel in the semiconducting substrate underneath the metallic layer. The photocarrier lifetime determines the time scale of the suppression. As we do not observe a direct impact of the optical pulse on the state of CuMnAs, all observed effects are primarily mediated by the substrate. The sample region of suppressed resistance switching is given by the optical spot size, thereby making our scheme potentially applicable for transient low-power masking of structured areas with feature sizes of ~100 nm and even smaller.

Spin-dependent transport phenomena due to relativistic spin-orbit coupling and broken space-inversion symmetry are often difficult to interpret microscopically, in particular when occurring at surfaces or interfaces. Here we present a theoretical and experimental study of spin-orbit torque and unidirectional magnetoresistance in a model room-temperature ferromagnet NiMnSb with inversion asymmetry in the bulk of this half-heusler crystal. Besides the angular dependence on magnetization, the competition of Rashba and Dresselhaus-like spin-orbit couplings results in the dependence of these effects on the crystal direction of the applied electric field. The phenomenology that we observe highlights potential inapplicability of commonly considered approaches for interpreting experiments. We point out that, in general, there is no direct link between the current-induced non-equilibrium spin polarization inferred from the measured spin-orbit torque and the unidirectional magnetiresistance. We also emphasize that the unidirectional magnetoresistance has not only longitudinal but also transverse components in the electric field -- current indices which complicates its separation from the thermoelectric contributions to the detected signals in common experimental techniques. We use the theoretical results to analyze our measurements of the on-resonance and off-resonance mixing signals in microbar devices fabricated from an epitaxial NiMnSb film along different crystal directions. Based on the analysis we extract an experimental estimate of the unidirectional magnetoresistance in NiMnSb., Comment: 29 pages, 13 figures

Electrical and optical pulsing allow for manipulating the order parameter and magnetoresistance of antiferromagnets, opening novel prospects for digital and analog data storage in spintronic devices. Recent experiments in CuMnAs have demonstrated giant resistive switching signals in single-layer antiferromagnetic films together with analog switching and relaxation characteristics relevant for neuromorphic computing. Here we report simultaneous electrical pulsing and scanning NV magnetometry of antiferromagnetic domains in CuMnAs performed using a pump-probe scheme. We observe a nano-scale fragmentation of the antiferromagnetic domains, which is controlled by the current amplitude and independent on the current direction. The fragmented antiferromagnetic state conserves a memory of the pristine domain pattern, towards which it relaxes. Domain fragmentation coexists with permanent switching due to the reorientation of the antiferromagnetic moments. Our simultaneous imaging and resistance measurements show a correlation between the antiferromagnetic domain fragmentation and the largest resistive switching signals in CuMnAs.

Recent research works have shown that the magnetic order in some antiferromagnetic materials can be manipulated and detected electrically, due to two physical mechanisms: Neel-order spin-orbit torques and anisotropic magnetoresistance. While these observations open up opportunities to use antiferromagnets for magnetic memory devices, different physical characterization methods are required for a better understanding of those mechanisms. Here we report a magnetic field induced rotation of the antiferromagnetic Neel vector in epitaxial tetragonal CuMnAs thin films. Using soft x-ray magnetic linear dichroism spectroscopy, x-ray photoemission electron microscopy, integral magnetometry and magneto-transport methods, we demonstrate spin-flop switching and continuous spin reorientation in antiferromagnetic films with uniaxial and biaxial magnetic anisotropies, respectively. From field-dependent measurements of the magnetization and magnetoresistance, we obtain key material parameters including the anisotropic magnetoresistance coefficients, magnetocrystalline anisotropy, spin-flop and exchange fields., Comment: 26 pages, 6 figures

Electrical detection of the 180 deg spin reversal, which is the basis of the operation of ferromagnetic memories, is among the outstanding challenges in the research of antiferromagnetic spintronics. Analogous effects to the ferromagnetic giant or tunneling magnetoresistance have not yet been realized in antiferromagnetic multilayers. Anomalous Hall effect (AHE), which has been recently employed for spin reversal detection in non-collinear antiferromagnets, is limited to materials that crystalize in ferromagnetic symmetry groups. Here we demonstrate electrical detection of the 180 deg N\'eel vector reversal in CuMnAs which comprises two collinear spin sublattices and belongs to an antiferromagnetic symmetry group with no net magnetic moment. We detect the spin reversal by measuring a second-order magnetotransport coefficient whose presence is allowed in systems with broken space inversion symmetry. The phenomenology of the non-linear transport effect we observe in CuMnAs is consistent with a microscopic scenario combining anisotropic magneto-resistance (AMR) with a transient tilt of the N\'eel vector due to a current-induced, staggered spin-orbit field. We use the same staggered spin-orbit field, but of a higher amplitude, for the electrical switching between reversed antiferromagnetic states which are stable and show no sign of decay over 25 hour probing times., Comment: 15 pages, 5 pictures, supplementary informations

Spin-orbit coupling in inversion-asymmetric magnetic crystals and structures has emerged as a powerful tool to generate complex magnetic textures, interconvert charge and spin under applied current, and control magnetization dynamics. Current-induced spin-orbit torques mediate the transfer of angular momentum from the lattice to the spin system, leading to sustained magnetic oscillations or switching of ferromagnetic as well as antiferromagnetic structures. The manipulation of magnetic order, domain walls and skyrmions by spin-orbit torques provides evidence of the microscopic interactions between charge and spin in a variety of materials and opens novel strategies to design spintronic devices with potentially high impact in data storage, nonvolatile logic, and magnonic applications. This paper reviews recent progress in the field of spin-orbitronics, focusing on theoretical models, material properties, and experimental results obtained on bulk noncentrosymmetric conductors and multilayer heterostructures, including metals, semiconductors, and topological insulator systems. Relevant aspects for improving the understanding and optimizing the efficiency of nonequilibrium spin-orbit phenomena in future nanoscale devices are also discussed., Comment: 90 pages, 50 figures

We study dynamics of antiferromagnets induced by simultaneous application of dc spin current and ac charge current, motivated by the requirement of all-electrically controlled devices in THz gap (0.1-30 THz). We show that ac electric current, via N\'eel spin orbit torques, can lock the phase of a steady rotating N\'eel vector whose precession is controlled by a dc spin current. In the phase-locking regime the frequency of the incoming ac signal coincides with the frequency of autooscillations which for typical antiferromagnets fall into the THz range. The frequency of autooscillations is proportional to the precession-induced tilting of the magnetic sublattices related to the so-called dynamical magnetization. We show how the incoming ac signal can be detected from the measurement of the dc-current dependencies of the constant dynamical magnetization. We formulate the conditions of phase-locking based on relations between parameters of an antiferromagnet and the characteristics of the incoming signal (frequency, amplitude, bandwidth, duration). We also show that the rotating N\'eel vector can generate ac electrical current via inverse N\'eel spin-orbit torque. Hence, antiferromagnets driven by dc spin current can be used as tunable detectors and emitters of narrow-band signals operating in the THz range., Comment: 5 pages, 5 figures

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

Antiferromagnets have a number of favourable properties as active elements in spintronic devices, including ultra-fast dynamics, zero stray fields and insensitivity to external magnetic fields . Tetragonal CuMnAs is a testbed system in which the antiferromagnetic order parameter can be switched reversibly at ambient conditions using electrical currents . In previous experiments, orthogonal in-plane current pulses were used to induce 90 degree rotations of antiferromagnetic domains and demonstrate the operation of all-electrical memory bits in a multi-terminal geometry . Here, we demonstrate that antiferromagnetic domain walls can be manipulated to realize stable and reproducible domain changes using only two electrical contacts. This is achieved by using the polarity of the current to switch the sign of the current-induced effective field acting on the antiferromagnetic sublattices. The resulting reversible domain and domain wall reconfigurations are imaged using x-ray magnetic linear dichroism microscopy, and can also be detected electrically. The switching by domain wall motion can occur at much lower current densities than those needed for coherent domain switching., Comment: 8 pages, 4 figures

The speed of writing of state-of-the-art ferromagnetic memories is physically limited by an intrinsic GHz threshold. Recently, an alternative research direction has been initiated by realizing memory devices based on antiferromagnets in which spin directions periodically alternate from one atomic lattice site to the next. In our work we experimentally demonstrate at room temperature that the speed of reversible electrical writing in a memory device can be scaled up to THz using an antiferromagnet. Efficient current-induced spin-torque mechanism is responsible for the switching in our memory devices throughout the twelve orders of magnitude range of writing speeds from Hz to THz. Our work opens the path towards the development of memory-logic technology reaching the elusive THz band.

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

Antiferromagnets are magnetically ordered materials which exhibit no net moment and thus are insensitive to magnetic fields. Antiferromagnetic spintronics aims to take advantage of this insensitivity for enhanced stability, while at the same time active manipulation up to the natural THz dynamic speeds of antiferromagnets is possible, thus combining exceptional storage density and ultra-fast switching. However, the active manipulation and read-out of the N\'eel vector (staggered moment) orientation is challenging. Recent predictions have opened up a path based on a new spin-orbit torque, which couples directly to the N\'eel order parameter. This N\'eel spin-orbit torque was first experimentally demonstrated in a pioneering work using semimetallic CuMnAs. Here we demonstrate for Mn$_2$Au, a good conductor with a high ordering temperature suitable for applications, reliable and reproducible switching using current pulses and readout by magnetoresistance measurements. The symmetry of the torques agrees with theoretical predictions and a large read-out magnetoresistance effect of more than $\simeq 6$~$\%$ is reproduced by ab initio transport calculations., Comment: 5 pages, 4 figures

We report on a picosecond-fast optical removal of spin polarization from a self-confined photo-carrier system at an undoped GaAs/AlGaAs interface possessing superior long-range and high-speed spin transport properties. We employed a modified resonant spin amplification technique with unequal intensities of subsequent pump pulses to experimentally distinguish the evolution of spin populations originating from different excitation laser pulses. We demonstrate that the density of spins, which is injected into the system by means of the optical orientation, can be controlled by reducing the electrostatic confinement of the system using an additional generation of photocarriers. It is also shown that the disturbed confinement recovers within hundreds of picoseconds after which spins can be again photo-injected into the system.

This focused issue attempts to provide a comprehensive introduction into the field of antiferromagnetic spintronics. Apart from the brief overview below, it features five review articles. The intention is to cover in a coherent and complementary way key physical aspects of the antiferromagnetic spintronics research. These range from microelectronic memory devices and optical manipulation and detection of antiferromagnetic spins, to the fundamentals of antiferromagnetic dynamics in uniform or spin-textured systems, and to the interplay of antiferromagnetic spintronics with topological phenomena. The antiferromagnetic ordering can take a number of forms including fully compensated collinear, non-collinear, and non-coplanar magnetic lattices, compensated and uncompensated ferrimagnets, or metamagnetic materials hosting an antiferromagnetic to ferromagnetic phase transition. Apart from the variety of distinct magnetic crystal structures, the focused issue also encompasses spintronic phenomena and devices studied in antiferromagnet/ferromagnet heterostructures and in synthetic antiferromagnets., Comment: 3 pages, 1 figure, Part of a collection of reviews on antiferromagnetic spintronics

Topological quantum matter and spintronics research have been developed to a large extent independently. In this Review we discuss a new role that the antiferromagnetic order has taken in combining topological matter and spintronics. This occurs due to the complex microscopic symmetries present in antiferromagnets that allow, e.g., for topological relativistic quasiparticles and the newly discovered N\'{e}el spin-orbit torques to coexist. We first introduce the concepts of topological semimetals and spin-orbitronics. Secondly, we explain the antiferromagnetic symmetries on a minimal Dirac semimetal model and the guiding role of $\textit{ab initio}$ calculations in predictions of examples of Dirac, and Weyl antiferromagnets: SrMnBi$_{\text{2}}$, CuMnAs, and Mn$_{\text{3}}$Ge. Lastly, we illustrate the interplay of Dirac quasiparticles, topology and antiferromagnetism on: (i) the experimentally observed quantum Hall effect in EuMnBi$_{\text{2}}$, (ii) the large anomalous Hall effect in Mn$_{\text{3}}$Ge, and (iii) the theoretically predicted topological metal-insulator transition in CuMnAs., Comment: 17 pages, 11 figures, review

Using x-ray magnetic circular and linear dichroism techniques, we demonstrate a collinear exchange coupling between an epitaxial antiferromagnet, tetragonal CuMnAs, and an Fe surface layer. A small uncompensated Mn magnetic moment is observed which is antiparallel to the Fe magnetization. The staggered magnetization of the 5nm thick CuMnAs layer is rotatable under small magnetic fields, due to the interlayer exchange coupling. This allows us to obtain the x-ray magnetic linear dichroism spectra for different crystalline orientations of CuMnAs in the (001) plane., Comment: 10 pages, 3 figures

Antiferromagnetic spintronics is an emerging research field whose focus is on the electrical and optical control of the antiferromagnetic order parameter and its utility in information technology devices. An example of recently discovered new concepts is the N\'{e}el spin-orbit torque which allows for the antiferromagnetic order parameter to be controlled by an electrical current in common microelectronic circuits. In this review we discuss the utility of antiferromagnets as active and supporting materials for spintronics, the interplay of antiferromagnetic spintronics with other modern research fields in condensed matter physics, and its utility in future "More than Moore" information technologies., Comment: Overview of the topics presented at the Workshop of Antiferromagnetic Spintronics, 2016, Mainz, Germany

Antiferromagnets (AFs) are remarkable magnetically ordered materials that due to the absence of a net magnetic moment do not generate dipolar fields and are insensitive to external magnetic field perturbations. However, it has been notoriously difficult to control antiferromagnetic moments by any practical means suitable for device applications. This has left AFs over their hundred years history virtually unexploited and only poorly explored, in striking contrast to the thousands of years of fascination and utility of ferromagnetism. Very recently it has been predicted and experimentally confirmed that relativistic spin-orbit torques can provide the means for efficient electrical control of an AF. Here we place the emerging field of antiferromagnetic spintronics on the map of non-volatile solid state memory technologies. We demonstrate the complete write/store/read functionality in an antiferromagnetic CuMnAs bit cell embedded in a standard printed circuit board communicating with a computer via a USB interface. We show that the elementary-shape bit cells fabricated from a single-layer AF are electrically written on timescales ranging from milliseconds to nanoseconds and we demonstrate their deterministic multi-level switching. The multi-level cell characteristics, reflecting series of reproducible, electrically controlled domain reconfigurations, allow us to integrate memory and signal counter functionalities within the bit cell., Comment: 13 pages, 3 figures

Recent breakthroughs in electrical detection and manipulation of antiferromagnets have opened a new avenue in the research of non-volatile spintronic devices. Antiparallel spin sublattices in antiferromagnets, producing zero dipolar fields, lead to the insensitivity to magnetic field perturbations, multi-level stability, ultra-fast spin dynamics and other favorable characteristics which may find utility in fields ranging from magnetic memories to optical signal processing. However, the absence of a net magnetic moment and the ultra-short magnetization dynamics timescales make antiferromagnets notoriously difficult to study by common magnetometers or magnetic resonance techniques. In this paper we demonstrate the experimental determination of the Neel vector in a thin film of antiferromagnetic CuMnAs which is the prominent material used in the first realization of antiferromagnetic memory chips. We employ a femtosecond pump-probe magneto-optical experiment based on magnetic linear dichroism. This table-top optical method is considerably more accessible than the traditionally employed large scale facility techniques like neutron diffraction and X-ray magnetic dichroism measurements. This optical technique allows an unambiguous direct determination of the Neel vector orientation in thin antiferromagnetic films utilized in devices directly from measured data without fitting to a theoretical model., Comment: 10 pages, 4 figures

We investigate the thickness and temperature dependence of a series of Ni0:8Fe0:2/Ir0:2Mn0:8 bilayer samples with varying thickness ratio of the ferromagnet/antiferromagnet (tFM/tAFM) in order to explore the exchange coupling strengths in tunneling anisotropic magnetoresistance (TAMR) devices. Specific values of tFM/tAFM lead to four distinct scenarios with specific electric responses to moderate magnetic fields. The characteristic dependence of the measured TAMR signal on applied voltage allows us to confirm its persistence up to room temperature despite an overlapped contribution by a thermal magnetic noise.

The magnetic order in antiferromagnetic (AF) materials is hard to control with external magnetic fields. However, recent advances in detecting and manipulating AF order electrically have opened up new prospects for these materials in basic and applied spintronics research. Using x-ray magnetic linear dichroism microscopy, we show here that staggered effective fields generated by electrical current can induce reproducible and reversible modification of the antiferromagnetic domain structure in microdevices fabricated from a tetragonal CuMnAs thin film. The current-induced domain switching is inhomogeneous at the submicron level. A clear correlation between the average domain orientation and the anisotropy of the electrical resistance is demonstrated., Comment: 5 pages, 4 figures

Antiferromagnetic spintronics is an emerging field; antiferromagnets can improve the functionalities of ferromagnets with higher response times, and having the information shielded against external magnetic field. Moreover, a large list of aniferromagnetic semiconductors and metals with N\'eel temperatures above room temperature exists. In the present manuscript, we persevere in the quest for the limits of how large can anisotropic magnetoresistance be in antiferromagnetic materials with very large spin-orbit coupling. We selected IrMn as a prime example of first-class moment (Mn) and spin-orbit (Ir) combination. Isothermal magnetotransport measurements in an antiferromagnetic-metal(IrMn)/ferromagnetic-insulator thin film bilayer have been performed. The metal/insulator structure with magnetic coupling between both layers allows the measurement of the modulation of the transport properties exclusively in the antiferromagnetic layer. Anisotropic magnetoresistance as large as 0.15 % has been found, which is much larger than that for a bare IrMn layer. Interestingly, it has been observed that anisotropic magnetoresistance is strongly influenced by the field cooling conditions, signaling the dependence of the found response on the formation of domains at the magnetic ordering temperature.

Domain wall motion driven by ultra-short laser pulses is a prerequisite for envisaged low-power spintronics combining storage of information in magneto electronic devices with high speed and long distance transmission of information encoded in circularly polarized light. Here we demonstrate the conversion of the circular polarization of incident femtosecond laser pulses into inertial displacement of a domain wall in a ferromagnetic semiconductor. In our study we combine electrical measurements and magneto-optical imaging of the domain wall displacement with micromagnetic simulations. The optical spin transfer torque acts over a picosecond recombination time of the spin polarized photo-carriers which only leads to a deformation of the internal domain wall structure. We show that subsequent depinning and micro-meter distance displacement without an applied magnetic field or any other external stimuli can only occur due to the inertia of the domain wall.

We report an experimental demonstration of a local amplification of the spin Hall voltage using an expanding depletion zone at a pn-junction in GaAs/AlGaAs Hall-bar microdevices. It is demonstrated that the depletion zone can be spatially expanded by applying reverse bias by at least 10~$\mu$m at low temperature. In the depleted regime, the spin Hall signals reached more than one order of magnitude higher values than in the normal regime at the same electrical current flowing through the micro-device. It is shown that the pn-bias has two distinct effects on the detected spin Hall signal. It controls the local drift field at the Hall cross which is highly non-linear in the pn-bias due to the shift of the depletion front. Simultaneously, it produces a change in the spin-transport parameters due to the non-linear change in the carrier density at the Hall cross with the pn-bias.

We report an experimental demonstration of a local amplification of the spin Hall voltage using an expanding depletion zone at a pn-junction in GaAs/AlGaAs Hall-bar microdevices. It is demonstrated that the depletion zone can be spatially expanded by applying reverse bias by at least 10~$\mu$m at low temperature. In the depleted regime, the spin Hall signals reached more than one order of magnitude higher values than in the normal regime at the same electrical current flowing through the micro-device. It is shown that the pn-bias has two distinct effects on the detected spin Hall signal. It controls the local drift field at the Hall cross which is highly non-linear in the pn-bias due to the shift of the depletion front. Simultaneously, it produces a change in the spin-transport parameters due to the non-linear change in the carrier density at the Hall cross with the pn-bias.

One of the main obstacles that prevents practical applications of antiferromagnets is the difficulty of manipulating the magnetic order parameter. Recently, following the theoretical prediction [J. \v{Z}elezn\'y et al., PRL 113, 157201 (2014)], the electrical switching of magnetic moments in an antiferromagnet has been demonstrated [P. Wadley et al., Science 351, 587 (2016)]. The switching is due to the so-called spin-orbit torque, which has been extensively studied in ferromagnets. In this phenomena a non-equilibrium spin-polarization exchange coupled to the ordered local moments is induced by current, hence exerting a torque on the order parameter. Here we give a general systematic analysis of the symmetry of the spin-orbit torque in locally and globally non-centrosymmetric crystals. We study when the symmetry allows for a nonzero torque, when is the torque effective, and its dependence on the applied current direction and orientation of magnetic moments. For comparison, we consider both antiferromagnetic and ferromagnetic orders. In two representative model crystals we perform microscopic calculations of the spin-orbit torque to illustrate its symmetry properties and to highlight conditions under which the spin-orbit torque can be efficient for manipulating antiferromagnetic moments., Comment: 17 pages, 9 figures

We demonstrate the possibility to drive an antiferromagnet domain-wall at high velocities by field-like N\'{e}el spin-orbit torques. Such torques arise from current-induced local fields that alternate their orientation on each sub-lattice of the antiferromagnet and whose orientation depend primarily on the current direction, giving them their field-like character. The domain-wall velocities that can be achieved by this mechanism are two orders of magnitude greater than the ones in ferromagnets. This arises from the efficiency of the staggered spin-orbit fields to couple to the order parameter and from the exchange-enhanced phenomena in antiferromagnetic texture dynamics, which leads to a low domain-wall effective mass and the absence of a Walker break-down limit. In addition, because of its nature, the staggered spin-orbit field can lift the degeneracy between two 180$^\circ$ rotated states in a collinear antiferromagnet and provides a force that can move such walls and control the switching of the states., Comment: 9 pages, Supplementary materials included

Materials that crystalize in diamond-related lattices, with Si and GaAs as their prime examples, are at the foundation of modern electronics. Simultaneoulsy, the two atomic sites in the unit cell of these crystals form inversion partners which gives rise to relativistic non-equilibrium spin phenomena highly relevant for magnetic memories and other spintronic devices. When the inversion-partner sites are occupied by the same atomic species, electrical current can generate local spin polarization with the same magnitude and opposite sign on the two inversion-partner sites. In CuMnAs, which shares this specific crystal symmetry of the Si lattice, the effect led to the demonstration of electrical switching in an antiferromagnetic memory at room temperature. When the inversion-partner sites are occupied by different atoms, a non-zero global spin-polarization is generated by the applied current which can switch a ferromagnet, as reported at low temperatures in the diluted magnetic semiconductor (Ga,Mn)As. Here we demonstrate the effect of the global current-induced spin polarization in a counterpart crystal-symmetry material NiMnSb which is a member of the broad family of magnetic Heusler compounds. It is an ordered high-temperature ferromagnetic metal whose other favorable characteristics include high spin-polarization and low damping of magnetization dynamics. Our experiments are performed on strained single-crystal epilayers of NiMnSb grown on InGaAs. By performing all-electrical ferromagnetic resonance measurements in microbars patterned along different crystal axes we detect room-temperature spin-orbit torques generated by effective fields of the Dresselhaus symmetry. The measured magnitude and symmetry of the current-induced torques are consistent with our relativistic density-functional theory calculations.

The spin-conserving length-scale is a key parameter determining functionalities of a broad range of spintronic devices including magnetic multilayer spin-valves in the commercialized magnetic memories or lateral spin transistors in experimental spin-logic elements. Spatially resolved optical pump-and-probe experiments in the lateral devices allow for the direct measurement of the lengthscale and the time-scale at which spin-information is transferred from the injector to the detector. Using this technique, we demonstrate that in an undoped GaAs/AlGaAs layer spins are detected at distances reaching more than ten microns from the injection point at times as short as nanoseconds after the pump-pulse. The observed unique combination of the long-range and highrate electronic spin-transport requires simultaneous suppression of mechanisms limiting the spin life-time and mobility of carriers. Unlike earlier attempts focusing on elaborate doping, gating, or heterostructures we demonstrate that the bare GaAs/AlGaAs layer intrinsically provides superior spin-transport characteristics whether deposited directly on the substrate or embedded in complex heterostructures.

Antiferromagnetic materials are magnetic inside, however, the direction of their ordered microscopic moments alternates between individual atomic sites. The resulting zero net magnetic moment makes magnetism in antiferromagnets invisible on the outside. It also implies that if information was stored in antiferromagnetic moments it would be insensitive to disturbing external magnetic fields, and the antiferromagnetic element would not affect magnetically its neighbors no matter how densely the elements were arranged in a device. The intrinsic high frequencies of antiferromagnetic dynamics represent another property that makes antiferromagnets distinct from ferromagnets. The outstanding question is how to efficiently manipulate and detect the magnetic state of an antiferromagnet. In this article we give an overview of recent works addressing this question. We also review studies looking at merits of antiferromagnetic spintronics from a more general perspective of spin-ransport, magnetization dynamics, and materials research, and give a brief outlook of future research and applications of antiferromagnetic spintronics., Comment: 13 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.

Exploiting both spin and charge of the electron in electronic micordevices has lead to a tremendous progress in both basic condensed-matter research and microelectronic applications, resulting in the modern field of spintronics. Current spintronics relies primarily on ferromagnets while antiferromagnets have traditionally played only a supporting role. Recently, antiferromagnets have been revisited as potential candidates for the key active elements in spintronic devices. In this paper we review approaches that have been employed for reading, writing, and storing information in antiferromagnets.

First-generation magnetic random access memories based on anisotropic magnetoresistance required magnetic fields for both writing and reading. Modern all-electrical read/write memories use instead non-relativistic spin-transport connecting the storing magnetic layer with a reference ferromagnet. Recent studies have focused on electrical manipulation of magnetic moments by relativistic spin-torques requiring no reference ferromagnet. Here we report the observation of a counterpart magnetoresistance effect in such a relativistic system which allows us to electrically detect the sign of the magnetization without an auxiliary magnetic field or ferromagnet. We observe the effect in a geometry in which the magnetization of a uniaxial (Ga,Mn)As epilayer is set either parallel or antiparallel to a current-induced non-equilibrium spin polarization of carriers. In our structure, this linear-in-current magnetoresistance reaches 0.2\% at current density of $10^6$ A cm$^{-2}$., Comment: 5 pages, 4 figures

The capacitance of a parallel plate capacitor can depend on applied magnetic field. Previous studies have identified capacitance changes induced via classical Lorentz force or spin-dependent Zeeman effects. Here we measure a magnetization direction dependent capacitance in parallel-plate capacitors where one plate is a ferromagnetic semiconductor, gallium manganese arsenide. This anisotropic magneto-capacitance is due to the anisotropy in the density of states dependent on the magnetization through the strong spin-orbit interaction., Comment: 5 pages, 4 figures