Altermagnetic lifting of Kramers spin degeneracy.

Lifted Kramers spin degeneracy (LKSD) has been among the central topics of condensed-matter physics since the dawn of the band theory of solids1,2. It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology3-7 to topological quantum matter8-14. Traditionally, LKSD has been considered to originate from two possible internal symmetry-breaking mechanisms. The first refers to time-reversal symmetry breaking by magnetization of ferromagnets and tends to be strong because of the non-relativistic exchange origin15. The second applies to crystals with broken inversion symmetry and tends to be comparatively weaker, as it originates from the relativistic spin-orbit coupling (SOC)16-19. A recent theory work based on spin-symmetry classification has identified an unconventional magnetic phase, dubbed altermagnetic20,21, that allows for LKSD 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 LKSD generated by the altermagnetic phase of centrosymmetric MnTe with vanishing net magnetization20-23. Our observation of the altermagnetic LKSD 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 superconductors20,21, that have been either identified recently or perceived for many decades as conventional antiferromagnets21,24,25.

X-Ray Magnetic Circular Dichroism in Altermagnetic α-MnTe.

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, ab initio theory, and experiments to explore x-ray magnetic circular dichroism (XMCD) in the altermagnetic class. As a representative material for our XMCD study we choose α-MnTe with compensated antiparallel magnetic order in which an anomalous Hall effect has been already demonstrated. We predict and experimentally confirm a characteristic XMCD line shape for compensated moments lying in a plane perpendicular to the light propagation vector. 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.

Spontaneous Anomalous Hall Effect Arising from an Unconventional Compensated Magnetic Phase in a Semiconductor.

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 noncollinear 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 nonmagnetic Te atoms is essential for establishing the unconventional phase and generating the anomalous Hall effect.

Electric Control of Dirac Quasiparticles by Spin-Orbit Torque in an Antiferromagnet.

Spin orbitronics and Dirac quasiparticles are two fields of condensed matter physics initiated independently about a decade ago. Here we predict that Dirac quasiparticles can be controlled by the spin-orbit torque reorientation of the Néel vector in an antiferromagnet. Using CuMnAs as an example, we formulate symmetry criteria allowing for the coexistence of topological Dirac quasiparticles and Néel spin-orbit torques. We identify the nonsymmorphic crystal symmetry protection of Dirac band crossings whose on and off switching is mediated by the Néel vector reorientation. We predict that this concept verified by minimal model and density functional calculations in the CuMnAs semimetal antiferromagnet can lead to a topological metal-insulator transition driven by the Néel vector and to the topological anisotropic magnetoresistance.

Imaging Current-Induced Switching of Antiferromagnetic Domains in CuMnAs.

The magnetic order in antiferromagnetic materials is hard to control with external magnetic fields. Using x-ray magnetic linear dichroism microscopy, we show that staggered effective fields generated by electrical current can induce modification of the antiferromagnetic domain structure in microdevices fabricated from a tetragonal CuMnAs thin film. A clear correlation between the average domain orientation and the anisotropy of the electrical resistance is demonstrated, with both showing reproducible switching in response to orthogonally applied current pulses. However, the behavior is inhomogeneous at the submicron level, highlighting the complex nature of the switching process in multidomain antiferromagnetic films.

High Antiferromagnetic Domain Wall Velocity Induced by Néel Spin-Orbit Torques.

We demonstrate the possibility to drive an antiferromagnetic domain wall at high velocities by fieldlike Néel spin-orbit torques. Such torques arise from current-induced local fields that alternate their orientation on each sublattice of the antiferromagnet and whose orientation depends primarily on the current direction, giving them their fieldlike character. The domain wall velocities that can be achieved by this mechanism are 2 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 breakdown limit. In addition, because of its nature, the staggered spin-orbit field can lift the degeneracy between two 180° rotated states in a collinear antiferromagnet, and it provides a force that can move such walls and control the switching of the states.

Electric control of the spin Hall effect by intervalley transitions.

Controlling spin-related material properties by electronic means is a key step towards future spintronic technologies. The spin Hall effect (SHE) has become increasingly important for generating, detecting and using spin currents, but its strength--quantified in terms of the SHE angle--is ultimately fixed by the magnitude of the spin-orbit coupling (SOC) present for any given material system. However, if the electrons generating the SHE can be controlled by populating different areas (valleys) of the electronic structure with different SOC characteristic the SHE angle can be tuned directly within a single sample. Here we report the manipulation of the SHE in bulk GaAs at room temperature by means of an electrical intervalley transition induced in the conduction band. The spin Hall angle was determined by measuring an electromotive force driven by photoexcited spin-polarized electrons drifting through GaAs Hall bars. By controlling electron populations in different (Γ and L) valleys, we manipulated the angle from 0.0005 to 0.02. This change by a factor of 40 is unprecedented in GaAs and the highest value achieved is comparable to that of the heavy metal Pt.

Room-temperature antiferromagnetic memory resistor.

The bistability of ordered spin states in ferromagnets provides the basis for magnetic memory functionality. The latest generation of magnetic random access memories rely on an efficient approach in which magnetic fields are replaced by electrical means for writing and reading the information in ferromagnets. This concept may eventually reduce the sensitivity of ferromagnets to magnetic field perturbations to being a weakness for data retention and the ferromagnetic stray fields to an obstacle for high-density memory integration. Here we report a room-temperature bistable antiferromagnetic (AFM) memory that produces negligible stray fields and is insensitive to strong magnetic fields. We use a resistor made of a FeRh AFM, which orders ferromagnetically roughly 100 K above room temperature, and therefore allows us to set different collective directions for the Fe moments by applied magnetic field. On cooling to room temperature, AFM order sets in with the direction of the AFM moments predetermined by the field and moment direction in the high-temperature ferromagnetic state. For electrical reading, we use an AFM analogue of the anisotropic magnetoresistance. Our microscopic theory modelling confirms that this archetypical spintronic effect, discovered more than 150 years ago in ferromagnets, is also present in AFMs. Our work demonstrates the feasibility of fabricating room-temperature spintronic memories with AFMs, which in turn expands the base of available magnetic materials for devices with properties that cannot be achieved with ferromagnets.

Piezoelectric control of the mobility of a domain wall driven by adiabatic and non-adiabatic torques.

The rich internal degrees of freedom of magnetic domain walls make them an attractive complement to electron charge for exploring new concepts of storage, transport and processing of information. Here we use the tunable internal structure of a domain wall in a perpendicularly magnetized GaMnAsP/GaAs ferromagnetic semiconductor and demonstrate devices in which piezoelectrically controlled magnetic anisotropy yields up to 500% mobility variations for an electrical-current-driven domain wall. We observe current-induced domain wall motion over a wide range of current-pulse amplitudes and report a direct observation and the piezoelectric control of the Walker breakdown separating two regimes with different mobilities. Our work demonstrates that in spin-orbit-coupled ferromagnets with weak extrinsic domain wall pinning, the piezoelectric control allows one to experimentally assess the upper and lower boundaries of the characteristic ratio of adiabatic and non-adiabatic spin-transfer torques in the current-driven domain wall motion.

Relativistic Néel-order fields induced by electrical current in antiferromagnets.

We predict that a lateral electrical current in antiferromagnets can induce nonequilibrium Néel-order fields, i.e., fields whose sign alternates between the spin sublattices, which can trigger ultrafast spin-axis reorientation. Based on microscopic transport theory calculations we identify staggered current-induced fields analogous to the intraband and to the intrinsic interband spin-orbit fields previously reported in ferromagnets with a broken inversion-symmetry crystal. To illustrate their rich physics and utility, we consider bulk Mn(2)Au with the two spin sublattices forming inversion partners, and a 2D square-lattice antiferromagnet with broken structural inversion symmetry modeled by a Rashba spin-orbit coupling. We propose an antiferromagnetic memory device with electrical writing and reading.

Antiferromagnetic half-skyrmions electrically generated and controlled at room temperature.

Topologically protected magnetic textures are promising candidates for information carriers in future memory devices, as they can be efficiently propelled at very high velocities using current-induced spin torques. These textures-nanoscale whirls in the magnetic order-include skyrmions, half-skyrmions (merons) and their antiparticles. Antiferromagnets have been shown to host versions of these textures that have high 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 merons and antimerons are localized on 180° domain walls, and move in the direction of the current pulses. 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.

A spin-valve-like magnetoresistance of an antiferromagnet-based tunnel junction.

A spin valve is a microelectronic device in which high- and low-resistance states are realized by using both the charge and spin of carriers. Spin-valve structures used in modern hard-drive read heads and magnetic random access memoriescomprise two ferromagnetic electrodes whose relative magnetization orientations can be switched between parallel and antiparallel configurations, yielding the desired giant or tunnelling magnetoresistance effect. Here we demonstrate more than 100% spin-valve-like signal in a NiFe/IrMn/MgO/Pt stack with an antiferromagnet on one side and a non-magnetic metal on the other side of the tunnel barrier. Ferromagneticmoments in NiFe are reversed by external fields of approximately 50 mT or less, and the exchange-spring effect of NiFe on IrMn induces rotation of antiferromagnetic moments in IrMn, which is detected by the measured tunnelling anisotropic magnetoresistance. Our work demonstrates a spintronic element whose transport characteristics are governed by an antiferromagnet. It demonstrates that sensitivity to low magnetic fields can be combined with large, spin-orbit-coupling-induced magnetotransport anisotropy using a single magnetic electrode. The antiferromagnetic tunnelling anisotropic magnetoresistance provides a means to study magnetic characteristics of antiferromagnetic films by an electronic-transport measurement.

Electrical measurement of antiferromagnetic moments in exchange-coupled IrMn/NiFe stacks.

We employ antiferromagnetic tunneling anisotropic magnetoresistance to study the behavior of antiferromagnetically ordered moments in IrMn exchange coupled to NiFe. Experiments performed by common laboratory tools for magnetization and electrical transport measurements allow us to directly link the broadening of the NiFe hysteresis loop and its shift (exchange bias) to the rotation and pinning of antiferromagnetic moments in IrMn. At higher temperatures, the broadened loops show zero shift, which correlates with the observation of fully rotating antiferromagnetic moments inside the IrMn film. The onset of exchange bias at lower temperatures is linked to a partial rotation between distinct metastable states and pinning of the IrMn antiferromagnetic moments in these states. The observation complements common pictures of exchange bias and reveals an electrically measurable memory effect in an antiferromagnet.

Detection of electrically modulated inverse spin hall effect in an Fe/GaAs microdevice.

We report the detection of the inverse spin Hall effect (ISHE) in n-gallium arsenide (n-GaAs) combined with electrical injection and modulation of the spin current. We use epitaxial ultrathin-Fe/GaAs injection contacts with strong in-plane magnetic anisotropy. This allows us to simultaneously perform Hanle spin-precession measurements on an Fe detection electrode and ISHE measurements in an applied in-plane hard-axis magnetic field. In this geometry, we can experimentally separate the ordinary from the spin-Hall signals. Electrical spin injection and detection are combined in our microdevice with an applied electrical drift current to modulate the spin distribution and spin current in the channel. The magnitudes and external field dependencies of the signals are quantitatively modeled by solving drift-diffusion and Hall-cross response equations.

Ferroelectric polymer gates for non-volatile field effect control of ferromagnetism in (Ga, Mn)As layers.

(Ga, Mn)As and other diluted magnetic semiconductors (DMS) attract a great deal of attention for potential spintronic applications because of the possibility of controlling the magnetic properties via electrical gating. Integration of a ferroelectric gate on the DMS channel adds to the system a non-volatile memory functionality and permits nanopatterning via the polarization domain engineering. This topical review is focused on the multiferroic system, where the ferromagnetism in the (Ga, Mn)As DMS channel is controlled by the non-volatile field effect of the spontaneous polarization. Use of ferroelectric polymer gates in such heterostructures offers a viable alternative to the traditional oxide ferroelectrics generally incompatible with DMS. Here we review the proof-of-concept experiments demonstrating the ferroelectric control of ferromagnetism, analyze the performance issues of the ferroelectric gates and discuss prospects for further development of the ferroelectric/DMS heterostructures toward the multiferroic field effect transistor.

Microscopic analysis of the valence band and impurity band theories of (Ga,Mn)As.

We analyze microscopically the valence and impurity band models of ferromagnetic (Ga,Mn)As. We find that the tight-binding Anderson approach with conventional parametrization and the full potential local-density approximation+U calculations give a very similar band structure whose microscopic spectral character is consistent with the physical premise of the k·p kinetic-exchange model. On the other hand, the various models with a band structure comprising an impurity band detached from the valence band assume mutually incompatible microscopic spectral character. By adapting the tight-binding Anderson calculations individually to each of the impurity band pictures in the single Mn impurity limit and then by exploring the entire doping range, we find that a detached impurity band does not persist in any of these models in ferromagnetic (Ga,Mn)As.

Systematic study of Mn-doping trends in optical properties of (Ga,Mn)As.

We report on a systematic study of optical properties of (Ga,Mn)As epilayers spanning the wide range of accessible Mn(Ga) dopings. The material synthesis was optimized for each nominal Mn doping in order to obtain films which are as close as possible to uniform uncompensated (Ga,Mn)As mixed crystals. We observe a broad maximum in the mid-infrared absorption spectra whose position exhibits a prevailing blueshift for increasing Mn doping. In the visible range, a peak in the magnetic circular dichroism also shifts with increasing Mn doping. The results are consistent with the description of ferromagnetic (Ga,Mn)As based on the microscopic valence band theory. They also imply that opposite trends seen previously in the optical data on a limited number of samples are not generic and cannot serve as an experimental basis for postulating the impurity band model of ferromagnetic (Ga,Mn)As.

Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets.

Electrons, commonly moving along the applied electric field, acquire in certain magnets a dissipationless transverse velocity. This spontaneous Hall effect, found more than a century ago, has been understood in terms of the time-reversal symmetry breaking by the internal spin structure of a ferromagnetic, noncolinear antiferromagnetic, or skyrmionic form. Here, we identify previously overlooked robust Hall effect mechanism arising from collinear antiferromagnetism combined with nonmagnetic atoms at noncentrosymmetric positions. We predict a large magnitude of this crystal Hall effect in a room temperature collinear antiferromagnet RuO2 and catalog, based on symmetry rules, extensive families of material candidates. We show that the crystal Hall effect is accompanied by the possibility to control its sign by the crystal chirality. We illustrate that accounting for the full magnetization density distribution instead of the simplified spin structure sheds new light on symmetry breaking phenomena in magnets and opens an alternative avenue toward low-dissipation nanoelectronics.

Non-volatile ferroelectric control of ferromagnetism in (Ga,Mn)As.

Multiferroic structures that provide coupled ferroelectric and ferromagnetic responses are of significant interest as they may be used in novel memory devices and spintronic logic elements. One approach towards this goal is the use of composites that couple ferromagnetic and ferroelectric layers through magnetostrictive and piezoelectric strain transmitted across the interfaces. However, mechanical clamping of the films to the substrate limits their response. Structures where the magnetic response is modulated directly by the electric field of the poled ferroelectric would eliminate this constraint and provide a qualitatively higher level of integration, combining the emerging field of multiferroics with conventional semiconductor microelectronics. Here, we report the realization of such a device using (Ga,Mn)As, which is an archetypical diluted magnetic semiconductor with well-understood carrier-mediated ferromagnetism, and a polymer ferroelectric gate. Polarization reversal of the gate by a single voltage pulse results in a persistent modulation of the Curie temperature of the ferromagnetic semiconductor. The non-volatile gating of (Ga,Mn)As has been made possible by applying a low-temperature copolymer deposition technique that is distinct from pre-existing technologies for ferroelectric gates on magnetic oxides. This accomplishment opens a way to nanometre-scale modulation of magnetic semiconductor properties with rewritable ferroelectric domain patterns, operating at modest voltages and subnanosecond times.

Writing and reading antiferromagnetic Mn2Au by Néel spin-orbit torques and large anisotropic magnetoresistance.

Using antiferromagnets as active elements in spintronics requires the ability to manipulate and read-out the Néel vector orientation. Here we demonstrate for Mn2Au, a good conductor with a high ordering temperature suitable for applications, reproducible switching using current pulse generated bulk spin-orbit torques and read-out by magnetoresistance measurements. Reversible and consistent changes of the longitudinal resistance and planar Hall voltage of star-patterned epitaxial Mn2Au(001) thin films were generated by pulse current densities of ≃107 A/cm2. The symmetry of the torques agrees with theoretical predictions and a large read-out magnetoresistance effect of more than ≃6% is reproduced by ab initio transport calculations.