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

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.

Landau Theory of Altermagnetism

We formulate a Landau theory for altermagnets, a class of collinear compensated magnets with spin-split bands. Starting from the nonrelativistic limit, this Landau theory goes beyond a conventional analysis by including spin-space symmetries, providing a simple framework for understanding the key features of this family of materials. We find a set of multipolar secondary order parameters connecting existing ideas about the spin symmetries of these systems, their order parameters, and the effect of nonzero spin-orbit coupling. We account for several features of canonical altermagnets such as RuO_{2}, MnTe, and CuF_{2} that go beyond symmetry alone, relating the order parameter to key observables such as magnetization, anomalous Hall conductivity, and magnetoelastic and magneto-optical probes. Finally, we comment on generalizations of our framework to a wider family of exotic magnetic systems derived from the zero spin-orbit coupled limit.

The Impact of Local Strain Fields in Noncollinear Antiferromagnetic Films

Antiferromagnets hosting structural or magnetic order that breaks time reversal symmetry are of increasing interest for "beyond von Neumann" computing applications because the topology of their band structure allows for intrinsic physical properties, exploitable in integrated memory and logic function. One such group are the noncollinear antiferromagnets. Essential for domain manipulation is the existence of small net moments found routinely when the material is synthesized in thin film form and attributed to symmetry breaking caused by spin canting, either from the Dzyaloshinskii-Moriya interaction or from strain. Although the spin arrangement of these materials makes them highly sensitive to strain, there is little understanding about the influence of local strain fields caused by lattice defects on global properties, such as magnetization and anomalous Hall effect. This premise is investigated by examining noncollinear antiferromagnetic films that are either highly lattice mismatched or closely matched to their substrate. In either case, edge dislocation networks are generated and for the former case, these extend throughout the entire film thickness, creating large local strain fields. These strain fields allow for finite intrinsic magnetization in seemingly structurally relaxed films and influence the antiferromagnetic domain state and the intrinsic anomalous Hall effect.

Emerging Antiferromagnets for Spintronics

Antiferromagnets constitute promising contender materials for next-generation spintronic devices with superior stability, scalability, and dynamics. Nevertheless, the perception of well-established ferromagnetic spintronics underpinned by spontaneous magnetization seemed to indicate the inadequacy of antiferromagnets for spintronics-their compensated magnetization has been perceived to result in uncontrollable antiferromagnetic order and subtle magnetoelectronic responses. However, remarkable advancements have been achieved in antiferromagnetic spintronics in recent years, with consecutive unanticipated discoveries substantiating the feasibility of antiferromagnet-centered spintronic devices. It is emphasized that, distinct from ferromagnets, the richness in complex antiferromagnetic crystal structures is the unique and essential virtue of antiferromagnets that can open up their endless possibilities of novel phenomena and functionality for spintronics. In this Perspective, the recent progress in antiferromagnetic spintronics is reviewed, with a particular focus on that based on several kinds of antiferromagnets with special antiferromagnetic crystal structures. The latest developments in efficiently manipulating antiferromagnetic order, exploring novel antiferromagnetic physical responses, and demonstrating prototype antiferromagnetic spintronic devices are discussed. An outlook on future research directions is also provided. It is hoped that this Perspective can serve as guidance for readers who are interested in this field and encourage unprecedented studies on antiferromagnetic spintronic materials, phenomena, and devices.

Wurtzite vs. rock-salt MnSe epitaxy: electronic and altermagnetic properties

Newly discovered altermagnets are magnetic materials exhibiting both compensated magnetic order, similar to antiferromagnets, and simultaneous non-relativistic spin-splitting of the bands, akin to ferromagnets. This characteristic arises from specific symmetry operation that connects the spin sublattices. In this report, we show with ab initio calculations that semiconductive MnSe exhibits altermagnetic spin-splitting in the wurtzite phase as well as a critical temperature well above room temperature. It is the first material from such a space group identified to possess altermagnetic properties. Furthermore, we demonstrate experimentally through structural characterization techniques that it is possible to obtain thin films of both the intriguing wurtzite phase of MnSe and more common rock-salt MnSe using molecular beam epitaxy on GaAs substrates. The choice of buffer layers plays a crucial role in determining the resulting phase and consequently extends the array of materials available for the physics of altermagnetism.

Direct observation of altermagnetic band splitting in CrSb thin films

Altermagnetism represents an emergent collinear magnetic phase with compensated order and an unconventional alternating even-parity wave spin order in the non-relativistic band structure. We investigate directly this unconventional band splitting near the Fermi energy through spin-integrated soft X-ray angular resolved photoemission spectroscopy. The experimentally obtained angle-dependent photoemission intensity, acquired from epitaxial thin films of the predicted altermagnet CrSb, demonstrates robust agreement with the corresponding band structure calculations. In particular, we observe the distinctive splitting of an electronic band on a low-symmetry path in the Brilliouin zone that connects two points featuring symmetry-induced degeneracy. The measured large magnitude of the spin splitting of approximately 0.6 eV and the position of the band just below the Fermi energy underscores the significance of altermagnets for spintronics based on robust broken time reversal symmetry responses arising from exchange energy scales, akin to ferromagnets, while remaining insensitive to external magnetic fields and possessing THz dynamics, akin to antiferromagnets.

Finite-momentum Cooper pairing in proximitized altermagnets

Finite-momentum Cooper pairing is an unconventional form of superconductivity that is widely believed to require finite magnetization. Altermagnetism is an emerging magnetic phase with highly anisotropic spin-splitting of specific symmetries, but zero net magnetization. Here, we study Cooper pairing in metallic altermagnets connected to conventional s-wave superconductors. Remarkably, we find that the Cooper pairs induced in the altermagnets acquire a finite center-of-mass momentum, despite the zero net magnetization in the system. This anomalous Cooper-pair momentum strongly depends on the propagation direction and exhibits unusual symmetric patterns. Furthermore, it yields several unique features: (i) highly orientation-dependent oscillations in the order parameter, (ii) controllable 0-π transitions in the Josephson supercurrent, (iii) large-oblique-angle Cooper-pair transfer trajectories in junctions parallel with the direction where spin splitting vanishes, and (iv) distinct Fraunhofer patterns in junctions oriented along different directions. Finally, we discuss the implementation of our predictions in candidate materials such as RuO2 and KRu4O8.

Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2

Altermagnets are an emerging elementary class of collinear 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 time-reversal 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 RuO2 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 interesting phenomena and functionalities in fields ranging from topological matter to spintronics, which are based on the unconventional time-reversal symmetry breaking in altermagnets.

Observation of the Anomalous Hall Effect in a Layered Polar Semiconductor

Progress in magnetoelectric materials is hindered by apparently contradictory requirements for time-reversal symmetry broken and polar ferroelectric electronic structure in common ferromagnets and antiferromagnets. Alternative routes can be provided by recent discoveries of a time-reversal symmetry breaking anomalous Hall effect (AHE) in noncollinear magnets and altermagnets, but hitherto reported bulk materials are not polar. Here, the authors report the observation of a spontaneous AHE in doped AgCrSe2 , a layered polar semiconductor with an antiferromagnetic coupling between Cr spins in adjacent layers. The anomalous Hall resistivity 3μ Ω c m $\mu \Omega \, \textnormal {cm}$ is comparable to the largest observed in compensated magnetic systems to date, and is rapidly switched off when the angle of an applied magnetic field is rotated to ≈80° from the crystalline c-axis. The ionic gating experiments show that the anomalous Hall conductivity magnitude can be enhanced by modulating the p-type carrier density. They also present theoretical results that suggest the AHE is driven by Berry curvature due to noncollinear antiferromagnetic correlations among Cr spins, which are consistent with the previously suggested magnetic ordering in AgCrSe2 . The results open the possibility to study the interplay of magnetic and ferroelectric-like responses in this fascinating class of materials.

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.

Electrical 180° switching of Néel vector in spin-splitting antiferromagnet

Antiferromagnetic spintronics have attracted wide attention due to its great potential in constructing ultradense and ultrafast antiferromagnetic memory that suits modern high-performance information technology. The electrical 180° switching of Néel vector is a long-term goal for developing electrical-controllable antiferromagnetic memory with opposite Néel vectors as binary "0" and "1." However, the state-of-art antiferromagnetic switching mechanisms have long been limited for 90° or 120° switching of Néel vector, which unavoidably require multiple writing channels that contradict ultradense integration. Here, we propose a deterministic switching mechanism based on spin-orbit torque with asymmetric energy barrier and experimentally achieve electrical 180° switching of spin-splitting antiferromagnet Mn5Si3. Such a 180° switching is read out by the Néel vector-induced anomalous Hall effect. On the basis of our writing and readout methods, we fabricate an antiferromagnet device with electrical-controllable high- and low-resistance states that accomplishes robust write and read cycles. Besides fundamental advance, our work promotes practical spin-splitting antiferromagnetic devices based on spin-splitting antiferromagnet.

Broken Kramers Degeneracy in Altermagnetic MnTe

Altermagnetism is a newly identified fundamental class of magnetism with vanishing net magnetization and time-reversal symmetry broken electronic structure. Probing the unusual electronic structure with nonrelativistic spin splitting would be a direct experimental verification of an altermagnetic phase. By combining high-quality film growth and in situ angle-resolved photoemission spectroscopy, we report the electronic structure of an altermagnetic candidate, α-MnTe. Temperature-dependent study reveals the lifting of Kramers degeneracy accompanied by a magnetic phase transition at T_{N}=267  K with spin splitting of up to 370 meV, providing direct spectroscopic evidence for altermagnetism in MnTe.

Altermagnetic surface states: towards the observation and utilization of altermagnetism in thin films, interfaces and topological materials

The altermagnetism influences the electronic states allowing the presence of non-relativistic spin-splittings. Since altermagnetic spin-splitting is present along specific k-paths of the 3D Brillouin zone, we expect that the altermagnetic surface stateswill be present on specific surface orientations. We unveil the properties of the altermagnetic surface states considering three representative materials belonging to the orthorhombic, hexagonal and tetragonal space groups. We calculate the 2D projected Brillouin zone from the 3D Brillouin zone. We study the surfaces with their respective 2D Brillouin zones establishing where the spin-splittings with opposite sign merge annihilating the altermagnetic properties and on which surfaces the altermagnetism is preserved. Looking at the three principal surface orientations, we find that for several cases two surfaces are blind to the altermagnetism, while the altermagnetism survives for one surface orientation. Which surface preserves the altermagnetism depends also on themagnetic order. We qualitatively show that an electric field orthogonal to the blind surface can activate the altermagnetism. Our projection method was proven for strong altermagnetism, but it will be equivalently valid for recently discovered weak altermagnetism. Our results predict which surfaces to cleave in order to preserve altermagnetism in surfaces or interfaces and this paves the way to observe non-relativistic altermagnetic spin-splitting in thin films via spin-resolved ARPES and to interface the altermagnetism with other collective modes. We open future perspectives for the study of altermagnetic effects on the trivial and topological surface states.

Efficient Spin-to-Charge Conversion via Altermagnetic Spin Splitting Effect in Antiferromagnet RuO_{2}

The relativistic spin Hall effect and inverse spin Hall effect enable the efficient generation and detection of spin current. Recently, a nonrelativistic altermagnetic spin splitting effect (ASSE) has been theoretically and experimentally reported to generate time-reversal-odd spin current with controllable spin polarization in antiferromagnet RuO_{2}. The inverse effect, electrical detection of spin current via ASSE, still remains elusive. Here we show the spin-to-charge conversion stemming from ASSE in RuO_{2} by the spin Seebeck effect measurements. Unconventionally, the spin Seebeck voltage can be detected even when the injected spin current is polarized along the directions of either the voltage channel or the thermal gradient, indicating the successful conversion of x- and z-spin polarizations into the charge current. The crystal axes-dependent conversion efficiency further demonstrates that the nontrivial spin-to-charge conversion in RuO_{2} is ascribed to ASSE, which is distinct from the magnetic or antiferromagnetic inverse spin Hall effects. Our finding not only advances the emerging research landscape of altermagnetism, but also provides a promising pathway for the spin detection.