In ferromagnets, the anomalous Hall effect (AHE) can exhibit time-dependent relaxation, including magnetic aftereffect and Barkhausen jumps, and thus provide insights into magnetic susceptibility and domain dynamics. Recently, a finite AHE has also been reported in compensated collinear magnets-termed altermagnets-which, due to their spin and crystal symmetries, combine properties usually attributed to either ferromagnets or antiferromagnets. To date, a possible time-dependent relaxation of the AHE in altermagnets has not been explored. Here, we study the Hall effect response of micrometer-scale Hall bars patterned into thin films of Mn5Si3, an altermagnet featuring a finite spontaneous AHE. Recording transport data as a function of time, at a fixed magnetic field magnitude, we observe a relaxation of the Hall voltage qualitatively and quantitatively similar to the magnetic aftereffect in ferromagnetic films. In addition, the Hall voltage time traces feature clear unidirectional jumps, which we interpret as Barkhausen jumps, i.e., as experimental evidence for abrupt reorientations of Hall vector domains in Mn5Si3. A quantitative analysis yields a Barkhausen length of around 18 nm in the Hall bar devices with the smallest width of 100 nm.

The injection, propagation and detection of spin currents are essential physical processes in spintronics. So far, the separation of charge and spin currents was facilitated by the electrical spin injection from a ferromagnet (FM) or the injection by a relativistic spin Hall effect. The devices employed are lateral spin valves comprising spatially separated injection and detection electrodes, connected by a spin-propagation channel. The time-reversal symmetry (TRS) breaking FM spin injection is realized in a geometry with an electrical bias applied between the injection electrode and the channel and is modelled by a conserved spin-polarized drift current. In contrast, the spin injection by the T-symmetric relativistic spin Hall mechanism is driven by an electrical bias applied across the injection electrode alone, and is modelled by a non-conserved spin current transverse to the applied bias. In this work, we use a lateral spin valve with a Mn5Si3 injection electrode to directly demonstrate a TRS-breaking spin injection from a compensated magnet with a vanishing net magnetization. Specifically, the TRS-breaking is demonstrated by the fact that switching between time-reversed states of the compensated magnet changes the detected spin signal. Moreover, the TRS-breaking nature of the spin injection is observed in both experimental geometries with the different electrical biasing, while using the same detection electrode. We show that this unconventional spin-injection is consistent with different magnitudes and propagation angles of electrical currents in the spin-up and spin-down channel in a d-wave altermagnet. Here our symmetry analysis and first-principles calculations are based on the compensated collinear altermagnetic order which has provided a comprehensive microscopic interpretation of earlier structural, magnetic, and anomalous Hall and Nernst measurements in Mn5Si3 thin films.

Altermagnetism as a third distinct type of collinear magnetic ordering lately attracts vivid attention. We here study the Hall effect response of micron-scale Hall bars patterned into Mn5Si3 thin films, an altermagnet candidate material. Recording transport data as a function of time, at fixed magnetic field magnitude, we observe a time-dependent relaxation of the Hall voltage qualitatively and quantitatively similar to the magnetic viscosity response well established in ferromagnetic films. In addition, the Hall voltage time traces feature clear unilateral steps, which we interpret as Barkhausen steps, i.e., as experimental evidence for abrupt reorientations of magnetic (Hall vector) domains in the altermagnetic candidate material. A quantitative analysis yields a Barkhausen length of around 18nm in the Hall bar devices with the smallest width of 100 nm.

The anomalous Nernst effect generates transverse voltage to the applied thermal gradient in magnetically ordered systems. The effect was previously considered excluded in compensated magnetic materials with collinear ordering. However, in the recently identified class of compensated magnetic materials, dubbed altermagnets, time-reversal symmetry breaking in the electronic band structure makes the presence of the anomalous Nernst effect possible despite the collinear spin arrangement. In this work, we investigate epitaxial Mn5Si3 thin films known to be an altermagnetic candidate. We show that the material manifests a sizable anomalous Nernst coefficient despite the small net magnetization of the films. The measured magnitudes of the anomalous Nernst coefficient reach a scale of microVolts per Kelvin. We support our magneto-thermoelectric measurements by density-functional theory calculations of the material's spin-split electronic structure, which allows for the finite Berry curvature in the reciprocal space. Furthermore, we present our calculations of the intrinsic Berry-curvature Nernst conductivity, which agree with our experimental observations.

The component of the resistivity tensor ρij corresponding to voltage transverse to both an applied current and a magnetic field can be separated into odd and even parts with respect to the applied magnetic field. The former contains information, for example, about the ordinary or anomalous Hall effect. The latter is often ascribed to experimental artifacts and ignored. Here, we show that upon suppressing these artifacts in carefully controlled experiments, useful information remains. We first investigate the well-explored ferromagnet CoFeB, where the even part of ρyx contains a contribution from the anisotropic magnetoresistance, which we confirm by Stoner–Wohlfarth modeling. We then apply our approach to magnetotransport measurements of Mn5Si3 thin films, which undergo a transition from non-collinear to an altermagnetic collinear state. In this material, the even part of the transverse signal is sizable only in the low-spin-symmetry phase below ≈80 K. Transverse resistivity measurements thus offer a simple and readily available probe of magnetic order transitions.

Slow magnetization relaxation processes are an important time-dependent property of many magnetic materials. We show that magnetotransport measurements based on a well-established current-reversal method can be utilized to implement a simple and robust screening scheme for such relaxation processes. We demonstrate our approach considering the anomalous Hall effect in a Pt/Co/AlOx trilayer model system, and then explore relaxation in tau-MnAl films. Compared to magnetotransport experiments based on ac lock-in techniques, we find that the dc current-reversal method is particularly sensitive to relaxation processes which happen on timescales on the order of few to many seconds.

Topologically protected magnetic states in condensed matter physics, particularly antiferromagnetic (AFM) skyrmions (Sks) and bimerons (Bms), offer promising prospects for terahertz dynamics and sustained current-induced motion, thanks to their compensating multiple sub-lattice structure. However, nucleating AFM Sks and Bms is challenging due to the lack of net magnetization. Previous attempts to imprint pre-defined Sks and Bms in a ferromagnet (FM) and transfer them to an AFM using interfacial exchange bias in FM/AFM heterostructures have been hindered by complex multilayers with discontinuities, polycrystallinity, or multipartite chiral AFMs. Employing atomistic spin simulations, we demonstrate the viability of texture imprinting for nucleating Sks and Bms in AFMs, using a prototypical bipartite AFM layer in a multilayer structure free from discontinuities. Such imprinting is a crucial step towards understanding the static and dynamic properties of natural antiferromagnetic textures and their unique properties.

The altermagnet candidate Mn5Si3 has attracted wide attention in the context of nonrelativistic spin physics, due to its composition of light elements. In this study, we demonstrate a hallmark of altermagnetism in Mn5Si3 thin films, namely the three options, or variants, for the checkerboard distribution of the magnetic Mn atoms. The magnetic symmetries were altered by field-rotation of the N & eacute;el vector along relevant crystal directions, resulting in anomalous Hall effect anisotropy. The experimental results in nanoscale devices were corroborated by a theoretical model involving atomic site dependent anisotropy and bulk Dzyaloshinskii-Moriya interaction for a single variant. These findings elevate Mn5Si3 from a candidate to a proven altermagnet.

Altermagnets are compensated magnets belonging to spin symmetry groups that allow alternating spin polarizations both in the coordinate space of the crystal and in the momentum space of the electronic structure. In these materials the anisotropic local crystal environment of the different sublattices lowers the symmetry of the system so that the opposite-spin sublattices are connected only by rotations, which results in an unconventional spin-polarized band structure in the momentum space. This low symmetry of the crystal structure is expected to be reflected in the anisotropy of the anomalous Hall effect. In this work, we study the anisotropy of the anomalous Hall effect in epitaxial thin films of Mn$_5$Si$_3$, an altermagnetic candidate material. We first demonstrate a change in the relative N\'eel vector orientation when rotating the external field orientation through systematic changes in both the anomalous Hall effect and the anisotropic longitudinal magnetoresistance. We then show that the anomalous Hall effect in this material is anisotropic with the N\'eel vector orientation relative to the crystal structure and that this anisotropy requires high crystal quality and unlikely correlates with the magnetocrystalline anisotropy. Our results provide further systematic support to the case for considering epitaxial thin films of Mn$_5$Si$_3$ as an altermagnetic candidate material.

Phases with spontaneous time-reversal ( T ) symmetry breaking are sought after for their anomalous physical properties, low-dissipation electronic and spin responses, and information-technology applications. Recently predicted altermagnetic phase features an unconventional and attractive combination of a strong T -symmetry breaking in the electronic structure and a zero or only weak-relativistic magnetization. In this work, we experimentally observe the anomalous Hall effect, a prominent representative of the T -symmetry breaking responses, in the absence of an external magnetic field in epitaxial thin-film Mn5Si3 with a vanishingly small net magnetic moment. By symmetry analysis and first-principles calculations we demonstrate that the unconventional d-wave altermagnetic phase is consistent with the experimental structural and magnetic characterization of the Mn5Si3 epilayers, and that the theoretical anomalous Hall conductivity generated by the phase is sizable, in agreement with experiment. An analogy with unconventional d-wave superconductivity suggests that our identification of a candidate of unconventional d-wave altermagnetism points towards a new chapter of research and applications of magnetic phases.

The detection of a voltage transverse to both an applied current and a magnetic field is one of the most common characterization techniques in solid-state physics. The corresponding component of the resistivity tensor $\rho_{ij}$ can be separated into odd and even parts with respect to the applied magnetic field. The former contains information, for example, about the ordinary or anomalous Hall effect. The latter is typically ascribed to experimental artefacts and ignored. We here show that upon suppressing these artefacts in carefully controlled experiments, useful information remains. We first investigate the well-explored ferromagnet CoFeB, where the even part of $\rho_{yx}$ contains a contribution from the anisotropic magnetoresistance, which we confirm by Stoner-Wohlfarth modelling. We then apply our approach to magnetotransport measurements in $\rm Mn_5Si_3$ thin films with a complex compensated magnetic order. In this material, the even part of the transverse signal is sizable only in the low-spin-symmetry phase below $\approx 80$ K and thus offers a simple and readily available probe of the magnetic order.

Some magnetically ordered phases of the Mn5Si3 crystal are proving to be prototypes for the study of the new fundamental spin physics related to the spontaneous breaking of the time-reversal symmetry despite a zero net magnetization. Here, we report on a route to grow epitaxial Mn5Si3 thin films on Si(111). To this end, we use Mn and Si codeposition in a molecular beam epitaxy system and carefully tune the deposition rates, the growth temperature, and the annealing temperature. We assessed the silicide phase-formation and morphology using reflection high-energy electron diffraction, x-ray diffraction, high-resolution transmission electron mi-croscopy (HRTEM) and atomic force microscopy. Layers containing only Mn5Si3 could be stabilized under very restrictive conditions, by tuning the Mn/Si flux ratio to match the compound stoichiometry and adjusting the substrate temperature during growth to 443 K. HRTEM imaging revealed the existence of an interfacial amorphous layer of few nanometers thickness. Annealing the heterostructure up to 573 K led to the formation of MnSi at the vicinity of the Mn5Si3/Si(111) interface, which significantly reduced the nucleation barrier of Mn5Si3. High-quality crystalline Mn5Si3 thin films were then formed with the following epitaxial relationships: Mn5Si3(0001)[01 (1) over bar 0]//MnSi(111)[(2) over bar 11]//Si(111)[1 $(1) over bar $0]. Our experiments showed that the formation of MnSi is enhanced at a growth temperature above 473 K or for a longer annealing step, while the crystalline quality of the Mn5Si3 overlayer is correspondingly degraded leading to textured thin films. The growth pathways and structural properties of the manganese silicides can be rationalized in terms of reactions maximizing the free-energy lowering rate. Moreover, we found that the magnetic and the magnetotransport properties can be used as an efficient tool to track both Mn5Si3 crystallinity and proportion in the deposited layers.

Controlling the magnetic order of antiferromagnets is challenging due to their vanishing net magnetization. For this reason, the study of local spin textures in antiferromagnets is restricted by the difficulty in nucleating such states. Here, using atomistic simulations we demonstrate a method for nucleating localized spin textures in the grains of thin film antiferromagnet, $\gamma$-IrMn$_3$. Utilising the exchange bias coupling between a ferromagnet and an antiferromagnet, we set the spin texture in the latter from a predefined spin texture in the former by means of a thermal cycling procedure. The local textures set in the antiferromagnetic grains are shown to be stable against field perturbations. We also discuss how various material parameters affect the efficiency of the setting and the characteristics of these set textures. The setting of antiferromagnetic spin textures provides a potential route to antiferromagnetic spintronic devices with non-collinear spin states such as skyrmions, bubbles and domain walls.

In antiferromagnets, the efficient transport of spin-waves has until now only been observed in the insulating antiferromagnet hematite, where circularly (or a superposition of pairs of linearly) polarized spin-waves diffuse over long distances. Here, we report long-distance spin-transport in the antiferromagnetic orthoferrite YFeO3, where a different transport mechanism is enabled by the combined presence of the Dzyaloshinskii-Moriya interaction and externally applied fields. The magnon decay length is shown to exceed hundreds of nanometers, in line with resonance measurements that highlight the low magnetic damping. We observe a strong anisotropy in the magnon decay lengths that we can attribute to the role of the magnon group velocity in the transport of spin-waves in antiferromagnets. This unique mode of transport identified in YFeO3 opens up the possibility of a large and technologically relevant class of materials, i.e., canted antiferromagnets, for long-distance spin transport.

Control over spin transport in antiferromagnetic systems is essential for future spintronic applications with operational speeds extending to ultrafast time scales. Here, we study the transition from the gigahertz (GHz) to terahertz (THz) regime of spin transport and spin-to-charge current conversion (S2C) in the prototypical antiferromagnet IrMn by employing spin pumping and THz spectroscopy techniques. We reveal a factor of 4 shorter characteristic propagation lengths of the spin current at THz frequencies (~ 0.5 nm) as compared to the GHz regime (~ 2 nm) which may be attributed to the ballistic and diffusive nature of electronic spin transport, respectively. The conclusion is supported by an extraction of sub-picosecond temporal dynamics of the THz spin current. We also report on a significant impact of the S2C originating from the IrMn/non-magnetic metal interface which is much more pronounced in the THz regime and opens the door for optimization of the spin control at ultrafast time scales.

The link between magnetization and Spin Hall Effect (SHE) has remained mostly unclear for now. In a first part of this contribution, we study oh the presence of the magnetization affect the SHE, by performing in the weak ferromagnet NiCu Spin Pumping-FMR measurements across the ferromagnetic / paramagnetic critical temperature. We show that the high spin Hall effects which can be obtained in 3d ferromagnets seems to be independent of the magnetic phase. In a second part, we show that the spin absorption process in a ferromagnetic material depends on the spin orientation relative to the magnetization. Using a ferromagnet to absorb the pure spin current created within a lateral spin valve, we evidence and quantify a sizable orientation dependence of the spin absorption in Co, CoFe, and NiFe. These experiments allow us to determine the spin-mixing conductance, an elusive but fundamental parameter of the spin-dependent transport.