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Recently, MnTe was established as an altermagnetic material that hosts spin-polarized electronic bands as well as anomalous transport effects like the anomalous Hall effect. In addition to these effects arising from altermagnetism, MnTe also hosts other magnetoresistance effects. Here, we study the manipulation of the magnetic order by an applied magnetic field and its impact on the electrical resistivity. In particular, we establish which components of anisotropic magnetoresistance are present when the magnetic order is rotated within the hexagonal basal plane. Our experimental results, which are in agreement with our symmetry analysis of the magnetotransport components, showcase the existence of an anisotropic magnetoresistance linked to both the relative orientation of current and magnetic order, as well as crystal and magnetic order.

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., Comment: 18 pages, 5 figures

The Edelstein effect is the origin of the spin-orbit torque: a current-induced torque that is used for the electrical control of ferromagnetic and antiferromagnetic materials. This effect originates from the relativistic spin-orbit coupling, which necessitates utilizing materials with heavy elements. Here we show that in magnetic materials with non-collinear magnetic order, the Edelstein effect and consequently also a current-induced torque can exist even in the absence of the spin-orbit coupling. Using group symmetry analysis, model calculations, and realistic simulations on selected compounds, we identify large classes of non-collinear magnet candidates and demonstrate that the current-driven torque is of similar magnitude as the celebrated spin-orbit torque in conventional transition metal structures. We also show that this torque can exist in an insulating material, which could allow for highly efficient electrical control of magnetic order., Comment: 11 pages, 5 figues

Resistance of certain (conductive and otherwise isotropic) ferromagnets turns out to exhibit anisotropy with respect to the direction of magnetisation: R$_\parallel$ different from R$_\perp$ with reference to the electric current direction. This century-old phenomenon is reviewed both from the perspective of materials and physical mechanisms involved. More recently, this effect has also been extended to antiferromagnets. This opens the possibility for industrial applications reaching far beyond the current ones, e.g. hard drive read heads or position sensors., Comment: 50 pages (excl. references), 16 figures

Anomalous Hall effect in very clean samples (high conductivity regime) is studied using a two-dimensional network model. We find that the off-diagonal conductivity comprises two parts: one which reflects the bulk properties as obtained by the Kubo formula and another which is sensitive to boundary conditions imposed on the network. The latter scales with the system width in the ideal case and for real-world samples, it will depend on the coherence length. It provides an alternative interpretation of the observed behaviour in the clean limit which is otherwise attributed to the skew scattering. We highlight analogies to friction in viscous fluids responsible for Couette flow., Comment: to appear in PRB

An effective model of the hexagonal (NiAs-structure) manganese telluride valence band in the vicinity of the A-point of the Brillouin zone is derived. It is shown that while for the usual antiferromagnetic order (magnetic moments in the basal plane) band splitting at A is small, their out-of-plane rotation enhances the splitting dramatically (to about 0.5 eV). We propose extensions of recent experiments (Moseley et al., Phys. Rev. Materials 6, 014404) where such inversion of magnetocrystalline anisotropy has been observed in Li-doped MnTe, to confirm this unusual sensitivity of a semiconductor band structure to magnetic order., Comment: 5+epsilon pages, 4 figures; to appear in PRB

We report on an infrared magneto-spectroscopy study of Pb$_{1-x}$Sn$_x$Se, a topological crystalline insulator. We have examined a set of samples, all in the inverted regime of electronic bands, with the tin composition varying from $x=0.2$ to $0.33$. Our analysis shows that the observed response, composed of a series of interband inter-Landau level excitations, can be interpreted and modelled using the relativistic-like Hamiltonian for three-dimensional massive Dirac electrons, expanded to include diagonal quadratic terms that impose band inversion. In our data, we have not found any clear signature of massless electron states that are present on the surface of Pb$_{1-x}$Sn$_x$Se crystals in the inverted regime. Reasons for this unexpected result are discussed., Comment: 11 pages, 7 figures, to be published in Phys. Rev. B

Ferromagnetic Co$_2$MnGa has recently attracted significant attention due to effects related to non-trivial topology of its band structure, however a systematic study of canonical magneto-galvanic transport effects is missing. Focusing on high quality thin films, here we systematically measure anisotropic magnetoresistance (AMR) and its thermoelectric counterpart (AMTP). We model the AMR data by free energy minimisation within the Stoner-Wohlfarth formalism and conclude that both crystalline and non-crystalline components of this magneto-transport phenomenon are present in Co$_2$MnGa. Unlike the AMR which is small in relative terms, the AMTP is large due to a change of sign of the Seebeck coefficient as a function of temperature. This fact is discussed in the context of the Mott rule and further analysis of AMTP components is presented., Comment: 19 pages, 5 figures

The interest in understanding scaling limits of magnetic textures such as domain walls spans the entire field of magnetism from its relativistic quantum fundamentals to applications in information technologies. The traditional focus of the field on ferromagnets has recently started to shift towards antiferromagnets which offer a rich materials landscape and utility in ultra-fast and neuromorphic devices insensitive to magnetic field perturbations. Here we report the observation that domain walls in an epitaxial crystal of antiferromagnetic CuMnAs can be atomically sharp. We reveal this ultimate domain wall scaling limit using differential phase contrast imaging within aberrationcorrected scanning transmission electron microscopy, which we complement by X-ray magnetic dichroism microscopy and ab initio calculations. We highlight that the atomically sharp domain walls are outside the remits of established spin-Hamiltonian theories and can offer device functionalities unparalleled in ferromagnets., Comment: 8 pages, 4 figures, Supplementary information

Anisotropic magnetoresistance (AMR) is a ubiquitous and versatile probe of magnetic order in contemporary spintronics research. Its origins are usually ascribed to extrinsic effects (i.e. spin-dependent electron scattering), whereas intrinsic (i.e. scattering-independent) contributions are neglected. Here, we measure AMR of polycrystalline thin films of the standard ferromagnets Co, Ni, Ni81Fe19 and Ni50Fe50 over the frequency range from DC to 28 THz. The large bandwidth covers the regimes of both diffusive and ballistic intraband electron transport and, thus, allows us to separate extrinsic and intrinsic AMR components. Analysis of the THz response based on Boltzmann transport theory reveals that the AMR of the Ni, Ni81Fe19 and Ni50Fe50 samples is of predominantly extrinsic nature. However, the Co thin film exhibits a sizeable intrinsic AMR contribution, which is constant up to 28 THz and amounts to more than 2/3 of the DC AMR contrast of 1%. These features are attributed to the hexagonal structure of the Co crystallites. They are interesting for applications in terahertz spintronics and terahertz photonics. Our results show that broadband terahertz electromagnetic pulses provide new and contact-free insights into magneto-transport phenomena of standard magnetic thin films on ultrafast time scales.

In hydrogen bonded systems, nuclear quantum effects such as zero-point motion and tunneling can significantly affect their material properties through underlying physical and chemical processes. Presently, direct observation of the influence of nuclear quantum effects on the strength of hydrogen bonds with resulting structural and electronic implications remains elusive, leaving opportunities for deeper understanding to harness their fascinating properties. We studied hydrogen-bonded one-dimensional quinonediimine molecular networks which may adopt two isomeric electronic configurations via proton transfer. Herein, we demonstrate that concerted proton transfer promotes a delocalization of {\pi}-electrons along the molecular chain, which enhances the cohesive energy between molecular units, increasing the mechanical stability of the chain and giving rise to new electronic in-gap states localized at the ends. These findings demonstrate the identification of a new class of isomeric hydrogen bonded molecular systems where nuclear quantum effects play a dominant role in establishing their chemical and physical properties. We anticipate that this work will open new research directions towards the control of mechanical and electronic properties of low-dimensional molecular materials via concerted proton tunneling.

Electrical spin-current generation is among the core phenomena driving the field of spintronics. Using {\em ab initio} calculations we show that a room-temperature metallic collinear antiferromagnet RuO$_2$ allows for highly efficient spin-current generation, arising from anisotropically-split bands with conserved up and down spins along the N\'eel vector axis. The zero net moment antiferromagnet acts as an electrical spin-splitter with a 34$^\circ$ propagation angle between spin-up and spin-down currents. Correspondingly, the spin-conductivity is a factor of three larger than the record value from a survey of 20,000 non-magnetic spin-Hall materials. We propose a versatile spin-splitter-torque concept utilizing antiferromagnetic RuO$_2$ films interfaced with a ferromagnet., Comment: 6 pages, 4 figures

Noncollinear magnetic moments in antiferromagnets (AFM) lead to a complex behavior of electrical transport, even to a decreasing resistivity due to an increasing temperature. Proper treatment of such phenomena is required for understanding AFM systems at finite temperatures; however first-principles description of these effects is complicated. With ab initio techniques, we investigate three models of spin fluctuations (magnons) influencing the transport in AFM CuMnAs; the models are numerically feasible and easily implementable to other studies. We numerically justified a fully relativistic collinear disordered local moment approach and we present its uncompensated generalization. A saturation or a decrease of resistivity caused by magnons, phonons, and their combination (above approx. 400 K) was observed and explained by changes in electronic structure. Within the coherent potential approximation, our finite-temperature approaches may be applied also to systems with impurities, which are found to have a large impact not only on residual resistivity, but also on canting of magnetic moments from the AFM to the ferromagnetic (FM) state., Comment: 25 pages, 8 figures, 2 tables; accepted version to JMMM

Helical edge states appear at the surface of two dimensional topological insulators and are characterized by spin up traveling in one direction and the spin down traveling in the opposite direction. Such states are protected by time reversal symmetry and no backscattering due to scalar impurities can occur. However, magnetic impurities break time reversal symmetry and lead to backscattering. Often their presence is unintentional, but in some cases they are introduced into the sample to open up gaps in the spectrum. We investigate the influence of random impurities on helical edge states, specifically how the gap behaves in the realistic case of impurities having both a magnetic and a scalar component. It turns out that for a fixed magnetic contribution the gap closes when either the scalar component, or Fermi velocity is increased. We compare diagrammatic techniques in the self-consistent Born approximation to numerical calculations which yields good agreement. For experimentally relevant parameters we find that even moderate scalar components can be quite detrimental for the gap formation., Comment: 6 pages, 6 figures

We compare GGA+U calculations with available experimental data and analyze the origin of magnetic anisotropies in MnF$_2$, FeF$_2$, CoF$_2$, and NiF$_2$. We confirm that the magnetic anisotropy of MnF$_2$ stems almost completely from the dipolar interaction, while magnetocrystalline anisotropy energy plays a dominant role in the other three compounds, and discuss how it depends on the details of band structure. The latter is critically compared to available optical measurements. The case of CoF$_2$, where magnetocrystalline anisotropy energy strongly depends on $U$, is put into contrast with FeF$_2$ where theoretical predictions of magnetic anisotropies are nearly quantitative., Comment: 9 pages, 8 figures, and 3 appendices

Conventional understanding implies that the ground state of a nonmagnetic quantum mechanical system should be nodeless. While this notion also provides a valuable guidance in understanding the ordering of energy levels in semiconductor nanostructures, there are reports that $\textit{nodal}$ ground states for holes are possible. However, the existence of such nodal states has been debated and even viewed merely as an artifact of a $\boldsymbol{k{\cdot}p}$ model. Using complementary approaches of both $\boldsymbol{k{\cdot}p}$ and tight-binding models, further supported by an effective Hamiltonian for a continuum model, we reveal that the nodal ground states in quantum dots are not limited to a specific approach. Remarkably, the emergence of the nodal hole states at the top of the valence band can be attributed to the formation of the orbital vortex textures through competition between the hole kinetic energy and the coupling to the conduction band states. We suggest an experimental test for our predictions of the reversed energy ordering and the existence of nodal ground states. We discuss how our findings and the studies of orbital textures could be also relevant for other materials systems., Comment: 19 pages, 14 figures, submitted to PRB, identical to v2 with pdf compatibility issue of figures resolved

The usefulness of semiconductor lasers is often limited by the undesired frequency modulation, or chirp, a direct consequence of the intensity modulation and carrier dependence of the refractive index in the gain medium. In spin-lasers, realized by injecting, optically or electrically, spin-polarized carriers, we elucidate paths to tailoring chirp. We provide a generalized expression for chirp in spin-lasers and introduce modulation schemes that could simultaneously eliminate chirp and enhance the bandwidth, as compared to the conventional (spin-unpolarized) lasers., Comment: 4 pages, 3 figures

Magnetic anisotropies in quantum dots (QDs) doped with magnetic ions are discussed in terms of two frameworks: anisotropic $g$-factors and magnetocrystalline anisotropy energy. It is shown that even a simple model of zinc-blende p-doped QDs displays a rich diagram of magnetic anisotropies in the QD parameter space. Tuning the confinement allows to control magnetic easy axes in QDs in ways not available for the better-studied bulk., Comment: submitted to PRB

Starting with a microscopic model based on the Kohn-Luttinger Hamiltonian and kinetic p-d exchange combined with Boltzmann formula for conductivity we identify the scattering from magnetic Mn combined with the strong spin-orbit interaction of the GaAs valence band as the dominant mechanism of the anisotropic magnetoresistance (AMR) in (Ga,Mn)As. This fact allows to construct a simple analytical model of the AMR consisting of two heavy-hole bands whose charge carriers are scattered on the impurity potential of the Mn atoms. The model predicts the correct sign of the AMR (resistivity parallel to magnetization is smaller than perpendicular to magnetization) and identifies its origin arising from the destructive interference between electric and magnetic part of the scattering potential of magnetic ionized Mn acceptors when the carriers move parallel to the magnetization., Comment: 9 pages, 3 figs, subm to PRB

Anisotropic magnetoresistance (AMR) is a relativistic magnetotransport phenomenon arising from combined effects of spin-orbit coupling and broken symmetry of a ferromagnetically ordered state of the system. In this work we focus on one realization of the AMR in which spin-orbit coupling enters via specific spin-textures on the carrier Fermi surfaces and ferromagnetism via elastic scattering of carriers from polarized magnetic impurities. We report detailed heuristic examination, using model spin-orbit coupled systems, of the emergence of positive AMR (maximum resistivity for magnetization along current), negative AMR (minimum resistivity for magnetization along current), and of the crystalline AMR (resistivity depends on the absolute orientation of the magnetization and current vectors with respect to the crystal axes) components. We emphasize potential qualitative differences between pure magnetic and combined electro-magnetic impurity potentials, between short-range and long-range impurities, and between spin-1/2 and higher spin-state carriers. Conclusions based on our heuristic analysis are supported by exact solutions to the integral form of the Boltzmann transport equation in archetypical two-dimensional electron systems with Rashba and Dresselhaus spin-orbit interactions and in the three-dimensional spherical Kohn-Littinger model. We include comments on the relation of our microscopic calculations to standard phenomenology of the full angular dependence of the AMR, and on the relevance of our study to realistic, two-dimensional conduction-band carrier systems and to anisotropic transport in the valence band of diluted magnetic semiconductors., Comment: 15 pages, Kohn-Littinger model added

We present a study of transport in multiple-band non-interacting Fermi metallic systems based on the Keldysh formalism, taking into account the effects of Berry curvature due to spin-orbit coupling. We apply this formalism to a Rashba 2DEG ferromagnet and calculate the anomalous Hall effect (AHE) and anisotropic magnetoresistance (AMR). The numerical calculations reproduce analytical results in the metallic regime revealing the crossover between the skew scattering mechanism dominating in the clean systems and intrinsic mechanism dominating in the moderately dirty systems. As we increase the disorder further, the AHE starts to diminish due to the spectral broadening of the quasiparticles. Although for certain parameters this reduction of the AHE can be approximated as $\sigma_{xy}\thicksim\sigma_{xx}^{\varphi}$ with $\varphi$ varying around 1.6, this is found not to be true in general as $\sigma_{xy}$ can go through a change in sign as a function of disorder strength in some cases. The reduction region in which the quasiparticle approximation is meaningful is relatively narrow; therefore, a theory with a wider range of applicability is called for. By considering the higher order skew scattering processes, we resolve some discrepancies between the AHE results obtained by using the Keldysh, Kubo and Boltzmann approaches. We also show that similar higher order processes are important for the AMR when the nonvertex and vertex parts cancel each other. We calculate the AMR in anisotropic systems properly taking into account the anisotropy of the non-equilibrium distribution function. These calculations confirm recent findings on the unreliability of common approximations to the Boltzmann equation., Comment: 21 pages, 14 figures

We present a procedure for finding the exact solution to the linear-response Boltzmann equation for two-dimensional anisotropic systems and demonstrate it on examples of non-crystalline anisotropic magnetoresistance in a system with spin-orbit interaction. We show that two decoupled integral equations must be solved in order to find the non-equilibrium distribution function up to linear order in the applied electric field. The examples are all based on the Rashba system with charged magnetic scatterers, a system where the non-equilibrium distribution function and anisotropic magnetoresistance can be evaluated analytically. Exact results are compared to earlier widely-used approximative approaches. We find circumstances under which approximative approaches may become unreliable even on a qualitative level., Comment: submitted to PRB

We present the analytical description of the anomalous Hall effect (AHE) in a 2DEG ferromagnet within the Keldysh formalism. These results unify all three linear response approaches to anomalous Hall transport and close a long standing debate. We are able to identify a new extrinsic AHE regime dominated by a hybrid skew scattering mechanism. This new contribution is inversely proportional to the impurity concentration, resembling the normal skew scattering, {\em but} independent of the impurity-strength, resembling the side-jump mechanism. Within the Kubo formalism this regime is captured by higher order diagrams which, although weak, dominate when both subbands are occupied; this regime can be detected by variable remote doping experiments that we describe., Comment: 5 pages, 2 figures

Using exact diagonalization we examine the response of several most prominent fractional quantum Hall states to a single local impurity. The 2/3 singlet state is found to be more inert than the polarized one in spite of its smaller incompressibility gap. Based on its spin-spin correlation functions we interpret it as a liquid of electron pairs with opposite spin. A comparison of different types of impurities, non-magnetic and magnetic, is presented., Comment: 6 pages, 9 figures, submitted to PRB

A system at filling factor 2/3 could be a candidate for a quantum Hall ferromagnet at integer filling factor of composite fermions. Using exact diagonalization with electrons on a torus we study the transition from the singlet ground state to the polarized ground state at this filling and look for signatures of quantum Hall ferromagnetism. Differences between the fractional and corresponding integer systems are emphasised. Most interestingly, we find around the transition a low excited half-polarized state which might become the ground state in the thermodynamical limit. We study its structure and compare it to the singlet and polarized ground states. A new interpretation of the singlet state is suggested and comparison of the filling factors 2/3 and 2/5 is presented. Adding magnetic inhomogeneities into the system we investigate the stability of all the three involved states and the tendency to build up domains like in conventional ferromagnets., Comment: 97 pages, 69 figures, submitted to Annalen der Physik

Common models describing magnetotransport properties of periodically modulated two--dimensional systems often either directly start from a semiclassical approach or give results well conceivable within the semiclassical framework. Recently, magnetoresistance oscillations have been found on samples with strong unilateral modulation and short period (d=15 nm) which cannot be explained on a semiclassical level (magnetic breakdown). We use a simple fully quantum mechanical model which gives us both magnetoresistance data nicely comparing to the experiments and a good intuitive insight into the effects taking place in the system., Comment: 7 pages, 5 figures, LaTeX, iopart, in proceedings of the 26th ICPS

The linear response theory is used to describe magnetoresistance oscillations of short-period unilateral superlattices with strong modulation (or alternatively arrays of coupled quantum wires). The semiclassical description of this system fails for strong magnetic fields (magnetic breakdown) and we employ a simple fully-quantum-mechanical tight-binding model in conjunction with Kubo's formula instead. The resulting magnetoresistance data nicely compare to the experiments while the model opens good intuitive insight into the effects taking place in the system., Comment: 8 pages, 8 figures, submitted to PRB