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We discuss spin-wave transport in anisotropic ferromagnets with an emphasis on the zeroes of the band edges as a function of a magnetic field. An associated divergence of the magnon spin should be observable by enhanced magnon conductivities in non-local experiments, especially in two-dimensional ferromagnets.

The duality between electric and magnetic dipoles in electromagnetism only partly applies to condensed matter. In particular, the elementary excitations of the magnetic and ferroelectric orders, namely magnons and ferrons, respectively, have received asymmetric attention from the condensed matter community in the past. In this perspective, we introduce and summarize the current state of the budding field of "ferronics" and speculate about its potential applications in thermal, information, and communication technology., Comment: To be published as invited "Perspective" in Physical Review Applied

The duality between the electric and magnetic dipoles inspires recent comparisons between ferronics and magnonics. Here we predict surface polarization waves or ``ferrons" in ferroelectric insulators, taking the long-range dipolar interaction into account. We predict properties that are strikingly different from the magnetic counterpart, \textit{i.e.} the surface ``Damon-Eshbach" magnons in ferromagnets. The dipolar interaction pushes the ferron branch with locked circular polarization and momentum to the ionic plasma frequency. The low-frequency modes are on the other hand in-plane polarized normal to their wave vectors. The strong anisotropy of the lower branch renders directional emissions of electric polarization and chiral near fields when activated by a focused laser beam, allowing optical routing in ferroelectric devices., Comment: 7 pages, 3 figures

Van der Waals materials are a new platform to study two-dimensional systems, including magnetic order. Since the number of spins is relatively small, measuring the magnetization is challenging. Here we report spin Hall magnetoresistance (SMR) up to room temperature caused by the magnetic surface texture of exfoliated flakes of magnetic van der Waals materials. For the antiferromagnet FePS3 the SMR amounts to 0.1 % for an applied magnetic field of 7 T at 5 K which implies a substantial canting of the magnetic moments relative to the colinear antiferromagnetic order. The canting is substantial even for a magnetic field along the N\'eel vector, which illustrates the unique power of the SMR to detect magnetic surface textures in van der Waals magnets.

Conductivities are key material parameters that govern various types of transport (electronic charge, spin, heat etc.) driven by thermodynamic forces. Magnons, the elementary excitations of the magnetic order, flow under the gradient of a magnon chemical potential in proportion to a magnon (spin) conductivity $\sigma_{m}$. The magnetic insulator yttrium iron garnet (YIG) is the material of choice for efficient magnon spin transport. Here we report an unexpected giant $\sigma_{m}$ in record-thin YIG films with thicknesses down to 3.7 nm when the number of occupied two-dimensional (2D) subbands is reduced from a large number to a few, which corresponds to a transition from 3D to 2D magnon transport. We extract a 2D spin conductivity ($\approx1$ S) at room temperature, comparable to the (electronic) spin conductivity of the high-mobility two-dimensional electron gas in GaAs quantum wells at millikelvin temperatures. Such high conductivities offer unique opportunities to develop low-dissipation magnon-based spintronic devices.

Magnonics is a field of science that addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operations in the GHz-to-THz frequency range, utilization of nonlinear and nonreciprocal phenomena, and compatibility with CMOS are just a few of many advantages offered by magnons. Although magnonics is still primarily positioned in the academic domain, the scientific and technological challenges of the field are being extensively investigated, and many proof-of-concept prototypes have already been realized in laboratories. This roadmap is a product of the collective work of many authors that covers versatile spin-wave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with Boolean digital data, unconventional approaches like neuromorphic computing, and the progress towards magnon-based quantum computing. The article is organized as a collection of sub-sections grouped into seven large thematic sections. Each sub-section is prepared by one or a group of authors and concludes with a brief description of the current challenges and the outlook of the further development of the research directions., Comment: 74 pages, 57 figures, 500 references

We report on spin Hall magnetoresistance (SMR) and spin Seebeck effect (SSE) in single crystal of the rare-earth antiferromagnet DyFeO$_{3}$ with a thin Pt film contact. The angular shape and symmetry of the SMR at elevated temperatures reflect the antiferromagnetic order of the Fe$^{3+}$ moments as governed by the Zeeman energy, the magnetocrystalline anisotropy and the Dzyaloshinskii-Moriya interaction. We interpret the observed linear dependence of the signal on the magnetic field strength as evidence for field-induced order of the Dy$^{3+}$ moments up to room temperature. At and below the Morin temperature of 50$\,$K, the SMR monitors the spin-reorientation phase transition of Fe$^{3+}$ spins. Below 23$\,$K, additional features emerge that persist below 4$\,$K, the ordering temperature of the Dy$^{3+}$ magnetic sublattice. We conclude that the combination of SMR and SSE is a simple and efficient tool to study spin reorientation phase transitions and sublattice magnetizations.

Magnon transport through a magnetic insulator can be controlled by current-biased heavy-metal gates that modulate the magnon conductivity via the magnon density. Here, we report nonlinear modulation effects in 10$\,$nm thick yttrium iron garnet (YIG) films. The modulation efficiency is larger than 40\%/mA. The spin transport signal at high DC current density (2.2$\times 10^{11}\,$A/m$^{2}$) saturates for a 400$\,$nm wide Pt gate, which indicates that even at high current levels a magnetic instability cannot be reached in spite of the high magnetic quality of the films.

We measure the mode-resolved direction of the precessional motion of the magnetic order, i.e., magnon polarization, via the chiral term of inelastic polarized neutron scattering spectra. The magnon polarisation is important in spintronics, affecting thermodynamic properties such as the magnitude and sign of the spin Seebeck effect. The observation of both signs of magnon polarization in Y3Fe5O12 also gives direct proof of its ferrimagnetic nature. The experiments agree very well with atomistic simulations of the scattering cross section., Comment: 6 pages, 4 figures

We report an electric field-induced in-plane magnetoresistance of an atomically flat paramagnetic insulator|platinum (Pt) interface at low temperatures with an ionic liquid gate. Transport experiments as a function of applied magnetic field strength and direction obey the spin Hall magnetoresistance phenomenology with perpendicular magnetic anisotropy. Our results establish the utility of ionic gating as an alternative method to control spintronic devices without using ferromagnets., Comment: 13 pages, 5 figures

We present the Co-Gd composition dependence of the spin-Hall magnetoresistance (SMR) and anisotropic magnetoresistance (AMR) for ferrimagnetic Co100-xGdx / Pt bilayers. With Gd concentration x, its magnetic moment increasingly competes with the Co moment in the net magnetization. We find a nearly compensated ferrimagnetic state at x = 24. The AMR changes sign from positive to negative with increasing x, vanishing near the magnetization compensation. On the other hand, the SMR does not vary significantly even where the AMR vanishes. These experimental results indicate that very different scattering mechanisms are responsible for AMR and SMR. We discuss a possible origin for the alloy composition dependence., Comment: 31 Pages, 9 figures

We experimentally identify the magnetostatic modes active for Brillouin light scattering in the optical whispering gallery modes of a yttrium iron garnet sphere. Each mode is identified by magnetic field dispersion of ferromagnetic-resonance spectroscopy and coupling strength to the known field distribution of the microwave drive antenna. Our optical measurements confirm recent predictions that higher-order magnetostatic modes can also generate optical scattering, according to the selection rules derived from the axial symmetry. From this we summarize the selection rules for Brillouin light scattering. We give experimental evidence that the optomagnonic coupling to non-uniform magnons can be higher than that of the uniform Kittel mode., Comment: 5 pages, 5 figures

The spin Seebeck effect (SSE) is observed in magnetic insulator|heavy metal bilayers as an inverse spin Hall effect voltage under a temperature gradient. The SSE can be detected nonlocally as well, viz. in terms of the voltage in a second metallic contact (detector) on the magnetic film, spatially separated from the first contact that is used to apply the temperature bias (injector). Magnon-polarons are hybridized lattice and spin waves in magnetic materials, generated by the magnetoelastic interaction. Kikkawa et al. [Phys. Rev. Lett. \textbf{117}, 207203 (2016)] interpreted a resonant enhancement of the local SSE in yttrium iron garnet (YIG) as a function of the magnetic field in terms of magnon-polaron formation. Here we report the observation of magnon-polarons in \emph{nonlocal} magnon spin injection/detection devices for various injector-detector spacings and sample temperatures. Unexpectedly, we find that the magnon-polaron resonances can suppress rather than enhance the nonlocal SSE. Using finite element modelling we explain our observations as a competition between the SSE and spin diffusion in YIG. These results give unprecedented insights into the magnon-phonon interaction in a key magnetic material., Comment: 5 pages, 6 figures

Spin caloritronics is the science and technology to control spin, charge, and heat currents in magnetic nanostructures. The spin degree of freedom provides new strategies for thermolelectric power generation that have not yet been fully explored. After an elementary introduction into conventional thermoelectrics and spintronics, we give a brief review of the physics of spin caloritronics. We discuss spin-dependent thermoelectrics based on the the two-current model in metallic magnets as well as the spin Seebeck and Peltier effects that are based on spin wave excitations in ferromagnets. We derive expressions for the efficiency and figure of merit ZT of several spin caloritronic devices., Comment: 14 pages, 14+ figures

Hall effects have been employed as sensitive detectors of magnetic fields and magnetizations. In spintronics, exotic phenomena often emerge from a non-equilibrium spin polarization or magnetization, that is very difficult to measure directly. The challenge is due to the tiny total moment, which is out of reach of superconducting quantum interference devices and vibrating sample magnetometers or spectroscopic methods such as X-ray magnetic circular dichroism. The Kerr effect is sufficiently sensitive only in direct gap semiconductors, in which the Kerr angle can be resonantly enhanced. Here we demonstrate that even one excess spin in a million can be detected by a Hall effect at room temperature. The novel Hall effect is not governed by the spin Hall conductivity but by its energy derivative thereby related to the spin Nernst effect.

Spin-transfer torques induced by temperature gradients in conducting ferromagnets are calculated microscopically for smooth magnetization textures. Temperature gradients are treated a la Luttinger by introducing a fictitious gravitational field that couples to the energy density. The thermal torque coefficients obtained by the Kubo formula contain divergences caused by equilibrium components that should be subtracted before applying the Einstein-Luttinger relation. Only by following this procedure a familiar Mott-like formula is obtained for the dissipative spin-transfer torque. The result indicates that a fictitious field coupled to the entropy rather than energy would solve the issue from the outset., Comment: 11 pages, 2 figures

We report the observation of the spin Peltier effect (SPE) in the ferrimagnetic insulator Yttrium Iron Garnet (YIG), i.e. a heat current generated by a spin current flowing through a Platinum (Pt)|YIG interface. The effect can be explained by the spin torque that transforms the spin current in the Pt into a magnon current in the YIG. Via magnon-phonon interactions the magnetic fluctuations modulate the phonon temperature that is detected by a thermopile close to the interface. By finite-element modelling we verify the reciprocity between the spin Peltier and spin Seebeck effect. The observed strong coupling between thermal magnons and phonons in YIG is attractive for nanoscale cooling techniques., Comment: 5 pages, 3 figures, 4 pages supplementary information, 4 supplementary figures

The effective field torque of an yttrium-iron-garnet film on the spin accumulation in an attached Pt film is measured by the spin-Hall magnetoresistance (SMR). As a result, the magnetization direction of a ferromagnetic insulating layer can be measured electrically. Experimental transverse and longitudinal resistances are well described by the theoretical model of SMR in terms of the direct and inverse spin-Hall effect, for different Pt thicknesses [3, 4, 8 and 35nm]. Adopting a spin-Hall angle of Pt $\theta_{SH}=0.08$, we obtain the spin diffusion length of Pt ($\lambda=1.1\pm0.3$nm) as well as the real ($G_r=(7\pm3)\times10^{14}\Omega^{-1}$m$^{-2}$) and imaginary part ($G_i=(5\pm3)\times10^{13}\Omega^{-1}$m$^{-2}$) of the spin-mixing conductance and their ratio ($G_r/G_i=16\pm4$)., Comment: 4 pages, 4 figures

Since the discovery of the giant magnetoresistance (GMR) effect the use of the intrinsic angular momentum of the electrons has opened up new spin based device concepts. The two channel model of spin-up and spin-down electrons with spin-dependent conductivities very well describes spin and charge transport in such devices. In studies of the interaction between heat and spin transport, or spin caloritronics, until recently it was assumed that both spin species are always at the same temperature. Here we report the observation of different temperatures for the spin up (T_\uparrow) and spin down (T_\downarrow) electrons in a nanopillar spin valve subject to a heat current. The weak relaxation, especially at room temperature, of the spin heat accumulation (T_s = T_\uparrow-T_\downarrow) is essential for its detection in our devices. Using 3D finite element modeling spin heat accumulation (SHA) values of 120 mK and 350 mK are extracted at room temperature and 77 K, respectively, which is of the order of 10% of the total temperature bias over the pillar. This technique uniquely allows the study of inelastic spin scattering at low energies and elevated temperatures, which is not possible by spectroscopic methods., Comment: 27 pages, 8 figures and 1 table (including supplementary information)

We report anisotropic magnetoresistance in Pt|Y3Fe5O12 bilayers. In spite of Y3Fe5O12 being a very good electrical insulator, the resistance of the Pt layer reflects its magnetization direction. The effect persists even when a Cu layer is inserted between Pt and Y3Fe5O12, excluding the contribution of induced equilibrium magnetization at the interface. Instead, we show that the effect originates from concerted actions of the direct and inverse spin Hall effects and therefore call it "spin Hall magnetoresistance.", Comment: 20 pages, 7 figures (including Supplemental Material)

We theoretically study field-induced domain wall (DW) motion in an electrically insulating ferromagnet with hard- and easy-axis anisotropies. DWs can propagate along a dissipationless wire through spin wave emission locked into the known soliton velocity at low fields. In the presence of damping, the mode appears before the Walker breakdown field for strong out-of-plane magnetic anisotropy, and the usual Walker rigid-body propagation mode becomes unstable when the field is between the maximal-DW-speed field and Walker breakdown field., Comment: 4 pages, 4 figures

The spin-Seebeck effect (SSE) in ferromagnetic metals and insulators has been investigated systematically by means of the inverse spin-Hall effect (ISHE) in paramagnetic metals. The SSE generates a spin voltage as a result of a temperature gradient in a ferromagnet, which injects a spin current into an attached paramagnetic metal. In the paramagnet, this spin current is converted into an electric field due to the ISHE, enabling the electric detection of the SSE. The observation of the SSE is performed in longitudinal and transverse configurations consisting of a ferromagnet/paramagnet hybrid structure, where thermally generated spin currents flowing parallel and perpendicular to the temperature gradient are detected, respectively. Our results explain the SSE in terms of a two-step process: (1) the temperature gradient creates a non-equilibrium state in the ferromagnet governed by both magnon and phonon propagations and (2) the non-equilibrium between magnons in the ferromagnet and electrons in the paramagnet at the contact interface leads to "thermal spin pumping" and the ISHE signal. The non-equilibrium state of metallic magnets (e.g. Ni81Fe19) under a temperature gradient is governed mainly by the phonons in the sample and the substrate, while in insulating magnets (e.g. Y3Fe5O12) both magnon and phonon propagations appear to be important. The phonon-mediated non-equilibrium that drives the thermal spin pumping is confirmed also by temperature-dependent measurements, giving rise to a giant enhancement of the SSE signals at low temperatures., Comment: 13 pages, 13 figures

Thermoelectric generation is an essential function of future energy-saving technologies. However, this generation has been an exclusive feature of electric conductors, a situation which inflicts a heavy toll on its application; a conduction electron often becomes a nuisance in thermal design of devices. Here we report electric-voltage generation from heat flowing in an insulator. We reveal that, despite the absence of conduction electrons, a magnetic insulator LaY2Fe5O12 converts a heat flow into spin voltage. Attached Pt films transform this spin voltage into electric voltage by the inverse spin Hall effect. The experimental results require us to introduce thermally activated interface spin exchange between LaY2Fe5O12 and Pt. Our findings extend the range of potential materials for thermoelectric applications and provide a crucial piece of information for understanding the physics of the spin Seebeck effect., Comment: 19 pages, 5 figures (including supplementary information)

Spin pumping is a mechanism that generates spin currents from ferromagnetic resonance (FMR) over macroscopic interfacial areas, thereby enabling sensitive detection of the inverse spin Hall effect that transforms spin into charge currents in non-magnetic conductors. Here we study the spin-pumping-induced voltages due to the inverse spin Hall effect in permalloy/normal metal bilayers integrated into coplanar waveguides for different normal metals and as a function of angle of the applied magnetic field direction, as well as microwave frequency and power. We find good agreement between experimental data and a theoretical model that includes contributions from anisotropic magnetoresistance (AMR) and inverse spin Hall effect (ISHE). The analysis provides consistent results over a wide range of experimental conditions as long as the precise magnetization trajectory is taken into account. The spin Hall angles for Pt, Pd, Au and Mo were determined with high precision to be $0.013\pm0.002$, $0.0064\pm0.001$, $0.0035\pm0.0003$ and $-0.0005\pm0.0001$, respectively., Comment: 11 pages

Spin Hall effects intermix spin and charge currents even in nonmagnetic materials and, therefore, ultimately may allow the use of spin transport without the need for ferromagnets. We show how spin Hall effects can be quantified by integrating permalloy/normal metal (N) bilayers into a coplanar waveguide. A dc spin current in N can be generated by spin pumping in a controllable way by ferromagnetic resonance. The transverse dc voltage detected along the permalloy/N has contributions from both the anisotropic magnetoresistance (AMR) and the spin Hall effect, which can be distinguished by their symmetries. We developed a theory that accounts for both. In this way, we determine the spin Hall angle quantitatively for Pt, Au and Mo. This approach can readily be adapted to any conducting material with even very small spin Hall angles., Comment: 4 pages, 4 figures

Torsional oscillations of a free-standing semiconductor beam are shown to cause spin-dependent oscillating potentials that spin-polarize an applied charge current in the presence of intentional or disorder scattering potentials. We propose several realizations of mechanical spin generators and manipulators based on this piezo-spintronic effect., Comment: 4 pages, 4 figures

We consider the possibility to extract spins that are generated by an electric current in a two-dimensional electron gas with Rashba-Dresselhaus spin-orbit interaction (R2DEG) in the Hall geometry. To this end, we discuss boundary conditions for the spin accumulations between a spin-orbit coupled region and contact without spin-orbit coupling, i.e. a normal two-dimensional electron gas (2DEG). We demonstrate that in contrast to contacts that extend along the whole sample, a spin accumulation can diffuse into the normal region through finite contacts and detected by e.g. ferromagnets. For an impedance-matched narrow contact the spin accumulation in the 2DEG is equal to the current induced spin accumulation in the bulk of R2DEG up to a geometry-dependent numerical factor., Comment: 18 pages, 7 figures, submitted to NJP focus issue on Spintronics

We investigate effects of spin-orbit splitting on electronic transport in a spin valve consisting of a large quantum dot defined on a two-dimensional electron gas with two ferromagnetic contacts. In the presence of both structure inversion asymmetry (SIA) and bulk inversion asymmetry (BIA) a giant anisotropy in the spin-relaxation times has been predicted. We show how such an anisotropy affects the electronic transport properties such as the angular magnetoresistance and the spin-transfer torque. Counterintuitively, anisotropic spin-relaxation processes sometimes enhance the spin accumulation., Comment: 8 pages

Details are presented of an efficient formalism for calculating transmission and reflection matrices from first principles in layered materials. Within the framework of spin density functional theory and using tight-binding muffin-tin orbitals, scattering matrices are determined by matching the wave-functions at the boundaries between leads which support well-defined scattering states and the scattering region. The calculation scales linearly with the number of principal layers N in the scattering region and as the cube of the number of atoms H in the lateral supercell. For metallic systems for which the required Brillouin zone sampling decreases as H increases, the final scaling goes as H^2*N. In practice, the efficient basis set allows scattering regions for which H^{2}*N ~ 10^6 to be handled. The method is illustrated for Co/Cu multilayers and single interfaces using large lateral supercells (up to 20x20) to model interface disorder. Because the scattering states are explicitly found, ``channel decomposition'' of the interface scattering for clean and disordered interfaces can be performed., Comment: 22 pages, 13 figures

The interface-induced magnetization damping of thin ferromagnetic films in contact with normal-metal layers is calculated from first principles for clean and disordered Fe/Au and Co/Cu interfaces. Interference effects arising from coherent scattering turn out to be very small, consistent with a very small magnetic coherence length. Because the mixing conductances which govern the spin transfer are to a good approximation real valued, the spin pumping can be described by an increased Gilbert damping factor but an unmodified gyromagnetic ratio. The results also confirm that the spin-current induced magnetization torque is an interface effect., Comment: 10 pages, 8 figures, RevTeX; modified according to Referees' requests

The spin-dependence of the interface resistance between ferromagnetic Fe and InAs is calculated from first-principles for specular and disordered (001) interfaces. Because of the symmetry mismatch in the minority-spin channel, the specular interface acts as an efficient spin filter with a transmitted current polarisation between 98 an 89%. The resistance of a specular interface in the diffusive regime is comparable to the resistance of a few microns of bulk InAs. Symmetry-breaking arising from interface disorder reduces the spin asymmetry substantially and we conclude that efficient spin injection from Fe into InAs can only be realized using high quality epitaxial interfaces., Comment: 4 pages, 4 figures

Because the physical interpretation of the spin-polarization of a ferromagnet determined by point-contact Andreev reflection (PCAR) is non-trivial, we have carried out parameter-free calculations of PCAR spectra based upon a scattering-theory formulation of Andreev reflection generalized to spin-polarized systems and a tight-binding linear muffin tin orbital method for calculating the corresponding scattering matrices. PCAR is found to measure the spin-dependent interface transparency rather than the bulk polarization of the ferromagnet which is strongly overestimated by free electron model fitting., Comment: 4 pages, 1figure. submitted

Recent theories of spin-current-induced magnetization reversal are formulated in terms of a spin-mixing conductance $G^{mix}$. We evaluate $G^{mix}$ from first-principles for a number of (dis)ordered interfaces between magnetic and non-magnetic materials. In multi-terminal devices, the magnetization direction of a one side of a tunnel junction or a ferromagnetic insulator can ideally be switched with negligible charge current dissipation., Comment: 4 pages, 1 figure

A theory of spin-transport in hybrid normal metal - ferromagnetic electronic circuits is developed, taking into account non-collinear spin-accumulation. Spin-transport through resistive elements is described by 4 conductance parameters. Microscopic expression for these conductances are derived in terms of scattering matrices and explicitly calculated for simple models. The circuit theory is applied to 2-terminal and 3-terminal devices attached to ferromagnetic reservoirs., Comment: 12 pages, 6 figures, to appear in Eur. Phys. J. B

We study the effect of interface disorder on the spin-dependent interface resistances of Co/Cu, Fe/Cr and Au/Ag multilayers using a newly developed method for calculating transmission matrices from first-principles. The efficient implementation using tight-binding linear-muffin-tin orbitals allows us to model interface disorder using large lateral supercells whereby specular and diffuse scattering are treated on an equal footing. Without introducing any free parameters, quantitative agreement with experiment is obtained. We predict that disorder {\it reduces} the majority-spin interface resistance of Fe/Cr(100) multilayers by a factor 3., Comment: 5 pages, 2 figures, submitted to PRL

We study transport in ferromagnetic single-electron transistors. The non- equilibrium spin accumulation on the island caused by a finite current through the system is described by a generalized theory of the Coulomb blockade. It enhances the tunnel magnetoresistance and has a drastic effect on the time- dependent transport properties. A transient decay of the spin accumulation may reverse the electric current on time scales of the order of the spin-flip relaxation time. This can be used as an experimental signature of the non- equilibrium spin accumulation., Comment: 9 postscript figures, to appear in The European Physical Journal B