Extending the notion of symmetry protected topological phases to insulating antiferromagnets (AFs) described in terms of opposite magnetic dipole moments associated with the magnetic Neel order, we establish a bosonic counterpart of topological insulators in semiconductors [1]. Making use of the Aharonov-Casher effect, induced by electric field gradients, we propose a magnonic analog of the quantum spin Hall effect (magnonic QSHE) for edge states that carry helical magnons. We show that such up and down magnons form the same Landau levels and perform cyclotron motion with the same frequency but propagate in opposite direction. The insulating AF becomes characterized by a topological Z2 number consisting of the Chern integer associated with each helical magnon edge state. Focusing on the topological Hall phase for magnons, we study bulk magnon effects such as magnonic spin, thermal, Nernst, and Ettinghausen effects, as well as the thermomagnetic properties of helical magnon transport both in topologically trivial and nontrivial bulk AFs and establish the magnonic Wiedemann-Franz law. We show that our predictions are within experimental reach with current device and measurement techniques.

Antiferromagnetic spintronics considers the active manipulation of the antiferromagnetic order parameter in spin-based devices. An additional concept that has emerged is that antiferromagnets provide a unifying platform for realizing synergies among three prominent fields of contemporary condensed matter physics: Dirac quasiparticles and topological phases. Here spintronic devices made of antiferromagnets with their unique symmetries will allow us to control the emergence and to study the properties of Dirac/Weyl fermion topological phases that are otherwise principally immune against external stimuli. In return, the resulting topological magneto-transport phenomena open the prospect of new, highly efficient means for operating the antiferromagnetic memory-logic devices. We discuss how these topological phases emerge and how their robustness depends on the relative orientation of the Neel order parameter that can be manipulated by Neel spin-orbit torques. Their natural excitations are in the THz but with the additional consideration that they can now be directly tuned.

Tetradymite narrow band gap semiconductors (Bi2Te3, Bi2Se3, Sb2Te3, and their alloys) are known to support topologically protected, two-dimensional (2D) helical Dirac fermion surface states characterized by a spin texture in momentum space [1-3]. The spin texture in these “3D topological insulators” has been measured using angle-resolved photoemission spectroscopy [4,5] and electrical transport measurements [6-10]. The spin-momentum locking of 2D helical Dirac states lends itself naturally to spintronic device applications that might exploit efficient spin--charge interconversion. This talk will present an overview of concepts and experiments that explore the emergence of “topological spintronics,” a potential device technology that exploits the strong spin-orbit coupling in topological insulators for efficiently manipulating the magnetization of a vicinal ferromagnet [11-15]. We will then focus on recent experiments that probe spin-charge interconversion at interfaces between a 3D topological insulator and an insulating ferrimagnet [16], with a particular view toward understanding how the spin Hall conductivity in topological insulators varies with chemical potential [17,18]. Finally, we address the interesting device possibilities presented by idealized topological insulator/ferromagnetic insulator devices [18] and discuss pathways for testing such proposals.

Topological insulators (TIs), a class of quantum materials, have special gapless edge/surface states, where the spin polarization of the Dirac fermions is locked to the momentum direction. This spin–momentum locking property gives rise to very interesting spin-dependent physical phenomena such as the Edelstein and inverse Edelstein effects.

In this talk, I will first present our experimental results that demonstrate the inverse Edelstein effect in the surface states of a topological Kondo insulator, SmB6. At low temperatures when only surface carriers are present, a clear spin signal is observed. Furthermore, the magnetic field angle dependence of the spin signal is consistent with spin–momentum locking property of surface states of SmB6. The second part of my talk will focus on the exchange coupling between the spins in the topological surface states and the magnetization in a ferromagnetic insulator. The spin pumping efficiency can be greatly enhanced due to the topological surface states.

One of the most intriguing and fundamental properties of topologically protected materials is the direct correspondence of the gapped bulk spectrum with the conducting edge states. Low spatial resolution, remnant bulk conductivity, as well as disorder have made it impossible so far to experimentally observe the evolution of the edge states and the correspondence principle. Here, we use a GaAs quantum wire, located at the cleaved edge interface of a GaAs/AlGaAs 2D electron gas, to perform momentum resolved tunneling spectroscopy using magnetic fields applied both perpendicular and in plane to the 2D gas at low temperatures. The measurements are sensitive to chirality and allow us to probe the magnetic field evolution of integer quantum Hall edge states with unprecedented precision from very low magnetic fields all the way to magnetic depopulation at large fields. Theoretical predictions based on consistent analytical as well as a numerical models for the evolution of edge states – inferred from the well-known bulk spectrum – for hard wall confinement, are in very good agreement with the measurements, thus providing conclusive evidence for bulk to edge correspondence. This novel method allows determination of the edge state position with a resolution down to 1 nm. Beyond single particle physics, we observe various features such as exchange enhanced spin splitting, Fermi level pinning and signatures of edge state reconstruction in the tunneling data.

Considering Rashba quantum wires with a proximity-induced superconducting gap as physical realizations of Majorana bound states and quantum dots, we calculate the overlap of the Majorana wave functions with the local wave functions on the dot. We determine the spin-dependent tunneling amplitudes between these two localized states and show that we can tune into a fully spin polarized tunneling regime by changing the distance between dot and Majorana bound state. Upon directly applying this to the tunneling model Hamiltonian, we calculate the effective magnetic field on the quantum dot flanked by two Majorana bound states. The direction of the induced magnetic field on the dot depends on the occupation of the nonlocal fermion formed from the two Majorana end states which can be used as a readout for such a Majorana qubit.

The development of practical superconducting spintronics has driven a renewed interest in ferromagnetic/superconducting systems [1]. At the end of 80's it was demonstrated that a ferromagnetic insulator (FI), such as e.g. EuS or EuO, in contact with a superconductor (S) induces, within a distance from the material interface comparable with the superconducting coherence length, an exchange field which generates a splitting of the Bardeen-Cooper-Schrieffer (BCS) density of states (DOS) singularity by a magnitude proportional to its magnetization [2]. We show our results on this long-range magnetic proximity effect in EuS/Al bilayers coupled to a tunnel Al probe. The tunnelling spectroscopy of our devices exhibits a clear exchange splitting of the BCS DOS peaks that can be related with the magnetic domain structure of the EuS [3]. The hard gap and clear intrinsic spin-splitting observed in our tunnelling spectroscopy measurements at zero field suggest that EuS/Al bilayers are an excellent platform for the development of large variety of devices requiring the coexistence of superconducting correlations and built-in spin-splitting exchange fields. We, therefore, discuss a viable technological exploitation of this hybrid materials demonstrating the “Absolute Spin-Valve effect” [4,5] by means of a tunnel junction device realized by a EuS/Al/AlOx/Al/EuS structure. The huge tunnelling magnetoresistance (TMR) ratios measured at low temperatures (< 1 K) demonstrate the capabilities of our valve to act as the main building block of future superconducting electronic devices.

Spin Hall effects are commonly utilized to interconvert between charge and spin currents. As an alternative mechanism for this interconversion, the Rashba-type spin splitting at the Bi (111)/Ag interface [1] or the spin-momentum locking at the Dirac surface state of a topological insulator (TI) have recently been used for highly efficient interconversion.

Our recent study on the spin-torque ferromagnetic resonance in TI ((Bi_1-xSb_x)₂Te₃)/non-magnetic metal/ferromagnetic-metal tri-layer films in bulk insulating conditions revealed that the interface conversion coefficient q_ICS (nm^-1) from charge to spin currents stayed at a nearly constant large value of about 0.5 nm^-1 [2].

In this talk we will show that the similar conversion from spin to charge currents could take place at the nonmagnetic metal/oxide interfaces [3] in an e-beam depositted Ni₈₀Fe₂₀(Py)(5nm)/Cu(15nm)/Bi₂O₃(10nm) trilayer structure. The study on both Cu and Bi₂O₃ thickness dependences revealed that the conversion coefficient λ_IRE (nm) varied as a function of the Cu thickness, reflecting the thickness dependent resistivity of a Cu layer. Rashba parameter α_R was estimated to be -0.46 eV·Å, about 50% of the reported value for Bi/Cu(111) interface [4].

Lastly we also show magnetic spin Hall effects found recently in a chiral antiferromagnet Mn₃Sn [5]. Th effects exhibit an anomalous sign change in the resulting spin accumulation when its triangularly ordered moments switch orientation. Our observations demonstrate that a novel type of contribution to the SHE (magnetic SHE, MSHE) and the inverse SHE (MISHE) that is absent in nonmagnetic materials can be dominant in some magnetic materials, including antiferromagnets.

Since the experimental discovery of the spin Hall effect (SHE) in semiconductors [1] and the report of current-induced magnetization switching in heavy metal/ferromagnet layers [2], there has been tremendous interest in the SHE as a fundamental transport phenomenon as well as for practical spintronic applications [3]. Yet, most measurements of the SHE in metals rely on nonmagnetic/magnetic structures, in which the SHE is detected indirectly through its influence on the magnetization of a ferro- or ferrimagnet [4-6] or through nonlocal resistance measurements [7,8]. This limitation is the cause of the wide uncertainty of the spin Hall angle and spin diffusion parameters reported in the literature, which rely heavily on theoretical models of the SHE-induced spin accumulation and sample magnetization.

In this work, we provide the first quantitative measurement of the SHE in nonmagnetic metals, namely Pt and W, performed using the magneto-optical Kerr effect (MOKE) [9]. Our results evidence a minute but unambiguous Kerr rotation signal that scales linearly with the current density and has opposite sign in Pt and W, which originates from the nonequilibrium magnetization of the two metals. By comparing the experimental results with ab-initio calculations of the SHE and MOKE, we determine quantitatively the current-induced spin accumulation at the Pt interface as 5x10-5 μB/atom for a current density of 107 A/cm2. From thickness-dependent measurements, we determine the spin diffusion length of Pt to be 11 ± 3 nm, which is significantly larger compared to that of Pt adjacent to a magnetic layer. We will discuss these results in comparison with recent spin-orbit torque and spin absorption measurements.

The magnetic order parameter in solids interacts with electromagnetic waves. The bare coupling constant between the magnetization of light is weak and can be treated by perturbation theory. This leads to the theory for the Brillouin light scattering by magnons, i.e. the generation of light with frequencies that are blue (red) shifted from the incident one by the annihilation (creation) of a spin wave or magnon.

The scattering can be enhanced by confining the field by a cavity, i.e. a region of space enclosed by reflecting boundaries. This generates bound states that for high quality cavities are spectrally sharp and can have large amplitudes in their antinodes.

Here I discuss Brillouin light scattering of whispering gallery modes of light by magnons confined to magnetic spheres with high dielectric constant. The asymmetry between the intensities of Stokes and anti-Stokes lines for forward scattering by the Kittel mode can be explained by linear birefringence. Back scattering of these light modes by Damon Eshbach surface magnons leads to reflection of the incoming light. These processes raise the option to cool the magnetic order by light in high-quality magnets such as yttrium iron garnets.

Low dimensional materials systems, such as graphene, transition metal dichalcogenides (TMDs) and 2-electron gas (2DEG) systems formed in oxides and compound semiconductors, have been collecting strong attention in spintronics. Our group is also much interested in these systems and reported room temperature spin current injection, transport and its conversion in them [1-4]. In this presentation, the recent achievement of spin transport in a 2DEG formed at an interface of LaAlO3/SrTiO3 by using a dynamical method [4] is discussed. The spins are injected from NiFe electrode under its ferromagnetic resonance, and propagating spin current in the 2DEG was detected by Pt and Ta wires, in which the spin Hall angles are positive and negative, respectively. As expected, a polarity of the electromotive forces detected from these wires was opposite, which supports successful spin current propagation in the 2DEG. Spin diffusion length of the 2DEG was estimated to be ca. 300 nm from the gap length dependence, and the experimental result was consistent with results of two different theoretical calculations and, in addition, that of broadband ferromagnetic spectroscopy. The detail will be introduced in the presentation, and if time permits, a challenge to inject spins into GaAs-based 2DEGs is also introduced [5].

These studies were carried out by the collaboration with Prof. S. Goennenwein (TU-Dresden), Dr. H. Huebl (WMI), Dr. M. Weiler (WMI), Mr. S. Klingler (TU-Muenchen), Dr. T. Susaki (TIT), Dr. K. Matsuzaki (TIT), Dr. E. Shikoh (Osaka City Univ.), Prof. T. Uemura (Hokkaido Univ.), and members of Shiraishi lab. in Kyoto Univ.

Spin Hall magnetoresistance (SMR) in heavy metal (HM)/ferromagnetic insulator (FMI) bilayers is a novel effect governed by the spin transport across the HM/FMI interface. I will show the importance of the interface details in SMR in 3 different FMI systems with complex magnetism at the surface: spinel CoFe2O4 (with antiphase boundaries), perovskite LaCoO3 (a ferromagnet induced by epitaxial strain) and garnet Y3Fe5O12 (with surface magnetic frustration due to ion-milling or to ultrathin growth).

We analyze the couplings induced in graphene in the vicinity of an insulating ferromagnet. In addition to an exchange term, a number of other interactions arise, typically of the same order of magnitude. These tems depend on the orientation of the magnetization, and lead to a rich phase diagram, ingluding topological insulator and anomalous hall insulator phases.

We show that two dimensional metals like graphene randomly decorated with adsorbates can generate spin currents via the so-called extrinsic spin-Hall effect [1] and also magnetize in response to the application of an electric field [2]. A sizable contribution to this current-induced non equilibrium magnetization arises from a newly discovered direct magneto-electric coupling, which we termed anisotropic spin-precession scattering (ASP) [2,4]. Signatures of the ASP in nonlocal resistance measurements will be also discussed [3]. We will also argue that the new mechanism is a fairly universal phenomenon in disordered spin-orbit coupled systems lacking inversion symmetry [4], which relevant for the understanding of spin-charge conversion mechanism that can have many potential applications. Time permitting a brief discussion of the experimental situation and some alternative explanations to the puzzling experiments on graphene will be included [5].

Magnetism and superconductivity are phenomena that cannot simultaneously exist in the same region of a material: weak applied magnetic fields are expelled out from the superconductor, while strong magnetic fields destroy the superconducting properties. An interesting playground to study the interplay between both phenomena are magnetic atoms interacting with a superconductor. A magnetic atom scatters Cooper pairs as a potential with broken time-reversal symmetry, what locally distorts superconductivity. The result is the formation of quasiparticles bound states inside the superconducting gap, named Yu-Shiba-Rusinov states (YSR) [1].

Using scanning tunneling spectroscopy, we investigate the YSR states caused by several atomic and molecular systems, resolving their origin and exploring basic properties of BCS superconductors [2]. We found that the shape of YSR states reflect the shape of d atomic orbitals [3] and are sensitive to magnetic anisotropies of the magnetic specie [4].

Increasing the exchange interaction of the impurity with the superconductor weakens the pairing energy and induce breaking of Cooper pairs. This brings the magnetic atom into a different magnetic ground state [4,5]. On the contrary, reducing the interaction by simply separating the magnetic atom from the surface remove YSR states from the gap. In this scenario, inelastic tunnelling processes mediate spin excitations between different magnetic states of the atom. An interesting outcome is that the presence of a superconducting gap at the substrate hiders the energy relaxation into the substrate, and spin excitations may survive for nanoseconds [6].

The chiral magnet Cu2OSeO3 hosts a skyrmion lattice, that may be equivalently described as a superposition of plane waves or lattice of particle-like topological defects. A thermal gradient may break up the skyrmion lattice and induce rotating domains raising the question which of these scenarios better describes the violent dynamics at the domain boundaries.

Here we show that in an inhomogeneous temperature gradient caused by illumination in a Lorentz Transmission Electron Microscope different parts of the skyrmion lattice can be set into motion with different angular velocities. Tracking the time dependence we show that the constant rearrangement of domain walls is governed by dynamic 5-7 defects arranging into lines. An analysis of the associated defect density is described by Frank's equation and agrees well with classical 2D-Monte Carlo simulations. Fluctuations of boundaries show surge-like rearrangement of skyrmion clusters driven by defect rearrangement consistent with simulations treating skyrmions as point particles. Our findings underline the particle character of the skyrmion.

Magnetic skyrmions are non-linear excitations stabilized by relativistic interactions in chiral magnets. They behave like particles subjected to a Magnus force stemming from the non-trivial topology of the magnetization field. In this talk, I will discuss the dynamics of these objects in electrically insulating materials and how they can be used as basic units of (topological) charge in low-dissipation spintronic applications. I will examine first the nucleation of skyrmion charge by current-induced torques. The analysis of the non-equilibrium dynamics at the interface with a diffusive metal will be based on energetics rather than spin conservation. A reactive torque on the magnetization induced by a spin-polarized current pumps skyrmion charge into the magnet, and reciprocally, the annihilation of skyrmion textures generates an electromotive force in the metal, manifested as a pumped current. I will consider two scenarios, a dilute gas of solitons and a skyrmion crystal, in which this phenomenon is revealed as an algebraically decaying (negative) drag signal. I will also discuss the manifestation of the skyrmion topology in the semiclassical regime, when quantum-size effects introduced by the microscopic lattice start to matter. The skyrmion spectrum is then arranged in bands characterized by non-trivial Berry curvatures, the quantum descendant of the Magnus force. I will focus on the semiclassical dynamics in the presence of a thermal bias and show that the circulation of energy provided by the skyrmion states close to the boundaries gives rise to a thermal Hall response.

We study a two-dimensional electron gas with a strong Rashba spin-orbit coupling (SOC) coupled to a system of diluted magnetic impurities. At low electron densities and in order to minimize the kinetic energy, the electron spins polarized in the x−y plane and the energy per electron is −m*α²/2ℏ²-J', being m* the electron effective mas, α the spin orbit coupling and J' the effective exchange coupling between a impurity spin and the conduction electron.

A strong magnetic field pointing in the z-direction polarizes the spins of the magnetic impurities. For large exchange coupling between the magnetic and the electronic systems the electron spins also point in the z-direction. However, for moderate values of J′, the systems become decoupled and the magnetic impurities become polarized in the z-direction whereas the electron spins prefer to be pointing in the x − y plane.

More interesting is the behavior of the coupled systems at moderate values of the magnetic field. We find that at low enough electron densities and large enough values of the exchange coupling, the carriers self trap into well defined non-overlapping magnetic polarons. In reciprocal space, electrons localize in gaussian-like wave packets centered at zero momentum. In real space and because of the Rashba spin orbit coupling, the spin polarization of the localized electron, gradually and smoothly rotates from pointing up at the edge of the wave function to down at the origin in circular symmetric form. Because the exchange coupling, the electron spin polarization engenders, in the magnetic impurity system, a spin texture with topological charge unity that corresponds to a skyrmion. The vorticity and the sign of the skyrmion topological charge are determined by the sign of the spin orbit coupling and the orientation of the magnetic field.

Therefore, we obtain that in a two dimensional diluted magnetic semiconductor with Rashba SOC, the carriers self-trap forming a magnetic skyrmionic polaron. In this new composite quasiparticle charge and spin are coupled and the skyrmionic polaron responds to both electric and magnetic fields.

In this work we present results on the following points,
• Study of the stability, size and spin of skyrmionic polarons as function of the magnetic field.
• Phase diagram as function of the magnetic field and exchange coupling for different values of the Rashba coupling
• Study of the stability of skyrmionic polarons against thermal fluctuations.
• Transport properties of the new quasiparticles.
• Connection between the model and diluted magnetic semiconductors of the family GeMnTe.

Materials with arrays of quantum spins forming well-defined lattices serve as model systems to study the phases of correlated magnetic quantum matter and may be exploited in future quantum spintronics applications. Ferromagnets with pyrochlore lattices and quantum spin dimer systems are two such classes of materials, for which the magnon Hall effect has been observed and magnon transport may be controlled in devices. Neutron spectroscopy is a unique tool for high-precision studies of the spin Hamiltonians and related correlations and elementary excitations in such materials, enabling a detailed microscopic understanding and modeling of the magnon transport in materials. Experimental results on pyrochlore and dimer materials will be presented together with ideas for quantum spintronics devices.

Spin-noise spectroscopy became one of the most powerful tools in studies of spin- related effects in solids [1]. Spectrum of the spin noise contains valuable info about collective and memory-related effects in spin fluctuations near the equilibrium. Here we present theoretical results on the spin noise spectroscopy for electrons in nanowires and for polaritons in semiconductor microcavites.

First, we present a theory of spin noise in semiconductor nanowires considered as prospective elements for spintronics and studies of the Majorana states. In these structures, spin-orbit coupling can be realized as a random function of a coordinate correlated on a spatial scale of the order of 10 nm. By analyzing different regimes of electron transport and spin dynamics, we demonstrate that the spin relaxation can be very slow, and the resulting noise power spectrum increases algebraically as the frequency goes to zero [2]. Next, we study theoretically the spin decoherence and intrinsic spin noise caused by an interplay of electron hopping between localized states and the hyperfine interaction of electron and nuclear spins. At a sufficiently low density of localization sites the hopping rates have an exponentially broad distribution. This broadness permits the description of the spin dynamics in terms of closely situated “pairs” of sites and single “reaching” states, from which the series of hops result in electron localization inside a “pair.” Somewhat similar to the case of the random spin-orbit coupling, the results demonstrate disorder-dependent algebraic tails in the spin decay and power-law singularities in the low-frequency part of the spectrum [3].

Next, we present a theory of spin fluctuations of exciton polaritons in a pumped semiconductor microcavity. The corresponding spin noise is sensitive to the scattering processes in the system, occupation of the ground state, statistics of polaritons, and interactions. Its spectrum drastically narrows in the polariton lasing regime due to formation of a polariton condensate, and the shape becomes non- Lorentzian owing to interaction-induced spin decoherence [4].

We theoretically study the effects of strong magnetoelastic coupling on the transport properties of magnetic insulators. We develop a Boltzmann transport theory for the mixed magnon-phonon modes (”magnon polarons”) and determine transport coefficients and spin diffusion length. Magnon-polaron formation causes anomalous features in the magnetic field and temperature dependence of the spin Seebeck effect when the disorder scattering in the magnetic and elastic subsystems is sufficiently different. Experimental data by Kikkawa et al. [PRL 117, 207203 (2016)] on yttrium iron garnet films can be explained by an acoustic quality that is much better than the magnetic quality of the material. We predict similar anomalous features in the spin and heat conductivity and non-local spin transport experiments.

To date, two types of spin currents, conduction-electron and spin-wave spin currents, have been explored experimentally. The former is mediated by the motion of electrons in metals and semiconductors while in the latter, the spin waves carry spin angular momentum even in insulators.

In a recent paper, we presented a new type of spin current: a spinon spin current in a quantum spin liquid (QSL) in one dimension. In general, QSL is a phase of a magnetic insulator in which frustration or quantum fluctuation prohibits magnetic order while keeping the spin correlation. A typical example of QSL is a one-dimensional spin liquid, and it appears in spin-1/2 chains with the spins coupled via antiferromagnetic interaction. A firmly established model material of such a QSL is the Mott insulator Sr2CuO3. In this material, the fluctuation of the spins of Cu2+ is strong enough to prevent magnetic ordering and to create a paramagnetic state with strong spin-singlet correlation. Spin excitations from the correlated state are known as spinons.

In this presentation, we will talk about the experimental observation that a one-dimensional QSL generates and conveys spin currents, which are attributed to spinon spin currents. This is demonstrated by observing a spinon-induced spin Seebeck effect in Sr2CuO3. The results show that spin currents can flow via quantum fluctuation in spite of the absence of magnetic order, suggesting that various quantum spin systems may be a playground for spintronic effects.

In this talk, I will show how we combine superconducting contacts with a magnetic texture proximal to a carbon nanotube. We demonstrate a large synthetic spin orbit interaction which deeply modifies the induced superconducting correlations in the carbon nanotube. We also observe a zero bias conductance peak which is the hallmark of Majorana zero modes. Our findings could be used for advanced experiments, including microwave spectroscopy and braiding operations.

In the spring of 1995 Giovanni Vignale spent part of a sabbatical semester at Indiana University. Some of you ( big city types ) might question his sanity, working in one midwest college town, Columbia Missouri, and choosing to spend more time than necessary in another one, Bloomington Indiana. As a matter of survival Giovanni dove into thinking about the surprising transport properties of electron gas bilayers when the form an exciton condensate state, which were mostly unexplained at the time although they had been well characterized experimentally. Exciton condensates are electron-hole pair condensates that do not break translational symmetry. They belong to the same class of ordered states as ferromagnets and share many of the same properties. I will discuss Giovanni’s 1995 explanation for the transport properties of bilayer exciton condensates, and its relationship to important current themes in spintronics.

Collective spin excitations such as spin plasmons and spin waves in quantum wells are potential candidates for information transfer within spintronics e.g. for the implementation of spin-routing devices. However their dynamics and coherence is shaped and affected by the interplay between many-body Coulomb interactions, spin-orbit coupling (SOC) and dissipative effects. There are many possible sources of dissipation: some of them can be controlled, for example by reducing disorder, whereas others are intrinsic and hence unavoidable. One such relaxation mechanism is the spin Coulomb drag (SCD), which occurs when two different spin populations move with different momentum while interacting via Coulomb scattering. The exchange of momentum leads to a drag force between the two spin populations which causes a decay—and eventually a halting—of spin currents. On the other hand, SCD favors coherent transport of spin packets in semiconductors by strongly decreasing the spin-diffusion coefficients with respect to the charge ones, while maintaining the high electron mobility. The standard phenomenological way of introducing the SCD is by considering a homogeneous system in which two populations of spin-up and spin- down electrons move with different velocity, The total SCD dissipation or power loss in an inhomogeneous system can then be obtained using a local approximation. However, such a description becomes questionable when considering nanoscale systems, where interfaces, quantum confinement, or local doping can lead to strong inhomogeneities. Here we discuss a formalism for the SCD valid in the general inhomogeneous case [1], and asses its interplay with SOC and extrinsic dissipation [2]. This nonlocal formulation of SCD is successfully applied to linewidths of intersubband spin plasmons in semiconductor quantum wells, where experiments have shown that the local approximation fails [3]. In view of the immense popularity of local approximations in condensed matter physics and other areas of science, these findings have important general implications for developing new ways for treating dynamical many-body effects in nanoscale systems.

Roughly twenty years ago the discovery of long spin lifetimes and of ferromagnetic semiconductors suggested a future technology built on spin transport electronics (spintronics). Early device proposals (including my first collaboration with Giovanni Vignale [1]) emphasized the reprogrammability of devices based on magnetic properties. Since then improved understanding of fundamental physics and device design principles has motivated different device paradigms. For long spin lifetimes the dominant applications now are extremely sensitive coherent sensors based on color centers in solids, with possible extensions to quantum information processing. For magnetic landscapes the response of spin dynamics to a voltage, rather than directly to a current or charge accumulation, provided the potential for faster, low-power switching[2]. Moving away entirely from charge motion in the magnetic material, the prediction [3] and observation [4] of electric-field control of spin-wave velocities in magnetic insulators such as YIG has opened up a design space of magnonic crystals with voltage-tunable spin-wave gaps[5]. In the process the nonlocal effect of flowing spin waves on neighboring magnetic material has been shown to be extremely weak[6].

Topological insulators (TIs) have a bulk energy gap that separates the highest occupied band from the lowest unoccupied band while gapless energy electronic states that are protected by time reversal symmetry live at the edge (2D TIs) or surface (3D TIs). When doped with the magnetic impurities the TIs show the quantum anomalous Hall effect i.e. a single circulating chiral mode at the boundary of 2D TI. Interestingly, in the odd space-time dimensions, one would expect that the formation of the quantum anomalous Hall effect is directly connected to the parity anomaly. We prove theoretically this relation and discuss the experimental consequences [1].

On the other hand, a topological insulator in the proximity to an s-wave superconductor is the prefect material to detect signatures of Majorana fermions. S-wave superconductor on the top of the surface states of 3D TI generates s-wave and p-wave pairing mixture in the surface state due to the spin-momentum locking [2,3]. We predict that in the Josephson junction setup, namely superconductor (S) /surface state of topological insulator/superconductor (S), existence of this p-wave component leads to novel features in transport like superconducting Klein tunneling i.e. the perfect transmission of hybridized Majorana states for normal incidence, the non-sinusoidal current phase relation [3] and unusual phase-dependent thermal conductance [4]. Further, we propose the experimental setups to observe signatures of Majorana fermions in the ac Josephson effect on TI hybrid structures [3,4,5] and in superconductors on hexagonal lattices [6].

Frequent collisions between constituents in a classical or quantum liquid (like 3He) manifest through a transport coefficient called the shear viscosity [1]. The flow of these liquids, and also that of exotic quantum many-particle systems like ultracold 6Li atoms near a Feshbach resonance [2] and quark-gluon plasmas at relativistic heavy-ion colliders [3], is often described by three equations expressing the conservation of mass, momentum (the Navier-Stokes equation), and energy.

Realizing hydrodynamic transport in a solid has proven challenging, because of ever present processes that lead to momentum dissipation in the electron subsystem [4]. Even when suitable conditions are met, key questions have remained largely unexplored: how do you diagnose the emergence of hydrodynamic electron flow in a conventional field-effect transistor? How do you measure the viscosity of an electron liquid in such a setup? What is the impact of viscosity on electron transport?

In this talk I will try and answer these questions. I will report on results of combined theoretical and experimental work [5,6,7] showing unambiguous evidence for the long-sought hydrodynamic solid-state transport regime. In particular, I will discuss how high-quality doped graphene sheets above liquid nitrogen temperatures exhibit negative non-local resistance near current injection points and whirlpools in the spatial current pattern [5,6,7]. Measurements of these non-local electrical signals allow to extract the value of the kinematic viscosity of the two-dimensional electron liquid in graphene, which is found to compare well with many-body theoretical predictions [8]. I will then move to present more recent work [9] on viscous electron flow across graphene classical point contacts. Finally, I will describe near-field optical experiments [10] carried out in encapsulated graphene sheets where tunable quantum non-local effects have been discovered and theoretically analyzed.

Graphene combined with other monolayer materials such as transition metal dichalcogenides is currently investigated as a very promising platform for spintronics applications. In this talk I will focus on Rashba-Dirac models, where the relativistic electron dispersion interplays with the spin-orbit due to the structure inversion asymmetry. In analogy with the case of the non relativistic quadratic spectrum for the two-dimensional electron gas, I will introduce the SU(2) gauge field description for  the Rashba spin-orbit coupling.  Such a description, when used together with the Ward identities of quantum field theory, provides a full solution to the problem in the presence of disorder scattering. This is  shown to be a powerful approach to unveil  the  diagrammatic structure of the theory.

This will be used to discuss results for both the spin Hall and spin galvanic effects in the Dirac-Rashba models with generalized valley-spin interactions. The results presented here are joint work with Mirco Milletarì, Manuel Offidani and Aires Ferreira. They have appeared in preprint form as arXiv:1705.08898 and  arXiv:1706.08973.

Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Lambda in the Brillouin zone (BZ) with protected degeneracies at Lambda. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ [1]. This Hamiltonian provides a faithful description of the protected edge states for both zigzag and armchair ribbons though the concept of a BZ is not part of such an effective model. We show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Lambda for the edge states without affecting the bulk spectrum.

In this talk I will discuss a Green's function formalism to describe transport between spin-polarized metallic reservoirs and magnetic insulators, and apply it to the situation of a strongly-interacting magnonic state viz. the magnon Mott insulator. I will show how the latter gives rise to a novel type of spin Hall magnetoresistance.

Spin transport in ferroic magnetic insulator systems has recently attracted significant interest due to low damping of magnonic spin currents in insulators and efficient transport in ferro-, ferri- and antiferromagnetic compounds.

We have studied the spin transport in ferro(i)magnetic insulators [1-3] and found that the detected spin current signals depend both on the bulk properties of the insulator [1,2] but also on the detector material and in particular the interface properties [3]. While spin transport in single insulating magnetic layers is thus attractive for applications, controlled manipulation of the magnonic spin current is necessary. For charge-based spintronic devices, the spin valve effect that leads to a different spin current transmission as a function of relative alignment of the two magnetic layers is well established [4], for magnonic spin currents in insulating magnets, the analog has been missing so far.

We report on spin pumping [5] measurements in a magnonic spin valve device made of collinear magnetic yttrium iron garnet (YIG)/CoO/Co multilayers. By means of microwaves and external magnetic fields YIG is brought into ferromagnetic resonance, resulting in a pure spin current propagating through the sample stack including the antiferromagnet and finally being detected in the Co layer via the inverse spin Hall effect. For parallel and antiparallel alignment of the YIG and Co layers, we observe a very different amplitude of the detected magnonic spin current signal with a spin valve effect amplitude of 120%. In addition to the spin pumping signal peak, a second peak is observed at ferromagnetic resonance that depends on the Co orientation, which is ascribed to an anomalous Hall effect induced spin rectification in the Co layer [5].

Finally we explore spin transport in pure antiferromagnetic insulator systems. We find a detectable spin Hall magnetoresistance above the spin flop transition field in 3d metal oxides with collinear spin structure. Furthermore we explore these systems for superfluid spin transport including coherence effects are recently suggested [6].

The Usadel equation is the standard theoretical tool for the description of superconducting structures in the diffusive limit. In this talk I introduce a generalized Usadel equation for gyrotropic materials with a generic linear in momentum spin-orbit coupling. It accounts for the spin- charge/singlet-triplet coupling, and in the normal state reduces to the system of spin-charge diffusion equations describing various magnetoelectric effects, such as the spin Hall effect (SHE), the spin-galvanic effect (SGE), and their inverses. Therefore the derived Usadel equation establishes a direct connection of these effects to their superconducting counterparts. The working power of new formalism is illustrated on the example of the bulk SGE.

The inversion symmetry breaking at the interface between different materials generates strong spin-orbit coupling (SOC). This interaction generates different spin-charge and spin-spin correlations crucial in spintronic transport setups. We will study through theoretical models various transport phenomena in metal-metal, metal-oxide and ferromagnet-oxide junctions. We will study the spin-to-charge, spin-to-spin and charge-to-charge conversion which is induced by this interaction.

An interplay of spin-orbit coupling and intrinsic magnetism is known to give rise to the quantum anomalous Hall and topological magnetoelectric effects under certain conditions. Their realization could open access to low power consumption electronics as well as many fundamental phenomena like image magnetic monopoles, Majorana fermions and others. Unfortunately, being realized very recently, these effects are only accessible at extremely low temperatures and the lack of appropriate materials that would enable the temperature increase is a most severe challenge. Here, we propose a novel material platform with unique combination of properties making it perfectly suitable for the realization of both effects at elevated temperatures. The key element of the computational material design is an extension of a topological insulator surface by a thin film of ferromagnetic insulator, which is both structurally and compositionally compatible with the topological insulator. Following this proposal, we suggest a variety of specific systems and discuss their numerous advantages, in particular wide band gaps with the Fermi level located in the gap.