We present a theory for a complete reconstruction of non-local spin correlations in ferromagnet-normal conductors. This quantum spin tomography is based on cross correlation measurements of electric currents into ferromagnetic terminals with controllable magnetization directions. For normal injectors, non-local spin correlations are universal and strong. The correlations are suppressed by spin-flip scattering and, for ferromagnetic injectors, by increasing injector polarization.
The quantum excitations of the collective magnetization dynamics in a ferromagnet (F) - magnons - enable spin transport without an associated charge current. This pure spin current can be transferred to electrons in an adjacent non-magnetic conductor (N). We evaluate the finite temperature noise of the magnon-mediated spin current injected into N by an adjacent F driven by a coherent microwave field. We find that the dipolar interaction leads to squeezing of the magnon modes giving them wavevector dependent non-integral spin, which directly manifests itself in the shot noise. For temperatures …
The recently introduced concept of "surface Berry plasmons" is studied in the concrete instance of a ferromagnetic conductor in which the Berry curvature, generated by spin-orbit (SO) interaction, has opposite signs for carriers parallel or antiparallel to the magnetization. By using collisionless hy- drodynamic equations with appropriate boundary conditions, we study both the surface plasmons of a three-dimensional ferromagnetic conductor and the edge plasmons of a two-dimensional one. The anomalous velocity and the broken inversion symmetry at the surface or the edge of the conductor create …
We present a comprehensive study of various electromagnetic wave propagation phenomena in a ferromagnetic bulk Rashba conductor from the perspective of quantum mechanical transport. In this system, both the space inversion and time reversal symmetries are broken, as characterized by the Rashba field $α$ and magnetization $M$, respectively. First, we present a general phenomenological analysis of electromagnetic wave propagation in media based on the dielectric tensor. Then, we calculate the microscopic electromagnetic response of the current and spin of conduction electrons subjected to $ α$ a…
We propose spin valves where a 2D non-magnetic conductor is intercalated between two ferromagnetic insulating layers. In this setup, the relative orientation of the magnetizations of the insulating layers can have a strong impact on the in-plane conductivity of the 2D conductor. We first show this for a graphene bilayer, described with a tight-binding model, placed between two ferromagnetic insulators. In the anti-parallel configuration, a band gap opens at the Dirac point, whereas in the parallel configuration, the graphene bilayer remains conducting. We then compute the electronic structure …
The ordinary Hall effect is driven by the Lorentz force, while its anomalous counterpart occurs in ferromagnets. Here we show that the Berry curvature monopole of non-magnetic 2D spin-3/2 holes leads to a novel Hall effect linear in an applied in-plane magnetic field B_x. There is no Lorentz force hence no ordinary Hall effect, while all disorder contributions vanish to leading order in B_x. This intrinsic phenomenon, which we term the anomalous planar Hall effect (APHE), provides a non-quantized footprint of topological transport directly accessible in p-type semiconductors.
Spin Hall effect at finite wave vector in a ferromagnetic conductor is theoretically studied by calculating the spin density as the linear response to an applied electric field. The cases of a spin-orbit interaction due to random impurities and a localized Rashba interaction are considered. It is shown that the spin Hall effect has a broad response for the wave vector $q\lesssim 2\kf$ where $\kf $ is the Fermi wave vector. This fact confirms the local nature of the spin-charge conversion effects.
In quantum nanoelectronics, time-dependent electrical currents are built from few elementary excitations emitted with well-defined wavefunctions. However, despite the realization of sources generating quantized numbers of excitations, and despite the development of the theoretical framework of time-dependent quantum electronics, extracting electron and hole wavefunctions from electrical currents has so far remained out of reach, both at the theoretical and experimental levels. In this work, we demonstrate a quantum tomography protocol which extracts the generated electron and hole wavefunction…
Advanced vector imaging techniques provide us with 3D maps of magnetization fields in which topological concepts can be directly applied to describe real-space experimental textures in non-ideal geometries. Here, the 3D magnetization of a low symmetry permalloy microstructure is obtained by X-ray vector magnetic tomography and analysed in detail in terms of topological charges and emergent fields. A central asymmetric domain wall with a complex 3D structure is observed in which magnetization chirality transitions are mediated by Bloch points arranged in several dipoles and a triplet. The ideal…
The spin-Seebeck effect refers to voltage signals induced in metals by thermally driven spin currents in adjacent magnetic systems. We present a theory of the spin-Seebeck signal in the case where the conductor that supports the voltage signal is the topologically protected two-dimensional surface-state system at the interface between a ferromagnetic insulator (FI) and a topological insulator (TI). Our theory uses a Dirac model for the TI surface-states and assumes Heisenberg exchange coupling between the TI quasiparticles and the FI magnetization. The spin-Seebeck voltage is induced by the TI…
Ferromagnetic materials are the widely used source of spin-polarized electrons in spintronic devices, which are controlled by external magnetic fields or spin-transfer torque methods. However, with increasing demand for smaller and faster spintronic components, utilization of spin-orbit phenomena provides promising alternatives. New materials with unique spin textures are highly desirable since all-electric creation and control of spin polarization is expected, where the strength, as well as an arbitrary orientation of the polarization, can be defined without the use of a magnetic field. In th…
Magnetic electric effects in ferromagnetic metals are discussed from the viewpoint of effective spin electromagnetic field that couples to conduction electron spin. The effective field in the adiabatic limit is the spin Berry's phase in space and time, and it leads to spin motive force (voltage generated by magnetization dynamics) and topological Hall effect due to spin chirality. Its gauge coupling to spin current describes the spin transfer effect, where magnetization structure is driven by an applied spin current. The idea of effective gauge field can be extended to include spin relaxation …
Spin-orbit coupling in inversion-asymmetric magnetic crystals and structures has emerged as a powerful tool to generate complex magnetic textures, interconvert charge and spin under applied current, and control magnetization dynamics. Current-induced spin-orbit torques mediate the transfer of angular momentum from the lattice to the spin system, leading to sustained magnetic oscillations or switching of ferromagnetic as well as antiferromagnetic structures. The manipulation of magnetic order, domain walls and skyrmions by spin-orbit torques provides evidence of the microscopic interactions bet…
We calculate current (shot) noise in a metallic diffusive conductor generated by spin imbalance in the absence of a net electric current. This situation is modeled in an idealized three-terminal setup with two biased ferromagnetic leads (F-leads) and one normal lead (N-lead). Parallel magnetization of the F-leads gives rise in spin-imbalance and finite shot noise at the N-lead. Finite spin relaxation results in an increase of the shot noise, which depends on the ratio of the length of the conductor ($L$) and the spin relaxation length ($l_s$). For $L\gg l_s$ the shot noise increases by a facto…
We consider electron transport in ferromagnets or antiferromagnets sandwiched between metals. When spins in the magnetic materials precess, they emit currents into the surrounding conductors. Generally, adiabatic pumping in mesoscopic systems also enhances current fluctuations. We generalize the description of current fluctuations driven by spin dynamics in three ways using scattering theory. First, our theory describes a general junction with any given electron scattering properties. Second, we consider antiferromagnets as well as ferromagnets. Third, we treat multiterminal devices. Using sho…
The magnetization of a ferromagnet (F) driven out of equilibrium injects pure spin current into an adjacent conductor (N). Such F$|$N bilayers have become basic building blocks in a wide variety of spin based devices. We evaluate the shot noise of the spin current traversing the F$|$N interface when F is subjected to a coherent microwave drive. We find that the noise spectrum is frequency independent up to the drive frequency, and increases linearly with frequency thereafter. The low frequency noise indicates super-Poissonian spin transfer, which results from quasi-particles with effective spi…
When a flow of electron passes through a paramagnetic layer with strong spin-orbit-coupling such as platinum (Pt), a net spin current is produced via spin Hall effect (SHE). This spin current can exert a torque on the magnetization of an adjacent ferromagnetic layer which can be probed via magnetization dynamic response, e.g. spin-torque ferromagnetic resonance (ST-FMR). Nevertheless, that effect in lower frequency magnetization dynamic regime (MHz) where skin effect occurs in high permeability ferromagnetic conductors namely the magneto-impedance (MI) effect can be fundamentally important whi…
We discuss the nonlinear Andreev current of an interacting quantum dot coupled to spin-polarized and superconducting reservoirs when voltage and temperature biases are applied across the nanostructure. Due to the particle-hole symmetry introduced by the superconducting (S) lead, the subgap spin current vanishes identically. Nevertheless, the Andreev charge current depends on the degree of polarization in the ferromagnetic (F) contact since the shift of electrostatic internal potential of the conductor depends on spin orientation of the charge carrier. This spin-dependent potential shift charac…
In metallic ferromagnets, the Berry curvature of underlying quasiparticles can cause an electric voltage perpendicular to both magnetization and an applied temperature gradient, a phenomenon called the anomalous Nernst effect (ANE). Here, we report the observation of a giant ANE in the full-Heusler ferromagnet Co$_2$MnGa, reaching $S_{yx}\sim -6$ $μ$V/K at room $T$, one order of magnitude larger than the maximum value reported for a magnetic conductor. With increasing temperature, the transverse thermoelectric conductivity or Peltier coefficient $α_{yx}$ shows a crossover between $T$-linear an…
Tuning Charge Density Wave in the Transition from Magnetically Frustrated Conductor to Ferrimagnetic Insulator in Carbon Nanowire within Boron Nitride Nanotube
With recent developments in spintronics, it is now possible to envision spin-driven devices with magnets and interconnects that require a new class of transport models using generalized Fermi functions and currents, each with four components: one for charge and three for spin. The corresponding impedance elements are not pure numbers but $4\times4$ matrices. Starting from the Non-Equilibrium Green's Function (NEGF) formalism in the elastic, phase-coherent transport regime, we develop spin generalized Landauer-Büttiker formulas involving such $4\times 4$ conductances, for multi-terminal devices…
