Spin Current Density Research Articles

Spin Funneling for Enhanced Spin Injection into Ferromagnets.

It is well-established that high spin-orbit coupling (SOC) materials convert a charge current density into a spin current density which can be used to switch a magnet efficiently and there is increasing interest in identifying materials with large spin Hall angle for lower switching current. Using experimentally benchmarked models, we show that composite structures can be designed using existing spin Hall materials such that the effective spin Hall angle is larger by an order of magnitude. The basic idea is to funnel spins from a large area of spin Hall material into a small area of ferromagnet using a normal metal with large spin diffusion length and low resistivity like Cu or Al. We show that this approach is increasingly effective as magnets get smaller. We avoid unwanted charge current shunting by the low resistive NM layer utilizing the newly discovered phenomenon of pure spin conduction in ferromagnetic insulators via magnon diffusion. We provide a spin circuit model for magnon diffusion in FMI that is benchmarked against recent experiments and theory.

Optimization of spin injection and spin detection in lateral nanostructures by geometrical means

Lateral spin devices are an important concept in nowadays all-metallic spintronic devices. One of the key problems is to obtain large spin injection and detection efficiency. Several concepts has been envisaged, such as to use half-metallic ferromagnetic electrodes or spin-polarized interface barriers. Within this work, we address the optimization of spin devices (namely optimization of spin current density, spin current and spin accumulation) based on adjustment of the geometry (dimensions) of the lateral device, material selection of spin conductors, jointly with optimization of the interface resistance.

Multi-Qhexagonal spin density waves and dynamically generated spin-orbit coupling: Time-reversal invariant analog of the chiral spin density wave

We study hexagonal spin-channel ("triplet") density waves with commensurate $M$-point propagation vectors. We first show that the three $Q=M$ components of the singlet charge density and charge-current density waves can be mapped to multi-component $Q=0$ nonzero angular momentum order in three dimensions ($3D$) with cubic crystal symmetry. This one-to-one correspondence is exploited to define a symmetry classification for triplet $M$-point density waves using the standard classification of spin-orbit coupled electronic liquid crystal phases of a cubic crystal. Through this classification we naturally identify a set of non-coplanar spin density and spin-current density waves: the chiral spin density wave and its time-reversal invariant analog. These can be thought of as $3D$ $L=2$ and $L=4$ spin-orbit coupled isotropic $\beta$-phase orders. In contrast, uniaxial spin density waves are shown to correspond to $\alpha$-phases. The non-coplanar triple-$M$ spin-current density wave realizes a novel $2D$ semimetal state with three flavors of four-component spin-momentum locked Dirac cones, protected by a crystal symmetry akin to non-symmorphic symmetry, and sits at the boundary between a trivial and topological insulator. In addition, we point out that a special class of classical spin states, defined as classical spin states respecting all lattice symmetries up to global spin rotation, are naturally obtained from the symmetry classification of electronic triplet density waves. These symmetric classical spin states are the classical long-range ordered limits of chiral spin liquids.

Hydrodynamics of Turning Flocks.

We present a hydrodynamic model of flocking that generalizes the familiar Toner-Tu equations to incorporate turning inertia of well-polarized flocks. The continuum equations controlled by only two dimensionless parameters, orientational inertia and alignment strength, are derived by coarse-graining the inertial spin model recently proposed by Cavagna etal. The interplay between orientational inertia and bend elasticity of the flock yields anisotropic spin waves that mediate the propagation of turning information throughout the flock. The coupling between spin-current density to the local vorticity field through a nonlinear friction gives rise to a hydrodynamic mode with angular-dependent propagation speed at long wavelengths. This mode becomes unstable as a result of the growth of bend and splay deformations augmented by the spin wave, signaling the transition to complex spatiotemporal patterns of continuously turning and swirling flocks.

Reduction of phase noise in nanowire spin orbit torque oscillators.

Spin torque oscillators (STOs) are compact, tunable sources of microwave radiation that serve as a test bed for studies of nonlinear magnetization dynamics at the nanometer length scale. The spin torque in an STO can be created by spin-orbit interaction, but low spectral purity of the microwave signals generated by spin orbit torque oscillators hinders practical applications of these magnetic nanodevices. Here we demonstrate a method for decreasing the phase noise of spin orbit torque oscillators based on Pt/Ni80Fe20 nanowires. We experimentally demonstrate that tapering of the nanowire, which serves as the STO active region, significantly decreases the spectral linewidth of the generated signal. We explain the observed linewidth narrowing in the framework of the Ginzburg-Landau auto-oscillator model. The model reveals that spatial non-uniformity of the spin current density in the tapered nanowire geometry hinders the excitation of higher order spin-wave modes, thus stabilizing the single-mode generation regime. This non-uniformity also generates a restoring force acting on the excited self-oscillatory mode, which reduces thermal fluctuations of the mode spatial position along the wire. Both these effects improve the STO spectral purity.

Imaging of current density distributions with a Nb weak-link scanning nano-SQUID microscope.

Superconducting quantum interference devices (SQUIDs) are accepted as one of the highest magnetic field sensitive probes. There are increasing demands to image local magnetic fields to explore spin properties and current density distributions in a two-dimensional layer of semiconductors or superconductors. Nano-SQUIDs have recently attracting much interest for high spatial resolution measurements in nanometer-scale samples. Whereas weak-link Dayem Josephson junction nano-SQUIDs are suitable to miniaturization, hysteresis in current-voltage (I-V) characteristics that is often observed in Dayem Josephson junction is not desirable for a scanning microscope. Here we report on our development of a weak-link nano-SQUIDs scanning microscope with small hysteresis in I-V curve and on reconstructions of two-dimensional current density vector in two-dimensional electron gas from measured magnetic field.

Controlling and probing non-abelian emergent gauge potentials in spinor Bose-Fermi mixtures.

Gauge fields, typified by the electromagnetic field, often appear as emergent phenomena due to geometrical properties of a curved Hilbert subspace, and provide a key mechanism for understanding such exotic phenomena as the anomalous and topological Hall effects. Non-abelian gauge potentials serve as a source of non-singular magnetic monopoles. Here we show that unlike conventional solid materials, the non-abelianness of emergent gauge potentials in spinor Bose-Fermi atomic mixtures can be continuously varied by changing the relative particle-number densities of bosons and fermions. The non-abelian feature is captured by an explicit dependence of the measurable spin current density of fermions in the mixture on the variable coupling constant. Spinor mixtures also provide us with a method to coherently and spontaneously generate a pure spin current without relying on the spin Hall effect. Such a spin current is expected to have potential applications in the new generation of atomtronic devices.

Long-range spin-triplet correlations and edge spin currents in diffusive spin–orbit coupled SNS hybrids with a single spin-active interface

Utilizing a SU(2) gauge symmetry technique in the quasiclassical diffusive regime, we theoretically study finite-sized two-dimensional intrinsic spin–orbit coupled superconductor/normal-metal/superconductor (S/N/S) hybrid structures with a single spin-active interface. We consider intrinsic spin–orbit interactions (ISOIs) that are confined within the N wire and absent in the s-wave superconducting electrodes (S). Using experimentally feasible parameters, we demonstrate that the coupling of the ISOIs and spin moment of the spin-active interface results in maximum singlet-triplet conversion and accumulation of spin current density at the corners of the N wire nearest the spin-active interface. By solely modulating the superconducting phase difference, we show how the opposing parities of the charge and spin currents provide an effective venue to experimentally examine pure edge spin currents not accompanied by charge currents. These effects occur in the absence of externally imposed fields and moreover are insensitive to the arbitrary orientations of the interface spin moment. The experimental implementation of these robust edge phenomena are also discussed.

Interfacial spin-filter assisted spin transfer torque effect in Co/BeO/Co magnetic tunnel junction

The first-principles calculation is employed to demonstrate the spin-selective transport properties and the non-collinear spin-transfer torque (STT) effect in the newly proposed Co/BeO/Co magnetic tunnel junction. The subtle spin-polarized charge transfer solely at O/Co interface gives rise to the interfacial spin-filter (ISF) effect, which can be simulated within the tight binding model to verify the general expression of STT. This allows us to predict the asymmetric bias behavior of non-collinear STT directly via the interplay between the first-principles calculated spin current densities in collinear magnetic configurations. We believe that the ISF effect, introduced by the combination between wurtzite-BeO barrier and the fcc-Co electrode, may open a new and promising route in semiconductor-based spintronics applications.

Spontaneous edge accumulation of spin currents in finite-size two-dimensional diffusive spin–orbit coupled SFS heterostructures

We theoretically study spin and charge currents through finite-size two-dimensional s-wave superconductor/uniform ferromagnet/s-wave superconductor (S/F/S) junctions with intrinsic spin–orbit interactions (ISOIs) using a quasiclassical approach. Considering experimentally realistic parameters, we demonstrate that the combination of spontaneously broken time-reversal symmetry and lack of inversion symmetry can result in spontaneously accumulated spin currents at the edges of finite-size two-dimensional magnetic S/F/S hybrids. Due to the spontaneous edge spin accumulation, the corners of the F wire host the maximum spin current density. We further reveal that this type edge phenomena is robust and independent of either the actual type of ISOIs or exchange field orientation. Moreover, we study the spin current-phase relations in these diffusive spin–orbit coupled S/F/S junctions. Our results unveil net spin currents, not accompanied by charge supercurrents, that spontaneously accumulate at the sample edges through a modulating superconducting phase difference. Finally, we discuss possible experimental implementations to observe these edge phenomena.

Spin Hall effect and irreversible thermodynamics: Center-to-edge transverse current-induced voltage

We examine the Dyakonov and Perel theory of the Spin Hall effect (SHE) from the viewpoint of irreversible thermodynamics, which is more constraining than the symmetry arguments of pure phenomenology. As thermodynamic driving forces we include the thermal gradient, the gradient of the electrochemical potential (rather than the potential gradient and density gradient separately), and the ``internal'' magnetic field that is thermodynamically conjugate to the magnetization. In turn, we obtain the form of bulk transport coefficients relating the fluxes to the thermodynamic forces. Relative to Dyakonov and Perel, in addition to the new terms due to thermal gradients, the Onsager relations require three new (nonlinear) terms in the current density, and minor revisions in the current density and spin current density. For a longitudinal current along a strip, the center-to-edge transverse voltage difference, due both to the $\ensuremath{-}\ensuremath{\beta}\stackrel{P\vec}{P}\ifmmode\times\else\texttimes\fi{}\stackrel{P\vec}{E}$ term of of the number current density $\stackrel{P\vec}{q}$ and to one of the new current density terms, is calculated. An ac capacitative probe likely would not significantly disturb this effect. An appendix explicitly relates the anomalous Hall Effect to the term in the (vector) number flux that is Onsager related to the SHE term in the (tensor) spin flux.

Modelling of multipurpose spintronic devices

Modelling of spin transport and spin dynamics, as a prerequisite for designing spintronic devices, is considered. Spin injection into a semiconductor under charge depletion, charge neutrality, and charge accumulation is investigated. The existence of a maximum spin current density in the bulk at a large spin current density at the interface in charge accumulation is related to the spin current at the charge neutrality condition. Then, a novel multipurpose spintronic device is proposed and its structure as well as its working principle is explained. Two important applications for this structure, a flip flop and a nano–scale oscillator, are further elucidated and the properties related to these applications are investigated.

Parity violating radiative emission of neutrino pairs in heavy alkaline earth atoms of even isotopes

Metastable excited states ${}^3P_2, {}^3P_0$ of heavy alkaline earth atoms of even isotopes are studied for parity violating (PV) effects in radiative emission of neutrino pair (RENP). PV terms arise from interference between two diagrams containing neutrino pair emission of valence spin current and nuclear electroweak charge density proportional to the number of neutrons in nucleus. This mechanism gives large PV effects, since it does not suffer from the suppression of 1/(electron mass) usually present for non-relativistic atomic electrons. A controllable magnetic field is crucial to identify RENP process by measuring PV observables. Results of PV asymmetries under the magnetic field reversal and the photon circular polarization reversal are presented for an example of Yb atom.

Spin injection in a semiconductor through a space-charge layer

The electron spin properties provided by semiconductors are of immense interest because of their potential for future spin-driven microelectronic devices. Modern charge-based electronics is dominated by silicon, and understanding the details of spin propagation in silicon structures is key for novel spin-based device applications. We performed simulations on electron spin transport in an n-doped silicon bar with spin-dependent conductivity. Special attention is paid to the investigation of a possible spin injection enhancement through an interface space-charge layer. We found substantial spin transport differences between the spin injection behavior through an accumulation and a depletion layer. However, in both cases the spin current density can not be significantly higher than the spin current density at charge neutrality. Thus, the maximum spin current in the bulk is determined by its value at the charge neutrality condition - provided the spin polarization at the interface as well as the charge current are fixed.

Electron spin and probability current density in quantum mechanics

This paper analyzes how the existence of electron spin changes the equation for the probability current density in the quantum-mechanical continuity equation. A spinful electron moving in a potential energy field experiences the spin-orbit interaction, and that additional term in the time-dependent Schrödinger equation places an additional spin-dependent term in the probability current density. Further, making an analogy with classical magnetostatics hints that there may be an additional magnetization current contribution. This contribution seems not to be derivable from a non-relativistic time-dependent Schrödinger equation, but there is a procedure described in the quantum mechanics textbook by Landau and Lifschitz to obtain it. We utilize and extend their procedure to obtain this magnetization term, which also gives a second derivation of the spin-orbit term. We conclude with an evaluation of these terms for the ground state of the hydrogen atom with spin-orbit interaction. The magnetization contribution is generally the larger one, except very near an atomic nucleus.

Triplet pair correlations and nonmonotonic supercurrent decay with Cr thickness in Nb/Cr/Fe/Nb Josephson devices

Supercurrents carry charge but not spin in the vast majority of superconductors. This is because the charge carriers are Cooper pairs which are formed of electrons with antiparallel spins (singlet pairs). It is now established that if singlet pairs propagate through a superconductor interface with an inhomogeneous ferromagnet, triplet pair correlations form so the supercurrents can acquire a net spin component. Although the spins at sputter-deposited Fe/Cr interfaces can be frustrated due to surface roughness and interdiffusion, an antiferromagnetic spin density wave (SDW) state can still form in Cr close to the interface. Here, we show evidence for triplet pair correlations in Josephson junctions with Cr/Fe and Cr/Fe/Cr barriers. Although the exact mechanism of pair conversion is unknown, we propose a simple model in which a SDW state in Cr and frustrated spins at the Cr/Fe interfaces serve as spin-mixers for generating triplet supercurrents and so provide a potential means to generating large superconducting spin current densities.

Anomalous scaling of spin accumulation in ferromagnetic tunnel devices with silicon and germanium

The magnitude of spin accumulation created in semiconductors by electrical injection of spin-polarized electrons from a ferromagnetic tunnel contact is investigated, focusing on how the spin signal detected in a Hanle measurement varies with the thickness of the tunnel oxide. An extensive set of spin-transport data for Si and Ge magnetic tunnel devices reveals a scaling with the tunnel resistance that violates the core feature of available theories, namely, the linear proportionality of the spin voltage to the injected spin current density. Instead, an anomalous scaling of the spin signal with the tunnel resistance is observed, following a power law with an exponent between 0.75 and 1 over 6 decades. The scaling extends to tunnel resistance values larger than 10 9 �μ m 2 , far beyond the regime where the classical impedance mismatch or back flow into the ferromagnet play a role.Thisscalingisincompatiblewithexistingtheoryfordirecttunnelinjectionofspinsintothesemiconductor.It also demonstrates conclusively that the large spin signal does not originate from two-step tunneling via localized states near the oxide/semiconductor interface. Control experiments show that spin accumulation in localized states within the tunnel barrier or artifacts are also not responsible. Altogether, the scaling results suggest that, contrary to all existing descriptions, the spin signal is proportional to the applied bias voltage, rather than the (spin) current.

Temperature dependence of the photo-induced inverse spin Hall effect in Au/InP hybrid structures

Photo-induced Inverse Spin Hall Effect (ISHE) measurements on Au/InP hybrid structures are performed over a temperature range of 45 to 300 K. Dependence of the spin current density on the degree of circular polarization and also on the angle of incidence of laser beam confirms the ISHE origin of measured signal. The magnitude of ISHE increases with sample cooling. A numerical model based on the spin relaxation of non-equilibrium spin-polarized electrons is proposed for predicting the temperature dependence of ISHE. Our results indicate that the proposed device can be used as a spin photodetector over a wide temperature range.

Topological defects of Néel order and Kondo singlet formation for the Kondo-Heisenberg model on a honeycomb lattice

Heavy fermion systems represent a prototypical setting to study magnetic quantum phase transitions. A particular focus has been on the physics of Kondo destruction, which captures quantum criticality beyond the Landau framework of order-parameter fluctuations. In this context, we study the spin one-half Kondo-Heisenberg model on a honeycomb lattice at half filling. The problem is approached from the Kondo destroyed, antiferromagnetically ordered insulating phase. We describe the local moments in terms of a coarse grained quantum non-linear sigma model, and show that the skyrmion defects of the antiferromagnetic order parameter host a number of competing order parameters. In addition to the spin Peierls, charge and current density wave order parameters, we identify for the first time Kondo singlets as the competing orders of the antiferromagnetism. We show that the antiferromagnetism and various competing singlet orders can be related to each other via generalized chiral transformations of the underlying fermions. We also show that the conduction electrons acquire a Berry phase through their coupling to the hedgehog configurations of the N\'eel order, which cancels the Berry phase of the local moments. Our results demonstrate the competition between the Kondo-singlet formation and spin-Peierls order when the antiferromagnetic order is suppressed, thereby shedding new light on the global phase diagram of heavy fermion systems at zero temperature.

Magnon Turbulence in Ferromagnetic Nanocontact

We theoretically examine the minimal factors for the emergence of magnon turbulence under current. We show that the turbulence emerges even in the nanocontact, where only the exchange term and the spin-transfer torque contribute in the determination of the magnetic structure and dynamics therein. Namely, the sufficient factors for the emergence of the turbulence are only the exchange and the spin-transfer torque. We also show that the critical spin current density of the magnon turbulence is related to a current-induced exchange length. The emergence of the magnon turbulence is characterized by a crossover of the length and the system size.