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We report on the optical characterization of non-magnetic metal/ferromagnetic (Co$_{20}$Fe$_{60}$B$_{20}$)/MgO heterostructures and interfaces by using mid infrared spectroscopic ellipsometry at room temperature. We extracted for the mid-infrared range the dielectric function of Co$_{20}$Fe$_{60}$B$_{20}$, that is lacking in literature, from a multisample analysis. From the optical modelling of the heterostructures we detected and determined the dielectric tensor properties of a two-dimensional gas (2DEG) forming at the non-magnetic metal and the CoFeB interface. These properties comprise independent Drude parameters for the in-plane and out-of plane tensor components, with the latter having an epsilon-near-zero frequency within our working spectral range. A feature assigned to spin-orbit coupling (SOC) is identified. Furthermore, it is found that both, the interfacial properties, 2DEG Drude parameters and SOC strength, and the apparent dielectric function of the MgO layer depend on the type of the underlying nonmagnetic metal, namely, Pt, W, or Cu. The results reported here should be useful in tailoring novel phenomena in such types of heterostructures by assessing their optical response noninvasively, complementing existing characterization tools such as angle-resolved photoemission spectroscopy, and those related to electron/spin transport., Comment: 11 pages, 7 figures. See supplemental material in 10.1088/1361-6463/acd00f/meta

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

Strong coupling between light and the fundamental excitations of a two-dimensional electron gas (2DEG) are of foundational importance both to pure physics and to the understanding and development of future photonic nanotechnologies. Here we study the relationship between spin polarization of a 2DEG in a monolayer semiconductor, MoSe$_2$, and light-matter interactions modified by a zero-dimensional optical microcavity. We find robust spin-susceptibility of the 2DEG to simultaneously enhance and suppress trion-polariton formation in opposite photon helicities. This leads to observation of a giant effective valley Zeeman splitting for trion-polaritons (g-factor >20), exceeding the purely trionic splitting by over five times. Going further, we observe robust effective optical non-linearity arising from the highly non-linear behaviour of the valley-specific strong light-matter coupling regime, and allowing all-optical tuning of the polaritonic Zeeman splitting from 4 to >10 meV. Our experiments lay the groundwork for engineering quantum-Hall-like phases with true unidirectionality in monolayer semiconductors, accompanied by giant effective photonic non-linearities rooted in many-body exciton-electron correlations.

Magnetic skyrmions, topological solitons characterized by a two-dimensional swirling spin texture, have recently attracted attention as stable particle-like objects. In a three-dimensional system, a skyrmion can extend in the third dimension forming a robust and flexible string structure, whose unique topology and symmetry are anticipated to host nontrivial functional responses. Here, we experimentally demonstrate the coherent propagation of spin excitations along skyrmion strings for the chiral-lattice magnet Cu2OSeO3. We find that this propagation is directionally non-reciprocal, and the degree of non-reciprocity, as well as the associated group velocity and decay length, are strongly dependent on the character of the excitation modes. Our theoretical calculation establishes the corresponding dispersion relationship, which well reproduces the experimentally observed features. Notably, these spin excitations can propagate over a distance exceeding 10^3 times the skyrmion diameter, demonstrating the excellent long-range nature of the excitation propagation on the skyrmion strings. Our combined experimental and theoretical results offer a comprehensive account of the propagation dynamics of skyrmion-string excitations, and suggest the possibility of unidirectional information transfer along such topologically-protected strings., Comment: Main text (15 pages, 4 figures) + Supplement (19 pages, 8 figures)

Spin-wave resonance measurements were performed in the mixed magnetic phase regime of a Pd-doped FeRh epilayer that appears as the first-order ferromagnetic-antiferromagnetic phase transition takes place. It is seen that the measured value of the exchange stiffness is suppressed throughout the measurement range when compared to the expected value of the fully ferromagnetic regime, extracted via the independent means of a measurement of the Curie point, for only slight changes in the ferromagnetic volume fraction. This behavior is attributed to the influence of the antiferromagnetic phase: inspired by previous experiments that show ferromagnetism to be most persistent at the surfaces and interfaces of FeRh thin films, we modelled the antiferromagnetic phase as forming a thin layer in the middle of the epilayer through which the two ferromagnetic layers are coupled up to a certain critical thickness. The development of this exchange stiffness is then consistent with that expected from the development of an exchange coupling across the magnetic phase boundary, as a consequence of a thickness dependent phase transition taking place in the antiferromagnetic regions and is supported by complimentary computer simulations of atomistic spin-dynamics. The development of the Gilbert damping parameter extracted from the ferromagnetic resonance investigations is consistent with this picture., Comment: Main manuscript: 11 pages, 6 figures. Supplemental material: 2 pages, 1 figure

Precise estimation of spin Hall angle as well as successful maximization of spin-orbit torque (SOT) form a basis of electronic control of magnetic properties with spintronic functionality. Until now, current-nonlinear Hall effect, or second harmonic Hall voltage has been utilized as one of the methods for estimating spin Hall angle, which is attributed to the magnetization oscillation by SOT. Here, we argue the second harmonic Hall voltage in magnetic/nonmagnetic topological insulator (TI) heterostructures, Cr$_x$(Bi$_{1-y}$Sb$_y$)$_{2-x}$Te$_3$/(Bi$_{1-y}$Sb$_y$)$_2$Te$_3$. From the angular, temperature and magnetic field dependence, it is unambiguously shown that the large second harmonic Hall voltage in TI heterostructures is governed not by SOT but mainly by asymmetric magnon scattering mechanism without magnetization oscillation. Thus, this method does not allow an accurate estimation of spin Hall angle when magnons largely contribute to electron scattering. Instead, the SOT contribution in a TI heterostructure is exemplified by current pulse induced non-volatile magnetization switching, which is realized with a current density of $\sim 2.5 \times 10^{10} \mathrm{A/m}^2$, showing its potential as spintronic materials., Comment: 22 pages, 4 figures

The spin-momentum locking at the Dirac surface state of a topological insulator (TI) offers a distinct possibility of a highly efficient charge-to-spin current (C-S) conversion compared with spin Hall effects in conventional paramagnetic metals. For the development of TI-based spin current devices, it is essential to evaluate its conversion efficiency quantitatively as a function of the Fermi level EF position. Here we exemplify a coefficient of qICS to characterize the interface C-S conversion effect by using spin torque ferromagnetic resonance (ST-FMR) for (Bi1-xSbx)2Te3 thin films whose EF is tuned across the band gap. In bulk insulating conditions, interface C-S conversion effect via Dirac surface state is evaluated as nearly constant large values of qICS, reflecting that the qICS is inversely proportional to the Fermi velocity vF that is almost constant. However, when EF traverses through the Dirac point, the qICS is remarkably suppressed possibly due to the degeneracy of surface spins or instability of helical spin structure. These results demonstrate that the fine tuning of the EF in TI based heterostructures is critical to maximizing the efficiency using the spin-momentum locking mechanism., Comment: 20 pages, 3 figures

We have measured spin Hall effects in spin glass metals, CuMnBi alloys, with the spin absorption method in the lateral spin valve structure. Far above the spin glass temperature Tg where the magnetic moments of Mn impurities are randomly frozen, the spin Hall angle of CuMnBi ternary alloy is as large as that of CuBi binary alloy. Surprisingly, however, it starts to decrease at about 4Tg and becomes as little as 7 times smaller at 0.5Tg. A similar tendency was also observed in anomalous Hall effects in the ternary alloys. We propose an explanation in terms of a simple model considering the relative dynamics between the localized moment and the conduction electron spin., Comment: 5 pages, 4 figures

We theoretically study the crossover between spin Hall effect and spin swapping, a recently predicted phenomenon that consists in the interchange between the current flow and its spin polarization directions [Lifshits and Dyakonov, Phys. Rev. Lett. 103, 186601 (2009)]. Using a tight-binding model with spin-orbit coupled disorder, spin Hall effect, spin relaxation and spin swapping are treated on equal footing. We demonstrate that spin Hall effect and spin swapping present very different dependences as a function of the spin-orbit coupling and disorder strengths. As a consequence, we show that spin swapping may even exceed spin Hall effect. Three set-ups are proposed for the experimental observation of the spin swapping effect in metals., Comment: 9 pages, 9 figures

Spin current, i.e. the flow of spin angular momentum or magnetic moment, has recently attracted much attention as the promising alternative for charge current with better energy efficiency. Genuine spin current is generally carried by the spin wave (propagating spin precession) in insulating ferromagnets, and should hold the chiral symmetry when it propagates along the spin direction. Here, we experimentally demonstrate that such a spin wave spin current (SWSC) shows nonreciprocal propagation characters in a chiral-lattice ferromagnet. This phenomenon originates from the interference of chirality between the SWSC and crystal-lattice, which is mediated by the relativistic spin-orbit interaction. The present finding enables the design of perfect spin current diode, and highlights the importance of the chiral aspect in SWSC., Comment: 23 pages, 7 figures

A long spin relaxation time (tausf) is the key for the applications of graphene to spintronics but the experimental values of tausf have been generally much shorter than expected. We show that the usual determination by the Hanle method underestimates tausf if proper account of the spin absorption by contacts is lacking. By revisiting series of experimental results, we find that the corrected tausf are longer and less dispersed, which leads to a more unified picture of tausf derived from experiments. We also discuss how the correction depends on the parameters of the graphene and contacts.

We present measurements of inverse spin Hall effects (ISHEs) in which the conversion of a spin current into a charge current via the ISHE is detected not as a voltage in a standard open circuit but directly as the charge current generated in a closed loop. The method is applied to the ISHEs of Bi-doped Cu and Pt. The derived expression of ISHE for the loop structure can relate the charge current flowing into the loop to the spin Hall angle of the SHE material and the resistance of the loop., Comment: 5 pages, 3 figures

The spin Hall effect (SHE), induced by spin-orbit interaction in nonmagnetic materials, is one of the promising phenomena for conversion between charge and spin currents in spintronic devices. The spin Hall (SH) angle is the characteristic parameter of this conversion. We have performed experiments of the conversion from spin into charge currents by the SHE in lateral spin valve structures. We present experimental results on the extrinsic SHEs induced by doping nonmagnetic metals, Cu or Ag, with impurities having a large spin-orbit coupling, Bi or Pb, as well as results on the intrinsic SHE of Au. The SH angle induced by Bi in Cu or Ag is negative and particularly large for Bi in Cu, 10 times larger than the intrinsic SH angle in Au. We also observed a large SH angle for CuPb but the SHE signal disappeared in a few days. Such an aging effect could be related to a fast mobility of Pb in Cu and has not been observed in CuBi alloys., Comment: 12 pages, 10 figures

We have succeeded in fully describing dynamic properties of spin current including the different spin absorption mechanism for longitudinal and transverse spins in lateral spin valves, which enables to elucidate intrinsic spin transport and relaxation mechanism in the nonmagnet. The deduced spin lifetimes are found independent of the contact type. From the transit-time distribution of spin current extracted from the Fourier transform in Hanle measurement data, the velocity of the spin current in Ag with Py/Ag Ohmic contact turns out much faster than that expected from the widely used model., Comment: 21 pages, 3 figures, 9 pages (supplementary information)

The spin Hall effect and its inverse play key roles in spintronic devices since they allow conversion of charge currents to and from spin currents. The conversion efficiency strongly depends on material details, such as the electronic band structure and the nature of impurities. Here we show an anomaly in the inverse spin Hall effect in weak ferromagnetic NiPd alloys near their Curie temperatures with a shape independent of material details, such as Ni concentrations. By extending Kondo's model for the anomalous Hall effect, we explain the observed anomaly as originating from the second-order nonlinear spin fluctuation of Ni moments. This brings to light an essential symmetry difference between the spin Hall effect and the anomalous Hall effect which reflects the first order nonlinear fluctuations of local moments. Our finding opens up a new application of the spin Hall effect, by which a minuscule magnetic moment can be detected., Comment: 6 pages, 4 figures

We demonstrate that a giant spin Hall effect (SHE) can be induced by introducing a small amount of Bi impurities in Cu. Our analysis based on a new 3-dimensional finite element treatment of spin transport shows that the sign of the SHE induced by the Bi impurities is negative and its spin Hall (SH) angle amounts to -0.24. Such a negative large SH angle in CuBi alloys can be explained by applying the resonant scattering model proposed by Fert and Levy [Phys. Rev. Lett. 106, 157208 (2011)] to 6p impurities., Comment: 5 pages, 4 figures

Spin-flip mechanism in Ag nanowires with MgO surface protection layers has been investigated by means of nonlocal spin valve measurements using Permalloy/Ag lateral spin valves. The spin flip events mediated by surface scattering are effectively suppressed by the MgO capping layer. The spin relaxation process was found to be well described in the framework of Elliott-Yafet mechanism and then the probabilities of spin-filp scattering for phonon or impurity mediated momentum scattering is precisely determined in the nanowires. The temperature dependent spin-lattice relaxation follows the Bloch-Gr\"uneisen theory and falls on to a universal curve for the monovalent metals as in the Monod and Beuneu scaling determined from the conduction electron spin resonance data for bulk., Comment: 18 pages, 3figures

The nonlocal spin injection in lateral spin valves is highly expected to be an effective method to generate a pure spin current for potential spintronic application. However, the spin valve voltage, which decides the magnitude of the spin current flowing into an additional ferromagnetic wire, is typically of the order of 1 {\mu}V. Here we show that lateral spin valves with low resistive NiFe/MgO/Ag junctions enable the efficient spin injection with high applied current density, which leads to the spin valve voltage increased hundredfold. Hanle effect measurements demonstrate a long-distance collective 2-pi spin precession along a 6 {\mu}m long Ag wire. These results suggest a route to faster and manipulable spin transport for the development of pure spin current based memory, logic and sensing devices., Comment: 23 pages, 4 figures

We study the extrinsic spin Hall effect induced by Ir impurities in Cu by injecting a pure spin current into a CuIr wire from a lateral spin valve structure. While no spin Hall effect is observed without Ir impurity, the spin Hall resistivity of CuIr increases linearly with the impurity concentration. The spin Hall angle of CuIr, $(2.1 \pm 0.6)$% throughout the concentration range between 1% and 12%, is practically independent of temperature. These results represent a clear example of predominant skew scattering extrinsic contribution to the spin Hall effect in a nonmagnetic alloy., Comment: 5 pages, 4 figures

We determine the dynamic magnetization induced in non-magnetic metal wedges composed of silver, copper and platinum by means of Brillouin light scattering (BLS) microscopy. The magnetization is transferred from a ferromagnetic Ni80Fe20 layer to the metal wedge via the spin pumping effect. The spin pumping efficiency can be controlled by adding an insulating but transparent interlayer between the magnetic and non-magnetic layer. By comparing the experimental results to a dynamical macroscopic spin-transport model we determine the transverse relaxation time of the pumped spin current which is much smaller than the longitudinal relaxation time.

We have investigated spin Hall effects in 4$d$ and 5$d$ transition metals, Nb, Ta, Mo, Pd and Pt, by incorporating the spin absorption method in the lateral spin valve structure; where large spin current preferably relaxes into the transition metals, exhibiting strong spin-orbit interactions. Thereby nonlocal spin valve measurements enable us to evaluate their spin Hall conductivities. The sign of the spin Hall conductivity changes systematically depending on the number of $d$ electrons. This tendency is in good agreement with the recent theoretical calculation based on the intrinsic spin Hall effect., Comment: 5 pages, 4 figures

We fabricated a current-perpendicular-to-plane pseudo-spin-valve nanopillar comprising a thick and a thin Co rings with deep submicron lateral sizes. The dc current can effectively induce the flux-closure vortex states in the rings with desired chiralities. Abrupt transitions between the vortex states are also realized by the dc current and detected with the giant magnetoresistance effect. Both Oersted field and spin-transfer torque are found important to the magnetic transitions, but the former is dominant. They can be designed to cooperate with each other in the vortex-to-vortex transitions by carefully setting the chirality of the vortex state in the thick Co ring.

We fabricated Co nano-rings incorporated in the vertical pseudo-spin-valve nanopillar structures with deep submicron lateral sizes. It is shown that the current-perpendicular-to-plane giant magnetoresistance can be used to characterize a very small magnetic nano-ring effectively. Both the onion state and the flux-closure vortex state are observed. The Co nano-rings can be switched between the onion states as well as between onion and vortex states not only by the external field but also by the perpendicularly injected dc current.

We investigate the influence of the vortex chirality on the magnetization processes of a magnetostatically coupled pair of magnetic disks. The magnetic vortices with opposite chiralities are realized by introducing asymmetry into the disks. The motion of the paired vortices are studied by measuring the magnetoresistance with lock-in resistance bridge technique. The vortex annihilation process is found to depend on the moving directions of the magnetic vorticies. The experimental results are well reproduced by the micromagnetic simulation., Comment: 10 pages, 4 figures

Reversible spin Hall effect comprising the "direct" and "inverse" spin Hall effects was successfully detected at room temperature. This experimental demonstration proves the fundamental relations called Onsager reciprocal relations between spin and charge currents. A platinum wire with a strong spin-orbit interaction is used not only as a spin current absorber but also as a spin current source in the present lateral structure specially designed for clear detection of both charge and spin accumulations via the spin-orbit interaction. The obtained spin Hall conductivity is much larger than the reported value of Aluminum wire because of the larger spin-orbit interaction., Comment: 12 pages, 4 figures

The induced motion of a magnetic vortex in a micron-sized ferromagnetic disk due to the DC current injection is studied by measuring planar Hall effect. The DC current injection is found to induce the spin torque that sweeps the vortex out of the disk at the critical current while bias magnetic field are applied. The current-induced vortex core displacement deduced from the change in planar Hall resistance is quantitatively consistent with theoretical prediction. Peak structures similar to those originated from spin wave excitations are observed in the differential planar Hall resistance curve., Comment: 12 pages, 4 figures

We have performed non-local spin injection into a nano-scale ferromagnetic particle configured in a lateral spin valve structure to switch its magnetization only by spin current. The non-local spin injection aligns the magnetization of the particle parallel to the magnetization of the spin injector. The responsible spin current for switching is estimated from the experiment to be about 200 $\mu$A, which is reasonable compared with the values obtained for conventional pillar structures. Interestingly the switching always occurs from anti-parallel to parallel in the particle/injector magnetic configurations, whereas no opposite switching is observed. Possible reasons for this discrepancy are discussed., Comment: 13 pages, 4 figures

We demonstrate the method to calculate the spatial distributions of the spin current and accumulation in the multi-terminal ferromagnetic/nonmagnetic hybrid structure using an approximate electro-transmission line. The analyses based on the obtained equation yield the results in good agreement with the experimental ones. This implies that the method allows us to determine the spin diffusion length of additionally connected electrically floating wire from the reduction of the spin signal., Comment: 19 pages, 6 figures

We have investigated experimentally the non-local voltage signal (NLVS) in the lateral permalloy (Py)/Cu/Py spin valve devices with different width of Cu stripes. We found that NLVS strongly depends on the distribution of the spin-polarized current inside Cu strip in the vicinity of the Py-detector. To explain these data we have developed a diffusion model describing spatial (3D) distribution of the spin-polarized current in the device. The results of our calculations show that NLVS is decreased by factor of 10 due to spin flip-scattering occurring at Py/Cu interface. The interface resistivity on Py/Cu interface is also present, but its contribution to reduction of NLVS is minor. We also found that most of the spin-polarized current is injected within the region 30 nm from Py-injector/Cu interface. In the area at Py-detector/Cu interface, the spin-polarized current is found to flow mainly close on the injector side, with 1/e exponential decay in the magnitude within the distance 80 nm., Comment: 10 pages, 14 figures

We present a formalism determining spin-polarized current and electrochemical potential inside arbitrary electric circuit within diffusive regime for parallel/antiparallel magnetic states. When arbitrary nano-structure is expressed by 3-dimensional (3D) electric circuit, we can determine 3D spin-polarized current and electrochemical potential distributions inside it. We apply this technique to (Cu/Co) pillar structures, where pillar is terminated either by infinitely large Cu layer, or by Cu wire with identical cross-sectional area as pillar itself. We found that infinitely large Cu layers work as a strong spin-scatterers, increasing magnitude of spin-polarized current inside the pillar twice and reducing spin accumulation nearly to zero. As most experimentally studied pillar structures are terminated by such a infinitely large layers, we propose modification of standard Valet-Fert formalism to simply include influence of such infinitely large layers., Comment: 13 pages, 12 figues, 1 table