Role of phonon skew scattering in the spin Hall effect of platinum
G. V. Karnad, C. Gorini, K. Lee, T. Schulz, R. Lo Conte, A. W. J. Wells, D. -S. Han, K. Shahbazi, J. -S. Kim, T. A. Moore, H. J. M. Swagten, U. Eckern, R. Raimondi, M. Kläui
We measure and analyze the effective spin Hall angle of platinum in the low residual resistivity regime by second harmonic measurements of the spin-orbit torques for a multilayer of Pt/Co/AlO$_x$. An angular dependent study of the torques allows us to extract the effective spin Hall angle responsible for the damping-like torque in the system. We observe a strikingly non-monotonic and reproducible temperature dependence of the torques. This behavior is compatible with recent theoretical predictions which include both intrinsic and extrinsic (impurities and phonons) contributions to the spin Hall effect at finite temperature.
We study the magnetoresistance of yttrium iron garnet/Pt heterostructures in which the Pt layer was grown via atomic layer deposition (ALD). Magnetotransport experiments in three orthogonal rotation planes reveal the hallmark features of spin Hall magnetoresistance. We estimate the spin transport parameters by comparing the magnitude of the magnetoresistance in samples with different Pt thicknesses. We compare the spin Hall angle and the spin diffusion length of the ALD Pt layers to the values reported for high-quality sputter-deposited Pt films. The spin diffusion length of 1.5nm agrees well …
The spin-Seebeck effect (SSE) in platinum (Pt) and tantalum (Ta) on yttrium iron garnet (YIG) has been investigated by both externally heating the sample (using an on-chip Pt heater on top of the device) as well as by current-induced heating. For SSE measurements, external heating is the most common method to obtain clear signals. Here we show that also by current-induced heating it is possible to directly observe the SSE, separate from the also present spin-Hall magnetoresistance (SMR) signal, by using a lock-in detection technique. Using this measurement technique, the presence of additional…
We report measurements of the spin torque efficiencies in perpendicularly-magnetized Pt/Co bilayers where the Pt resistivity $ρ_{Pt}$ is strongly dependent on thickness $t_{Pt}$ . The damping-like spin Hall torque efficiency per unit current density, $ξ^j_{DL}$ , varies significantly with $t_{Pt}$, exhibiting a peak value $ξ^j_{DL}=0.12$ at $t_{Pt} = 2.8 - 3.9$ nm. In contrast, $ξ^j_{DL}/ρ_{Pt}$ increases monotonically with $t_{Pt}$ and saturates for $t_{Pt} > 5$ nm, consistent with an intrinsic spin Hall effect mechanism, in which $ξ^j_{DL}$ is enhanced by an increase in $ρ_{Pt}$ . Assuming t…
Central focus of spintronics is concentrated on generation of pure spin current and associated spin torque. Pure spin current can be generated by spin Hall effect in heavy metals by passing charge current. By spin Seebeck effect pure spin current can also be generated in ferromagnet. In this work we experimentally demonstrate that if heavy metals like Platinum with high spin orbit coupling carry heat current it can convert it into spin current due to relativistic spin orbit interaction. This conversion of heat current into spin current in non magnet is equivalent of thermally driven spin Hall …
We carried out a concerted effort to determine the absolute sign of the inverse spin Hall effect voltage generated by spin currents injected into a normal metal. We focus on yttrium iron garnet (YIG)|platinum bilayers at room temperature, generating spin currents by microwaves and temperature gradients. We find consistent results for different samples and measurement setups that agree with theory. We suggest a right-hand-rule to define a positive spin Hall angle corresponding to with the voltage expected for the simple case of scattering of free electrons from repulsive Coulomb charges.
Electric gating can strongly modulate a wide variety of physical properties in semiconductors and insulators, such as significant changes of conductivity in silicon, appearance of superconductivity in SrTiO3, the paramagnet-ferromagnet transition in (In,Mn)As and so on. The key to such modulation is charge accumulation in solids. Thus, it has been believed that such modulation is out of reach for conventional metals where the number of carriers is too large. However, success in tuning the Curie temperature of ultrathin cobalt gave hope of finally achieving such degree of control even in metall…
The spin Hall effect (SHE) converts charge current to pure spin currents in orthogonal directions in materials that have significant spin-orbit coupling.The efficiency of the conversion is described by the spin Hall Angle (SHA). The SHA can most readily be inferred by using the generated spin currents to excite or rotate the magnetization of ferromagnetic films or nano-elements via spin-transfer torques.Some of the largest spin torque derived spin Hall angles (ST-SHA) have been reported in platinum. Here we show, using spin torque ferromagnetic resonance (ST-FMR) measurements, that the transpa…
The spin Hall effect in a heavy metal thin film allows to probe the magnetic properties of an adjacent magnetic insulator via magnetotransport measurements. Here, we investigate the magnetoresistive response of yttrium iron garnet/platinum heterostructures from room temperature to beyond the Curie temperature $T_\mathrm{C, YIG} \approx 560\,\mathrm{K}$ of the ferrimagnetic insulator. We find that the amplitude of the (local) spin Hall magnetoresistance decreases monotonically from $300\,\mathrm{K}$ towards $T_\mathrm{C}$, mimicking the evolution of the saturation magnetization of yttrium iron …
Direct Electrical Detection of Spin Chemical Potential Due to Spin Hall Effect in $β$-Tungsten and Platinum Using a Pair of Ferromagnetic and Normal Metal Voltage Probes
Indian Institute of Science Education and Research, Kolkata（印度科学教育研究所加尔各答分校）
We study the magnon spin transport in the magnetic insulator yttrium iron garnet (YIG) in a nonlocal experiment and compare the magnon spin excitation and detection for the heavy metal paramagnetic electrodes platinum (Pt|YIG|Pt) and tantalum (Ta|YIG|Ta). The electrical injection and detection processes rely on the (inverse) spin Hall effect in the heavy metals and the conversion between the electron spin and magnon spin at the heavy metal|YIG interface. Pt and Ta possess opposite signs of the spin Hall angle. Furthermore, their heterostructures with YIG have different interface properties, i.…
A diversity of spin Hall effects in metallic systems is known to rely on Mott skew scattering. In this work its high-temperature counterpart, phonon skew scattering, which is expected to be of foremost experimental relevance, is investigated. In particular, the phonon skew scattering spin Hall conductivity is found to be practically $T$-independent for temperatures above the Debye temperature $T_D$. As a consequence, in Rashba-like systems a high-$T$ linear behavior of the spin Hall angle demonstrates the dominance of extrinsic spin-orbit scattering only if the intrinsic spin splitting is smal…
Current-induced spin-orbit torques in Co$_2$FeAl/Pt ultrathin bilayers are studied using a magnetoresistive harmonic response technique, which distinguishes the dampinglike and fieldlike contributions. The presence of a temperature-dependent magnetic proximity effect is observed through the anomalous Hall and anisotropic magnetoresistances, which are enhanced at low temperatures for thin platinum thicknesses. The fieldlike torque efficiency decreases steadily as the temperature is lowered for all Pt thicknesses studied, which we propose is related to the influence of the magnetic proximity eff…
Hanle magnetoresistance (HMR) is a type of magnetoresistance where interplay of the spin Hall effect, Hanle-type spin precession, and spin-dependent scattering at the top/bottom surfaces in a heavy metal controls the effect. In this study, we modulate HMR in ultrathin Pt by ionic gating, where the surface Rashba field created by a strong electric field at the interface between the ionic gate and Pt plays the dominant role in the modulation. This finding can facilitate investigations of gate-tunable, spin-related effects and fabrication of spin devices.
We report a tunable spin mixing conductance, up to $\pm 22\%$, in a Y${}_{3}$Fe${}_{5}$O${}_{12}$/Platinum (YIG/Pt) bilayer.This control is achieved by applying a gate voltage with an ionic gate technique, which exhibits a gate-dependent ferromagnetic resonance line width. Furthermore, we observed a gate-dependent spin pumping and spin Hall angle in the Pt layer, which is also tunable up to $\pm$ 13.6\%. This work experimentally demonstrates spin current control through spin pumping and a gate voltage in a YIG/Pt bilayer, demonstrating the crucial role of the interfacial charge density for the…
We present a rigorous microscopic theory of the extrinsic spin Hall effect in disordered graphene based on a nonperturbative quantum diagrammatic treatment incorporating skew scattering and anomalous---impurity concentration-independent---quantum corrections on equal footing. The leading skew scattering contribution to the spin Hall conductivity is shown to quantitatively agree with Boltzmann transport theory over a wide range of parameters. Our self-consistent approach---where all topologically equivalent noncrossing diagrams are resummed---unveils that the skewness generated by spin--orbit-a…
Anomalous Hall-like signals in platinum in contact with magnetic insulators are common observations that could be explained by either proximity magnetization or spin Hall magnetoresistance. In this work, longitudinal and transverse magnetoresistances are measured in a pure gold thin film on the ferrimagnetic insulator Y$_3$Fe$_5$O$_{12}$ (Yttrium Iron Garnet, YIG). We show that both the longitudinal and transverse magnetoresistances have quantitatively consistent scaling in YIG/Au and in a YIG/Pt reference system when applying the Spin Hall magnetoresistance framework. No contribution of an an…
We report a novel spin injection and detection mechanism via the anomalous Hall effect in a ferromagnetic metal. The anomalous spin Hall effect (ASHE) refers to the transverse spin current generated within the ferromagnet. We utilize the ASHE and its reciprocal effect to electrically inject and detect magnons in a magnetic insulator in a non-local geometry. Our experiments reveal that permalloy can have a higher spin injection and detection efficiency to that of platinum, owing to the ASHE. We also demonstrate the tunability of the ASHE via the orientation of the permalloy magnetization, thus …
An oscillographic study of the Hall voltage with an unpolarized alternating current through a platinum sample revealed choral features of the Hall effect, which clearly demonstrate the presence of the spin Hall effect in metals with a noticeable spin-orbit interaction. It was confirmed that, as in the case of direct current, the possibility of a spin-Hall effect is associated with the presence of an imbalance of the spins and charges at the edges of the samples, which is realized using their asymmetric geometry. In particular, it was found that such chiral features of the nonequilibrium spin-H…
We consider an extrinsic contribution to the anomalous and spin Hall effect in dilute alloys based on Fe, Co, Ni, and Pt hosts with different substitutional impurities. It is shown that a strong skew-scattering mechanism is absent in such crystals with multi-sheeted Fermi surfaces. Based on this finding, we conclude on the mutual exclusion of strong intrinsic and skew-scattering contributions to the considered transport phenomena. It also allows us to draw general conditions for materials where the anomalous Hall effect caused by the skew scattering can be achieved giant.
In this note we summarize our recent results for the temperature dependence of transport coefficients of metallic films in the presence of spin-orbit coupling. Our focus is on (i) the spin Nernst and the thermal Edelstein effects, and (ii) the phonon skew scattering contribution to the spin Hall conductivity, which is relevant for the temperature dependence of the spin Hall angle. Depending on the parameters, the latter is expected to show a non-monotonous behavior.
We have studied the spin transport and the spin Hall effect as a function of temperature for platinum (Pt) and gold (Au) in lateral spin valve structures. First, by using the spin absorption technique, we extract the spin diffusion length of Pt and Au. Secondly, using the same devices, we have measured the spin Hall conductivity and analyzed its evolution with temperature to identify the dominant scattering mechanisms behind the spin Hall effect. This analysis confirms that the intrinsic mechanism dominates in Pt whereas extrinsic effects are more relevant in Au. Moreover, we identify and quan…
Recent experimental observations of unexpectedly large thermal Hall conductivities, $κ_H$, in insulating materials, including the parent compounds of the high temperature superconducting cuprates, likely reflect an extrinsic contribution from a yet to be identified extrinsic source of skew scattering of acoustic phonons. We show that resonant scattering of phonons from a certain class of three-level systems produces strong skew scattering in the presence of a modest magnetic field. We interpret this as a first step towards understanding the experiments.
Spin pumping by ferromagnetic resonance is one of the most common technique to determine spin hall angles, Edelstein lengths or spin diffusion lengths of a large variety of materials. In recent years, rising concerns have appeared regarding the interpretation of these experiments, underlining that the signal could arise purely from thermoelectric effects, rather than from coherent spin pumping. Here, we propose a method to evaluate the presence or absence of thermal effects in spin pumping signals, by combining bolometry and spin pumping by ferromagnetic resonance measurements, and comparing t…
Intrinsic spin Hall conductivities are calculated for strong spin-orbit Bi$_{1-x}$Sb$_x$ semimetals, from the Kubo formula and using Berry curvatures evaluated throughout the Brillouin zone from a tight-binding Hamiltonian. Nearly-crossing bands with strong spin-orbit interaction generate giant spin Hall conductivities in these materials, ranging from 474 ($\hbar$/e)($Ω$cm)$^{-1}$ for bismuth to 96 ($\hbar$/e)($Ω$cm)$^{-1}$ for antimony; the value for bismuth is more than twice that of platinum. The large spin Hall conductivities persist for alloy compositions corresponding to a three-dimensio…
We quantify the relative weight of inverse spin Hall and spin rectification effects occurring in RF-sputtered polycrystalline permalloy, molecular beam epitaxy-grown epitaxial iron and liquid phase epitaxy-grown yttrium-iron-garnet bilayer systems with different capping materials. To distinguish the spin rectification signal from the inverse spin Hall voltage the external magnetic field is rotated in-plane to take advantage of the different angular dependencies of the prevailing effects. We prove that in permalloy anisotropic magnetoresistance is the dominant source for spin rectification whil…
The second-order nonlinear Hall effect illuminates a frequency-doubling transverse current emerging in quantum materials with broken inversion symmetry even when time-reversal symmetry is preserved. This nonlinear response originates from both the Berry curvature dipole and the chiral Bloch electron skew scatterings, reflecting various information of the lattice symmetries, band dispersions, and topology of the electron wavefunctions. Even though many efforts have been put in detecting the nonlinear Hall effect in diverse condensed matter systems, effective manipulation of the two principal me…
Spin-transfer torque and spin Hall effects combined with their reciprocal phenomena, spin-pumping and inverse spin Hall (ISHE) effects, enable the reading and control of magnetic moments in spintronics. The direct observation of these effects remains elusive in antiferromagnetic-based devices. We report sub-terahertz spin-pumping at the interface of a uniaxial insulating antiferromagnet MnF2 and platinum. The measured ISHE voltage arising from spin-charge conversion in the platinum layer depends on the chirality of the dynamical modes of the antiferromagnet, which is selectively excited and mo…
The anomalous Hall effect in ferromagnetic metals is classified into two based on the mechanism. The first one is the intrinsic Hall effect due to the Berry curvature in momentum space; this is a Hall effect that solely arises from the band structure of solids. On the other hand, another contribution to the Hall effect, so-called extrinsic mechanism, comes from impurity scatterings such as skew scattering and side jump; for the extrinsic mechanism, the spin-orbit interaction of the impurity ions is often required. These two mechanisms are often discussed separately; the intrinsic Hall effect i…
We formulate a theory of the AC spin Hall magnetoresistance (SMR) in a bilayer system consisting of a magnetic insulator such as yttrium iron garnet (YIG) and a heavy metal such as platinum (Pt). We derive expressions for the DC voltage generation based on the drift-diffusion spin model and quantum mechanical boundary condition at the interface that reveal a spin torque ferromagnetic resonance (ST-FMR). We predict that ST-FMR experiments will reveal valuable information on the current-induced magnetization dynamics of magnetic insulators and AC spin Hall effect.
Giant Spin Hall Effect Induced by Skew Scattering from Bismuth Impurities inside Thin Film CuBi Alloys
我们证明了通过在Cu中引入少量Bi杂质可以诱导巨自旋霍尔效应（SHE）。基于一种新的三维自旋输运有限元方法的分析表明，Bi杂质诱导的SHE符号为负，其自旋霍尔角为-0.24。CuBi合金中的这种负的大SH角可以通过应用由Fert和Levy [Phys. Rev. Lett. 106，157208（2011）]至6p杂质。
Impact of current-induced magnons on spin-orbit torque analysis
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；University of Groningen（格罗宁根大学）；HUN-REN Centre for Energy Research, Institute of Technical Physics and Materials Science（匈牙利研究与教育网络能源研究中心技术物理与材料科学研究所）
We measure the low-frequency thermal fluctuations of pure spin current in a Platinum film deposited on yttrium iron garnet via the inverse spin Hall effect (ISHE)-mediated voltage noise as a function of the angle $α$ between the magnetization and the transport direction. The results are consistent with the fluctuation dissipation theorem in terms of the recently discovered spin Hall magnetoresistance (SMR). We present a microscopic description of the $α$ dependence of the voltage noise in terms of spin current fluctuations and ISHE.
Iridium is a very promising material for spintronic applications due to its interesting magnetic properties such as large RKKY exchange coupling as well as its large spin-orbit coupling value. Ir is for instance used as a spacer layer for perpendicular synthetic antiferromagnetic or ferrimagnet systems. However, only a few studies of the spintronic parameters of this material have been reported. In this paper, we present inverse spin Hall effect - spin pumping ferromagnetic resonance measurements on CoFeB/Ir based bilayers to estimate the values of the effective spin Hall angle, the spin diffu…
There exists considerable confusion in estimating the spin diffusion length of materials with high spin-orbit coupling from spin pumping experiments. For designing functional devices, it is important to determine the spin diffusion length with sufficient accuracy from experimental results. An inaccurate estimation of spin diffusion length also affects the estimation of other parameters (e.g., spin mixing conductance, spin Hall angle) concomitantly. The spin diffusion length for platinum (Pt) has been reported in literature in a wide range of 0.5 - 14 nm, and particularly it is a constant value…
Exciton Valley Hall effect is the spatial separation of the valley-tagged excitons in the presence of a drag force. Usually, the effect is associated with the anomalous velocity acquired by the particles due to the Berry curvature of the Bloch bands. Here we show that the anomalous velocity plays no role in the exciton valley Hall effect, which is governed by the side-jump and skew scattering mechanisms. We develop microscopic theory of the exciton valley Hall effect in the presence of synthetic electric field and phonon drag and calculate all relevant contributions to the valley Hall current …
