The spin Hall effect is a phenomenon that an electric field induces a spin Hall current. In this Letter, we examine the inverse effect that, in a ferromagnetic conductor, a charge Hall current is induced by a spin motive force, or a spin-dependent effective ` electric' field ${\bm E}_{\rm s}$, arising from the time variation of magnetization texture. By considering skew-scattering and side-jump processes due to spin-orbit interaction at impurities, we obtain the Hall current density as $σ_{\rm SH} {\bm n}\times{\bm E}_{\rm s}$, where ${\bm n}$ is the local spin direction and $σ_{\rm SH}$ is the spin Hall conductivity. The Hall angle due to the spin motive force is enhanced by a factor of $P^{2}$ compared to the conventional anomalous Hall effect due to the ordinary electric field, where $P$ is the spin polarization of the current. The Hall voltage is estimated for a field-driven domain wall oscillation in a ferromagnetic nanowire.
We formulate a quantitative theory of an electromotive force of spin origin, i.e., spin-motive force, by the equation-of-motion approach. In a ferromagnetic metal, electrons couple to the local magnetization via the exchange interaction. Electrons feel spin dependent forces due to this interaction, and then the spin-motive force and the anomalous Hall effect appears. We have revealed that the origin of these phenomena is a misalignment between the conduction electron spin and the local magnetization.
Non-uniform magnetic structures produce emergent electromagnetic phenomena such as the topological Hall effect and the spin-motive force (SMF). The experimental reports on the SMF, however, are very few and the relationship between the SMF and material parameters is still unclear. In this study, we investigated the SMF in ferrimagnetic GdFeCo alloy films using the spin-torque-induced ferromagnetic resonance method and clarified the relationship. The amplitude of the detected SMF becomes larger than that of the transition metal alloy FeCo by the Gd doping and reaches the maximum near a Gd compo…
It is demonstrated that upon pulsed microwave excitation, the temporal behavior of a spin-wave induced inverse spin Hall voltage in a magnetic insulator-nonmagnetic metal structure is distinctly different from the temporal evolution of the directly excited spin-wave mode from which it originates. The difference in temporal behavior is attributed to the excitation of long-lived secondary spin-wave modes localized at the insulator-metal interface.
We theoretically examine the spin-transfer torque in the presence of spin-orbit interaction (SOI) at impurities in a ferromagnetic metal on the basis of linear response theory. We obtained, in addition to the usual spin-transfer torque, a new contributioin $\sim {\bm j}_{\rm SH}^{\phantom{\dagger}} \cdot \nabla {\bm n}$ in the first order in SOI, where ${\bm j}_{\rm SH}^{\phantom{\dagger}}$ is the spin Hall current driven by an external electric field. This is a reaction to inverse spin Hall effect driven by spin motive force in a ferromagnet.
Conversion of traveling magnons into an electron carried spin current is demonstrated in a time resolved experiment using a spatially separated inductive spin-wave source and an inverse spin Hall effect (ISHE) detector. A short spin-wave packet is excited in a yttrium-iron garnet (YIG) waveguide by a microwave signal and is detected at a distance of 3 mm by an attached Pt layer as a delayed ISHE voltage pulse. The delay in the detection appears due to the finite spin-wave group velocity and proves the magnon spin transport. The experiment suggests utilization of spin waves for the information …
We study the coupled dynamics of spin and charge currents in a two-dimensional electron gas in the transport diffusive regime. For systems with inversion symmetry there are established relations between the spin Hall effect, the anomalous Hall effect and the inverse spin Hall effect. However, in two-dimensional electron gases of semiconductors like GaAs, inversion symmetry is broken so that the standard arguments do not apply. We demonstrate that in the presence of a Rashba type of spin-orbit coupling (broken structural inversion symmetry) the anomalous Hall effect, the spin Hall and inverse s…
We have proposed a method to synchronize multiple spin-transfer torque oscillators based on spin pumping, inverse spin Hall, and spin Hall effects. The proposed oscillator system consists of a series of nano-magnets in junction with a normal metal with high spin-orbit coupling, and an accumulative feedback loop. We conduct simulations to demonstrate the effect of modulated charge currents in the normal metal due to spin pumping from each nano-magnet. We show that the interplay between the spin Hall effect and inverse spin Hall effect results in synchronization of the nano-magnets.
We studied the electric current induced in a two-dimensional electron gas by the spin current, in the presence of Rashba and cubic Dresselhaus spin-orbit interactions. We found out that the factor relating these currents is not universal, but rather depends on the origin of the spin current. Drastic distinction has been found between two cases: the spin current created by diffusion of an inhomogeneous spin density, and the pure homogeneous spin current. We found out that in the former case the ISHE electric current is finite, while it turns to zero in the latter case, if the spin-orbit couplin…
We measure magnetic field dependence of the Hall angle in a metallic ferromagnetic nanomagnet with stable local magnetic moments where the adopted mechanisms of Hall effect predict linear plus a constant dependence on the external field originating from the ordinary and anomalous Hall effects, respectively. We suggest that the experimentally observed deviations from this dependence is caused by the inverse spin Hall effect (ISHE) and develop a phenomenological theory, which predicts a unique nonlinear dependence of the ISHE contribution on the external magnetic field. Perfect agreement between…
We present gauge-invariant theory of the dynamic inverse spin Hall effect driven by the spin--orbit interaction in metallic systems. Charge conservation is imposed diagrammatically by including vertex corrections. We show the charge current is induced by an effective electric field that is proportional to the spin current pumped by the magnetization dynamics. The result is consistent with recent experiments.
We study theoretically and experimentally the spin pumping signals induced by the resonance of canted antiferromagnets with Dzyaloshinskii-Moriya interaction and demonstrate that they can generate easily observable inverse spin-Hall voltages. Using a bilayer of hematite/heavy metal as a model system, we measure at room temperature the antiferromagnetic resonance and an associated inverse spin-Hall voltage, as large as in collinear antiferromagnets. As expected for coherent spin-pumping, we observe that the sign of the inverse spin-Hall voltage provides direct information about the mode handedn…
We report an intrinsic form of the inverse spin Hall effect (ISHE) in ferromagnetic (FM) metal with Rashba spin orbit coupling (RSOC), which is driven by a normal charge current. Unlike the conventional form, the ISHE can be induced without the need for spin current injection from an external source. Our theoretical results show that Hall voltage is generated when the FM moment is perpendicular to the ferromagnetic layer. The polarity of the Hall voltage is reversed upon switching the FM moment to the opposite direction, thus promising a useful readback mechanism for memory or logic applicatio…
The polarization of the spin current pumped by a precessing ferromagnet into an adjacent normal metal has a constant component parallel to the precession axis and a rotating one normal to the magnetization. The former component is now routinely detected in the form of a DC voltage induced by the inverse spin Hall effect (ISHE). Here we compute AC-ISHE voltages much larger than the DC signals for various material combinations and discuss optimal conditions to observe the effect. Including the backflow of spins is essential for distilling parameters such as the spin Hall angle from ISHE-detected…
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 spin Hall angle (SHA) is a measure of the efficiency with which a transverse spin current is generated from a charge current by the spin-orbit coupling and disorder in the spin Hall effect (SHE). In a study of the SHE for a Pt$|$Py (Py=Ni$_{80}$Fe$_{20}$) bilayer using a first-principles scattering approach, we find a SHA that increases monotonically with temperature and is proportional to the resistivity for bulk Pt. By decomposing the room temperature SHE and inverse SHE currents into bulk and interface terms, we discover a giant interface SHA that dominates the total inverse SHE current…
It is shown that magnetic forces as the Lorentz force, exerted on electric currents, and the force μDiv(B), exerted on electron spins at rest, account for both the transverse spin imbalance typical of spin Hall effect and the transverse charge imbalance associated with pure spin currents (inverse spin Hall effect). Considering that for stationary currents the laboratory reference frame and those for which the spin up and spin down carriers are at rest are inertial systems, one can easily find the forces exerted by the lattice on both spin sub-bands, as well as the force between sub-bands.
Dynamical antiferromagnets pump spins efficiently into adjacent conductors as ferromagnets. The high antiferromagnetic resonance frequencies represent a challenge for experimental detection, but magnetic fields can reduce these resonance frequencies. We compute the inverse spin Hall voltages resulting from dynamical spin excitations as a function of a magnetic field along the easy axis and the polarization of the driving AC magnetic field perpendicular to the easy axis. We consider the insulating antiferromagnets MnF$_2$, FeF$_2$, and NiO. Near the spin-flop transition, there is a significant …
Spin pumping in ferromagnets provides a source of pure spin currents. Via the inverse spin Hall effect a spin current is converted into a charge current and a corresponding detectable DC-voltage. The ratio of injected spin current to resulting charge current is given by the spin Hall angle. However, the number of experiments more or less equals the number of different values for spin Hall angles, even for the most studied normal metal platinum. This publication provides a full study of inverse spin Hall effect and anisotropic magnetoresistance for different NiFe(Py) / normal metal bilayers usi…
We performed photoinduced inverse spin Hall effect (ISHE) measurements on a Pt/Ge(001) junction at room temperature. The spin-oriented electrons, photogenerated at the direct gap of Ge using circularly polarized light, provide a net spin current which yields an electromotive field E_ISHE in the Pt layer. Such a signal is clearly detected at room temperature despite the strong Γ to L scattering which electrons undergo in the Ge conduction band. The ISHE signal dependence on the exciting photon energy is in good agreement with the electron spin polarization expected for optical orientation at th…
The measured Hall angle in a ferromagnetic nanomagnet shows a substantial non-linear dependence on an external magnetic field, which cannot be explained by adopted mechanisms of the Ordinary and Anomalous (AHE) Hall effects implying a linear plus constant dependence on the external magnetic field. We suggest that there is an additional non-linear contribution from the Inverse Spin Hall effect (ISHE). The significant contribution of ISHE in a ferromagnet is supported by perfect agreement of experiment with a phenomenological theory of ISHE. We observed different dependencies of AHE and ISHE on …
We report observation of intrinsic inverse spin Hall effect in un-doped GaAs multiple quantum wells with a sample temperature of 10 K. A transient ballistic pure spin current is injected by a pair of laser pulses through quantum interference. By time-resolving the dynamics of the pure spin current, the momentum relaxation time is deduced, which sets the lower limit of the scattering time between electrons and holes. The transverse charge current generated by the pure spin current via the inverse spin Hall effect is simultaneously resolved. We find that the charge current is generated well befo…
We measured the spin rectify effect and the inverse spin Hall effect in Nb-doped SrTiO$_3$ by injecting the spins from ferromagnetic thin films to SrTiO$_3$ using spin pumping. It was shown that the spin injection is increased when the doping level is increased. However, the spin Hall angle decreases when Nb occupies more than $\sim$2\% of the Ti sites, which is due to that beyond this concentration, the electron contributed the spin Hall effect is from the $d-$orbitals of Nb instead those from the Ti. Our work points to the importance of orbital occupations in the (inverse) spin Hall effect. …
We report on the deformation of microwave absorption spectra and of the inverse spin Hall voltage signals in thin film bilayers of yttrium iron garnet (YIG) and platinum at high microwave power levels in a 9.45-GHz TE011 cavity. As the microwave power increases from 0.15 to 200 mW, the resonance field shifts to higher values, and the initially Lorentzian spectra of the microwave absorption intensity as well as the inverse spin Hall voltage signals become asymmetric. The contributions from opening of the magnetization precession cone and heating of YIG cannot well reproduce the data. Control me…
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…
The dc voltage obtained from the inverse spin Hall effect (iSHE) due to spin pumping in ferromagnet/normal-metal (NM) bilayers can be unintentionally superimposed with magnetoresistive rectification of ac charge currents in the ferromagnetic layer. We introduce a geometry in which these spurious rectification voltages vanish while the iSHE voltage is maximized. In this geometry, a quantitative study of the dc iSHE is performed in a broad frequency range for Permalloy/NM multilayers with NM={Pt, Ta, Cu/Au, Cu/Pt}. The experimentally recorded voltages can be fully ascribed to the iSHE due to spi…
In ferromagnet/normal-metal bilayers, the sensitivity of the spin Hall magnetoresistance and the spin Nernst magnetothermopower to the boundary conditions at the interface is of central importance. In general, such boundary conditions can be substantially affected by current-induced spin polarizations. In order to quantify the role of the latter, we consider a Rashba two-dimensional electron gas with a ferromagnet attached to one side of the system. The geometry of such a system maximizes the effect of current-induced spin polarization on the boundary conditions, and the spin Hall magnetoresis…
Josephson phase shift and diode effect due to the inverse spin Hall effect
RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Graduate School of Advanced Science and Engineering, Hiroshima University（广岛大学先进理工学研究科）；CINaM, Aix-Marseille University（艾克斯-马赛大学中子与磁性材料中心）
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.
We measure electrically detected ferromagnetic resonance in microdevices patterned from ultra-thin Co/Pt bilayers. Spin pumping and rectification voltages are observed and distinguished via their angular dependence. The spin-pumping voltage shows an unexpected increase as the cobalt thickness is reduced below 2 nm. This enhancement allows more efficient conversion of spin to charge current and motivates a theory modelling the dependence of impurity scattering on surface roughness.
We consider DC supercurrents in SNS junctions. Spin-orbit coupling in combination with Zeeman fields can induce an effective vector potential in the normal conductor. As a consequence, an out-of-plane spin-density varying along the transverse direction causes a longitudinal phase difference between the superconducting terminals. The resulting equilibrium phase coherent supercurrent is analogue to the non-equilibrium inverse spin Hall effect in normal conductors. We explicitly compute the effect for the Rashba spin orbit coupling in a disordered two-dimensional electron gas with an inhomogeneou…
Based on first-principles calculations, we propose a sandwich structure composed of a G-type anti-ferromagnetic (AFM) Mott insulator LaCrO$_3$ grown along the [001] direction with one atomic layer replaced by an inverse-perovskite material Sr$_3$PbO. We show that the system is in a topologically nontrivial phase characterized by simultaneous nonzero charge and spin Chern numbers, which can support a spin-polarized and dissipationless edge current in a finite system. Since these two materials are stable in bulk and match each other with only small lattice distortions, the composite material is …
We report on a comparative study of spin Hall related effects and magnetoresistance in YIG|Pt and YIG|Ta bilayers. These combined measurements allow to estimate the characteristic transport parameters of both Pt and Ta layers juxtaposed to YIG: the spin mixing conductance $G_{\uparrow \downarrow}$ at the YIG$|$normal metal interface, the spin Hall angle $Θ_{SH}$, and the spin diffusion length $λ_{sd}$ in the normal metal. The inverse spin Hall voltages generated in Pt and Ta by the pure spin current pumped from YIG excited at resonance confirm the opposite signs of spin Hall angles in these tw…
Here, we investigate spin Hall angle of Pt in Ni80Fe20/Pt bilayer system by using a broadband spin pumping and inverse spin Hall effect measurement. An out-of-plane excitation geometry with application of external magnetic field perpendicular to the charge current direction is utilized in order to suppress unwanted galvanomagnetic effects. Magnetization precession angle on ferromagnetic resonance for wide excitation frequency range (4-14 GHz) is estimated from the rectification voltage of anisotropic magnetoresistance (AMR) and a conventional method of using microwave power in a coplanar waveg…
Bismuth Selenide (Bi2Se3) is a topological insulator exhibiting helical spin polarization and strong spin-orbit coupling. The spin-orbit coupling links the charge current to spin current via the spin Hall effect (SHE). We demonstrate a Bi2Se3 spin detector by injecting the pure spin current from a magnetic permalloy layer to a Bi2Se3 thin film and detect the inverse SHE in Bi2Se3. The spin Hall angle of Bi2Se3 is found to be 0.0093 and the spin diffusion length in Bi2Se3 to be 6.2 nm at room temperature. Our results suggest that topological insulators with strong spin-orbit coupling can be use…
Recent progress in orbitronics reveals the possibility of using orbit current as an information carrier. The interconversion between orbit currents and charge currents is crucial for orbit information processing. Although orbit currents can be created from charge currents via the orbital Hall effect, the conversion from orbit currents into charge currents has been observed only in very few systems due to the lack of a reliable orbit current source and the disturbance of the omnipresent inverse spin Hall effect. In this study, we show that ultrafast pulses of orbit current can be generated in N…
Inverse spin Hall effect (ISHE) in ferromagnetic metals (FM) can also be used to detect the spin current generated by longitudinal spin Seebeck effect in a ferromagnetic insulator YIG. However, anomalous Nernst effect(ANE) in FM itself always mixes in the thermal voltage. In this work, the exchange bias structure (NiFe/IrMn)is employed to separate these two effects. The exchange bias structure provides a shift field to NiFe, which can separate the magnetization of NiFe from that of YIG in M-H loops. As a result, the ISHE related to magnetization of YIG and the ANE related to the magnetization …
Through combined ferromagnetic resonance, spin-pumping and inverse spin Hall effect experiments in Co|Pt bilayers and Co|Cu|Pt trilayers, we demonstrate consistent values of spin diffusion length $\ell_{\rm sf}^{\rm Pt}=3.4\pm0.4$ nm and of spin Hall angle $θ_{\rm SHE}^{\rm Pt}=0.051\pm0.004$ for Pt. Our data and model emphasize on the partial depolarization of the spin current at each interface due to spin-memory loss. Our model reconciles the previously published spin Hall angle values and explains the different scaling lengths for the ferromagnetic damping and the spin Hall effect induced v…
We theoretically consider the spin-wave mode- and wavelength-dependent enhancement of the Gilbert damping in magnetic insulator--normal metal bilayers due to spin pumping as well as the enhancement's relation to direct and alternating inverse spin Hall voltages in the normal metal. In the long-wavelength limit, including long-range dipole interactions, the ratio of the enhancement for transverse volume modes to that of the macrospin mode is equal to two. With an out-of-plane magnetization, this ratio decreases with both an increasing surface anisotropic energy and mode number. If the surface a…
In an easy-plane antiferromagnet with the Dzyaloshinskii-Moriya interaction (DMI), magnons are subject to an effective spin-momentum locking. An in-plane temperature gradient can generate interfacial accumulation of magnons with a specified polarization, realizing the magnon thermal Edelstein effect. We theoretically investigate the injection and detection of this thermally-driven spin polarization in an adjacent heavy metal with strong spin Hall effect. We find that the inverse spin Hall voltage depends monotonically on both temperature and the DMI but non-monotonically on the hard-axis aniso…
We investigated the self-induced inverse spin Hall effect in ferromagnets. Temperature (T), thickness (t) and angular-dependent measurements of transverse voltage in spin pumping experiments were performed with permalloy films. Results revealed non-monotonous T-dependence of the self-induced transverse voltage. Qualitative agreement was found with first-principle calculations unravelling the skew scattering, side-jump, and intrinsic contributions to the T-dependent spin Hall conductivity. Experimental data were similar whatever the material in contact with permalloy (oxides or metals), and rev…
We show the first experimental observation of the platinum (Pt) thickness dependence in a hybrid YIG/Pt system of the inverse spin-Hall effect from spin pumping, over a large frequency range and for different rf powers. From the measurement of the dc voltage ($Δ\textrm{V}$) at the resonant condition and the resistance ($R$) of the Pt layer, a strong enhancement of the ratio $Δ\textrm{V}/R$ has been observed, which is not in agreement with previous studies on the NiFe/Pt system. The origin of this behaviour is still unclear and cannot be explained by the spin transport model that we have used.
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.
Pure spin current based research is mostly focused on ferromagnet (FM)/heavy metal (HM) system. Because of the high spin orbit coupling (SOC) these HMs exhibit short spin diffusion length and therefore possess challenges for device application. Low SOC (elements of light weight) and large spin diffusion length make the organic semiconductors (OSCs) suitable for future spintronic applications. From theoretical model it is explained that, due to $π$ - $σ$ hybridization the curvature of the C$_{60}$ molecules may increase the SOC strength. Here, we have investigated spin pumping and inverse spin …
Anomalous spin-Hall effects (SHE) and anomalous inverse spin-Hall effects (ISHE) are predicted when the order parameters are involved in the charge-spin interconversion. A spin current whose propagation and polarization are collinear and transverse to an applied charge current can be generated when the charge current is parallel to the magnetization $\vec M$ in a ferromagnet or to the Neel order $\vec n$ in an anti-ferromagnet. When the applied charge current is perpendicular to the order parameter, two spin currents can be generated. One is the spin current polarized along the order parameter…
We give a theory of the inverse spin Hall effect (ISHE) in ferromagnetic metals based on skew scattering via collective spin fluctuations. This extends Kondo's theory of the anomalous Hall effect (AHE) to include short-range spin-spin correlations. We find a relation between the ISHE and the four-spin correlations near the Curie temperature TC. Such four-spin correlations do not contribute to the AHE, which relates to the three-spin correlations. Thus our theory shows an essential difference between the AHE and ISHE, providing an essential complement to Kondo's classic theory of the AHE in met…
We report that the spin current generated by spin Seebeck effect (SSE) in yttrium iron garnet (YIG) can be detected by a ferromagnetic metal (NiFe). By using the FM/AFM exchange bias structure (NiFe/IrMn), inverse spin Hall effect (ISHE) and planar Nernst effect (PNE) of NiFe can be unambiguously separated, allowing us to observe a pure ISHE signal. After eliminating the in plane temperature gradient in NiFe, we can even observe a pure ISHE signal without PNE from NiFe itself. It is worth noting that a large spin Hall angle (0.098) of NiFe is obtained, which is comparable with Pt. This work pr…
An inverse spin Hall effect (ISHE) in n-type silicon was observed experimentally when conduction electrons were scattered on the spin-orbit potential of bismuth. The spin current in the silicon layer was generated by excitation of the magnetization precession during ferromagnetic resonance in a thin permalloy (Py) layer deposited on a Si layer doped by phosphor and bismuth. From the angular dependences of the dc voltage for different Py/n-Si:Bi structures aligned along the [011] or [100] crystal axes, we were able to distinguish the planar Hall effect (PHE) and ISHE contributions. The ISHE dc …
The understanding of spin dynamics in laterally confined structures on sub-micron length scales has become a significant aspect of the development of novel magnetic storage technologies. Numerous ferromagnetic resonance measurements, optical characterization by Kerr microscopy and Brillouin light scattering spectroscopy and x-ray studies were carried out to detect the dynamics in patterned magnetic antidot lattices. Here, we investigate Oersted-field driven spin dynamics in rectangular Ni80Fe20/Pt antidot lattices with different lattice parameters by electrical means and compare them to microm…
We quantify the spin Hall angle θSH and spin diffusion length lsd of Nb from inverse spin-Hall effect (iSHE) measurements in Nb/Ni80Fe20 bilayers under ferromagnetic resonance. By varying the Nb thickness tNb and comparing to a Ni80Fe20/Pt reference sample, room temperature values of θSH and lsd for Nb are estimated to be approximately -0.001 and 30 nm, respectively. We also investigate the iSHE as a function of temperature T for different tNb. Above the superconducting transition temperature Tc of Nb, a clear tNb-dependent T evolution of the iSHE is observed whereas below Tc, the iSHE voltage…
