Spin Flow Research Articles

Effect of in situ and ex situ magnetic field on the microstructural transformation of the thermally reduced graphene oxide

The control over microstructural characteristics of graphene oxide (GO) is one of the most serious issues in the domain of graphene synthesis as this affects the graphene’s properties, and functionality. In this study, the primary objective is electrochemical synthesis graphene in the presence of magnetic field that is applied externally. During the synthesis process, the magnetic field was applied in a direction that was perpendicular to the applied potential. This causes the electrolyte to spin flow around the cell. Subsequently, the goal is to provide a comparative analysis between the microstructural characteristics of graphene that has been synthesized in situ and ex situ magnetic field. The cylindrical graphite was used as an anode, and a carbon electrode that had been recovered from a waste dry cell battery was used as a cathode. The pre-oxidized graphite was sonicated (synthesized under magnetic field, and without magnetic field) in sterilized water for 10[Formula: see text]min with a probe-type sonicator and thermally reduced at same temperature i.e., 850∘C followed by furnace cooling. The findings of the Raman spectroscopy, atomic force microscopy (AFM), field emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM) characterizations indicate that the magnetic flux that was applied has a significant influence on the surface height and roughness, microstructure, and surface state, a structural disorder in comparison to when there was no magnetic field applied to the thermally reduced graphene oxide (rGO). On the other side, from the data obtained by XRD and TGA analysis, the applied magnetic field seems to have very little effect on phase, lattice parameter and thermal stability.

Electrosprayed curcumin‐zein@polycaprolactone‐mucilage capsules for an improved sustained release

AbstractNanocapsules of curcumin‐zein as core and polycaprolactone‐mucilage (PCL‐MUC) as a shell were effectively made by using an electrospray process for drug delivery applications. Because of its anticancer and anti‐inflammatory qualities, curcumin (Cur) was chosen as a model medicine, and its stability was improved by combining it with zein. The monodisperse and spherical shapes of CUR‐ZEIN@PCL‐MUC nanocapsules with an average diameter of 200 nm were obtained and validated by SEM and TEM images by altering spinning voltage, flow rates, polymeric concentrations, and drug content. FTIR was used to determine the chemical structure of the nanocapsules. In addition, the in vitro release was investigated, with samples exhibiting a burst release for the first 6 h followed by a sustained release for the next 24 h. The results show that adding opuntia mucilage and zein improved the curcumin release rate. Overall, 30% curcumin release was observed after 24 h, as described by the Ritger–Peppas model. In summary, our study developed an electrospray method for fabricating CUR‐ZEIN@PCL‐MUC nanocapsules with the potential to regulate curcumin release.

Ultrafast magnetization and energy flow in the laser-induced dynamics of transition metal compounds

An electronic theory of the laser-induced ultrafast magnetization dynamics in transition-metal alloys is presented. A many-body model Hamiltonian is considered that incorporates the fundamental electronic hopping, local Coulomb interaction, and spin-orbit coupling (SOC) on the same footing. Exact time propagations are performed on a tetrahedral cluster, from which the time dependencies of the local spin moments, orbital occupations, and single-particle energies of homogeneous systems and binary alloys are obtained. The consequences of inhomogeneities in the laser absorption and in the SOC strengths are investigated giving emphasis to the nature of spin-density transfers between the alloy components. A local perspective on the optically induced spin transfer is proposed in terms of which two main steps emerge: a dominantly local optical excitation followed by hopping-driven spin-density transfers among the different alloy components. The conjoint action of the spin-orbit interactions at the origin of local spin flips and spin-to-orbital angular-momentum transfer and the interatomic hoppings responsible for charge, spin, and energy flows between different sublattices is demonstrated. Transient and steady-state dynamical regimes are identified that result in delays in the onset of the local demagnetizations and in ultrafast redistributions of the spin. The central role of electron delocalization and electronic hopping in the spin-density redistribution and demagnetization of the different alloy components is demonstrated.

First principles study of coherent electron/spin transport across metallothionein: A cadmium-binding protein

Metallothioneins (MTs) play an important role in controlling the concentration of heavy metals in the body by forming metal-thiolate clusters. In addition, the proteins can scavenge free radicals, to exhibit an antioxidant effect. To clarify the precise physiological function of these proteins, it is necessary to examine the non-equilibrium state of electron/spin transport in the molecule. In this study, coherent spin transport in MTs connected to metal electrodes has been calculated to examine the behavior of the molecule toward spin flow (radicals) in the body. The estimated values of conductance were found to be very low, while the spin polarization appears to derive considerable spin filtering. Furthermore, spin polarization did not localize on cadmium but on the sulfur atoms of cadmium-thiolate clusters. These results confirmed that cysteine plays an important role in the scavenging of free radicals even when forming the cadmium-thiolate cluster.Significance Statement.The purpose of this study is to better understand how spin polarization (induced radical) flows in metallothionein, even if it forms cadmium-thiolate clusters. This is important because it can be known where the radical is stored and processed in the body. Our results provide a guide to examine non-equilibrium electron transient in the metallothionein by observing the single-molecule electric conduction with scanning tunneling microscope.

Spin and spin current—From fundamentals to recent progress

Along with the progress of spin science and spintronics research, the flow of electron spins, i.e., spin current, has attracted interest. New phenomena and electronic states were explained in succession using the concept of spin current. Moreover, as many of the conventionally known spintronics phenomena became well organized based on spin current, it has rapidly been recognized as an essential concept in a wide range of condensed matter physics. In this article, we focus on recent developments in the physics of spin, spin current, and their related phenomena, where the conversion between spin angular momentum and different forms of angular momentum plays an essential role. Starting with an introduction to spin current, we first discuss the recent progress in spintronic phenomena driven by spin-exchange coupling: spin pumping, topological Hall torque, and emergent inductor. We, then, extend our discussion to the interaction/interconversion of spins with heat, lattice vibrations, and charge current and address recent progress and perspectives on the spin Seebeck and Peltier effects. Next, we review the interaction between mechanical motion and electron/nuclear spins and argue the difference between the Barnett field and rotational Doppler effect. We show that the Barnett effect reveals the angular momentum compensation temperature, at which the net angular momentum is quenched in ferrimagnets.

Spin-orbit torque efficiency improved by BiSePt alloy

In order to achieve high-efficiency spin-orbit torque devices, higher charge-spin conversion efficiency, and lower resistivity are required in the strong spin-orbit coupling layer that provides the spin current. In this work we prepare BiSePt alloy/Co heterostructures with in-plane magnetic anisotropy by magnetron sputtering deposition. The alloy layer is deposited via one of two procedures, either co-sputtering or alternative-sputtering. We study the BiSePt alloy samples and find that the spin orbit torque (SOT) efficiency decreases with the increase of Pt component, which is attributed to the change of topological order of Bi<sub>2</sub>Se<sub>3</sub> amorphous surface, caused by Pt doping. And the resistivity decreases with the increase of Pt component, which depends on the increase of metallic property. Due to the balance of these two competing mechanisms, the spin Hall conductivity of the alloy layer varies non-monotonically with the concentration ratio, and reach an optimal value at a ratio of 67% of Bi<sub>2</sub>Se<sub>3</sub> component. With the increase of the Bi<sub>2</sub>Se<sub>3</sub> component, the SOT efficiency, electrical resistivity and spin Hall conductance of the alloy layer show different trends. At about 20%–70%, they increase/decrease tardily. At about 70%–100%, the resistivity ascends more prominently than the SOT efficiency, which leads the spin Hall conductance to decrease. Comparing with using the co-sputtering deposition, the electrical conductivity and spin Hall angle of the alloy layer obtained using alternating sputtering deposition are small, which is attributed to the enhancing of interfacial scattering and the filter effect of Pt on the spin flow. In contrast to traditional pure heavy metal materials (such as Pt, Ta) and topological insulator materials like Bi<sub>2</sub>Se<sub>3</sub>, our BiSePt alloy devices obtained by co-sputtering deposition achieve industry-matched preparation conditions, greater SOT efficiency, and considerable electrical conductivity of the alloy layer, thus making further applications of SOT devices possible.

Field-driven Modulation of Spin Hall Magnetoresistance in Nanoscale-layered Pt/IrMn₃/NiFe Heterostructures

Spin Hall magnetoresistance (SMR) emerges from both spin Hall effect (SHE) and inverse spin Hall effect (ISHE), which is usually investigated in a nonmagnetic heavy metal (NM) in contact with a ferromagnet (FM). Depending on the orientation of FM magnetization and spin polarization of NM layer, the transmission or reflection of the spin current at the FM\NM interface could occur. SMR was investigated in 1.5 nm NiFe\3.0 nm IrMn₃\3.0 nm Pt magnetic heterostructures. IrMn₃ thin film grown on ferromagnetic NiFe layer exhibits the glassy magnetic behavior and displays spin reorientation transition in the magnetic field-temperature space. Below the Néel temperature of IrMn₃, the angle dependence of MR measurement in the xy and xz plane showed a normal positive SMR. However, a sign change in SMR was observed in the magnetic field applied in the yz plane. The switching from negative to positive SMR occurs at the field above a critical value of 6 kG. Our results provide a potential advantage for the source of spin flow in the signal in multilayer heterostructures and highlight the importance of magnetic structure (Néel vector) in AF, which opens the possible way to manipulate the spin current transportation and AF memory devices.

Stationary states of open XX -spin chains

We study an open quantum spin chain of arbitrary length with nearest neighbor $XX$ interactions of strength $g$, immersed in an external constant magnetic field $\mathrm{\ensuremath{\Delta}}$ along the $z$ direction, whose end spins are weakly coupled to two heat baths at different temperatures. In the so-called global approach, namely, without neglecting interspin interactions, using standard weak-coupling limit techniques, we first derive the open chain master equation written in terms of fermionic mode operators. Then, we focus on the study of the dependence of the resulting open dynamics from the ratio $r\ensuremath{\equiv}g/\mathrm{\ensuremath{\Delta}}$. By increasing $r$, some of the chain Bohr transition frequencies become negative; when this occurs, both the generator of the dissipative time evolution and its stationary states behave discontinuously. As a consequence, the asymptotic spin and heat flows also exhibit discontinuities, but in a different way: while source terms in the spin flow continuity equation show jumps, the heat flow instead is continuous but with discontinuous first derivatives with respect to $r$. These two behaviors might be experimentally accessible; in particular, they could discriminate between the global and the local approaches to open quantum spin chains. Indeed, the latter one, which neglects interspin interactions in the derivation of the master equation, does not show any kind of discontinuous behavior.

Significant Role of Interfacial Spin–Orbit Coupling in the Spin-to-Charge Conversion in Pt/NiFe Heterostructure

For the spin-to-charge conversion (SCC) in heavy metal/ferromagnet (HM/FM) heterostructure, the contribution of interfacial spin-orbit coupling (SOC) remains controversial. Here, we investigate the SCC process of the Pt/NiFe heterostructure by the spin pumping in YIG/Pt/NiFe/IrMn multilayers. Due to the exchange bias of NiFe/IrMn structure, the NiFe magnetization can be switched between magnetically unsaturated and saturated states by opposite resonance fields of YIG layer. The spin-pumping signal is found to decrease significantly when the NiFe magnetization is changed from the saturated state to the unsaturated state. Theoretical analysis indicates that the interfacial spin absorption is enhanced for the above-mentioned NiFe magnetic state change, which results in the increased and decreased spin flow in the Pt layer and across the Pt/NiFe interface, respectively. These results demonstrate that in our case the interfacial SOC effect at the Pt/NiFe interface is dominant over the bulk inverse spin Hall effect in the Pt layer. Our work reveals a significant role of interfacial SOC in the SCC in HM/FM heterostructure, which can promote the development of high-efficiency spintronic devices through interfacial engineering.

Spin Hall effect of vorticity

Using mapping between topological defects in an easy-plane magnet and electrical charges, we study interplay between vorticity and spin currents. We demonstrate that the flow of vorticity is accompanied by the transverse spin current generation -- an effect which can be termed as the spin Hall effect of vorticity. We study this effect across the BKT transition and establish the role of dissipation and spin non-conservation in the crossover from spin superfluidity to diffusive spin transport. Our results pave the way for low power computing devices relying on vorticity and spin flows.

Chiral separation of rotating robots through obstacle arrays

The interplay between active matter and environmental complexity can be applied to achieve complex functions ranging from rectification, separation, and capture to sorting of active particles. Here, we experimentally realize chiral separation of disk-shaped active rotors by using the interactions between the rotors and the obstacle array. Differently chiral active particles passing through the obstacle array exhibit opposite lateral drifts. The separation efficiency is excellent provided that the obstacle array is of sufficient length. The spin and longitudinal flow of the rotors and the friction between rotors and obstacles jointly determine the lateral drift of the rotors, thus leading to chiral separation. Furthermore, we propose a simple theoretical model, which captures the essential mechanism underlying the chiral separation and properly reproduces the experimental critical collision angle. This scheme could separate objects with static chiral structures, once an external source can power the objects to spin with different angular velocities.

Utilizing Valley–Spin Hall Effect in Monolayer WSe2 for Designing Low Power Nonvolatile Spintronic Devices and Flip-Flops

In this article, we propose low power nonvolatile flip-flops (NVFFs) utilizing valley–spin Hall effect (VSHE) in monolayer tungsten diselenide (WSe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ). The proposed designs are based on nonvolatile spintronic devices comprising of WSe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -based charge-to-spin converter coupled with magnetic tunnel junctions. The proposed devices have an integrated back-gate to control the flow of charge and spin currents. VSHE leads to the flow of opposite spins in divergent directions perpendicular to the WSe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> layer with valley/spin Hall angle ~1. This enables encoding true and complementary bits in a single device utilizing magnets with perpendicular magnetic anisotropy (PMA). By introducing exchange coupling between PMA magnets mediated by Ta and FeCo-oxide layers, we electrically isolate but magnetically couple the PMA free layers, which enable the design of backup/restore module of NVFFs with minimal number of transistors. Using object-oriented micromagnetic framework (OOMMF) simulation, we establish the robustness of the exchange-coupled PMA systems and show that the misalignment and reduction in exchange coupling strength, induced by process variations, have a minimal impact on their functionality. Exploiting the unique features of the proposed devices, we design two flavors of VSHE-based NVFFs (VSHE-NVFFs) and carry out their energy–delay characterization, including an extensive variation analysis. The proposed VSHE-NVFFs achieve 74%–75% lower backup energy and 55%–59% lower restore energy than the existing NVFFs based on giant spin Hall effect (GSHE).

Acoustically Excited Magnetic Dynamics and Spin Flow in Spin-Valve Structures

Acoustic waves and strain pulses created by a piezoelectric or optical transducer represent an attractive tool for the generation of spin dynamics in magnetoelastic materials and heterostructures. The advantage of acoustic excitation consists in much lower power consumption compared with the classical excitation by a microwave magnetic field. The magnetization precession driven by elastic waves can be further used for spin pumping into normal metals and semiconductors. Here we describe theoretically the magnetization dynamics and spin flow induced by plane acoustic waves traversing trilayer structures involving two ferromagnetic ($F$) films separated by a layer of normal metal ($N$). The problem is solved by advanced micromagnetoelastic simulations, which allow for the two-way coupling between spins and strains in the $F$ films and their long-range dynamic interaction resulting from the spin flow across the $N$ spacer. To derive the expression for such an interaction, we solve the spin-diffusion equation in $N$ with the account of spin pumping created by dynamically strained $F$ films and spin backflow through the interfaces. Performing numerical simulations for the ${\mathrm{Fe}}_{81}{\mathrm{Ga}}_{19}{/\mathrm{Au}/\mathrm{Fe}}_{81}{\mathrm{Ga}}_{19}$ trilayers excited by longitudinal and transverse elastic waves, we quantify the inhomogeneous magnetization precession in the galfenol films and determine the spatial distributions of the oscillating spin current and spin accumulation in the Au spacers of different thickness. These distributions are further used to calculate the mean spin current and total spin accumulation in the spacer. It is found that both ac and dc parts of these quantities exhibit strong variations with the spacer thickness. Remarkably, the nonzero components of the total spin accumulation and mean spin current mostly have pronounced maxima at $\mathrm{Au}$ thicknesses amounting to about 0.25 and 0.75 of the wavelength ${\ensuremath{\lambda}}_{N}$ of the elastic wave in $\mathrm{Au}$, which is explained by an analytical model of strain distribution in the trilayer. Our theoretical results, which shed light on the acoustically excited generation of spin imbalance in magnetoelastic spin-valve structures, could be useful for the development of energy-efficient spin injectors into normal conductors with weak spin-flip scattering.

Ultrafast time-evolution of chiral N\xe9el magnetic domain walls probed by circular dichroism in x-ray resonant magnetic scattering

Non-collinear spin textures in ferromagnetic ultrathin films are attracting a renewed interest fueled by possible fine engineering of several magnetic interactions, notably the interfacial Dzyaloshinskii-Moriya interaction. This allows for the stabilization of complex chiral spin textures such as chiral magnetic domain walls (DWs), spin spirals, and magnetic skyrmions among others. We report here on the behavior of chiral DWs at ultrashort timescale after optical pumping in perpendicularly magnetized asymmetric multilayers. The magnetization dynamics is probed using time-resolved circular dichroism in x-ray resonant magnetic scattering (CD-XRMS). We observe a picosecond transient reduction of the CD-XRMS, which is attributed to the spin current-induced coherent and incoherent torques within the continuously varying spin texture of the DWs. We argue that a specific demagnetization of the inner structure of the DW induces a flow of spins from the interior of the neighboring magnetic domains. We identify this time-varying change of the DW texture shortly after the laser pulse as a distortion of the homochiral Néel shape toward a transient mixed Bloch-Néel-Bloch texture along a direction transverse to the DW.

Promotion of ferrofluid microchannel flows by gradient magnetic fields

• Ferrofluid Couette-Poiseuille flows subject to gradient magnetic field are analyzed. • Steady gradient magnetic fields promote the ferrofluid Couette-Poiseuille flows. • The backflow is completely suppressed and the flow separation disappears. • The gradient magnetic field enhances the effect of magnetization relaxation. • The gradient magnetic field increases magnetic stress and reduces shear stress. Inspired from the wide engineering applications of ferrofluids, we investigated the ferrofluid microchannel flows subject to a gradient magnetic field applied perpendicular to the channel walls. The ferrohydrodynamic problem encompassing the Fokker-Planck magnetization equation in a Couette-Poiseuille configuration is solved numerically. The velocity and spin profiles, vorticity, magnetization, flow rate, and stresses acting on the moving plate are examined for favorable and unfavorable field gradients, as well as the adding of different pressure gradients. We show that the steady gradient magnetic fields promote the flow of both pure Couette and Couette-Poiseuille flows in the microchannel geometry. The increment of the velocity attains 35% and the resulting volumetric flow rate increases by about 24% at the most. This phenomenon was only observed in ferrofluid flows subject to high frequency AC magnetic fields or temperature gradient field in the past. The backflow occurs in normal Couette-Poiseuille flows can be completely suppressed by the gradient fields and the flow separation disappears correspondingly. The gradient magnetic fields are able to enhance the effect of magnetization relaxation and dramatically increase the magnetic stress and reduce the shear stress by comparison with the cases subject to uniform magnetic fields, yet the tradeoff between them leads to a rise in the total tangential stress acting on the moving plate.

Anisotropic Magnon Spin Transport in Ultrathin Spinel Ferrite Thin Films─Evidence for Anisotropy in Exchange Stiffness.

Magnon-mediated spin flow in magnetically ordered insulators enables long-distance spin-based information transport with low dissipation. In the materials studied to date, no anisotropy has been observed in the magnon propagation length as a function of propagation direction. Here, we report measurements of magnon spin transport in a spinel ferrite, magnesium aluminum ferrite MgAl0.5Fe1.5O4 (MAFO), which has a substantial in-plane 4-fold magnetic anisotropy. We observe spin diffusion lengths > 0.8 μm at room temperature in 6 nm films, with spin diffusion lengths 30% longer along the easy axes compared to the hard axes. The sign of this difference is opposite to the effects just of anisotropy in the magnetic energy for a uniform magnetic state. We suggest instead that accounting for anisotropy in exchange stiffness is necessary to explain these results. These findings provide an approach for controlling magnon transport via strain, which opens new opportunities for designing magnonic devices.

Resonant precession of magnetization and precession—induced DC voltages in FeGaB thin films

Measurements of frequency dependent ferromagnetic resonance and spin pumping driven dc voltage (V dc) are reported for amorphous films of Fe78Ga13B9 alloy to address the phenomenon of self-induced inverse spin Hall effect (ISHE) in plain films of metallic ferromagnets (FMs). The V dc signal, which is anti-symmetric on field reversal, comprises of symmetric and asymmetric Lorentzians centered around the resonance field. Dominant role of thin film size effects is seen in setting the magnitude of static magnetization, V dc and dynamics of magnetization precession in thinner films (⩽8 nm). The film thickness dependence of magnetization parameters indicates the presence of a magnetically disordered region at the film—substrate interface, which may promote preferential flow of spins generated by the precessing magnetization towards the substrate. However, the V dc signal also draws contributions from rectification effects of a ≈0.4% anisotropic magnetoresistance and a large (≈54 nΩ m) anomalous Hall resistivity (AHR) of these films which ride over the effect of spin–orbit coupling driven spin-to-charge conversion near the film—substrate interface. We have addressed these data in the framework of the existing theories of electrodynamics of a ferromagnetic film subjected to radio-frequency field in a coplanar waveguide geometry. Our estimation of the self-induced ISHE for the sample with 54 nΩ m AHR shows that it may contribute significantly (≈90%) to the measured symmetric voltage. This study is expected to be very useful for fully understanding the spin pumping induced dc voltages in metallic FMs with disordered interfaces and large anomalous Hall effect.

Energy flows in tight focus of optical vortices

In this paper we investigated tight focusing of optical vortex with topological charge m = 2 and left circular polarization. The simulation was based on Richards-Wolf equation. Light with wavelength 532 nm was focused by aplanatic lens with numerical aperture NA=0.95. It was shown that the longitudinal component of Poynting vector has negative values on the optical axis. The reason of the energy backflow is due to the fact that the projection of the spin flow onto the optical axis is negative and exceeds in absolute value the projection of the orbital energy flow, which is always positive.

Directional effects of whole-body spinning and visual flow in virtual reality on vagal neuromodulation.

Neural circuits allow whole-body yaw rotation to modulate vagal parasympathetic activity, which alters beat-to-beat variation in heart rate. The overall output of spinning direction, as well as vestibular-visual interactions on vagal activity still needs to be investigated. This study investigated direction-dependent effects of visual and natural vestibular stimulation on two autonomic responses: heart rate variability (HRV) and pupil diameter. Healthy human male subjects (n = 27) underwent constant whole-body yaw rotation with eyes open and closed in the clockwise (CW) and anticlockwise (ACW) directions, at 90°/s for two minutes. Subjects also viewed the same spinning environments on video in a VR headset. CW spinning significantly decreased parasympathetic vagal activity in all conditions (CW open p = 0.0048, CW closed p = 0.0151, CW VR p = 0.0019,), but not ACW spinning (ACW open p = 0.2068, ACW closed p = 0.7755, ACW VR p = 0.1775,) as indicated by an HRV metric, the root mean square of successive RR interval differences (RMSSD). There were no direction-dependent effects of constant spinning on sympathetic activity inferred through the HRV metrics, stress index (SI), sympathetic nervous system index (SNS index) and pupil diameter. Neuroplasticity in the CW eyes closed and CW VR conditions post stimulation was observed. Only one direction of yaw spinning, and visual flow caused vagal nerve neuromodulation and neuroplasticity, resulting in an inhibition of parasympathetic activity on the heart, to the same extent in either vestibular or visual stimulation. These results indicate that visual flow in VR can be used as a non-electrical method for vagus nerve inhibition without the need for body motion in the treatment of disorders with vagal overactivity. The findings are also important for VR and spinning chair based autonomic nervous system modulation protocols, and the effects of motion integrated VR.

Spin Hall effect in heavy-ion collisions

Spin Hall effect (SHE) is the generation of spin current due to an electric field, and has been observed in a variety of materials. In this work, we use linear response theory to verify that the analogous spin Hall current can be induced by chemical potential and temperature gradient, both of which are present in hot and dense nuclear matter created in heavy-ion collisions. We propose to measure ``directed spin flow'', the first Fourier coefficients of local spin polarization of $\mathrm{\ensuremath{\Lambda}}$ $(\overline{\mathrm{\ensuremath{\Lambda}}})$ hyperon, at central collisions to probe spin Hall current in heavy-ion collision experiments. We benchmark the magnitude of the induced ``directed spin flow'' at two representatively collisions energies, namely ${\sqrt{s}}_{NN}=200\text{ }\text{ }\mathrm{GeV}$ and ${\sqrt{s}}_{NN}=19.6\text{ }\text{ }\mathrm{GeV}$, by employing a phenomenologically motivated freeze-out prescription. At both beam energies, the resulting ``directed spin flow'' ranges from ${10}^{\ensuremath{-}4}$ to ${10}^{\ensuremath{-}3}$, and is very sensitive to the rapidity.