Giant spin hydrodynamic generation in laminar flow

Abstract

Hydrodynamic motion can generate a flux of electron-spin's angular momentum via the coupling between fluid rotation and electron spins. Such hydrodynamic generation, called spin hydrodynamic generation (SHDG), has recently attracted attention in a wide range of fields, especially in spintronics. Spintronics deals with spin-mediated interconversion taking place on a micro or nano scale because of the spin-diffusion length scale. To be fully incorporated into the interconversion, SHDG physics should also be established in such a minute scale, where most fluids exhibit a laminar flow. Here, we report electric voltage generation due to the SHDG in a laminar flow of a liquid-metal mercury. The experimental results show a scaling rule unique to the laminar-flow SHDG. Furthermore, its energy conversion efficiency turns out to be about 10⁵ greater than of the turbulent one. Our findings reveal that the laminar-flow SHDG is suitable to downsizing and to extend the coverage of fluid spintronics.

Fig. 1. Spin hydrodynamic generation in a cylindrical channel.

a A schematic illustration of SHDG. v, ω, σ, j^S, and E_SHDG are the flow velocity, the vorticity, the spin polarization, the spin current caused by SHDG and the electromotive force caused by the inverse spin Hall effect in a liquid metal flow, respectively. b, c Geometries for SHDG in a turbulent flow (b) and in a laminar flow (c). Each illustration represents a cut-out part of a fluid flow in a cylindrical channel where SHDG is induced.

Fig. 2. Measurements of hydrodynamic voltage generation.

a A schematic illustration of the fluid channel used in the present study. A flow of liquid Hg in a quartz-glass fluid channel is induced by applying pulsed pressure, P. V_e denotes electric voltage difference between the ends of the channel. HI and LO denote the high and low terminals, respectively. b Time evolution of V_e for various values of P in the fluid channel whose inner diameter ϕ is 50 μm and the length L is 100 mm. c P dependences of the mean flow velocity v for the channel used in (b). v is estimated by averaging the data obtained from repetitive measurements. The experimental results are well reproduced by a relation for laminar flow states: v ∝ P. d P dependence of v for the channel of ϕ = 400 μm, reproduced well by a relation for turbulent flow states: $v\propto \sqrt{P}$. e v dependences of V_e for the channels of ϕ = 50 μm (blue filled circles) and ϕ = 400 μm (open circles). V_e (blue filled circle) is obtained by averaging the data obtained from repetitive measurements. In each measurement, V_e is estimated by taking a time average. The results obey the SHDG scaling law for laminar flow states: V_e ∝ v, totally different from that for turbulent one: V_e ∝ v².

Fig. 3. Voltage measurement in laminar flows for channels.

a ϕ dependences of v for several values of P. Dimensional tolerance with respect to ϕ is 5 μm for the channels whose ϕ are 50, 112 and 126 μm, and 10 μm for the channels whose ϕ are 70 and 90 μm, respectively. The v data for each P is consistent with the relation for a laminar flow: $v\propto {r_0}^2$, indicated by black curves. b v dependences of V_e for several values of ϕ. c P dependence of V_e. The open circles are the data of ϕ-400-μm channel. The red solid line is the fit line obtained from the equation V_e = CP and the black solid line is an approximate line for the turbulent-flow SHDG. The values of v and V_e in (a–c) were obtained by averaging the data obtained from 60-times repetitive measurements. Error bars in (a) and (b) are smaller than the marker sizes and those in (c) represent one standard error of the mean in the repetitive measurements.

Fig. 4. Voltage measurement in transition flow and conversion efficiency.

a P dependence of v for the channel of ϕ = 200 μm. v is estimated by averaging the data obtained from repetitive measurements. The experimental results are well reproduced by a relation for laminar flow states in low P region (v ∝ P) and a relation for turbulent flow states in high P region ($v\propto \sqrt{P}$). b P dependence of V_e for the channel used in (a). V_e is estimated by averaging the data obtained from repetitive measurements. The black solid line represents the theoretical calculation of the laminar-flow SHDG shown in Fig. 3c (red solid line). c v_∗r₀ vs. ${r_0}^3{V}_{\mathrm{e}}{L}^{-1}$ plot. v_∗ and r₀ represent the friction-velocity and the inner radius, respectively. The black solid curve represents the theoretical calculation of the turbulent-flow SHDG shown in. d Dependence of the energy conversion efficiency η on the Reynolds number Re for various values of ϕ. η estimated from the experimental results of the present study, indicated by filled circles in the laminar and the transition region, are shown together with that in the turbulent region (open circles). Inset shows Re dependence of η for the ϕ-200-μm channel with a linear scale. e Re vs. ${r_0}^3\eta$ plot for various values of ϕ. The black solid lines represent the relations of ${r_0}^3\eta \propto {\mathrm{Re}}^{-1}$ and ${r_0}^3\eta \propto \mathrm{Re}$. Inset shows Re vs. ${r_0}^3\eta$ plot for the ϕ-200-μm and the ϕ-400-μm channels with a linear scale.