Nanomechanical detection of the spin Hall effect

The spin Hall effect creates a spin current in response to a charge current in a material that has strong spin-orbit coupling. The size of the spin Hall effect in many materials is disputed, requiring independent measurements of the effect. We develop a novel mechanical method to measure the size of the spin Hall effect, relying on the equivalence between spin and angular momentum. The spin current carries angular momentum, so the flow of angular momentum will result in a mechanical torque on the material. We determine the size and geometry of this torque and demonstrate that it can be measured using a nanomechanical device. Our results show that measurement of the spin Hall effect in this manner is possible and also opens possibilities for actuating nanomechanical systems with spin currents.

Figure 1

(a) Schematic representation of the spin Hall effect. Oppositely polarized spins scatter in opposite directions, resulting in a spin accumulation at the wire boundary. (b) Graphical representation of the spin accumulation in a cross section of the wire. The blue lines and vector plot illustrate the accumulation for ${\lambda }_{sf}$ comparable to the wire size and the red lines represent a much smaller ${\lambda }_{sf}$. (c) Deflection (not to scale) caused in a platinum wire due to the spin-transport-induced torque density. The bottom of the wire is fixed in place while the rest may deform freely.

Figure 2

(a) Representation of the doubly clamped beam to be used in experiments (Pt and ${\mathrm{Al}}_2{\mathrm{O}}_3$ layers not shown). The inset illustrates the layers used in constructing the beam. (b) Several of the lowest order mode shapes for the doubly clamped beam according to a numerical simulation in comsol.

Figure 3

(a) Deflection of the beam due to steady-state (dc) applied current. (b) Voltage response of oscillator when excited via the spin Hall effect (blue) and piezoelectrically (red) when driven by a 1 mV electric potential. (c) Mode shapes of the three eigenmodes most strongly excited by the spin Hall effect.