Magnetization-dependent spin Hall effect in a perpendicular magnetized film

In the spin Hall effect (SHE), the vector cross-product relations among charge current, spin current, and spin polarization are strictly followed, so that only the in-plane spin accumulation can be induced at the film surface. But, recently this restriction has been lifted by the symmetry breaking of a magnet, where spin polarization can be additionally manipulated by the magnetization directions. In this work, we demonstrated the magnetization-dependent spin-to-charge signals in yttrium iron garnet/Pt/Co/Pt heterostructure. Without the complications in all-metallic structures, we explicitly identified the magnetization-dependent spin Hall effect. We compared its size with the SHE, and further estimated the magnetization-dependent spin Hall angle. Our approach provides an explicit route in exploring the spin-to-charge conversion with arbitrary and controllable orientations of spin polarization, which offers significant advantages in developing electrically controlled energy-efficient spintronic devices.

Figure 1

Schematic drawing of (a) spin Hall effect, (b) magnetization-dependent spin Hall effect in perpendicular magnetized film, (c) magnetization-dependent spin Hall effect in in-plane magnetized film, (d) inverse spin Hall effect, (e) magnetization-dependent inverse spin Hall effect in perpendicular magnetized film, (f) magnetization-dependent inverse spin Hall effect in in-plane magnetized film. For simplicity, one polarization of opposite spins is drawn for the pure spin current.

Figure 2

Schematic drawing of the anomalous Hall measurement geometry featuring the Hall-bar-patterned YIG(67)/Pt(2)/Co(0.5)/Pt(2) multilayer with charge current flowing along $x$, Hall voltage being measured along y, and magnetic field being applied along (a) $z$, (c) $x$, and (e) $y$. (b) Anomalous Hall resistance with field being applied along $z$. Hall resistance with ${\mathit{m}}_{\mathbf{PML}}$ fixed along $+z$ (gray) or $-z$ (black), while sweeping magnetic field along (e) $x$ and (f) $y$.

Figure 3

Schematic drawing of the magnetic inverse spin Hall effect measurement geometry of (a) Si/YIG(67)/Pt(2)/Co(0.5)/Pt(2) and (c) Si/Pt(2)/Co(0.7)/Pt(2) with magnetic field applied and thermal voltage measured both along $x$. Magnetic inverse spin Hall voltage for (b) Si/YIG/Pt(2)/Co(0.5)/Pt(2) and (d) Si/Pt(2)/Co(0.7)/Pt(2) with ${\mathit{m}}_{\mathbf{PML}}$ fixed along $+z$ (upper) or $-z$ (lower) directions and magnetic field swept along $x$ direction.

Figure 4

Schematic drawing of the inverse spin Hall effect measurement geometry of (a) YIG(67)/Pt(2)/Co(0.5)/Pt(2) and (c) Pt(2)/Co(0.7)/Pt(2) with magnetic field applied along $y$ and thermal voltage measured along $x$. (b) Inverse spin Hall voltage for YIG/Pt(2)/Co(0.5)/Pt(2) and (d) ordinary Nernst voltage for Pt(2)/Co(0.7)/Pt(2) with ${\mathit{m}}_{\mathbf{PML}}$ magnetized in $+z$ (upper) or $-z$ (lower) directions and magnetic field swept along $y$ direction.