Observation of the magnetic spin Hall effect in a ferromagnet
The conventional spin Hall effect generates spin currents whose flow direction, spin polarization, and driving electric field are mutually perpendicular. Magnetic order lifts this symmetry restriction and enables additional time-reversal-symmetry-odd components of the spin-conductivity tensor, giving rise to the magnetic spin Hall effect (MSHE). These components also couple the generated spin polarization to the magnetic order, providing a degree of control absent in the conventional spin Hall effect. Although the MSHE has been observed in antiferromagnets, its experimental identification in conventional ferromagnets has remained elusive. Here, using a non-local lateral spin-valve geometry, we electrically identify the MSHE and its reciprocal effect in a perpendicularly magnetized Co-based multilayer. Reversal of the multilayer magnetization reverses the MSHE and magnetic inverse spin Hall signals, revealing their time-reversal-symmetry-odd character and magnetization control. By contrast, the conventional spin Hall and inverse spin Hall signals measured in the same devices remain unchanged under magnetization reversal, consistent with their time-reversal-symmetry-even character. We obtain a magnetic spin Hall angle of $θ_{\mathrm{MSH}} = (3.8 \pm 0.6)\%$, comparable in magnitude to the spin Hall angle of heavy metals commonly used in spintronic devices, such as Pt. These results establish the MSHE as a sizable, magnetically switchable spin-charge interconversion mechanism in conventional ferromagnets.