Magneto-Optical Detection of the Orbital Hall Effect in Chromium

The orbital Hall effect has been theoretically predicted but its direct observation is a challenge. Here, we report the magneto-optical detection of current-induced orbital accumulation at the surface of a light $3d$ transition metal, Cr. The orbital polarization is in-plane, transverse to the current direction, and scales linearly with current density, consistent with the orbital Hall effect. Comparing the thickness-dependent magneto-optical measurements with ab initio calculations, we estimate an orbital diffusion length in Cr of $6.6\pm 0.6\mathrm{nm}$.

Figure 1

(a) Schematics of the orbital Hall effect. The charge current $j$ generates a transverse orbital current, leading to orbital accumulation on the sample’s surfaces. (b) Measurement setup utilizing the longitudinal MOKE to detect the in-plane orbital accumulation.

Figure 2

Magneto-optical Kerr rotation induced by the orbital and spin Hall effect. (a) MOKE line scan across a $20\mathrm{\mu }\mathrm{m}$ wide, 30 nm thick Cr channel at rms current density $j=0.28\times {10}^{11}\mathrm{A}/{\mathrm{m}}^2$. MOKE signal as a function of current density: (b) for the laser beam incidence shown in Fig. 1, (c) for the reversed optical path of the laser beam (30 nm sample), (d) for device rotated 90° about the surface normal (40 nm sample).

Figure 3

Magneto-optical Kerr rotation induced by the orbital Hall effect. (a) MOKE line scan across a $20\mathrm{\mu }\mathrm{m}$ wide Cr/MgO ($30/3\mathrm{nm}$) channel at current density $j=0.26\times {10}^{11}\mathrm{A}/{\mathrm{m}}^2$ (b) MOKE line scan across a 40 nm thick Pt channel at $j=0.10\times {10}^{11}\mathrm{A}/{\mathrm{m}}^2$ (c) and (d) MOKE signal as a function of current density for Cr and Pt, respectively.

Figure 4

(a) The ab initio calculated magneto-optical conductivity $\mathrm{Im}{\sigma }_{zx}(\omega )$ of Cr for an induced spin moment $m_s$ or orbital moment $m_{\ell }$ of 0.1 ${\mu }_{\mathrm{B}}$. (b) The calculated longitudinal Kerr rotation ${\theta }_{\mathrm{K}}$ of Cr due to a spin or an orbital moment. Note that ${\theta }_{\mathrm{K}}$ for the induced spin polarization is multiplied by 10.

Figure 5

Measured Kerr rotation ${\theta }_{\mathrm{K}}$ as function of Cr film thickness (symbols), for a current density of ${10}^{11}{\mathrm{Am}}^{-2}$. The full curve is a fit to the measured MOKE rotation based on Eq. (1) with ab initio calculated quantities to obtain the orbital diffusion length $l_o$. The dashed curve shows ${\theta }_{\mathrm{K}}$ based on the SHE ($\times 100$).