Orbital Hanle Magnetoresistance in a $3d$ Transition Metal

The Hanle magnetoresistance is a telltale signature of spin precession in nonmagnetic conductors, in which strong spin-orbit coupling generates edge spin accumulation via the spin Hall effect. Here, we report the existence of a large Hanle magnetoresistance in single layers of Mn with weak spin-orbit coupling, which we attribute to the orbital Hall effect. The simultaneous observation of a sizable Hanle magnetoresistance and vanishing small spin Hall magnetoresistance in $\mathrm{BiYIG}/\mathrm{Mn}$ bilayers corroborates the orbital origin of both effects. We estimate an orbital Hall angle of 0.016, an orbital relaxation time of 2 ps and diffusion length of the order of 2 nm in disordered Mn. Our findings indicate that current-induced orbital moments are responsible for magnetoresistance effects comparable to or even larger than those determined by spin moments, and provide a tool to investigate nonequilibrium orbital transport phenomena.

Figure 1

(a) Schematic representation of the Hanle effect. The angular momentum $\mathit{\zeta }$ induced by an electric current ${\mathbf{j}}_{\mathrm{c}}$ via the spin or orbital Hall effect precesses about the magnetic field $\mathbf{B}$. The net $\mathit{\zeta }$ decreases because electrons traveling along different paths accumulate different phases. (b) Hanle effect in three different configurations. Left: when $\mathbf{B}\parallel \mathit{\zeta }$, no precession occurs, and the spin (orbital) current ${\mathbf{j}}_{\mathit{\zeta }}$ polarized along $-y$ is converted by the inverse spin (orbital) Hall effect into a charge current ${\mathbf{j}}_{\mathrm{c}}$ along $x$. The resistance is thus minimum. Middle and right: $\mathbf{B}$ induces the precession of $\mathit{\zeta }$, reducing ${\zeta }_{\mathrm{y}}$, and suppressing both ${\mathbf{j}}_{\mathit{\zeta }}$ and ${\mathbf{j}}_{\mathrm{c}}$. The resistance is maximum. When $\mathbf{B}\parallel \mathbf{z}$ (middle), an additional charge current flows along $y$ because of the field-induced ${\zeta }_{\mathrm{x}}$. This current induces the transverse HMR.

Figure 2

(a) Optical image of a Hall bar device and sketch of the measurement configuration. $R$ and $R_{\mathrm{H}}$ are the longitudinal and transverse resistance, respectively. (b) Coordinate system showing the angle of the applied field in the $xy$, $zx$, and $zy$ planes. (c) Longitudinal resistance measured in Mn(6) by $zx$ and $zy$ angle scans in a field of 7 T. (d) Longitudinal resistance in the same device during $zy$ angle scans at increasing magnetic fields. The solid lines in (c),(d) are fits to a ${\cos }^2(\beta )$ function. The angle scans are limited to the $[25°-355°]$ range because of technical constraints.

Figure 3

(a)–(b) Longitudinal and transverse resistance of Mn(9) measured during field scans along three orthogonal directions. The contribution from the ordinary Hall effect was subtracted from the transverse resistance measured in the $z$-field scan. The solid line in (a) is a fit with shared parameters of Eq. (3) to both the $x$- and $z$-field-scan magnetoresistance. The solid line in (b) is a fit of Eq. (4) to the $z$-field-scan magnetoresistance. (c)–(d) Same as (a)–(b) for Pt(5).

Figure 4

(a) Thickness dependence of the normalized longitudinal and transverse HMR. (b) Temperature dependence of the longitudinal HMR (left axis) and longitudinal resistance (right axis) in Mn(9).

Figure 5

(a) Longitudinal resistance of $\mathrm{BiYIG}/\mathrm{Mn}(10)$ measured by rotating a constant magnetic field of 1 T in the $xy$, $zx$, and $zy$ planes. The red and gray lines are fits of ${\cos }^2(\alpha ,\beta )$ to the data. (b) Same as (a) in $\mathrm{BiYIG}/\mathrm{Pt}(5)$.