Impact of crystallinity on orbital torque generation in ferromagnets

We investigate the impact of crystallinity on the generation of orbital torques in Ni, which is predicted to exhibit the strongest orbital response among conventional $3d$ ferromagnetic metals. We show that the current-induced torques in Hf/Ni bilayers are primarily dominated by the orbital torque, arising from the orbital Hall effect in the Hf layer. We find that the orbital torque efficiency is enhanced by a factor of 2 when the stacking order of the Hf/Ni bilayer is altered. Through the examination of bulk and interfacial structural properties of the Ni and Hf layers, and by quantifying the torque efficiency in a symmetric Hf/Ni/Hf trilayer, we show that the orbital torque efficiency is strongly dependent on the crystallinity of the Ni layer. This dependence is in stark contrast to conventional spin-orbit torques, which arise from the spin Hall effect and are typically insensitive to the crystallinity of the ferromagnetic layer. These findings highlight the significant role of the crystalline structure of the ferromagnetic layer in its orbital response and illustrate the potential of crystal structure engineering in optimizing orbital torques.

Figure 1

(a) ST-FMR spectra for the Hf(10 nm)/Ni(12 nm) bilayer at ${\theta }_H={45}^{\circ }$. The frequency $f$ was varied from 7 to 12 GHz. The solid circles and curves represent the experimental data and the fitting results, respectively. In-plane magnetic field angle ${\theta }_H$ dependence of (b) the symmetric component $S$ and (c) the antisymmetric component $A$ for the Hf(10 nm)/Ni(12 nm) bilayer. The solid circles are the experimental data. The solid curve is the fitting result using a function proportional to $cos{\theta }_{H}sin2{\theta }_H$.

Figure 2

(a) Hf-layer-thickness $t_{\mathrm{Hf}}$ dependence of the DL torque efficiency ${\xi }_{\mathrm{DL}}^E$ for the $\mathrm{Hf}\left(t_{\mathrm{Hf}}\right)/\mathrm{Ni}$(12 nm) bilayer (blue) and the Ni(12 nm)/$\mathrm{Hf}\left(t_{\mathrm{Hf}}\right)$ bilayer (red). (b) Ni-layer-thickness $t_{\mathrm{Ni}}$ dependence of the DL torque efficiency ${\xi }_{\mathrm{DL}}^E$ for the Hf(10 nm)/$\mathrm{Ni}\left(t_{\mathrm{Ni}}\right)$ bilayer (blue) and the $\mathrm{Ni}\left(t_{\mathrm{Ni}}\right)/\mathrm{Hf}$(10 nm) bilayer (red). The open circles are the experimental data. The solid curves are the fitting results.

Figure 3

(a) ST-FMR spectra for the Ni(12 nm)/Hf(10 nm) bilayer at ${\theta }_H={45}^{\circ }$. The frequency $f$ was varied from 7 to 12 GHz. The solid circles and curves represent the experimental data and the fitting results, respectively. In-plane magnetic field angle ${\theta }_H$ dependence of (b) the symmetric component $S$ and (c) the antisymmetric component $A$ for the Ni(12 nm)/Hf(10 nm) bilayer. The solid circles are the experimental data. The solid curve is the fitting result using a function proportional to $cos{\theta }_{H}sin2{\theta }_H$.

Figure 4

(a) XRD patterns for the Hf(28 nm) layer in the Hf(28 nm)/Ni(12 nm) bilayer (blue) and the Ni(12 nm)/Hf(28 nm) bilayer (red). The XRD patterns show that the Hf layer is a hexagonal closed-packed (hcp) structure. (b) XRD patterns for the Ni(12 nm) layer in the Hf(28 nm)/Ni(12 nm) bilayer (blue) and the Ni(12 nm)/Hf(28 nm) bilayer (red). The XRD patterns show that the Ni layer is a face-centered cubic (fcc) structure.

Figure 5

Cross-sectional transmission electron microscope images of the (a) Hf/Ni and (b) Ni/Hf bilayers. Fast Fourier transform patterns for the Ni layers of the (c) Hf/Ni and (d) Ni/Hf bilayers, and the Hf layers of the (e) Hf/Ni and (f) Ni/Hf bilayers.

Figure 6

XRR profiles for (a) the Hf(28 nm)/Ni(12 nm) bilayer and (b) the Ni(12 nm)/Hf(28 nm) bilayer. The solid circles and curves are the experimental data and the fitting results, respectively. Schematic illustration of the structure with the thickness of the intermixing layer is also shown in the inset.

Figure 7

(a) ST-FMR spectra for the Hf(10 nm)/Ni(12 nm)/ Hf(10 nm) trilayer at ${\theta }_H={45}^{\circ }$. The frequency $f$ was varied from 9.5 GHz to 12 GHz. The solid circles and curves represent the experimental data and the fitting results, respectively. (b) In-plane magnetic field angle ${\theta }_H$ dependence of the symmetric component $S$ and the antisymmetric component $A$. The solid circles are the experimental data. The solid curves are the fitting result using functions proportional to $cos{\theta }_{H}sin2{\theta }_H$.

Figure 8

XRR profiles for the Hf(28 nm)/Ni(12 nm)/Hf(28 nm) trilayer. The solid circles and curves are the experimental data and the fitting results, respectively. Schematic illustration of the structure with the thicknesses of the intermixing layers is also shown in the inset.