Full angular dependence of the spin Hall and ordinary magnetoresistance in epitaxial antiferromagnetic NiO(001)/Pt thin films

We report the observation of the three-dimensional angular dependence of the spin Hall magnetoresistance (SMR) in a bilayer of the epitaxial antiferromagnetic insulator NiO(001) and the heavy metal Pt, without any ferromagnetic element. The detected angular-dependent longitudinal and transverse magnetoresistances are measured by rotating the sample in magnetic fields up to 11 T, along three orthogonal planes ($xy$-, $yz$-, and $xz$-rotation planes, where the $z$ axis is orthogonal to the sample plane). The total magnetoresistance has contributions arising from both the SMR and ordinary magnetoresistance. The onset of the SMR signal occurs between 1 and 3 T and no saturation is visible up to 11 T. The three-dimensional angular dependence of the SMR can be explained by a model considering the reversible field-induced redistribution of magnetostrictive antiferromagnetic S and T domains in the NiO(001), stemming from the competition between the Zeeman energy and the elastic clamping effect of the nonmagnetic MgO substrate. From the observed SMR ratio, we estimate the spin mixing conductance at the NiO/Pt interface to be greater than $2\times {10}^{14}{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-2}$. Our results demonstrate the possibility to electrically detect the Néel vector direction in stable NiO(001) thin films, for rotations in the $xy$ and $xz$ planes. Moreover, we show that a careful subtraction of the ordinary magnetoresistance contribution is crucial to correctly estimate the amplitude of the SMR.

Figure 1

(a) Measurement scheme of spin Hall magnetoresistance (SMR) in MgO//NiO(001)/Pt. A charge current ${\mathrm{J}}_{\mathrm{c}}$ flows in the Pt layer, yielding a transverse spin current ${\mathrm{J}}_{\mathrm{s}}$ in the NiO, via the spin Hall effect. Depending on the relative orientation between the Néel vector N (blue arrow) and the current-induced spin polarization ${\mathbf{\mu }}_s$, the spin current polarization is modified, and the spin current is converted into an additional charge current by the inverse spin Hall effect, yielding the SMR. The spin structure of one of the twelve possible {$11\overline{2}$} S domains of the NiO is shown, as well as the (111) easy plane. (b)–(d) Geometry of xy-, yz- and $xz$-plane scans, and definition of the angles α, β, and γ. (e) XMLD image showing the antiferromagnetic domains in NiO at ${\mu }_0\mathrm{H}=0\mathrm{T}$. The arrows indicate the orientation of the crystalline axes of the sample and of the electric field E of the x-ray beam. (f) Optical microscope image of the Hall bar design used for the magnetoresistance experiments.

Figure 2

Longitudinal $\left[\mathrm{\Delta }{R}_{xx}=R_{xx}\left(\theta \right)-\min \left(R_{xx}\right)\right]$ and transverse $[\mathrm{\Delta }{R}_{xy}=R_{xx}\left(\theta \right)-\left({\overline{R}}_{xy}\right)]$ angular dependence of the resistance variation of NiO/Pt bilayers at 199.46 ± 0.02 K, where $\overline{R}$ is the angle-averaged resistance. [(a) and (b)] Longitudinal resistance variation $\mathrm{\Delta }{R}_{xx}$ and transverse resistance variation $\mathrm{\Delta }{R}_{xy}$ in the $xy$-plane scan, as a function of the in-plane angle α for applied field of 1, 5, 8, and 11 T. [(c) and (d)] $\mathrm{\Delta }{R}_{xx}$ and $\mathrm{\Delta }{R}_{xy}$ in the $yz$-plane scan, as a function of the out-of-plane angle β. [(e) and (f)] $\mathrm{\Delta }{R}_{xx}$ and $\mathrm{\Delta }{R}_{xy}$ in the $xz$-plane scan, as a function of the out-of-plane angle γ. The continuous lines show the $\mathrm{\Delta }{R}^{*}\mathrm{si}{\mathrm{n}}^2\left(\theta +{\theta }_0\right)$ fit of the data, except for the $\mathrm{\Delta }{R}_{xy}$ data in the $xz$- and $yz$-plane scans, which is fitted by $\mathrm{\Delta }{R}^{*}\cos \left(\theta +{\theta }_0\right)$. Note the predominance of the 2π-periodic Hall effect in the transverse resistance (blue circles) shown in (d) and (f). The residuals, shown as black squares in (d) and (f), have been obtained by subtracting the fitted cosine curve to the $\mathrm{\Delta }{R}_{xy}$ data and by multiplying the results by the geometrical factor length/width of the Hall bar (8.67).

Figure 3

Comparison between the longitudinal and transverse angular dependence of the resistance variation in MgO//NiO(90 nm)/Pt(7.5 nm), shown by black dots, and a MgO//Pt(7.5 nm) sample, shown by red dots, in an applied field at ${\mu }_0\mathrm{H}=11\mathrm{T}$ at 199.46 ± 0.02 K. The resistances are measured by rotating the samples in (a) and (b) $xy$, [(c) and (d)] $yz$, and [(e) and (f)] $xz$ planes. Note that the longitudinal and transverse resistance are significantly different between the MgO and the NiO [(a), (b), and (e)], while the longitudinal resistance in the $yz$-plane scan (c) and the Hall effect in the out of plane scans [(d) and (f)] are the same.

Figure 4

Amplitude ΔR of the longitudinal and transverse resistance variation obtained by the $\mathrm{\Delta }{R}^{*}\mathrm{si}{\mathrm{n}}^2\left(\theta +{\theta }_0\right)$ fit of the data for different magnetic field amplitude and divided by the angle-averaged resistance $\overline{R}$. The data were acquired in the $xy$-, $xz$-, and $yz$-plane scans at 199.46 ± 0.02 K and are compared to the theoretical model (green solid line). No saturation is observed in the field range used up to 11 T.