Abstract
Spin Hall effect, an electric generation of spin current, allows for efficient control of magnetization. Recent theory revealed that orbital Hall effect creates orbital current, which can be much larger than spinHallinduced spin current. However, orbital current cannot directly exert a torque on a ferromagnet, requiring a conversion process from orbital current to spin current. Here, we report two effective methods of the conversion through spinorbit coupling engineering, which allows us to unambiguously demonstrate orbitalcurrentinduced spin torque, or orbital Hall torque. We find that orbital Hall torque is greatly enhanced by introducing either a rareearth ferromagnet Gd or a Pt interfacial layer with strong spinorbit coupling in Cr/ferromagnet structures, indicating that the orbital current generated in Cr is efficiently converted into spin current in the Gd or Pt layer. Our results offer a pathway to utilize the orbital current to further enhance the magnetization switching efficiency in spinorbittorquebased spintronic devices.
Introduction
Spin Hall effect (SHE) that creates a transverse spin current by a charge current in a nonmagnet (NM) with strong spin–orbit coupling (SOC)^{1} has received much attention because the resulting spin–orbit torque (SOT) offers efficient control of magnetization in NM/ferromagnet (FM) heterostructures of various spintronic devices^{2,3,4,5,6,7,8,9}. Similar to the SHE, the orbital Hall effect (OHE) generates an orbital current, a flow of orbital angular momentum^{10,11,12,13}. The OHE has distinctive features compared to the SHE; first, the OHE originates from momentumspace orbital textures, so it universally occurs in multiorbital systems regardless of the magnitude of SOC^{12}. For example, it has been reported nontrivial orbital current can be generated in 3d transition metals, graphene, or twodimensional transition metal dichalcogenides^{13,14,15,16,17,18}. Second, theoretical calculations show that orbital Hall conductivity is much larger than spin Hall conductivity in many materials, including those commonly used for SOT such as Ta and W^{10,11,13}. This suggests that the spin torque caused by the OHE, or orbital Hall torque (OHT)^{19,20}, can be larger than the SHEinduced spin torque, enhancing the spintorque efficiency in spintronic devices. Recently, several experimental reports have claimed that significant SOT and magnetoresistance observed in FM/Cu/oxide structures, in which the SHE is known to be negligible, is of orbital current origin^{21,22,23,24}. However, it seems that the underlying mechanism of the OHE and associated OHT are not yet fully understood. One issue is that there is no exchange coupling between orbital angular momentum (L) and local magnetic moment, and thus the orbital current cannot directly give a torque on magnetization. To make the OHT exerts on the local magnetic moment of the FM, the L must be converted to the spin angular momentum (S)^{19,20}. Therefore, finding an efficient method of “L–S conversion” is crucial to utilizing the OHT for the manipulation of the magnetization direction.
In this article, we experimentally demonstrate two effective L–S conversion techniques of engineering SOC of either an FM or an NM/FM interface. We employ Cr as an orbital current source material because it has been theoretically predicted that Cr has a large orbital Hall conductivity \(\sigma _{{{{{{{{\mathrm{OH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\) of ~8200 (ħ/e)(Ω cm)^{−1} while having a relatively small spin Hall conductivity \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\) of −130 (ħ/e)(Ω cm)^{−1} with the opposite sign^{13}. Here, ħ is the reduced Planck constant and e is the electron charge. For the Cr/FM bilayers, overall chargetospin conversion efficiency referred as effective spin Hall angle \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\), is expressed as^{19}
where \(\sigma _{xx}^{{{{{{{{\mathrm{Cr}}}}}}}}}\) is the electrical conductivity of Cr and \(\eta _{L  S}\) is the L–S conversion coefficient. Here, we assume perfect transmission (\(T_{{{{{{{{\mathrm{int}}}}}}}}}\) = 1) of both spin and orbital currents through the Cr/FM interface. Note that the second term on the right side of Eq. (1) corresponds to the OHE contribution to \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\), which depends on the magnitude and sign of \(\eta _{L  S}\). We demonstrate how to achieve a large \(\eta _{L  S}\) by engineering the SOC of an FM or an NM interfacial layer. First, we employ a rareearth FM of Gd with strong SOC, which increases the OHT in Cr/Gd heterostructures by ten times compared to that in Cr/Co heterostructures, indicating that the orbital current generated in Cr is efficiently converted to spin current in the FM Gd layer. Second, we modify the Cr/Co_{32}Fe_{48}B_{20} (CoFeB) interface by inserting a 1 nm Pt layer to facilitate L–S conversion. This leads to an enhancement in OHT, allowing us to demonstrate OHTinduced magnetization switching of perpendicular magnetization in Cr/Pt/CoFeB heterostructures. Since the OHE is expected to occur generally in various materials, our results demonstrating the significant OHT generated through the L–S conversion techniques broaden the scope of material engineering to improve spintorque switching efficiency for the development of lowpower spintronic devices.
Results and discussion
Orbital Hall torque generated by orbital current in Cr
To demonstrate the OHE in Cr and associated OHT, we investigate the currentinduced spintorque in Cr/FM heterostructures for two different FMs of Co and Ni. Figure 1a, b illustrates the role of \(\eta _{L  S}\) in \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) of the Cr/FM samples, where \({{{S}}}_{{{{{{{{\rm{SHE}}}}}}}}}\) is the spin angular momentum generated by SHE and \({{{S}}}_{{{{{{{{\rm{OHE}}}}}}}}}\) is the spin angular momentum converted from orbital angular momentum due to OHE (\({{{L}}}_{{{{{{{{\rm{OHE}}}}}}}}}\)). Note that we assume that Ni has a greater \(\eta _{L  S}\) than that of Co (\(\eta _{L  S}^{{{{{{{{\mathrm{Ni}}}}}}}}} \, > \,\eta _{L  S}^{{{{{{{{\mathrm{Co}}}}}}}}}\)) because \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Ni}}}}}}}}}\) is an order of magnitude larger than \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Co}}}}}}}}}\)^{25,26}. This is also supported by a recent first principle calculation demonstrating that the W/Ni bilayer exhibits a positive \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) despite the negative \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{\mathrm{W}}}}}}}}\) of W^{20}. This is attributed to the increased orbital current contribution to \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) by the large and positive \(\eta _{L  S}^{{{{{{{{\mathrm{Ni}}}}}}}}}\). Figure 1a shows the case of a Cr/Co bilayer with \(\eta _{L  S}^{{{{{{{{\mathrm{Co}}}}}}}}}\) ~ 0, where \({{{S}}}_{{{{{{{{\rm{SHE}}}}}}}}}\) is dominant and thus \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) is mainly determined by \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\) of negative sign. On the other hand, for the Cr/Ni bilayer having sizable \(\eta _{L  S}^{{{{{{{{\mathrm{Ni}}}}}}}}}\), nonnegligible \({{{S}}}_{{{{{{{{\rm{OHE}}}}}}}}}\) caused by the conversion of \(\sigma _{{{{{{{{\mathrm{OH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\) contributes to \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) (Fig. 1b). Since \({{{S}}}_{{{{{{{{\rm{OHE}}}}}}}}}\) is a positive value \((\eta _{L  S}^{{{{{{{{\mathrm{Ni}}}}}}}}} \, > \,0\,\& \,\sigma _{{{{{{{{\mathrm{OH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}} \, > \,0),\) opposite to \({{{S}}}_{{{{{{{{\rm{SHE}}}}}}}}}\), \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) of the Cr/Ni heterostructures becomes positive when the magnitude of \({{{S}}}_{{{{{{{{\rm{OHE}}}}}}}}}\) is larger than that of \({{{S}}}_{{{{{{{{\rm{SHE}}}}}}}}}\). To test whether the orbital current generated in Cr gives rise to OHT, we perform inplane harmonic Hall measurements of Co (3.0 nm)/Cr (7.5 nm) and Ni (2.0 nm)/Cr (7.5 nm) Hallbar patterned samples (Fig. 1c). Figure 1d, e shows representative second harmonic Hall resistance (\(R_{xy}^{2\omega }\)) versus azimuthal angle (\(\varphi\)) curves under different external magnetic fields (\(B_{{{{{{{{\mathrm{ext}}}}}}}}}\)). \(R_{xy}^{2\omega }(\varphi )\) is expressed as^{27}
where \(R_{{{{{{{{\mathrm{AHE}}}}}}}}}^{1\omega }\) and \(R_{{{{{{{{\mathrm{PHE}}}}}}}}}^{1\omega }\) are the first harmonic anomalous Hall and planar Hall resistances, respectively; \(B_{{{{{{{{\mathrm{DLT}}}}}}}}}\,(B_{{{{{{{{\mathrm{FLT}}}}}}}}})\) is the dampinglike (fieldlike) effective field; \(B_{{{{{{{{\mathrm{eff}}}}}}}}}\) is the effective magnetic field, including the demagnetization field and anisotropy field of FM; \(R_{\nabla T}\) is the thermal contributions, and \(B_{{{{{{{{\mathrm{Oe}}}}}}}}}\) is the currentinduced Oersted field. The \(R_{{{{{{{{\mathrm{AHE}}}}}}}}}^{1\omega }\) and \(R_{{{{{{{{\mathrm{PHE}}}}}}}}}^{1\omega }\) data are shown in Supplementary Note 1. Figure 1f shows the \({{{{{{{\mathrm{cos}}}}}}}}\varphi\) component of \(R_{xy}^{2\omega }\) divided by \(R_{{{{{{{{\mathrm{AHE}}}}}}}}}^{1\omega }\) [\(R_{{{{{{{{\mathrm{cos}}}}}}}}\varphi }^{2\omega }\)/\(R_{{{{{{{{\mathrm{AHE}}}}}}}}}^{1\omega }\)] as a function of \(1/B_{{{{{{{{\mathrm{eff}}}}}}}}}\) for the two FM/Cr samples, of which the slope represents B_{DLT} and associated \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\). We find that the Co/Cr sample shows a negative slope, and thus a negative \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\). This is consistent with the negative \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\) reported both theoretically and experimentally^{28,29,30}. In contrast, the Ni/Cr sample exhibits a positive slope, indicating a positive \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\). The sign reversal of \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) in the Ni/Cr sample is attributed to the increased contribution of the orbital current in Cr by the L–S conversion in Ni (\(\sigma _{{{{{{{{\mathrm{OH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\eta _{L  S}^{{{{{{{{\mathrm{Ni}}}}}}}}} \, > \,0\)). Note that the \((2{{{{{{{\mathrm{cos}}}}}}}}^3\varphi  {{{{{{{\mathrm{cos}}}}}}}}\varphi )\) component of \(R_{xy}^{2\omega }\) divided by \(R_{{{{{{{{\mathrm{PHE}}}}}}}}}^{1\omega }\), representing \(B_{{{{{{{{\mathrm{FLT}}}}}}}}} + B_{{{{{{{{\mathrm{Oe}}}}}}}}}\), of the Ni/Cr sample is larger than that of the Co/Cr sample. This might also be related to the increased orbital current in the Ni/Cr sample as discussed in Supplementary Note 2.
To verify whether the orbital current in Cr is the main cause of the measured torque, we perform two control experiments. First, we investigate the role of FM in determining \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) by measuring the \(R_{{{{{{{{\mathrm{cos}}}}}}}}\varphi }^{2\omega }\)/\(R_{{{{{{{{\mathrm{AHE}}}}}}}}}^{1\omega }\) of the Co (3 nm)/Pt (5 nm) and Ni (2 nm)/Pt (5 nm) structures, in which Cr is replaced by Pt, which has positive \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Pt}}}}}}}}}\) and \(\sigma _{{{{{{{{\mathrm{OH}}}}}}}}}^{{{{{{{{\mathrm{Pt}}}}}}}}}\)^{10,11,13,31}. Figure 1f shows positive slopes and corresponding positive \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\)’s for both the FM/Pt samples, indicating that the sign change of \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) in the FM/Cr samples is not due to the FM layer itself^{26}. Note that the dampinglike torque efficiency^{31}, \(\xi _{{{{{{{{\mathrm{DLT}}}}}}}}} = (2e/\hbar )(M_{{{{{{{\mathrm{S}}}}}}}}t_{{{{{{{{\mathrm{FM}}}}}}}}}B_{{{{{{{{\mathrm{DLT}}}}}}}}}/J_{{{{{{{{\mathrm{Pt}}}}}}}}})\) where, M_{S} is the saturation magnetization, t_{FM} is the FM thickness, and J_{Pt} is the current density flowing in Pt (Supplementary Note 3), between the Co/Pt and Ni/Pt samples differs by a factor of two. This indicates that interface transmission (\(T_{{{{{{{{\mathrm{int}}}}}}}}}\)) plays a critical role in determining ξ_{DLT} in these samples, where the spin current is primarily generated by the SHE in the Pt layer^{32}. It implies that \(T_{{{{{{{{\mathrm{int}}}}}}}}}\) can affect the ξ_{DLT} even in the FM/Cr sample, where the OHE is dominated. However, \(T_{{{{{{{{\mathrm{int}}}}}}}}}\) cannot account for the different signs of the \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) (or ξ_{DLT}) between the Co/Cr and Ni/Cr samples since it can only reduce the magnitude of the ξ_{DLT} by diminishing the transmission of spin (or orbital) currents. Second, we examine the interfacial contributions^{33,34,35,36,37,38} to \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) by measuring the Cr thickness (t_{Cr}) dependence of the ξ_{DLT} for the FM/Cr samples. If the positive \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) of the Ni/Cr samples is due to the interfacial effect, ξ_{DLT} decreases with increasing t_{Cr} and eventually changes its sign to negative for thicker t_{Cr}’s where bulk Cr with negative \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\) dominates. However, this is not the case, as shown in Fig. 1g; for both FM/Cr samples, the magnitude of ξ_{DLT} increases with t_{Cr}, while maintaining its sign unchanged, which demonstrates that there is no significant interfacial contribution to \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) in the FM/Cr samples. Note that we analyze the t_{Cr} dependence of ξ_{DLT} using a method of analyzing the SHEinduced SOT^{31}, \(\xi _{{{{{{{{\mathrm{DLT}}}}}}}}}\sim \left[ {1  {{{{{{{\mathrm{sech}}}}}}}}\left( {\frac{{t_{{{{{{{{\mathrm{Cr}}}}}}}}}}}{{\lambda _{{{{{{{{\mathrm{Cr}}}}}}}}}}}} \right)} \right]\), where, λ_{Cr} is the spin or orbital diffusion length. The extracted λ_{Cr} value is 6.1 ± 1.7 nm for the Ni/Cr and 1.8 ± 0.6 nm for the Co/Cr samples, which can be regarded as the orbital and spin diffusion lengths of Cr, respectively, since the ξ_{DLT} of the Ni/Cr (Co/Cr) sample is governed predominantly by the OHE (SHE). This result indicates that the orbital diffusion length is much greater than the spin diffusion length in Cr, as expected by theoretical calculations (Supplementary Note 4). These results corroborate that the OHE in Cr primarily governs the \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) of the FM/Cr samples, providing an excellent platform to study L–S conversion engineering.
Efficient L–S conversion through rareearth ferromagnet Gd
We now present two techniques to enhance the \(\eta _{L  S}\) of the Cr/FM structures. First, we introduce a rareearth FM Gd, which is expected to have a large \(\eta _{L  S}\) due to its strong SOC^{39,40}. Figure 2a illustrates the L–S conversion process in Cr/Gd heterostructures, where \(\eta _{L  S}^{{{{{{{{\mathrm{Gd}}}}}}}}}\) is negative because of its negative spin Hall angle^{41}. In this case, \({{{S}}}_{{{{{{{{\rm{OHE}}}}}}}}}\) due to the orbital current (\(\eta _{L  S}^{{{{{{{{\mathrm{Gd}}}}}}}}}\sigma _{{{{{{{{\mathrm{OH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\) < 0) is the same sign as \({{{S}}}_{{{{{{{{\rm{SHE}}}}}}}}}\) (\(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\) < 0), so they add up constructively with each other. This would result in enhanced \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) in the Cr/Gd heterostructure compared to the Cr/Co heterostructure. To verify this idea, we prepare Hallbar patterned samples of Gd (10 nm)/Cr (7.5 nm) and Co (10 nm)/Cr (7.5 nm) structures and conduct inplane harmonic Hall measurements at 10 K to avoid any side effects due to the large difference in Curie temperatures between Gd (~293 K) and Co (~1400 K). Note that Cr is known to be antiferromagnetic at 10 K^{42}, however, the exchange coupling of the Gd (Co)/Cr sample is negligibly small and therefore does not affect the harmonic Hall measurements (Supplementary Note 5). Figure 2b, c shows the \(R_{xy}^{2\omega }(\varphi )\) data measured under different B_{ext}’s of the Gd/Cr and Co/Cr samples, respectively, which are well described by Eq. (2) as represented by solid curves. The \(R_{{{{{{{{\mathrm{AHE}}}}}}}}}^{1\omega }\) and \(R_{{{{{{{{\mathrm{PHE}}}}}}}}}^{1\omega }\) data are shown in Supplementary Note 1. Figure 2d shows \(R_{{{{{{{{\mathrm{cos}}}}}}}}\varphi }^{2\omega }\)/\(R_{{{{{{{{\mathrm{AHE}}}}}}}}}^{1\omega }\) versus \(1/B_{{{{{{{{\mathrm{eff}}}}}}}}}\) for the Gd/Cr and Co/Cr samples. We find two points; first, both samples exhibit negative slopes, indicating \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}} < 0\). Second, the Gd/Cr sample has a much larger slope or \(B_{{{{{{{{\mathrm{DLT}}}}}}}}}\) than that of the Co/Cr sample. The estimated ξ_{DLT} of the Gd/Cr sample is −0.21 ± 0.01, which is about ten times greater than that of the Co/Cr sample (−0.018 ± 0.002). Note that ξ_{DLT} of the Gd/Cr samples increases with the t_{Cr} (Supplementary Note 6), indicating that ξ_{DLT} originates from the orbital current in bulk Cr. The large enhancement of ξ_{DLT} or \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) demonstrates that the OHT contribution can be increased by introducing FMs with large \(\eta _{L  S}\).
We estimate effective spin Hall conductivity \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}({{{{{{{\mathrm{eff}}}}}}}}) = \sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}} + \sigma _{{{{{{{{\mathrm{OH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\eta _{L  S}\) of the samples using the relation^{31} \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\left( {{{{{{{{\mathrm{eff}}}}}}}}} \right)\) = (ħ/2e)·(ξ_{DLT} × \(\sigma _{xx}^{{{{{{{{\mathrm{Cr}}}}}}}}}\)). The calculated \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}({{{{{{{\mathrm{eff}}}}}}}})\) of the Gd/Cr sample is −999 (ħ/e)·(Ω cm)^{−1}, which is much larger than the theoretical spin Hall conductivity of Cr^{13}, \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}} =\) −130 (ħ/e)·(Ω cm)^{−1}. The large \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}({{{{{{{\mathrm{eff}}}}}}}})\) value of the Gd/Cr sample supports our claim that the enhanced ξ_{DLT} is due to the orbital current in Cr, subject to the effective conversion into spin currents in Gd (\(\sigma _{{{{{{{{\mathrm{OH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\eta _{L  S}^{{{{{{{{\mathrm{Gd}}}}}}}}}\)). On the other hand, the \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}({{{{{{{\mathrm{eff}}}}}}}})\) of the Co/Cr sample is −86 (ħ/e)·(Ω cm)^{−1}, which is comparable to the theoretical \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\) value. This is consistent with the fact that the orbital current contribution is negligible in the Co/Cr sample with \(\eta _{L  S}^{{{{{{{{\mathrm{Co}}}}}}}}}\) ~ 0. Furthermore, we observe that the ξ_{DLT} of the Gd/Cr sample decreases with increasing temperature (Supplementary Note 7). This can be attributed to phonon scattering since the orbital angular momentum is strongly coupled to the lattice through the crystal field potential^{20}. At higher temperatures, more phonons are generated, reducing the OHE.
Magnetization switching by efficient L–S conversion through Pt interfacial layer
We next demonstrate another L–S conversion technique that modifies the NM/FM interface by inserting a Pt layer. This method has the advantage that it can be easily incorporated into perpendicularly magnetized CoFeB/MgO structures, which is a basic component of various spintronic devices^{43,44,45}. Figure 3a illustrates the conversion process in a Cr/Pt/CoFeB structure, where the \({{{L}}}_{{{{{{{{\rm{OHE}}}}}}}}}\) originating from Cr is converted to \({{{S}}}_{{{{{{{{\rm{OHE}}}}}}}}}\) in the Pt layer. Since Pt has a positive \(\eta _{L  S}^{{{{{{{{\mathrm{Pt}}}}}}}}}\) due to positive \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Pt}}}}}}}}}\), \({{{S}}}_{{{{{{{{\rm{OHE}}}}}}}}}\) would be positive (\(\sigma _{{{{{{{{\mathrm{OH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}}\eta _{L  S}^{{{{{{{{\mathrm{Pt}}}}}}}}} \, > \,0\)), while \({{{S}}}_{{{{{{{{\rm{SHE}}}}}}}}}\) is negative (\(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Cr}}}}}}}}} \, < \,0\)). Thus, the OHT due to \({{{S}}}_{{{{{{{{\rm{OHE}}}}}}}}}\) is the opposite of the spin Hall torque due to \({{{S}}}_{{{{{{{{\rm{SHE}}}}}}}}}\). To examine the effect of Pt insertion on OHT, we perform currentinduced magnetization switching experiments as schematically illustrated in Fig. 3b. Figure 3c shows switching curves as a function of pulse current density (J_{pulse}) for Cr (10.0 nm)/Pt (0 or 1.0 nm)/CoFeB (0.9 nm)/MgO (1.6 nm) Hallbar patterned samples. Note that an inplane magnetic field B_{x} of +20 mT is applied along the current direction for deterministic switching of the perpendicular magnetization^{2,4,46}. The Cr/CoFeB sample shows a counterclockwise switching curve consistent with negative \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\), caused primarily by the SHE in Cr. The switching polarity is reversed by introducing a Pt (1 nm) insertion layer. The clockwise switching curve of the Cr/Pt/CoFeB sample corresponds to positive \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\), which is the expected sign in the OHT scenario (Fig. 3a). The sign reversal of \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) of the samples is also confirmed by perpendicular harmonic Hall measurements (Supplementary Note 8). Note that the switching polarity is abruptly reversed when t_{Pt} is greater than 0.6 nm (Supplementary Note 9), where Pt forms a continuous film that effectively converts orbital currents to spin currents. This makes the OHE dominant over the SHE.
The sign change in \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) can be caused by the inserted Pt itself with positive \(\sigma _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{Pt}}}}}}}}}\). To rule out this possibility, we investigate the t_{Cr} dependence of the currentinduced magnetization switching for the samples, where t_{Cr} ranges from 2.0 to 12.5 nm. Figure 3d shows the switching efficiency^{47,48} \(\xi ^{{{{{{{{\mathrm{SW}}}}}}}}}\,[ = (2e/\hbar )(M_{{{{{{{\mathrm{S}}}}}}}}t_{{{{{{{{\mathrm{CoFeB}}}}}}}}}B_{{{{{{{\mathrm{P}}}}}}}}/J_{{{{{{{{\mathrm{SW}}}}}}}}})]\) as a function of t_{Cr}. Here, \(t_{{{{{{{{\mathrm{CoFeB}}}}}}}}}\) is the CoFeB thickness, \(B_{{{{{{{\mathrm{P}}}}}}}}\) is the domain wall propagation field, and \(J_{{{{{{{{\mathrm{SW}}}}}}}}}\) is the switching current density (Supplementary Note 10). We find that the magnitude of \(\xi ^{{{{{{{{\mathrm{SW}}}}}}}}}\) for both samples increases with increasing t_{Cr}, while its sign remains unchanged for all t_{Cr}’s used in this study. Since the contribution of the spin current generated from Pt to \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) in the Cr/Pt/CoFeB structures will decrease with increasing t_{Cr}, the similar thickness dependence of \(\xi ^{{{{{{{{\mathrm{SW}}}}}}}}}\) indicates that the \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) of both samples predominantly originates from the Cr layer, not from the Pt interfacial layer; the SHE and OHE in Cr are the main sources of \(\theta _{{{{{{{{\mathrm{SH}}}}}}}}}^{{{{{{{{\mathrm{eff}}}}}}}}}\) for the Cr/CoFeB and Cr/Pt/CoFeB samples, respectively. These results demonstrate that the OHT can be effectively modified by interface SOC engineering and is capable of switching the perpendicular magnetization.
In conclusion, we experimentally demonstrate nontrivial OHT, spin torques originating from the orbital current in Cr, by introducing two effective ways of orbitaltospin (L–S) conversion, which is a key ingredient of OHT generation. First, we employ a rareearth FM of Gd having a larger L–S conversion efficiency than that of conventional 3d FMs. This greatly improves the SOT efficiency of the Cr/Gd bilayers compared to that of the Cr/Co bilayers. Second, we introduce a Pt interfacial layer in the Cr/CoFeB bilayers to facilitate L–S conversion. This allows the OHT to control the perpendicular magnetization in the Cr/Pt/CoFeB heterostructures. Since orbital currents can occur in various materials regardless of the SOC strength, our results provide a unique strategy based on orbital currents to develop material systems with enhanced SOT efficiency.
Methods
Film preparation and Hallbar fabrication
Bilayers of FM (Co, Ni)/Cr, FM (Co, Ni)/Pt, Gd /Cr, and Co/Cr for harmonic measurements were deposited on Si/SiO_{2} or Si/Si_{3}N_{4} substrates using DC magnetron sputtering under a base pressure of <2.6 × 10^{−5} Pa, while Cr/CoFeB and Cr/Pt/CoFeB structures for switching experiments were deposited on a highly resistive Si substrate using DC and RF magnetron sputtering under a base pressure of <4.0 × 10^{−6} Pa. An underlayer of Ta (1 nm)/AlO_{x} (2 nm), or Ta (1.5 nm) layers were used to obtain smooth roughness; a capping layer of Ta (2–3 nm) was used to prevent further oxidation. All metallic layers and the MgO layer were grown with a working pressure of 0.4 Pa and a power of 30 W at room temperature. The AlO_{x} layer was formed by deposition of an Al layer and subsequent plasma oxidation with an O_{2} pressure of 4.0 Pa and a power of 30 W for 75 s. Hallbarpatterned devices with widths of 5, 10, or 15 μm were defined using photolithography and Ar ionmilling.
Spin–orbit torque characterization
Inplane harmonic measurement with AC current (frequency of 11 Hz) was performed to evaluate the spin–orbit torque of the heterostructures. Both \(R_{xy}^{1\omega }\) and \(R_{xy}^{2\omega }\) were recorded by two lockin amplifiers at the same time while varying the azimuthal angle (\(\varphi\)) under a constant external field B_{ext} and a current density J_{x} of 1 × 10^{11} A/m^{2}.
Currentinduced magnetization switching measurements
Magnetization switching experiments were conducted by applying a current pulse (pulse width of 30 μs) with a constant external magnetic field (B_{x}) of +20 mT. The magnetization state was checked by anomalous Hall resistance (R_{AHE}) after applying the current pulse.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. H. & Jungwirth, T. Spin Hall effects. Rev. Mod. Phys. 87, 1213–1260 (2015).
Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced by inplane current injection. Nature 476, 189–193 (2011).
Liu, L. et al. Spintorque switching with the giant spin Hall effect of tantalum. Science 336, 555–558 (2012).
Liu, L., Lee, O. J., Gudmundsen, T. J., Ralph, D. C. & Buhrman, R. A. Currentinduced switching of perpendicularly magnetized magnetic layers using spin torque from the spin Hall effect. Phys. Rev. Lett. 109, 096602 (2012).
Demidov, V. E. et al. Magnetic nanooscillator driven by pure spin current. Nat. Mater. 11, 1028–1031 (2012).
Emori, S., Bauer, U., Ahn, S. M., Martinez, E. & Beach, G. S. D. Currentdriven dynamics of chiral ferromagnetic domain walls. Nat. Mater. 12, 611–616 (2013).
Ryu, K. S., Thomas, L., Yang, S.H. & Parkin, S. Chiral spin torque at magnetic domain walls. Nat. Nanotechnol. 8, 527–533 (2013).
Manchon, A. et al. Currentinduced spinorbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys. 91, 035004 (2019).
Ryu, J., Lee, S., Lee, K. J. & Park, B.G. Currentinduced spin–orbit torques for spintronic applications. Adv. Mater. 32, 1907148 (2020).
Tanaka, T. et al. Intrinsic spin Hall effect and orbital Hall effect in 4d and 5d transition metals. Phys. Rev. B 77, 165117 (2008).
Kontani, H., Tanaka, T., Hirashima, D. S., Yamada, K. & Inoue, J. Giant orbital Hall effect in transition metals: origin of large spin and anomalous Hall effects. Phys. Rev. Lett. 102, 016601 (2009).
Go, D., Jo, D., Kim, C. & Lee, H.W. Intrinsic spin and orbital Hall effects from orbital texture. Phys. Rev. Lett. 121, 086602 (2018).
Jo, D., Go, D. & Lee, H.W. Gigantic intrinsic orbital Hall effects in weakly spinorbit coupled metals. Phys. Rev. B 98, 214405 (2018).
Bhowal, S. & Satpathy, S. Intrinsic orbital moment and prediction of a large orbital Hall effect in twodimensional transition metal dichalcogenides. Phys. Rev. B 101, 121112(R) (2020).
Canonico, L. M., Cysne, T. P., MolinaSanchez, A., Muniz, R. B. & Rappoport, T. G. Orbital Hall insulating phase in transition metal dichalcogenide monolayers. Phys. Rev. B 101, 161409(R) (2020).
Bhowal, S. & Satpathy, S. Intrinsic orbital and spin Hall effects in monolayer transition metal dichalcogenides. Phys. Rev. B 102, 035409 (2020).
Bhowal, S. & Vignale, G. Orbital Hall effect as an alternative to valley Hall effect in gapped graphene. Phys. Rev. B 103, 195309 (2021).
Cysne, T. P. et al. Disentangling orbital and valley Hall effects in bilayers of transition metal dichalcogenides. Phys. Rev. Lett. 126, 056601 (2021).
Go, D. & Lee, H.W. Orbital torque: torque generation by orbital current injection. Phys. Rev. Res. 2, 013177 (2020).
Go, D. et al. Theory of currentinduced angular momentum transfer dynamics in spinorbit coupled systems. Phys. Rev. Res. 2, 033401 (2020).
Ding, S. et al. Harnessing orbitaltospin conversion of interfacial orbital currents for efficient spinorbit torques. Phys. Rev. Lett. 125, 177201 (2020).
Kim, J. et al. Nontrivial chargetospin conversion in ferromagnetic metal/Cu/Al_{2}O_{3} by orbital transport. Phys. Rev. B 103, L020407 (2021).
Tazaki, Y. et al. Currentinduced torque originating from orbital current. Preprint at arXiv http://arXiv.org/abs/2004.09165 (2020).
Ding, S. et al. Observation of the orbital RashbaEdelstein magnetoresistance. Preprint at arXiv http://arXiv.org/abs/2105.04495 (2021).
Amin, V. P., Li, J., Stiles, M. D. & Haney, P. M. Intrinsic spin currents in ferromagnets. Phys. Rev. B 99, 220405(R) (2019).
Wang, W. et al. Anomalous spin–orbit torques in magnetic singlelayer films. Nat. Nanotechnol. 14, 819–824 (2019).
Avci, C. O. et al. Interplay of spinorbit torque and thermoelectric effects in ferromagnet/normalmetal bilayers. Phys. Rev. B 90, 224427 (2014).
Du, C., Wang, H., Yang, F. & Hammel, P. C. Systematic variation of spinorbit coupling with dorbital filling: Large inverse spin Hall effect in 3d transition metals. Phys. Rev. B 90, 140407(R) (2014).
Chuang, T. C., Pai, C. F. & Huang, S. Y. Crinduced perpendicular magnetic anisotropy and fieldfree spinorbittorque switching. Phys. Rev. Appl. 11, 061005 (2019).
Cui, B. et al. Current induced magnetization switching in Pt/Co/Cr structures with enhanced perpendicular magnetic anisotropy and spin Hall effect. Appl. Phys. Express 12, 043001 (2019).
Nguyen, M.H., Ralph, D. C. & Buhrman, R. A. Spin torque study of the spin Hall conductivity and spin diffusion length in platinum thin films with varying resistivity. Phys. Rev. Lett. 116, 126601 (2016).
Zhang, W., Han, W., Jiang, X., Yang, S.H. & Parkin, S. S. P. Role of transparency of platinumferromagnet interfaces in determining the intrinsic magnitude of the spin Hall effect. Nat. Phys. 11, 496–502 (2015).
Gambardella, P. & Miron, I. M. Currentinduced spinorbit torques. Philos. Trans. R. Soc. A 369, 3175–3197 (2011).
Emori, S. et al. Interfacial spinorbit torque without bulk spinorbit coupling. Phys. Rev. B 93, 180402(R) (2016).
Amin, V. P. & Stiles, M. D. Spin transport at interfaces with spinorbit coupling: formalism. Phys. Rev. B 94, 104419 (2016).
Amin, V. P. & Stiles, M. D. Spin transport at interfaces with spinorbit coupling: phenomenology. Phys. Rev. B 94, 104420 (2016).
Baek, S.h. C. et al. Spin currents and spinorbit torques in ferromagnetic trilayers. Nat. Mater. 17, 509–513 (2018).
Lee, H.Y. et al. Enhanced spinorbit torque via interface engineering in Pt/CoFeB/MgO heterostructures. APL Mater. 7, 031110 (2019).
Krupin, O. et al. Rashba effect at magnetic metal surfaces. Phys. Rev. B 71, 201403(R) (2005).
Stöhr, J. & Siegmann, H. C. Magnetism: From Fundamentals to Nanoscale Dynamics. Vol. 152 (Springer Series in Solidstate Sciences, 2006).
Ueda, K., Pai, C. F., Tan, A. J., Mann, M. & Beach, G. S. D. Effect of rare earth metal on the spinorbit torque in magnetic heterostructures. Appl. Phys. Lett. 108, 232405 (2016).
Zabel, H. Magnetism of chromium at surfaces, at interfaces and in thin films. J. Phys. Condens. Matter 11, 9303–9346 (1999).
Ikeda, S. et al. A perpendicularanisotropy CoFeBMgO magnetic tunnel junction. Nat. Mater. 9, 721–724 (2010).
Torrejon, J. et al. Neuromorphic computing with nanoscale spintronic oscillators. Nature 547, 428–431 (2017).
Borders, W. A. et al. Integer factorization using stochastic magnetic tunnel junctions. Nature 573, 390–393 (2019).
Qiu, X. et al. Angular and temperature dependence of current induced spinorbit effective fields in Ta/CoFeB/MgO nanowires. Sci. Rep. 4, 4491 (2014).
Lee, O. J. et al. Central role of domain wall depinning for perpendicular magnetization switching driven by spin torque from the spin Hall effect. Phys. Rev. B 89, 024418 (2014).
Mishra, R. et al. Anomalous currentinduced spin torques in ferrimagnets near compensation. Phys. Rev. Lett. 118, 167201 (2017).
Acknowledgements
We acknowledge fruitful discussion with HyunWoo Lee, KyoungWhan Kim, and Daegeun Jo. We also thank Byoung Kook Kim at the KAIST Analysis Center for Research Advancement (KARA) for his support on the magnetic properties measurement. We acknowledge the Jülich Supercomputing Centre for providing computational resources under project jiff40. This work was supported by the National Research Foundation of Korea (2015M3D1A1070465, 2020R1A2C2010309, and 2020R1A2C3013302) and by the German Research Foundation (Deutsche Forschungsgemeinschaft)—TRR 173—268565370 (project A11), TRR 288—422213477 (project B06).
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The study was performed under the supervision of B.G.P., S.L. and M.G.K. fabricated samples and conducted the inplane harmonic measurements and spin–orbit torque switching experiments with the help of D.K., J.H.K., T.L., G.H.L., N.J.L., J.K. and S.K. D.G. and Y.M. performed theoretical calculations. S.L., M.G.K. and B.G.P. performed data analysis with the help of D.G., K.J.K. and K.J.L. S.L., M.G.K. and B.G.P. wrote the paper with the help of all authors.
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Lee, S., Kang, MG., Go, D. et al. Efficient conversion of orbital Hall current to spin current for spinorbit torque switching. Commun Phys 4, 234 (2021). https://doi.org/10.1038/s42005021007377
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DOI: https://doi.org/10.1038/s42005021007377
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