Introduction

The Spin Hall effect (SHE)1,2,3,4 allows for the generation of spin currents from charge currents that are passed through the interior of thin metallic layers. The magnitude and polarization direction of the spin current are widely inferred from the spin-torque ferromagnetic resonance technique (ST-FMR)5,6,7,8 in which the spin current is used to provide torques on proximal ferromagnetic layers. The polarization of the spin current is typically observed to lie in the plane9 of the metallic layer but the quest for out-of-plane polarized spin currents10,11,12,13,14,15,16,17,18 has attracted much attention as they could be used to manipulate perpendicularly magnetized layers without any external magnetic field, an essential ingredient for spintronic applications.

The polarization direction of the spin current in conventional non-magnetic metals is always even under a magnetic field, but it has been predicted that currents passed through non-collinear antiferromagnet (AFM), such as the Mn3X (X = Sn, Ir), can give rise to additional spin currents that are odd under magnetic field19,20. Subsequently, a dominant odd magnetic SHE with an out-of-plane spin-polarization along with a small even conventional SHE was inferred in single crystals of Mn3Sn from spin-pumping and ST-FMR experiments21,22. Although the magnetic SHE has been argued to be one of the fundamental mechanisms to generate out-of-plane polarized spin current in non-collinear antiferromagnetic thin films23,24, its direct correlation with the antiferromagnetic order parameter by temperature dependent studies has not yet been established.

Here, we explore the SHE generated in high-quality epitaxial thin films of Mn3Sn (0001) via studies of the spin-orbit torque (SOT) on thin epitaxial layers of ferromagnet, permalloy (Ni80Fe20 = Py), which are grown on top of the Mn3Sn layers. We observe robust in-plane (\({p}_{{{{{{\rm{y}}}}}}}\)) and out-of-plane (\({p}_{{{{{{\rm{z}}}}}}}\)) polarized spin currents for various thicknesses of Mn3Sn when a charge current is passed through the Mn3Sn/Py device (Fig. 1d). The in-plane (out-of-plane) polarized spin currents give rise to in-plane anti-damping-like (field-like) and out-of-plane field-like (anti-damping) torques, respectively. Both \({p}_{{{{{{\rm{y}}}}}}}\) and \({p}_{{{{{{\rm{z}}}}}}}\) retain the same magnitude and sign when large in-plane magnetic fields are applied to reverse the AFM structure of the Mn3Sn layer. By performing temperature-dependent ST-FMR, we demonstrate that \({p}_{{{{{{\rm{y}}}}}}}\) strongly depends on the AFM structure whereas \({p}_{{{{{{\rm{z}}}}}}}\) is unrelated to the antiferromagnetic ordering of Mn3Sn, rather it originates from the scattering at the Py interface. We further substantiate the origin of \({p}_{{{{{{\rm{z}}}}}}}\) by measurements on various non-magnetic metals (Cu, Ru, Re and Pt)/Py bilayers with different strengths of bulk spin–orbit coupling (SOC). Based on these experimental results, we demonstrate that this interface-scattered \({p}_{{{{{{\rm{z}}}}}}}\) originates from the spin swapping mechanism25,26,27,28,29.

Fig. 1: X-ray diffraction, schematic of ST-FMR set-up and origin of spin polarizations.
figure 1

a Structure of Mn3Sn viewed along the [0001] direction. Pink and gray balls represent Mn and Sn atoms, respectively. b X-ray diffraction pattern of Ru/Mn3Sn (0001)/Py structures grown on Al2O3 (0001) substrates. Mn3Sn layer thicknesses are 3 nm (black) and 12 nm (green). c Phi (ϕ) scan across the Al2O3 \(\left\{10\bar{1}4\right\}\), Ru \(\left\{10\bar{1}2\right\}\) and Mn3Sn \(\left\{20\bar{2}1\right\}\) reflections for the Ru/Mn3Sn (0001)/Py structures with 12 nm Mn3Sn film. d Schematic of the ST-FMR experimental set-up and Mn3Sn/Py device. The directions of IRF, Hext and angle (φ) between IRF and Hext are also shown. e The direction and origin of \({p}_{{{{{{\rm{y}}}}}}}\) and \({p}_{{{{{{\rm{z}}}}}}}\) for the Mn3Sn/Py structure are shown schematically. The upper panel shows that \({p}_{{{{{{\rm{y}}}}}}}\) originates from the SHE, which is related to the AFM structure of Mn3Sn. \({p}_{{{{{{\rm{z}}}}}}}\) arises when the spin-polarized current from Py is scattered at the interface due to the spin swapping effect (lower panel). Note that \({{{{{{\bf{p}}}}}}}_{{{{{{\rm{i}}}}}}}={p}_{{{{{{\rm{i}}}}}}}\hat{{{{{{\boldsymbol{i}}}}}}}\) (i = y or z). The interfacial spin-orbit field (ISOF) is also shown schematically.

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Results and discussion

Mn3Sn crystallizes in a hexagonal DO19 crystal structure with a kagome inverse triangular antiferromagnetic spin configuration within the (0001) plane (Fig. 1a) that is a result of the interplay between the geometric frustration of the spins coupled by Heisenberg exchange interaction and the Dzyaloshinskii-Moriya interaction. A small single-ion anisotropy results in a small in-plane moment30, which allows for an external magnetic field to set the AFM structure in a specific domain structure. Epitaxial thin films of Mn3Sn with thicknesses (dAFM) ranging from 3 nm to 12 nm were grown on Ru buffered Al2O3 (0001) substrates using an ultra-high vacuum d.c. magnetron sputtering. A 5 nm thick Ni80Fe20 (Py) layer was sputtered on top of the Mn3Sn layer and capped with a 3 nm thick TaN layer (see Methods). Figure 1b shows typical X-ray diffraction (XRD) patterns of two representative samples with 3 nm and 12 nm thick Mn3Sn layers. The (0002) and (0004) reflections from Ru and Mn3Sn establish their epitaxial growth along (0001), which is further confirmed by transverse phi \((\phi )\) scans of the Al2O3 \(\left\{10\bar{1}4\right\}\), Ru \(\left\{10\bar{1}2\right\}\), and Mn3Sn \(\left\{20\bar{2}1\right\}\) reflections (Fig. 1c). A detailed structural analysis confirms that the crystal symmetry of Mn3Sn belongs to P63/mmc (see section I, Supplementary Information (SI)). Atomic force micrographs display a smooth surface of all films with a typical roughness of ~0.5 nm (Fig. S4a in SI). Transmission electron microscopy imaging confirms the high quality of the film structure (Fig. S4b in SI).

The properties of Ru/Mn3Sn/TaN films grown without any Py layer were investigated by magnetization and transport measurements. A small magnetization within the kagome plane (0001) is observed when an in-plane magnetic field is used to orient the AFM into a single domain. The magnitude of this magnetization is consistent with the expected chiral AFM structure of the Mn3Sn thin film31 and, moreover, decreases as the temperature is increased close to the Néel temperature (Fig. S5a in SI). Again consistent with prior work32 no anomalous Hall effect is observed when the current is applied within the kagome plane (Fig. S6b in SI).

The ST-FMR technique as shown in Fig. 1d was used to measure SOTs in GSG-type devices formed from the Ru(5 nm)/Mn3Sn (dAFM)/Py(5 nm) structures (hereinafter referred to as Mn3Sn/Py), which were fabricated to allow for the RF current (\({I}_{{{{{{\rm{RF}}}}}}}\)) to be oriented along two distinct in-plane crystallographic directions. The devices were prepared by standard optical lithography and a lift-off technique was used to prepare the Ti/Au electrical contacts (see Methods). \({I}_{{{{{{\rm{RF}}}}}}}\) gives rise to a d.c. mixing voltage, \({V}_{{{{{{\rm{mix}}}}}}}\), that is measured when a magnetic field is swept through the resonance condition for the Py. \({V}_{{{{{{\rm{mix}}}}}}}\) is given by the equation5,8,

$${V}_{{{{{{\rm{mix}}}}}}}={V}_{0}\left[{V}_{{{{{{\rm{S}}}}}}}\frac{\Delta {H}^{2}}{\Delta {H}^{2}+{\left({H}_{{{{{{\rm{ext}}}}}}}-{H}_{{{{{{\rm{res}}}}}}}\right)}^{2}}+{V}_{{{{{{\rm{A}}}}}}}\frac{\Delta H\left({H}_{{{{{{\rm{ext}}}}}}}-{H}_{{{{{{\rm{res}}}}}}}\right)}{\Delta {H}^{2}+{\left({H}_{{{{{{\rm{ext}}}}}}}-{H}_{{{{{{\rm{res}}}}}}}\right)}^{2}}\right]$$
(1)

where \({V}_{0}\) is a constant pre-factor, \({V}_{{{{{{\rm{S}}}}}}}\) and \({V}_{{{{{{\rm{A}}}}}}}\) are the amplitudes of a symmetric and antisymmetric Lorentzian, respectively, \({H}_{{{{{{\rm{res}}}}}}}\) is the resonance field, \(\Delta H\) is the linewidth and \({H}_{{{{{{\rm{ext}}}}}}}\) is the external magnetic field. First, we consider what we name the “\(0^\circ \hbox{''}\) device in which \({I}_{{{{{{\rm{RF}}}}}}}\) is along the in-plane crystallographic direction \([01\bar{1}0]\) of Mn3Sn. \({V}_{{{{{{\rm{mix}}}}}}}\) is measured as a function of \(\varphi\), the angle between \({I}_{{{{{{\rm{RF}}}}}}}\) and \({H}_{{{{{{\rm{ext}}}}}}}\). \({V}_{{{{{{\rm{S}}}}}}}\) and \({V}_{{{{{{\rm{A}}}}}}}\) are extracted by fitting \({V}_{{{{{{\rm{mix}}}}}}}\)(\(\varphi\)) with Eq. (1). The magnitude of \({V}_{{{{{{\rm{S}}}}}}}\) and \({V}_{{{{{{\rm{A}}}}}}}\) are different at \(\varphi=40^\circ\) and \(150^\circ\) compared to \(\varphi=220^\circ\) and 33\(0^\circ\) (see Fig. 2a–d for dAFM = 12 nm). Thus \({V}_{{{{{{\rm{S}}}}}}}\)(\(\varphi\)) and VA(φ) display an asymmetric angular variation (Fig. 3a, b for dAFM = 12 nm). Similar results are found for all dAFM (Fig. S8 in SI). By fitting \({V}_{{{{{{\rm{S}}}}}}}\left(\varphi \right)\) and \({V}_{{{{{{\rm{A}}}}}}}\left(\varphi \right)\) to the following equations13, the in-plane and out-of-plane SOTs can be extracted:

$${V}_{{{{{{\rm{S}}}}}}}\left(\varphi \right)=-A({\tau }_{{{{{{\rm{x}}}}}},{{{{{\rm{AD}}}}}}}{\sin }\,\varphi \,{\sin }\,2\varphi+{\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}{{\cos }}\varphi \,{{\sin }}2\varphi+{\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}{{\sin }}\,2\varphi )$$
(2)
$${V}_{{{{{{\rm{A}}}}}}}\left(\varphi \right)=-A\sqrt{1{+M}_{{{{{{\rm{eff}}}}}}}/{H}_{{{{{{\rm{res}}}}}}}}({\tau }_{{{{{{\rm{x}}}}}},{{{{{\rm{FL}}}}}}}{{\sin }}\,\varphi \,{{\sin }}\,2\varphi+{\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}{{\cos }}\varphi \,{{\sin }}\,2\varphi+{\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}{{\sin }}\,2\varphi )$$
(3)

where \(A=-\frac{{I}_{{{{{{\rm{RF}}}}}}}}{2}\frac{1}{\alpha \left(2{\mu }_{0}{H}_{{{{{{\rm{res}}}}}}}+{\mu }_{0}{M}_{{{{{{\rm{eff}}}}}}}\right)}\) is a constant. \({\tau }_{{{{{{\rm{i}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{i}}}}}},{{{{{\rm{FL}}}}}}}\) correspond to anti-damping-like and field-like torques resulting from the components of polarization, \({p}_{{{{{{\rm{i}}}}}}}\) (\({{{{{\rm{i}}}}}}={{{{{\rm{x}}}}}},{{{{{\rm{y}}}}}},{{{{{\rm{z}}}}}}\)), of the spin current along z. We find that \({\tau }_{{{{{{\rm{x}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{x}}}}}},{{{{{\rm{FL}}}}}}}\) due to \({p}_{{{{{{\rm{x}}}}}}}\) are negligibly small whereas the magnitude of \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}\) is large compared to \({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}\) and \({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\)/\({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}\). Note that \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\), \({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\) are normalized to \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}\), which is dominated by Oersted field, for ease of comparison with other systems that we discuss later. Hereinafter, the absolute value of \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}\), \({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}\) and \({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\)/\({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}\) are referred to as \({\tau }_{y,{AD}}^{{\prime} }\), \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\), respectively. Note that the effective magnetization which is used to calculate the torques, is independent of dAFM (Fig. S7b in SI). We also note that the addition of a spin-pumping contribution33 to \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\) does not reproduce the unusual variation of \({V}_{{{{{{\rm{S}}}}}}}\)(\(\varphi\)) (Fig. S8 in SI). The directions of \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\), \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}\), \({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\) are shown schematically in Fig. 2e for several \(\varphi\). The interplay between \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\) (\({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}\) and \({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\)) at different \(\varphi\) results in the unusual variation of \({V}_{{{{{{\rm{S}}}}}}}\)(\(\varphi\)) (\({V}_{{{{{{\rm{A}}}}}}}\)(\(\varphi\))). In the second set of “9\(0^\circ\)” devices \({I}_{{{{{{\rm{RF}}}}}}}\) is along the in-plane crystallographic direction \([2\bar{1}\bar{1}0]\) of Mn3Sn (Fig. 3c, d). Note that the angle between the \([2\bar{1}\bar{1}0]\) and \([01\bar{1}0]\) directions is \(90^\circ\). \({\tau }_{y,{AD}}^{{\prime} }\) remains unchanged whereas \({\tau }_{z,{AD}}^{{\prime} }\), \({\tau }_{z,{FL}}^{{\prime} }\) are reduced to a small but non-zero value (Fig. S10, in SI). Previously, it has been shown in other materials that \({p}_{{{{{{\rm{z}}}}}}}\) displays a cosine angular dependence as a function of \(\varphi\) when \({p}_{{{{{{\rm{z}}}}}}}\) originates due to either low crystal symmetry or low magnetic symmetry10,14,15. Theoretically, the same cosine angular dependence of \({p}_{{{{{{\rm{z}}}}}}}\) is also calculated for Mn3Sn assuming a chiral AFM structure (see section VI in SI). Thus, the finite \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) that we measure for the \(90^\circ\) device necessitates a distinct origin for \({p}_{{{{{{\rm{z}}}}}}}\).

Fig. 2: ST-FMR d.c. voltage for different in-plane angles and torques directions.
figure 2

a–d ST-FMR d.c. voltages, \({V}_{{{{{{\rm{mix}}}}}}}\), along with the fits based on Eq. 1 are shown for the pristine Mn3Sn(12 nm)/Py(5 nm) structures at φ = 40°, 150°, 220° and 330°, respectively. The individual \({V}_{{{{{{\rm{S}}}}}}}\) and \({V}_{{{{{{\rm{A}}}}}}}\) contributions are also plotted in the same figures. e Schematic illustration of \({p}_{{{{{{\rm{y}}}}}}}\) and \({p}_{{{{{{\rm{z}}}}}}}\) and respective torques due to these polarizations at the same φ. The vector forms of \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\), \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}\) and \({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\), \({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\) are (m×(m×py)), (m×py), (m×(m×pz)) and (m×pz), respectively, where m is the magnetization of Py and \({{{{{{\bf{p}}}}}}}_{{{{{{\rm{i}}}}}}}={p}_{{{{{{\rm{i}}}}}}}\hat{{{{{{\boldsymbol{i}}}}}}}\) (i = y or z). Note that the in-plane moment of Mn3Sn remains in the same direction for various \(\varphi\) during ST-FMR measurements.

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Fig. 3: Angular variation of VS and VA for two different devices.
figure 3

a, b Angular variation of \({V}_{{{{{{\rm{S}}}}}}}\) and \({V}_{{{{{{\rm{A}}}}}}}\) along with the fits based on Eqs. (2, 3) are shown in the range of \(0^\circ\) to \(360^\circ\) for the Mn3Sn(12 nm)/Py(5 nm) film. Here \({I}_{{{{{{\rm{RF}}}}}}}\) is along the in-plane crystallographic direction \([01\bar{1}0]\) of Mn3Sn. c, d Angular variation of \({V}_{{{{{{\rm{S}}}}}}}\) and \({V}_{{{{{{\rm{A}}}}}}}\) along with the fits are shown for the 9\(0^\circ\) device where \({I}_{{{{{{\rm{RF}}}}}}}\) is along the in-plane crystallographic direction \([2\bar{1}\bar{1}0]\) of Mn3Sn. The optical images of both the devices are also shown.

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We find that neither \({\tau }_{y,{AD}}^{{\prime} }\) nor \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) have a significant dependence on dAFM, which suggests that they arise from the interface between Mn3Sn and Py (Fig. 4a–c) or, equivalently, that the spin diffusion length in Mn3Sn is small34. The 6-fold symmetry of the AFM structure of Mn3Sn means that there are six equivalent magnetic ground states35. The AFM structure of Mn3Sn can be set in a single domain state (or its twin) by applying a sufficiently large in-plane positive (or negative) magnetic field36. Here using \({H}_{{{{{{\rm{set}}}}}}}={\pm } \! 7\,{{{{{\rm{T}}}}}}\) at 300 K we find, however, that \({V}_{{{{{{\rm{S}}}}}}}\)(\(\varphi\)) and VA(φ) remain the same (Fig. S9 in SI). Consequently, the strength of \({\tau }_{y,{AD}}^{{\prime} }\), \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) are unchanged for the twin AFM domains, which shows that both \({p}_{{{{{{\rm{y}}}}}}}\) and \({p}_{{{{{{\rm{z}}}}}}}\) are even under magnetic field. Since thickness and external magnetic field dependence of SOTs do not provide an insight into the mechanism of \({p}_{{{{{{\rm{y}}}}}}}\) and \({p}_{{{{{{\rm{z}}}}}}}\), we explore the temperature dependence of the SOTs close to the Néel temperature of Mn3Sn (TN = 420 K). Interestingly, we find that \({\tau }_{y,{AD}}^{{\prime} }\) is significantly reduced with increase in temperature (Fig. 4d). This is a clear evidence that \({\tau }_{y,{AD}}^{{\prime} }\) is directly related to the AFM structure of Mn3Sn. With increase in temperature, AFM domains start to fluctuate which causes a reduction in \({\tau }_{y,{AD}}^{{\prime} }\). Although \({p}_{{{{{{\rm{y}}}}}}}\) arises from the AFM structure, it shows a thickness independent behavior due to the small spin diffusion length of Mn3Sn34. On the other hand, \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) remain unchanged in the temperature range of 300-400 K (Fig. 4d), which implies that \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) are unrelated to the AFM structure of Mn3Sn. The temperature and thickness independent behavior of \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) indicates the interfacial origin of \({p}_{{{{{{\rm{z}}}}}}}\), which is distinct compared to recent reports on the non-collinear AFM Mn3GaN13.

Fig. 4: Normalized torques, their temperature dependence and determination of SHE and spin swapping contribution.
figure 4

a–c \({\tau }_{y,{AD}}^{{\prime} }\) (\({|\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}|\)), \({\tau }_{z,{AD}}^{{\prime} }\) (\({|\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}|\)) and \({\tau }_{z,{FL}}^{{\prime} }\) (\(|{\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\)/\({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}|\)) for Cu(5 nm)/Py(5 nm), Ru(5 nm)/Py(5 nm), Mn3Sn (dAFM = 3-12 nm)/Py(5 nm), Re(5 nm)/Py(5 nm) and Pt(5 nm)/Py(5 nm) films, which are grown on Al2O3 substrate. d Temperature dependence of \({\tau }_{y,{AD}}^{{\prime} }\), \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) for the Mn3Sn(12 nm)/Py(5 nm) film. e, f The absolute value of \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\) for Mn3Sn/Py and non-magnetic (Cu, Ru, Re and Pt)/Py bilayers. SHE and spin-swapping contribute to all the bilayers and SHE dominates in Pt and Re whereas spin-swapping influences in Cu and Ru. As a function of disorder, spin swapping is large for Cu/Py and Pt/Py bilayers grown on Al2O3 substrates whereas SHE is relatively significant when the same structures are grown on Si/SiO2 substrates. Note that the value of \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\) for Al2O3/Cu/Py structure is multiplied by 10 for better visibility compared to other data points. All the data presented in this figure are measured on 0° device.

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To investigate how the Mn3Sn/Py interface influences \({p}_{{{{{{\rm{z}}}}}}}\), we modified the interface by inserting a 2 nm thick Cu layer. The magnitude of VS(φ) and the strength of \({\tau }_{y,{AD}}^{{\prime} }\), \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) remain similar to the structure without the Cu insertion layer (Fig. S14a, b in SI). This is because \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\) is negligibly small in Cu. On the other hand, \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\) is large in Pt and indeed when a Pt layer (2 nm thick) is inserted the magnitude of VS(φ) is significantly modified (Fig. S14c, d in SI). We also find that \({\tau }_{y,{AD}}^{{\prime} }\) is enhanced due to the additional \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\) from Pt, but \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) remain almost unchanged. The fact that \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) are nearly equal for both 2 nm Cu and Pt insertion layers shows that the Py layer plays a key role in generating \({p}_{{{{{{\rm{z}}}}}}}\).

There are two distinct theories that account for the origin of \({p}_{{{{{{\rm{z}}}}}}}\) related to a proximal in-plane magnetized layer. Amin et al.37,38 predict that an in-plane magnetized ferromagnetic (FM) layer proximal to a non-magnetic layer (NM) can generate a \({p}_{{{{{{\rm{z}}}}}}}\) as observed experimentally in FM1/NM/FM2 tri-layers39. The bottom FM1 layer generates an in-plane spin-polarized current which is transmitted through the NM layer and gives rise to \({p}_{{{{{{\rm{z}}}}}}}\) that applies torques on the top FM2 layer. However, in our case, we only have a single FM layer. Thus, the second model in which the generation of \({p}_{z}\) can be understood from a spin swapping mechanism25,26,27,28,29 in a SOT layer/FM bilayer structure is more relevant. The spin-polarized currents (along ‘x’) from the proximal FM are reflected from the interface (between SOT layer and FM) and, simultaneously, precess in the presence of an interfacial spin-orbit field (lower panel in Fig. 1e). After the precession, the primary spin-polarized current generates a secondary spin current with out-of-plane spin-polarization, \({p}_{z}\) which successively induces substantial torques.

The spin-swapping effect is differentiated by the presence of a \({\tau }_{z,{AD}}\)-like torque and \({\tau }_{z,{FL}}\)-like torque as opposed to the \({\tau }_{y,{AD}}\)-like torque due to the SHE. The ratios \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\) thus indicate the dominant mechanism whether arising from spin swapping or the SHE. To corroborate this, we have replaced Mn3Sn with various non-magnetic metals with a wide range of SOC strengths, which includes Cu, Ru, Re, and Pt with the expectation that as the SOC increases the nature of the torque will show a crossover from a pure spin swapping regime to an SHE dominating regime. In our experiments, indeed we find that \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}/{\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\) are minimal for small SOC metals such as Cu and Ru (Fig. 4e, f). On the other hand, heavy metals such as Re and Pt display a significant \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}/{\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\) due to the dominance of an SHE. Interestingly, we find that Mn3Sn lies in the transition region between these two mechanisms (Fig. 4e, f). Even though \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\) increase monotonically with SOC, the magnitude of \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) is almost independent for different transition metals (Fig. 4b, c), indicating that the spin-swapping effect is nearly constant for the elements considered. This independent behavior of \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) further shows that the generation of \({p}_{z}\) is controlled by the proximal Py layer. On the other hand, the SHE causes an enhancement of \({\tau }_{y,{AD}}^{{\prime} }\) as a function of their SOC (Fig. 4a). Furthermore, theoretical predictions also show that the creation of \({p}_{z}\) via a spin-swapping process is more effective when disorder at the interface is reduced. Indeed, we find that \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\) are significantly larger when Cu/Py and Pt/Py are grown on Si/SiO2 with a lower degree of crystallinity whereas \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{AD}}}}}}}\) and \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{AD}}}}}}}\)/\({\tau }_{{{{{{\rm{z}}}}}},{{{{{\rm{FL}}}}}}}\) are smaller when highly crystalline Cu/Py and Pt/Py are grown on an (0001) oriented Al2O3 single crystalline substrate (Fig. 4e, f). Additionally, we have replaced the Py layer in Al2O3/Cu/Py structures with Fe and Ni to tune the magnetization of the FM in order to investigate the dependence of the SOTs on the strength of the magnetization. Interestingly, we do see a relatively weak magnetization dependence of \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) whereas \({\tau }_{y,{AD}}^{{\prime} }\) strongly depends on the magnetization (see Fig. S18 in SI). Recently, the experimental and theoretical development of the orbital Hall effect (OHE) shows the existence of only \({p}_{{{{{{\rm{y}}}}}}}\) polarization, which strongly depends on the magnetization of the FM40,41,42,43. Assuming the same analogy if the OHE generates \({p}_{z}\), it should strongly depend on the magnetization of the ferromagnets. The weak magnetization dependence of \({\tau }_{z,{AD}}^{{\prime} }\) and \({\tau }_{z,{FL}}^{{\prime} }\) rules out \({p}_{{{{{{\rm{z}}}}}}}\) being derived from an OHE and rather further supports the spin-swapping mechanism. Note that it has been predicted theoretically that \({p}_{{{{{{\rm{z}}}}}}}\) generated by spin swapping shows a weak magnetization dependence28, which we observe in our study.

Conclusion

In summary, we have shown the presence of robust and thickness independent \({p}_{{{{{{\rm{y}}}}}}}\) and \({p}_{{{{{{\rm{z}}}}}}}\) in Mn3Sn/Py bilayers. From their temperature dependence, we have demonstrated that \({p}_{{{{{{\rm{y}}}}}}}\) originates from the AFM structure of Mn3Sn whereas \({p}_{{{{{{\rm{z}}}}}}}\) is unrelated to the AFM structure and is generated at the Py interface. Moreover, the observation of \({p}_{{{{{{\rm{z}}}}}}}\) when Mn3Sn is replaced by several different non-magnetic metals, i.e., Cu, Ru, Re, and Pt is consistent with an interfacial origin by a spin swapping mechanism. This work provides insights into the origin of unconventional spin polarizations not only in chiral non-collinear antiferromagnets but also in various non-magnetic metals. Our observation of interface-scattered \({p}_{{{{{{\rm{z}}}}}}}\) will further enrich the field of spin-orbitronics.

Methods

Sample preparation

All the thin-films were grown by d.c. magnetron sputtering in an ultra-high vacuum system with a base pressure of 1 × 10−9 Torr. Atomically flat Al2O3 (0001) substrates were prepared by a wet etching procedure followed by a heat treatment at 1200 °C for 4 h. A 5 nm thick Ru buffer layer was first sputtered onto an Al2O3 (0001) substrate at ambient temperature using a sputtering power of 15 W and an Ar pressure of 3 mTorr. The Mn3Sn layer was formed by co-sputtering of Mn and Sn from elemental sputter targets onto the Ru (0002) buffer layer at 200 °C and at an Ar pressure of 3 mTorr. An optimized composition of Mn3.1Sn was used where the excess Mn helps to stabilize the hexagonal D019 phase. The sputtering powers were of 43 W and 8 W, respectively, for Mn and Sn. The Mn3Sn layer thickness was varied from 3 to 12 nm. Cu, Ru, Pt and Re films, with layer thicknesses of ~5 nm were grown at room temperature directly onto Al2O3 (0001) substrates using sputtering powers of 30 W, 15 W, 30 W and 30 W, respectively, and at an Ar pressure of 3 mTorr. A 5 nm thick Ni80Fe20 (Py) layer was sputtered on top of Mn3Sn and other non-magnetic metals with a sputtering power of 30 W and an Ar pressure of 3 mTorr. Also, Cu(5 nm)/Py(5 nm) and Pt(5 nm)/Py(5 nm) were sputtered on Si (001)/SiO2 (25 nm) at room temperature. All the films were capped with a 3 nm thick TaN layer to prevent oxidation.

Device fabrication

The films were patterned into ST-FMR devices (Fig. 1d) oriented along different crystallographic directions with device lengths (75 µm) and widths (25 µm) using conventional photolithography techniques (365 nm maskless laser writer; MLA150, Heidelberg). Etching was carried out using Ar ion beam milling and in-situ secondary ion mass spectroscopy was used for end point detection. Electrical contacts were formed using magnetron sputtered Ti (2 nm)/Au (100 nm) bilayers.

Sample characterization

Rutherford backscattering (RBS) was used to determine the composition of Mn3Sn film. The crystal structure of the films was characterized using a Bruker D8 Discover diffractometer with Cu Kα source and Gallium-Jet X-ray source. Atomic force microscopy measurements were performed to probe the surface topography. A FEI TITAN 80–300 transmission electron microscope (TEM) with a probe corrector was used at an accelerating voltage of 300 kV for scanning TEM studies. The magnetic properties of films were characterized using a Quantum Design MPMS3 SQUID magnetometer. Temperature-dependent measurements of the longitudinal resistivity and the anomalous Hall resistivity were carried out in a Quantum Design Physical Property Measurement System (PPMS). Spin-orbit torques were measured using a home-made spin-torque ferromagnetic resonance set-up at 300 K and another set-up in a Lake-Shore probe station for temperature dependence measurements in the range of 300 K-400 K.

ST-FMR measurements

In the ST-FMR measurements, an RF current (\({I}_{{{{{{\rm{RF}}}}}}}\)) with power of 21 dBm at different frequencies was applied and the in-plane magnetic field was swept between 1200 Oe to 0. \({V}_{{{{{{\rm{mix}}}}}}}\) at φ = 45° was measured at different frequencies to calculate Meff and Gilbert damping constant. Using Meff and Hres for a particular frequency (f = 8 GHz), the strengths of individual torques are calculated from the fit of VS(φ) and VA(φ) using Eqs. (2, 3). Note that we did not evaluate the constant ‘A’ as all the torques are finally normalized by \({\tau }_{{{{{{\rm{y}}}}}},{{{{{\rm{FL}}}}}}}\) for ease comparison. For the temperature dependence, the temperature was stabilized at a particular temperature then the angular dependence was carried out to evaluate the torques.