Introduction

A spin-orbit torque (SOT) provides an effective approach to manipulate the magnetization in spintronic devices1,2,3,4,5. In a typical SOT device, an in-plane charge current J generates a spin polarization p via spin-orbit coupling and exerts a torque on the magnetization m of a neighboring ferromagnetic layer. The most efficient SOT driven magnetization switching would require p to be parallel to the easy axis of m, so that its associated anti-damping torque ~m × (m × p) can directly change the effective damping and switch the magnetization of a ferromagnet (FM)6. In the conventional spin Hall effect (SHE)3,4 or the Rashba-Edelstein effect (REE)1,2, the induced spin polarization p, either in a heavy metal (HM) or at a nonmagnetic metal (NM)/FM interface, is always aligned with the in-plane direction determined by J×z (where z is normal to the film plane)7,8. The associated in-plane anti-damping torque is thus favorable to switch a magnet with in-plane magnetization, while its use for the switching of a magnet with perpendicular magnetization is inefficient and nondeterministic6. Although this deficiency could be alleviated by applying an external assisting magnetic field and a high current density (Fig. 1a), these additional requirements would eventually hinder the application of the SOT technique in high-density low-power spintronic devices. To eliminate the need of an applied magnetic field for perpendicular SOT switching, an exchange bias induced by an adjacent antiferromagnet (such as IrMn or PtMn)9,10, a stray field from a neighboring ferromagnetic layer11, or structure engineering (such as gradient or crystal-growth direction) have been employed12,13,14,15. The interplay between spin-orbit and spin-transfer torques has been also shown to produce field-free magnetization switching in a magnetic tunnel junction16.

Fig. 1: Switching of perpendicular magnetization by damping-like SOTs.
figure 1

a A schematic of a conventional bilayer SOT device. An in-plane charge current passes along x direction in the bottom spin source layer, generates an out-of-plane spin current with y-polarized spin through SHE. This spin current exerts an in-plane damping-like torque ~m×m×y on the perpendicular magnetization in the top ferromagnetic layer. In this case, a sizable external magnetic field is required for a deterministic switching, and the charge current required is large. b A schematic of a bilayer SOT device supporting the out-of-plane anti-damping torque, where the in-plane charge current generates an out-of-plane spin current with z-polarized spin. This spin current exerts an out-of-plane anti-damping torque ~m×m×z on the perpendicular magnetization in the top layer to realize a field-free switching, which does not require a large charge current. c The structure of the noncollinear antiferromagnetic Mn3Sn. The left panel is the side view of the unit cell. The right panel shows the top view of the triangular magnetic alignments of Mn moments within each Mn-Sn Kagome plane. There are two types of the magnetic alignments observed in Mn3Sn, denoted as AFM1 and AFM2. d The calculated magnetic spin Hall conductivity \({\sigma }_{{zx}}^{z}\) and \({\sigma }_{{zy}}^{z}\) in Mn3Sn. Left panel shows the \({\sigma }_{{zx}}^{z}\) and \({\sigma }_{{zy}}^{z}\) as a function of energy for AFM1 and AFM2. Right panel shows the sign change of \({\sigma }_{{zx}}^{z}\) and \({\sigma }_{{zy}}^{z}\) at EF when the magnetic moments in AFM1 and AFM2 are reversed by in-plane magnetic fields. The finite \({\sigma }_{{zx}}^{z}\) and \({\sigma }_{{zy}}^{z}\) indicate Mn3Sn can be a spin source for the device shown in (b) to support an out-of-plane anti-damping torque.

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The symmetry and efficiency restrictions of the SOT devices with conventional in-plane anti-damping torques can be overcome using a more efficient approach exploiting an out-of-plane anti-damping torque ~m × (m × z) that directly counteracts the magnetization damping in a perpendicular magnet (Fig. 1b)17,18,19,20. Therefore, extensive efforts have been devoted to create a z-polarized spin current that is capable to produce this kind of SOTs21. It has been shown that using a spin source with low crystal symmetry22,23 and/or an additional magnetic order23,24,25,26 can give rise to the z-polarized spin current that is not allowed to appear in the conventional HM spin sources. Alternatively, a proper interface engineering has been reported as a possible mechanism to polarize spins along the z-direction through combined actions of spin-orbit filtering, spin precession, and scattering27,28,29,30,31,32. Recently, an out-of-plane anti-damping torque switching of a perpendicular magnet has been experimentally realized in FM/NM/FM trilayers where a z-polarized spin current was generated by the FM/NM interface32, in a heterostructure where the symmetry was lowered by the interface33, or using a collinear antiferromagnetic (AFM) spin-source layer with a low-symmetry growth direction34. While these advances are significant, from the practical perspective, it would be desirable to realize an out-of-plane anti-damping torque switching of a perpendicular magnet relying entirely on the bulk property of the spin source with a conventional epitaxial growth direction.

Here, we demonstrate that such an out-of-plane anti-damping torque switching can be realized using a noncollinear antiferromagnet Mn3Sn via the magnetic spin Hall effect35,36. We show that this switching is deterministic even in the absence of an applied magnetic field and requires a much lower critical current density than that based on the conventional SHE. Due to being odd with respect to time reversal symmetry, the observed magnetic spin Hall effect and thus the resulting spin-orbit torque can be reversed by an external magnetic field with reversal of the chiral AFM order of Mn3Sn.

Results and discussion

Bulk Mn3Sn is a hexagonal compound with the Ni3Sn-type crystal structure37. As depicted in Fig. 1c, Mn atoms form Kagome-type lattice planes stacked along the c axis, whereas Sn atoms are located at the center of the Mn-hexagons. The frustration from the triangular geometry of the Kagome lattice results in the chiral alignment of the Mn moments within each plane, leading to a noncollinear AFM order of Mn3Sn with the Néel temperature (TN) of ~420 K38,39,40. The noncollinear antiferromagnetism in Mn3Sn results in many interesting properties, such as the large room-temperature anomalous Hall effect37, the Weyl semimetal phase41, and the magnetic spin Hall effect (MSHE)36 relevant to our studies. Different from the conventional SHE being even under time reversal symmetry, the MSHE is odd with respect to this symmetry and hence reversable by flipping the magnetic orders. Resulting from symmetry breaking caused by the noncollinear magnetic structure, the MSHE can be intuitively regarded as a “magnetic” version of the SHE35,42,43. The MSHE gives rise to the unconventional spin currents with distinct symmetries providing useful implications for SOT devices. For example, an out-of-plane spin current with a finite z-spin component can be induced by the in-plane charge current (along the x or y direction) in the Mn3Sn (0001) film (Fig. 1c). This spin current is related to the magnetic spin Hall conductivity (MSHC) \({\sigma }_{{zx}}^{z}\) or \({\sigma }_{{zy}}^{z}\) (in the form of \({\sigma }_{{jk}}^{i}\), where i, j, and k are the spin polarization, spin-current and charge-current directions, respectively). There are two types of the inverse triangular alignment of the magnetic moments in Mn3Sn, denoted as AFM1 and AFM2 in Fig. 1c. The magnetic group symmetry of these alignments supports a small but nonvanishing in-plane net magnetizations along the x (\([01\bar{1}0]\)) direction for AFM1 and along the y (\([2\bar{1}\bar{1}0]\)) direction for AFM238,39. The presence of this magnetization allows, in particular, the control of AFM domains by a small in-plane magnetic field38. This is reflected by our first-principles calculation (Fig. 1d), showing that the \({\sigma }_{{zx}}^{z}\) and \({\sigma }_{{zy}}^{z}\) are finite and reversable for AFM1 and AFM2 of Mn3Sn, respectively (Supplementary Note 1). These sizable MSHCs allow using Mn3Sn as a spin source material to generate the out-of-plane anti-damping SOT and switch the magnetization of an adjacent ferromagnet.

On this basis, we design a MSHE SOT device consisting of a crystalline Mn3Sn (0001) film to generate the MSHE, a [Ni/Co]3 multilayer with perpendicular magnetic anisotropy to control its magnetization, and a thin Cu spacer layer to magnetically decouple Mn3Sn and [Ni/Co]3. Figure 2a schematically shows the designed stack of Mn3Sn(7)/Cu(1)/[Ni(0.4)/Co(0.2)]3/Cu(1)/SiO2(2) (number in the parentheses indicate thickness in nanometers) which is epitaxially prepared by dc magnetron sputtering on cubic MgO (111) substrate. Hall bar devices are subsequently fabricated by standard lithography and etching process for electrical measurements. Resistivities of Mn3Sn and Cu/[Ni/Co]3/Cu are determined to be 367.5 μΩ∙cm and 45.0 μΩ∙cm, respectively. The saturation magnetization of the Ni/Co multilayer is measured to be 496 emu/cm3. Through combined characterization techniques of X-ray diffraction, high-resolution transmission electron microscopy, and magneto-transport measurements (Supplementary Note 1, Note 3), the Mn3Sn film is confirmed to have well-defined (0001) crystallographic orientation with a quality comparable to the previously fabricated bulk Mn3Sn crystal41 and sputtered epitaxial films44,45,46, and the whole stack of Mn3Sn(7)/Cu(1)/[Ni(0.4)/Co(0.2)]3 exhibits sharp interfaces and negligible interlayer diffusion. Strong perpendicular magnetic anisotropy of the [Ni/Co]3 multilayer is confirmed by anomalous Hall effect (AHE) measurements (Supplementary Note 4).

Fig. 2: Z-polarized spin current generated by Mn3Sn thin film.
figure 2

a The schematic of Mn3Sn (7)/Cu (1)/FM (1.8) stack (left) and optical image of the device using for electrical transport measurements (right). The spins with both ±y and ±z polarizations generated by bottom Mn3Sn thin film will act on the ferromagnetic layer and induce spin orbit torques simultaneously. b, c RAHE vs. Hz curve when the bias currents are ±4 mA and ±16 mA. d A summary of the shift (ΔHz) at different bias currents (I). The threshold I to cause a shift in AHE curve is about 10 mA. +I will shift the AHE curve to the +x while -I leads to the opposite shift.

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We first verify the existence of the z-polarized component in the spin current by measuring the hysteresis loop of the anomalous Hall resistance RAHE versus the out-of-plane magnetic field Hz in the presence of a bias dc current I along the x (\(\left[01\bar{1}0\right]\)) direction. If there was a z-polarized spin component, the associated out-of-plane anti-damping torque would cause an abrupt shift of the RAHE-Hz hysteresis loop when the torque is sufficiently strong to overcome the intrinsic damping of the Ni/Co multilayer32. Indeed, we find no shift of the loop when the amplitude of I is at 4 mA (Fig. 2b), while a sizable positive or negative shift occurs when I = +16 mA or −16 mA, respectively (Fig. 2c). Here, we define the shift of the RAHE-Hz hysteresis loop as \(\triangle {H}_{z}={H}_{{center}}\left({I}^{+}\right)-{H}_{{center}}\left({I}^{-}\right)\), where \({H}_{{center}}\left({I}^{\pm }\right)=\frac{\left[{H}_{r}^{+}\left({I}^{\pm }\right)-{H}_{r}^{-}\left({I}^{\pm }\right)\right]}{2}\) is the center of the hysteresis loop determined by the difference of positive and negative magnetization-reversal fields \({H}_{r}^{\pm }\left(I\right)\), and \({I}^{\pm }\) are positive and negative currents. Figure 2d shows that the threshold current to produce the finite ΔHz is around 10 mA, above which the ΔHz increases almost linearly with the increase of I. This phenomenon cannot emerge in the conventional SOT devices where ΔHz can only be generated by a y-polarized spin current in the presence of an external magnetic field along the x direction (Hx)32. Based on the measurements of ΔHz with different Hx, we estimate the effective SOT fields contributed by the y-polarized and z-polarized spin currents separately, and derive the sizable spin current conductivities as \(\left|{\sigma }_{{zx}}^{y}\right|\;\approx\) 6.02 × 104 [(\(\hslash\)/2e) (Ω m)−1] and \(\left|{\sigma }_{{zx}}^{z}\right|\;\approx\) 1.83 × 104 [(\(\hslash\)/2e) (Ω m)−1] which are comparable to these in prior reports (Supplementary Note 5)22,23,29,47. The \(\left|{\sigma }_{{zx}}^{z}/{\sigma }_{{zx}}^{y}\right|\) ratio of ~30.5% is notable and consistent with the recently reported value for a Mn3Sn single crystal48, indicating the efficient generation of the z-polarized spin current in our Mn3Sn thin films by the MSHE.

The emergence of the z-polarized spin current in Mn3Sn allows the realization of the deterministic field-free magnetization switching. Figure 3a shows that the measured AHE resistance as a function of a pulse current I applied along the \(\left[01\bar{1}0\right]\) direction exhibits a hysteretic behavior and a sign change in the absence of applied magnetic field. This behavior reflects the magnetization reversal in the Ni/Co multilayer. We note that in our SOT device, the exchange coupling between the Mn3Sn and Ni/Co multilayer is eliminated by the Cu spacer, and hence it does not contribute to the magnetization switching (Supplementary Note 6). Instead, the field-free switching is entirely caused by the out-of-plane anti-damping torque. Furthermore, we find that about 60% of the magnetic Ni/Co layer volume switches as estimated from the measured RAHE-I loop (Fig. 3a) with respect to the saturation AHE resistance. This partial switching behavior is due to the multi-domain structure of the AFM Mn3Sn film. Due to small magnetic anisotropy and nearly identical energies of AFM1 and AFM2 magnetic orders, the as-grown Mn3Sn films exhibit multiple AFM domains that have a tendency to align randomly in zero field. This gives rise to variation in the magnitude and sign of MSHC \({\sigma }_{{zx}}^{z}\) among different domains, and eventually leads to a reduced effective \({\sigma }_{{zx}}^{z}\). Therefore, the switching ratio is expected to increase if we align the AFM domains. This can be done by applying a finite magnetic field due to a small in-plane magnetization in Mn3Sn38. Figure 3b shows the measured RAHE-I loops for different magnetic fields Hx along the \(\left[01\bar{1}0\right]\) direction, and Fig. 3c displays the corresponding switching ratio as a function of Hx. As seen, by aligning more domains into one configuration, the switching ratio increases as the magnitude of the field increases, with a maximum value of ~80% at a field as small as ~30 Oe. Importantly, the switching polarity is reversed upon reversing the field to opposite direction. All these observations corroborate with the MSHE scenario showing that the MSHC \({\sigma }_{{zx}}^{z}\) is controlled by the reorientation of Mn3Sn domains44,49. It is notable that flipping the switching polarity, accompanied by a vanished switching ratio, does not appear at zero field but at a small negative field of about −8 Oe (Fig. 3c). It is likely that some preferred AFM domain orientation is induced by structural reconstructions at interfaces or near defects during the deposition process, which as if there were a small bias field (~−8 Oe) on Mn3Sn. Similar behavior is found when the current and magnetic field are both along the y (\([2\bar{1}\bar{1}0]\)) direction (Supplementary Note 7). We have estimated the Joule heating effect induced by the application of current and found the actual device temperature is ~ 360 K during switching. This temperature is still well below the TN of Mn3Sn, and therefore the AFM spin texture and the associated spin current largely remain unaffected by the thermal effects (see Supplementary Note 8 for more details). This eliminates Joule heating as the possible origin of the observed effect.

Fig. 3: External magnetic field tuning polarity of current induced magnetization switching.
figure 3

a Current induced magnetization switching with clockwise polarity in the absence of an external magnetic field for the Mn3Sn (7)/Cu (1)/FM (1.8) device. b The switching curve under different external magnetic fields from negative to positive. c The evolution of the switching polarity and switching ratio under different magnetic fields. Here the direction of magnetic field is in-plane and parallel to the current. The two opposite Mn3Sn domains contribute opposite z spins and thus induce clockwise and anticlockwise switching polarity as indicated as solid and hollow dots.

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A remaining question is the role of the z-polarized spin current in the observed field-free switching: Whether the switching indeed occurs due to an out-of-plane antidamping torque, or the z-polarized spin current only generates a symmetry breaking perturbation to assist a conventional SOT switching by the y-polarized spin current from the SHE. To answer this question, we have performed macro-spin simulations as described in Supplementary Note 10 and Note 11. We find that for sizable \(\left|{\sigma }_{{zx}}^{z}/{\sigma }_{{zx}}^{y}\right|\) of 30.5%, as estimated for our Mn3Sn device, the switching dynamics exhibits typical characteristics associated with an out-of-plane antidamping torque. This indicates that the switching of our device occurs through the z-polarized spin current driven by the MSHE. On the contrary, for small \(\left|{\sigma }_{{zx}}^{z}/{\sigma }_{{zx}}^{y}\right|\), we find that the switching is dominated by the y-polarized spin current due to the SHE. Importantly, our simulation results indicate that the critical current required for the MSHE-driven switching is much smaller compared to the SHE-driven switching.

Finally, we compare the SOT switching efficiency of the Mn3Sn based MSHE device with a conventional β-Ta based SHE device. The two devices have the same geometry and thickness of the corresponding layers (Fig. 4a, b). Here, a thicker 2 nm Cu spacer layer is used in both devices as this is the minimum thickness required to achieve good perpendicular anisotropy in a [Ni/Co]3 multilayer for the β-Ta based device. As a widely explored spin source, β-Ta has a large charge-spin conversion efficiency to generate the spin current with a conventional in-plane spin polarization4. This source, however, requires an assistive magnetic field applied parallel to the charge current for deterministic switching due to the lack of z-polarized spin component (Supplementary Note 10 and Note 11). We find that only a small switching ratio of ~17% is realized in this device at the sacrifice of a large current density of 1.3 × 107 A cm−2 and a moderate field of 300 Oe (Fig. 4a). On the contrary, a much larger switching ratio of ~60% is achieved in the Mn3Sn based MSHE device even in the absence of external field and under application of a much lower current density of 4.6 × 106 A cm−2 (Fig. 4b). The comparison of SOT switching between the Mn3Sn and β-Ta based devices unambiguously proves the superior efficiency of the MSHE induced out-of-plane anti-damping torque for the deterministic switching of perpendicular magnetization.

Fig. 4: High MSHE based SOT efficiency with the assistance of z spin polarization.
figure 4

a The conventional SHE based SOT device with a structure of β-Ta (7)/Cu (2)/FM (1.8) and its maximum current induced magnetization switching curve at the external magnetic field of 300 Oe. b. The novel MSHE based SOT device with a structure of Mn3Sn (7)/Cu (2)/FM (1.8) and its current induced magnetization switching curve of Mn3Sn based device with the absent of external magnetic field. Note that the current density is calculated by considering the shunting effect of Cu and FM layer in both devices.

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In conclusion, we have demonstrated the efficient current-induced field-free switching of a ferromagnet with perpendicular magnetization. The magnetization switching is driven by an out-of-plane anti-damping SOT generated by noncollinear antiferromagnet Mn3Sn resulting from the MSHE. Due to the magnetic spin Hall current being collinear to its spin polarization, this observed mechanism of switching requires much lower critical current density compared to the conventional SHE based SOT devices and allows control through the reorientation of magnetic domains in Mn3Sn. Our findings pinpoint the enormous potential of the MSHE as the spin-torque source to engineer novel energy-efficient spintronic devices.

Methods

First-principles density functional theory (DFT) calculations were performed using a plane-wave pseudopotential method with the fully-relativistic ultrasoft pseudopotentials50 implemented in Quantum-ESPRESSO51. The exchange and correlation effects were treated within the generalized gradient approximation (GGA)52. In the calculations, we used the plane-wave cut-off energy of 35 Ry and a 16 × 16 × 16 k-point mesh in the irreducible Brillouin zone. The experimental lattice parameters a = 5.689 Å and c = 4.522 Å measured in this work were used in the calculation. All the atomic co-ordinates were relaxed until the force on each atom was less than 0.001 eV/Å. In the calculations, we firstly set the initial magnetic configurations according to the experimentally observed noncollinear AFM states, and then performed full relaxations of the magnetic structure, and the electronic structure without any constraint.

The tight-binding Hamiltonians were obtained from the maximally localized Wannier functions53 within the Wannier90 code54 to calculate the MSHC35

$${\sigma }_{{ij}}^{k}=-\frac{e{{\hslash }}}{\pi }\int \frac{{d}^{3}\vec{k}}{{\left(2\pi \right)}^{3}} \mathop{\sum}_{n,m}\frac{{\Gamma }^{2}{{{{{\rm{Re}}}}}}\left(\left\langle n\vec{k} \vert\, {J}_{i}^{k} \,|\, m\vec{k}\right\rangle \left\langle m\vec{k} \,|\, {v}_{j} \,|\, n\vec{k}\right\rangle \right)}{\left[{\left({E}_{F}-{E}_{n\vec{k}}\right)}^{2}+{\Gamma }^{2}\right]\left[{\left({E}_{F}-{E}_{m\vec{k}}\right)}^{2}+{\Gamma }^{2}\right]}$$
(1)

where \({J}_{i}^{k}=\tfrac{1}{2}\{{v}_{i},\;{s}_{k}\}\) is the spin-current operator, \({v}_{i}\) and \({s}_{k}\) are velocity and spin operators, respectively, and \(i,j,k=x,y,z\). Γ = 50 meV35 and a 200 × 200 × 200 k-point mesh were used to evaluate the integral of Eq. (1).

The symmetry determined geometries of conductivity tensors were obtained using the linear response symmetry code55.

Sample preparation

All samples were deposited on MgO (111) substrates using DC magnetron sputtering with a base pressure of 5 × 10−8 Torr. Mn3Sn films were deposited with a stoichiometric target at the Ar pressure of 2 × 10−3 Torr, the deposition was performed at 100 °C, followed by annealing at 400 °C for 1 h. After the Mn3Sn film cooled down to the room temperature, Cu and Ni/Co multilayers were then deposited on the Mn3Sn film with a Cu, Ni, and Co target, respectively. Standard photolithography and Ar ion etching were used to fabricate the 8 μm wide and 35μm long Hall bar.

Sample characterization

Structural properties of the samples were characterized using a Bruker D8 Discover X-ray diffraction (XRD) system with Cu Kα radiation. The HR-TEM were performed with an electron microscope operated at 200 kV (FEI Titan Themis 200). For the current induced magnetization switching and anomalous Hall loop shift measurements, current pulses with an 800 μs pulse width were applied. In-between two adjacent writing pulses, the magnetization state of the Ni/Co multilayer was read by current pulses with the same duration as that of the writing pulse but at a much smaller amplitude of 1 mA. The current density is calculated using the standard parallel resistor model which takes into account the shunting effect.