Cluster magnetic octupole induced out-of-plane spin polarization in antiperovskite antiferromagnet

Out-of-plane spin polarization σz has attracted increasing interests of researchers recently, due to its potential in high-density and low-power spintronic devices. Noncollinear antiferromagnet (AFM), which has unique 120° triangular spin configuration, has been discovered to possess σz. However, the physical origin of σz in noncollinear AFM is still not clear, and the external magnetic field-free switching of perpendicular magnetic layer using the corresponding σz has not been reported yet. Here, we use the cluster magnetic octupole in antiperovskite AFM Mn3SnN to demonstrate the generation of σz. σz is induced by the precession of carrier spins when currents flow through the cluster magnetic octupole, which also relies on the direction of the cluster magnetic octupole in conjunction with the applied current. With the aid of σz, current induced spin-orbit torque (SOT) switching of adjacent perpendicular ferromagnet is realized without external magnetic field. Our findings present a new perspective to the generation of out-of-plane spin polarizations via noncollinear AFM spin structure, and provide a potential path to realize ultrafast high-density applications.

It would be of interest to compare the absolute magnitude of the extracted torque values with other material systems. Firstly directly with reference 14. Can the comparison be made at the same reduced temeprture T/Tn so a direct comparison can be made. Clearly the measurements here are at room temperature. How robust are the result to temperature? How does the strength of the torque compare to other systems where an out of plane torque component has been created. Although the direct achievement shown in the paper is impressive, putting the work into a wider context would improve the paper readability.
For applications, achieving a magnetic field free switching result is an important milestone. Can the authors comment on the current density required to achieve this, and again how does this compare to other technologies and how can it be improved upon. More perspective in this direction would be useful for the wider community.
Finally only one switching cycle is shown. Although the main result is the current orientation it is interesting to ask how robust is the measurement. More reliable in a bulk measurement than an interfacial effect, as the authors state in the introduction. So do they have any information on how many times can the device be cycled robustly?
Reviewer #2: Remarks to the Author: This manuscript reports a study of antiperovskite antiferromagnet Mn3SnN which is capable of generating an out-of-plane spin polarization. The authors claim that the Sigma_z is induced by the precession of carrier spins as an electrical current flows though the cluster magnetic octupole in Mn3SnN, which depends on the direction of the cluster magnetic octupole with respect to the current. Current-induced SOT switching of an adjacent Co/Pd multiplayer stack with perpendicular 1

Response Letter of NCOMMS-21-23942
We very much appreciate the positive evaluation of our manuscript (NCOMMS-21-23942) by Reviewer #1 (" So this paper is certainly timely with some aspects that are clearly original.") and the positive evaluation of Reviewer #2 ("The results presented are quite interesting to the spintronics community."). Their comments are helpful for our improvements further. We address the issues raised by them point by point below. Amendments of our revised manuscript are summarized below in bold face style.
The main modifications include: 1) We redraw Fig. 1a, which focuses on the (110) plane of the Mn 3 SnN crystal structure. 2) We add the description of the composition and out-of-plane lattice constant of the Mn 3 SnN film in the Antiperovskite noncollinear AFM Mn 3 SnN part. 3) We use the spin torque ratio to show the absolute magnitude of the extracted torque in the Spin-torque ferromagnetic resonance measurement part and add the relevant calculation in the Methods part. 4) We find that the mechanism proposed for is also applicable to the (001)-oriented Mn 3 SnN film. We add the ST-FMR measurement of (001)-oriented Mn 3 SnN/Py sample in the Supplementary information. 5) We add the ST-FMR measurement of (110)-oriented Mn 3 SnN/Py sample at 380 K in the Supplementary information. 6) We add the calculation of the resistivity of the film in the Supplementary information, and calculate the critical current density for SOT switching in the Magnetic field-free SOT switching part. 7) We add the cycling behavior of the magnetic field-free SOT switching in the Supplementary information, which reveals the robustness of our device. 8) We revise the explanation of the magnetic field-free SOT switching in the Magnetic field-free SOT switching part.

Reply:
We are grateful to the reviewer for carefully reviewing our manuscript and positive evaluation "So this paper is certainly timely with some aspects that are clearly original." The paper arXiv:2107.10426v1 (Phys. Rev. Appl. 16, 024003 (2021)) studied the SOT switching of Mn 3 GaN/heavy metal (Pt, Ta) system, which is quite related to our research, so we cite this paper in the revision as Ref. 17.
I have a few remarks: 1. Have the experiments been performed (ST-FMR) when the films are grown on (001) oriented substrates?

Reply:
We have performed the ST-FMR measurement of (001)-oriented Mn 3 SnN(16 nm)/Py(12 nm) sample at room temperature. We find that the out-of-plane spin polarization also exists in the (001)-orientated Mn 3 SnN film, which is also dependent on the direction of the current and the cluster magnetic octupole moment. Therefore, we revise the Spin-torque ferromagnetic resonance measurement part (Page 10 Line 7 from the bottom): We find that the mechanism is also applicable to the (001)-oriented Mn 3 SnN film ( Supplementary Fig. S3) by performing identical ST-FMR measurements of (001)-oriented Mn 3 SnN(16 nm)/Py(12 nm) sample at room temperature.
Accordingly, we add the ST-FMR measurement of (001)-oriented Mn 3 SnN/Py sample as Fig. S3 in the Supplementary information. Differently, for the case in Fig. S3g, where the current is applied perpendicular to the cluster magnetic octupole moment, the antidamping and field-like spin torque ratios of , , and , are 0.001±0.001 and 0.016±0.004, respectively, much smaller than that of Figs. S3a and S3d. A quite weak still exists, which may be caused by the slight misalignment of the device or/and the imperfect growth of the film. In a word, the ST-FMR results of (001)-oriented Mn 3 SnN also support our conclusions in the main text. Unfortunately, we can not grow ideal perpendicular magnetic anisotropy layer on the (001)-orientated Mn 3 SnN film for SOT switching, thus we focus on (110) counterpart in the main text. other systems where an out of plane torque component has been created. Although the direct achievement shown in the paper is impressive, putting the work into a wider context would improve the paper readability.
Reply: Thanks for the referee's kind reminding. Since Mn 3 SnN has much higher Néel temperature (475 K) than Mn 3 GaN (345 K), it is quite difficult to compare the values directly at the same reduced temperature T/T n . Considering that most of the ST-FMR experiments are conducted at room temperature, we compare the values of different materials at room temperature. The absolute magnitude of the extracted torque values can be compared by the spin torque ratio, which represents the spin torque relative to the charge current density R1 . The calculation process is added to the Method Part (Page 17). The calculated absolute values for AD, and FL, are 0.003±0.001, and 0.053±0.005, respectively. Although AD, of Mn 3 SnN is smaller than that of Mn 3 GaN R1 , WTe 2 R2 and MnPd 3

R3
, FL, of Mn 3 SnN is larger than that of WTe 2 and MnPd 3 , reflecting that z mainly contributes to the field-like torque in Mn 3 SnN/Py system. The comparatively large field-like torque is most likely due to the spin accumulation at the Mn 3 SnN/Py interface, which interacts with the adjacent Py layer, producing an exchange field R4 . The relatively large FL, affirms the existence of z in our material, which is promising for designing high-density and low-power spintronics devices.
We also perform the ST-FMR measurement at 380 K (the highest of our equipment). We find that z still exists at 380 K but the antidamping and field-like spin torque ratios of z , AD, and FL, , are smaller than their counterparts at room temperature. The existence of σ z but with smaller spin torque ratios supports σ z is related to the magnetic configuration (the cluster magnetic octupole).
Accordingly, we revise the Spin-torque ferromagnetic resonance measurement part and Methods part as follows.
Page 10 Line 7: The generation of the spin torque relative to the charge current density can be parameterized into the spin-torque ratio 14 (See Methods). The antidamping and field-like spin torque ratios of , , and , are 0.003±0.001, and 0.053±0.005, respectively. , of Mn 3 SnN is larger than that of WTe 2 and MnPd 3 (Supplementary Table S1), reflecting that mainly contributes to the field-like torque in Mn 3 SnN/Py system. The comparatively large field-like torque is most 6 likely due to the spin accumulation at the Mn 3 SnN/Py interface, which interacts with the adjacent Py layer, producing an exchange field 8 .
Page 10 Line 4 from the bottom: Moreover, ST-FMR measurements show that z still exists at 380 K, but the antidamping and field-like spin torque ratios of z , , and , , are smaller than their counterparts at room temperature ( Supplementary Fig. S4).
ST-FMR analysis. The relation of the frequency f and the resonance position 0 is fitted by the Kittel formula, which is expressed as = 2 [ 0 ( 0 + eff )] 1/2 , where eff and γ represent the effective magnetization and the gyromagnetic ratio, respectively. Using the line-shape fitting equation: both in-plane (the first term) and out-of-plane (the second term) torque components can be obtained individually. The symmetric ( ) and antisymmetric ( ) amplitude of the Lorentzian line shape are proportional to the amplitude of the in-plane ∥ and out-of-plane ⊥ torque components, respectively, with the following relationship: where, is the width of the resonance peak, I rf is the microwave current, R is the resistance as a function of the in-plane magnetic field angle due to the AMR of Py, and is the Gilbert damping coefficient. According to the spin rectification theory of AMR, ( ) depends on the product of the angular related AMR and ∥ ( ⊥ ). Taking into account the presence of , and can be calculated as: where S, B, A and C are constant terms. When we leave out the AMR rectification ( ) , the angular dependencies of the in-plane and perpendicular torque amplitudes are: In the supporting Information, we add a table and corresponding discussion: Table S1 makes a comparison of the antidamping and field-like spin torque ratios of , , and , , for the present Mn 3 SnN and three typical materials with , e.g., Mn 3 GaN S6 , WTe 2 S7 and MnPd 3

S8 . Although
, of Mn 3 SnN is smaller than that of other three materials, , of Mn 3 SnN is larger than that of WTe 2 and MnPd 3 , reflecting that in Mn 3 SnN/Py system, the out-of-plane spin polarization mainly contributes to the field-like torque. The comparatively large field-like torque is most likely due to the spin accumulation at the Mn 3 SnN/Py interface, which interacts with the adjacent Py layer, producing an exchange field S9 . The relatively large , affirms the existence of in our material, which is promising for high-density and low-power spintronics. ST-FMR measurement of (110)-oriented Mn 3 SnN/Py sample at 380 K is presented as Fig. S4 in the Supplementary information. 3. For applications, achieving a magnetic field free switching result is an important milestone. Can the authors comment on the current density required to achieve this, and again how does this compare to other technologies and how can it be improved upon. More perspective in this direction would be useful for the wider community.

Reply:
The current density required to achieve the field-free SOT switching of our Mn 3 SnN/(Co/Pd) 3 samples is estimated to be approximately 9 × 10 6 A cm -2 . This value is in between, taking ~4.6 × 10 6 A cm -2 for Mn 3 Sn/[Ni/Co] 3 (Ref. R5) and ~2.5-3.7×10 7 A cm -2 for MnPd 3 /Co (Ref. R3) into account. The present current density is also comparable to that of traditional field-free switching by wedged structure or exchange bias R6,R7 . High crystal quality Mn 3 SnN films with a highly ordered magnetic configuration or other noncollinear AFM are highly warranted for stronger z , to decrease the current density for the z -induced field-free switching.
Accordingly, we revise the Magnetic field-free SOT switching part (Page 12 Line 14) as follows.
The current density required to achieve the field-free SOT switching of our Mn 3 SnN/(Co/Pd) 3 sample is estimated to be approximately 9 × 10 6 A cm -2 (Supplementary Fig. S5). The present current density is comparable to that of traditional field-free switching by wedged structure or exchange bias 43,44 . High crystal quality Mn 3 SnN films with a highly ordered magnetic configuration or other noncollinear AFM are highly warranted for stronger , to decrease the current density for the -induced field-free switching.
We add the calculation of the resistivity as Fig. S5 in the Supplementary information. Figure S5 shows the measurement configuration of the resistivity of Mn 3 SnN and Mn 3 SnN/(Co/Pd) 3 samples at room temperature. The resistivity of Mn 3 SnN film deposited on the MgO substrate is 913.1±0.2 μΩ cm and the resistivity of (Co/Pd) 3 multilayer is 74.8±0.1 μΩ cm based on the simple parallel resistance formula. Then the current density to achieve the field-free SOT switching is estimated to be ~9 × 10 6 A cm -2 , taking the film thickness of Mn 3 SnN(12nm)/(Co(0.4nm)/Pd(0.8nm)) 3 sample, the channel width of 5 µm and the average critical switching current of ~28 mA into account. 4. Finally only one switching cycle is shown. Although the main result is the current orientation it is interesting to ask how robust is the measurement. More reliable in a bulk measurement than an interfacial effect, as the authors state in the introduction. So do they have any information on how many times can the device be cycled robustly?
Reply: We also perform the cycling experiments. The SOT switching does not decline after cycling 10 times. Therefore, we add a sentence to Page 13 Line 4：The SOT switching does not decline after cycling 10 times ( Supplementary Fig. S6), reflecting the robustness of the device.
Accordingly, we add the cycling behavior of the magnetic field-free SOT switching in the Supplementary information as Fig. S6. Figure S6 illustrates typical field-free SOT switching for 10 times. Remarkably, the SOT switching does not decline after 10 cycles, revealing the robustness of our device.

Fig. S6
Field-free SOT switching of 10 cycles. The red one is the same loop in Fig. 4c.

Response to Reviewer #2:
This manuscript reports a study of antiperovskite antiferromagnet Mn3SnN which is capable of generating an out-of-plane spin polarization. The authors claim that the Sigma_z is induced by the precession of carrier spins as an electrical current Before this manuscript can be published, I suggest the authors to address the following comments and questions.

Reply:
We are grateful to the reviewer for carefully reviewing our manuscript and the positive opinion, "The results presented are quite interesting to the spintronics community." The comments are reasonable and helpful to revise our manuscript. Reply: Through the energy dispersive spectrometer (EDS) and the X-ray photoelectron spectroscopy (XPS) quantitative analysis, the atomic Mn:Sn:N ratio of our film is 3:0.94:1.03 (normalized to Mn = 3). The stoichiometry of our film is close to the nominal composition of Mn 3 SnN, which is also supported by the x-ray diffraction and Φ-scan. So here, for the sake of convenience, we call our Mn 3 SnN film in the main text.
Accordingly, we add a sentence to Page 6 Line 6：Through the energy dispersive spectrometer (EDS) and the X-ray photoelectron spectroscopy (XPS) quantitative analysis, the Mn:Sn:N atomic ratio of our film is 3:0.94:1.03, which is close to the nominal composition of Mn 3 SnN. Figure 2a Accordingly, we add a sentence to Page 5 Line 1 from the bottom：The out-of-plane lattice constant is calculated to be 3.98 Å from the XRD 12 pattern.

From
3. Figure 1a does not have the black spheres for N as indicated in the caption.
Reply: The black sphere for N in the previous Fig. 1a has been shielded by the (111) plane. To make the crystal structure of Mn 3 SnN more clear, we redraw Fig. 1a, where the yellow plane denotes the (110) plane. This inconsistency should be clarified for the (110) films.
Reply: Fig. 1a shows the crystal structure of Mn 3 SnN. To avoid the inconsistency here, we change the Fig. 1a as shown above, which focuses on the (110) plane (the yellow plane) of the crystal structure.
The magnetic moments of Mn atoms in Mn 3 SnN are located at the Kagome plane, that is, the (111) plane. Therefore, in Fig. 1b, in order to be more visual, we use the (111) plane to illustrate the concept of the cluster magnetic octupole. The scenario of the cluster magnetic octupole in the (110) oriented Mn 3 SnN film is shown in Figs. 3d and 3g. 13 5. In Figures 4c and 4d, the maximum current applied is about 35 mA, which is just above the switching current. Is this the limit of current that can be applied before the samples get burned? If not, higher current should be used to show cleaner switching loops.

Reply:
The limit of current that can be applied before the samples getting burned is around 38 mA. We have tried higher current, but unfortunately, we can not obtain better switching loops. The imperfect switching loops may be caused by the heat brought about by the relatively large current pulse. On the one hand, as calculated below, our Mn 3 SnN film has a relatively large resistivity. On the other hand, the magnetic anisotropy of the PMA layer is also influenced by the large current. Therefore, higher quality noncollinear AFM film with small resistivity and large out-of-plane spin polarization is expected to show better switching performance, which is potential for high-density and low-power spintronics. Reply: Thanks for the suggestion. The critical current density required to achieve the field-free SOT switching of our Mn 3 SnN/(Co/Pd) 3 sample is estimated to be approximately 9 × 10 6 A cm -2 .
Accordingly, we revise the Magnetic field-free SOT switching part (Page 12 Line 14) as follows.
The current density required to achieve the field-free SOT switching of our Mn 3 SnN/(Co/Pd) 3 sample is estimated to be approximately 9 × 10 6 A cm -2 (Supplementary Fig. S5). The present current density is comparable to that of traditional field-free switching by wedged structure or exchange bias 43,44 .
We add the calculation of the resistivity as Fig. S5 in the Supplementary information. Figure S5 shows the measurement configuration of the resistivity of Mn 3 SnN and Mn 3 SnN/(Co/Pd) 3 samples at room temperature. The resistivity of Mn 3 SnN film deposited on the MgO substrate is 913.1±0.2 14 μΩ cm and the resistivity of (Co/Pd) 3 multilayer is 74.8±0.1 μΩ cm based on the simple parallel resistance formula. Then the current density to achieve the field-free SOT switching is estimated to be ~9 × 10 6 A cm -2 , taking the film thickness of Mn 3 SnN(12nm)/(Co(0.4nm)/Pd(0.8nm)) 3 sample, the channel width of 5 µm and the average critical switching current of ~28 mA into account.  Figure 4h. Considering how the Hall leads detect the AHE signal, the current-induced switching yields a smaller AHE voltage than the field-induced case.
Reply: Thanks for pointing out our handwaving explanation and providing us a more convincing explanation. By examining the switching data together with the MOKE figures, we agree with the reviewer's opinion, and we revise the magnetic field-free SOT switching part (Page 13 Line 8) as follows.
Combined with the MOKE figure, we owe this phenomenon to the following reason. For the magnetic field-induced switching, the whole area of the Co/Pd multilayer in the cross pattern switches, including the Hall leads. But for the current-induced switching, only the current path switches while the Hall leads do not switch, as shown in Fig. 4h. Considering how the Hall leads detect the AHE signal, the current-induced switching yields a smaller AHE voltage than the magnetic field-induced case.
8. Figure S2 shows a magnetization of 16 emu/cc^3, which is small for FMs, but for AFMs, is substantial. Can the authors comment on this magnitude and how it may impact the switching measurement?
Reply: For collinear AFMs, the magnetization of 16 emu/cm 3 is kind of large, but for noncollinear AFM films, it is reasonable. It's common for noncollinear AFM films to possess weak uncompensated magnetization, which may be caused by the imperfect growth or the spin canting of the films. However, massive researches have shown that the uncompensated magnetization is not the reason for the large anomalous Hall effect, anomalous Nernst effect or the magneto-optical Kerr effect in noncollinear AFM. In fact, the Berry curvature in momentum space of the special AFM spin texture, that is, the cluster magnetic octupole, gives rise to the above physical phenomena. Here, our experiments show that both the out-of-plane spin polarization and the field-free SOT switching is dependent on the direction of the current and the cluster magnetic octupole moment. For the case when the cluster magnetic octupole moment is perpendicular to the current, there is no out-of-plane spin polarization, consequently, no switching signal. Hence, the weak magnetization of the film does not have obvious impact on switching.
Accordingly, we revise the magnetic field-free SOT switching part (Page 14 Line 7) as follows.
The direction related field-free SOT switching here also illustrates that the weak magnetization of the film does not have obvious influence on the switching measurement (Supplementary Table S2).
In the supporting Information, we add Table S2 and corresponding discussion: Table S2 makes a comparison of the magnetization of different noncollinear AFM films. We can see that the magnitude of our Mn 3 SnN film is reasonable. The weak uncompensated magnetization may be caused by the imperfect growth or the spin canting of the films. Massive researches have shown that the uncompensated magnetization is not the reason for the large anomalous Hall effect, anomalous Nernst effect or the magneto-optical Kerr effect in noncollinear AFM. In fact, the Berry curvature in momentum space of the special AFM spin texture, that is, the cluster magnetic octupole, gives rise to the above physical phenomena. The direction related and field-free SOT switching here also illustrates that the weak magnetization of the film does not have obvious influence on the switching measurement.