Observation of anti-damping spin-orbit torques generated by in-plane and out-of-plane spin polarizations in MnPd3

High spin-orbit torques (SOTs) generated by topological materials and heavy metals interfaced with a ferromagnetic layer show promise for next generation magnetic memory and logic devices. SOTs generated from the in-plane spin polarization along y-axis originated by the spin Hall and Edelstein effects can switch magnetization collinear with the spin polarization in the absence of external magnetic fields. However, an external magnetic field is required to switch the magnetization along x and z-axes via SOT generated by y-spin polarization. Here, we present that the above limitation can be circumvented by unconventional SOT in magnetron-sputtered thin film MnPd3. In addition to the conventional in-plane anti-damping-like torque due to the y-spin polarization, out-of-plane and in-plane anti-damping-like torques originating from z-spin and x-spin polarizations, respectively have been observed at room temperature. The spin torque efficiency corresponding to the y-spin polarization from MnPd3 thin films grown on thermally oxidized silicon substrate and post annealed at 400 Deg C is 0.34 - 0.44. Remarkably, we have demonstrated complete external magnetic field-free switching of perpendicular Co layer via unconventional out-of-plane anti-damping-like torque from z-spin polarization. Based on the density functional theory calculations, we determine that the observed x- and z- spin polarizations with the in-plane charge current are due to the low symmetry of the (114) oriented MnPd3 thin films. Taken together, the new material reported here provides a path to realize a practical spin channel in ultrafast magnetic memory and logic devices.

are spin and charge conductivities, respectively.  needs to be high for efficient control of the magnetization.Furthermore, to avoid current shunting through a conducting ferromagnetic layer high    is also required 25 .Another important requirement for the integration of a spin channel into semiconductor IC technology is the tolerance of SOT materials to thermal annealing at 400 ℃.However, there has not been a practical spin channel which can handle post annealing at that temperature, and also possesses high  , along with  , and  , , enabling deterministic switching of in-plane magnetization along y, in-plane magnetization along x, and out-of-plane magnetization, respectively, without the need of applying an external magnetic field.
To achieve high density magnetic memory and logic devices, perpendicular magnetic anisotropy (PMA) is desired 26 .PMA switching via SOT from heavy metals [5][6][7] and topological insulators 11,12,27,28 has been reported at the room temperature in the presence of an external magnetic field.Partial PMA switching has been observed on PtMn/[Co/Ni] x 13 , IrMn/CoFeB 14 , and PtMn/CoFeB/Gd/CoFeB 16 stack structures, in the absence of external magnetic field, but with the help of exchange bias.Stray fields from an in-plane magnetic layer present above or below the spin channel can facilitate external magnetic field-free PMA switching, but current shunting and magnetic interference between different magnetic layers pose severe design constraints in this approach 29,30 .Combination of SOT and spin transfer torque (STT) can also switch PMA in the absence of external magnetic field, but STT could lead to reduced endurance of magnetic tunnel barrier and slower magnetization switching 31 .Fast switching of the magnetization with lower critical current densities (  ) can be achieved when the charge current flow and magnetization are collinear, however, this geometry still requires an external magnetic field to achieve magnetization switching 7 .Here, we present SOT from sputtered MnPd 3 thin films post annealed at 400 ℃ that can generate a spin current with  ̂ along all three axes due to the charge current flow along x-direction, which represents a major advance over the literature and overcomes significant limitations of the existing SOT materials.The MnPd 3 thin films were magnetron sputtered at room temperature on 300 nm thick thermally oxidized silicon substrates.The thin films with the stack structure Si/SiO 2 /MnPd 3 (t nm)/CoFeB (5 nm)/MgO (2 nm)/Ta (2 nm) with IMA were prepared for the SOT characterization with t = 4, 6, 8, 10, 12, 16, 20, and 24 nm, respectively.Unless otherwise stated, these films will be labeled MP4 -MP24, in which the number denotes the MnPd 3 thickness.All samples were post annealed at 400 ℃ for 30 minutes.Using Rutherford backscattering, the atomic composition of Mn and Pd in MnPd 3 film is 28% and 72% (data not shown), respectively.
Fig. 1a shows the unit cell of MnPd 3 .We performed grazing incidence θ -2θ X-ray diffraction (XRD) measurements on a Si/SiO 2 /MnPd 3 (50 nm) sample, as shown in Fig. 1b.For the grazing incidence XRD measurement Φ and Ω were fixed at 20° and 3.5°, respectively.From the intensity of the peaks and pole figures (Methods and Extended Data Fig. 1), its notable that where  is MnPd 3 film thickness.This drift-diffusion model considers that the spin current generated by the bulk of thin films is completely absorbed by the ferromagnetic layer without any dissipation at the interface and back-flow of the spin current.  ( ≈ ∞) and  obtained by ordinary drift-diffusion model are 0.34 and 6.30 nm, respectively.Now by considering spin-back flow the drift-diffusion model can be modified into [34][35][36] : where  is bulk resistivity,  ↑↓ is spin-mixing conductivity, respectively.The red line in Fig. 2d is a fit to Eqn. ( 2 15,37 , heavy metals 6,38,39 , topological insulators 8,11 , and Weyl semimetals 19 .  2 in the control samples does not show any field or  dependence indicating that the SOTs in the MP samples originates from the MnPd 3 layer (Methods and Extended Data Fig. 5 and Fig. 6).The values for the spin-orbit fields associated with  , and   of the reference Pt10 sample are estimated to be (0.040 ± 0.003) and (0.012 ± 0.001) mT per 10 6 A/cm 2 , respectively (Methods and Extended Data Fig. 7).The estimated value of    and    are (0.07 ± 0.01) and (0.02 ± 0.002), respectively in agreement with the previous reports 6,33,40 .After post annealing at 400 ℃, the reference Pt10 sample does not show a SHH signal, suggesting that its SOT did not withstand such annealing.
As presented in Fig. 2e (Methods and Extended Data Fig. 9).However, after post annealing at 400 ℃ the reference Pt samples do not show a ST-FMR signal, suggesting that SOT did not withstand the annealing process.   of as deposited W sample is determined to be -0.43 ± 0.03 at 6 GHz excitation frequency.The estimated   , is -1.43 × 10 5 ℏ 2 ⁄ Ω -1 m -1 .This value of    of the as deposited W sample is comparable to the previous report 41 .   of the W sample post annealed at 400 ℃ for 30 minutes is estimated to be -0.011 and the corresponding    is -0.13 × 10 5

ℏ 2𝑒
⁄ Ω -1 m -1 (Methods and Extended Data Fig. 9).In order to demonstrate external magnetic field-free PMA switching, we prepared Si/SiO 2 /MnPd 3 (10 and 12 nm)/Co (1 nm)/MgO (2 nm)/Ta (2 nm) samples (will be labelled as MP10/Co1 and MP12/Co1 samples).MP10/Co1 and MP12/Co1 samples were annealed at 400 ºC for 30 minutes in vacuum and subsequently field-cooled under the application of an out-ofplane magnetic field of 0.45 T. Fig. 3a shows anomalous Hall resistance (R AHE ) as a function of out-of-plane magnetic field.The hysteretic R AHE loop confirms PMA is present in the Co layer.
Alternatively, magnetometry was also used to confirm that PMA is present in MP10/Co1 sample (Methods and Extended Data Fig. 3). in both PMA samples.  values observed in our PMA samples without external magnetic field is comparable or better than the previously reported values in Pt/Co 5,6 ( ~23-100 MA/cm 2 ), Pd 0.25 Pt 0.75 /Co 43 (~22 MA/cm 2 ), Pt/antiferromagnet 44 with external magnetic field.The SOT switching of magnetization in our PMA samples results from the interplay of  , ,  , ,  , , and   .In the presence of external magnetic field the R AHE vs I loop shows similar behavior as that of positive    such as in the case of Pt/Co/AlOx 5,6 .In the absence of an external magnetic field, if there is only  , , PMA switching occurs via anti-damping process, which is confirmed by numerically solving Landau-Lifshitz-Gilbert (LLG) equation (Methods and Extended Data Fig. 10b).In the presence of a relatively weaker  , and  , and strong  , the magnetization is partially switched at a lower current (~10 mA), which results in an intermediate state.The intermediate state can occur due to an insufficient external magnetic field, which is unable to completely break mirror symmetry 45 .Previously, intermediate magnetic states were observed below threshold   (Ref. 46).The external magnetic field-free switching of PMA unambiguously demonstrates the presence of  ̂ generated  , in the MP samples.
These experimental results of PMA switching have been qualitatively reproduced by the LLG simulations (Methods and Extended Data Fig. 10c and 10d).The intermediate states observed could be utilized for neuromorphic computing 13 .In addition to field-free PMA switching, we also performed field-free magnetization switching of the in-plane CoFeB layer in MP24 sample, as detected by using unidirectional spin Hall magnetoresistance (USMR) mechanism 47,48 (Methods and Extended Data Fig. 11).  is estimated to be ~11.0MA/cm 2 using the parallel resistor model.
We also performed SHH measurements on the PMA samples, as detailed in Methods and Extended Data Fig. 13.The magnitude of the SHH resistance (  2 ) is not symmetric at up and down magnetizations when the field is swept along y-axis.If there were only   and   present in MP samples, the magnitude and field dependence of   2 would remain the same since the spin-orbit field associated to them is independent of the magnetization polarity as in the case of Ta/CoFeB/MgO 23   To quantitatively evaluate the contribution from this mechanism, we perform first-principles density functional theory calculations of spin Hall conductivity of bulk MnPd 3 assuming a roomtemperature paramagnetic phase.Figure 4a shows the calculated band structure of MnPd 3 .There are several bands crossing the Fermi level (E F ), indicating the metallic ground state.The small gaps between the bands near E F are favorable for the sizable spin Hall conductivity 49 , which is given by 50

MnPd 3
film has a strong (114) texture.The lattice parameters are estimated to be a = 3.89 Å, b = 3.88 Å, and c = 15.42Å indexed by using ref.( 32 ).The cross-section transmission electron microscopy (TEM) bright image of the MP10 sample is presented in Fig.1c.The high angle annular dark field (HAADF) image (data not shown) and the bright image both show that the MnPd 3 layer grown on thermally oxidized silicon is polycrystalline.The CoFeB and MgO layers are also polycrystalline.The electric and magnetotransport measurements were performed on Si/SiO 2 /MnPd 3 (10 nm)/MgO (2 nm)/Ta (2 nm) heterostructure, it will be labelled as MnPd (10 nm) sample (Methods and Extended Data Fig.2).The resistivity shows metallic behavior coinciding with the possible transition from a paramagnetic to an antiferromagnetic state below 50 K, as shown in Fig.1d.The ordinary Hall resistance as a function of the external magnetic field is non-linear at small fields.From the high-field linear region, we estimate a carrier concentration of 4.4 × 10 22 /cm 3 .At room temperature the values of anisotropic magnetoresistance (AMR) and planar Hall resistance (PHR) are estimated to be 0.012% and 20 mΩ in MnPd (10 nm) sample, respectively.The Néel temperature of MnPd (10 nm) sample is approximately 37 K inferred from using temperature-dependent magnetometry (Methods and Extended Data Fig.3).Polarized neutron reflectometry (PNR) measurements show weak ferromagnetism, persisting upto room temperature, in MnPd 3 films possibly originating from uncompensated Mn moments, Mn clusters, or local ferromagnetic Mn-based compound formation.At room temperature the ferromagnetic component of the magnetization in MnPd 3 is determined to be 9 ± 1.9 kA/m using polarized neutron reflection (PNR) whereas at 6 K it is ~ 43 ± 3.4 kA/m (Methods and Extended Data Fig.4).

Fig. 3 .
Fig. 3. Demonstration of external magnetic field-free out-of-plane magnetization switching Fig. 3b shows current-induced SOT magnetization switching under the presence of negative external magnetic fields.The write d.c.current pulse width used for PMA switching is 20 ms, which is followed by a read current of 0.4 mA.The full switching of magnetization occurs in MP10/Co1 and MP12/Co1 samples at ~ 10.1 mA and 9.5 mA, respectively.Then, in the absence of external magnetic field, the d.c.current in pulses is swept from -36 mA to + 36 mA with a step size of 1.06 mA.For MP10/Co1 as shown in Fig. 3c, partial switching of the magnetization occurs at a positive current of about 10.78 mA, and complete switching occurs at ~ 32.4 mA (~37.0MA/cm 2 ).In the subsequent reverse sweep partial switching of magnetization occurs at ~ -10.87 mA and complete switching occurs at ~-31.63 mA.For MP12/Co1 sample as shown in Fig. 3d, partial switching of magnetization occurs at a positive current of ~ 11.35 mA.Continuously sweeping the d.c.pulses switches the remaining magnetization at ~ 30.92 mA (~24.7 MA/cm 2 ).Subsequently reverse sweeping the current pulses, partial switching of magnetization occurs at ~ -9.60 mA and switching of remaining magnetization occurs at ~ -33.32 mA.Since the R AHE values obtained by field sweep and current sweep are close, we can conclude that the full switching of PMA has been observed

Fig. 4 :
Fig. 4: Effect of (114) texture on the spin polarization.a, The calculated band structure of stoichiometric MnPd 3 at room temperature.b, c, and d, The calculated    ,    , and    as a function of energy for MnPd 3 (114) film, where the x axis is oriented along the [4 ̅ 01] direction.

conductivities for MnPd 3 (
114) film as a function of energy when the charge current flows along the [4 ̅ 01] direction (the x-direction).We find a high conventional    energy.It is evident that the    and    values are approximately an order of magnitude smaller than    , which is consistent with our experimental observation.Similarly, other MnPd 3 grains with different orientations can also contribute to the unconventional spin Hall conductivity.In summary, we studied anti-damping spin-orbit torques generated by the  ̂,  ̂, and  ̂ in MnPd 3 /ferromagnet heterostructure.At least two independent characterizations were performed to verify the presence of torques.DFT simulations confirmed the low crystal symmetry present in the (114) oriented MnPd3 thin films as the origin of the observed unconventional SOTs.We demonstrated successful growth of conductive MnPd 3 thin films with high    ,    , and    after post annealing at 400 ℃ for half an hour.Complete external magnetic field-free switching of both IMA and PMA were realized.The observed SOTs were robust against thermal treatment, and compatible with low damping constant of CoFeB even after post annealing.All of these are key factors for the integration of a practical spin current source based on MnPd 3 into next generation of SOT-based spintronics devices.
dependencies with , we can extract   2 due to different types of torques using SHH.In MP10 sample, the extracted spin-orbit fields associated with the  , ,  , ,  , , and   are utilized to extract bulk spin-torque efficiency figure of merit (  ( ≈ ∞)) and spin-diffusion length () , ) with   ( ≈ ∞) and  as independent fitting parameters. ↑↓ values of MP4 and MP24 samples are estimated to be 4.54 × 10 14 m -2 and 3.70 × 10 15 m -2 , respectively.The extracted values of   ( ≈ ∞) and  are 0.44 and 5.88 nm, respectively for  ↑↓ value of 4.54 × 10 14 m -2 . value used for the fitting was 60 µΩcm obtained by measuring four terminal resistance of MnPd 3 (20 nm) sample.The extracted values of   ( ≈ ∞) and  are 0.36 and 6.30 nm, respectively for  ↑↓ value of 3.70 × 10 15 m -2 .The values of the    corresponding to   (0.34 ,    and    do not depend on the MnPd 3 film thickness as    does.   shown in Fig. 2d also does not show any specific MnPd 3 film thickness dependence.The   , value in MP12 sample is as large as ~ 0.14 × 10 5 ℏ 2 ⁄ Ω -1 m -1 . , in MP samples is comparable or better than recent reports on WTe 2 /Py 18 and Mn 3 GaN/Py 17 .  , in MP12 sample is 0.77 × 10 5 ℏ 2 ⁄ Ω -1 m -1 .These values of   and    are largest among the reported values as listed in Table 1.The difference in the thickness dependence of the  ,,  indicate that their origins are also different.We also performed ST-FMR measurement on MP10 sample as a confirmation of the observed SOT with SHH technique.The details of ST-FMR are presented in Methods and

and ρ of different spin channels post annealed at different temperatures and measured at room temperature.
. The spin-orbit field associated with  , ( , ~( ̂ ×  ̂)) switches sign as the magnetization switches sign, which results in the unequal and different field dependence of   2 .This clearly shows the presence of torque generated by  ̂ in MP samples.
, where   ⃗ is the Fermi-Dirac distribution function for band n and wave vector  ⃗ , Ω ,  ( ⃗ ) is the spin Berry curvature,    = 1 2 {  ,   } is the spin-current operator,   and   are velocity and spin operators, respectively, and , ,  = , , .As expected, for MnPd 3 textured in the (001) plane, only the conventional spin Hall conductivity (   ) is non-vanishing (Table 2 in Extended Data).However, for the dominant (114) stacking texture, the unconventional spin Hall conductivities (   and    ) emerge (Table 2 in Extended Data).Figures 4b-d show the calculated spin Hall