Sign Reversal of Spin‐Transfer Torques

Abstract Spin‐transfer torque (STT) and spin‐orbit torque (SOT) form the core of spintronics, allowing for the control of magnetization through electric currents. While the sign of SOT can be manipulated through material and structural engineering, it is conventionally understood that STT lacks a degree of freedom in its sign. However, this study presents the first demonstration of manipulating the STT sign by engineering heavy metals adjacent to magnetic materials in magnetic heterostructures. Spin torques are quantified through magnetic domain‐wall speed measurements, and subsequently, both STT and SOT are systematically extracted from these measurements. The results unequivocally show that the sign of STT can be either positive or negative, depending on the materials adjacent to the magnetic layers. Specifically, Pd/Co/Pd films exhibit positive STT, while Pt/Co/Pt films manifest negative STT. First‐principle calculations further confirm that the sign reversal of STT originates from the sign reversal of spin polarization of conduction electrons.


Introduction
Spintronics facilitates the manipulation of magnets through electric currents.[13][14] Spin-orbit torque (SOT) [15][16][17] and spin-transfer torque (STT) [2] serve as the primary driving forces behind magnetic DW motion, with the key distinction lying in how the spin current is generated.In the case of SOT, the spin current emerges within heavy metals adjacent to magnets, attributed to the spin-Hall effect [15] or interfacial Rashba effect. [16]Conversely, in the case of STT, the spin current is generated within magnets, arising from the exchange interaction between the spin of conduction electrons and local magnetization. [2]his fundamental difference gives rise to distinct features in SOT-and STT-induced DW motion, particularly in terms of the degree of freedom in its direction.The former has degree of freedom in its direction, while the latter does not.[20][21][22][23] In contrast, conventional STT theory posits that STT always propels the DW along the electron-flow direction due to the angular momentum transfer occurring within the conduction electrons within magnets. [1,2]owever, recent studies by two independent groups challenge conventional STT theories, suggesting the possibility of STTinduced DW motion along the current direction instead of the electron-flow direction.Both groups systematically decomposed SOT and STT from the total spin torques exerted on magnetic DWs in Pt/Co/Pt films. [24,25]The experimental results revealed that negative STT itself drives the DW along the current direction.Note that if the direction of STT-induced DW is along the current direction (electron-flow direction), we refer to it as negative (positive) STT.It is speculated that such negative STT might be attributed either to negative non-adiabaticity or negative spin polarization of conduction electrons. [24]However, neither an engineering scheme for manipulating the STT sign nor verification of the underlying physics of the sign reversal of STT remains known.
In our work, we present the first demonstration of manipulating the STT sign (either positive or negative) by engineering heavy metal layers adjacent to magnetic layers.After measuring total spin torques exerting on magnetic DW motion, we extracted both SOT and STT from the total spin torques, leveraging the anti-symmetric and symmetric nature of SOT and STT with respect to the handedness of chiral DWs.Various magnetic thin films were investigated (for details, please refer to Section SV, Supporting Information), revealing that Pt/Co/Pt films exhibit negative STT, while Pd/Co/Pd films exhibit positive STT.The fundamental origin of the opposite signs of STT is further verified through first-principles calculations, attributing them to the spin polarization of conduction electrons.Significantly, our work sheds new light on STT by introducing a novel degree of freedom in its manipulation-the sign of STT-while also providing insight into its physical origin.

Extraction of the STT and the SOT from Total Spin-Torques
The STT and SOT are each generated by electric currents flowing through the magnetic layer and the adjacent heavy metal layer, respectively.Consequently, individually quantifying them through conventional electric transport measurements proves challenging.In this study, we introduce symmetry analysis to decompose the STT and SOT, capitalizing on their distinct symmetric behaviors in relation to the handedness of chiral DWs (for details, please see Section SVIII, Supporting Information).As indicated in ref. [24] it is well-known that STT and SOT exhibit symmetric and anti-symmetric behaviors with respect to the handedness of chiral DWs, respectively.Therefore, by measuring the total spintorques and identifying the symmetric (anti-symmetric) axis, we can extract the STT and SOT individually.
First of all, symmetric/anti-symmetric axis was determined by measuring the DW speed as a function of in-plane magnetic field H x .Figure 1a,b shows the plots of measured v DW with respect to H x for the Pt/Co/Pt and Pd/Co/Pd films, respectively, where both films have the same t Co = 0.3 nm (for detailed film structures, please see Section 4, Experimental Section).According to ref. [26, 27] the symmetric axis (dashed vertical lines) of the v DW variation corresponds to the condition H x = − H DMI , where H x exactly compensate H DMI so that the chiral DW is of Blochtype.This axis will serve as the symmetric/anti-symmetric axis during the decomposition of STT and SOT from the total spin torques.
The spin-torques acting on the DW were then measured in these films (for details, please refer to Section SIII, Supporting Information).Following the conventional spin-torque quantification scheme [19][20][21][22][23] we introduce the spin-torque efficiency  tot., defined as  tot.≡ ∂H tot./∂j, where H tot. is the effective out-ofplane magnetic field induced by spin torques, and j is the electric current density.By definition,  tot.represents how strongly spin torque is exerted on DWs per unit current density.Figure 1c,d display plots of measured  tot.as a function of H x .The STT efficiency  STT and the SOT efficiency SOT were then decomposed from  tot.(Please note that  tot.=  STT +  SOT ).As aforementioned, these  STT and  SOT are typically symmetric and anti-symmetric, respec-tively, for inversion with respect to the axis (dashed vertical lines) ofH x = −H DMI as given below: Therefore, one can uniquely decompose the STT and SOT contributions from the experimental variation of  tot.(H x ) by the above symmetry argument.

Demonstrating the Sign Reversal of STTs
Figure 1e,f show the results of the decomposition into  STT (colored) and  SOT [28] respectively.The present experimental results deliver two interesting points.First, the signs of STTs are opposite between the Pt/Co/Pt and Pd/Co/Pd films: A positive  STT is observed in the Pt/Co/Pt film, while a negative  STT is observed in the Pd/Co/Pd film.The positive  STT drives DWs along the current direction (so-called negative STT), while the negative  STT drives DWs against the current direction (i.e., along the electron-flow direction).Second, both films exhibit huge  STT values.Such huge  STT of Pt/Co/Pt films have been already reported in ref. [26, 27] However, it is interesting to see that the Pd/Co/Pd film exhibits even larger  STT , almost three times larger than the Pt/Co/Pt films, which is the largest value of ferromagnetic film that has been ever reported to the best of our knowledge.
To see more detailed nature, the STT was further investigated by changing t Co for the series of Pd/Co/Pd and Pt/Co/Pt films.Each panel of Figure 2 presents the plot of  STT (blue for Pd/Co/Pd and red for Pt/Co/Pt) and  SOT (black), respectively, as functions of H x for different t Co .The results clearly reveal that both of series of Pd/Co/Pd (Pt/Co/Pt) films have positive (negative)  STT irrespective of t Co , while the magnitude of  STT shrinks as increasing t Co .Figure 3 summarizes our STT measurement results by presenting a plot of  max STT as a function of t Co for Pt/Co/Pt and Pd/Co/Pd films.This plot unambiguously demonstrates that one can manipulate not only the sign but also the magnitude of STT through material and structural (thickness) engineering of magnetic films.
According to the STT theories [29]  STT follows the relation  STT = (ℏ/2eM S )P, where ℏ is the Planck constant and e (> 0) is the absolute value of the elementary charge.Since the saturation magnetization M S and DW width  are also defined as positive quantities, (ℏ/2eM S ) is always yields a positive value.Thus, the sign of  STT follows the sign of P, where  represents the non-adiabaticity and P is the spin polarization of conduction electrons.Recently, Je et al. [26] confirmed the appearance of negative P through giant magneto-resistance measurements in the Pt/Co/Pt films, attributing the negative  STT in these films to this phenomenon.Both  and P generally possess positive values.However, specific situations may arise where either  or P becomes negative: DWs narrower than several nanometers [30,31] result in a negative  and/or CoPt alloys with dilute Co concentration [32] exhibits a negative P. Since both  and P can change their signs, it remains unclear which one is responsible for the negative sign of STT in these films.

The Microscopic Origin of STT Sign Reversal
To identify the origin responsible for the negative sign of STT, the electronic structure of these films was investigated by first-principles calculations.A structure of 7-monolayer Pt (or Pd)/1-monolayer Co/7-monolayer Pt (or Pd) is taken into account with fcc (111) crystalline lattice (to see XRD spectrum, please find Section SIV, Supporting Information).Then, P is estimated as a function of energy E by use of the relation where N l  is the partial density of state (DOS) for the spin  (↑ or ↓) and orbital l (s, p, or d).Here, f FD (E) is the Fermi-Dirac function that accounts for the occupied sp and empty d states.Accordingly, a positive (or negative) spin polarization appears when the majority (or minority) spin channel contributes larger than the other.In this simplistic picture, the interaction is accounted as the scattering events between the itinerant sp and rather localized d electrons.
The calculation results of the total P in the Pt/Co/Pt and Pd/Co/Pd structures are shown by Figure 4a,b, respectively, with respect to E, where the Fermi level E F is set to zero.It is worthwhile to note that the electrons in the vicinity of E F dominate conduction.Remarkably, two structures exhibit opposite signs of P near E F , as shown by the insets that P < 0 for the Pt/Co/Pt structure and P > 0 for the Pd/Co/Pd structure at E F .The present observation is accordant to the experimental observation of  STT < 0 for the Pt/Co/Pt films and  STT > 0 for the Pd/Co/Pd films, signaling that the opposite signs of P are responsible for the opposite STTs in these films.Furthermore, the magnitude of P in the Pt/Co/Pt structure is smaller than that in the Pd/Co/Pd structure, which is also in accordance to the experimental observation. [33,34]he feature of P is investigated more in detail by analyzing the layer-resolved contributions.Figure 4c,d shows the L2 − L7 layer contributions to P in the Pt/Co/Pt and Pd/Co/Pd structures, respectively.Also, Figure 4e,f shows the L1 layer contributions to P in the Pt/Co/Pt and Pd/Co/Pd structures, respectively.Finally, Figure 4g,h shows the Co layer contributions to P in the Pt/Co/Pt and Pd/Co/Pd structures, respectively.It is clearly seen from the figures that, in both structures, the L2 − L7 layer contributions show large P values fluctuating over the range up to ± 0.4, whereas the other layer contributions exhibit smaller variation of P within the range of ± 0.01.Therefore, the total P over the whole structure is dominated by the L2 − L7 layer contributions.It is interesting to note that, in both structures, the Co layers exhibit P < 0 in contrast to the bulk characteristics.Such negative P might be a consequence of strong electronic hybridization with heavy metal through the interfaces.
Recalling that the electrons in the vicinity of E F dominate conduction, in the Pd/Co/Pd structures, the L2 − L7 layer contribution exhibits a large positive P (≈ 0.2) as seen in Figure 4d.Such large L2 − L7 layer contribution overwhelms the other contributions of small negative P (≈ −0.01) as seen in Figure 4f,h.Therefore, it is natural to see that the total P is determined as positive as seen in Figure 4b.On the other hand, in the Pt/Co/Pt structure, the L2 − L7 layer contribution exhibits P≅0 as seen by the inset of Figure 4c.In addition, the L1 layer contribution also vanishes in the vicinity of E F as seen by the inset of Figure 4e.Thus, the total P is dominated by the small negative P from the Co layer contribution as seen in Figure 4a,g

Conclusion
We demonstrated the sign reversal of STT through the chiral DW motion, contradicting theoretical predictions.Based on systematic symmetry analysis, we individually quantified both STT and SOT acting on chiral DWs.It was then unambiguously observed that the sign of STT can be reversed depending on the materials adjacent to magnets.In Pd/Co/Pd and Pt/Co/Pt magnetic films, positive and negative STT was exhibited, resulting in DW motion along the electron-flow and current directions, respectively.First-principle calculationsverified that the STT sign reversal originates from the spin polarization reversal of conduction

Figure 1 .
Figure 1.Plots of v DW as a function of H x for the a) Pt/Co/Pt and b) Pd/Co/Pd films, respectively.The dashed vertical lines indicate H x = − H DMI .Plots of  tot.as a function of H x for the c) Pt/Co/Pt and d) Pd/Co/Pd films, respectively.Plots of  STT (colored) and  SOT as functions of H x for the e) Pt/Co/Pt and f) Pd/Co/Pd films, respectively.The solid curves guide the symmetric and anti-symmetric nature of STT and SOT, respectively.The horizontal dashed lines guide eyes to  max STT .Schematic diagrams of STT-induced DW motion for g) Pt/Co/Pt and h) Pd/Co/Pd films.The red and the blue arrows represent the STT-induced DW motion along current direction and electron-flow direction, respectively.

Figure 2 .
Figure 2. Plots of  STT (colored symbol) and  SOT (black symbol), respectively, as functions of H x for the Pd/Co/Pd and Pt/Co/Pt films with different t Co .The dashed vertical lines indicate H x = − H DMI .The solid lines show the best fittings of the symmetry and anti-symmetry of STT and SOT, respectively.The horizontal dashed lines guide eyes to  max STT .

Figure 3 .
Figure 3. Plots of  max STT as a function of t Co for the Pt/Co/Pt films (red symbol) and Pd/Co/Pd (blue symbol).

Figure 4 .
Figure 4.The total P as function of E for the a) Pt/Co/Pt and b) Pd/Co/Pd structures, respectively, where E F is set to zero.The layer-resolved spin polarization contributions: (c) and (d) for the sum of the L2 − L7 layers, (e) and (f) for the L1 layers, and (g) and (h) for the Co-layer, respectively, for the Pt/Co/Pt and Pd/Co/Pd structures.The insets show P in the energy window of E F ± 0.02 eV for better visibility.
. The present calculations thus provide an insight on the origin of the opposite P in the Pt/Co/Pt and Pd/Co/Pd films.One can therefore conclude that the L2 − L7 layer contribution plays a decisive role in determination of the total P. To further elucidate the detailed origin, the DOS of the L2 − L7 layers are shown in Figure 5a,b for the Pt/Co/Pt and Pd/Co/Pd structures, respectively.Although the overall features of the DOS do not differ much, yet the Pd/Co/Pd structure has slightly larger DOS than the Pt/Co/Pt structure in the vicinity of E F .We further analyze DOS around E F in the context of the orbital-resolved spin polarization.For this analysis, we define ΔN lm (E) = N ↑ lm (E) − N ↓ lm (E), where N  lm (E) is DOS at energy E for the spin state , orbital l, and magnetic quantum number m.Here, d orbitals (l = 2) are decomposed into m = 0, ± 1, and ± 2 based on the irreducible representation of the fcc (111) lattice, which are commonly expressed as z 2 for m = 0, xz and yz for m = ± 1, and x 2

Figure 5 .
Figure 5. Spin-dependent DOS of the L2 − L7 layers as function of E for the a) Pt/Co/Pt and b) Pd/Co/Pd structures, respectively, where E F is set to zero.Plots of N lm for d orbitals with different m: (c) and (d) for m = 0, (e) and (f) for m = ± 1, and (g) and (h) for m = ± 2, for the Pt/Co/Pt and Pd/Co/Pd structures, respectively.