Introduction

Chiral magnetic materials, the phenomena associated with them, and the technological opportunities provided by emerging spintronic devices1,2 have recently attracted increasing academic attention. Such chiral magnetic phenomena are caused by an antisymmetric exchange interaction, which is the so-called Dzyaloshinskii–Moriya interaction (DMI).3,4 In magnetic thin films, a sizeable DMI generates built-in chirality of magnetic domain walls (DWs), which is essential for current-induced DW motion via spin–orbit torques (SOTs).5,6 The ultimate speed of the DW motion has been revealed to also be governed by the DMI strength.7 In addition, a sizeable DMI is an essential ingredient for generating topological objects, such as magnetic skyrmions,8,9 which can be used in high-density digital devices for racetrack memory and so on.1,2,8

Because of the academic interest and technological importance, numerous efforts have been devoted to understanding the DMI and its role on magnetic phenomena. Belabbes et al.10 recently showed the theoretical relationship between the DMI and Hund’s rule in Co/X and other 3d/5d bilayer structures. Torrejon et al.11 reported the dependence of the DMI on materials in NM/CoFeB/MgO (NM = Hf, Ta, and W) with the nitrification of the Ta layer. Yu et al.12 provided a way to resolve the contributions on the DMI at each Pt/Co and Co/X interface in a Pt/Co/[Ni/Co]4/X multilayer structure. Kim et al.13 revealed the DMI-induced asymmetry of the DW speed in a Pt/Co/X trilayer system. Since the physical origin of the DMI at a metallic interface still remains elusive, an experimental study of the key intrinsic parameters of the DMI will be of great help and can provide an empirical guideline in terms of both experiment and sample structure design for application and to help understand the DMI.

Therefore, we are interested in the DMI at interfaces between ferromagnetic metal and nonmagnetic metals in a bilayer system. The interfacial DMI in such metallic bilayers arises from a three-site indirect exchange mechanism among two atomic spins and a neighboring atom with a large spin–orbit coupling (SOC).2,4,14 In antiferromagnetic crystals, the DMI is known to originate from an anisotropic superexchange interaction that linearly depends on the strength of the SOC.4 In this case, the DMI magnitude is proportional to (Δg/g)Jex, where g is the gyromagnetic ratio, Δg is its deviation from the value of a free electron, and Jex is related to the magnitude of the exchange interaction.4

Whether associating this elegant picture to polycrystalline metallic systems is possible is an interesting question. Spin–glass alloy systems shed light on the origin of the DMI in metallic systems in which the DMI arises from the spin–orbit scattering of conducting electrons by nonmagnetic transition-metal impurities.14 This condition inspired us to investigate the material parameters that may be correlated with the scattering potential at the metal–metal interface. If we can find a correlation between the DMI strength and other material parameters, such as the work function, electronegativity, and SOC constant, this would provide a productive guideline for engineering the DMI strength. In this paper, we report an experimental observation of the correlation between the DMI strength and the work function difference at the metal–metal interface.

Materias and methods

Sample fabrication and detail structure

The detailed film structure is 5 nm Ta/2.5 nm Pt/0.9 nm Co/2.5 nm X/1.5 nm Pt, where X was selected as Ti, Cu, W, Ta, Al, Ru, Pd, Au, or Pt, which was deposited by dc-magnetron sputtering on Si wafers with a 300 nm SiO2 layer. This structure was chosen to observe the relative DMI tendency of bilayer systems while keeping the bottom Pt layer and Co thickness the same. The lowermost Ta layer is a seed layer used to enhance the crystallinity of the films, and the uppermost Pt layer is a protective layer used to prevent oxidation. To keep the quality of the Pt/Co/X films as similar as possible and to exclude other unknown factors that affect the depinning field measurement, the sputtering conditions (Ar working pressure ~2 mTorr, sputtering power ~10 W) were carefully kept the same for all Pt/Co/X films. High-resolution transmission electron microscopy15 revealed that the Pt layer has an fcc (111) crystalline structure along the growth direction,16 which is known to exhibit a strong perpendicular magnetic anisotropy (PMA).17,18,19 The overall film roughness, R, was measured via atomic force microscopy as listed in Table 1. No clear grain structure was observed, possibly due to the thin thickness of our films.16 The depinning fields, HP, are also listed in Table 1. These measurements confirm that there is no significant variation in both R and HP among all the samples.

Table 1 HDMI, HK, Keff, D, Wmea, R, and HP for the Pt/Co/X samples with material X
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Measurement of the SOT efficiency to quantify the DMI of the trilayer-structured samples

To measure the SOT efficiency, ε, and the HDMI, which is the DMI-induced effective magnetic field, the samples were patterned to 20 μm-wide and 350 μm-long microwires by photolithography and an ion-milling process, as shown in Fig. 1a. The ε and HDMI were measured from the depinning field of the DWs with respect to the in-plane magnetic field, Hx.15,20,21 The measurement procedure is described as follows. First, a large perpendicular external magnetic field was applied to saturate the magnetization of the sample either up or down. Next, a DW was created at the position inside the microwire and adjacent to the DW writing electrode, as shown by the white vertical line in Fig. 1a. Then, under application of a fixed current bias, an out-of-plane magnetic field was swept until the DW moved from the initial position. By repeating this procedure using different magnitudes of the current bias as shown in Fig. 1b, the depinning field, Hdep, was measured as a function of the total current density, J. From the linear dependence of Hdep on J, as shown in Fig. 1c, we quantified ε using the relation ε = −∂Hdep/∂J.15,20,21 The measurement was repeated for different Hx values.

Fig. 1: Measurement of the SOT efficiency.
figure 1

a Schematic drawing of the measurement setup with an optical image of a sample. The gray horizontal rectangle is the 20 μm-wide and 350 μm-long microwire, and the white areas are 5 and 100 nm-thick Ti/Au electrodes. The white vertical line shows the electrode for the DW writing. The red circular dot indicates the position of the laser spot for the magneto-optical Kerr effect (MOKE) signal detection. The polarities of the external magnetic field and current are designated in the figure. b Normalized MOKE signals with respect to Hz for different current biases of J = (red) + 1.2 × 1010, (black) 0, and (blue) −1.2 × 1010 A/m2. c Hdep with respect to J for a fixed in-plane magnetic field bias (−300 mT). The red line shows the best linear fit

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Based on the SOT theory, it is known that the damping-like torque has the direction parallel to \(\hat m \times (\hat m \times \hat y)\),5 which corresponds to a situation in which there exists an effective magnetic field parallel to the \(\hat m \times \hat y\) term. Here, \(\hat m\) is the magnetization vector inside a DW. The microwire lies on the x–y plane, and the current flows along the x-axis. Therefore, the finite x-component of \(\hat m\) generates the z-component of \(\hat m \times \hat y\), i.e., the perpendicular component of the SOT-induced effective magnetic field. This perpendicular component of the SOT-induced effective magnetic field assists the DW depinning process. For the case of a Bloch-type DW, due to the zero x-component of \(\hat m\), there is no z-component for the effective magnetic field, and thus ε = 0. Hence, the intercept to the x-axis in Fig. 2 indicates that the DW stays in the Bloch-type DW configuration.

Fig. 2: SOT efficiency of Pt/Co/X.
figure 2

Plots of ε with respect to Hx for different X values as denoted in the figures. The curved solid lines are best fits to guide the eye. The red horizontal lines show the axis of ε = 0 for each measurement. The red vertical lines indicate the positions of \(H_{x}^0\) for ε = 0. The values of ε for X = Ru, Pd, and Au are magnified for better resolution of the data with amplification factors denoted in the figure

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Figure 2 shows the plot of ε with respect to Hx for the samples with different X values, as denoted in each panel. All the plots of ε exhibit three distinct regimes that are frequently observed in SOT-induced DW motions: two saturation regimes of the Néel-type DW configurations and a transition regime in between.22 In the transition regime, a Bloch-type DW configuration appeared at the intercept to the abscissa (as shown by the red vertical lines) in which magnetic field \(H_{x}^0\) exactly compensated for HDMI (i.e., \(H_{x}^0 + H_{{\mathrm{DMI}}} = 0\)). We could, therefore, quantify HDMI from these measurements. All the samples with broken inversion symmetry exhibited nonzero HDMI, except the sample with X = Pt, which had an almost zero HDMI because of its symmetrically layered structure.

The ε corresponds to the overall SOT efficiency with respect to J, where J is defined as the total current divided by the section of the wire. Since ε is composed of the contributions from the upper X and lower Pt layers, of which the local current densities are different to each other due to their different conductivities, there may be several other ways to define the current density.23 However, a different definition of J changes only the scale of the ordinate in Fig. 2, whereas the intercept to the abscissa (i.e., \(H_{x}^0\)) can be uniquely determined. Of note, the DMI can be determined without current injection (i.e., no SOT phenomena) by purely field-induced DW motion or spin wave propagation.24,25

Results and discussion

Correlations between the material parameters and the DMI

Tables 1 and 2 list the measured values of HDMI, anisotropy field, HK, effective uniaxial magnetic anisotropy, Keff, DMI strength, D, work function, Wmea measured by ultraviolet photoelectron spectroscopy (UPS), overall sample roughness, R, depinning field, Hp, and the literature values of the work function, Wref, electronegativity, χ, and SOC constant, ξ. These material parameters were chosen because of their potential relationship with the electrostatic potential barrier at the interface between the Co and X layers. In addition, the correlation between these easily accessible bulk values may be better as a practical guideline for the selection of the top and bottom non-magnetic layers from the literature. From the tables, we see that HDMI has a better correlation with W than the other parameters. The correlations between W, χ, and ξ are plotted and shown in Fig. 3, where the Wmea values are denoted by red symbols and the Wref values are black symbols, which confirm that a better correlation exists in Fig. 3a than in the other figures.

Table 2 Wref, χ (Pauling scale), and ξ for material X
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Fig. 3: Parameter relationships with HDMI.
figure 3

a Work function, W; b electronegativity, χ; and c SOC constant, ξ, as functions of HDMI for Pt/Co/X samples with different X values, as denoted in the figure. In each plot, HDMI was determined using the ε measurement from the data shown in Fig. 2, Wmea (red symbols) is the measurement work function, and Wref (black symbols), χ, and ξ are the literature values from refs. 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56. The error bars for HDMI correspond to the experimental accuracy determined from several repeated measurements. The error bars for Wmea and Wref were obtained from measurement error and from the standard deviation of several different values from references

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More specific and precise measurements would provide a more accurate relationship between the DMI and work function. Since the present Wmea was measured after in situ surface cleaning on relatively thick X layers, there may be artefacts, such as crystal deformation, induced strain, and atomic mixing, which formed during the surface cleaning process. Additionally, since the X layers must be thicker than the penetration depth of the UPS measurement, accurate information at the vicinity of the interface might not have been precisely collected. Despite these experimental limits and possible artefacts, our observation suggests the possibility that the work function may play a more significant role in the generation of HDMI.

Based on the concept of the potential gradient at the interface, the electronegativity may also have a relationship with the DMI, as shown in Fig. 3b, with a rough correlation between χ and HDMI. Although the electronegativity difference between Co and X also implies a potential gradient at the interface, it is relevant to atomic and/or molecular systems, but less relevant to metallic bilayer system because it is associated with the chemical energy of the valence bond. In addition, because the spin–orbit scattering-mediated spin–chiral effect may play a leading role in our trilayer system, our Pt/Co/X metallic system shows a better relationship between the DMI and work function compared with the DMI and electronegativity.

Another important factor in determining the strength of the DMI is the SOC. The strength, D, of the DMI could be linearly proportional to the strength of the SOC, which is similar to that in antiferromagnetic crystals.4 However, the experimental correlation between HDMI and ξ was found to be pretty scattered, as shown in Fig. 3c. Because our values of ξ correspond to the atomic SOCs from the literature, if more specific and precise SOC values relevant to the metallic bilayer systems were available, we may possibly see a more accurate relationship between the DMI and SOC.

The magnitude of D was estimated from the relation of D = μ0HDMIMSλ with a Bloch-type DW width of λ \(\left( { = \sqrt {A/K_{{\mathrm{eff}}}} } \right)\),5,7,26 where A is the exchange stiffness. The Co value of A (2.2 × 10−11 J/m) and MS of Co (1.4 × 106 A/m) were used in the estimation for a qualitative comparison.26,27 The effective anisotropy was quantified from the relation Keff = MSHK/2. The D was defined as the total effective DMI, which includes contributions from the upper Pt/Co and lower Co/X interfaces. The scattering potential barrier was presumed to be associated with the work function difference, ΔW, at the Co/X interface. Figure 4 shows a summary of the D values as a function of ΔWmea (≡Wmea,X − Wmea,Co) and ΔWref (≡Wref,X − Wref,Co), where ΔWmea values are denoted by red symbols measured via UPS and ΔWref values are shown as black symbols, which were obtained from the literature. The correlation between D and ΔW is better than between HDMI and W.

Fig. 4: Plot of D as a function of ΔW for the Pt/Co/X samples with different X values, as denoted near the data symbols.
figure 4

The ΔWmea values are denoted by red symbols, and ΔWref values are shown by black symbols. The blue line shows the best linear fit. The error bars for D were obtained from the statistical summation of the experimental accuracy of HDMI and HK determination. The error bars for Wmea are from measurement errors, and those for Wref were obtained from the standard deviation of several different values from references

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Reference14 described how to calculate the magnitude of the DMI for nonmagnetic transition-metal impurities (Ti, Ni, Pd, Fe, Co, and Pt) in CuMn spin–glass alloys. The DMI is associated with “the shift in the ground state energy of gas of conduction electrons interacting with two localized spins.14” “On the site of nonmagnetic transition-metal impurities, the spin–orbit coupling of a conduction electron is considerably enhanced because the admixture of the impurity d states into the conduction band allows the conduction electrons to experience the strong spin–orbit forces of the d states.14” They showed that the DMI is due to spin–orbit scattering of conduction electrons by nonmagnetic impurities, and the strength of the DMI is proportional to the magnitude of the scattering potential.14 In the FM/HM bilayer systems, such as those in our experiments, the work function difference between the two metals provides such a scattering potential. When two metals with different work functions are brought into contact, the Fermi energy levels of two metals are aligned to build a very narrow potential barrier within the Thomas-Fermi length. The height of this potential barrier is proportional to the work function difference of the two metals. Consequently, the strength of the DMI may be related to the work function difference between two metals.

The signs of the DMI are all negative for the samples of the Pt/Co/X trilayer structure, except for X = Pt. The negative DMI generates left-handed chiral DWs.20 For the case of X = Pt, a negligibly small DMI was expected due to its symmetric structure; however, several recent studies have reported a small but positive DMI, which is possibly due to the different interfaces that form between Pt/Co and Co/Pt.24,28 Our observation of negative DMIs in the other samples is in agreement with other studies for the Pt/Co/Pd,29 Pt/Co/Al,30 Pt/Co/Cu,30 Pt/Co/Ta,31 Pt/Co/[Ni/Co]4/Cu,12 and Pt/Co/[Ni/Co]4/Ta12 films after consideration of sign conventions. It is known that a strong SOC exists at the Pt/Co interface, and consequently, the DMI strength is very large at the Pt/Co bilayer interface.10,32 From these results, we infer that the sign of the DMI may be determined in our trilayer samples by the underlayer Pt. Because our measurement is the sum of the effects on the DMI of the two interfaces, the effect of each interface cannot be independently observed. Even if the underlayer Pt is dominant in the total DMI, directly knowing the sign and magnitude of the DMI at the Co/X bilayer interface is difficult. However, the relative strength of the DMI between the Pt/Co/X trilayers remains significant.

In summary, we presented experimental observations regarding the correlation between the DMI strength and the work function. This correlation may be related to the spin–orbit scattering in the electric potential barrier due to the work function difference at the interfaces. This correlation suggests that the DMI strength can be engineered via material selection following guidelines related to the intrinsic material parameters.