We report the Dzyaloshinskii–Moriya interaction (DMI) in Pt/Co/Re films. By measuring the current-induced hysteresis loop shift, we find that the interfacial DMI in the Pt/Co/Re structure is 2.1 pJ/m, which is stronger than that in Ir/Co/Pt asymmetric multilayers. The large DMI in this system can be attributed to an additive DMI at the Pt/Co and Co/Re interfaces; the Co/Re interface hosts a large DMI whose sign is the same as that at the Pt/Co interface. The additive DMI due to the large DMI at the Co/Re interface is consistent with theoretical predictions. The result provides a way to control the formation of chiral spin textures, such as magnetic skyrmions and chiral domain walls.

The Dzyaloshinskii–Moriya interaction (DMI), an antisymmetric magnetic exchange interaction, has attracted great interest in recent years due to its fundamental role in the stabilization of topologically non-trivial chiral magnetic textures, such as skyrmions.1–7 Magnetic skyrmions are promising building blocks for next-generation data storage and information processing devices due to their topological stability, their nanoscale size, and the ultralow current required to drive them. Since the DMI arises from the spin–orbit coupling in magnetic systems with broken inversion symmetry,8,9 skyrmions were experimentally observed in non-centrosymmetric magnets, where the bulk inversion symmetry is broken,10–13 and in asymmetric magnetic multilayers, where the inversion symmetry is broken at the interface.3,6,14–23

The DMI at ferromagnetic-metal/heavy-metal (FM/HM) interfaces appears to be particularly important for practical applications. The reason for this is that the DMI in this structure can be designed by the choice of materials for the HM and FM layers because the sign and strength of the interfacial DMI at FM/HM interfaces depend strongly on the degree of hybridization between the 3d–5d states around the Fermi level.24 In particular, an additive large DMI can be achieved in HM/FM/HM systems when the top and bottom interfaces show the same sign of the interfacial DMI.3 

In this work, we investigate the DMI in Pt/Co/Re films to explore the possibility of achieving a large DMI. The Pt/Co interface is a prototypical system for a strong interfacial DMI. Among Co/HM combinations, the Co/Re interface is predicted to have a strong DMI with the same sign as that of the Pt/Co interface.25 We determine the DMI for the Pt/Co/Re structure using the current-induced hysteresis loop shift measurement.26,27 The result shows that the interfacial DMI constant in this system is 2.1 pJ/m, consistent with the prediction of the additive DMI at the two interfaces of the Co layer sandwiched between Re and Pt. This result provides useful information for designing the size and stabilizing magnetic skyrmions, as well as for understanding the DMI at interfaces.

The samples used for the current-induced hysteresis loop shift measurement are Ti(2 nm)/Pt(2.5 nm)/Co(1.28 nm)/Re(tRe)/Pt(5 nm)/Ti(3 nm) films [see Fig. 1(a)], where the numbers in parentheses represent the thickness. The films were fabricated on Si substrates with a 300 nm thermal oxide layer by magnetron sputtering at room temperature. The base pressure in the chamber was better than 1 × 10−6 Pa, and the deposition pressure was 0.2 Pa. The 2-nm-thick Ti seed layer was fabricated to improve the quality of the upper layers, and the top 3-nm-thick Ti cap layer was fabricated to prevent oxidation of the lower layers. The samples were patterned in the shape of 8-μm-wide and 120-μm-long Hall bars by photolithography. Figure 1(b) shows the device structure for the current-induced hysteresis loop shift measurement. We measured the out-of-plane field Hz dependence of the anomalous Hall (AH) resistance RAH when applying a direct-current (dc) charge current Idc and the in-plane bias field Hx.

FIG. 1.

(a) Ti(2 nm)/Pt(2.5 nm)/Co(1.28 nm)/Re(tRe)/Pt(5 nm)/Ti(3 nm) thin-film heterostructures. The Re layer thickness tRe is varied from tRe = 0 to 1.58 nm. (b) Setup for current-induced hysteresis loop shift measurement. L, d, and t represent the length, width, and thickness of the Hall bar, respectively. (c) AH-loops for a Ti/Pt/Co/Re(1.31 nm)/Pt/Ti structure with an applied dc current Idc of ±10 mA and an in-plane external magnetic field μ0Hx of −140 mT. Idc corresponds to an applied electric field E = V/L = ±1.44 × 105 V/m, where V is the voltage applied along the Hall bar of length L. (d) Switching fields HSW for down-to-up (red squares) and up-to-down (blue circles) magnetization reversals as functions of E, with μ0Hx = −140 mT. Black triangles represent the center of the AH loops, with the effect of Joule heating eliminated, which corresponds to Heffz. The black solid line represents linear fit to Heffz. (e) In-plane bias field Hx dependence of the damping-like torque efficiency per unit applied electric field ξDLE for the Ti/Pt/Co/Re(1.31 nm)/Pt/Ti structure. We define μ0HDMI as the intersection point of the averaged value of ξDLE saturated in the high-field region and linear fitting result in the low-order field region. The red line represents the fitting line used to determine μ0HDMI.

FIG. 1.

(a) Ti(2 nm)/Pt(2.5 nm)/Co(1.28 nm)/Re(tRe)/Pt(5 nm)/Ti(3 nm) thin-film heterostructures. The Re layer thickness tRe is varied from tRe = 0 to 1.58 nm. (b) Setup for current-induced hysteresis loop shift measurement. L, d, and t represent the length, width, and thickness of the Hall bar, respectively. (c) AH-loops for a Ti/Pt/Co/Re(1.31 nm)/Pt/Ti structure with an applied dc current Idc of ±10 mA and an in-plane external magnetic field μ0Hx of −140 mT. Idc corresponds to an applied electric field E = V/L = ±1.44 × 105 V/m, where V is the voltage applied along the Hall bar of length L. (d) Switching fields HSW for down-to-up (red squares) and up-to-down (blue circles) magnetization reversals as functions of E, with μ0Hx = −140 mT. Black triangles represent the center of the AH loops, with the effect of Joule heating eliminated, which corresponds to Heffz. The black solid line represents linear fit to Heffz. (e) In-plane bias field Hx dependence of the damping-like torque efficiency per unit applied electric field ξDLE for the Ti/Pt/Co/Re(1.31 nm)/Pt/Ti structure. We define μ0HDMI as the intersection point of the averaged value of ξDLE saturated in the high-field region and linear fitting result in the low-order field region. The red line represents the fitting line used to determine μ0HDMI.

Close modal

From the current-induced hysteresis loop shift measurement, we can determine the effective fields due to the DMI HDMI and the current-induced damping-like spin–orbit torque Heffz. Here, when Hx = 0, the net effective field Heffz due to the damping-like torque acting on the domain-wall (DW) magnetizations is zero in the case of homochiral Néel-type DWs because of the opposite signs of Heffz for up-to-down and down-to-up DWs. In contrast, when Hx is large enough to overcome the DMI effective field HDMI, the DW magnetizations align parallel to Hx, and thus, the damping-like effective field points in the same direction for both up-to-down and down-to-up DWs, resulting in a nonzero net Heffz. This indicates that the out-of-plane hysteresis loop is shifted by the current-induced Heffz when Hx ≠ 0. From Hx dependence of the current-induced hysteresis shift, HDMI and Heffz can be determined.

Figure 1(c) shows the AH-loops for the Ti/Pt/Co/Re/Pt/Ti structure with tRe = 1.31 nm and when μ0Hx = −140 mT and Idc = ±10 mA corresponding to an applied electric field E = V/L = ±1.44 × 105 V/m. Here, V is the voltage applied along the Hall bar of length L. This result shows that the magnetization switching field depends on the direction of Idc, showing that the switching field is affected by a nonzero damping-like torque, as well as the Joule heating, in this system. In Fig. 1(d), we show the E dependence of the down-to-up switching field HSWdown-to-up and up-to-down switching field HSWup-to-down. From this result, the damping-like torque efficiency per unit applied electric field ξDLE can be obtained from28,29

ξDLE=2eMstFMμ0HeffzE,
(1)

where Heffz=(HSWup-to-down+HSWdown-to-up)/2 is the damping-like effective field,26,27Ms is the saturation magnetization, and tFM is the thickness of the Co layer. Here, ξDLE corresponds to the effective spin Hall conductivity.

Figure 1(e) presents the in-plane bias field Hx dependence of the damping-like torque efficiency per unit applied electric field ξDLE for the Ti/Pt/Co/Re/Pt/Ti structure with tRe = 1.31 nm. This result shows that ξDLE is quasilinear to Hx in the small range of Hx and it saturates at larger Hx. This observation is consistent with a picture of the damping-like torque acting upon Néel-type chiral DWs, stabilized by the DMI, where ξDLE=ξDL,effEcosϕ. Here, ξDL,effE is the damping-like effective torque efficiency per unit applied electric field, and ϕ is the angle between the DW moment and the x axis. In this scenario, the DW orientations in the heterostructure change from an average of ⟨ cos ϕ⟩ ≈ 0 to ⟨ cos ϕ⟩ ≈ 1 when Hx approaches the effective field of the DMI HDMI, showing that the saturation value of ξDLE corresponds to ξDL,effE and the saturation field corresponds to HDMI. We define μ0HDMI as the intersection point of the averaged value of ξDLE saturated in the high-field region and the linear fitting result in the low-order field region.

To determine tRe dependence of the damping-like torque efficiency and the DMI effective field HDMI, we plot Hx dependence of ξDLE for the Ti/Pt/Co/Re/Pt/Ti structure with tRe = 0, 0.50, 0.77, 1.04, 1.31, and 1.58 nm, as shown in Fig. 2. This result shows that ξDLE is quasilinear to Hx in the small range of Hx and it saturates at larger Hx. From this result, we determine HDMI and ξDLE for these structures. For tRe = 0, HDMI is negligible because the DMIs at the Pt/Co and Co/Pt interfaces cancel each other out. The small but nonzero HDMI in this structure arises from incomplete cancellation of the DMI.30,31Figure 2 also shows that HDMI is clearly enhanced by inserting the Re layer. Here, for tRe = 0.50 and 1.58 nm, we found small but non-negligible ξDLE (=ξDL,WedgedE) at Hx = 0, which can be attributed to the asymmetry of the sample.26 For these samples, we estimate ξDL,effE by subtracting ξDL,WedgedE from the measured data.

FIG. 2.

In-plane bias field Hx dependence of the damping-like torque efficiency per unit applied electric field ξDLE for Ti/Pt/Co/Re(tRe)/Pt/Ti structures with the Re layer thickness: (a) tRe = 0 nm, (b) tRe = 0.50 nm, (c) tRe = 0.77 nm, (d) tRe = 1.04 nm, (e) tRe = 1.31 nm, and (f) tRe = 1.58 nm.

FIG. 2.

In-plane bias field Hx dependence of the damping-like torque efficiency per unit applied electric field ξDLE for Ti/Pt/Co/Re(tRe)/Pt/Ti structures with the Re layer thickness: (a) tRe = 0 nm, (b) tRe = 0.50 nm, (c) tRe = 0.77 nm, (d) tRe = 1.04 nm, (e) tRe = 1.31 nm, and (f) tRe = 1.58 nm.

Close modal

First, we investigate the damping-like torque efficiency. Figure 3(a) shows tRe dependence of ξDL,effE. ξDL,effE can be decomposed into bulk and interface contributions: ξDL,effE = ξBulkELowerPt+ξBulkEUpperPt+ξInterfaceEPt/Co+ξInterfaceECo/Pt, where ξBulkELowerPt and ξBulkEUpperPt are the torque efficiencies due to the spin Hall effect in the lower and upper Pt layers, respectively; ξInterfaceEPt/Co and ξInterfaceECo/Pt arise from the interfacial spin–orbit coupling, such as the Rashba–Edelstein effect and interfacial spin–orbit scattering, at the lower Pt/Co and upper Co/Pt interfaces, respectively.32–34 The sign of the torque efficiencies due to the lower Pt layer is positive, ξBulkELowerPt>0 and ξInterfaceEPt/Co>0, while that due to the upper Pt layer is negative, ξBulkEUpperPt<0 and ξInterfaceECo/Pt<0.

FIG. 3.

(a) Dependence of Re layer thickness tRe of the damping-like effective torque efficiency per unit applied electric field ξDL,effE. (b) tRe dependence of the interfacial DMI constant Ds.

FIG. 3.

(a) Dependence of Re layer thickness tRe of the damping-like effective torque efficiency per unit applied electric field ξDL,effE. (b) tRe dependence of the interfacial DMI constant Ds.

Close modal

When tRe = 0 nm, ξInterfaceEPt/Co and ξInterfaceECo/Pt cancel each other out, indicating ξDL,effEξBulkELowerPt+ξBulkEUpperPt. This indicates |ξBulkELowerPt|<|ξBulkEUpperPt| because of the negative value of ξDL,effE when tRe = 0 nm [see Fig. 2(a)]. The larger torque efficiency of the upper Pt layer is consistent with a drift-diffusion model, which predicts that the spin transparency at the Pt/Co interface increases with increasing thickness of the Pt layer when the Pt thickness is around the spin diffusion length.35,36Figure 3(a) also shows that the sign of ξDL,effE is changed from negative to positive by inserting the Re layer, suggesting that ξDL,effE is dominated by the torque generated by the lower Pt layer when tRe ≠ 0. This result can be attributed to a suppression of the spin–orbit torque ξInterfaceECo/Pt originating at the upper Co/Pt interface induced by the insertion of a thin nonmagnetic layer at the interface.37 Here, the spin Hall effect in Re is negligible compared to that in Pt.38 

Next, we investigate the DMI effective field. In Fig. 3(b), we show tRe dependence of the interfacial DMI constant Ds, obtained by using39 

Ds=MsΔtFMμ0HDMI,
(2)

where Δ=A/Ku is the width of the DW and A is the exchange stiffness. Here, Ku is the anisotropy energy of the Co layer, which can be determined from the effective anisotropy field Hk using Ku=Hkμ0Ms/2.31 Using Ms and Hk measured by vibrating sample magnetometry (VSM) and by assuming A = 2.2 × 10−11 J/m,40 we estimate Δ as 16 nm. Figure 3(b) shows that at tRe = 0 nm, Ds is negligibly small, Ds=0.14 pJ/m, due to the cancellation of the DMIs at the lower Pt/Co and upper Co/Pt interfaces. The negligible |Ds| when tRe = 0 nm confirms that the film quality of the upper and lower interfaces of the Co layer is almost comparable. By inserting the thin Re layer, Ds is enhanced by an order of magnitude: Ds=1.4 pJ/m at tRe = 0.50 nm. Notable is that the interfacial DMI constant Ds is almost constant, Ds=2.1 pJ/m, when tRe ≥ 0.77 nm. This result suggests that the surface of the Co layer is fully covered by the Re layer when tRe ≥ 0.77 nm and Ds=2.1 pJ/m is the sum of interfacial DMIs at the Pt/Co and Co/Re interfaces. Ds=2.1 pJ/m can be converted to a DMI constant D=1.6 mJ/m2 using Ds=DtFM.27 Since D is known to vary with tFM values,41,Ds will be used in the following discussion and comparison with other reference values. From this value, we confirm that Néel-type DWs are stabilized in the Pt/Co/Re structure. Here, the DW type can be estimated from the relation between Ds and the threshold of the interfacial DMI constant Dsth that stabilizes Néel-type DWs,42 

Dsth=2tFM2ln(2)μ0Ms2/π2.
(3)

When DsDsth, Néel-type DWs are stabilized, while the domain is a mixture of Néel-type and Bloch-type DWs when Ds<Dsth. For the Pt/Co/Re film, using Eq. (3) with the measured value of Ms, we obtain Dsth=0.11 pJ/m, which is about an order of magnitude smaller than Ds when tRe > 0.50 nm.

To investigate the contribution of the Pt/Co and Co/Re interfaces to the DMI of the Pt/Co/Re structure, we measured the DMI for a Ti/Pt/Co/Ti structure, where the Re layer is replaced with Ti. Figure 4 shows Hx dependence of ξDLE for the Ti(2 nm)/Pt(2.5 nm)/Co(1.28 nm)/Ti(5 nm) structure. In the structure, we also observed that ξDLE is quasilinear to Hx in the small range of Hx and it saturates at larger Hx. From this result, Ds was estimated as 0.89 pJ/m. This value is close to Ds=0.7 pJ/m at the Pt/Co interface,43 showing that Ds in the Pt/Co/Ti structure is dominated by the Pt/Co interface. This result indicates that the large Ds = 2.1 pJ/m in the Pt/Co/Re structure can only be explained by the additive effect of the DMI of the Pt/Co and Co/Re interfaces; the Co/Re interface is also an efficient source of the DMI. Using Ds=0.7 pJ/m at the Pt/Co interface, we obtain Ds=1.4 pJ/m at the Co/Re interface, which is consistent with the theoretical prediction, Ds2 pJ/m.25 

FIG. 4.

In-plane bias field Hx dependence of the damping-like torque efficiency per unit applied electric field ξDLE for a Ti(2 nm)/Pt(2.5 nm)/Co(1.28 nm)/Ti(5 nm) structure.

FIG. 4.

In-plane bias field Hx dependence of the damping-like torque efficiency per unit applied electric field ξDLE for a Ti(2 nm)/Pt(2.5 nm)/Co(1.28 nm)/Ti(5 nm) structure.

Close modal

The interfacial DMI in the Pt/Co/Re structure, Ds=2.1 pJ/m, is stronger than that in Ir/Co/Pt asymmetric multilayers, Ds0.41 pJ/m.3,31,44 In the Ir/Co/Pt multilayer, the DMIs at the Ir/Co and Co/Pt interfaces provide a strong and additive DMI, which has been shown to stabilize stable sub-100 nm skyrmions at room temperature. The strong DMI in the asymmetric Pt/Co/Re structure is evidence for an additive DMI at the two interfaces of the Co layer sandwiched between Re and Pt. In fact, Ds=2.1 pJ/m is comparable to the value derived from ab initio calculations. This calculation predicts strong DMIs with opposite signs for Co on Re and Co on Pt,25 which correspond to an additive DMI at the Pt/Co and Co/Re interfaces.

In summary, we have investigated the DMI and spin-orbit torque efficiency of the Pt/Co/Re film. By measuring the current-induced hysteresis loop shift, we find that the interfacial DMI in the Pt/Co/Re structure is 2.1 pJ/m, which is stronger than that in Ir/Co/Pt asymmetric multilayers. The large DMI in the Pt/Co/Re can be attributed to the additive DMI at the top and bottom interfaces of the Co layer, showing that the Co/Re interface hosts a strong DMI whose sign is the same as that at the Pt/Co interface. The results will be useful not only for the understanding of the interfacial DMI but also for stabilizing skyrmions.

This work was supported by the JSPS KAKENHI (Grant No. 19H00864), the JST FOREST Program (Grant No. JPMJFR2032), the Asahi Glass Foundation, and the Spintronics Research Network of Japan (Spin-RNJ).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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