Introduction

The possibility to manipulate magnetization at nanoscale using the coupling between electron’s spin and its motion (orbital angular momentum) has led to the emergence of a new research field named “spin-orbitronics”. A fascinating example of the impact of the spin-orbit coupling (SOC) on the magnetization profile is the chiral spiral or skyrmion magnetic orders observed at the surface of magnetic ultrathin films1,2,3,4,5,6,7,8,9,10. Such spin configurations are driven by an additional term in the exchange interaction, namely Dzyaloshinskii-Moryia interaction (DMI)11,12,13,14,15,16,17,18,19,20,21, which arises from the presence of SOC and inversion symmetry breaking21,22. Novel out-of-equilibrium spin transport phenomena also result in such structure, such as the spin-orbit torques (SOT) exerted on the magnetization when injecting a current, leading to fast current induced domain wall motion and magnetization reversal23,24,25,26,27. This has led to new concept of magnetic memory, such as skyrmion-based memory, where the information is coded by nm scale magnetic skyrmions in nanotracks and manipulated using current pulses22,28,29. However, for the applications, there are still many issues to solve, for example in order to increase the stability of the chiral dependent domain walls (DW), a large DMI amplitude is critical. Furthermore, the maximum velocity of domain wall motion is also shown to strongly depend on DMI amplitude. Therefore, the search for material stack with a large DMI is the key to realize stable skyrmions and chiral DW for spin-orbitronic devices.

In this Article, we propose several approaches to enhance DMI in ultrathin magnetic films. First, we show that DMI can be magnified via multilayer stacking of FM and NM metals when the ferromagnetic (FM) layer is sandwiched between nonmagnetic (NM) layers inducing additive DMI in NM1/FM/NM2 structures16,30,31,32. Here, in case of DMI enhancement, the key is to find required DMI chiralities for additive effects at successive interfaces. For example, in asymmetric trilayers of Pb/Co/Pt, where the DMI chirality at separated Co/Pt and Co/Pb interfaces is opposite as shown in Fig. 1(a,b), respectively. Due to the inversion geometry stacking from Co/Pb to Pb/Co in forming Pb/Co/Pt trilayers, the sign of DMI at the interface of Pb/Co is reversed resulting in an overall enhanced anticlockwise DMI as schematiclly shown in Fig. 1(c). Another approach we propose is to use a cap** oxidized layer, such as MgO, on top of Co/Pt bilayers, which is shown to efficiently enhance the DMI. Here, the DMI enhancement mechanism arising from MgO/Co interface is found due to Rashba effect. Finally, we demonstrate that DMI can be efficiently tailored by applying an electric field (EF). This unveils the possibility to control DMI and perpendicular magnetic anisotropy (PMA) simultaneously via electric field which opens an efficient route towards EF-manipulation of magnetic skyrmions.

Figure 1
figure 1

Schematic structures with anticlockwise DMI in Co/Pt bilayers (a), clockwise DMI in Co/Pb bilayers (b) and enhanced DMI in Pb/Co/Pt trilayers (c).

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Methods

To calculate DMI, we employ the same approach as in our previous work33 based on the Vienna ab initio simulation package (VASP)34,35, which represents an adaptation to the case of layered structures of the method used for DMI calculations in bulk frustrated systems and insulating chiral-lattice magnets10,15,23,24,25,26,41 in domain walls, skyrmions or nanomagnets via spin-orbit torques, where DMI is known to play an essential role in the magnetization reversal27,42,43,44. We consider the MgO/Co/Pt structure comprises 3 ML of Pt, 3 to 5 ML of Co, and MgO with surface passivated by hydrogen as shown in Fig. 4(c). The results show that DMI in MgO/Co/Pt is much larger, about 1.6 times, compared to that of Co/Pt bilayers for all the Co thicknesses considered. Furthermore, when varying the thickness of Co layer from 3–5 MLs in both Co/Pt and MgO/Co/Pt structures, the microscopic DMI d is not affected much suggesting that the Co/MgO interface has a similar impact on the electronic structure of the Co layer up to at least 5 monolayers (shown in Fig. 4(a)). Note, however, that the micromagnetic DMI constant D defined according to Eq. 4 in ref.33 is expected to decrease with increasing Co thickness as shown in Fig. 4(b). Recently, a large value of the DMI of 2 mJ/m2 has been measured using Brillouin Light Scattering experiments in sputtered ultrathin Pt/Co(1 nm)/MgO multilayer corresponding to 5 ML of Co, which is among the largest value measured so far in ultrathin sputtered films. Our simulations predict a large value of 3.9 mJ/m2 for this system. The lower experimental value can be explained by the disordered interface and grain structure in the case of sputtered thin films. In order to understand the mechanism of the DMI enhancement due to the MgO cap**, we first calculated the DMI at MgO/Co interface and found the DMI amplitude about 1.88 meV/atom (Fig. 4(a)). Next, we performed the comparative analysis of SOC energy difference between CW and ACW spin spirals for Co/Pt [black bars] and MgO/Co/Pt [red bars] shown in Fig. 4(c). Very interestingly, one can see that SOC energy source for DMI at Co/Pt interface is located within the interfacial Pt layer, in agreement with Fert-Levy mechanism for DMI at metallic interfaces33. At MgO/Co interface, however, both the DMI and its SOC energy source are localized within the interfacial Co layer indicating a different mechanism. Recently, it was proposed that the Rashba spin-orbit coupling at the interface between a ferromagnet and an oxide can lead to DMI. This additional interaction can be explained as induced by the Rashba effect45,46,47 and can be expressed as d = 2 kRA where A indicates the exchange stiffness, \({k}_{R}=\frac{2{\alpha }_{R}{m}_{e}}{{\hslash }^{2}}\) is determined by the Rashba coefficient, αR, and effective mass, me. The effective mass in Co was measured to be about 0.45 m048 and the exchange stiffness, A, could be between 15.5 and 30 × 10−12 J/m10,16,49. The Rashba coefficient, αR, can then be extracted from αR = 2E0/k0, where E0 is the Rashba splitting at the wave vector k0. We calculated the Rashba splitting for the MgO capped 3 ML of Co case by switching on SOC and putting the magnetization along \(\langle 110\rangle \) and \(\langle \bar{1}\bar{1}0\rangle \)50, as shown in Fig. 4(d,e) with black and red curves, respectively. We used the band around Fermi level at the \(\bar{{\rm{\Gamma }}}\) point, as shown in Fig. 4(e), to estimate the Rashba-type DMI, where the splitting, E0, is about 1.68 meV at k0 = 0.015 Å−1, which leads to a Rashba coefficient, αR, of 224 meV Å. Using this value, one obtains kR = 26.6 × 10−3 Å−1 which gives d being between 0.81 and 1.55 meV. This value is smaller than the DFT calculated DMI 1.88 meV, which can be ascribed to the fact that the Rashba-type DMI was calculated by using only one band close to Fermi level, whereas other bands further from Fermi level may also contribute to the total DMI.

Figure 4
figure 4

(a) Ab initio calculated DMI for microscopic, d, in Co/Pt (solid black squires) and MgO/Co/Pt (solid red balls) and MgO/Co (blue star) structures as a function of Co thickness. (b) Ab initio calculated micromagnetic DMI, D, in Co/Pt (empty black squires) and MgO/Co/Pt (empty red circles) as a function Co thickness. (c) spin-orbit coupling energy difference, ΔESOC, in Co/Pt (black bars) and MgO/Co/Pt (red bars) between clockwise and anticlockwise spin spirals. (d) Band structure for MgO capped 3 ML of Co when the magnetization is setting along \(\langle 110\rangle \) (black) and \(\langle \bar{1}\bar{1}0\rangle \) (red) when SOC is switched on. (e) Zoom in of the band structure around \(\bar{{\rm{\Gamma }}}\) point to calculate Rashba coefficient.

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Electric Field Control of DMI

Finally, we explore the possibility of electric field control of DMI in Oxide/FM/NM structures, or voltage-controlled DMI (VCDMI). Electric field control of interfacial magnetism has recently attracted a very large attention51,52,53,54, as it provides an additional degree of freedom to manipulate magnetization using gate electric field. While most studies adressed electric field controlled of PMA (VCMA), there is no first-principles study of electric field control of DMI even though it has been experimentally reported recently for the very small DMI case in MgO/Fe/Au multilayer with small DMI55. Here we study the effect of an electric field on the DMI in MgO/Co/Pt trilayers. We used 3 ML of Co structure to calculate DMI as a function of external electric field E (see Fig. 5). The electric field is applied perpendicularly to the plane of the interface with positive voltage pointing from insulator to metal. It is shown that both microscopic DMI d and micromagnetic D, are increasing approximately linearly as a function of E [Fig. 5]. Similarly to the electric field control of the PMA, the efficiency of the EF control of the DMI (or VCDMI efficiency) can be characterized by the slope of the curve β defined as a ratio of the DMI change to E, which is found to be equal to 26.02 fJ/(Vm). Interestingly, this parameter is comparable to the slope in electric field control of PMA for Fe(Co)/MgO structures54,55,56,57. This unveils the possibility of simultaneous tuning of both PMA and DMI within the same range using gate electric field suggesting a route towards an efficient way for controlling magnetic skyrmions since their size and stabilizy depend on both DMI and PMA.

Figure 5
figure 5

Microscopic and micromagetic DMI for MgO/Co/Pt structure shown in Fig. 4 as a function of electric field applied along normal orientation of the surface. Positive electric field means the electric field is applied from insulator to metal. The slope β is indicated for micromagetic DMI.

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Conclusion

In conclusion, we proposed three approaches for the efficient tuning of Dzyaloshinskii-Moriya interaction (DMI). The first one is to use NM/FM/Pt trilayers with inverse stacking of FM/Pt and FM/NM structures characterized by DMI with opposite chiralities. This allows the enhancement of DMI up to 50% as compared to the corresponding FM/Pt bilayers. Moreover, we demonstrated that in case of Ir/Fe/Co/Pt multilayers a giant DMI values up to 5.5 meV/atom can be achieved, which is almost twice of that for Co/Pt bilayers. The second approach is to cap Co/Pt structure with an oxidized layer, which can cause a dramatic DMI enhancement due to the Rashba type DMI. Finally, we demonstrated that DMI can be controlled by the application of an electric field in MgO/Co/Pt structure and showed that its efficiency is comparable to E-field control for PMA. These three very efficient approaches pave the way for engineering giant DMI for spintronic applications.