Measurement of the Dzyaloshinskii–Moriya Interaction in Mn4N Films That Host Skyrmions

Mn4N thin film is one of the potential magnetic mediums for spintronic devices due to its ferrimagnetism with low magnetization, large perpendicular magnetic anisotropy (PMA), thermal stability, and large domain wall velocity. Recent experiments confirmed the existence of tunable magnetic skyrmions in MgO/Mn4N/CuxPt1−x(x = 0, 0.5, 0.9, 0.95), and density functional theory (DFT) calculation provided a large theoretical value of the interfacial Dzyaloshinskii–Moriya interaction (iDMI) of Mn4N/Pt, which is consistent with the predicted chemical trend of the DMI in transition metal/Pt films. So far, the measured DMI has not been reported in Mn4N, which is needed in order to support the predicted large DMI value. This paper reports the average DMI of MgO/Mn4N(17 nm)/CuxPt1−x(3 nm) extracted from the anomalous Hall effect with various tilted angles, which is based on magnetic droplet theory with DMI effects. The DMI decreases from 0.267 mJ/m2 to 0.011 mJ/m2 with non-linear tendencies as Cu concentration in the CuxPt1−x capping layer increases from 0 to 1, demonstrating the control of the DMI through the CuxPt1−x capping layer. Furthermore, a solid solution model is developed based on an X-ray photoelectron spectroscopy (XPS) compositional depth profile to analyze the possible effects on the DMI from the mixing layers at the surface of Mn4N. After taking into account the mixing layers, the large DMI in Mn4N film with Pt capping is consistent with the predicted DMI.


Introduction
As information technologies keep developing, the demand for faster processing and highdensity data storage is increasing [1,2]. A spintronics device, which utilizes and manipulates the spin degrees of freedom in materials, is a promising candidate for next-generation energyefficient electronic devices with high-speed operation and ample data storage [1][2][3][4][5]. In a spintronic device, the magnetic medium is the critical component that determines the device's performance [2][3][4][5]. Ferrimagnetic systems with two antiparallelly coupled spin sublattices have drawn increasing attention for two reasons. The first reason is that ferrimagnetic materials have faster switching processes than ferromagnetic materials [6,7]. The other reason is the high-speed current-induced magnetic domain-wall motion in ferrimagnets [8][9][10].
Among numerous ferrimagnetic materials, anti-perovskite Mn 4 N thin films with a Curie temperature of 710K have attracted more investigations recently [11,12]. Figure 1 shows a schematic diagram of the Mn 4 N crystal structure with spins. The spins of Mn I atoms (3.47 µ B ), which sit at the corners, are ferromagnetically coupled with the spins of Mn IIa atoms (0.75 µ B ), which sit at the face center of the top and bottom surfaces in the unit cell. The spins of Mn I and Mn IIb atoms (−2.36 µ B ), which sit at the face center of side surfaces in the unit cell, are anti-ferromagnetically coupled [13]. It has been reported that the epitaxial Mn 4 N thin films grown on various substrates, such as MgO(001), STO(001), LaAlO 3 (001), and LSTO(001) [10,[13][14][15][16][17][18][19], exhibit perpendicular magnetic anisotropy (PMA), which is essential for some spintronic devices. The magnetization of Mn 4 N thin films is tunable by doping Ni (Mn 4−x Ni x N) or Co (Mn 4−x Co x N), and magnetic compensation (zero net magnetization) can be achieved with suitable Ni or Co composition [20][21][22]. More importantly, compared to ferrimagnetic rare-earth transition metal amorphous thin films, the Mn 4 N thin films have better thermal stability because Mn 4 N films are deposited at 400-450 • C, and no structural transition or loss of PMA has been reported after annealing and cooling processes. Furthermore, experiments have reported high domain wall velocity(~1 km/s) [10,23], high spin polarization (0.8) [22], and magnetic skyrmions in Mn 4 N [23], which indicates that the Mn 4 N thin film is a potential material for spintronic devices, such as racetrack memory and skyrmion-based magnetic tunnel junctions [24,25]. Additionally, the skyrmions' diameter in MgO(001)/Mn 4 N/Cu x Pt 1−x can be tuned by changing the composition of the capping layer, which would vary the interfacial Dzyaloshinskii-Moriya interaction (iDMI) [23].
at 400-450 °C, and no structural transition or ing and cooling processes. Furthermore, expe locity(~1 km/s) [10,23], high spin polarization [23], which indicates that the Mn4N thin film such as racetrack memory and skyrmion-bas tionally, the skyrmions' diameter in MgO(00 the composition of the capping layer, which Moriya interaction (iDMI) [23]. The iDMI is an antisymmetric exchange ments of neighboring spins [26,27]. It arises fr interfaces with broken inversion symmetry. in recent years, is one of the crucial interactio plications [27]. For example, the iDMI is vital magnetic textures, such as Néel magnetic s which are candidates to serve as building blo of DMI and spin-orbit torque (SOT) provide free current-induced switching of perpendic energy and high-speed calculations [28,29]. The iDMI is an antisymmetric exchange interaction that favors the noncolinear alignments of neighboring spins [26,27]. It arises from the spin-orbit coupling at magnetic layer interfaces with broken inversion symmetry. The iDMI, which has attracted great interest in recent years, is one of the crucial interactions to develop new promising spintronic applications [27]. For example, the iDMI is vital in stabilizing topologically non-trivial chiral magnetic textures, such as Néel magnetic skyrmions and chiral domain walls [3,4,26], which are candidates to serve as building blocks in data storage. In addition, the interplay of DMI and spin-orbit torque (SOT) provides a fast and power-saving method of field-free current-induced switching of perpendicular magnetization, which is critical in low-energy and high-speed calculations [28,29].
It has been predicted by first-principle calculations that, at the interface of 3D transition metals (TMs) (V, Cr, Mn, Fe, Co, Ni) and 5D heavy metals (HMs) (W, Re, Os, Ir, Pt), the 3D orbit occupation of TMs serves an important role in the strength of the DMI. The Mn element has the largest DMI due to its half-filled 3D band [30]. While many DMI measurements have been applied to often studied Co and Co-based films with HM interface [31][32][33][34][35][36][37][38][39], no measured DMI of Mn or Mn-based magnetic films has been reported to support the systematic trend of increasing the iDMI. Additionally, density functional theory (DFT) has predicted a large iDMI at the Mn 4 N/Pt interface, where DMI is only considered between the Mn nearest neighbors (Mn I and Mn IIa atoms) at the Mn 4 N/Pt interface [23]. Thus, the experimental DMI in Mn 4 N is necessary to confirm the calculations and comprehensively explore the material for applications. Kim et al. developed a method, based on magnetic droplet theory with the DMI effect, to extract the average DMI from in-plane field dependence of the out-of-plane nucleation field for a reversed domain. This method can be completed with a magnetoresistance measurement setup or a magnetooptical Kerr effect (MOKE) microscope [40]. Here, to confirm the calculated large Mn 4 N DMI and comprehensively explore the material for spintronic applications, the DMI of MgO/Mn 4 N(17 nm)/Cu x Pt 1−x (x = 0, 0.5, 0.9, 1) is determined by extracting the effective field of the DMI from the angular dependence anomalous Hall effect. The average DMI of the MgO/Mn 4 N/Cu x Pt 1−x decreases non-linearly from 0.267 mJ/m 2 to 0.011 mJ/m 2 as Cu concentration increases from 0 to 1. Furthermore, MgO/Mn 4 N(17 nm)/Pt has a larger interfacial DMI constant (Ds) than MgO/Co(0.5-1.2 nm)/Pt film [31][32][33][34][35][36][37][38][39], where Ds is the product of the average DMI and the thickness of the magnetic layer. The larger Ds of MgO/Mn 4 N/Pt is consistent with the DMI trend calculated by A. Belabbes et al. [30]. Moreover, the possible effect on the DMI of the mixing layer at the surface of Mn 4 N is discussed. The multilayers are divided into tens of sublayers using a compositional gradient. The composition of each sublayer is estimated by X-ray photoelectron spectroscopy (XPS). A solid solution model is used to calculate the average DMI of MgO/Mn 4 N(17 nm)/Cu x Pt 1−x , which incorporates the effect from the mixing layers at the surfaces of Mn 4 N layers.

Materials and Methods
Seventeen-nm-thick Mn 4 N thin films were deposited on the MgO(001) 5 × 5 × 0.5 mm substrate by reactive radio frequency (rf) sputtering at 450 • C. The MgO substrates were wetcleaned and heat-treated ex situ. The base pressure was 5 × 10 −8 Torr and the deposition pressure was 1 × 10 −3 Torr. The flow rates ratio of Ar and N 2 gases was maintained at a flow rate ratio of 93:7. Three-nm-thick capping layers of Cu x Pt 1−x (where x = 1, 0.5, 0.1, 0) were deposited on the Mn 4 N layer at room temperature by co-sputtering Pt and Cu targets to tune the DMI. Then, a 3 nm-thick Pt layer is deposited on top to prevent oxidation. The structure of the films is shown in Figure 2a. Details of the deposition process and cleaning MgO substrates were reported in a previous work [18]. The composition of the capping layers was calibrated with 10 nm-thick Cu x Pt 1−x films on MgO(100) substrates using PHI VersaProbe III X-ray photoelectron spectroscopy (XPS). The out-of-plane and in-plane magnetic hysteresis loops of each sample were measured at 300 K by a Quantum Design VersaLab III vibrating sample magnetometer (VSM). The Mn 4 N films were patterned into a 5 µm-wide Hall cross-structure by photolithography and an Ar ion milling technique. A 100 nm-thick Pt layer was deposited on the patterned samples as contact pads for anomalous Hall effect (AHE) measurements.
We measured the average DMI using the method proposed by Kim et al., which is based on the magnetic droplet nucleation model [40]. The schematic of the measurement setup is shown in Figure 2b. The angular-dependent coercivity field H c of the Mn 4 N Hall cross-structure was measured. By definition, the perpendicular component (H z ) and in-plane component (H x ) of H c are given by H z ≡ H c cosθ and H x ≡ H c sinθ, where θ is the angle between the external magnetic field (H) and the normal sample. θ varied from 0 • to 65 • in this experiment. The external magnetic field was swept within ± 2 T at each angle to observe the coercivity field H c . Figure 2d shows normalized anomalous Hall effect loops of MgO/Mn 4 N/Pt with different tilted angles θ. With the DMI, there is a threshold point in the H z 1/2 vs. the H x curve, where H z 1/2 begins to decrease linearly with increasing H x . This threshold point corresponds to the effective magnetic field induced by DMI(H DMI ).
XPS measurements were performed to obtain the compositional depth profile using the PHI VersaProbe III XPS instrument. XPS data were collected after sputtering off a few layers from the surface. Each sputtering lasted 15 s, and the total sputtering time was 10 min. The analysis method followed the method in [41]. magnetic hysteresis loops of each sample were measured at 300 K by a Quantum Design VersaLab III vibrating sample magnetometer (VSM). The Mn4N films were patterned into a 5 µm-wide Hall cross-structure by photolithography and an Ar ion milling technique. A 100 nm-thick Pt layer was deposited on the patterned samples as contact pads for anomalous Hall effect (AHE) measurements.    [24]. This agrees with the intuition that smaller DMI produces smaller skyrmions [24]. The DMIs of different capping layers are calculated based on the following equation:

DMI Measurement
where A is the exchange stiffness, K eff is the effective perpendicular magnetic anisotropy energy, and M s is the saturation magnetization.  Figure 3e. The errors in the measured DMI mostly come from the uncertainties of the tilted angle and fitting. As Cu concentration rises, the DMI decreases from 0.267 ± 0.065 mJ/m 2 to 0.011 ± 0.01 mJ/m 2 . This decrease in DMI can be explained by two reasons. First, the addition of Cu diluted the concentration of Pt, which reduced the large iDMI at the interface of Pt/Mn 4 N. Second, the iDMI at the Cu/Mn 4 N interface is small and has the opposite sign of the iDMI at the Pt/Mn 4 N interface. This would further decrease the iDMI as Cu concentration increases. We note that the decrease in the DMI is not linear as a function of Cu composition x. When x increases from 0 to 0.5, the DMI decreases from 0.267 ± 0.065 mJ/m 2 to 0.224 ± 0.053 mJ/m 2 . Compared to the large change in the CuPt capping layer composition, the change in the DMI is small and the difference is within the measurement error. This indicates that when the Cu concentration is smaller than 0.5, the DMI is almost insensitive to the change in Cu concentration. When x further increases to 0.9, the DMI decreases to 0.115 ± 0.041 mJ/m 2 , which is about half of the DMI when x is 0.5. When it is pure Cu capping (x = 1), the DMI decreases more to near zero. Since a small amount of Pt in the capping layer can provide a large DMI, it indicates that the DMI is more sensitive to the Pt concentration than the Cu concentration. This can be explained by the larger spin-orbit coupling (SOC) between Pt and Mn than the SOC between Cu and Mn [23,42]. The non-linear composition dependence of the DMI has also been reported in Pt/CoGd/W x Pt 1−x [43]. Since DMIs in these thin films are interfacial effects originating from the interface, the measured DMIs decrease with thicker magnetic layers. To compare the DMI with other materials that have different thicknesses, we use the interfacial DMI constant Ds, where Ds is the average DMI multiplied by the magnetic layer thickness(t m ). The result is shown in Figure 3f in the capping layer can provide a large DMI, it indicates that the DMI is more sensitive to the Pt concentration than the Cu concentration. This can be explained by the larger spin-orbit coupling (SOC) between Pt and Mn than the SOC between Cu and Mn [23,42]. The non-linear composition dependence of the DMI has also been reported in Pt/CoGd/WxPt1−x [43]. Since DMIs in these thin films are interfacial effects originating from the interface, the measured DMIs decrease with thicker magnetic layers. To compare the DMI with other materials that have different thicknesses, we use the interfacial DMI constant Ds, where Ds is the average DMI multiplied by the magnetic layer thickness(tm). The result is shown in Figure 3f; the Mn4N data point is from our measurement of MgO/Mn4N/Pt and the Co data point is the average of several reported Ds in the Co single layer with different thicknesses sandwiched by MgO and Pt, where the error bar is the standard deviation [31][32][33][34][35][36][37][38][39]. The Ds of MgO/Mn4N/Pt is about twice the Ds of MgO/Co/Pt, which is consistent with the chemical trend of the DMI in transition metals from firstprinciple calculations [30]. The measured DMI of MgO/Mn4N/Pt (0.267 mJ/m 2 ) is one magnitude smaller than the DFT-predicted iDMI of Mn4N/Pt (6.969 m J/m 2 ) [23]. The reason is that the calculated iDMI is based on Mn4N [23] or Mn [33] ultrathin films, while our measurement was performed on a 17 nm-thick film. The DMI we measured is the average DMI over the film. As The measured DMI of MgO/Mn4N/Pt (0.267 mJ/m 2 ) is one magnitude smaller than the DFT-predicted iDMI of Mn 4 N/Pt (6.969 m J/m 2 ) [23]. The reason is that the calculated iDMI is based on Mn 4 N [23] or Mn [33] ultrathin films, while our measurement was performed on a 17 nm-thick film. The DMI we measured is the average DMI over the film. As mentioned previously, since the predicted iDMI is an interfacial effect and decays away from the surface, the average DMI decreases significantly as the thickness increases and is much smaller than the predicted iDMI. To further investigate the relationship between our measured DMI and predicted DMI, we conducted a detailed comparison of the DMIs. In Figure 3e, the red dots correspond to the average DMI (D average ) in MgO/Mn 4 N/Pt and MgO/Mn 4 N/Cu obtained from DFT calculations [23].
where D(t) is the DMI distribution function, which describes the exponentially decaying iDMI from the surface [44]. D 0 is the iDMI at the surface from the DFT [23], as shown in Table 1, and t is the distance from the surface in nm. As seen in Figure 3e, there is a clear discrepancy between the calculated DMI and the experimental DMI. One of the possible reasons is the presence of the mixing layers at the Mn 4 N interfaces. In the DFT, the interface between two layers is assumed to be an ideal surface, which means that there are no atomic mixings. However, XPS and polarized neutron reflectometry (PNR) found that the interfaces of Mn 4 N/Pt and MgO/Mn 4 N are not ideal [41]. There are 3-4 nm of mixing layers present at the interfaces, including some MnO at the surface of Mn 4 N. These mixing layers at the interface decrease the accuracy of the iDMI from the DFT calculation, which can explain the discrepancy between the predicted DMI and the measured DMI.

Mixing Layer Effect on the DMI
To investigate the possible effect of the mixing layers on the DMI, a solid solution model is built. In this model, the multilayer is divided into tens of sublayers with a thickness of 0.4 nm, as shown in Figure 4. The composition of each sublayer is estimated by XPS data using the method by Ma et al. [43]. There are two assumptions in this model. First, the DMI between the two sublayers is originated from the interactions between Cu, Pt, and Mg in one layer (L n ) and Mn atoms the other layer (L n ). This means that the DMI is proportional to the concentration of Pt(y n ) in layer L n and the concentration of Mn(z n ) of L n . It is the same for the DMI between Cu and Mn, or Mg and Mn. Second, the DMI from one sublayer L n decays exponentially from the surface of layer L n , which is given by Equation (2).
The total DMI from Pt acting on a sublayer L n (DMI Pt−L n ) is the sum of the DMI of Pt from all over other sublayers: DMI Pt−L n = ∑ n ,n =n z n * y n * D n,n S n,n S n,n = 1, t n < t n −1, t n < t n (6) where D 0−Pt/Mn4N is the calculated DMI at the Pt/Mn 4 N interface [24], as shown in Table 1, and S n,n is a function that assigns the direction of the DMI. The DMI from the Pt atoms under the layer L n (t n < t n ) has an opposite sign compared to the DMI from the Pt atoms above the layer L n (t n < t n ). The total average DMI from Pt (DMI Pt ) is the sum from all layers, n: where T is the total thickness of the samples. The same method was used to calculate the total average DMI from Cu (DMI Cu ) and Mg (DMI Mg ). The total DMI ( DMI tot ) in the film is given in Equation (7) as the sum of the DMI from Pt, Cu, and Mg. where D(t) is the DMI distribution function, which describes the exponentially decaying iDMI from the surface [44]. D0 is the iDMI at the surface from the DFT [23], as shown in Table 1, and t is the distance from the surface in nm. As seen in Figure 3e, there is a clear discrepancy between the calculated DMI and the experimental DMI. One of the possible reasons is the presence of the mixing layers at the Mn4N interfaces. In the DFT, the interface between two layers is assumed to be an ideal surface, which means that there are no atomic mixings. However, XPS and polarized neutron reflectometry (PNR) found that the interfaces of Mn4N/Pt and MgO/Mn4N are not ideal [41]. There are 3-4 nm of mixing layers present at the interfaces, including some MnO at the surface of Mn4N. These mixing layers at the interface decrease the accuracy of the iDMI from the DFT calculation, which can explain the discrepancy between the predicted DMI and the measured DMI.

Mixing Layer Effect on the DMI
To investigate the possible effect of the mixing layers on the DMI, a solid solution model is built. In this model, the multilayer is divided into tens of sublayers with a thickness of 0.4 nm, as shown in Figure 4. The composition of each sublayer is estimated by XPS data using the method by Ma et al. [43]. There are two assumptions in this model. First, the DMI between the two sublayers is originated from the interactions between Cu, Pt, and Mg in one layer ( )and Mn atoms the other layer ( ). This means that the DMI is proportional to the concentration of Pt( ) in layer and the concentration of Mn( ) of . It is the same for the DMI between Cu and Mn, or Mg and Mn. Second, the DMI from one sublayer decays exponentially from the surface of layer , which is given by Equation (2).
. | | deposition and CuPt deposition, and the MnO at the surface of Mn4N/MgO is due to the oxygen diffusion from the MgO substrate to the Mn4N layer [41]. Using the compositional depth profile in Figure 5a-d, the average DMIs of MgO/Mn4N/CuxPt1−x were estimated by the solid solution model. Figure 5e shows the comparison between the calculated DMI using the solid solution model and the measured DMI. The calculated DMIs, which are indicated by the green triangles, are in agreement with the measured DMIs, indicated by black squares.

Conclusions
The Dzyaloshinskii-Moriya interactions (DMIs) of MgO/Mn 4 N/Cu x Pt 1−x multilayers were measured by extracting H DMI from the angular dependence of the coercivity field based on the magnetic droplet nucleation model. The compositional dependence of the DMI is non-linear in Cu concentrations. The interfacial DMI constant D s of MgO/Mn 4 N/Pt is larger than that of MgO/Co/Pt, which is consistent with the chemical trend of the DMI among the transition metals. To study the effect of mixing layers on the DMI, a simple solid solution model with the mixing layers effect is built, based on the X-ray photoelectron spectroscopy (XPS) measurement, and the average DMI from this model is in good agreement with the measured DMI. Our experimental results provide a promising approach to control the DMI in Mn 4 N-based thin films, with implications in achieving small skyrmion and enabling future spintronics technologies. Our results also provide a method to connect the density functional theory (DFT), calculated DMI, and measured DMI.

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