Dzyaloshinskii-Moriya Interaction Energy Research Articles

Unusual Dzyaloshinskii-Moriya Interaction in Graphene/Fe3GeTe2 Van der Waals Heterostructure.

Dzyaloshinskii-Moriya interaction (DMI) is shown to induce a topologically protected chiral spin texture in magnetic/nonmagnetic heterostructures. In the context of van der Waals spintronic devices, graphene emerges as an excellent candidate material. However, due to its negligible spin-orbit interaction, inducing DMI to stabilize topological spins when coupled to 3d-ferromagnets remains challenging. Here, it is demonstrated that, despite these challenges, a sizeable Rashba-type spin splitting followed by significant DMI is induced in graphene/Fe3GeTe2. This is made possible due to an interfacial electric field driven by charge asymmetry together with the broken inversion symmetry of the heterostructure. These findings reveal that the enhanced DMI energy parameter, resulting from a large effective electron mass in Fe3GeTe2, remarkably contributes to stabilizing non-collinear spins below the Curie temperature, overcoming the magnetic anisotropy energy. These results are supported by the topological Hall effect, which coexists with the non-trivial breakdown of Fermi liquid behavior, confirming the interplay between spins and non-trivial topology. This work paves the way toward the design and control of interface-driven skyrmion-based devices.

Helimagnet-based nonvolatile multi-bit memory units

In this Letter, we present a design of a helimagnet-based emerging memory device that is capable of storing multiple bits of information per device. The device consists of a helimagnet layer placed between two ferromagnetic layers, which allows us to lock-in specific spin configurations. The bottom pinned layer has high anisotropy energy or stays exchange biased, which keeps its spin configuration fixed on a specific direction, while the top layer is free to rotate under the influence of in-plane magnetic fields. We begin by finding the relaxed spin structure, which is the result of the competition between the Dzyaloshinskii–Moriya interaction (DMI) and exchange energy and is referred to as the equilibrium state (“0”). The writing of a memory state is simulated by applying an in-plane field that rotates and transforms the spin configurations of the memory device. Our results indicate that stable configurations can be achieved at rotations of an integer multiple of 180° (corresponding to states “−2,” “−1,” “1,” “2,” etc.), where the anisotropy stabilizes the free layer and, thus, the exchange coupled helimagnet. These states are separated by magnetic energy barriers and intermediate, unstable spin configurations tend to revert to their adjacent states. By simply changing the direction of the field, we can achieve multi-bit data storage per unit memory cell. The maximum number of bits is reached when the anisotropy energy barriers cannot withstand the strong DMI energy. Reading can be done by evaluating the different resistance states due to the twisted spin texture.

Electric field manipulation of spin chirality and skyrmion dynamic.

The Dzyaloshinskii-Moriya interaction (DMI) is an antisymmetric exchange interaction that stabilizes spin chirality. One scientific and technological challenge is understanding and controlling the interaction between spin chirality and electric field. In this study, we investigate an unconventional electric field effect on interfacial DMI, skyrmion helicity, and skyrmion dynamics in a system with broken inversion symmetry. We design heterostructures with a 3d-5d atomic orbital interface to demonstrate the gate bias control of the DMI energy and thus transform the DMI between opposite chiralities. Furthermore, we use this voltage-controlled DMI (VCDMI) to manipulate the skyrmion spin texture. As a result, a type of intermediate skyrmion with a unique helicity is created, and its motion can be controlled and made to go straight. Our work shows the effective control of spin chirality, skyrmion helicity, and skyrmion dynamics by VCDMI. It promotes the emerging field of voltage-controlled chiral interactions and voltage-controlled skyrmionics.

Local well-posedness of the Landau–Lifshitz equation with helicity term

We consider the initial value problem for the Landau–Lifshitz equation with a helicity term (chiral interaction term), which arises from the Dzyaloshinskii–Moriya interaction energy. We prove that it is well-posed locally in-time in the space k̄+Hs for s ≥ 3 with s∈Z and k̄=(0,0,1)t. We also show that if we further assume that the solution is homotopic to constant maps, then local well-posedness holds in the space k̄+Hs for s > 2 with s∈R. Our proof is based on two different approaches: One is the geometric energy method by McGahagan and the other is via the modified Schrödinger map equation. In the present analysis, we exploit a special structure of the helicity term, which enables us to overcome the difficulty in the quadratic derivative nonlinearity of the helicity term.

Magnon dynamics during phase transitions in FeRh by Brillouin light scattering

FeRh has been extensively studied because of metamagnetic phase transitions between the antiferromagnetic (AFM) and the ferromagnetic (FM) phase observed in this material. In this work, Brillouin light scattering is used to detect magnons in metamagnetic FeRh. Appearance and disappearance of magnon scattering peaks with variation of temperature illustrate the transformation of FeRh into the FM and AFM phases, respectively. The dependence of frequency on temperature indicates significant change thus characterizing metamagnetic phase transitions in FeRh, since the temperature dependence of the magnon frequency shift mainly follows the saturation magnetization temperature dependence. In addition, a considerable increase of full width at half maximum linewidth of the Stokes peak for FeRh is explained by the enhancement of magnetic damping. It is further found that the Dzyaloshinskii–Moriya interaction (DMI) takes place in single-layer FeRh with the DMI energy D affected by the first-order phase transitions in FeRh. These results provide an insight into the magnon dynamics in metamagnetic materials as well as offering new ways toward a modulation of magnetic damping in a wide range, which will be useful in the design of multifunctional spintronic devices.

Dzyaloshinskii–Moriya interaction determined from spin wave nonreciprocity and magnetic bubble asymmetry in Pt/Co/Ir/Co/Pt synthetic ferrimagnets

We present analysis of the effect of Dzyaloshinskii–Moriya interaction (DMI) on spin wave nonreciprocity and bubble expansion asymmetry in Pt/Co/Ir/Co/Pt synthetic ferrimagnets with perpendicular magnetic anisotropy. We propose analysis of the DMI by Brillouin light scattering technique (BLS) and Kerr microscopy (MOKE) in the presence of interlayer exchange coupling strongly changing spin wave dispersion law and field dependences of domain wall velocity in comparison with those observed earlier in Ir/Co/Pt structures with a single Co layer. We have determined DMI values of each Co layer from unusually inverted dependence of velocity of the domain wall on in-plane magnetic field. Opposite signs of effective fields and DMI fields in the two Co layers invert field dependence of the domain wall velocity. DMI energy determined from BLS is higher than values, determined by bubble expansion.

Modulations of interfacial magnetic properties using structurally inverted magnetic tri-layer systems: Toward skyrmion formation

Various magnetic properties such as the interfacial Dzyaloshinskii–Moriya interaction (DMI) and the perpendicular magnetic anisotropy (PMA) in structurally inverted Pd/Co/Pt and Pt/Co/Pd tri-layer stacks are systematically investigated by performing an inelastic light scattering method. Two examined individual multilayer structures are identical, but the stacking order is inverted for each other. Here, we demonstrate that the interfacial DMI energy densities and the saturation magnetization values for both systems are almost similar. However, the surface magnetic anisotropy energy densities of Pd/Co/Pt systems are dramatically decreased up to 34% compared with Pt/Co/Pd system, while the interfacial DMI is kept. Since a large interfacial DMI and a small PMA (or domain wall energy) are required to form magnetic skyrmion phases, the Pd/Co/Pt system can be one of the promising candidates. According to the thickness dependent measurements, we show a possibility of the existence of skyrmion phases in the Pd/Co/Pt system within a certain range of Co layer thickness at room temperature without external magnetic fields.

Dzyaloshinskii-Moriya interaction and chiral damping effect in symmetric epitaxial Pd/Co/Pd(111) trilayers

We investigate the creep of domain walls (DWs) in the combination of in-plane (IP) and out-of-plane magnetic fields in a series of epitaxial Cu(2 nm)/Pd(0--3 nm)/Co(0.7 nm)/Pd(3 nm) samples. Measured velocity curves, $v({H}_{x})$, are fitted with an extended dispersive elasticity model, which considers the dependence of both the elastic energy of the DWs and a velocity prefactor in the creep law on the IP magnetic field. The results of the calculations indicate that strong asymmetry in the $v({H}_{x})$ curves in the investigated system is primarily defined by the dependence of the velocity prefactor on the IP magnetic field, which may be related to a chiral damping effect. The effective energy of the Dzyaloshinskii-Moriya interaction (DMI) increases with increasing thickness of the Pd bottom layer from \ensuremath{-}0.16 \ifmmode\pm\else\textpm\fi{} 0.03 to $0.19\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}/{\mathrm{m}}^{2}$. We attribute the complex dependence of the effective DMI energy on the thickness of the Pd bottom layer in the epitaxial Pd/Co/Pd(111) system and the existence of the nonzero DMI in the symmetric Pd(3 nm)/Co(0.7 nm)/Pd(3 nm) samples to unequal strains in the bottom Pd/Co and top Co/Pd interfaces. The elastic strains in the interfaces varying depending on the thickness of the Pd bottom layer strongly influence the magnitude and even the sign of the contributions to the net DMI energy from each interface.

Thickness dependence of interfacial Dzyaloshinskii-Moriya interaction, magnetic anisotropy and spin waves damping in Pt/Co/Ir and Ir/Co/Pt trilayers

Asymmetric Ir/Co/Pt and Pt/Co/Ir trilayers with a wedged Co layer (Co thickness d = 0 ÷ 3.6 nm) were deposited by magnetron sputtering on naturally oxidized Si substrates with a Ta/Au buffer. Their magnetic properties have been investigated using magneto-optical polar Kerr effect and Brillouin light scattering (BLS) technique in the Damon-Eshbach geometry. The BLS measurements shows a frequency asymmetry between Stokes and anti-Stokes peaks position, exploited to determine interfacial Dzyaloshinskii-Moriya interaction energy density DS. DS was nearly two times larger for the Ir/Co/Pt trilayer than for the Pt/Co/Ir with opposite chirality. The effective uniaxial magnetic anisotropy and Ds depend non-monotonically on d with a maximum at d ≈ 1.2 nm. The asymmetry in linewidth for Stokes and anti-Stokes peaks is observed for both Ir/Co/Pt and Pt/Co/Ir trilayers for d < 1.6 nm, and it is increasing with decrease of Co thickness.

Measuring the Dzyaloshinskii-Moriya interaction of the epitaxial Co/Ir(111) interface

The in-plane orientation of the magnetization in the center of domain walls is measured in Co/Ir(111) as a function of Co thickness via scanning electron microscopy with polarization analysis. Uncapped, thermally evaporated cobalt on an Ir(111) single-crystal surface is imaged in situ in ultra-high vacuum. The initial pseudomorphic growth with an atomically flat interface of cobalt on iridium ensures comparability to theoretical calculations and provides a study of an interface that is as ideal as possible. Below a cobalt thickness of 8.8 monolayers, the magnetic domain walls are purely N\'eel oriented and show a clockwise sense of rotation. For larger thicknesses the plane of rotation changes and the domain walls show a significant Bloch-like contribution, allowing to calculate the strength of the Dzyaloshinskii-Moriya interaction (DMI) from energy minimization. From the angle between the plane of rotation and the domain-wall normal an interfacial DMI parameter $D_s = -(1.07 \pm 0.05)$ pJ/m is determined, which corresponds to a DMI energy per bond between two Co atoms at the interface of $d_{tot} = -(1.04 \pm 0.05)$ meV.

BPS soliton-impurity models and supersymmetry

We find supersymmetric extensions of the half-BPS soliton-impurity models in (1+1) dimensions which preserve half of the mathcal{N} = 1 supersymmetry. This is related to the fact that in the bosonic sector (i.e., the half-BPS soliton-impurity model), only one soliton (for example, the kink) is a BPS configuration which solves the pertinent Bogomolnyi equation and saturates the topological energy bound. On the other hand, the topological charge conjugate state (the antikink) is not a BPS solution. This means that it obeys the full Euler-Lagrange equation and does not saturate the topological energy bound. The supersymmetric approach also allows us to construct half-BPS soliton-impurity models in (2+1) dimensions. Concretely, in the case of the CP1 model, its BPS impurity generalisation preserves one-quarter of the mathcal{N} = 2 SUSY, while for the Abelian Higgs model at critical coupling both impurity generalisations preserving one-quarter (the case of a new, so-called Higgs impurity) as well as one-half of the mathcal{N} = 2 SUSY (the case of the previously known magnetic impurity) are possible. We also discuss a possible relation between the BPS CP1-impurity model and the Dzyaloshinskii-Moriya interaction energy.

Effect of Dzyaloshinskii–Moriya Interaction Energy Confinement on Current‐Driven Dynamics of Skyrmions

Magnetic skyrmions, which are topological spin configuration, have gained interest in the past few years. However, skyrmions suffer from the skyrmion Hall effect, a phenomenon where skyrmions deflect from the path of the electron flow and annihilate at the edge of the track. There are attempts to overcome this effect using synthetic antiferromagnetic layer structures and ferrimagnetic layer structures. Herein, a new approach based on introducing Dzyaloshinskii–Moriya interaction (DMI) energy wells is reported to direct the motion of skyrmions in a nanowire. It is shown through simulations that by creating DMI energy wells with a critical DMI value, a skyrmion moves within the boundaries set by the energy wells. It is also shown that the diameter of a skyrmion can be reduced by decreasing the space between the DMI energy wells. The proposed DMI energy well enables packing of skyrmion tracks at a high density. In this view, the effect of magnetostatic interactions between multiple skyrmions on their motion in parallel tracks is also investigated. Furthermore, the effect of changing the distance between skyrmions on magnetostatic interactions is studied. These results offer a new path toward maneuvering the skyrmion motion for racetrack memory or logic devices.

Edge effects on Dzyaloshinskii domain wall tilting

Abstract Interfacial Dzyaloshinskii-Moriya interaction (DMI) of a heavy metal (HM)/ferromagnetic (FM) metal heterostructure is vital to the current-induced fast domain wall motion. The tilting of the moving Dzyaloshinskii domian wall (DW) has been paid much attention. In this work, using the micromagnetic simulation, we find the DW tilting is originated from different initial DW velocity at two edges because of the initial antisymmetric magnetic structure at two edges. In the very early stage of DW motion, the DMI energy traps the DW motion at one edge. For a track whose width is smaller than a critical value, the edge effect plays a major role for DW tilting. This modifies the track width dependence of tilting angle and relaxation time derived from the collective coordinate method without considering edge effect. When the track is wide enough, a temporary vortex-like moment structure inside DW and variation of DW chirality at the edge appear in the process of generating DW tilting for reducing DMI and demagnetization energy.

An achiral ferromagnetic/chiral antiferromagnetic bilayer system leading to controllable size and density of skyrmions

Magnetic skyrmions are topologically protected domain structures related to the Dzyaloshinskii-Moriya interaction (DMI). To understand how magnetic skyrmions occur under different circumstances, we propose a model for skyrmion formation in a bilayer system of ferromagnetic/antiferromagnetic (FM/AFM) films, in which the bulk DMI is only present in the AFM film. Micromagnetic simulations reveal that skyrmions are formed in this system due to the competition between the DMI and demagnetization energies. A critical interfacial exchange energy (Ai = 6.5 mJ/m2) is determined, above which the competition occurs at its full extent. More skyrmions are formed with increasing external magnetic field till a critical value above which the external field is too large and thus leading to the annihilation of skyrmions. The spacing between two skyrmions can be as small as 45 nm. Our results may give technological implications for future skyrmion applications.

Electrical field enhanced interfacial Dzyaloshinskii-Moriya interaction in MgO/Fe/Pt system

We report electric field control of the interfacial Dzyaloshinskii-Moriya interaction (DMI) in MgO/Fe/Pt multilayers. The interfacial DMI is obtained and quantified by Brillouin light scattering measurements based on the frequency nonreciprocity of spin waves in a ferromagnet. The magnitude of the induced DMI is found to linearly increase as a function of electric field intensity. The efficiency of electric field control of the interfacial DMI characterized as a ratio of the DMI energy change to the electric field, which is found to be equal to 67 fJ/(Vm) with a positive electric field. We further demonstrate that the origin of the enhanced DMI results from the MgO/Fe interface. The Rashba spin-orbit coupling and electric field induced anisotropy at the MgO/Fe interface might be responsible for the enhanced interfacial DMI. Our findings open up a way for exploring the spintronic devices with a tunable DMI.

Robust emergence of a topological Hall effect in MnGa/heavy metal bilayers

We have investigated the topological Hall effect (THE) in MnGa/Pt and MnGa/Ta bilayers induced by interfacial Dzyaloshinskii-Moriya interaction (DMI). The most evident THE signals have been found based on the MnGa films with small critical DMI energy constant Dc. The large topological portion of the Hall signal from the total Hall signal has been extracted in the whole temperature range from 5 to 300 K. These results open up the exploration of the DMI induced magnetic behavior based on the bulk perpendicular magnetic anisotropy materials for fundamental physics and magnetic storage technologies.

Topological Hall effect in ferromagnetic/non-ferromagnetic metals heterojunctions

In a magnetic system, the spin orbit coupling can combine with the exchange interaction to generate an anisotropic exchange interaction that favors a chiral arrangement of the magnetization. This is known as the Dzyaloshinskii-Moriya interaction (DMI). Contrary to the Heisenberg exchange interaction, which leads to collinear alignment of lattice spins, the form of DMI is therefore very often to cant the spins by a small angle. If DMI is strong enough to compete with the Heisenberg exchange interaction and the magnetic anisotropy, it can stabilize chiral domain wall structure such as skyrmion. When a conduction electron passes through a chiral domain wall, the spin of the conduction electron will experience a fictitious magnetic field (Berry curvature) in real space, which deflects the conduction electrons perpendicular to the current direction. Therefore, it will cause an additional contribution to the observed Hall signal that is termed topological Hall effect (THE). The THE has attracted much attention since it is a promising tool for probing magnetic skyrmions. Recent extensive experiments have focused on the the THE in the ferromagnetic/non-ferromagnetic metal heterojunctions due to the inherent tunability of magnetic interactions in two dimensions. We firstly review the THE in ferromagnetic multilayers, in which the domain wall energy with interfacial DMI can be written as =4AK-D, where Dis the effective DMI energy constant, A the exchange constant, K the anisotropy constant. For the most favorable chirality, it lowers the energy. The limit of this situation is when goes to zero, which defines the critical DMI energy constant Dc=4AK/. Therefore, the domain wall energy would be negative and the chiral domain walls should proliferate if D Dc, and the methods that can modulate D and Dc to reduce have been explored. We have also reviewed the THE in MnGa/heavy metal bilayers. The largest THE signals have been found based on the MnGa films with smallest Dc, which correspondingly results in the smallest . The large topological portion of the Hall signal from the total Hall signal has been extracted in the whole temperature range from 5 to 300 K and the magnitude of fictitious magnetic field has been determined.

Insight into the Dzyaloshinskii-Moriya interaction through first-principles study of chiral magnetic structures

This work advances a physical picture of the Dzyaloshinskii-Moriya interaction (DMI), capable of addressing the apparently contradicting conclusions of recent studies about the location of the DMI energy in the real and reciprocal space as well as about the relation between the values of atomic moments and DMI strength. It is demonstrated on the example of a Co/Pt bilayer how DMI emerges from the chirality-dependent hybridization of the Co and Pt magnetic-spiral states under the influence of spin-orbit coupling and broken spatial inversion.

Magnetic droplet nucleation with a homochiral Néel domain wall

We investigate the effect of the Dzyaloshinskii Moriya interaction (DMI) on magnetic domain nucleation in a ferromagnetic thin film with perpendicular magnetic anisotropy. We propose an extended droplet model to determine the nucleation field as a function of the in-plane field. The model can explain the experimentally observed nucleation in a CoNi microstrip with the interfacial DMI. The results are also reproduced by micromagnetic simulation based on the string model. The electrical measurement method proposed in this study can be widely used to quantitatively determine the DMI energy density.

Spin-Orbit-Torque Efficiency in Compensated Ferrimagnetic Cobalt-Terbium Alloys

Despite the potential advantages of information storage in antiferromagnetically coupled materials, it remains unclear whether one can control the magnetic moment orientation efficiently because of the cancelled magnetic moment. Here, we report spin-orbit torque induced magnetization switching of ferrimagnetic Co1-xTbx films with perpendicular magnetic anisotropy. Current induced switching is demonstrated in all of the studied film compositions, including those near the magnetization compensation point. The spin-orbit torque induced effective field is further quantified in the domain wall motion regime. A divergent behavior that scales with the inverse of magnetic moment is confirmed close to the compensation point, which is consistent with angular momentum conservation. Moreover, we also quantify the Dzyaloshinskii-Moriya interaction energy in the Ta/Co1-xTbx system and we find that the energy density increases as a function of the Tb concentration. The demonstrated spin-orbit torque switching, in combination with the fast magnetic dynamics and minimal net magnetization of ferrimagnetic alloys, promises spintronic devices that are faster and with higher density than traditional ferromagnetic systems.