We studied electric field modification of magnetic properties in a Pt/Co/AlO$_x$ trilayer via magneto-optical Kerr microscopy. We observed the spontaneous formation of labyrinthine magnetic domain structure due to thermally activated domain nucleation and propagation under zero applied magnetic field. A variation of the period of the labyrinthine structure under electric field is observed as well as saturation magnetization and magnetic anisotropy variations. Using an analytical formula of the stripe equilibrium width we estimate the variation of the interfacial Dzyaloshinskii-Moriya interaction under electric field as function of the exchange stiffness constant.
The Dzyaloshinskii-Moriya interaction in ultrathin ferromagnets can result in nonreciprocal propagation of spin waves. We examine theoretically how spin wave power flow is influenced by this interaction. We show that the combination of the dipole-dipole and Dzyaloshinskii-Moriya interactions can result in unidirectional caustic beams in the Damon-Eshbach geometry. Morever, self-generated interface patterns can also be induced from a point-source excitation.
We theoretically investigate spin-wave propagation through a magnetic metamaterial with spatially modulated Dzyaloshinskii-Moriya interaction. We establish an effective Sch{ö}dinger equation for spin-waves and derive boundary conditions for spin-waves passing through the boundary between two regions having different Dzyaloshinskii-Moriya interactions. Based on these boundary conditions, we find that the spin-wave can be amplified at the boundary and the spin-wave bandgap is tunable either by an external magnetic field or the strength of Dzyaloshinskii-Moriya interaction, which offers a spin-wa…
Using symmetry analysis and density functional theory calculations, we uncover the nature of Dzyaloshinskii-Moriya interaction in Fe$_3$GeTe$_2$ monolayer. We show that while such an interaction might result in small distortion of the magnetic texture on the short range, on the longrange Dzyaloshinskii-Moriya interaction favors in-plane Néel spin-spirals along equivalent directions of the crystal structure. Whereas our results show that the observed Néel skyrmions cannot be explained by the Dzyaloshinskii-Moriya interaction at the monolayer level, they suggest that canted magnetic texture shal…
The determination of the interfacial Dzyaloshinskii-Moriya interaction for perpendicularly magnetized thin layered films is not trivial and therefore needs some experimental efforts to determine its sign and magnitude, especially in the exchange biased system. Here, we developed a method proposed by D.-S. Han et al. [Nano Lett. 16, (2016) 4438], which opens a way to investigate this interaction using a conventional PMOKE magnetometer, also in exchange biased systems. Using our approach we demonstrated that the Au/Co/NiO layered system has a strong negative Dzyaloshinskii-Moriya interaction, wh…
For a thin ferromagnetic film with the Dzyaloshinskii-Moriya interaction (DMI), we derive an expression of the extrinsic ferromagnetic resonance (FMR) linewidth in a quantum mechanical way, taking into account scatterings from structural inhomogeneity. In the presence of the DMI, the magnon dispersion exhibits rich resonant states, especially in small external magnetic fields and strong DMI strength. It is found that the FMR linewidth shows several characteristic features such as a finite linewidth at zero frequency and peaks in the low frequency range.
We investigate the effect of inhomogeneous Dzyaloshinskii-Moriya interaction (DMI) on antiferromagnetic spin-wave propagation theoretically and numerically. We find that antiferromagnetic spin waves can be amplified at a boundary where the DMI varies. The inhomogeneous DMI also provides a way to construct a magnonic crystal with forbidden and allowed antiferromagnetic spin-wave bands in terahertz frequency ranges. In contrast to ferromagnetic spin waves, antiferromagnetic spin waves experience a polarization-dependent phase shift when passing through the inhomogeneous DMI, offering a magnonic …
The microscopic origin of the electric Dzyaloshinskii-Moriya interaction (eDMI) is unveiled and discussed by analytical analysis and first-principles based calculations. As similar to the magnetic Dzyaloshinskii-Moriya interaction (mDMI), eDMI also originates from electron-mediated effect and more specifically from certain electron hoppings that are being activated due to certain local inversion symmetry breaking. However, the eDMI energy is found to be at least a third-order interaction in atomic displacements instead of bilinear in magnetic dipole moments for mDMI. Furthermore, the eDMI ener…
An new and accurate scheme to calculate the interatomic Dzyaloshinskii-Moriya interaction (DMI) parameters is presented, which is based on the fully relativistic Korringa-Kohn-Rostoker Green function (KKR-GF) technique. Corresponding numerical results are compared with those obtained using other schemes reported in the literature. The differences found can be attributed primarily to the different reference states used in the various approaches. In addition an expression for the DMI parameters formulated for a micromagnetic model Hamiltonian is presented that provides a connection to the DMI pa…
Brillouin light spectroscopy is a powerful and robust technique for measuring the interfacial Dzyaloshinskii-Moriya interaction in thin films with broken inversion symmetry. Here we show that the magnon visibility, i.e. the intensity of the inelastically scattered light, strongly depends on the thickness of the dielectric seed material - SiO$_2$. By using both, analytical thin-film optics and numerical calculations, we reproduce the experimental data. We therefore provide a guideline for the maximization of the signal by adapting the substrate properties to the geometry of the measurement. Suc…
In contrast to conventional assumptions, we show that the Dzyaloshinskii-Moriya interaction can be of non-relativistic origin, in particular in materials with a non-collinear magnetic configuration, where non-relativistic contributions can dominate over spin-orbit effects. The weak antiferromagnetic phase of Mn$_{3}$Sn is used to illustrate these findings. Using electronic structure theory as a conceptual platform, all relevant exchange interactions are derived for a general, non-collinear magnetic state. It is demonstrated that non-collinearity influences all three types of exchange interacti…
The Dzyaloshinskii Moriya interaction (DMI) generates intriguing chiral magnetic objects such as magnetic skyrmions and chiral domain walls that can be used as building blocks in emerging magnetic nanodevices. To achieve better stability and functionality of these chiral objects, it is essential to achieve a larger DMI. In this paper, we report an experimental observation that in magnetic trilayer films, the DMI strength is mainly determined by the work functions of the nonmagnetic layers interfaced with the magnetic layer. The clear correlation with the intrinsic material parameters provides …
The interfacial Dzyaloshinskii Moriya Interaction (DMI) in ultrathin magnetic thin film heterostructures provides a new approach for controlling spin textures on mesoscopic length scales. Here we investigate the dependence of the interfacial DMI constant D on a Pt wedge insertion layer in Ta_CoFeB_Pt(wedge)_MgO thin films by observing the asymmetric spin wave dispersion using Brillouin light scattering. Continuous tuning of D by more than a factor of three is realized by inserting less than one monolayer of Pt. The observations provide new insights for designing magnetic thin film heterostruct…
The Dzyaloshinskii-Moriya interaction (DMI), which is essential for the stabilization of topologically non-trivial chiral magnetic textures such as skyrmions, is particularly strong in heterostructures of ultra-thin magnetic materials and heavy elements. We explore by density-functional theory calculations the possibility to modify the magnetic properties at Co/Pt interfaces with chemical disorder. In these systems, we find a particular robustness of the DMI against intermixing. Upon dusting the interface with a third element (all $4d$ transition metals and B, Cu, Au and Bi), a strong reductio…
The interface between a ferromagnet (FM) or antiferromagnet (AFM) and a heavy metal (HM) results in an antisymmetric exchange interaction known as the interfacial Dzyaloshinskii-Moriya interaction (iDMI) which favors non-collinear spin configurations. The iDMI is responsible for stabilizing noncollinear spin textures such as skyrmions in materials with bulk inversion symmetry. Interfacial DMI values have been previously determined theoretically and experimentally for FM/HM interfaces, and, in this work, values are calculated for the metallic AFM MnPt and the insulating AFM NiO. The heavy metal…
The rich interaction phenomena at antiferromagnet (AFM)/ ferromagnet (FM) interfaces are key ingredients in AFM spintronics, where many underlying mechanisms remain unclear. Here we report a correlation observed between interfacial Dzyaloshinskii-Moriya interaction (DMI) Ds and effective spin mixing conductance g at IrMn/CoFeB interface. Both Ds and g are quantitatively determined with Brillouin light scattering measurements, and increase with IrMn thickness in the range of 2.5~7.5 nm. Such correlation likely originates from the AFM-states-mediated spin-flip transitions in FM, which promote bo…
Chiral magnets are of fundamental interest and have important technological ramifications. The origin of chiral magnets lies in the Dzyaloshinskii-Moriya interaction (DMI), an interaction whose experimental and theoretical determination is laborious. We derive an expression that identifies the electric dipole moment as descriptor for the systematic design of chiral magnetic multilayers. Using density functional theory calculations, we determine the DMI of (111)-oriented metallic ferromagnetic $Z$/Co/Pt multilayers of ultrathin films. The non-magnetic layer $Z$ determines the DMI at the Co-Pt i…
Ruderman-Kittel-Kasuya-Yosida interaction even if their wave functions lack direct overlap. Theory predicts that spin-orbit scattering leads to a Dzyaloshinskii-Moriya type enhancement of this indirect exchange interaction, giving rise to chiral exchange terms. Here we present a combined spin-polarized scanning tunneling microscopy, angle-resolved photoemission, and density functional theory study of MnO$_2$ chains on Ir(100). Whereas we find antiferromagnetic Mn--Mn coupling along the chain, the inter-chain coupling across the non-magnetic Ir substrate turns out to be chiral with a $120^{\cir…
We report on the Dzyaloshinskii-Moriya (DMI) interaction at the interface between a ferromagnet and an oxide. We demonstrate experimentally that oxides can give rise to DMI. By comparison of systems comprised of Pt/Co90Fe10/Oxide and Cu/Co90Fe10/Oxide, we also show how oxidation of one interface can enhance and add to the total DMI of that generated by the Pt interface. This is due to the fact that the DMI on both interfaces promotes left-handed chirality. Finally, by use of ferromagnetic resonance spectroscopy, we show that the DMI and the spectroscopic splitting factor, which is a measure of…
The antiferromagnet (AFM) / ferromagnet (FM) interfaces are of central importance in recently developed pure electric or ultrafast control of FM spins, where the underlying mechanisms remain unresolved. Here we report the direct observation of Dzyaloshinskii Moriya interaction (DMI) across the AFM/FM interface of IrMn/CoFeB thin films. The interfacial DMI is quantitatively measured from the asymmetric spin wave dispersion in the FM layer using Brillouin light scattering. The DMI strength is enhanced by a factor of 7 with increasing IrMn layer thickness in the range of 1- 7.5 nm. Our findings p…
Dzyaloshinskii-Moriya interactions and magnetic texture in the Fe films deposited on transition-metal dichalcogenides
采用第一性原理密度泛函方法研究了二维过渡金属二硫属化合物（TMDC）材料的磁性，即Fe插层的体相Fe $_{1/4}$ TaS $_2$化合物和沉积Fe膜的TMDC单层材料.改变由TMDC单层上的Fe覆盖层组成的系统的结构和组成导致其物理性质的相当大的变化。对于所考虑的系统的Dzyaloshinskiii-Moriya（DM）的相互作用已被确定，并用于随后的调查，他们的磁结构使用蒙特卡罗模拟。在这些材料中的一些中已经获得了相当强的DM相互作用以及大的$D/J$比率，这可以导致形成随所施加的外部磁场的强度而变化的skyrmionic结构。
We report the observation of a Pt layer thickness dependence on the induced interfacial Dzyaloshinskii-Moriya interaction in ultra-thin Pt($d_{\text{Pt}}$)/CoFeB films. Taking advantage of the large spin-orbit coupling of the heavy metal, the interfacial Dzyaloshinskii-Moriya interaction is quantified by Brillouin light scattering measurements of the frequency non-reciprocity of spin-waves in the ferromagnet. The magnitude of the induced Dzyaloshinskii-Moriya coupling is found to saturate to a value $0.45$ mJ$/$m${}^2$ for Pt thicknesses larger than $\sim 2$ nm. The experimental results are ex…
We propose a method to all-electrically control a domain-wall position in a ferromagnetic nanowire with Dzyaloshinskii-Moriya interaction. The strength of this interaction can be controlled by an external electric field, which in turn allows a fine tuning of the pinning potential of a spin-spiral domain wall. It allows to create more mobile pinning sites and can also be advantageous for ultra-low power electronics.
We formulate a microscopic linear response theory of nonequilibrium magnonic torques and magnon pumping applicable to multiple-magnonic-band uniform ferromagnets with Dzyaloshinskii-Moriya interactions. From the linear response theory, we identify the extrinsic and intrinsic contributions where the latter is expressed via the Berry curvature of magnonic bands. We observe that in the presence of a time-dependent magnetization Dzyaloshinskii-Moriya interactions can act as fictitious electric fields acting on magnons. We study various current responses to this fictitious field and analyze the rol…
The Dzyaloshinskii Moriya Interaction (DMI) has laid the foundation for many novel chiral structures such as Skyrmions. In most of the studies so far, the DMI is present in the whole of the magnetic layer. Here, we report our investigations on a ferromagnetic nanowire where DMI is confined to a nanoscale region. We observe that the local modulation of magnetic properties causes oscillation of domain walls under the influence of spin-transfer torque. The oscillation frequency is tunable within a few GHz, making this observation potentially useful for applications in neuromorphic computing.
The possibility of utilizing the rich spin-dependent properties of graphene has attracted great attention in pursuit of spintronics advances. The promise of high-speed and low-energy consumption devices motivates a search for layered structures that stabilize chiral spin textures such as topologically protected skyrmions. Here we demonstrate that chiral spin textures are induced at graphene/ferromagnetic metal interfaces. This is unexpected because graphene is a weak spin-orbit coupling material and is generally not expected to induce sufficient Dzyaloshinskii-Moriya interaction to affect magn…
Synthetic antiferromagnet (SAF) nanostructures with interfacial Dzyaloshinskii-Moriya interaction can host topologically distinct spin textures such as skyrmions and thus are regarded as promising candidates for both spintronics and magnonics applications. Here, we present comprehensive micromagnetic simulations of such material systems and discuss the rich phase diagrams that contain various types of magnetic configurations. Aside from the static properties, we further discuss the resonant excitations of the calculated magnetic states which include individual skyrmions and skyrmioniums. Final…
The antisymmetric Dzyaloshinskii-Moriya interaction (DMI) in noncentrosymmetric systems leads to various nonuniform chiral magnetic textures. Polarized neutron scattering is a powerful method for investigation such chiral distributions. The most used technique is a small-angle neutrons scattering (SANS). Multilayered magnetic films with the interface induced DMI (iDMI) can't be investigated by SANS because of their small volume. The appropriate technique is a polarized neutron reflectometry. Within the framework of the continuum theory of micromagnetics, we explore the impact of the iDMI on th…
We have studied the domain wall resistance in W/Ta/CoFeB/MgO heterostructures. The Ta layer thickness is varied to control the type of domain walls via changes in the interfacial Dzyaloshinskii Moriya interaction. We find a nearly constant domain wall resistance against the Ta layer thickness. Adding contributions from the anisotropic magnetoresistance, spin Hall magnetoresistance and anomalous Hall effect describe well the domain wall resistance of the thick Ta layer films. However, a discrepancy remains for the thin Ta layer films wherein chiral Néel-like domain walls are found. These result…
This Topical Review presents an overview of the recent experimental results on the quantitative determination of the magnetic exchange parameters in ultrathin magnetic films and multilayers, grown on different substrates. The experimental approaches to probe both the symmetric Heisenberg as well as the antisymmetric Dzyaloshinskii--Moriya exchange interaction in ultrathin magnetic films and at interfaces are discussed in detail. It is explained how the experimental spectrum of magnetic excitations can be used to quantify the strength of these interactions.
Multilayers of heavy metals and ferromagnets are the basis for the formation of various structures with inhomogeneous chiral magnetic distributions. The most informative method for studying magnetic states in such structures with a high spatial resolution is Lorentz transmission electron microscopy (L-TEM). Here, we report on the observation of chiral Néel domain walls by means of L-TEM in Co/Pt multilayers with perpendicular magnetic anisotropy. We explain the existence of chiral Néel internal structure due to the overcritical, giant interfacial induced Dzyaloshinskii-Moriya interaction. Our …
We theoretically study the effect of Dzyaloshinskii-Moriya interaction (DMI) on the focusing of a spin-wave lens that is constructed by a circular interface between two magnetic films. We analytically derive the generalized Snell's law in the curved geometry and the position of the focal point which exhibits a peculiar off-axial focusing behavior. We uncover a strong dependence of the focal point on both the material parameters and the frequency of incident spin waves. Full micromagnetic simulations compare well with theoretical predictions. Our findings would be helpful to manipulate spin wav…
Using relativistic first-principles calculations, we show that the chemical trend of Dzyaloshinskii-Moriya interaction (DMI) in 3d-5d ultrathin films follows Hund's first rule with a tendency similar to their magnetic moments in either the unsupported 3d monolayers or 3d-5d interfaces. We demonstrate that, besides the spin-orbit coupling (SOC) effect in inversion asymmetric noncollinear magnetic systems, the driving force is the 3d orbital occupation and their spin flip/mixing processes with the spin-orbit active 5d states control directly the sign and magnitude of the DMI. The magnetic chiral…
We present a comprehensive theory of the magnetic phases in monolayer nickel-based Janus dihalides (NiIBr, NiICl, NiBrCl) through a combination of first-principles calculations and atomistic simulations. Phonon band structure calculations and finite temperature molecular dynamics simulations show that Ni-dihalide Janus monolayers are stable. The parameters of the interacting spin Hamiltonian extracted from ab initio calculations show that nickel-dihalide Janus monolayers exhibit varying degrees of magnetic frustration together with a large Dzyaloshinskii-Moriya interaction due to their inheren…
We study the interaction of surface acoustic waves with spin waves in ultra-thin CoFeB/Pt bilayers. Due to the interfacial Dzyaloshinskii-Moriya interaction (DMI), the spin wave dispersion is non-degenerate for oppositely propagating spin waves in CoFeB/Pt. In combination with the additional nonreciprocity of the magnetoacoustic coupling itself, highly nonreciprocal acoustic wave transmission through the magnetic film is observed. We systematically characterize the magnetoacoustic wave propagation in a thickness series of CoFeB($d$)/Pt samples as a function of magnetic field magnitude and dire…
Weak antiferromagnetism due to Dzyaloshinskii-Moriya interaction in Ba$_3$Cu$_2$O$_4$Cl$_2$
反铁磁绝缘铜氧化物Ba $_3$ Cu $_2$ O $_4$ Cl $_2$含有折叠的CuO $_2$链，每个晶胞具有四个磁性铜离子（$S=1/2$）。一个潜在的多轨道哈伯德模型制定和超交换理论的发展，以获得一个有效的自旋哈密顿量的铜酸盐。得到的自旋哈密顿量除了包含各向同性交换作用外，还包含一个Dzyaloshinskiii-Moriya项和一个更弱的对称各向异性交换项.相应的Dzyaloshinskiii-Moriya矢量的每个磁性Cu-Cu键链中揭示了一个定义良好的空间秩序。超交换理论和互补群理论的考虑，都导致了关于这种秩序的性质的相同结论。的基态磁特性的推导模型的分析导致预测的反铁磁结构的一个额外的非共线调制。这种弱反铁磁性仅限于其中一个铜亚晶格。
We have investigated magnetoelectric coupling in the single-molecule magnet $\mathrm{Mn}_{4}\mathrm{Te}_{4}(\mathrm{P}\mathrm{Et}_{3})_{4}$ with tetrahedral spin frustration. Our density functional studies found that an electric dipole moment can emerge with various non-collinear spin orderings. The forms of spin-dependent dipole are determined and consistent with that in non-centrosymmetric magnets driven by the Dzyaloshinskii-Moriya interaction. Writing a parameterized spin Hamiltonian, after solving for eigenvalues and eigenstates we quantified the magnetoelectric coupling by calculating th…
The Dzyaloshinskii-Moriya interaction (DMI) is a chiral interaction that favors formation of domain walls. Recent experiments and ab initio calculations show that there are multiple ways to modify the strength of the interfacially induced DMI in thin ferromagnetic films with perpendicular magnetic anisotropy. In this paper we reveal theoretically the effects of spatially varied DMI on the magnetic state in thin films. In such heterochiral 2D structures we report several emergent phenomena, ranging from the equilibrium spin canting at the interface between regions with different DMI, over parti…
We have used Brillouin Light Scattering spectroscopy to independently determine the in-plane Magneto-Crystalline Anisotropy and the Dzyaloshinskii-Moriya Interaction (DMI) in out-of-plane magnetized Au/Co/W(110). We found that the DMI strength is 2-3 times larger along the bcc$[\bar{1}10]$ than along the bcc$[001]$ direction. We use analytical considerations to illustrate the relationship between the crystal symmetry of the stack and the anisotropy of microscopic DMI. Such an anisotropic DMI is the first step to realize isolated elliptical skyrmions or anti-skyrmions in thin film systems with …
