Noncollinear State Research Articles

Torque equilibrium spin wave theory study of anisotropy and Dzyaloshinskii-Moriya interaction effects on the indirect K -edge RIXS spectrum of a triangular lattice antiferromagnet

We apply the recently formulated torque equilibrium spin wave theory (TESWT) to compute the $1/S$-order interacting $K$ -edge bimagnon resonant inelastic x-ray scattering (RIXS) spectra of an anisotropic triangular lattice antiferromagnet with Dzyaloshinskii-Moriya (DM) interaction. We extend the interacting torque equilibrium formalism, incorporating the effects of DM interaction, to appropriately account for the zero-point quantum fluctuation that manifests as the emergence of spin Casimir effect in a noncollinear spin spiral state. Using inelastic neutron scattering data from Cs$_2$CuCl$_4$ we fit the 1/S corrected TESWT dispersion to extract exchange and DM interaction parameters. We use these new fit coefficients alongside other relevant model parameters to investigate, compare, and contrast the effects of spatial anisotropy and DM interaction on the RIXS spectra at various points across the magnetic Brillouin zone. We highlight the key features of the bi- and trimagnon RIXS spectrum at the two inequivalent rotonlike points, $M(0,2 \pi/\sqrt{3})$ and $M^{\prime}(\pi,\pi/\sqrt{3})$, whose behavior is quite different from an isotropic triangular lattice system. While the roton RIXS spectrum at the $M$ point undergoes a spectral downshift with increasing anisotropy, the peak at the $M^\prime$ location loses its spectral strength without any shift. With the inclusion of DM interaction the spiral phase is more stable and the peak at both $M$ and $M^\prime$ point exhibits a spectral upshift. Our calculation offers a practical example of how to calculate interacting RIXS spectra in a non-collinear quantum magnet using TESWT. Our findings provide an opportunity to experimentally test the predictions of interacting TESWT formalism using RIXS, a spectroscopic method currently in vogue.

Symmetry-breaking interlayer Dzyaloshinskii-Moriya interactions in synthetic antiferromagnets.

The magnetic interfacial Dzyaloshinskii-Moriya interaction (DMI) in multilayered thin films can lead to chiral spin states, which are of paramount importance for future spintronic technologies1,2. Interfacial DMI typically manifests as an intralayer interaction, mediated via a paramagnetic heavy metal in systems lacking inversion symmetry3. Here we show that, by designing synthetic antiferromagnets with canted magnetization states4,5, it is also possible to observe direct evidence of the interfacial interlayer DMI at room temperature. The interlayer DMI breaks the symmetry of the magnetic reversal process via the emergence of non-collinear spin states, which results in chiral exchange-biased hysteresis loops. The spin chiral interlayer interactions reported here are expected to manifest in a range of multilayered thin-film systems, opening up as yet unexplored avenues for the development and exploitation of chiral effects in magnetic heterostructures6-8.

Hydrodynamic description of long-distance spin transport through noncollinear magnetization states: Role of dispersion, nonlinearity, and damping

Nonlocal compensation of magnetic damping by spin injection has been theoretically shown to establish dynamic, noncollinear magnetization states that carry spin currents over micrometer distances. Such states can be generically referred to as dissipative exchange flows (DEFs) because spatially diffusing spin currents are established by the mutual exchange torque exerted by neighboring spins. Analytical studies to date have been limited to the weak spin injection assumption whereby the equation of motion for the magnetization is mapped to hydrodynamic equations describing spin flow and then linearized. Here, we analytically and numerically study easy-plane ferromagnetic channels subject to spin injection of arbitrary strength at one extremum under a unified hydrodynamic framework. We find that DEFs generally exhibit a nonlinear profile along the channel accompanied by a nonlinear frequency tuneability. At large injection strengths, we fully characterize a novel magnetization state we call a contact-soliton DEF (CS-DEF) composed of a stationary soliton at the injection site, which smoothly transitions into a DEF and exhibits a negative frequency tuneability. The transition between a DEF and a CS-DEF occurs at the maximum precessional frequency and coincides with the Landau criterion: a subsonic to supersonic flow transition. Leveraging the hydraulic-electrical analogy, the current-voltage characteristics of a nonlinear DEF circuit are presented. Micromagnetic simulations of nanowires that include magnetocrystalline anisotropy and non-local dipole fields are in qualitative agreement with the analytical results. The magnetization states found here along with their characteristic profile and spectral features provide quantitative guidelines to pursue an experimental demonstration of DEFs in ferromagnetic materials and establishes a unified description for long-distance spin transport.

Non-collinear magnetism in Mn monolayer on Ag(111) fcc: Density functional calculations

The magnetic properties of Mn monolayer on Ag (111) surface have been studied, using the first-principle plane-wave implementation of the density-functional theory (DFT). Several collinear and non-collinear magnetic configurations have been considered including the effects of different stacking sequences for the surface termination. We compare our results with recent experimental data of Gao et al. [C. L. Gao, W. Wulfhekel and J. Kirschner, Phys. Rev. Lett. 101, 267205 (2008)]. Our simulations reveal that the lowest energy state is antiferromagnetic, and corresponds to an out-of-plane collinear antiferromagnetic state, when we take into account the spin-orbit interactions while the 120° antiferromagnetic Néel structures has an excess energy of 56.06 meV/Mn. The magnetic anisotropy energy found between the antiferromagnetic out-of-plane and in-plane structures is of 2.65 meV. These findings are in agreement with the previous electronic structure calculations, which pointed to a collinear row-by-row antiferromagnetic ground state but in disagreement with the experimental finding. Also, our results for Mn/Ag (111) suggest that a non-collinear ground state corresponding to the clean surface can be excluded while more complex systems, including surface contamination or oxidation, should be considered to reproduce the experimental 120° Néel structure.

Magnonic Band Structure Established by Chiral Spin-Density Waves in Thin-Film Ferromagnets

Recent theoretical studies have demonstrated the possibility to excite and sustain noncollinear magnetization states in ferromagnetic nanowires. The resulting state is referred to as a spin-density wave (SDW). SDWs can be interpreted as hydrodynamic states with a constant fluid density and fluid velocity in systems with easy-plane anisotropy. Here, we consider the effect of the nonlocal dipole field arising from the finite thickness of magnetic thin films on the spatial profile of the SDW and on the associated magnon dispersion. Utilizing a hydrodynamic formulation of the Larmor torque equation, it is found that the nonlocal dipole field modulates the fluid velocity. Such a modulation induces a magnonic band structure unlike the typical dispersion relation for magnons on uniform magnetization. The analytical results are validated by micromagnetic simulations. Band gaps on the order of gigahertz are numerically observed to depend on the SDW fluid velocity and film thickness for realistic material parameters. The presented results suggest that SDWs can find applications as reconfigurable magnonic crystals.

Spin canting and orbital order in spinel vanadate thin films

We report on the epitaxial film growth and characterization of CoV$_2$O$_4$, a near-itinerant spinel vanadate, grown on (001) SrTiO$_3$. The symmetry lowering of the unit cell from cubic in the bulk to orthorhombic in the films results in dramatic differences in the magnetic anisotropy compared to bulk, as determined from structural and magnetic characterization. Bulk cubic CoV$_2$O$_4$ has been found to defy predictions by showing orbital degeneracy seemingly lasting to very low temperatures, with only small anomalies in magnetization and neutron experiments signaling a possible spin/orbital glass transition at T = 90 K. In epitaxial thin films presented in this paper, structurally tuning the CoV$_2$O$_4$ away from cubic symmetry leads to a completely different low temperature non-collinear ground state. Via magnetization and neutron scattering measurements we show that the 90 K transition is associated with a major spin reorientation away from the ferrimagnetic easy axis [001] to the [110] direction. Furthermore, the V-spins cant away from this direction with extracted perpendicular moments providing evidence of a larger canting angle compared to bulk. This result indicates that compressive strain pushes the system deeper into the insulating state, i.e., away from the localized - itinerant crossover regime.

Mixing A -type and G -type B -site antiferromagnetism in AMn1−xFexO3(A=La,Nd)

Using a classical Heisenberg model with anisotropic nearest-neighbor superexchange and uniaxial anisotropy, I investigate the magnetic order of the transition metals on the $B$ sites in $A\mathrm{M}{\mathrm{n}}_{1\text{\ensuremath{-}}x}\mathrm{F}{\mathrm{e}}_{x}{\mathrm{O}}_{3}\phantom{\rule{4pt}{0ex}}(A=\mathrm{La}$, Nd; $x=[0,1])$ with Monte Carlo methods. Magnetic parameters are extracted from preexisting experimental data when available and otherwise estimated with calculations. Superexchange energies are compared to density functional theory and anisotropy energies to ligand field theory, and the potential for doping-induced strain affecting these parameters is considered. I find coexistence regions of different types of magnetic order ($A$-type and $G$-type antiferromagnetism), regions with distinct magnetic transitions for the two order parameters, noncollinear ground states for intermediate values of $x$ that decrease the amplitude of the ordered moment in a way consistent with experiment for low dopings, and a reproduction of the experimentally determined, nonmonotonic interpolation of the ordering temperatures. The detailed shape of the phase boundaries in $(x,T$) space is found to be diagnostic of the magnetic interactions. These results also suggest a ferrimagnetic ground state for the ${A}_{2}\mathrm{MnFe}{\mathrm{O}}_{6}$ double perovskite with ${T}_{\mathrm{N}}\ensuremath{\approx}270\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for $A=\mathrm{La}$ and Nd.

Toroidal quantum states in molecular spin-frustrated triangular nanomagnets with weak spin-orbit coupling: Applications to molecular spintronics

We theoretically investigate the ground-state spin texture and spin transport properties of triangular rings with on-site spins ${S}_{q}=\frac{1}{2}\phantom{\rule{0.28em}{0ex}}(q=1--3)$. In the limit of strong antiferromagnetic exchange coupling and weak spin-orbit coupling, we find it is possible to prepare a noncollinear degenerate ground state with a zero magnetic moment and a nonzero toroidal moment $\mathbf{\ensuremath{\tau}}=g{\ensuremath{\mu}}_{B}{\ensuremath{\sum}}_{q}{\mathbf{r}}_{q}\ifmmode\times\else\texttimes\fi{}{\mathbf{S}}_{q}$, aligned along the ${C}_{3}$-symmetry axis. These pure toroidal states can be prepared: (i) within the fourfold degenerate spin-frustrated ground state even without any spin-orbit coupling; (ii) within the ground Kramers doublet resulting from weak spin-orbit splitting of the fourfold degenerate frustrated manifold via Dzyaloshinskii-Moriya antiferromagnetic exchange coupling. We also investigate the relationship between toroidal states and chiral spin states, characterized by the eigenvalues of the scalar spin chirality operator $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\chi}}=\frac{4}{\sqrt{3}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{S}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{S}}}_{2}\ifmmode\times\else\texttimes\fi{}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{S}}}_{3}$, and find that, since $[\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{\ensuremath{\tau}}},\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\chi}}]\ensuremath{\ne}0$, it is not possible to prepare states that are both toroidal and chiral simultaneously. Finally, by setting up a quantum transport model in the Coulomb blockade regime, we find that a spin current injected through a spin-polarized source electrode into the triangle is partially reversed upon scattering with the molecular toroidal states. This spin-switching effect is, in fact, a signature of molecular spin-transfer torque, which can be harnessed to modify the nonequilibrium populations of the $+\ensuremath{\tau}$- and $\ensuremath{-}\ensuremath{\tau}$-toroidal states, thus, to induce a net toroidal magnetization in the device using a spin current.

Non-collinear spin states in bottom-up fabricated atomic chains

Non-collinear spin states with unique rotational sense, such as chiral spin-spirals, are recently heavily investigated because of advantages for future applications in spintronics and information technology and as potential hosts for Majorana Fermions when coupled to a superconductor. Tuning the properties of such spin states, e.g., the rotational period and sense, is a highly desirable yet difficult task. Here, we experimentally demonstrate the bottom-up assembly of a spin-spiral derived from a chain of iron atoms on a platinum substrate using the magnetic tip of a scanning tunneling microscope as a tool. We show that the spin-spiral is induced by the interplay of the Heisenberg and Dzyaloshinskii-Moriya components of the Ruderman-Kittel-Kasuya-Yosida interaction between the iron atoms. The relative strengths and signs of these two components can be adjusted by the interatomic iron distance, which enables tailoring of the rotational period and sense of the spin-spiral.

Electrical switching of the topological anomalous Hall effect in a non-collinear antiferromagnet above room temperature

The anomalous Hall effect is allowed by symmetry in some non-collinear antiferromagnets and is associated with Bloch-band topological features. This topological anomalous Hall effect is of interest in the development of low-power electronic devices, but such devices are likely to demand electrical control over the effect. Here we report the observation of the anomalous Hall effect in high-quality thin films of the cubic non-collinear antiferromagnet Mn3Pt epitaxially grown on ferroelectric BaTiO3 substrates. We demonstrate that epitaxial strain can alter the anomalous Hall conductivity of the Mn3Pt films by more than an order of magnitude. Furthermore, we show that the anomalous Hall effect can be turned on and off by applying a small electric field to the BaTiO3 substrate when the heterostructure is at a temperature of around 360 K and the Mn3Pt is close to the phase transition between a low-temperature non-collinear antiferromagnetic state and a high-temperature collinear antiferromagnetic state. The switching effect is due to piezoelectric strain transferred from the BaTiO3 substrate to the Mn3Pt film by interfacial strain mediation.

Noncollinear magnetic ordering in the Shastry-Sutherland Kondo lattice model: Insulating regime and the role of Dzyaloshinskii-Moriya interaction

We investigate the necessary conditions for the emergence of complex, noncoplanar magnetic configurations in a Kondo lattice model with classical local moments on the geometrically frustrated Shastry-Sutherland lattice and their evolution in an external magnetic field. We demonstrate that topologically nontrivial spin textures, including a new canted flux state, with nonzero scalar chirality arise dynamically from realistic short-range interactions. Our results establish that a finite Dzyaloshinskii-Moriya (DM) interaction is necessary for the emergence of these novel magnetic states when the system is at half filling, for which the ground state is insulating. We identify the minimal set of DM vectors that are necessary for the stabilization of chiral magnetic phases. The noncoplanarity of such structures can be tuned continually by applying an external magnetic field. This is the first part in a series of two papers; in the following paper the effects of frustration, thermal fluctuations, and magnetic field on the emergence of novel noncollinear states at metallic filling of itinerant electrons are discussed. Our results are crucial in understanding the magnetic and electronic properties of the rare-earth tetraboride family of frustrated magnets with separate spin and charge degrees of freedom.

Noncollinear magnetic ordering in a frustrated magnet: Metallic regime and the role of frustration

We explore the magnetic phases in a Kondo lattice model on the geometrically frustrated Shastry-Sutherland lattice at metallic electron densities, searching for noncollinear and noncoplanar spin textures. Motivated by experimental observations in many rare-earth-based frustrated metallic magnets, we treat the local moments as classical spins and set the coupling between the itinerant electrons and local moments as the largest energy scale in the problem. Our results show that a noncollinear flux state is stabilized over an extended range of Hamiltonian parameters. These spin states can be quenched efficiently by external fields like temperature and magnetic field as well as by varying the degree of frustration in the electronic itinerancy and exchange coupling between local moments. Interestingly, unlike insulating electron densities that we discussed in paper I of this sequence, a Dzyaloshinskii-Moriya interaction between the local moments is not essential for the emergence of their noncollinear ordering.

Magnetic Frustration Driven by Itinerancy in Spinel CoV2O4

Localized spins and itinerant electrons rarely coexist in geometrically-frustrated spinel lattices. They exhibit a complex interplay between localized spins and itinerant electrons. In this paper, we study the origin of the unusual spin structure of the spinel CoV2O4, which stands at the crossover from insulating to itinerant behavior using the first principle calculation and neutron diffraction measurement. In contrast to the expected paramagnetism, localized spins supported by enhanced exchange couplings are frustrated by the effects of delocalized electrons. This frustration produces a non-collinear spin state even without orbital orderings and may be responsible for macroscopic spin-glass behavior. Competing phases can be uncovered by external perturbations such as pressure or magnetic field, which enhances the frustration.

Magnetic helices as metastable states of finite XY ferromagnetic chains: An analytical study

We investigated a simple but non trivial model, consisting of a chain of N classical XY spins with nearest neighbor ferromagnetic interaction, where each of the two end-point spins is assumed to be exchange-coupled to a fully-pinned fictitious spin. In the mean field approximation, the system might be representative of a soft ferromagnetic film sandwiched between two magnetically hard layers. We show that, while the ground state is ferromagnetic and collinear, the system can attain non-collinear metastable states in the form of magnetic helices. The helical solutions and their stability were studied analytically in the absence of an external magnetic field. There are four possible classes of solutions. Only one class is metastable, and its helical states contain an integer number of turns. Among the remaining unstable classes, there is a class of helices which contain an integer number of turns. Therefore, an integer number of turns in a helical configuration is a necessary, but not a sufficient, condition for metastability. These results may be useful to devise future applications of metastable magnetic helices as energy-storing elements.

Magnetic Möbius stripe without frustration: Noncollinear metastable states

The recently introduced area of topological magnetism searches for equilibrium structures stabilized by a combination of interactions and specific boundary conditions. Until now, the internal energy of open magnetic chains has been explored. Here, we study the energy landscape of closed magnetic chains with on-site anisotropy coupled with antiferromagnetic exchange and dipolar interactions analytically and numerically. We show that there are many stable stationary states in closed geometries. These states correspond to the noncollinear spin spirals for vanishing anisotropy or to kink solitons for high magnetic anisotropy. Particularly, the noncollinear M\obius magnetic state can be stabilized at finite temperatures in nonfrustrated rings or other closed shapes with an even number of sites without the Dzyaloshinskii-Moriya interaction. We identify the described configurations with the stable stationary states, which appear due to the finite length of a ring.

Temperature-Induced Increase of Spin Spiral Periods.

Spin-polarized scanning tunneling microscopy investigations reveal a significant increase of the magnetic period of spin spirals in three-atomic-layer-thick Fe films on Ir(111), from about 4nm at 8K to about 65nm at room temperature. We attribute this considerable influence of temperature on the magnetic length scale of noncollinear spin states to different exchange interaction coefficients in the different Fe layers. We thus propose a classical spin model that reproduces the experimental observations and in which the crucial feature is the presence of magnetically coupled atomic layers with different interaction strengths. This model might also apply for many other systems, especially magnetic multilayers.

Theory of magnons in spin systems with Dzyaloshinskii–Moriya interaction

We study in this paper magnetic properties of a system of quantum Heisenberg spins interacting with each other via a ferromagnetic exchange interaction J and an in-plane Dzyaloshinskii–Moriya interaction D. The non-collinear ground state due to the competition between J and D is determined. We employ a self-consistent Green’function theory to calculate the spin-wave spectrum and the layer magnetizations at finite T in two and three dimensions as well as in a thin film with surface effects. Analytical details and the validity of the method are shown and discussed. Numerical solutions are shown for realistic physical interaction parameters. Discussion on possible experimental verifications is given.

Tuning magnetic properties of non-collinear magnetization configuration in Pt/[Pt/Co]6/Pt/Co/Pt multilayer structure

In this study, effects of Pt spacer and Co reference layers thickness in [Co/Pt]6/Pt/Co multilayer have been revealed to tailor magnetization directions in non-collinear configuration. Magneto-optic Kerr effect and ferromagnetic resonance techniques were employed to investigate magnetic properties. Bilinear coupling between [Co/Pt]6 and Co layers and anisotropy constants were determined by a micromagnetic simulation based on metropolis algorithm. 3nm spacer causes ferromagnetic coupling while the samples have 4 and 5nm spacer are coupled anti-ferromagneticaly. Also, tuning magnetic anisotropy of [Co/Pt]6 layer was accomplished by Co reference layer. It is revealed that controlling of non-collinear states in such systems is possible by variation of thickness of spacer and reference layers and [Co/Pt]6/tPt/tCo trilayer system can be used in multilayered magnetic systems.

Ultrafast Magnetism of a Ferrimagnet across the Spin-Flop Transition in High Magnetic Fields.

We show that applying magnetic fields up to 30T has a dramatic effect on the ultrafast spin dynamics in ferrimagnetic GdFeCo. Upon increasing the field beyond a critical value, the dynamics induced by a femtosecond laser excitation strongly increases in amplitude and slows down significantly. Such a change in spin response is explained by different dynamics of the Gd and FeCo magnetic sublattices following a spin-flop phase transition from a collinear to a noncollinear spin state.

Cluster multipole theory for anomalous Hall effect in antiferromagnets

We introduce a cluster extension of multipole moments to discuss the anomalous Hall effect (AHE) in both ferromagnetic (FM) and antiferromagnetic (AFM) states in a unified framework. We first derive general symmetry requirements for the AHE in the presence or absence of the spin-orbit coupling, by considering the symmetry of the Berry curvature in k space. The cluster multipole (CMP) moments are then defined to quantify the macroscopic magnetization in non-collinear AFM states, as a natural generalization of the magnetization in FM states. We identify the macroscopic CMP order which induces the AHE. The theoretical framework is applied to the non-collinear AFM states of Mn3Ir, for which an AHE was predicted in a first-principles calculation, and Mn3Z (Z=Sn, Ge), for which a large AHE was recently discovered experimentally. We further compare the AHE in Mn3Z and bcc Fe in terms of the CMP. We show that the AHE in Mn3Z is characterized with the magnetization of a cluster octupole moment in the same manner as that in bcc Fe characterized with the magnetization of the dipole moment.