Spin Spiral Phase Research Articles

X-ray holographic imaging of magnetic surface spirals in FeGe lamellae

Isotropic helimagnets are known to host a diverse range of chiral magnetic states. In 2016, F.N. Rybakov et al. theorized the presence of a surface-pinned stacked spin spiral phase [F.N. Rybakov et al., 2016 New J. Phys. 18 045002], which has yet to be observed experimentally. Here we present experimental evidence for the observation of this state in lamellae of FeGe using resonant x-ray holographic imaging data and micromagnetic simulations. The identification of this state has significant implications for the stability of other coexisting spin textures, and will help complete our understanding of helimagnetic systems.

Spin-phonon and magnetoelectric coupling in oxygen-isotope substituted TbMnO3 investigated by Raman scattering

In order to investigate the effects leading to the strong magnetoelectric coupling in the type II multiferroic $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_{3}$ we have studied the thermal properties and temperature dependence of the lattice vibrations of ${\mathrm{TbMn}}^{16}{\mathrm{O}}_{3}$ and its isotopically substituted counterpart ${\mathrm{TbMn}}^{18}{\mathrm{O}}_{3}$. Heat capacity measurements on powder samples revealed no significant change in the ${\mathrm{Mn}}^{3+}$ and ${\mathrm{Tb}}^{3+}$ magnetic phase transition temperatures, as well as the multiferroic ordering temperature upon isotope substitution, indicating that a change in the dynamical modulation of the $\mathrm{Mn}{\mathrm{O}}_{6}$ octahedral distortions and rotations altering the Mn-O-Mn bond angles has no influence on the magnetic properties of $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_{3}$. Raman light scattering experiments have been performed on isotopically substituted single crystals to determine the temperature induced changes in phonon energies and linewidths at the sinusoidal and multiferroic phase transitions. A detailed modeling indicates that the spin-phonon coupling can be accounted for the pronounced anomalies in the temperature dependence of the phonon behaviors at the transition to the sinusoidal spin phase at ${T}_{\mathrm{N}}^{\mathrm{Mn}}=41$ K and to the multiferroic spin-spiral phase at ${T}_{\mathrm{FE}}=28$ K. No further effects such as the appearance of the electric polarization or the electromagnon were required to explain the data, especially below the multiferroic phase transition.

Unveiling the shape-selective CoCr2-yScyO4 nanomagnetism

In this study CoCr2-yScyO4 (y = 0, 0.01, 0.02, and 0.03) nanoparticles (NPs) have been synthesized following the solution combustion method and characterized by combining experimental techniques with high-throughput Density Functional Theory calculations. The structural analysis confirmed the crystalline nature with spinel cubic structure exhibiting an average particle size between 7 and 10 nm. The morphological analysis confirmed the exposure of the (220), (311), (400), and (422) planes in agreement with theoretical results based on Wulff Construction. Magnetic analysis indicated the existence of paramagnetic to ferrimagnetic phase transition at the critical temperature (Tc) and a conical spiral spin phase was found at the spiral transition temperature (Ts). In both the cases, the transition temperature was seen to decrease with increase in the Sc content in agreement with the exchange-coupling constants calculated by DFT, where a singular magneto-structural behavior was observed. Theoretical results for shape-oriented magnetic properties indicate the anisotropic spin density distribution and surface exposure, providing a general picture of shape-selective control of nanomagnetism.

An optically active spiral

Multiferroics The material cupric oxide exhibits magnetoelectric coupling, meaning that its magnetic properties can be controlled by electric fields. In its spin spiral phase, cupric oxide has a spiral magnetic ordering that can be right- or left-handed. Masuda et al. used electric fields to create purely left- or right-handed samples and then studied their optical activity. The samples exhibited natural optical activity, which the researchers were then able to control with electric fields. Science , this issue p. [496][1] [1]: /lookup/doi/10.1126/science.aaz4312

Electric field control of natural optical activity in a multiferroic helimagnet

Controlling the chiral degree of freedom in matter has long been an important issue for many fields of science. The spin-spiral order, which exhibits a strong magnetoelectric coupling, gives rise to chirality irrespective of the atomic arrangement of matter. Here, we report the resonantly enhanced natural optical activity on the electrically active magnetic excitation, that is, electromagnon, in multiferroic cupric oxide. The electric field control of the natural optical activity is demonstrated through magnetically induced chirality endowed with magnetoelectric coupling. These optical properties inherent to multiferroics may lead to optical devices based on the control of chirality.

Magnetic field dependence of low-energy magnons, anisotropic heat conduction, and spontaneous relaxation of magnetic domains in the cubic helimagnet ZnCr2Se4

Anisotropic low-temperature properties of the cubic spinel helimagnet ZnCr2Se4 in the single-domain spin-spiral state are investigated by a combination of neutron scattering, thermal conductivity, ultrasound velocity, and dilatometry measurements. In an applied magnetic field, neutron spectroscopy shows a complex and nonmonotonic evolution of the spin-wave spectrum across the quantum-critical point that separates the spin-spiral phase from the field-polarized ferromagnetic phase at high fields. A tiny spin gap of the pseudo-Goldstone magnon mode, observed at wave vectors that are structurally equivalent but orthogonal to the propagation vector of the spin helix, vanishes at this quantum critical point, restoring the cubic symmetry in the magnetic subsystem. The anisotropy imposed by the spin helix has only a minor influence on the lattice structure and sound velocity but has a much stronger effect on the heat conductivities measured parallel and perpendicular to the magnetic propagation vector. The thermal transport is anisotropic at T < 2 K, highly sensitive to an external magnetic field, and likely results directly from magnonic heat conduction. We also report long-time thermal relaxation phenomena, revealed by capacitive dilatometry, which are due to magnetic domain motion related to the destruction of the single-domain magnetic state, initially stabilized in the sample by the application and removal of magnetic field. Our results can be generalized to a broad class of helimagnetic materials in which a discrete lattice symmetry is spontaneously broken by the magnetic order.

Magnetoelectric coupling in a frustrated spinel studied using high-field scanning probe microscopy

Below its Neél temperature, the frustrated magnet CdCr2O4 exhibits an antiferromagnetic spin-spiral ground state. Such states can give rise to a sizable magnetoelectric coupling. In this report, we measure the electric polarization induced in single-crystalline CdCr2O4 by large applied magnetic field. Because the detection of a macroscopic polarization is hindered by the structural domains in the tetragonal spin-spiral phase, we have pioneered an alternative method of measuring polarization induced by high magnetic fields, using electrostatic force microscopy. This method enables us to measure polarization from nanoscale areas of the sample surface, as well as imaging how charge inhomogeneities change with magnetic field.

Instability of skyrmions in magnetic fields

In this combined experimental and theoretical work, we report on the evolution of the skyrmion radius and its destruction in the system Co/Ru(0001) when an out-of-plane magnetic field is applied. At low fields, skyrmions are metastable and display an elliptical instability in which along the short axis, the spin texture approaches that of the spin-spiral phase and the long axis expands in order to go back to the spin-spiral ground state. At high fields, we observe round skyrmions of finite size up to the collapse field Bc, where they are destroyed and the topological charge is annihilated. We estimate Bc via numerical methods based on magnetization dynamics simulations parametrized by density functional theory calculations and compare it to experimental scanning tunneling microscopy observations obtained at ≈ 30 mK.

Critical size limits for collinear and spin-spiral magnetism in CoCr2O4

The multiferroic behavior of CoCr$_2$O$_4$ results from the appearance of conical spin-spiral magnetic ordering, which induces electric polarization. The magnetic ground state has a complex size dependent behavior, which collapses when reaching a critical particle size. Here, the magnetic phase stability of CoCr$_2$O$_4$ in the size range of 3.6 - 14.0 nm is presented in detail using the combination of neutron diffraction with XYZ polarization analysis and macroscopic magnetization measurements. We establish critical coherent domain sizes for the formation of the spin spiral and ferrimagnetic structure and reveal the evolution of the incommensurate spin spiral vector with particle size. We further confirm the presence of ferroelectric polarization in the spin spiral phase for nanocrystalline CoCr$_2$O$_4$.

Topological Hall effect and emergent skyrmion crystal at manganite-iridate oxide interfaces

Scalar spin chirality is expected to induce a finite contribution to the Hall response at low temperatures. We study this spin-chirality-driven Hall effect, known as the topological Hall effect, at the manganite side of the interface between La$_{1-x}$Sr$_{x}$MnO$_{3}$ and SrIrO$_3$. The ferromagnetic double-exchange hopping at the manganite layer, in conjunction with the Dzyaloshinskii-Moriya (DM) interaction which arises at the interface due to broken inversion symmetry and strong spin-orbit coupling from the iridate layer, could produce a skyrmion-crystal (SkX) phase in the presence of an external magnetic field. Using the Monte Carlo technique and a two-orbital spin-fermion model for manganites, supplemented by an in-plane DM interaction, we obtain phase diagrams which reveal at low temperatures a clear SkX phase and also a low-field spin-spiral phase. Increasing temperature, a skyrmion-gas phase, precursor of the SkX phase upon cooling, was identified. The topological Hall effect primarily appears in the SkX phase, as observed before in oxide heterostructures. We conclude that the manganite-iridate superlattices provide another useful platform to explore a plethora of unconventional magnetic and transport properties.

First-Principles Prediction of Skyrmionic Phase Behavior in GdFe2 Films Capped by 4d and 5d Transition Metals

In atomic GdFe 2 films capped by 4d and 5d transition metals, we show that skyrmions with diameters smaller than 12 nm can emerge. The Dzyaloshinskii–Moriya interaction (DMI), exchange energy, and the magnetocrystalline anisotropy (MCA) energy were investigated based on density functional theory. Since DMI and MCA are caused by spin–orbit coupling (SOC), they are increased with 5d capping layers which exhibit strong SOC strength. We discover a skyrmion phase by using atomistic spin dynamic simulations at small magnetic fields of ∼1 T. In addition, a ground state that a spin spiral phase is remained even at zero magnetic field for both films with 4d and 5d capping layers.

Supervised learning approach for recognizing magnetic skyrmion phases

We propose and apply simple machine learning approaches for recognition and classification of complex non-collinear magnetic structures in two-dimensional materials. The first approach is based on the implementation of the single-hidden-layer neural network that only relies on the z projections of the spins. In this setup one needs a limited set of magnetic configurations to distinguish ferromag- netic, skyrmion and spin spiral phases, as well as their different combinations in transitional areas of the phase diagram. The network trained on the configurations for square-lattice Heisenberg model with Dzyaloshinskii-Moriya interaction can classify the magnetic structures obtained from Monte Carlo calculations for triangular lattice and vice versa. The second approach we apply, a minimum distance method performs a fast and cheap classification in cases when a particular configuration is to be assigned to only one magnetic phase. The methods we propose are also easy to use for analysis of the numerous experimental data collected with spin-polarized scanning tunneling microscopy and Lorentz transmission electron microscopy experiments.

Properties of the spin-liquid phase in the vicinity of the Lifshitz transition from Néel to spin-spiral state in frustrated magnets

Three decades ago Ioffe and Larkin pointed out a generic mechanism for the formation of a gapped spin liquid. In the case when a classical two-dimensional (2D) frustrated Heisenberg magnet undergoes a Lifshitz transition between a collinear N\'eel phase and a spin spiral phase, quantum effects usually lead to the development of a spin-liquid phase sandwiched between the N\'eel and spin spiral phases. In the present work, using field theory techniques, we study properties of this universal spin liquid phase. We examine the phase diagram near the Lifshitz point and calculate the positions of critical points, excitation spectra, and spin-spin correlations functions. We argue that the spin liquid in the vicinity of 2D Lifshitz point (LP) is similar to the gapped Haldane phase in integer-spin 1D chains. We also consider a specific example of a frustrated system with the spiral-N\'eel LP, the $J_1-J_3$ antiferromagnet on the square lattice that manifests the spin liquid behavior. We present numerical series expansion calculations for this model and compare results of the calculations with predictions of the developed field theory.

Spin-resolved inelastic electron scattering by spin waves in noncollinear magnets

Topological non-collinear magnetic phases of matter are at the heart of many proposals for future information nanotechnology, with novel device concepts based on ultra-thin films and nanowires. Their operation requires understanding and control of the underlying dynamics, including excitations such as spin-waves. So far, no experimental technique has attempted to probe large wave-vector spin-waves in non-collinear low-dimensional systems. In this work, we explain how inelastic electron scattering, being suitable for investigations of surfaces and thin films, can detect the collective spin-excitation spectra of non-collinear magnets. To reveal the particularities of spin-waves in such non-collinear samples, we propose the usage of spin-polarized electron-energy-loss spectroscopy augmented with a spin-analyzer. With the spin-analyzer detecting the polarization of the scattered electrons, four spin-dependent scattering channels are defined, which allow to filter and select specific spin-wave modes. We take as examples a topological non-trivial skyrmion lattice, a spin-spiral phase and the conventional ferromagnet. Then we demonstrate that, counter-intuitively and in contrast to the ferromagnetic case, even non spin-flip processes can generate spin-waves in non-collinear substrates. The measured dispersion and lifetime of the excitation modes permit to fingerprint the magnetic nature of the substrate.

Spin Structures and Phase Diagrams of Extended Spatially Completely Anisotropic Triangular Lattice Antiferromagnets

Motivated by recently discovered organic antiferromagnets, we examine an extended triangular lattice that consists of two types of triangles of bonds with exchange coupling constants \(J_{\ell }\) and \(J'_{\ell }\) (\(\ell \) = 1, 2, and 3), respectively. The simplified system with \(J_{\ell } = J'_{\ell } > 0\) is the spatially completely anisotropic triangular lattice (SCATL) antiferromagnet examined previously. The extended system, which we call an extended SCATL (ESCATL), has two different spatial anisotropy parameters J3/J2 and \(J'_{3}/J'_{2}\) when \(J_{1} = J'_{1}\) is assumed. We derive classical phase diagrams and spin structures. It is found that the ESCATL antiferromagnet exhibits two up–up–down–down (uudd) phases when the imbalance of the anisotropy parameters is significant, in addition to the three Neel phases that occur in the SCATL. When the model parameters vary, these collinear phases are continuously connected by the spiral-spin phase. Using the available model parameters for the orga...

Subpicometer-scale atomic displacements and magnetic properties in the oxygen-isotope substituted multiferroic DyMnO3

We have investigated $\mathrm{DyMn}\phantom{\rule{0.16em}{0ex}}^{16}\mathrm{O}_{3}$ and its isotopically substituted counterpart $\mathrm{DyMn}\phantom{\rule{0.16em}{0ex}}^{18}\mathrm{O}_{3}$ by neutron powder diffraction, x-ray diffraction, and heat capacity measurements to investigate the mechanism leading to its magnetically induced electric polarization. $^{18}\mathrm{O}$ isotope substitution does not influence the magnetic ordering temperature of the Mn ions ${T}_{\mathrm{N},\mathrm{Mn}}$ or the multiferroic ordering temperature ${T}_{\mathrm{l}}$ coinciding with the onset of the spin spiral phase; however, it does reduce the ordering temperature of Dy into its incommensurate magnetic state ${T}_{\mathrm{N},\mathrm{Dy}}$ from 7.0(1) K to 5.9(1) K. The temperature dependence of the magnetic propagation vector, ${\mathbf{q}}_{\mathrm{IC}}$, changes with $^{18}\mathrm{O}$ substitution, while ${T}_{\mathrm{l}}$ remains almost constant, independent of ${\mathbf{q}}_{\mathrm{IC}}$. Pronounced changes in the lattice parameters occur at the various phase transitions. Furthermore, distinct subpicometer-scale distortions of the $\mathrm{Mn}{\mathrm{O}}_{6}$ octahedra and displacements of the Dy ions are observed below the ferroelectric phase transition at ${T}_{\mathrm{l}}$ in both samples, pointing toward the mechanism for electric polarization and its coupling to the orbital degrees of freedom.

Multiferroic phases of the frustrated quantum spin-chain compound linarite

The dielectric properties of the prototypical frustrated ferromagnetic spin-chain compound PbCuSO$_4$(OH)$_2$ known as linarite, are studied across its strongly anisotropic magnetic phase diagram in single crystal samples. The ferroelectric character of the principal low-field spin spiral phase is confirmed. The measured polarization is fully consistent with the previously proposed magnetic structure. Spontaneous polarization is also detected in two other field-induced phases but in some cases is incompatible with previously suggested models for the spin arrangement.

Quantum melting of magnetic order in an organic dimer Mott-insulating system

Quantum entanglement effects between the electronic spin and charge degrees of freedom are examined in an organic molecular solid, termed a dimer-Mott insulating system, in which molecular dimers are arranged in a crystal as fundamental units. A low energy effective model includes an antisymmetric exchange interaction, as one of the dominant magnetic interactions. This interaction favors a 90 degree spin configuration, and competes with the Heisenberg-type exchange interaction. Stabilities of the magnetic ordered phases are examined by using the spin-wave theory, as well as the Schwinger-boson theory. It is found that the spin-charge interaction promotes an instability of the long-range magnetic ordered state around a parameter region where two spin-spiral phases are merged. Implication for the quantum spin liquid state observed in $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ is discussed.

Magnetic phase diagram of the helimagnetic spinel compound ZnCr2Se4 revisited by small-angle neutron scattering

We performed small-angle neutron scattering (SANS) measurements on the helimagnetic spinel compound ZnCr2Se4. The ground state of this material is a multi-domain spin-spiral phase, which undergoes domain selection in a magnetic field and reportedly exhibits a transition to a proposed spin-nematic phase at higher fields. We observed a continuous change in the magnetic structure as a function of field and temperature, as well as a weak discontinuous jump in the spiral pitch across the domain-selection transition upon increasing field. From our SANS results we have established the absence of any long-range magnetic order in the high-field (spin-nematic) phase. We also found that all the observed phase transitions are surprisingly isotropic with respect to the field direction.

Spin excitation spectra of spin–orbit coupled bosons in an optical lattice**Project supported by the National Natural Science Foundation of China (Grant Nos. 11347197, 11404225, and 11474205).

Spin-wave excitation plays important roles in the investigation of the magnetic phases. In this paper, we study the spin-wave excitation spectra of two-component Bose gases with spin–orbit coupling in a deep square optical lattice using the spin-wave theory. We find that, while the excitation spectrum of the vortex crystal phase is gapless with a linear dispersion in the vicinity of the minimum point, the spectra of the commensurate spiral spin phase and the skyrmion crystal phase are gapped. Significantly, the spin fluctuations strongly destabilize the classical ground state of the skyrmion phase with the appearance of an imaginary part in the eigenfrequencies of spin excitations. Such features of the spin excitation spectra provide further insights into the exotic spin phases.