Helical Wavevector Research Articles

Transition from spiral to ferromagnetic structure in Fe[formula omitted]Co[formula omitted]Si compounds: Small-angle neutron scattering study

The cubic noncentrosymmetric structure of the B20 compounds produces the spin helix with the wave vector ks=D/J balanced by the competition of two interactions: the large ferromagnetic exchange interaction J and small antisymmetric Dzyaloshinskii–Moriya (DM) interaction D. The mixed Fe1−xCoxSi compounds demonstrate a switch of the sign of magnetic chirality in dependence of concentration x. The sign of magnetic chirality is dictated by the structural chirality and chemical elements (Fe, Co) as well. The switch of chirality is accompanied by transformation of the helix structure to the ferromagnet and is observed at xc=0.65. Moreover, this transformation (helimagnet–ferromagnet) occurs as a function of temperature. We observe the decrease of the helical wave vector ks with lowering temperature from Tc=17 K and its abrupt zeroing at Tf=7 K. The magnetic field applied not along the easy but along the hard anisotropic axis is able to restore the helical structure in the temperature range below Tf. The mechanism of the transformation is theoretically described by a competition between the cubic anisotropy and the DM interaction. We show that anisotropy-induced ferromagnet has nonreciprocal magnon spectrum due to DM interaction even in the absence of external magnetic field.

Spin excitation spectra in helimagnetic states: Proper-screw, cycloid, vortex-crystal, and hedgehog lattices

We investigate the spin excitation spectra in chiral and polar magnets by the linear spin-wave theory for an effective spin model with symmetric and antisymmetric long-range interactions. In one dimension, we obtain the analytic form of the dynamical spin structure factor for proper-screw and cycloidal helical spin states with uniform twists, which shows a gapless mode with strong intensity at the helical wave number. When introducing spin anisotropy in the symmetric interactions, we numerically show that the stable spin spirals become elliptically anisotropic with nonuniform twists and the spin excitation is gapped. In higher dimensions, we find that similar anisotropy stabilizes multiple-$Q$ spin states, such as vortex crystals and hedgehog lattices. We show that the anisotropy in these states manifests itself in the dynamical spin structure factor: a strong intensity in the transverse components to the wave number appears only when the helical wave vector and the corresponding easy axis are perpendicular to each other. Our findings could be useful not only to identify the spin structure but also to deduce the stabilization mechanism by inelastic neutron scattering measurements.

Experimental evidence of a change of exchange anisotropy sign with temperature in Zn-substituted Cu2OSeO3

We report small-angle neutron scattering from the conical state in a single crystal of Zn-substituted Cu2OSeO3. Using a 3D vector-field magnet to reorient the conical wavevector, our measurements show that the magnitude of the conical wavevector changes as a function of crystallographic direction. These changes are caused by the anisotropic exchange interaction (AEI), whose magnitude transitions from a maxima to a minima along the <111> and <100> crystallographic directions respectively. We further find that the AEI constant undergoes a change of sign from positive to negative with decreasing temperature. Unlike in the related compound FeGe, where similar behaviour of the AEI induces a reorientation of the helical wavevector, we show that the zero field helical wavevector in (Cu0.98Zn0.02)2OSeO3 remains along the <100> directions at all temperatures due to the competing fourth-order magnetocrystalline anisotropy becoming dominant at lower temperatures.

Helical magnetic order and Fermi surface nesting in noncentrosymmetric ScFeGe

An investigation of the structural, magnetic, thermodynamic, and charge transport properties of noncentrosymmetric hexagonal ScFeGe reveals it to be an anisotropic metal with a transition to a weak itinerant incommensurate helimagnetic state below TN=36 K. Neutron diffraction measurements discovered a temperature and field independent helical wave vector k = (0 0 0.193) with magnetic moments of 0.53 μB per Fe confined to the ab plane. Density functional theory calculations are consistent with these measurements and find several bands that cross the Fermi level along the c axis with a nearly degenerate set of flat bands just above the Fermi energy. The anisotropy found in the electrical transport is reflected in the calculated Fermi surface, which consists of several warped flat sheets along the c axis with two regions of significant nesting, one of which has a wave vector that closely matches that found in the neutron diffraction. The electronic structure calculations, along with a strong anomaly in the c -axis conductivity at TN, signal a Fermi surface driven magnetic transition, similar to that found in spin density wave materials. Magnetic fields applied in the ab plane result in a metamagnetic transition with a threshold field of ≈6.7 T along with a sharp, strongly temperature dependent discontinuity and a change in sign of the magnetoresistance for in-plane currents. Thus, ScFeGe is an ideal system to investigate the effect of in-plane magnetic fields on a helimagnet with a c -axis propagation vector, where the relative strength of the magnetic interactions and anisotropies determine the topology and magnetic structure.6 MoreReceived 18 September 2020Revised 9 December 2020Accepted 11 January 2021DOI:https://doi.org/10.1103/PhysRevB.103.014443©2021 American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsNoncentrosymmetric materialsNoncollinear magnetsTechniquesDensity functional calculationsMagnetization measurementsNeutron diffractionResistivity measurementsCondensed Matter & Materials Physics

Anomalous helimagnetic domain shrinkage due to the weakening of the Dzyaloshinskii-Moriya interaction in CrAs.

CrAs is a well-known helimagnet with the double-helix structure originating from the competition between the Dzyaloshinskii-Moriya interaction (DMI) and antiferromagnetic exchange interaction J. By resonant soft-x-ray scattering, we observe the magnetic peak (0 0 ) that emerges at the helical transition with ≈ 267.5 K. Intriguingly, the helimagnetic domains significantly shrink on cooling below ~255 K, opposite to the conventional thermal effect. The weakening of DMI on cooling is found to play a critical role here. It causes the helical wave vector to vary, ordered spins to rotate, and extra helimagnetic domain boundaries to form at local defects, thus leading to the anomalous shrinkage of helimagnetic domains. Our results indicate that the size of magnetic helical domains can be controlled by tuning DMI in certain helimagnets.

Twists in ferromagnetic monolayers with trigonal prismatic symmetry

Two-dimensional materials such as graphene or hexagonal boron nitride are indispensable in industry. The recently discovered 2D ferromagnetic materials also promise to be vital for applications. In this work, we develop a phenomenological description of non-centrosymmetric 2D ferromagnets with trigonal prismatic crystal structure. We chose to study this special symmetry group since these materials do break inversion symmetry and therefore, in principle, allow for chiral spin structures such as magnetic helices and skyrmions. However, unlike all non-centrosymmetric magnets known so far, we show that the symmetry of magnetic trigonal prismatic monolayers neither allow for an internal relativistic Dzyaloshinskii-Moriya interaction (DMI) nor a reactive spin-orbit torque. We demonstrate that the DMI only becomes important at the boundaries, where it modifies the boundary conditions of the magnetization and leads to a helical equilibrium state with a helical wavevector that is inherently linked to the internal spin orientation. Furthermore, we find that the helical wavevector can be electrically manipulated via dissipative spin-torque mechanisms. Our results reveal that 2D magnets offer a large potential for unexplored magnetic effects.

Magnetic structure in Mn1−xCoxGe compounds

The magnetic system of the pseudobinary compound Mn$_{1-x}$Co$_{x}$Ge has been studied using small-angle neutron scattering and SQUID-measurements. It is found that Mn$_{1-x}$Co$_{x}$Ge orders magnetically at low temperatures in the whole concentration range of $x \in [0 \div 0.9]$. Three different states of the magnetic structure have been found: a short-periodic helical state at $x \leq 0.45$, a long-periodic helical state at $0.45 < x \leq 0.8$, and a ferromagnetic state at $x \sim 0.9$. Taking into account that the relatively large helical wavevector $k \gg 1$ nm$^{-1}$ is characteristic for systems with mainly Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction, we suggest that the short-periodic helical structure at $x \leq 0.45$ is based on an effective RKKY interaction. Also the decay of $k$ with increasing $x$ is ascribed to a reduction of the interaction between second nearest neighbors and, therefore, to an increase of the influence of the Dzyaloshinskiy-Moriya interaction (DMI). As a result of the competition between these two interactions the quantum phase transition from a long-range ordered (LRO) to a short-range ordered (SRO) helical structure has been observed upon increase of the Co-concentration at $x_{c1} \sim 0.25$. Further increase of $x$ leads to the appearance of a double peak in the scattering profile at $0.45 < x < 0.7$. The transition from a helical structure to a ferromagnetic state found at $x = 0.9$ is caused by the weakening of DMI as compared to the cubic anisotropy. In summary, the evolution of the magnetic structure of Mn$_{1-x}$Co$_{x}$Ge with increasing $x$ is an example of a continuous transition from a helical structure based on the effective RKKY interaction to a ferromagnetic structure passing through a helical structure based on DMI.

Magnetoelectric coupling in superconductor-helimagnet heterostructures

The Ginzburg-Landau free energy of a conventional superconductor coupled to a helimagnet is microscopically derived using functional field integral techniques. We show that the spin texture leads to a Lifshitz invariant in the free energy, which couples the momentum density of the superconducting condensate to the magnetization of the helimagnet. For helimagnets with a conical texture, the Lifshitz invariant yields a spatial modulation of the superconducting phase along the helical wavevector of the magnetic texture. Based on self-consistent numerical calculations, we verify the theoretical formalism by investigating a superconductor that contains a helical Yu-Shiba-Rusinov (YSR) chain. We demonstrate that the texture-induced magnetoelectric coupling produces a strong supercurrent along the YSR chain, which induces a detectable magnetic field.

Spin chirality is flipped in transition-metal monogermanides

Using high pressure method polycrystalline powder samples of Mn1-xFexGe and Fe1-yCoyGe have been synthesized with x/y running from 0.0 to 1.0. The crystallite size for these compounds is in the order of 10 microns. SQUID magnetization and small angle neutron scattering (using SANS-1 at the MLZ, Garching) have revealed the helical magnetic ordering of the samples within the concentration range of x = [0.0 – 1.0] and y = [0.0 – 0.8]. The values of the helical wavevector k have been taken from the SANS pattern. As it could be seen in Fig.1 a) for Mn1-xFexGe the wavevector k remains roughly constant around 2 nm^-1 for x ≤ 0.4, while going down to a minimum for (|k| -&gt; 0) at xc ≍ 0.75 and increases again to a value of 0.09 nm^-1 for pure FeGe. For Fe1-yCoyGe the k value smoothly decreases from 0.09 nm-1 for pure FeGe to its minimum at yc ≍ 0.6 and increase again for y = 0.8 to its maximum of 0.14 nm^-1 (Fig.1 b). For x/y -&gt; xc/yc we observe a transformation of the helical magnetic structure to a ferromagnetic-like one at the critical concentrations. The change of the magnetic structure from helimagnetic to ferromagnetic-like goes along with a different sign of the magnetic chirality for x/y &lt; xc/yc and x/y &gt; xc/yc [1,2].

Helical spin textures in dipolar Bose-Einstein condensates

We numerically study elongated helical spin textures in ferromagnetic spin-1 Bose-Einstein condensates subject to dipolar interparticle forces. Stationary states of the Gross-Pitaevskii equation are solved and analyzed for various values of the helical wave vector and dipolar coupling strength. We find two helical spin textures which differ by the nature of their topological defects. The spin structure hosting a pair of Mermin-Ho vortices with opposite mass flows and aligned spin currents is stabilized for a nonzero value of the helical wave vector.

Molecular theoretical calculations for temperature induced phase transition and helix inversion in single component cholesteric liquid crystals

A chiral nematic phase of liquid crystals is studied using both the molecular field theory and the two-particle cluster theory. The interacting chiral molecules (as derived by van der Meer et al.) are placed at the sites of a three-dimensional, simple cubic lattice with orientations confined to two dimensions. The equilibrium pitch, internal energy, second- and fourth-rank order parameters as functions of temperature are calculated, and numerical results are compared with those predicted by the Monte Carlo computer simulation. The fourth-order terms in the interaction potential give rise to temperature-dependent pitch, and a helix inversion takes place in certain temperature. Both the molecular theories show a first order chiralnematic–isotropic phase transition when the fourth-order terms in the interaction potential are included. The two-partcile cluster theory, taking into account short-range correlations between molecules, yields improved values for the temperature dependence of the helical wavevector and of the scaled internal energy compared with the molecular field theory.

Reflectivity of cholesteric liquid crystals with spatially varying pitch.

Solids with spatially varying photonic structure offer gaps to light of a wider range of frequencies than do simple photonic systems. We solve numerically the field distribution in a cholesteric with a linearly varying inverse pitch (helical wavevector) using equations we derive for the general case. The simple idea that the position where the Bragg condition is locally satisfied is where reflection takes place is only true in part. Here, reflection is due to a region where the waves are forced to become evanescent, and the rate of variation of structure determines over which distance the waves decay and therefore how complete reflection is. The approximate local Bragg-de Vries schemes are shown to break down in detail at the edges of the gap, and an analytical estimate is given for the transmission coefficient.

The flexoelectro-optic effect in cholesterics

The flexoelectro-optic effect in short-pitch cholesterics [1] is analysed in terms of applied electric field strengths and material parameters such as the two flexoelectric coefficients es and eb and the three elastic constants. Starting from the free energy density of the uniformly lying-helix (ULH) configuration, including the flexoelectric polarization term, the equation describing the field-induced tilt angle of the bulk optic axis is derived. It is convenient to introduce the flexoelectric “anisotropy” Deltae as the difference between the splay and bend flexoelectric coefficients, hence defined by Deltae es eb. Our results then show that Deltae is the essential material parameter controlling the sign and magnitude of the electrically induced tilt. In the region of linear approximation, the tilt is proportional to Deltae and to the electric field E, and inversely proportional to the helical wave vector k, as well as the effective elastic constant (K11 K33). The individual values of the elastic constants K11, K22 and K33 do have an influence on the magnitude of the effect, but not on its linearity. The Deltae dependence conforms in the simplest way to the physical requirement that the flexoelectro-optic effect must be particularly pronounced in the case that es and eb are of opposite sign.

Structural and magnetic properties of holmium-scandium alloys and superlattices

The properties of Ho-Sc alloys and superlattices grown by molecular-beam epitaxy have been investigated using x-ray and neutron-diffraction techniques. Structural studies reveal that the alloy samples have different a lattice parameters for the Sc-seed layer and the Ho:Sc alloy grown on top of the seed layer; while the superlattices have different a lattice parameters for the Sc seed, and for both the Ho and Sc in the superlattice layers. The structural characteristics are related to the large lattice mismatches (of the order 7{percent}) between the constituent elements. The magnetic moments in the alloys form a basal-plane helix at all temperatures, with distortions of the helical arrangement for samples with the highest Ho concentrations. The dependences of the N{acute e}el temperature, T{sub N}, and the helical wave vector upon both temperature and concentration are compared with those of other alloy systems. It is found that a good description of the dependence of T{sub N} upon concentration is given by a virtual-crystal model where the peak in the conduction-electron susceptibility varies linearly between that of the pure constituents. In the superlattices, the moments also form a basal-plane helix at T{sub N}. In this helical phase, some samples exhibit a short-range coherence ofmore » an antiferromagnetic coupling between adjacent Ho blocks. For one superlattice, there is a low-temperature transition to a ferromagnetic phase, in which moments are ferromagnetically aligned within Ho blocks, and coupled antiferromagnetically between adjacent Ho blocks. The contrast with systems which have Y or Lu as the nonmagnetic element is discussed in terms of the structural properties of the samples, band-structure calculations, and the possible influence of dipolar forces. {copyright} {ital 1997} {ital The American Physical Society}« less

Computer simulation studies of anisotropic systems. Part 25.—Chiral nematics, the Dzyaloshinsky–Moriya model

A Monte Carlo computer simulation study of a model chiral nematogen has been undertaken. The chiral molecules are confined to the sites of a simple cubic lattice with their long axes in the xy plane and the helix axis along the z direction. The intermolecular interaction takes the form proposed by van der Meer et al. which is the simplest possible for chiral nematogens. For the lattice model the chiral part proves to be equivalent to the Dzyaloshinsky–Moriya model used to explain the weak antiferromagnetism in certain transition-metal oxides. To ensure that the periodic images are commensurate with the particles in the simulation box we have developed twisted boundary conditions. The chiral model exhibits a chiral nematic phase with a helical wavevector which is independent of temperature. This behaviour is entirely expected because the chiral term can be removed from the pair potential by a helical transformation with a constant wavevector. We have studied the transformed chiral model in detail in the vicinity of the order–disorder phase transition. In particular we have determined the internal energy and the heat capacity to locate the transition which is found to be second order or higher. The long-range order parameters, T2 and T4, have been evaluated together with the second- and fourth-rank angular correlation coefficients which characterise the short-range order. The spatial-director fluctuations have also been calculated to establish the extent of the monodomain formed. Finally, the properties simulated for the transformed chiral model are compared with those of its achiral analogue.

Orientational Fluctuations in Ferroelectric Liquid Crystals in Static External Electric Field

Abstract The effect of external static electric field on the dynamics of Goldstone orientational mode in ferroelectric liquid crystal was studied by photon correlation spectroscopy in the Sm C* phase of 4-(2′-methylbutyl) phenyl 4′-n-octylbiphenyl-4-carboxylate (CE8). In the field lower than the critical field necessary to unwind the helical structure of the crystal, the relaxation rate of the mode is almost field independent at all scattering wave vectors. At the critical field it suddenly increases and then continues to slowly increase with the field. The spatial dispersion of the mode which is parabolic with minimum at helical wave vector qo in the undisturbed sample, remains unchanged below the critical field. Above the critical field the minimum in the dispersion at qo disappears.

Non-linear c-f exchange interaction effect and magnetic properties of rare-earth metals. I. Phase boundaries

The authors have investigated the role of non-linear c-f exchange interaction effect on the magnetic properties of the rare-earth metals. Using a simple band model they obtained the magnetic phase diagram at zero temperature. The non-linear effect stabilised the cone structure without the crystal field and caused the ferromagnetic transition. The magnitude of the helical wavevector Q decreased as the helical component mod (S(Q)) mod increased. When (S) was regarded as the observed magnetisation, the temperature dependence of Q agreed with the experimental results. The magnetic properties of Gd and its alloys were considered on this phase diagram. The effective lifetimes of the c electrons were also important for the phase diagram. The crystal field made the phase diagram complicated. For the easy plane anisotropy, the fan appeared instead of the cone. For the easy axis anisotropy, the helix was squared by the higher harmonics and became the antiphase domain structure in infinitesimal c-f exchange.

Magnon-phonon interaction in rare earth metals with helical spin structures

The authors investigate the effects of dynamic magnetostriction in producing energy gaps in the magnon-phonon dispersion of systems of magnetic ions spatially ordered on hexagonal lattices with the magnetic moments ordered in helical fashion. Examples of these systems are found among the heavy rare earth metals. Except for certain special cases, gaps should be expected whenever E(k)= omega lambda (k+or-nQ), where E(k) is the unperturbed magnon dispersion, omega lambda (k) is the unperturbed phonon dispersion, Q is the helical wavevector and n=0, 1, 2. Numerical estimates of the gaps occurring for E(k)= omega lambda (k+or-Q) have been made for Dy, Ho for modes propagating in the c direction, yielding values between about 0.04 and 0.14 meV.