The magneto-elastic interaction in cubic helimagnets with B20 symmetry is considered. It is shown that this interaction is responsible for negative contribution to the square of the spin-wave gap $Δ$ which is alone has to disrupt assumed helical structure. It is suggested that competition between positive part of $Δ^2_I$ which stems from magnon-magnon interaction and its negative magneto-elastic part leads to the quantum phase transition observed at high pressure in $Mn Si$ and $Fe Ge$. This transition has to occur when $Δ^2=0$. For $Mn Si$ from rough estimations at ambient pressure both parts $Δ_I$ and $|Δ_{ME}|$ are comparable with the experimentally observed gap. The magneto-elastic interaction is responsible also for $2\m k$ modulation of the lattice where $\m k$ is the helix wave-vector and contribution to the magnetic anisotropy.
Experimental observation by $x$-ray and neutron scattering the lattice modulation allows determine the strength of anisotropic part of the magneto-elastic interaction responsible for above phenomena and the lattice helicity.
We present a detailed AC susceptibility investigation of the fluctuation regime in the insulating cubic helimagnet Cu2OSeO3. For magnetic fields mu_0 H >= 200 mT, and over a wide temperature range, the system behaves according to the scaling relations characteristic of the classical 3D Heisenberg model. For lower magnetic fields the scaling is preserved only at higher T, and becomes renormalized in a narrow T range above the transition temperature. Contrary to the well-studied case of MnSi, where the renormalization has been interpreted within the Brazovskii theory, our analysis of the renorma…
The phase diagram of cubic helimagnets near the critical temperature is obtained from a Landau-Ginzburg model, including fluctuations to gaussian level. The free energy is evaluated via a saddle point expansion around the local minima of the Landau-Ginzburg functional. The local minima are computed by solving the Euler-Lagrange equations with appropriate boundary conditions, preserving manifestly the full nonlinearity that is characteristic of skyrmion states. It is shown that the fluctuations stabilize the skyrmion lattice in a region of the phase diagram close to the critical temperature, wh…
We report on detailed magnetic measurements on the cubic helimagnet FeGe in external magnetic fields and temperatures near the onset of long-range magnetic order at $T_C= 278.2(3)$ K. Precursor phenomena display a complex succession of temperature-driven crossovers and phase transitions in the vicinity of $T_C$. The A-phase region, present below $T_C$ and fields $H<0.5$ kOe, is split in several pockets. Relying on a modified phenomenological theory for chiral magnets, the main part of the A-phase could indicate the existence of a $+π$ Skyrmion lattice, the adjacent A$_2$ pocket, however, appea…
The critical behavior of the cubic helimagnet FeGe was obtained from isothermal magnetization data in very close vicinity of the ordering temperature. A thorough and consistent scaling analysis of these data revealed the critical exponents $β=0.368$, $γ=1.382$, and $δ=4.787$. The anomaly in the specific heat associated with the magnetic ordering can be well described by the critical exponent $α=-0.133$. The values of these exponents corroborate that the magnetic phase transition in FeGe belongs to the isotropic 3D-Heisenberg universality class. The specific heat data are well described by ab i…
We investigate the spin $S=1/2$ Heisenberg model on the body centered cubic lattice in the presence of ferromagnetic and antiferromagnetic nearest-neighbor $J_{1}$, second-neighbor $J_{2}$, and third-neighbor $J_{3}$ exchange interactions. The classical ground state phase diagram obtained by a Luttinger-Tisza analysis is shown to host six different (noncollinear) helimagnetic orders in addition to ferromagnetic, Néel, stripe and planar antiferromagnetic orders. Employing the pseudofermion functional renormalization group (PFFRG) method for quantum spins ($S=1/2$) we find an extended nonmagneti…
The stability of the four known stationary points of the cubic helimagnet energy functional: the ferromagnetic state, the conical helix, the conical helicoid, and the skyrmion lattice, is studied by solving the corresponding spectral problem. The only stable points are the ferromagnetic state at high magnetic field and the conical helix at low field, and there is no metastable state. Thermal fluctuations around the stationary point, included to quadratic order in the saddle point expansion, destabilize the conical helix in a region where the ferromagnetic state is unstable. Thus, a new interme…
We present a detailed study of the ground state phase diagram of the classical frustrated Heisenberg model on the face-centered-cubic lattice. By considering exchange interactions up till third nearest neighbors, we find commensurate, helimagnetic, as well as noncollinear multi-{\bf Q} orders which include noncoplanar and chiral spin structures. We reveal the presence of subextensively degenerate manifolds that appear at triple points and certain phase boundaries in the phase diagram. Within these manifolds, the spin Hamiltonian can be recast as a complete square of spins on finite motifs, per…
A direct three-dimensional minimization of the standard energy functional shows that in thin films of cubic helimagnets chiral skyrmions are modulated along three spatial directions. The structure of such 3D skyrmions can be thought of as a superposition of conical modulations along the skyrmion axis and double-twist rotation in the perpendicular plane. Numerical solutions for chiral modulations demonstrate that 3D skyrmion lattices and helicoids are thermodynamically stable in a broad range of applied magnetic fields. Our results disclose a basic physical mechanism underlying the formation of…
We theoretically address the problem of cubic B20 helimagnets with small concentration ${c \ll 1}$ of defect bonds in external magnetic field $\bf H$, which is relevant to mixed B20 compounds at small dopant concentrations. We assume that Dzyaloshinskii-Moriya interaction and the exchange coupling constant are changed on imperfect bonds which leads to distortion of the conical spiral ordering. In one-impurity problem, we find that the distortion of the spiral pitch is long-ranged and it is governed by the Poisson equation for an electric dipole. The variation of the cone angle is described by …
Helimagnetic materials are identified as promising for novel spintronic applications. Since helical spin order is manifested as a compromise of competing magnetic exchange interactions, its emergence is limited by unique constraints imposed by the crystalline lattice and the interaction geometries, as exemplified by the multiferroic perovskite manganites with large orthorhombic distortion. Here we show that a simple cubic perovskite SrCoO$_3$ with room-temperature ferromagnetism has the potential to host helimagnetic order upon isotropic lattice expansion. Increasing the Ba content $x$ in Sr$_…
Single helicity of the triple-$q$ triangular skyrmion lattice state in cubic chiral helimagnet EuPtSi
Hiroshima University（广岛大学）；Japan Atomic Energy Agency（日本原子能机构）；Institute of Materials Structure Science, High Energy Accelerator Research Organization（高能加速器研究机构物质结构研究所）；University of the Ryukyus（琉球大学）；RIKEN Center for Emergent Matter Science（理化学研究所 新兴物质科学中心）
A model of B20 helimagnet with strong (frustrating) defect bonds is considered. Single defect provides dipolar field-like distortion of the helical magnetic ordering. At finite defect bond concentrations, the spiral vector acquires correction to its value in the pure system. Moreover, it is shown that the strong defects of sufficient but small concentration are able to destroy long-range order driving the system to the phase with short-range helical ordering. It is argued that the developed approach allows describing main experimental observations in Mn$_{1-x}$Fe$_x$Si and Mn$_{1-x}$Co$_x$Si c…
Magnetoelastic mapping of the high-field phase diagram in the topological cubic helimagnet SrFeO$_{3}$
University of Tokyo（东京大学）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所物质结构科学研究中心）；Hiroshima University（广岛大学）；High Energy Accelerator Research Organization（高能加速器研究机构）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料与能源中心）
A Surface-confined Spiral State With the Double Period in the Cubic Chiral Helimagnet Cu$_2$OSeO$_3$
The University of Tokyo（东京大学）；Paul Scherrer Institute (PSI)（保罗谢勒研究所）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Institute for Basic Science（基础科学研究所）；Durham University（杜伦大学）；Rutherford Appleton Laboratory（卢瑟福·阿普尔顿实验室）；ALBA Synchrotron Light Source（阿尔巴同步辐射光源）；Institut Laue–Langevin（朗之万研究所）
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 …
SANS and magnetometry study of the magnetic phase diagram of the B20 helimagnet FeRhSi
Saint Petersburg State University（圣彼得堡国立大学）；Vereshchagin Institute for High Pressure Physics, Russian Academy of Sciences（俄罗斯科学院韦列夏金高压物理研究所）；Mozhaisky Military Space Academy（莫扎伊斯基军事航天学院）
Ferroelectric properties in magnetic fields of varying magnitude and direction have been investigated for a triangular-lattice helimagnet CuFe1-xGaxO2 (x=0.035). The magnetoelectric phase diagrams were deduced for magnetic fields along [001], [110], and [1-10] direction, and the in-plane magnetic field was found to induce the rearrangement of six possible multiferroic domains. Upon every 60-degree rotation of in-plane magnetic field around the c-axis, unique 120-degree flop of electric polarization occurs as a result of the switch of helical magnetic q-vector. The chirality of spin helix is al…
Below a temperature of approximately 29 K the manganese magnetic moments of the cubic binary compound MnSi order to a long-range incommensurate helical magnetic structure. Here, we quantitatively analyze a high-statistic zero-field muon spin rotation spectrum recorded in the magnetically ordered phase of MnSi by exploiting the result of representation theory as applied to the determination of magnetic structures. Instead of a gradual rotation of the magnetic moments when moving along a <111> axis, we find that the angle of rotation between the moments of certain subsequent planes is essentiall…
A three-dimensional chiral helimagnet is analyzed using a mean-field (MF) analysis and a classical Monte Carlo (MC) simulation at finite temperatures. We consider a Hamiltonian containing Heisenberg exchange and uni-axial Dzyaloshinskii-Moriya interactions on a simple cubic lattice. Magnetization curves calculated by the MF theory are qualitatively consistent with those observed in experiments. A comparison between lattice and continuum models clarifies the region where the continuum approximation can be applied. By combining the MF theory with the classical MC method, it is also clarified tha…
The skyrmion crystal (SkX) characterized by a multiple-q helical spin modulation has been reported as a unique topological state that competes with the single-q helimagnetic order in non-centrosymmetric materials. Here we report the discovery of a rich variety of multiple-q helimagnetic spin structures in the centrosymmetric cubic perovskite SrFeO3. On the basis of neutron diffraction measurements, we have identified two types of robust multiple-q topological spin structures that appear in the absence of external magnetic fields: an anisotropic double-q spin spiral and an isotropic quadruple-q…
A-phase origin in cubic helimagnets ($M n S i,F e G e$ etc) is explained. It is shown that its upper bound is a result of the spin-wave instability at $H_\perp>\sqrt{8/3}Δ=H_{A2}$ where $H_\perp$ are the magnetic field perpendicular to the helix axis $\m k$ and $Δ$ the spin-wave gap respectively. The last appears due to the spin-wave interaction if one takes into account that the Dzyaloshinskii-Moriya interaction acts between different spins. The infra-red divergences (IRD) in the 1/S series for the magnetic energy at $H_\perp\to H_{A2}$ are responsible for the lower A-phase boundary $H_{A1}$.…
Understanding the role of spin-orbit coupling (SOC) has been crucial to controlling magnetic anisotropy in magnetic multilayer films. It has been shown that electronic structure can be altered via interface SOC by varying the superlattice structure, resulting in spontaneous magnetization perpendicular or parallel to the plane. In lieu of magnetic thin films, we study the similarly anisotropic helimagnet Cr$_{1/3}$NbS$_2$, where the spin polarization direction, controlled by the applied magnetic field, can modify the electronic structure. As a result, the direction of spin polarization can modu…
B20 compounds are a class of cubic helimagnets harboring nontrivial spin textures such as spin helices and skyrmions. It has been well understood that the Dzyaloshinskii-Moriya (DM) interaction is the origin of these textures, and the physics behind the DM interaction is the spin-orbital coupling (SOC). However the SOC shows its effect not only on the spins, but also on the electrons. In this paper, we will discuss effects of the SOC on the electron and spin transports in B20 compounds. An effective Hamiltonian is presented from symmetry analysis, and the spin-orbital coupling therein shows an…
We present magnetodielectric measurements in single crystals of the cubic spin-1/2 compound Cu$_2$OSeO$_3$. A magnetic field-induced electric polarization ($\vec{P}$) and a finite magnetocapacitance (MC) is observed at the onset of the magnetically ordered state ($T_c = 59$ K). Both $\vec{P}$ and MC are explored in considerable detail as a function of temperature (T), applied field $\vec{H}_a$, and relative field orientations with respect to the crystallographic axes. The magnetodielectric data show a number of anomalies which signal magnetic phase transitions, and allow to map out the phase d…
We investigate the static and ultrafast magneto-optical response of the hexagonal chiral helimagnet $Cr_{1/3}NbS_{2}$ above and below the helimagnetic ordering temperature. The presence of a magnetic easy plane contained within the crystallographic ab-plane is confirmed, while degenerate optical pump-probe experiments reveal significant differences in the dynamic between the parent, $NbS_{2}$, and Cr-intercalated compounds. Time resolved magneto-optical Kerr effect measurements show a two-step demagnetization process, where an initial, sub-ps relaxation and subsequent buildup ($τ> 50$ ps) in t…
Some unexpected features of the phase diagram of the monoaxial helimagnet in presence of an applied magnetic field perpendicular to the chiral axis are theoretically predicted. A rather general hamiltonian with long range Heisenberg exchange and Dzyaloshinskii--Moriya interactions is considered. The continuum limit simplifies the free energy, which contains only a few parameters which in principle are determined by the many parameters of the hamiltonian, although in practice they may be tuned to fit the experiments. The phase diagram contains a Chiral Soliton Lattice phase and a forced ferroma…
The chiral helimagnet, $Cr_{1/3}NbS_{2}$, hosts exotic spin textures, whose influence on the magneto-transport properties, make this material an ideal candidate for future spintronic applications. To date, the interplay between macroscopic magnetic and transport degrees of freedom is believed to result from a reduction in carrier scattering following spin order. Here, we present electronic structure measurements through the helimagnetic transition temperature, $T_{C}$ that challenges this view by showing a Fermi surface comprised of strongly hybridized Nb- and Cr- derived electronic states, an…
Chirality is breaking of mirror symmetry in matter. In the fields of biology and chemistry, this is particularly important because some of the essential molecules in life such as amino acids and DNA have chirality. It is a long-standing mystery how one of the enantiomers was chosen at the beginning stage of life. The understanding of the emergence of homochirality under some conditions is indispensable for the study of the origin of life as well as pharmaceutical science. The chirality is also emergent in magnetic structures. The longitudinal helical magnetic structure is the chiral object com…
Chiral skyrmion states exist in non - centrosymmetric magnetic crystals as a consequence of the asymmetric exchange Dzyaloshinskii-Moriya interactions that destroy the homogeneous magnetic state and generally lead to twisted incommensurate magnetic spin-structures. Recently, skyrmion lattices and free skyrmions in magnetic layers of the chiral helimagnets with the noncentrosymmetric cubic B20 crystal structure have been observed. The stabilization of these states and their transformation properties impressively illustrate the theoretically predicted solitonic nature of these chiral two-dimensi…
Using high resolution neutron diffraction and capacitance dilatometry we show that the thermal evolution of the helimagnetic state in CoMnSi is accompanied by a change in inter-atomic distances of up to 2%, the largest ever found in a metallic magnet. Our results and the picture of competing exchange and strongly anisotropic thermal expansion that we use to understand them sheds light on a new mechanism for large magnetoelastic effects that does not require large spin-orbit coupling.
We report on magnetic susceptibility and specific heat measurements of the cubic helimagnet FeGe in external magnetic fields and temperatures near the onset of long-range magnetic order at T_C=278.2(3)K. Pronounced anomalies in the field-dependent chi_ac(H) data as well as in the corresponding imaginary part chi"_ac(H) reveal a precursor region around T_C in the magnetic phase diagram. The occurrence of a maximum at T_0=279.6K in the zero-field specific heat data indicates a second order transition into a magnetically ordered state. A shoulder evolves above this maximum as a magnetic field is …
The B20 chiral magnets with broken inversion symmetry and C4 rotation symmetry have attracted much attention. The broken inversion symmetry leads to the Dzyaloshinskii-Moriya that gives rise to the helical and Skyrmion states. We report the unusual magnetoresistance (MR) of B20 chiral magnet Fe0.85Co0.15Si that directly reveals the broken C4 rotation symmetry. We present a microscopic theory, a minimal theory with two spin-orbit terms, that satisfies all the symmetry requirements and accounts for the transport experiments.
We report complex magnetic, magnetoresistance (MR) and magnetocaloric properties of Gd4RhAl and Tb4RhAl forming in the Gd4RhIn type cubic structure. Though the synthesis of the compounds was reported long ago, to our knowledge, no attempt was made to investigate the properties of these compounds. The present results of ac and dc magnetization, electrical resistivity and heat-capacity measurements down to 1.8 K establish that these compounds undergo antiferromagnetic order initially, followed by complex spin-glass features with decreasing temperature. These characteristic temperatures are: For …
We investigate magnetic, thermal, and dielectric properties of SrCuTe2O6, which is isostructural to PbCuTe2O6, a recently found, Cu-based 3D frustrated magnet with a corner sharing triangular spin network having dominant first and second nearest neighbor (nn) couplings [B. Koteswararao, et al. Phys. Rev. B 90, 035141 (2014)]. Although SrCuTe2O6 has a structurally similar spin network, but the magnetic data exhibit the characteristic features of a typical quasi -one-dimensional magnet, which mainly resulted from the magnetically dominant third nn coupling, uniform chains. The magnetic propertie…
Up to now the crystallographic structure of the magnetoelectric perovskite EuTiO3 was considered to remain cubic down to low temperature. Here we present high resolution synchrotron X-ray powder diffraction data showing the existence of a structural phase transition, from cubic Pm-3m to tetragonal I4/mcm, involving TiO6 octahedra tilting, in analogy to the case of SrTiO3. The temperature evolution of the tilting angle indicates a second-order phase transition with an estimated Tc=235K. This critical temperature is well below the recent anomaly reported by specific heat measurement at TA\sim282…
We report high-precision small angle neutron scattering of the orientation of the skyrmion lattice in a spherical sample of MnSi under systematic changes of the magnetic field direction. For all field directions the skyrmion lattice may be accurately described as a triple-$\vec{Q}$ state, where the modulus $\vert \vec{Q} \vert$ is constant and the wave vectors enclose rigid angles of $120^{\circ}$. Along a great circle across $\langle 100\rangle$, $\langle 110\rangle$, and $\langle 111\rangle$ the normal to the skyrmion-lattice plane varies systematically by $\pm3^{\circ}$ with respect to the …
Magneto-cubic and magneto-linear dependence observed in an in-plane anomalous Hall magnet
Institute of Science Tokyo（东京科学大学）；Institute for Materials Research (IMR), Tohoku University（东北大学物质材料研究所）；Advanced Science Research Center, Japan Atomic Energy Agency (JAEA)（日本原子能研究开发机构先进科学研究中心）；Institute for Solid State Physics (ISSP), The University of Tokyo（东京大学固体物理研究所）；Toyota Physical and Chemical Research Institute (TPCRI)（丰田物理化学研究所）
We study in this paper the phase transition in superlattices formed by alternate magnetic and ferroelectric layers, by the use of Monte Carlo simulation. We study effects of temperature, external magnetic and electric fields, magnetoelectric coupling at the interfaceon the phase transition. Magnetic layers in this work are modeled as thin films of simple cubic lattice with Heisenbergspins. Electrical polarizations of $\pm{1}$ are assigned at simple cubic lattice sites in the ferroelectric layers. The transition temperature, the layer magnetizations, the layer polarizations, the susceptibility,…
