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 renormalization at H = 0 shows the fluctuation regime in Cu2OSeO3 to lie closer to that expected within the Wilson-Fischer scenario.
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…
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…
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…
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 helical spin texture is of great current interest for a host of novel spin-dependent transport phenomena. We report a rich variety of nontrivial, helimagnetic phases in the simple cubic perovskite SrFeO3 under magnetic fields up to 42 T. Magnetic and resistivity measurements revealed that the proper-screw spin phase proposed for SrFeO3 can be subdivided into at least five kinds of ordered phases. Near the multicritical point, an unconventional anomalous Hall effect was found to show up and was interpreted as due to a possible long-period noncoplanar spin texture with scalar spin chirality.
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 …
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…
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 $H_{A1}$.…
Neutron scattering is used to study magnetic field induced ordering in the quasi-1D quantum spin-tube compound Sul--Cu$_2$Cl$_4$ that in zero field has a non-magnetic spin-liquid ground state. The experiments reveal an incommensurate chiral high-field phase stabilized by a geometric frustration of the magnetic interactions. The measured critical exponents $β\approx0.235$ and $ν\approx0.34$ at $H_c\approx3.7$ T point to an unusual sub-critical scaling regime and may reflect the chiral nature of the quantum critical point.
In this work, the magnetism of the single crystal Cr$_{1/3}$NbS$_{2}$, which exhibits chiral magnetic soliton lattice (CSL) state, is investigated. The magnetization displays strong magnetic anisotropy when the field is applied perpendicularly and parallel to the $c$-axis in low field region ($H<H_{S}$, $H_{S}$ is the saturation field). The critical exponents of Cr$_{1/3}$NbS$_{2}$ are obtained as $β=$ 0.370(4), $γ=$ 1.380(2), and $δ=$ 4.853(6), which are close to the theoretical prediction of three-dimensional Heisenberg model. Based on the scaling equation and the critical exponents, the $H-…
A complete phase diagram of Zn substituted quantum quasi-two-dimensional helimagnet LiCu2O2 has been presented. Helical ordering transition temperature (T_h) of the original LiCu2O2 follows finite size scaling for less than ~ 5.5% Zn substitution, which implies the existence of finite helimagnetic domains with domain boundaries formed with nearly isolated spins. Higher Zn substitution > 5.5% quenches the long-range helical ordering and introduces an intriguing Zn level dependent magnetic phase transition with slight thermal hysteresis and a universal quadratic field dependence for T_c (Zn > 0.…
Two centuries of research on phase transitions have repeatedly highlighted the importance of critical fluctuations that abound in the vicinity of a critical point. They are at the origin of scaling laws obeyed by thermodynamic observables close to second-order phase transitions resulting in the concept of universality classes, that is of paramount importance for the study of organizational principles of matter. Strikingly, in case such soft fluctuations are too abundant they may alter the nature of the phase transition profoundly; the system might evade the critical state altogether by undergo…
We present magnetodielectric measurements in single crystals of the cubic spin-1/2 compound Cu$_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…
Magnetic skyrmions are nano-sized topological spin textures stabilized by a delicate balance of magnetic energy terms. The chemical substitution of the underlying crystal structure of skyrmion-hosting materials offers a route to manipulate these energy contributions, but also introduces additional effects such as disorder and pinning. While the effects of doping and disorder have been well studied in B20 metallic materials such as Fe$_{1-x}$Co$_x$Si and Mn$_{1-x}$Fe$_x$Si, the consequences of chemical substitution in the magnetoelectric insulator Cu$_2$OSeO$_3$ have not been fully explored. In…
We report investigations on the ground state magnetic properties of intermetallic compound GdCu through dc magnetization measurements. GdCu undergoes first order martensitic type structural transition over a wide temperature window of coexisting phases. The high temperature cubic and the low temperature orthorhombic phases have different magnetic character and they show antiferromagnetic and helimagnetic orderings below 145 K and 45 K respectively. We observe clear signature of a glassy magnetic phase below the helimagnetic ordering temperature, which is marked by thermomagnetic irreversibilit…
Low-energy spin excitations in any long-range ordered magnetic system in the absence of magnetocrystalline anisotropy are gapless Goldstone modes emanating from the ordering wave vectors. In helimagnets, these modes hybridize into the so-called helimagnon excitations. Here we employ neutron spectroscopy supported by theoretical calculations to investigate the magnetic excitation spectrum of the isotropic Heisenberg helimagnet ZnCr2Se4 with a cubic spinel structure, in which spin-3/2 magnetic Cr3+ ions are arranged in a geometrically frustrated pyrochlore sublattice. Apart from the conventional…
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…
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…
We report on the slow magnetization dynamics observed upon the magnetic phase transitions of GaV4S8, a multiferroic compound featuring a long-ranged cycloidal magnetic order and a Néel-type skyrmion lattice in a relatively broad temperature range below its Curie temperature. The fundamental difference between GaV4S8 and the chiral helimagnets, wherein the skyrmion phase was first discovered, lies within the polar symmetry of GaV4S8, promoting a cycloidal instead of a helical magnetic order and rendering the magnetic phase diagram essentially different from that in the cubic helimagnets. Our ac…
Axisymmetric magnetic strings with a fixed sense of rotation and nanometer sizes (chiral magnetic vortices or Skyrmions) have been predicted to exist in a large group of non-centrosymmetric crystals more than two decades ago. Recently these extraordinary magnetic states have been directly observed in thin layers of cubic helimagnet (Fe,Co)Si. In this report we apply our earlier theoretical findings to review main properties of chiral Skyrmions, to elucidate their physical nature, and to analyse these recent experimental results on magnetic-field-driven evolution of Skyrmions and helicoids in c…
Multiple intriguing low temperature phenomena have recently been discovered in the family of chiral cubic Co-Zn-Mn compounds with $β-$Mn-type structure. In particular, Co$_8$Zn$_8$Mn$_4$ displays a reduction of the helical spiral pitch on cooling, along with lattice shape transformations of metastable skyrmions and the manifestation of peculiar magnetic textures due to strong magnetocrystalline anisotropy. Here we report on temperature-dependent measurements of helimagnon excitations in the field polarized regime Co$_8$Zn$_8$Mn$_4$ using the spin wave small-angle neutron scattering (SWSANS) te…
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 …
Magnetic materials can host skyrmions, which are topologically non-trivial spin textures. In chiral magnets with cubic lattice symmetry, all previously-observed skyrmion phases require thermal fluctuations to become thermodynamically stable in bulk materials, and therefore exist only at relatively high temperature, close to the helimagnetic transition temperature. Other stabilization mechanisms require a lowering of the cubic crystal symmetry. Here, we report the identification of a second skyrmion phase in Cu$_{2}$OSeO$_{3}$ at low temperature and in the presence of an applied magnetic field.…
High-resolution DC magnetization and AC-specific heat data of the cubic helimagnet FeGe have been measured as function of temperature and magnetic field. The magnetization data as well as the isothermal susceptibility data confirm the complexity of the magnetic phase diagram in the vicinity of the onset of long-rang magnetic order (Tc = 278.5 K) and the existence of a segmented A-phase region. Moreover, these data revealed independent and clear indications of phase boundaries and crossovers within the A-phase region. Together with the anomalies in the specific-heat data around Tc and at small …
A skyrmion state in a non-centrosymmetric helimagnet displays topologically protected spin textures with profound technological implications for high density information storage, ultrafast spintronics, and effective microwave devices. Usually, its equilibrium state in a bulk helimagnet occurs only over a very restricted magnetic-field--temperature phase space and often in the low temperature region near the magnetic transition temperature Tc. We have expanded and enhanced the skyrmion phase region from the small range of 55-58.5 K to 5-300 K in single-crystalline Cu2OSeO3 by pressures up to 42…
The optical spectrum of the cubic helimagnetic metal FeGe has been investigated in the frequency range from 0.01 - 3.1 eV for different temperatures from 30 K to 296 K. The optical conductivity shows the evolution of a low energy (0.22 eV) interband transition and the development of a narrow free carrier response with a strong energy and temperature dependence. The frequency dependent effective mass and scattering rate derived from the optical data indicate the formation of dressed quasi-particles with a mass renormalization factor of 12. Similar to FeSi the spectral weight in FeGe is not reco…
We present a comprehensive and systematic magnetization and ac susceptibility study of Mn$_{1-x}$Fe$_{x}$Si over an extensive range of ten Fe concentrations between $x$ = 0 - 0.32. With increasing Fe substitution, the critical temperature decreases but the magnetic phase diagrams remain qualitatively unaltered for $x$ $\leq$ $x^*$ $\approx$ 0.11 with clear boundaries between the helical, conical, and skyrmion lattice phase as well as an enhanced precursor phase. A notably different behavior sets in for $x$ $=$ 0.11, 0.13 and 0.14, where certain characteristics of helimagnetic correlations pers…
Nonreciprocal resistance, depending on both directions of current ($j$) and magnetic-field ($H$) or magnetization ($M$), is generally expected to emerge in a chiral conductor, and be maximized for $j$ $\parallel$ $H$($M$). This phenomenon, electrical magnetochiral effect (eMChE), is empirically known to increase with $H$ in a paramagnetic or fully ferromagnetic state on chiral lattice or to depend on fluctuation properties of a helimagnetic state. We report here the eMChE over a wide temperature range in the chiral-lattice magnet MnGe in which the spin hedgehog lattice (HL) forms with the trip…
We report the magnetization, ac susceptibility, and specific heat of optically float-zoned single crystals of Fe$_{1-x}$Co$_{x}$Si, $0.20 \leq x \leq 0.50$. We determine the magnetic phase diagrams for all major crystallographic directions and cooling histories. After zero-field cooling, the phase diagrams resemble that of the archetypal stoichiometric cubic chiral magnet MnSi. Besides the helical and conical state, we observe a pocket of skyrmion lattice phase just below the helimagnetic ordering temperature. At the phase boundaries between these states evidence for slow dynamics is observed.…
We study the Néel-paramagnetic quantum phase transition in two-dimensional dimerized $S=1/2$ Heisenberg antiferromagnets using finite-size scaling of quantum Monte Carlo data. We resolve the long standing issue of the role of cubic interactions arising in the bond-operator representation when the dimer pattern lacks a certain symmetry. We find non-monotonic (monotonic) size dependence in the staggered (columnar) dimerized model, where cubic interactions are (are not) present. We conclude that there is an irrelevant field in the staggered model that is not present in the columnar case, but, at …
Spin waves in chiral magnetic materials are strongly influenced by the Dzyaloshinskii-Moriya interaction resulting in intriguing phenomena like non-reciprocal magnon propagation and magnetochiral dichroism. Here, we study the non-reciprocal magnon spectrum of the archetypical chiral magnet MnSi and its evolution as a function of magnetic field covering the field-polarized and conical helix phase. Using inelastic neutron scattering, the magnon energies and their spectral weights are determined quantitatively after deconvolution with the instrumental resolution. In the field-polarized phase the …
Motivated by its relation to an $\cal{NP}$-hard problem, we analyze the ground state properties of anti-ferromagnetic Ising-spin networks embedded on planar cubic lattices, under the action of homogeneous transverse and longitudinal magnetic fields. This model exhibits a quantum phase transition at critical values of the magnetic field, which can be identified by the entanglement behavior, as well as by a Majorization analysis. The scaling of the entanglement in the critical region is in agreement with the area law, indicating that even simple systems can support large amounts of quantum corre…
We analyze the temperature dependence of the entropy of the spin-1/2 Heisenberg model on the three-dimensional simple-cubic lattice, for both the case of antiferromagnetic and ferromagnetic nearest neighbor exchange interactions. Using optimized extended ensemble quantum Monte Carlo simulations, we extract the entropy at the critical temperature for magnetic order from a finite-size scaling analysis. For the antiferromagnetic case, the critical entropy density equals 0.341(5)$k_B$, whereas for the ferromagnet, a larger value of 0.401(5) $k_B$ is obtained. We compare our simulation results to e…
