We present the theory of nonlinear ac magnetic response for the highly nonlinear regime of the chiral soliton lattice. Increasing of the dc magnetic field perpendicularly to the chiral axis results in crossover inside the phase, when nearly isolated $2π$-kinks are partitioned by vast ferromagnetic domains. Assuming that each of the kink reacts independently from the other ones to the external ac field, we demonstrate that internal deformations of such a kink give rise to the nonlinear response.
The effect of thermal fluctuations on the phase structure of monoaxial helimagnets with external magnetic field parallel to the chiral axis is analyzed by means of a saddle point expansion of the free energy. The phase transition that separates the conical and forced ferromagnetic phases is changed to first order by the thermal fluctuations. In a purely monoaxial system the pitch of the conical state remains independent of temperature and magnetic field, as in mean field theory, even when fluctuations are taken into account. However, in presence of weak Dzyaloshinskii-Moriya interactions in th…
Chiral solitons are one dimensional localized magnetic structures that are metastable in some ferromagnetic systems with Dzyaloshinskii-Moriya interactions and/or uniaxial magnetic anisotropy. Though topological textures in general provide a very interesting playground for new spintronics phenomena, how to properly create and control single chiral solitons is still unclear. We show here that chiral solitons in monoaxial helimagnets, characterized by a uniaxial Dzyaloshinskii-Moriya interaction, can be stabilized with external magnetic fields. Once created, the soliton moves steadily in respons…
Monoaxial chiral magnets can form a noncollinear twisted spin structure called the chiral helimagnetic state. We study magnetic properties of such a chiral helimagnetic state, with emphasis on the effect of itinerant electrons. Modeling a monoaxial chiral helimagnet by a one-dimensional Kondo lattice model with the Dzyaloshinskii--Moriya interaction, we perform a variational calculation to elucidate the stable spin configuration in the ground state. We obtain a chiral helimagnetic state as a candidate for the ground state, whose helical pitch is modulated by the model parameters: the Kondo cou…
The phase diagram of the monoaxial chiral helimagnet as a function of temperature (T ) and magnetic field with components perpendicular (H x ) and parallel (H z ) to the chiral axis is theoretically studied via the variational mean field approach in the continuum limit. A phase transition surface in the three dimensional thermodynamic space separates a chiral spatially modulated phase from a homogeneous forced ferromagnetic phase. The phase boundary is divided into three parts: two surfaces of second order transitions of instability and nucleation type, in De Gennes terminology, are separated …
Successive phase transitions in a rare-earth monoaxial chiral magnet DyNi$_3$Ga$_{9}$ have been investigated by resonant x-ray diffraction. Magnetic dipole and electric quadrupole degrees of freedom arising from the large angular moment of $J=15/2$, in combination with the symmetric and antisymmetric exchange interactions and the crystal field anisotropy, give rise to competing ordered phases. We show that the antiferromagnetically coupled Dy moments in the $ab$-plane form an incommensurate helimagnetic order with $q\sim(0, 0, 0.43)$ just below $T_{\text{N}}=10$ K, which further exhibits succe…
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 $H-…
Helical magnetic structures and its responses to external magnetic fields in Yb(Ni$_x$Cu$_{1-x}$)$_3$Al$_9$, with a chiral crystal structure of the space group $R32$, have been investigated by resonant X-ray diffraction. It is shown that the crystal chirality is reflected to the helicity of the magnetic structure by a one to one relationship, indicating that there exists an antisymmetric exchange interaction mediated via the conduction electrons. When a magnetic field is applied perpendicular to the helical axis ($c$ axis), the second harmonic peak of $(0, 0, 2q)$ develops with increasing the …
We present a comprehensive study of the magnetization dynamics and phase evolution in Cr$_{1/3}$NbS$_{2}$, which realizes a chiral soliton lattice (CSL). The magnetic field dependence of the ac magnetic response is analyzed for five harmonic components, $M_{nω}(H)$ $(n =1-5)$, using a phase sensitive measurement over a frequency range, $f = 11 - 10,000$ Hz. At a critical field, the modulated CSL continuously evolves from a helicity-rich to a ferromagnetic domain-rich structure, where the crossover is revealed by the onset of an anomalous nonlinear magnetic response that coincides with extremel…
The magnon spectral problem is solved in terms of the spectrum of a diagonalizable operator for a generic class of magnetic states that includes several types of domain walls and the chiral solitons of monoaxial helimagnets. Focusing on the isolated solitons of monoaxial helimagnets, it is shown that the spin waves scattered (reflected and transmitted) by the soliton suffer a lateral displacement analogous to the Goos-Hanchen effect of optics. The displacement is a fraction of the wavelength, but can be greatly enhanced by using an array of well separated solitons. Contrarily to the Goos-Hanch…
We show that the stability (existence/absence) and interaction (repulsion/attraction) of chiral solitons in monoaxial chiral magnets can be varied by tilting the direction of magnetic field. We, thereby, elucidate that the condensation of attractive chiral solitons causes the discontinuous phase transition predicted by a mean field calculation. Furthermore we theoretically demonstrate that the metastable field-polarized-state destabilizes through the surface instability, which is equivalent to the vanishing surface barrier for penetration of the solitons. We experimentally measure the magnetor…
We thoroughly study the zero temperature properties of monoaxial chiral spin systems under a tilted magnetic field. The magnetic phase diagram includes two kinds of continuous phase transitions and one discontinuous phase transition. We clarify the properties of the phase transition in terms of the helical wave picture and the particle (soliton) picture and also in terms of the interaction between solitons. The interacting-soliton picture properly describes most of the discontinuous phase transition. In addition, we investigate several instabilities of the modulated structures such as an isola…
We show the existence of an isolated soliton excitation over the topological ground state configuration in chiral helimagnet with the Dzyaloshinskii-Moryia exchange and the strong easy-plane anisotropy. The magnetic field perpendicular to the helical axis stabilizes the kink crystal state which plays a role of "topological protectorate" for the traveling soliton with a definite handedness. To find new soliton solution, we use the Bäcklund transformation technique. It is pointed out that the traveling soliton carries the magnon density and a magnetic solition transport may be realized.
Motivated by the spin current problem in chiral helimagnet, we rigorously elucidated the hidden Galilean invariance in the chiral XY model under the magnetic field. The Lie group analysis is applied to the differential equations of the continuum theory of the chiral helimagnet with the parity-violating Dzyaloshinskii-Morya coupling under a transversal magnetic field. Lie point symmetries and the invariant solutions under these symmetries are found. They present sliding solutions that come up as a consequence of breaking of both spin rotational symmetry by the external magnetic field and a pari…
Frustration of harmonic and solitonic helimagnetism on the body-centered tetragonal lattice of GdAlSi
The University of Tokyo（东京大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所 新兴物质科学中心）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；High Energy Accelerator Research Organization（高能加速器研究机构）；Nagoya University Synchrotron Radiation Research Center (NUSR), Nagoya University（名古屋大学同步辐射研究中心）
The tensile strain is a promising tool for creation and manipulation of magnetic solitonic textures in the chiral helimagnets via tunable control of magnetic anisotropy and Dzyaloshinskii-Moriya interaction. Here, by using the in-situ resonant small-angle x-ray scattering we demonstrate that the skyrmion and chiral soliton lattices can be achieved as metastable states in FeGe lamella as distinct states or even simultaneously by combining the tensile strain and magnetic fields in various orientations with respect to the deformation. The small-angle scattering data are discussed in the frame of …
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…
We demonstrated that the chiral soliton lattice formed out of a chiral helimagnet exhibits coherent sliding motion by applying a time-dependent magnetic field parallel to the helical axis, in addition to a static field perpendicular to the helical axis. To describe the coherent sliding, we use the collective coordinate method and numerical analysis. We also show that the time-dependent sliding velocity causes a time-varying Berry cap which causes the spin-motive-force. A salient feature of the chiral soliton lattice is appearance of the strongly amplified spin motive force which is directly pr…
Intricate spin textures in helimagnets, identified as stable topological Skyrmions, were observed experimentally, where Skyrme lattice was supposed to exhibit symmetric structures in the ground state. We show the possibility of asymmetric Skyrmions in a helimagnetic model, for individual Skyrmion as well as for the hexagonal Skyrme crystal with higher charge, as perturbative deformation and stabilization of exact ferromagnetic solitons. Such nonsymmetric configurations for the Skyrme lattice, predicted here theoretically, need to be verified in precision experiments.
The Dzyaloshinskii-Moriya (DM) interaction is present in the transition metal dichalcogenides (TMDC) magnets of form $M_{1/3}T$S$_{2}$ ($M$ $=$ 3d transition metal, $T$ $\in$ {Nb, Ta}), given that the intercalants $M$ form $\sqrt{3}\times\sqrt{3}$ superlattices within the structure of the parent materials $T$S$_2$ and break the centrosymmetry. Competition between the DM and ferromagnetic exchange interactions in these systems has been shown to stabilize a topological defect known as a chiral soliton in select intercalated TMDCs, initiating interest both in terms of fundamental physics and the …
We investigate the spin structure of a uni-axial chiral magnet near the transition temperatures in low fields perpendicular to the helical axis. We find a fan-type modulation structure where the clockwise and counterclockwise windings appear alternatively along the propagation direction of the modulation structure. This structure is often realized in a Yoshimori-type (non-chiral) helimagnet but it is rarely realized in a chiral helimagnet. To discuss underlying physics of this structure, we reconsider the phase diagram (phase boundary and crossover lines) through the free energy and asymptotic…
Monoaxial chiral magnets can form a peculiar noncollinear spin structure called the chiral soliton lattice in an applied magnetic field perpendicular to the helical axis. We study magnetic properties and electrical transport in the chiral soliton lattice by a Monte Carlo simulation for a one-dimensional Kondo lattice model including the Dzyaloshinskii-Moriya interaction between classical localized spins. We show that the model exhibits a helical spin structure at a zero magnetic field, which turns into the chiral soliton lattice, and finally, to a forced ferromagnetic state with increasing the…
Spin polarized currents originate a spin-transfer torque that enables the manipulation of magnetic textures. Here we theoretically study the effect of a spin-polarized current on the magnetic texture corresponding to a chiral soliton lattice in a monoaxial helimagnet under a transverse magnetic field. At sufficiently small current density the chiral soliton lattice reaches a steady motion state with a velocity proportional to the intensity of the applied current, the mobility being independent of the density of solitons and the magnetic field. This motion is accompanied with a small conical di…
We show that the bulk transport magnetic current is generated by the moving magnetic kink crystal (chiral soliton lattice) formed in the chiral helimagnet under the static magnetic field applied perpendicular to the helical axis. The current is caused by the non-equilibrium transport momentum with the kink mass being determined by the spin fluctuations around the kink crystal state. An emergence of the transport magnetic currents is then a consequence of the dynamical off-diagonal long range order along the helical axis. We derive an explicit formula for the inertial mass of the kink crystal a…
We study magnetoelastic resonance phenomena in a mono-axial chiral helimagnet belonging to hexagonal crystal class. By computing the spectrum of coupled elastic wave and spin wave, it is demonstrated how hybridization occurs depending on their chirality. Specific features of the magnetoelastic resonance are discussed for the conical phase and the soliton lattice phase stabilized in the mono-axial chiral helimagnet. The former phase exhibits appreciable non-reciprocity of the spectrum, the latter is characterized by a multi-resonance behavior. We propose that the non-reciprocal spin wave around…
Chiral magnets often show intriguing magnetic and transport properties associated with their peculiar spin textures. A typical example is a chiral soliton lattice, which is found in monoaxial chiral magnets, such as CrNb$_3$S$_6$ and Yb(Ni$_{1-x}$Cu$_x$)$_3$Al$_9$ in an external magnetic field perpendicular to the chiral axis. Here, we theoretically investigate the electronic and magnetic properties in the chiral soliton lattice by a minimal itinerant electron model. Using variational calculations, we find that the period of the chiral soliton lattice can be locked at particular values dictate…
The chiral helimagnet Cr1/3NbS2 has been investigated by magnetic, transport and thermal properties measurements on single crystals and by first principles electronic structure calculations. From the measured field and temperature dependence of the magnetization for fields applied perpendicular to the c axis, the magnetic phase diagram has been constructed in the vicinity of the phase transitions. A transition from a paramagnetic to a magnetically ordered phase occurs near 120 K. With increasing magnetic field and at temperatures below 120 K, this material undergoes transitions from a helimagn…
We give detailed description of the transport spin current in the chiral helimagnet. Under the static magnetic field applied perpendicular to the helical axis, the magnetic kink crystal (chiral soliton lattice) is formed. Once the kink crystal begins to move under the Galilean boost, the spin-density accumulation occurs inside each kink and there emerges periodic arrays of the induced magnetic dipoles carrying the transport spin current. The coherent motion of the kink crystal dynamically generates the spontaneous demagnetization field. This mechanism is analogous to the Döring-Becker-Kittel m…
Magnetic-field effect on the magnetic and electric properties in a chiral polar ordered corundum Ni$_2$InSbO$_6$ has been investigated. Single-crystal soft x-ray and neutron diffraction measurements confirm long-wavelength magnetic modulation. The modulation direction tends to align along the magnetic field applied perpendicular to the polar axis, suggesting that the nearly proper-screw type helicoid should be formed below 77\,K. The application of a high magnetic field causes a metamagnetic transition. In a magnetic field applied perpendicular to the polar axis, a helix-to-canted antiferromag…
The topologically-protected, chiral soliton lattice is a unique state of matter offering intriguing functionality and it may serve as a robust platform for storing and transporting information in future spintronics devices. While the monoaxial chiral magnet Cr$_{1/3}$NbS$_2$ is known to host this exotic state in an applied magnetic field, its detailed microscopic origin has remained a matter of debate. Here we work towards addressing this open question by measuring the spin wave spectrum of Cr$_{1/3}$NbS$_2$ over the entire Brillouin zone with inelastic neutron scattering. The well-defined spi…
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 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 …
We grew thin films of a heavy fermion chiral magnet YbNi$_3$Al$_9$ by using molecular beam epitaxy. They were grown on $c$-plane sapphire substrates under ultra-high vacuum while maintaining a deposition rate at a stoichiometric ratio among Yb, Ni, and Al. The resulting thin films contain epitaxial grains with a $c$ axis parallel to the substrate surface: The YbNi$_3$Al$_9$ $c$ axis is parallel to the sapphire $b$ or $a$ axis. The temperature dependence of the resistivity exhibits a typical feature of a dense Kondo system with a broad shoulder structure at $\sim$40\,K, as well as a kink as a s…
Helical-to-Fan Transitions under Magnetic Fields in the Noncentrosymmetric Tetragonal Magnet EuRhGe$_3$
Hiroshima University（广岛大学）；Institute of Materials Structure Science, High Energy Accelerator Research Organization（高能加速器研究机构材料结构科学研究所）；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）
The Skyrme-particle, the $skyrmion$, was introduced over half a century ago and used to construct field theories for dense nuclear matter. But with skyrmions being mathematical objects - special types of topological solitons - they can emerge in much broader contexts. Recently skyrmions were observed in helimagnets, forming nanoscale spin-textures that hold promise as information carriers. Extending over length-scales much larger than the inter-atomic spacing, these skyrmions behave as large, classical objects, yet deep inside they are of quantum origin. Penetrating into their microscopic root…
