Monoaxial Chiral Magnets Research Articles

Continuum of metastable helical states of monoaxial chiral magnets: Effect of boundary conditions

Continuum of metastable helical states of monoaxial chiral magnets: Effect of boundary conditions

Transformation from Magnetic Soliton to Skyrmion in a Monoaxial Chiral Magnet.

Topological spin textures are of great interest for both fundamental physics and applications in spintronics. The Dzyaloshinskii-Moriya interaction underpins the formation of single-twisted magnetic solitons or multi-twisted magnetic skyrmions in magnetic materials with different crystallographic symmetries. However, topological transitions between these two kinds of topological objects have not been verified experimentally. Here, the direct observation of transformations from a chiral soliton lattice (CSL) to magnetic skyrmions in a nanostripe of the monoaxial chiral magnet CrNb3 S6 using Lorentz transmission electron microscopy is reported. In the presence of an external magnetic field, helical spin structures first transform into CSLs and then evolve into isolated elongated magnetic skyrmions. The detailed spin textures of the elongated magnetic skyrmions are resolved using off-axis electron holography and are shown to comprise two merons, which enclose their ends and have unit total topological charge. Magnetic dipolar interactions are shown to play a key role in the magnetic soliton-skyrmion transformation, which depends sensitively on nanostripe width. The findings here, which are consistent with micromagnetic simulations, enrich the family of topological magnetic states and their transitions and promise to further stimulate the exploration of their emergent electromagnetic properties.

Soliton locking phenomenon in bulk single crystal of monoaxial chiral magnet MnNb3S6

MnNb3S6 is a monoaxial chiral magnet and stabilizes magnetic solitons in the presence of a magnetic field (H). The number of solitons can be controlled by varying H. Furthermore, MnNb3S6 exhibits magnetization relaxation due to soliton annihilation, that is, a nonequilibrium chiral soliton lattice (CSL) state. In this study, we observed soliton locking phenomena in a CSL state on bulk MnNb3S6 crystal, as on micro-processed crystals of CrNb3S6. Thus, we could create nonequilibrium and equilibrium CSL states and switch between them. A numerical simulation revealed that the soliton number was preserved in the soliton locking region; thus, magnetization relaxation was not observed.

Magnetic ground state dependent magnetostriction effects on the chiral magnet CrNb3S6

A prototype of the monoaxial chiral magnet ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$ exhibited two magnetostriction (MS) effects: (1) spontaneous MS due to the exchange interaction and spin-orbit coupling (SOC) at zero dc magnetic field ($H$) [Phys. Rev. B 102, 014446 (2020)] and (2) paramagnetic MS due to SOC and Zeeman energy at room temperature [Phys. Rev. B 105, 104412 (2022)]. ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$ has various magnetic structures, such as helimagnetic, first chiral soliton lattice (CSL-1), second CSL (CSL-2), CSL-2 with irreversibility, and forced ferromagnetic phases, resulting from the Dzyaloshinskii--Moriya interaction as a function of $H$ below the magnetic ordering temperature (${T}_{\mathrm{c}}$). In this study, we conducted powder x-ray diffraction analyses to investigate the effects of $H$ and temperature ($T$) on the MS at the atomic level. The $T$ dependence of the lattice constants reveals that below ${T}_{\mathrm{c}}$, the MS depends on the magnetic structure. The MS below ${T}_{\mathrm{c}}$ is discussed in this study in terms of both the hybridization between the ${z}^{2}$ orbital of $\mathrm{Nb}(4f)$ and delocalized ${a}_{1}$ orbital of Cr and the structural symmetry of the ${\mathrm{CrS}}_{6}$ octahedron.

Competition between helimagnetic and ferroquadrupolar ordering in a monoaxial chiral magnetDyNi3Ga9studied by resonant x-ray diffraction

Successive phase transitions in a rare-earth monoaxial chiral magnet ${\mathrm{DyNi}}_{3}{\mathrm{Ga}}_{9}$ 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 $\mathbit{q}\ensuremath{\sim}(0,0,0.43)$ just below ${T}_{\text{N}}=10$ K, which further exhibits successive first-order transitions to the commensurate helimagnetic order with $\mathbit{q}=(0,0,0.5)$ at ${T}_{\text{N}}^{\ensuremath{'}}=9.0$ K, and to the canted antiferromagnetic order with $\mathbit{q}=(0,0,0)$ at ${T}_{\text{N}}^{\ensuremath{''}}=8.5$ K, both with large coexistence regions. The relation of the magnetic helicity and the crystal chirality in ${\mathrm{DyNi}}_{3}{\mathrm{Ga}}_{9}$ is also uniquely determined. Splitting of the (6,0,0) Bragg peak is observed below ${T}_{\text{N}}^{\ensuremath{''}}$, reflecting the lattice distortion due to the ferroquadrupole order. In the canted antiferromagnetic phase, a spin-flop transition takes place at 5 K when the temperature is swept in a weak magnetic field. We discuss these transitions from the viewpoint of the competing energies described above.

Controlling avalanche soliton nucleation in a chiral soliton lattice on a monoaxial chiral magnet CrNb3S6 by dynamic strain

The monoaxial chiral magnet CrNb3S6 exhibits a chiral soliton lattice (CSL) upon application of an external magnetic field (H) perpendicular to the helical axis (c-axis). The increase in the soliton (kink) number of the CSL in the process of decreasing H accompanies soliton penetration after nucleation at the surface. Avalanche soliton nucleation occurs during the initial process of soliton nucleation. We applied dynamic strain with scores of MHz to the crystal with the crystal size along the c-axis of 10 μm from the edge of the c-axis, so that we controlled the avalanche soliton nucleation by modifying the surface barrier. The present results suggest that the acoustic wave is useful for controlling the soliton number.

Single-crystal growth and magnetic phase diagram of the enantiopure crystal of NdPt2B

Chirality, which is a fundamental property of symmetry, can produce unique electronic and magnetic properties. The problem is that many of the chiral inorganic compounds form a racemic mixture consisting of right- and left-handed enantiomers. Here, the authors succeeded in growing the enantiopure single crystal of Nd-based monoaxial chiral magnet, demonstrating the nontrivial magnetic phase diagram in this rare-earth chiral magnet with the DM interaction. This ternary rare-earth platinum boride system provides an attractive platform for examining chiral magnetism and the role of DM interaction.

Soliton locking phenomenon over finite magnetic field region in the monoaxial chiral magnet CrNb3S6

Previous magnetic measurements for the chiral magnet CrNb3S6 have shown that the soliton penetration and soliton dissipation in the chiral soliton lattice state strongly depend on the crystal's size and shape. We performed magnetic measurements for a thin single crystal of CrNb3S6 with a thickness 3 μm, permitting the existence of approximately 60 solitons, and observed the magnetization (M)—magnetic field (H) curve with a remarkable full M–H loop. By investigating the minor loop of the M–H curve in detail, we found that the inside of the full M–H loop allows an infinite number of quasi-stable states for each eigen number of solitons, utilizing a non-negligible distribution of the thickness around 3 μm. This study reveals that in a microcrystal with a chiral axis length of a few micrometers, any magnetic state with an arbitrary soliton number can be created in a certain H range within the full M–H loop.

Instabilities in monoaxial chiral magnets under a tilted magnetic field

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 isolated soliton and the surface modulation, since their instabilities should be important to the changes of the magnetic properties. For this purpose, we perform the analyses based on the energy landscape as well as the excitation spectrum; the former approach gives an intuitive interpretation. We clarify the mechanisms of the instabilities through these analyses and draw the stability lines of solitons in the magnetic phase diagram.

Pressure Effect on the Chiral Helimagnetic Order in YbNi3Al9

The monoaxial chiral magnet YbNi3Al9 undergoes a chiral helimagnetic (CHM) order at around TM = 3.4 K. By applying magnetic field perpendicular to the chiral c-axis, the magnetic phase transition t...

Spin-current diode with a monoaxial chiral magnet

Monoaxial chiral magnets exhibit a chiral conical magnetic state in a magnetic field parallel to the chiral axis. The conical spins carry the potential for nonreciprocal transport phenomena, as they break both spatial inversion and time reversal symmetries. Here, we study the spin-dependent transport in the chiral conical magnetic state, using the Landauer method based on Green's functions for a one-dimensional Kondo lattice model. We show that the system exhibits nonreciprocal spin transport, which depends on the chirality, period, cone angle, and polarization of the spin current. In particular, we find the distinct cone angle dependence between the spin textures with long and short periods. We also show that the nonreciprocity is related to the spin states of itinerant electrons near the leads. Our results indicate that the chiral cone acts as a spin-current diode, which can be flexibly controlled by a magnetic field.

Chiral solitons in monoaxial chiral magnets in tilted magnetic field

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 magnetoresistance (MR) of micrometer-sized samples in the tilted fields in demagnetization-free configuration. We corroborate the scenario that hysteresis in MR is a sign for existence of the solitons, through agreement between our theory and experiments.

Extended exchange interactions stabilize long-period magnetic structures in Cr1∕3NbS2

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 spintronic devices. While the monoaxial chiral magnet Cr1∕3NbS2 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 Cr1∕3NbS2 over the entire Brillouin zone with inelastic neutron scattering. The well-defined spin wave modes allow us to determine the values of several microscopic interactions for this system. The experimental data are well-explained by a Heisenberg Hamiltonian with exchange constants up to the third nearest neighbor and an easy plane magnetocrystalline anisotropy term. Our work shows that both the second and third nearest neighbor exchange interactions contribute to the formation of the helimagnetic and chiral soliton lattice states in this robust three-dimensional magnet.

Intrinsic hysteresis due to the surface barrier for chiral solitons in monoaxial chiral helimagnets

Chiral solitons in monoaxial chiral magnets undergo a surface barrier, which is analogous to the Bean-Livingston barrier in type-II superconductors. The authors argue here that the surface barrier is the main mechanism for large hysteresis observed in magnetoresistance (MR) measurements on micrometer-sized samples of CrNb${}_{3}$S${}_{6}$. In the MR hysteresis, a conspicuous jump is observed at the field ${H}_{\mathrm{b}}$ for decreasing fields. Experimental results for ${H}_{\mathrm{b}}\ensuremath{\sim}0.4{H}_{\mathrm{c}}$ (with thermodynamic critical field ${H}_{\mathrm{c}}$) and the theoretical result ${H}_{\mathrm{b}}/{H}_{\mathrm{c}}=4/{\ensuremath{\pi}}^{2}$ are in good agreement with each other. The surface barrier is regarded as a common property of systems (superconductors, chiral magnets, and chiral liquid crystals) that exhibit continuous transitions of the nucleation type.

Lock-in of a Chiral Soliton Lattice by Itinerant Electrons

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 dictated by the Fermi wave number, in stark contrast to spin-only models. We discuss this behavior caused by the spin-charge coupling as a possible mechanism for the lock-in discovered in Yb(Ni$_{1-x}$Cu$_x$)$_3$Al$_9$. We also show that the same mechanism leads to the spontaneous formation of the chiral soliton lattice even in the absence of the magnetic field.

Nonlinear magnetic responses at the phase boundaries around helimagnetic and skyrmion lattice phases in MnSi: Evaluation of robustness of noncollinear spin texture

The phase diagram of a cubic chiral magnet MnSi with multiple Dzyaloshinskii-Moriya (DM) vectors as a function of temperature $T$ and dc magnetic field ${H}_{\mathrm{dc}}$ was investigated using intensity mapping of the odd-harmonic responses of ac magnetization $({M}_{1\ensuremath{\omega}}$ and ${M}_{3\ensuremath{\omega}})$, and the responses at phase boundaries were evaluated according to a prescription [J. Phys. Soc. Jpn. 84, 104707 (2015)]. By evaluating ${M}_{3\ensuremath{\omega}}/{M}_{1\ensuremath{\omega}}$ appearing at phase boundaries, the robustness of noncollinear spin texture in both the helimagnetic (HM) and the skyrmion lattice (SkL) phases of MnSi was discussed. The robustness of vortices-type solitonic texture SkL in MnSi is smaller than those of both the single DM HM and chiral soliton lattice phases of a monoaxial chiral magnet ${\mathrm{Cr}}_{1/3}{\mathrm{NbS}}_{2}$, and furthermore the robustness of the multiple DM HM phase in MnSi is smaller than that of its SkL. Through magnetic diagnostics over the wide $T\ensuremath{-}{H}_{\mathrm{dc}}$ range, we found a new paramagnetic (PM) region with ac magnetic hysteresis, where spin fluctuations have been observed via electrical magnetochiral effect. The anomalies observed in the previous ultrasonic attenuation measurement correspond to the peak positions of out-of-phase ${M}_{1\ensuremath{\omega}}$. The appearance of a new PM region occurs at a characteristic magnetic field, above which indeed the SkL phase appears. It has us suppose that the new PM region could be a phase with spin fluctuation like the skyrmion gas phase.

Effects of dynamic stress in magnetic superlattice of a monoaxial chiral magnet Cr1/3NbS2

A monoaxial chiral magnet forms a kind of spin superlattice structure, termed chiral soliton lattice (CSL), by the application of a magnetic field H perpendicular to a helical chiral axis. It has been reported that the CSL accompanies the magnetoresistance effect as well as a discrete change in magnetization and magnetoresistance. In order to verify the effect of the structural modification on the CSL state, we measured the magnetoresistance under the dynamic stress (DS) with a frequency of the order of MHz, which was applied by a piezoelectric ceramic oscillator. The steady application of DS while decreasing H resulted in a suppression of the insertion of chiral soliton. On the other hand, the application of a pulse-like DS while H decreased assisted the insertion of chiral soliton. These results demonstrate that DS modifies the spin structure of the monoaxial chiral magnet, and we can therefore change the activation energy for the insertion of chiral soliton while H is decreased.

Geometrical protection of topological magnetic solitons in microprocessed chiral magnets

A chiral soliton lattice stabilized in a monoaxial chiral magnet ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$ is a magnetic superlattice consisting of magnetic kinks with a ferromagnetic background. The magnetic kinks are considered to be topological magnetic solitons (TMSs). Changes in the TMS number yield discretized responses in magnetization and electrical conductivity, and this effect is more prominent in smaller crystals. We demonstrate that, in microprocessed ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$ crystals, TMSs are geometrically protected through element-selected micromagnetometry using soft x-ray magnetic circular dichroism (MCD). A series of x-ray MCD data is supported by mean-field and micromagnetic analyses. By designing the microcrystal geometry, TMS numbers can be successfully changed and fixed over a wide range of magnetic fields.

Chiral helimagnetic state in a Kondo lattice model with the Dzyaloshinskii–Moriya interaction

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 coupling, the Dzyaloshinski–Moriya interaction, and electron filling.

Monte Carlo Study of Magnetoresistance in a Chiral Soliton Lattice

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 external magnetic field. In the chiral soliton lattice state, we find negative magnetoresistance proportional to the number of solitons at low temperature, which corroborates the spin scattering of electrons by chiral solitons. We also discuss the temperature and magnetic field dependence of the spin structure factor and electrical resistivity, in comparison with experiments for CrNb$_{3}$S$_{6}$.