Squeezing N\'eel-type Magnetic Modulations by Enhanced Dzyaloshinskii-Moriya interaction of $4d$ Electrons
Ádám ButykaiK. GeirhosD. SzallerL. F. KissLászló BaloghMaria AzharMarkus GarstLisa DeBeer‐SchmittTakeshi WakiYoshikazu TabataHiroyuki NakamuraI. KézsmárkiS. Bordács
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In polar magnets, such as GaV$_4$S$_8$, GaV$_4$Se$_8$ and VOSe$_2$O$_5$, modulated magnetic phases namely the cycloidal and the N\'eel-type skyrmion lattice states were identified over extended temperature ranges, even down to zero Kelvin. Our combined small-angle neutron scattering and magnetization study shows the robustness of the N\'eel-type magnetic modulations also against magnetic fields up to 2 T in the polar GaMo$_4$S$_8$. In addition to the large upper critical field, enhanced spin-orbit coupling produces a variety of modulated phases with sub-10 nm periodicity and a peculiar distribution of the magnetic modulation vectors. Thus, our work demonstrates that non-centrosymmetric magnets with $4d$ and $5d$ electron systems are ideal candidates to host highly compressed magnetic spirals and skyrmions.Keywords:
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Magnetic skyrmions have attracted attention as particlelike swirling spin textures with nontrivial topology, and their self-assembled periodic order i.e., the skyrmion crystal (SkX) is anticipated to host unique magnonic properties. In this paper, we investigate magnetic resonance in the quenched SkX state, which is obtained by the rapid cooling of the high-temperature equilibrium SkX phase in the chiral magnetic insulator ${\mathrm{Cu}}_{2}\mathrm{O}\mathrm{Se}{\mathrm{O}}_{3}$. At low temperatures, sextupole and octupole excitation modes of skyrmions are identified, which are usually inactive for oscillating magnetic fields ${B}^{\ensuremath{\nu}}$ with GHz-range frequency $\ensuremath{\nu}$ but turn out to be detectable through the hybridization with the ${B}^{\ensuremath{\nu}}$-active counterclockwise and breathing modes, respectively. The observed magnetic excitation spectra are well reproduced by theoretical calculations, which demonstrates that the effective magnetic anisotropy enhanced at low temperatures is the key for the observed hybridization between the ${B}^{\ensuremath{\nu}}$-active and ${B}^{\ensuremath{\nu}}$-inactive modes.
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We report the results of neutron diffraction and inelastic neutron scattering on a powder sample of Gd_{3}Ga_{5}O_{12} at high magnetic fields. Analysis of the diffraction data shows that in high fields (B≳1.8 T) the spins are not fully aligned, but are canted slightly as a result of the dipolar interaction. The magnetic phase for fields ≲1.8 T is characterized by antiferromagnetic peaks at (210) and an incommensurate wave vector. The dominant contribution to inelastic scattering at large momentum transfers is from a band of almost dispersionless excitations. We show that these correspond to the spin waves localized on ten site rings, expected on the basis of nearest neighbor exchange interaction, and that the spectrum at high fields B≳1.8 T is well described by a spin wave theory.
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Broadband microwave spectroscopy has been performed on single-crystalline GaV$_4$S$_8$, which exhibits a complex magnetic phase diagram including cycloidal, N\'eel-type skyrmion lattice, as well as field-polarized ferromagnetic phases below 13 K. At zero and small magnetic fields two collective modes are found at 5 and 15 GHz, which are characteristic of the cycloidal state in this easy-axis magnet. In finite fields, entering the skyrmion lattice phase, the spectrum transforms into a multi-mode pattern with absorption peaks near 4, 8, and 15 GHz. The spin excitation spectra in GaV$_4$S$_8$ and their field dependencies are found to be in close relation to those observed in materials with Bloch-type skyrmions. Distinct differences arise from the strong uniaxial magnetic anisotropy of GaV4S8 not present in so-far known skyrmion hosts.
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Laser driven cold atoms in front of a retro-reflecting mirror exhibit self-organization above pump threshold. It was recently demonstrated how this system can be used to mimic a transverse lattice of interacting spins. The spontaneously formed lattice breaks both translational and rotational symmetries of the initial homogeneous spin state. By applying a constant longitudinal magnetic field of |B z | ~ 100 mG a switching between antiferromagnetic square and ferri-magnetic hexagonal pattern ordering can be induced. We study the coupling between this magnetic field and modulations in the atomic magnetization.
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In polar magnets with axial symmetry, such as GaV$_4$S$_8$, GaV$_4$Se$_8$ and VOSe$_2$O$_5$, the Neel-type skyrmion lattice state, formed by the superposition of cycloidal modulations, was found stable over extended temperature ranges, even down to zero Kelvin. Based on a combined small-angle neutron scattering and magnetization study, we show the robustness of the Neel-type magnetic modulations also against external fields up to 1.7 T in the polar GaMo$_4$S$_8$. This $4d$ electron system is subject to a stronger spin-orbit coupling (SOC) than the known skyrmion-hosts mainly composed of $3d$ transition metals. The enhanced SOC produces a variety of modulated phases with very short periodicity, $\lambda<10$ nm and a peculiar distribution of the magnetic modulation vectors.
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We have investigated the low-energy dynamics of the triangular lattice of Skyrmions in a helimagnetic insulator Cu2OSeO3 in terms of microwave response. We have observed two elementary excitations of the Skyrmion with different polarization characteristics: the counterclockwise circulating mode at 1 GHz with the magnetic field polarization parallel to the Skyrmion plane and the breathing mode at 1.5 GHz with a perpendicular magnetic field polarization. These modes reflect the topological nature of Skyrmions and may play a central role in the Skyrmion dynamics.
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We theoretically study spin-wave modes and their intense excitations activated by microwave magnetic fields in the skyrmion-crystal phase of insulating magnets by numerically analyzing a two-dimensional spin model using the Landau-Lifshitz-Gilbert equation. Two peaks of spin-wave resonances with frequencies of ~1 GHz are found for in-plane a.c. magnetic field where distribution of the out-of-plane spin components circulates around each skyrmion core. Directions of the circulations are opposite between these two modes, and hence the spectra exhibit salient dependence on the circular polarization of irradiating microwave. A breathing-type mode is also found for out-of-plane a.c. magnetic field. By intensively exciting these collective modes, melting of the skyrmion crystal accompanied by a red shift of the resonant frequency is achieved within nano seconds.
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Antiferromagnets (AFMs), in contrast to ferromagnets, show a nontrivial magnetic structure with zero net magnetization. However, they share a number of spintronic effects with ferromagnets, including spin pumping and spin-transfer torques. Both phenomena stem from the coupled dynamics of free carriers and localized magnetic moments. In the present paper I study the adiabatic dynamics of spin-polarized electrons in a metallic AFM exhibiting a noncollinear ${120}^{\ensuremath{\circ}}$ magnetic structure. I show that the slowly varying AFM spin texture produces a non-Abelian gauge potential related to the time and space gradients of the N\'eel vectors. Corresponding emergent electric and magnetic fields induce rotation of spin and influence the orbital dynamics of free electrons. I discuss both the possibility of a topological spin Hall effect in the vicinity of topological AFM solitons with nonzero curvature and rotation of the electron spin traveling through the AFM domain wall.
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We study spin-wave excitation modes of $k\pi$ skyrmion in a magnetic nanodot under an external magnetic field along $z$-direction using micromagnetic simulations based on Landau-Lifshitz-Gilbert equation. We find that a transition of $k\pi$ skyrmion to other skyrmion-like structures appears under some critical external field, the corresponding spin-wave spectra are simulated for each state in the process of applying magnetic field. For skyrmion, the frequencies of excitation modes increases and then decreases with the low frequency modes splitting at a critical magnetic field. In addition to the well known two in-plane rotational modes and a out-of-plane breathing mode of skyrmion, a higher number of excitation modes are found with increasing $k$ ($k=2, 3$). The excitation modes vary as a function of magnetic field, and the excitation frequencies for different modes exhibit a rapid or slight change depending on the field induced change of magnetization profile. Our study indicates the rich spin-wave excitations for $k\pi$ skyrmion and opens a possibility in theoretical or experimental investigation of magnonics application.
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The microscopic conditions for the emergence of nonreciprocal magnon excitations in noncentrosymmetric magnets are theoretically investigated. We show that asymmetric magnon excitations appear when a bond magnetic toroidal dipole becomes active, which is defined as a parallel component between the Dzyaloshinskii-Moriya vector and the averaged spin moments at the ends of the bonds. Depending on magnetic structures accompanying the bond magnetic toroidal dipoles, the higher-rank magnetic toroidal multipoles can also be activated in a magnetic cluster, which describes various angle dependences of asymmetric magnon excitations. We demonstrate a variety of asymmetric magnon excitations for two magnetic systems in the noncentrosymmetric lattice structures; a one-dimensional breathing chain under a uniform crystalline electric field and a three-dimensional layered breathing kagome structure. We show that a bottom shift of magnon bands occurs by the magnetic toroidal dipole and a valley splitting occurs by the magnetic toroidal octupole under magnetic orderings.
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