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.

Magnetic skyrmion, a topologically stable spin-swirling object, can host emergent electromagnetism, as exemplified by the topological Hall effect and electric-current-driven skyrmion motion. To achieve efficient manipulation of nano-sized functional spin textures, it is imperative to exploit the resonant motion of skyrmions, analogously to the role of the ferromagnetic resonance in spintronics. The magnetic resonance of skyrmions has recently been detected with oscillating magnetic fields at 1-2 GHz, launching a search for new skyrmion functionality operating at microwave frequencies. Here we show a microwave magnetoelectric effect in resonant skyrmion dynamics. Through microwave transmittance spectroscopy on the skyrmion-hosting multiferroic crystal Cu 2 OSeO 3 combined with theoretical simulations, we reveal nonreciprocal directional dichroism (NDD) at the resonant mode, that is, oppositely propagating microwaves exhibit different absorption. The microscopic mechanism of the present NDD is not associated with the conventional Faraday effect but with the skyrmion magnetoelectric resonance instead, suggesting a conceptually new microwave functionality.

Spin current, i.e. the flow of spin angular momentum or magnetic moment, has recently attracted much attention as the promising alternative for charge current with better energy efficiency. Genuine spin current is generally carried by the spin wave (propagating spin precession) in insulating ferromagnets, and should hold the chiral symmetry when it propagates along the spin direction. Here, we experimentally demonstrate that such a spin wave spin current (SWSC) shows nonreciprocal propagation characters in a chirallattice ferromagnet. This phenomenon originates from the interference of chirality between the SWSC and crystal-lattice, which is mediated by the relativistic spin-orbit interaction.The present finding enables the design of perfect spin current diode, and highlights the importance of the chiral aspect in SWSC.

Magnetic skyrmions, topological solitons characterized by a two-dimensional swirling spin texture, have recently attracted attention as stable particle-like objects. In a three-dimensional system, a skyrmion can extend in the third dimension forming a robust and flexible string structure, whose unique topology and symmetry are anticipated to host nontrivial functional responses. Here, we experimentally demonstrate the coherent propagation of spin excitations along skyrmion strings for the chiral-lattice magnet Cu 2 OSeO 3 . We find that this propagation is directionally non-reciprocal, and the degree of non-reciprocity, as well as the associated group velocity and decay length, are strongly dependent on the character of the excitation modes. Our theoretical calculation establishes the corresponding dispersion relationship, which well reproduces the experimentally observed features. Notably, these spin excitations can propagate over a distance exceeding 10 3 times the skyrmion diameter, demonstrating the excellent long-range nature of the excitation propagation on the skyrmion strings. Our combined experimental and theoretical results offer a comprehensive account of the propagation dynamics of skyrmion-string excitations, and suggest the possibility of unidirectional information transfer along such topologicallyprotected strings.Recently, the concept of a magnetic skyrmion, i.e. topologically stable spin configuration whose spins point in all of the directions wrapping a sphere, has attracted enormous attention [1][2][3][4]. In a magnetically two-dimensional system, a skyrmion appears as a vortexlike swirling spin texture with particle nature as shown in Fig. 1j. The stable particle nature of the skyrmion suggests its potential application as a novel magnetic bit for future data storage devices, and the nontrivial topology and symmetry of the skyrmion also cause exceptional electromagnetic responses [3,4].In three dimensional systems, the skyrmion can form a string structure by extending in the third dimension, which consists of the uniform stacking of two-dimensional skyrmions along the string direction ( Fig. 1a) [5,6]. Skyrmion strings can be considered as an analogue of the vortex-line in superfluids [7,8], type-II superconductors[9] and trapped dilute-gas Bose-Einstein condensates [10] or the cosmic string in the universe [11]. They are all flexible, and some of these strings are proposed to host a resonant oscillation mode propagating through the string path. This implies the possible coherent signal transfer along skyrmion strings, while the propagation character of their excitations has rarely been investigated before.Experimentally, such skyrmion strings appear in a series of bulk magnets with chiral cubic atomic lattice. The examples are metallic B20 [1,2] or β-Mn type Co-Zn-Mn[12] alloys and insulating Cu 2 OSeO 3 [13,14], the latter of which is the target of this work. In these materials, the Dzyaloshinskii-Moriya (DM) interaction is the key for the skyrmion formation. For a limited temperature (T ) r...

Dissipation-less electric control of magnetic state variable is an important target of contemporary spintronics. The non-volatile control of magnetic skyrmions, nanometre-sized spin-swirling objects, with electric fields may exemplify this goal. The skyrmion-hosting magnetoelectric chiral magnet Cu2OSeO3 provides a unique platform for the implementation of such control; however, the hysteresis that accompanies the first-order transition associated with the skyrmion phase is negligibly narrow in practice. Here we demonstrate another method that functions irrespective of the transition boundary. Combination of magnetic-susceptibility measurements and microwave spectroscopy reveals that although the metastable skyrmion lattice is normally hidden behind a more thermodynamically stable conical phase, it emerges under electric fields and persists down to the lowest temperature. Once created, this metastable skyrmion lattice remains without electric fields, establishing a bistability distinct from the transition hysteresis. This bistability thus enables non-volatile electric-field control of the skyrmion lattice even in temperature/magnetic-field regions far from the transition boundary.