Establishing the Fundamental Magnetic Interactions in the Chiral Skyrmionic Mott InsulatorCu2OSeO3by Terahertz Electron Spin Resonance

Abstract

The recent discovery of skyrmions in Cu2OSeO3 has established a new platform to create and manipulate skyrmionic spin textures. We use high-field electron spin resonance (ESR) spectroscopy combining a terahertz free electron laser and pulsed magnetic fields up to 64 T to probe and quantify its microscopic spin-spin interactions. Besides providing direct access to the long-wavelength Goldstone mode, this technique probes also the high-energy part of the excitation spectrum which is inaccessible by standard low-frequency ESR. Fitting the behavior of the observed modes in magnetic field to a theoretical framework establishes experimentally that the fundamental magnetic building blocks of this skyrmionic magnet are rigid, highly entangled and weakly coupled tetrahedra.In recent years there has been an enormous experimental activity in non-centrosymmetric helimagnets [1][2][3][4][5][6][7][8], where the chiral Dzyaloshinsky-Moriya (DM) interactions [9] stabilize skyrmions, topological particle-like magnetization textures, originally introduced by Skyrme in the context of subatomic particle physics [10]. As first predicted by Bogdanov and Yablonskii [11], skyrmions may condense spontaneously into a lattice at thermodynamic equilibrium [12], in analogy to Abrikosov vortices in type-II syperconductors [13], or the "blue phases" in cholesteric liquid crystals [14]. While most of the well-known skyrmionic helimagnets, such as MnSi [1,2], Fe 1−x Co x Si [3,4], and FeGe [5] are metallic, the recent discovery [6][7][8] of skyrmionic mesophases in Cu 2 OSeO 3 , a strongly correlated insulator with localized Cu 2+ spins [15][16][17], has opened a route to explore skyrmion physics in Mott insulators. In addition Cu 2 OSeO 3 manifests a magnetoelectric coupling [6,18,19] which brings exciting perspectives on the application front, since it allows to manipulate skyrmions by an external electric field [20][21][22].Another very attractive aspect rooted in the insulating nature of Cu 2 OSeO 3 is that a reliable modeling of its magnetic interactions becomes possible which, in conjunction with powerful experimental techniques like the one presented below, offers the unique opportunity to gain a precise understanding of the microscopic magnetic structures and interactions in this skyrmionic material. Having a noncentrosymmetric space group P 2 1 3, the magnetic Cu 2+ ions in Cu 2 OSeO 3 reside at the vertices of a distorted pyrochlore lattice, featuring two symmetry-inequivalent Cu sites, Cu1 and Cu2, with ratio 1:3 (in total there are 16 Cu sites per unit cell), see Fig. 1. While the basic local magnetism is believed to be roughly pictured in terms of a semiclassical 3up-1down structure [15][16][17], density functional based bandstructure calculations suggest that the basic building blocks of helimagnetism are not individual Cu spins but rather quantummechanical (QM) tetrahedral spin entities (shaded circle in Fig. 1) persisting far above the magnetic ordering temperature of T C ≃ 60 K [23]. From the calculations two wellseparated exch...

The quantum nature of skyrmions and half-skyrmions in Cu2OSeO3

“…Therefore, besides the canonical Goldstone mode, a distinct set of weakly dispersive high-energy magnetic excitation modes should appear, where the highest mode goes up to an energy of B450 K. The detailed form of this structure has been reported by Romhányi et al 23 , using a fully quantum-mechanical multiboson expansion. Quite remarkably, this structure was firmly established very recently by Ozerov et al 36 , using high-field electron spin resonance experiments with a terahertz free electron laser source. The characteristic dispersions associated with the hierarchy of magnetic interactions in Cu 2 OSeO 3 can be further probed by inelastic neutron scattering.…”

Low-energy magnon dynamics and magneto-optics of the skyrmionic Mott insulator Cu2OSeO3

“…Such a full quantum treatment has been performed by Janson et al 29 and Romhányi et al 44 , while corresponding neutron scattering 42,43 , high field THz ESR 36 , and Raman spectroscopy 35 experiments reveal a striking agreement between the theoretical and experimentally observed excitation spectrums.…”

“…Spectroscopic investigations have since been performed from the microwave 11,[32][33][34] to the visible 31 frequency ranges. However, experiments performed at infrared or terahertz (THz) frequencies have so far only occurred at two extremes of the phase diagram, either in zero applied magnetic field 30,35 or in large pulsed magnetic fields of order µ 0 H ≈ 10T 36 . To date, no THz experiments have been performed in weak magnetic fields (µ 0 H ≤ 200 mT), within the various magnetic phases of Cu 2 OSeO 3 , including the skyrmion phase.…”

Spin excitations in the skyrmion hostCu2OSeO3

“…Although we are unable to resolve the details of the high-energy dispersion expected according to the model, our measurements also prove to be sensitive to the energy scale and overall bandwidth of the modes at higher energies, which fix the relationship between J electron spin resonance data [23], Raman data [16], and far-infrared data [18] and the model-calculated dispersion on two independent grids throughout two-dimensional (2D) (J near the various minima in five-dimensional parameter space and comparing best-local-fit SSE as well as full predicted spectra, we have found a set of best-global-fit parameters, which are detailed in Table I. A mean-field approximation for the high-temperature susceptibility of this model gives…”