The quantum nature of skyrmions and half-skyrmions in Cu2OSeO3

Abstract

The Skyrme-particle, the skyrmion, was introduced over half a century ago in the context of 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. Extending over length scales much larger than the interatomic spacing, they behave as large, classical objects, yet deep inside they are of quantum nature. Penetrating into their microscopic roots requires a multi-scale approach, spanning the full quantum to classical domain. Here, we achieve this for the first time in the skyrmionic Mott insulator Cu 2 OSeO 3 . We show that its magnetic building blocks are strongly fluctuating Cu 4 tetrahedra, spawning a continuum theory that culminates in 51 nm large skyrmions, in striking agreement with experiment. One of the further predictions that ensues is the temperature-dependent decay of skyrmions into half-skyrmions.

Transverse field muon-spin rotation signature of the skyrmion-lattice phase inCu2OSeO3

“…Ferrimagnetic (FiM) ordering of these spins is favored, with one Cu ion (Cu1) oriented in the opposite direction to that of the others (Cu2) [17,20]. This ordered configuration persists when we build more complicated spin configurations described in the following [21]. In systems such as Cu 2 OSeO 3 which lack inversion symmetry, chiral interactions are capable of stabilizing helically ordered configurations of spins [22].…”

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

“…As a guiding principle, we keep the weak-coupling values of [23] intact (namely, J Since these couplings directly determine the system's thermodynamic properties they can be considered fixed by fits to experimental magnetization data [23]. In fact, the striking agreement in the energy of our ESR mode A, which depends practically only on J w , gives a direct experimental verification of these values.…”

“…1). The rigid Cu 4 entities are then engendered by the strong couplings J s : the magnetic ground state (GS) of an isolated 'strong' tetrahedron is separated from its excited states by a large gap of ∆ ≃ 280 K. Such a separation of energy scales identified by the calculations will very strongly affect the long-wavelength physics, the stability and interplay of skyrmionic and halfskyrmionic phases and the magnetoelectricity [23,24]. Here, we set out to test its presence experimentally.…”

“…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 exchange energy scales can be distinguished, defined by inter-and intra-tetrahedra exchange coupling interactions (hereafter 'weak' and 'strong' interactions, |J w | ∼ 20-50 K and |J s | ∼ 100-150 K, respectively, Fig.…”

Spin excitations in the skyrmion hostCu2OSeO3

“…It offers an ideal laboratory to explore the microscopic ingredients that lead to skyrmion formation in a quantitative manner, since its Bloch-type ground-state properties and low-energy excitations are fully governed by the magnetic interactions between localized spins and are not affected by the presence of itinerant carriers. Exchange pathway considerations, susceptibility measurements, and ab initio calculations reveal that two magnetic energy scales divide the system into weakly coupled Cu 4 tetrahedra [15]. These Cu 4 "molecules," with an effective spin of S = 1, are the elementary magnetic building blocks of Cu 2 OSeO 3 instead of the single Cu ions.…”