Quantum spin liquids are long-range entangled states of matter with emergent gauge fields and fractionalized excitations. While candidate materials, such as the Kitaev honeycomb ruthenate $alpha$-RuCl$_3$, show magnetic order at low temperatures $T$,
here we demonstrate numerically a dynamical crossover from magnon-like behavior at low $T$ and frequencies $omega$ to long-lived fractionalized fermionic quasiparticles at higher $T$ and $omega$. This crossover is akin to the presence of spinon continua in quasi-1D spin chains. It is further shown to go hand in hand with persistent typicality down to very low $T$. This aspect, which has also been observed in the spin-1/2 kagome Heisenberg antiferromagnet, is a signature of proximate spin liquidity and emergent gauge degrees of freedom more generally, and can be the basis for the numerical study of many finite-$T$ properties of putative spin liquids.
The Skyrme-particle, the $skyrmion$, was introduced over half a century ago and used to construct field theories for 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 that hold promise as information carriers. Extending over length-scales much larger than the inter-atomic spacing, these skyrmions behave as large, classical objects, yet deep inside they are of quantum origin. Penetrating into their microscopic roots requires a multi-scale approach, spanning the full quantum to classical domain. By exploiting a natural separation of exchange energy scales, we achieve this for the first time in the skyrmionic Mott insulator Cu$_2$OSeO$_3$. Atomistic ab initio calculations reveal that its magnetic building blocks are strongly fluctuating Cu$_4$ tetrahedra. These spawn a continuum theory with a skyrmionic texture that agrees well with reported experiments. It also brings to light a decay of skyrmions into half-skyrmions in a specific temperature and magnetic field range. The theoretical multiscale approach explains the strong renormalization of the local moments and predicts further fingerprints of the quantum origin of magnetic skyrmions that can be observed in Cu$_2$OSeO$_3$, like weakly dispersive high-energy excitations associated with the Cu$_4$ tetrahedra, a weak antiferromagnetic modulation of the primary ferrimagnetic order, and a fractionalized skyrmion phase.
We explore the phase diagram and the low-energy physics of three Heisenberg antiferromagnets which, like the kagome lattice, are networks of corner-sharing triangles but contain two sets of inequivalent short-distance resonance loops. We use a combin
ation of exact diagonalization, analytical strong-coupling theories, and resonating valence bond approaches, and scan through the ratio of the two inequivalent exchange couplings. In one limit, the lattices effectively become bipartite, while at the opposite limit heavily frustrated nets emerge. In between, competing tunneling processes result in short-ranged spin correlations, a manifold of low-lying singlets (which can be understood as localized bound states of magnetic excitations), and the stabilization of valence bond crystals with resonating building blocks.
We present magnetodielectric measurements in single crystals of the cubic spin-1/2 compound Cu$_2$OSeO$_3$. A magnetic field-induced electric polarization ($vec{P}$) and a finite magnetocapacitance (MC) is observed at the onset of the magnetically or
dered state ($T_c = 59$ K). Both $vec{P}$ and MC are explored in considerable detail as a function of temperature (T), applied field $vec{H}_a$, and relative field orientations with respect to the crystallographic axes. The magnetodielectric data show a number of anomalies which signal magnetic phase transitions, and allow to map out the phase diagram of the system in the $H_a$-T plane. Below the 3up-1down collinear ferrimagnetic phase, we find two additional magnetic phases. We demonstrate that these are related to the field-driven evolution of a long-period helical phase, which is stabilized by the chiral Dzyalozinskii-Moriya term $D vec{M} cdot(bs{ abla}timesvec{M})$ that is present in this non-centrosymmetric compound. We also present a phenomenological Landau-Ginzburg theory for the ME$_H$ effect, which is in excellent agreement with experimental data, and shows three novel features: (i) the polarization $vec{P}$ has a uniform as well as a long-wavelength spatial component that is given by the pitch of the magnetic helices, (ii) the uniform component of $vec{P}$ points along the vector $(H^yH^z, H^zH^x, H^xH^y)$, and (iii) its strength is proportional to $eta_parallel^2-eta_perp^2/2$, where $eta_parallel$ is the longitudinal and $eta_perp$ is the transverse (and spiraling) component of the magnetic ordering. Hence, the field dependence of P provides a clear signature of the evolution of a conical helix under a magnetic field. A similar phenomenological theory is discussed for the MC.
We report the microscopic magnetic model for the spin-1/2 Heisenberg system CdCu2(BO3)2, one of the few quantum magnets showing the 1/2-magnetization plateau. Recent neutron diffraction experiments on this compound [M. Hase et al., Phys. Rev. B 80, 1
04405 (2009)] evidenced long-range magnetic order, inconsistent with the previously suggested phenomenological magnetic model of isolated dimers and spin chains. Based on extensive density-functional theory band structure calculations, exact diagonalizations, quantum Monte Carlo simulations, third-order perturbation theory, as well as high-field magnetization measurements, we find that the magnetic properties of CdCu2(BO3)2 are accounted for by a frustrated quasi-2D magnetic model featuring four inequivalent exchange couplings: the leading antiferromagnetic coupling J_d within the structural Cu2O6 dimers, two interdimer couplings J_t1 and J_t2, forming magnetic tetramers, and a ferromagnetic coupling J_it between the tetramers. Based on comparison to the experimental data, we evaluate the ratios of the leading couplings J_d : J_t1 : J_t2 : J_it = 1 : 0.20 : 0.45 : -0.30, with J_d of about 178 K. The inequivalence of J_t1 and J_t2 largely lifts the frustration and triggers long-range antiferromagnetic ordering. The proposed model accounts correctly for the different magnetic moments localized on structurally inequivalent Cu atoms in the ground-state magnetic configuration. We extensively analyze the magnetic properties of this model, including a detailed description of the magnetically ordered ground state and its evolution in magnetic field with particular emphasis on the 1/2-magnetization plateau. Our results establish remarkable analogies to the Shastry-Sutherland model of SrCu2(BO3)2, and characterize the closely related CdCu2(BO3)2 as a material realization for the spin-1/2 decorated anisotropic Shastry-Sutherland lattice.
