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.

We present magnetodielectric measurements in single crystals of the cubic spin-1/2 compound Cu2OSeO3. A magnetic field-induced electric polarization (P) and a finite magnetocapacitance (MC) is observed at the onset of the magnetically ordered state (Tc = 59 K). Both P and MC are explored in considerable detail as a function of temperature (T), applied field Ha, 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 Ha-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 M·(∇×M) that is present in this non-centrosymmetric compound. We also present a phenomenological LandauGinzburg theory for the MEH effect, which is in excellent agreement with experimental data, and shows three novel features: (i) the polarization 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 P points along the vector (, and (iii) its strength is proportional to η 2 − η 2 ⊥ /2, where η is the longitudinal and η ⊥ 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.

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We report a detailed 1 H NMR study on the spin dynamics of single molecule magnets as a function of temperature and external magnetic field. A gradual loss of the 1 H NMR signal intensity ͑wipeout effect͒ is observed on decreasing the temperature for all the investigated ferromagnetic clusters. This effect is accompanied by a simultaneous enhancement of the spin-spin and spin-lattice relaxation rate T 2 −1 and T 1 −1 , respectively. The complications entered in the interpretation of the signal loss by the wipeout effect are overcome, and the information about the spin dynamics is retrieved, by implementing a simple and intuitive model that captures the main physical characteristics of the problem and reveals a universal behavior of the spin dynamics for all the clusters. According to our analysis the origin of the wipeout effect as well as the enhancement of the relaxation rates T 1 −1 and T 2 −1 in the FM clusters is related to a decrease of the lifetime broadening parameter of the magnetic energy levels, down to the range of the 1 H Larmor frequency. The temperature dependence of the lifetime broadening can be described at intermediate temperatures by a power law dependence on T similar to that observed in antifferomagnetic rings ͓S. H. Baek et al., Phys. Rev. B 70, 134434 ͑2004͔͒.

55Mn NMR line shape measurements in La1-xCaxMnO3 for 0.20< or =x< or =0.50 provide experimental evidence about the existence of two distinct regions in the T-x magnetic phase diagram, where the homogeneous ferromagnetic (FM) metallic state is separated into FM metallic and FM insulating regions. These results are in agreement with recent theoretical predictions, which reveal a novel electronic phase separation in two FM states, providing orbital ordering and Jahn-Teller phonons are taken into consideration.

55Mn and 139La NMR measurements on a high quality single crystal of ferromagnetic (FM) La0.80Ca0.20MnO3 demonstrate the formation of localized Mn(3+,4+) states below 70 K, accompanied by a strong cooling-rate dependent increase of certain FM neutron Bragg peaks. (55,139)(1/T(1)) spin-lattice and (139)(1/T(2)) spin-spin relaxation rates are strongly enhanced on approaching this temperature from below, signaling a genuine phase transition at T(tr) approximately 70 K. The disappearance of the FM metallic signal by applying a weak external magnetic field, the different NMR radio-frequency enhancement of the FM metallic and insulating states, and the observed finite size scaling of T(tr) with Ca (hole) doping, as observed in powder La(1-x)CaxMnO3 samples, are suggestive of freezing into an inhomogeneous FM insulating and orbitally ordered state embodying "metallic" hole-rich walls.

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...

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