Uniquely in Cu 2 OSeO 3 , the Skyrmions, which are topologically protected magnetic spin vortexlike objects, display a magnetoelectric coupling and can be manipulated by externally applied electric (E) fields. Here, we explore the E-field coupling to the magnetoelectric Skyrmion lattice phase, and study the response using neutron scattering. Giant E-field induced rotations of the Skyrmion lattice are achieved that span a range of ∼25°. Supporting calculations show that an E-field-induced Skyrmion distortion lies behind the lattice rotation. Overall, we present a new approach to Skyrmion control that makes no use of spin-transfer torques due to currents of either electrons or magnons. [12,13]. All have the chiral-cubic space group P2 1 3, a weak magnetocrystalline anisotropy, and common phase diagrams with a helimagnetic ground state. Despite these similarities, the diverse transport properties lead to material specific mechanisms for Skyrmion manipulation and the associated dynamics. In the well-studied itinerant compounds, spin-transfer torques (STTs) exerted by the conduction electrons of an ultralow current density, j ≲ 10 6 A·m −2 drive the Skyrmion motion [5,[14][15][16][17][18][19]. More generally, in both MnSi and insulating Cu 2 OSeO 3 , Skyrmion lattice (SKL) rotations are observed to be driven by STTs exerted by the magnon currents induced by a thermal gradient [20]. Even though electric currents and thermal gradients have been established to generate Skyrmion motion, it remains vital to find new control mechanisms which may lead to further efficient Skyrmion-based functionalities.In the insulating SKL host compounds, the chiral lattice promotes a magnetoelectric (ME) coupling between electric (E) and magnetic orders which can be expected to lie at the heart of new Skyrmion control paradigms. The use of ME coupling for Skyrmion manipulation is also attractive for applications since losses due to Joule heating are negligible. Presently, however, open questions remain concerning the basic understanding of how an applied E field can manipulate the Skyrmion spin texture. To address this issue, we have used small-angle neutron scattering (SANS) to study the giant E-field-induced SKL rotations generated in a bulk sample of ME Cu 2 OSeO 3 . Surprisingly, the rotations saturate at an angle dependent on both the size and sign of the E field. With supporting calculations, we explain our observations, and show that an E-field-induced Skyrmion distortion leads to the observed rotations. This amounts to a new approach for Skyrmion control that does not require STTs.In Cu 2 OSeO 3 , the ME coupling exists in all magnetic phases [12,[21][22][23][24][25][26][27][28], and is generated by the d-p hybridization mechanism [12,24,29,30]. This mechanism dictates a particular ME coupling anisotropy; for a magnetic field μ 0 H∥½110 or [111], an electric polarization P emerges ∥½001 or [111], respectively [24]. In our experiments, we chose E∥½111 (which corresponds to a negative applied voltage) or ∥½111 (positive voltage). T...

Small-angle neutron scattering has been employed to study the influence of applied electric (E-)fields on the skyrmion lattice in the chiral lattice magnetoelectric Cu(2)OSeO(3). Using an experimental geometry with the E-field parallel to the [111] axis, and the magnetic field parallel to the [11(-)0] axis, we demonstrate that the effect of applying an E-field is to controllably rotate the skyrmion lattice around the magnetic field axis. Our results are an important first demonstration for a microscopic coupling between applied E-fields and the skyrmions in an insulator, and show that the general emergent properties of skyrmions may be tailored according to the properties of the host system.

We report a comprehensive study of magnetic properties of Ni 3 TeO 6 . The system crystallizes in a noncentrosymmetric rhombohedral lattice, space group R3. There are three differently coordinated Ni atoms in the unit cell. Two of them form an almost planar honeycomb lattice, while the third one is placed between the layers. Magnetization and specific heat measurements revealed a single magnetic ordering at T N = 52 K. Below T N the susceptibility with the magnetic field parallel to the c axis drops towards zero while the perpendicular susceptibility remains constant, a characteristic of antiferromagnetic materials. Neutron diffraction confirmed that the system is antiferromagnet below T N with ferromagnetic ab planes stacked antiferromagnetically along the c axis. All Ni moments are in the S = 1 spin state and point along the c axis.

NMR measurements of the (29)Si spin-lattice relaxation time T(1) were used to probe the spin-1/2 random Heisenberg chain compound BaCu(2)(Si(1-x)Ge(x))(2)O(7). Remarkable differences between the pure (x=0) and the fully random (x=0.5) cases are observed, indicating that randomness generates a distribution of local magnetic relaxations. This distribution, which is reflected in a stretched exponential NMR relaxation, exhibits a progressive broadening with decreasing temperature, caused by a growing inequivalence of magnetic sites. Compelling independent evidence for the influence of randomness is also obtained from magnetization data and Monte Carlo calculations. These results suggest the formation of random-singlet states in this class of materials, as previously predicted by theory.

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We present the investigation of a monoclinic compound SeCuO 3 using x-ray powder diffraction, magnetization, torque, and electron-spin-resonance. Structurally based analysis suggests that SeCuO 3 can be considered as a three-dimensional network of tetramers. The values of intratetramer exchange interactions are extracted from the temperature dependence of the susceptibility and amount to ∼ 200 K. The intertetramer coupling leads to the development of long-range antiferromagnetic order at T N = 8 K. An unusual temperature dependence of the effective g tensors is observed, accompanied with a rotation of macroscopic magnetic axes. We explain this unique observation as due to site-selective quantum correlations.

Using superconducting quantum interference device magnetometry techniques, we have studied the change in magnetization versus applied ac electric field, i.e. the magnetoelectric (ME) susceptibility dM/dE, in the chiral-lattice ME insulator Cu 2 OSeO 3 . Measurements of the dM/dE response provide a sensitive and efficient probe of the magnetic phase diagram, and we observe clearly distinct responses for the different magnetic phases, including the skyrmion lattice phase. By combining our results with theoretical calculation, we estimate quantitatively the ME coupling strength as λ = 0.0146 meV/(V/nm) in the conical phase. Our study demonstrates the ME susceptibility to be a powerful, sensitive, and efficient technique for both characterizing and discovering new multiferroic materials and phases. Multiferroic and magnetoelectric (ME) materials that display directly coupled magnetic and electric properties may lie at the heart of new and efficient applications. Two intensely studied prototypical ME compounds with spiral order are Another exciting group of ME materials are chiral-lattice systems, since interactions that may promote symmetrybreaking magnetic order do not cancel when evaluated over the unit cell. The decisive role of noncentrosymmetry has been most clearly exemplified in itinerant MnSi [6,7], FeGe [8] and semiconducting Fe 1−x Co x Si [9]. In these compounds the principal phases are; (i) multiple q-domain helimagnetic order (helical phase) for 0 < B < B c1 (T ), (ii) single-q helimagnetic order modulated along the field (conical phase) for B c1 (T ) < B < B c2 (T ), and (iii) a small phase pocket close to T N where a novel triple-q state described by three coupled helices ( i q i = 0) is stabilized, and which corresponds to a lattice of skyrmions. This latter phase is particularly interesting, since in MnSi the nanosized ( 15 nm [10]) skyrmions can be coherently manipulated by the conduction electrons of an applied current [7], leading to both emergent electrodynamics, [11] and promise for applications.Most recently, the first skyrmion lattice (SkL) phase in an insulating material was discovered in the chiral-lattice material Cu 2 OSeO 3 [12][13][14]. In direct analogy with the metallike SkL compounds, Cu 2 OSeO 3 also has the chiral-cubic P 2 1 3 space group, and the magnetic phase diagram is similarly composed of helical, conical, and SkL phases [12,13]. The earlier proposed ferrimagnetic state * henrik.ronnow@epfl.ch in this compound exists for fields B > B c2 (T ) [15][16][17]. The discovery at lower fields that Cu 2 OSeO 3 displays the seemingly generic magnetic phase diagram of a SkL compound is enthralling since a variety of studies show Cu 2 OSeO 3 to display a ME coupling [12,15,[18][19][20][21]. Indeed, the microscopic origin for the ME coupling is identified as caused by the d-p hybridization mechanism [21][22][23][24]. Most recently, emergent ME properties of the individual skyrmion particles were proposed [21,25], and demonstrated to exist experimentally [26]. Cu 2 OSeO 3 represents a thu...

We present a detailed ac susceptibility investigation of the fluctuation regime in the insulating cubic helimagnet Cu 2 OSeO 3 . For magnetic fields μ 0 H 200 mT, and over a wide temperature (T ) range, the system behaves according to the scaling relations characteristic of the classical three-dimensional Heisenberg model. For lower magnetic fields, the scaling is preserved only at higher T and becomes renormalized in a narrow-T range above the transition temperature. Contrary to the well-studied case of MnSi, where the renormalization has been interpreted within the Brazovskii theory, our analysis of the renormalization at H = 0 shows the fluctuation regime in Universality is a concept that lies at the heart of modern physics since it describes the general scaling behavior of widespread physical phenomena within the vicinity of a critical point. In condensed matter physics, universal scaling laws are readily applied to interpret measurements of thermodynamic observables in order to discern the symmetry of the physical properties close to phase transitions. A classic example where these concepts have been extensively tested, both theoretically and experimentally, is the second-order paramagnetic (PM) to ferromagnetic (FM) transition [1]. In general, as the system approaches the critical point, both the size and the number of fluctuations of the relevant order parameter increase. It is also known that if the interactions between the fluctuations are strong enough, this may even alter the order of the phase transition. In a recent comprehensive study, it was proposed [2] that a specific type of renormalization put forward by Brazovskii [3] can be applied to describe the weakly first-order nature of the PM to helimagnetic (HM) transition at zero magnetic field in metallic MnSi [4,5]. In this scenario, the renormalization arises due to the crucial role played by the Dzyaloshinskii-Moriya (DM) interaction which alters the nature of fluctuations close to T HM , and so causes the system to avoid the second-order transition expected within mean field theory. Other studies of the unusual critical behavior in MnSi include recent polarized neutron scattering experiments [4], from which it was proposed that a "skyrmion-liquid" phase exists for a narrow-temperature range (T ∼ 1 K) above T HM . A similar claim was deduced from a Monte Carlo study where an analogy with blue phases in liquid crystals has been established [6].Recently, Cu 2 OSeO 3 was identified as a new compound to display a direct PM to HM transition in zero magnetic field. Cu 2 OSeO 3 crystallizes in the same space group as MnSi (P 213), and has two crystallographically inequivalent Cu sites with a dominant antiferromagnetic interaction between the nearest neighbors [7]. The ratio of Cu ions within the two inequivalent sites is 3:1, giving rise to the formation of the local ferrimagnetic (FiM) 3-up-1-down state [5] which * zivkovic@ifs.hr is then modulated by the DM interaction. Similar as for MnSi, by applying a weak magnetic field close to the ordering tem...