PACS numbers:2 Skyrmions, topologically-protected nanometric spin vortices, are being investigated 1-11 extensively in various magnets.Among them, many of structurally-chiral cubic magnets host the triangular-lattice skyrmion crystal (SkX) as the thermodynamic equilibrium state. However, this state exists only in a narrow temperature and magnetic-field region just below the magnetic transition temperature T c , while a helical or conical magnetic state prevails at lower temperatures. Here we describe that for a room-temperature skyrmion material 12 , β-Mn-type Co 8 Zn 8 Mn 4 , a field-cooling via the equilibrium SkX state can suppress the transition to the helical or conical state, instead realizing robust metastable SkX states that survive over a very wide temperature and magnetic-field region, including down to zero temperature and up to the critical magnetic field of the ferromagnetic transition. Furthermore, the lattice form of the metastable SkX is found to undergo reversible transitions between a conventional triangular lattice and a novel square lattice upon varying the temperature and magnetic field. These findings exemplify the topological robustness of the once-created skyrmions, and establish metastable skyrmion phases as a fertile ground for technological applications. Skyrmions are promising for spintronics applications firstly because they are stable due to their topological nature, and secondly because they can be manipulated by an ultra-low current density [17][18][19][20][21] . The recent discovery of skyrmion formation at and above room temperature in a new group of chiral magnets, β-Mn-type Co-Zn-Mn alloys, has provided a significant step toward applications 12 . These materials possess a chiral cubic crystal structure with space group P 4 1 32 as shown in Fig. 1 A square-lattice SkX state, characterized by double-q vectors orthogonal to each other and perpendicular to the magnetic field, also shows up as a 4 spot pattern in the H beam geometry. In the H ⊥ beam geometry, the helical multi-domain state shows 4 spots, the conical state 2 spots on the horizontal axis, and both the triangular and square-lattice SkX states each 2 spots on the vertical axis.Keeping the above relations in mind, we next consider the results (Fig. 3) of the FC process at 0.04 T, i.e. by way of the thermodynamical equilibrium triangular-lattice SkX region (green region in Fig. 1(b)). The SANS images in Fig. 3(b) show that the pattern obtained from the equilibrium triangular-lattice SkX generated at 295 K persists down to 200K. This is a direct demonstration of the realization of the metastable SkX state that exists outside of the equilibrium state for temperatures below 284 K. The lifetime of this metastable SkX is very long and becomes essentially time-independent below 260 K ( Supplementary Fig. S4). At 120 K, the triangular-lattice SkX pattern has partially transformed into 4 spots.At 40 K, the 4 spots become clearer and their |q|(≡ q) values become larger than they were 6 at higher temperatures. The 4 spot patter...

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...

We have studied the magnetic order inside the superconducting phase of CeCoIn5 for fields along the [1 0 0] crystallographic direction using neutron diffraction. We find a spin-density wave order with an incommensurate modulation Q=(q,q,1/2) and q=0.45(1), which within our experimental uncertainty is indistinguishable from the spin-density wave found for fields applied along [1 -1 0]. The magnetic order is thus modulated along the lines of nodes of the d{x{2}-y{2}} superconducting order parameter, suggesting that it is driven by the electron nesting along the superconducting line nodes. We postulate that the onset of magnetic order leads to reconstruction of the superconducting gap function and a magnetically induced pair density wave.

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.