A. Çakır, M. Acet, and M. Farle
Phys. Rev. B 93, 094411 (2016)
| M−H curves for x=10.1 between 10 and 70 K. Open and closed symbols represent FC and ZFC measurements, respectively. |
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| M−H curves for x=10.1 between 10 and 70 K. Open and closed symbols represent FC and ZFC measurements, respectively. |
| Sketch of the intrinsic magnetization m(z) (red) (not to scale) of one-dimensional (a) Néel and (b) Bloch (not used in the calculations) domain walls in the order parameter n(z) (green). The equilibrium magnetization profile was calculated from Eq. (14). We note that the magnetization is so small that in a one-dimensional system, the domain-wall spin must be treated quantum mechanically. However, for higher-dimensional extended systems, the total spin of domain walls could be of appreciable size because the intrinsic magnetization is additive in the perpendicular directions. |
| (a) Schematics of magnetic helix with the easy-tangential anisotropy (magnetic moments are shown with red arrows, TNB-basis is shown with green arrows. (b) The rotation angle ψ for different torsions σ and curvatures ϰ. The onion state is energetically preferable in the grey region37. Solid lines correspond to analytics37, filled circles and open squares correspond to SLaSi and Nmag simulations, respectively; see Methods for details. (c,d) Discrete magnetic moments at equilibrium for right- and left-handed helices, respectively. The effective anisotropy axis is shown with thin black arrow e1. |
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| Magnetricity in spin ice Dy2Ti2O7 at 65 mK arising from non-equilibrium populations of magnetic monopoles. |
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| The interaction between two magnetic atoms (red/green) is mediated by scattering of conduction electrons at a substrate atom (grey) with strong spin-orbit coupling (SOC)2,15,16. The shown scattering process leads to a contribution to the Heisenberg-like exchange (J) and DM vector (D), which is oriented perpendicular to the indicated triangle constituted by the two magnetic atoms and the substrate atom. The overall J and D are given by the contributions of all substrate atoms resulting in a nonzero D=(D||, D⊥, Dz) (orientation of the components as indicated) because of broken inversion symmetry at the surface18. The orientation of the spins S1 and S2 of the coupled pair is determined by the interplay between the single ion magnetic anisotropy of each atom (Ki), J, D, and the applied magnetic field (Bz). |
| (a) Rendering of eight dipoles as arrows located at the corners of a cube. The colored and translucent arrows show selected orientations in the ground state of the system which is a continuum of infinitely many configurations. The continuum corresponds to rotations of the dipoles in planes perpendicular to the cube's volume diagonal of the respective corner in analogy to the mechanical system in Fig. 2. Pairs of dipoles in opposing corners are always parallel. (b) Magnetic energy landscape for eight dipoles located at the corners of a cube. The energy is shown as a function of the two orientation angles of one dipole, covering all possible orientations. The other seven dipoles adjust to the respective minimum energy configuration. The white line through the “valley” marks the continuous ground state. (c) Rendering of eight bevel gears located at the corners of a cube. The rotation axes point to the cube's center and every gear interlocks with its three edge neighbors. The motion of this mechanical system, indicated by the red arrows, corresponds to the motion of the ground state continuum in the magnetic system. |
| Energy barriers normalized to |
| (a, b) Examples of microscopic configurations used for static
calculations. Color scheme gives the energy per dipole. (c) Total energy
cost due to formation of DSs of length |
| Capping-layer structure. |