Topological protection is an elegant way of warranting the integrity of quantum and nanosized systems. In magnetism one example is the Bloch-point, a peculiar object implying the local vanishing of magnetization within a ferromagnet. Its existence had been postulated and described theoretically since several decades, however it has never been observed. We confirm experimentally the existence of Bloch points, imaged within domain walls in cylindrical magnetic nanowires, combining surface and transmission XMCD-PEEM magnetic microscopy. This opens the way to the experimental search for peculiar phenomena predicted during the motion of Bloch-point-based domain walls.There is a rising interest for physical systems providing topological protection. The interest is both fundamental to elucidate the underlying physical phenomena, and applied as a mean to provide robustness to a state against external perturbations and decoherence pathways. For example, the peculiar topology of the band structure of carbon nanotubes and graphene forbids backscattering of charge carriers [1], an effect which is often invoked to explain the high mobilities up to room temperature [2]. A similar effect occurs at the surface of so-called topological insulators, together with a locking of the spin of charge carriers; this provides spin currents protected against depolarization [3]. A photonic analogue was also designed by combining helical wave guides on a lattice with a graphene-like honeycomb topology, removing time-reversal symmetry and thereby preventing backscattering of light [4].In systems displaying a directional order parameter such as liquid crystals and ferromagnets, interesting phenomena are associated with the slowly-varying texture of the order field (magnetization for a ferromagnet). The requirement of local continuity of a vector field with fixed magnitude provides a topological protection against the transformation of the texture. A prototypical case in magnetism is skyrmions, which are essentially local two-dimensional chiral spin textures stabilized by the Dzyaloshinskii-Moriya interaction, embedded in an otherwise uniformly-magnetized surrounding. Despite these surroundings skyrmions cannot unwind continuously as explained by the above continuity constraints of the magnetization field, explaining their topological protection. Skyrmions have first been predicted theoretically [5], then confirmed experimentally in both bulk [6] and thin film forms [7].Bloch points are yet another type of topologicallyprotected magnetic texture which cannot be unwound, however of a three-dimensional nature. Bloch points are such that given the distribution of magnetization set on a closed surface like a sphere, the enclosed volume cannot be mapped with a continuous magnetization field of finite magnitude. This occurs e.g. for hedge-hog configurations, or more generally whenever all directions of magnetization are mapped on the closed surface (Fig. 1a-b). Such boundary conditions imply the local cancellation of the modulus of magnetization on a...

Néel's theory of magnetostatic coupling between two magnetic layers with inplane magnetization separated by a non-magnetic spacer has been extended to the case of multilayers with perpendicular anisotropy. It is shown that the presence of a correlated roughness between the successive interfaces induces an interlayer coupling through the spacer analogous to the well-known orange peel coupling. However, depending on the parameters describing the interfacial roughness, the magnetic anisotropy and the exchange stiffness constant, this coupling can favor either parallel or an antiparallel alignment of the magnetization in the two ferromagnetic layers. This model was used to quantitatively interpret the variation of interlayer coupling vs. thickness of Pt spacer layer in out-of-plane magnetized exchange-biased spin-valves comprising (Pt/Co) multilayers as free and pinned layers. It is shown that the net coupling can be interpreted by the coexistence of perpendicular orange peel and oscillatory RKKY couplings. Interestingly, since these two couplings have different thickness dependence, in certain range of Pt thickness, the coupling changes sign during growth, being antiferromagnetic at the early stage of the growth of the top (Co/Pt) multilayer but ferromagnetic once the growth is completed.

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In this paper, we rigorously study an order 2 scheme that was previously proposed by some of the authors. A slight modification is proposed that enables us to prove the convergence of the scheme while simplifying in the same time the inner iteration.

Cylindrical nanowires made of soft magnetic materials, in contrast to thin strips, may host domain walls of two distinct topologies. Unexpectedly, we evidence experimentally the dynamic transformation of topology upon wall motion above a field threshold. Micromagnetic simulations highlight the underlying precessional dynamics for one way of the transformation, involving the nucleation of a Bloch-point singularity, however, fail to reproduce the reverse process. This rare discrepancy between micromagnetic simulations and experiments raises fascinating questions in material and computer science.

While the usual approach to tailor the behavior of condensed matter and nanosized systems is the choice of material or finite-size or interfacial effects, topology alone may be the key. In the context of the motion of magnetic domain-walls (DWs), known to suffer from dynamic instabilities with low mobilities, we report unprecedented velocities > 600 m/s for DWs driven by spin-transfer torques in cylindrical nanowires made of a standard ferromagnetic material. The reason is the robust stabilization of a DW type with a specific topology by the OErsted field associated with the current. This opens the route to the realization of predicted new physics, such as the strong coupling of DWs with spin waves above > 600 m/s.

We used single-crystalline Fe dots self-assembled under UHV as a model system to discuss micromagnetic properties of sub-micron size magnetic dots and show what properties may or may not be scaled down from macroscopic samples. Landau and diamond states were identified by MFM and reproduced by simulations. These states are surprisingly well reproduced by the the Van den Berg model despite the small dots'size. On the contrary, it is argued theoretically that the usual determination procedure of demagnetizing factors Ni's using initial susceptibility or the over-loop area underestimate the real values of Ni's in sub-micron size dots. This point is confirmed both experimentally and in simulations.

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