Geometrical Frustration, Correlated Disorder, and Emerging Order in a Corrugated C_{60} Monolayer.

Under certain experimental conditions, the deposition of C_{60} molecules onto an atomically flat copper surface gives rise to the formation of corrugated islands. This corrugation, which reflects a molecular displacement perpendicular to the surface plane, presents an astonishing pattern: It is well described by a frustrated Ising spin Hamiltonian whose thermodynamics is compatible with a spin liquid about to transit toward an ordered zigzag state. Here we study the statistical properties of such a molecular corrugation using a structure factor analysis, a tool generally employed in frustrated magnetism. More specifically, the real and reciprocal space analysis of pairwise molecule correlations allows us to demonstrate that the C_{60}/Cu system, in which magnetism is totally absent, has all the characteristics of a triangular Ising antiferromagnet. Our results indicate that the organization of two-dimensional matter, at the molecular length scale, sometimes turns out to be particularly close to that encountered in highly frustrated magnets.

Magnetic Arctic Circle in a Square Ice Qubit Lattice.

Under certain boundary conditions, the square ice model exhibits a phase separation in which the core of the system is disordered while its outer region remains ordered. This phenomenon, known as the "arctic circle," has been studied theoretically in combinatorial mathematics and statistical mechanics. Here, we realize the physics of the arctic circle experimentally for the first time, using a programmable lattice of superconducting qubits, and investigate its properties under the prism of a highly frustrated magnet. Our work reveals two unexpected properties. First, the disordered spin manifold confined within the arctic curve is a spin liquid whose average spin texture resembles that of an antivortex, i.e., it is a topologically charged Coulomb phase. Second, monopole quasiparticle excitations, which are totally absent in theoretical works, can be isolated in a phase-separated system. Remarkably, a monopole segregation mechanism is observed, in which the monopoles are sorted according to the magnetic charge and magnetic moment they carry, without the application of an external driving force.

Approaching the Topological Low-Energy Physics of the F Model in a Two-Dimensional Magnetic Lattice.

We demonstrate that the physics of the F model can be approached very closely in a two-dimensional artificial magnetic system. Faraday lines spanning across the lattice and carrying a net polarization, together with chiral Faraday loops characterized by a zero magnetic susceptibility, are imaged in real space using magnetic force microscopy. Our measurements reveal the proliferation of Faraday lines and Faraday loops as the system is brought from low- to high-energy magnetic configurations. They also reveal a link between the Faraday loop density and icelike spin-spin correlations in the magnetic structure factor. Key for this Letter, the density of topological defects remains small, on the order of 1% or less, and negligible compared to the density of Faraday loops. This is made possible by replacing the spin degree of freedom used in conventional lattices of interacting nanomagnets by a micromagnetic knob, which can be finely tuned to adjust the vertex energy directly, rather than modifying the two-body interactions.

Bypassing Dynamical Freezing in Artificial Kagome Ice.

Spin liquids are correlated, disordered states of matter that fluctuate even at low temperatures. Experimentally, the extensive degeneracy characterizing their low-energy manifold is expected to be lifted, for example, because of dipolar interactions, leading to an ordered ground state at absolute zero. However, this is not what is usually observed, and many systems, whether they are chemically synthesized or nanofabricated, dynamically freeze before magnetic ordering sets in. In artificial realizations of highly frustrated magnets, ground state configurations, and even low-energy manifolds, thus remain out of reach for practical reasons. Here, we show how dynamical freezing can be bypassed in an artificial kagome ice. We illustrate the efficiency of our method by demonstrating that the a priori dynamically inaccessible ordered ground state and fragmented spin liquid configurations can be obtained reproducibly, imaged in real space at room temperature, and studied conveniently. We then identify the mechanism by which dynamical freezing occurs in the dipolar kagome ice.

Coherent x-ray scattering in an XPEEM setup.

X-ray photoemission electron microscopy, one of the most successful imaging tools at synchrotrons, is known to have limitations related to the application of external fields and to the short electron mean free path. In order to overcome such issues, we adapt an existing XPEEM instrument to simultaneously perform coherent x-ray scattering measurements in reflectivity mode, thus adding a complementary method to XPEEM. Photon-in photon-out x-ray scattering provides the sensitivity to buried interfaces as well as the possibility to work under external fields, which is challenging when using charged particles for imaging. XPEEM, in turn, greatly alleviates the difficulties associated with the reconstruction methods used in coherent diffraction imaging. The combination of the two methods is demonstrated for an artifical spin-ice lattice showing both chemical and magnetic contrast.

Unconventional magnetisation texture in graphene/cobalt hybrids.

Magnetic domain structure and spin-dependent reflectivity measurements on cobalt thin films intercalated at the graphene/Ir(111) interface are investigated using spin-polarised low-energy electron microscopy. We find that graphene-covered cobalt films have surprising magnetic properties. Vectorial imaging of magnetic domains reveals an unusually gradual thickness-dependent spin reorientation transition, in which magnetisation rotates from out-of-the-film plane to the in-plane direction by less than 10° per cobalt monolayer. During this transition, cobalt films have a meandering spin texture, characterised by a complex, three-dimensional, wavy magnetisation pattern. In addition, spectroscopy measurements suggest that the electronic band structure of the unoccupied states is essentially spin-independent already a few electron-Volts above the vacuum level. These properties strikingly differ from those of pristine cobalt films and could open new prospects in surface magnetism.

Third type of domain wall in soft magnetic nanostrips.

Magnetic domain walls (DWs) in nanostructures are low-dimensional objects that separate regions with uniform magnetisation. Since they can have different shapes and widths, DWs are an exciting playground for fundamental research, and became in the past years the subject of intense works, mainly focused on controlling, manipulating, and moving their internal magnetic configuration. In nanostrips with in-plane magnetisation, two DWs have been identified: in thin and narrow strips, transverse walls are energetically favored, while in thicker and wider strips vortex walls have lower energy. The associated phase diagram is now well established and often used to predict the low-energy magnetic configuration in a given magnetic nanostructure. However, besides the transverse and vortex walls, we find numerically that another type of wall exists in permalloy nanostrips. This third type of DW is characterised by a three-dimensional, flux closure micromagnetic structure with an unusual length and three internal degrees of freedom. Magnetic imaging on lithographically-patterned permalloy nanostrips confirms these predictions and shows that these DWs can be moved with an external magnetic field of about 1 mT. An extended phase diagram describing the regions of stability of all known types of DWs in permalloy nanostrips is provided.

Indirect localization of a magnetic domain wall mediated by quasi walls.

The manipulation of magnetic domain walls in thin films and nanostructures opens new opportunities for fundamental and applied research. But controlling reliably the position of a moving domain wall still remains challenging. So far, most of the studies aimed at understanding the physics of pinning and depinning processes in the magnetic layer in which the wall moves (active layer). In these studies, the role of other magnetic layers in the stack has been often ignored. Here, we report an indirect localization process of 180° domain walls that occurs in magnetic tunnel junctions, commonly used in spintronics. Combining Scanning Transmission X-Ray Microscopy and micromagnetic simulations, magnetic configurations in both layers are resolved. When nucleating a 180° domain wall in the active layer, a quasi wall is created in the reference layer, atop the wall. The wall and its quasi wall must then be moved or positioned together, as a unique object. As a mutual effect, a localized change of the magnetic properties in the reference layer induces a localized quasi wall in the active layer. The two types of quasi walls are shown to be responsible for an indirect localization process of the 180° domain wall in the active layer.

Size distribution of magnetic charge domains in thermally activated but out-of-equilibrium artificial spin ice.

A crystal of emerging magnetic charges is expected in the phase diagram of the dipolar kagomé spin ice. An observation of charge crystallites in thermally demagnetized artificial spin ice arrays has been recently reported by S. Zhang and coworkers and explained through the thermodynamics of the system as it approaches a charge-ordered state. Following a similar approach, we have generated a partial order of magnetic charges in an artificial kagomé spin ice lattice made out of ferrimagnetic material having a Curie temperature of 475 K. A statistical study of the size of the charge domains reveals an unconventional sawtooth distribution. This distribution is in disagreement with the predictions of the thermodynamic model and is shown to be a signature of the kinetic process governing the remagnetization.

Energy levels of interacting curved nanomagnets in a frustrated geometry: increasing accuracy when using finite difference methods.

The accuracy of finite difference methods is related to the mesh choice and cell size. Concerning the micromagnetism of nano-objects, we show here that discretization issues can drastically affect the symmetry of the problem and therefore the resulting computed properties of lattices of interacting curved nanomagnets. In this paper, we detail these effects for the multi-axis kagome lattice. Using the OOMMF finite difference method, we propose an alternative way of discretizing the nanomagnet shape via a variable moment per cell scheme. This method is shown to be efficient in reducing discretization effects.

Direct observation of massless domain wall dynamics in nanostripes with perpendicular magnetic anisotropy.

Domain wall motion induced by nanosecond current pulses in nanostripes with perpendicular magnetic anisotropy (Pt/Co/AlO(x)) is shown to exhibit negligible inertia. Time-resolved magnetic microscopy during current pulses reveals that the domain walls start moving, with a constant speed, as soon as the current reaches a constant amplitude, and no or little motion takes place after the end of the pulse. The very low "mass" of these domain walls is attributed to the combination of their narrow width and high damping parameter α. Such a small inertia should allow accurate control of domain wall motion by tuning the duration and amplitude of the current pulses.

Current-induced domain wall motion and magnetization dynamics in CoFeB/Cu/Co nanostripes.

Current-induced domain wall motion and magnetization dynamics in the CoFeB layer of CoFeB/Cu/Co nanostripes were studied using photoemission electron microscopy combined with x-ray magnetic circular dichroism (XMCD-PEEM). Quasi-static measurements show that current-induced domain wall motion in the CoFeB layer is similar to the one observed in the NiFe layer of NiFe/Cu/Co trilayers, although the threshold current densities for domain wall depinning are lower. Time-resolved XMCD-PEEM measurements are used as an efficient probe of domain wall depinning statistics. They also reveal that, during the application of current pulses, the CoFeB magnetization rotates in the direction transverse to the nanostripe. The corresponding tilt angles have been quantified and compared to analytical and micromagnetic calculations, highlighting the influence of magnetostatic interactions between the two magnetic layers on the magnetization rotation.

Artificial kagome arrays of nanomagnets: a frozen dipolar spin ice.

Magnetic frustration effects in artificial kagome arrays of nanomagnets are investigated using x-ray photoemission electron microscopy and Monte Carlo simulations. Spin configurations of demagnetized networks reveal unambiguous signatures of long range, dipolar interaction between the nanomagnets. As soon as the system enters the spin ice manifold, the kagome dipolar spin ice model captures the observed physics, while the short range kagome spin ice model fails.

Controlled switching of Néel caps in flux-closure magnetic dots.

While magnetic hysteresis usually considers magnetic domains, the switching of the core of magnetic vortices has recently become an active topic. We considered Bloch domain walls, which are known to display at the surface of thin films flux-closure features called Néel caps. We demonstrated the controlled switching of these caps under a magnetic field, occurring via the propagation of a surface vortex. For this we considered flux-closure states in elongated micron-sized dots, so that only the central domain wall can be addressed, while domains remain unaffected.

Labyrinthine island growth during Pd/Ru(0001) heteroepitaxy.

Using low energy electron microscopy we observe that Pd deposited on Ru only attaches to small sections of the atomic step edges surrounding Pd islands. This causes a novel epitaxial growth mode in which islands advance in a snakelike motion, giving rise to labyrinthine patterns. Based on density functional theory together with scanning tunneling microscopy and low energy electron microscopy we propose that this growth mode is caused by a surface alloy forming around growing islands. This alloy gradually reduces step attachment rates, resulting in an instability that favors adatom attachment at fast advancing step sections.

Spin-induced forbidden evanescent states in III-V semiconductors.

Within the band gap of a semiconductor no electronic propagating states are allowed, but there exist evanescent states which govern charge transport such as tunneling. In this Letter, we address the issue of their spin dependence in III-V semiconductors. Taking into account the spin-orbit interaction, we treat the problem using a k . p 14 x 14 Hamiltonian that we numerically compute for GaAs. Our results show that the removed spin degeneracy in the band gap can lead to giant energy splittings and induces forbidden zones in space where evanescent states are suppressed.