Magnetic skyrmions and hopfions are topological solitons1-well-localized field configurations that have gained considerable attention over the past decade owing to their unique particle-like properties, which make them promising objects for spintronic applications. Skyrmions2,3 are two-dimensional solitons resembling vortex-like string structures that can penetrate an entire sample. Hopfions4-9 are three-dimensional solitons confined within a magnetic sample volume and can be considered as closed twisted skyrmion strings that take the shape of a ring in the simplest case. Despite extensive research on magnetic skyrmions, the direct observation of magnetic hopfions is challenging10 and has only been reported in a synthetic material11. Here we present direct observations of hopfions in crystals. In our experiment, we use transmission electron microscopy to observe hopfions forming coupled states with skyrmion strings in B20-type FeGe plates. We provide a protocol for nucleating such hopfion rings, which we verify using Lorentz imaging and electron holography. Our results are highly reproducible and in full agreement with micromagnetic simulations. We provide a unified skyrmion-hopfion homotopy classification and offer insight into the diversity of topological solitons in three-dimensional chiral magnets. 

Hopfion rings in a cubic chiral magnet

Cultural heritage is a crucial resource to increase our society's resilience. However, degradation processes, enhanced by environmental and anthropic risks, inevitably affect works of art, hindering their accessibility and socioeconomic value. In response, interfacial and colloidal chemistry has proposed valuable solutions over the past decades, overcoming the limitations of traditional restoration materials and granting cost- and time-effective remedial conservation of the endangered artifacts. Ranging from inorganic nanoparticles to hybrid composites and soft condensed matter (gels, microemulsions), a wide palette of colloidal systems has been made available to conservators worldwide, targeting the consolidation, cleaning, and protection of works of art. The effectiveness and versatility of the proposed solutions allow the safe and effective treatment of masterpieces belonging to different cultural and artistic productions, spanning from classic ages to the Renaissance and modern/contemporary art. Despite these advancements, the formulation of materials for the preservation of cultural heritage is still an open, exciting field, where recent requirements include coping with the imperatives of the Green Deal to foster the production of sustainable, low-toxicity, and environmentally friendly systems. This review gives a critical overview starting from pioneering works up to the latest advancements in colloidal systems for art conservation, a challenging topic where effective solutions can be transversal to multiple sectors even beyond cultural heritage preservation, from the pharmaceutical and food industry, to cosmetics, tissue engineering, and detergency. 

From Nanoparticles to Gels: A Breakthrough in Art Conservation Science

Plasma Enhanced Chemical Vapor Deposition (PECVD) of SiO x thin ﬁlms has been applied to the stone surface under laboratory conditions in order to assess its feasibility as an alternative method for stone protection. SiO x thin layers were deposited on oolitic limestone lithologies known to have been used for the construction and restoration of the Batalha Monastery in Portugal surface by PECVD from tetraethoxysilane (TEOS) as the reaction precursor, in capacitively coupled parallel-plate reactor. The thickness, morphologies and chemical properties of the deposited ﬁlm were characterized by attenuated total reﬂectance -Fourier transform infrared (ATR-FTIR) spectroscopy and scanning electron microscopy (SEM + EDS). Laboratory simulated decay and natural aging tests were implemented to evaluate the protective effect of the deposited micron-size SiO x thin ﬁlms. Results suggested that, due to the good barrier effect, SiO x ﬁlms were able to isolate the stones from aggressive acidic solution, thus reducing possible dissolution-related damage. Natural aging tests proved that SiO x thin ﬁlms were also able to inhibit to a high extent bio-colonization while, at the same time reducing soiling of the stone appearance. Durability and wetting property of this SiO x thin ﬁlm were preliminarily assessed. This research tested, for the ﬁrst time, the feasibility of applying micron-size SiO x ﬁlm quickly and directly via cold plasma deposition and its versatile protection performance on carbonate stone.

Plasma enhanced chemical vapor deposition (PECVD) of SiOx thin films on Portuguese limestone: An experimental study

Recent advances in the research area of 3D magnetic topological solitons (hopfions) in restricted geometries are reviewed. The description of the magnetic solitons is based on a macroscopic micromagnetic approach and the Landau–Lifshitz equation of the magnetization motion. The concepts of the gauge emergent vector potential and emergent magnetic field are widely used to calculate the 3D topological charge (the Hopf index) of magnetic textures. The relation of the magnetic hopfions with classical field theory is demonstrated, and a special role of the curvilinear toroidal coordinates in the description of the hopfions is underlined. The hopfion stability and dynamics in ferromagnetic films and dots are considered. A critical discussion of calculations of the magnetization emergent magnetic field and the Hopf index of the toroidal magnetic hopfions in restricted geometries is presented. 

Magnetic Hopfions: A Review

At first glance, the larger the object, the larger should be its effect on the surroundings – in particular, the larger should be its effect on the surrounding flow. However, in many practical situations, we observe the opposite effect: smaller-size particles affect the flow much more than larger-size particles. This seemingly counterintuitive phenomena has been observed in many situations: lava flow in the volcanoes, air circulation in tornadoes, blood flow in a body, the effect of fish on water circulation in the ocean, and the effect of added particles on seeping water that damages historic buildings. In this paper, we show that all these phenomena can be explained in natural geometric terms. 

Why Smaller-Size Objects Affect the Flow Much More than Larger Ones: A Geometric Explanation with Applications Ranging from Volcanoes and Tornadoes to Blood, Fish, and Buildings Preservation

Spatial topology endows topological solitons, such as skyrmions and hopfions, with fascinating dynamics. However, the temporal dimension has so far provided a passive stage on which topological solitons evolve. Here we construct spacetime magnetic hopfions: magnetic textures in two spatial dimensions that when excited by a time-periodic drive develop spacetime topology. We uncover two complementary construction routes using skyrmions by braiding their center of mass position and by controlling their internal low-energy excitations. Spacetime magnetic hopfions can be realized in nanopatterned grids to braid skyrmions and in frustrated magnets under an applied AC electric field. Their topological invariant, the spacetime Hopf index, can be tuned by the applied electric field as demonstrated by our collective coordinate modeling and micromagnetic simulations. The principles we have introduced to actively control spacetime topology are not limited to magnetic solitons, opening avenues to explore spacetime topology of general order parameters and fields.

pdf/spacetime-magnetic-hopfions-from-internal-excitations-and-1gyrakhs.pdf

Spacetime magnetic hopfions: from internal excitations and braiding of skyrmions

Abstract Spatial topology endows topological solitons, such as skyrmions and hopfions, with fascinating dynamics. However, the temporal dimension has so far provided a passive stage on which topological solitons evolve. Here we construct spacetime magnetic hopfions: magnetic textures in two spatial dimensions that when excited by a time-periodic drive develop spacetime topology. We uncover two complementary construction routes using skyrmions by braiding their center of mass position and by controlling their internal low-energy excitations. Spacetime magnetic hopfions can be realized in nanopatterned grids to braid skyrmions and in frustrated magnets under an applied AC electric field. Their topological invariant, the spacetime Hopf index, can be tuned by the applied electric field as demonstrated by our collective coordinate modeling and micromagnetic simulations. The principles we have introduced to actively control spacetime topology are not limited to magnetic solitons, opening avenues to explore spacetime topology of general order parameters and fields. 

Spacetime magnetic hopfions from internal excitations and braiding of skyrmions

Mineral nanoparticle suspensions with consolidating properties have been successfully applied in the restoration of weathered architectural surfaces. However, the design of these consolidants is usually stone-specific and based on trial and error, which prevents their robust operation for a wide range of highly heterogeneous monumental stone materials. In this work, we develop a facile and versatile method to systematically study the consolidating mechanisms in action using a surface forces apparatus (SFA) with real-time force sensing and an X-ray surface forces apparatus (X-SFA). We directly assess the mechanical tensile strength of nanosilica-treated single mineral contacts and show a sharp increase in their cohesion. The smallest used nanoparticles provide an order of magnitude stronger contacts. We further resolve the microstructures and forces acting during evaporation-driven, capillary-force-induced nanoparticle aggregation processes, highlighting the importance of the interactions between the nanoparticles and the confining mineral walls. Our novel SFA-based approach offers insight into nano- and microscale mechanisms of consolidating silica treatments, and it can aid the design of nanomaterials used in stone consolidation.

https://www.duo.uio.no/bitstream/10852/100838/1/acs.langmuir.2c00486.pdf

Cohesion Gain Induced by Nanosilica Consolidants for Monumental Stone Restoration

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Spacetime magnetic hopfions: from internal excitations and braiding of skyrmions

Spacetime magnetic hopfions from internal excitations and braiding of skyrmions

Cohesion Gain Induced by Nanosilica Consolidants for Monumental Stone Restoration