Topological Hall effect (THE), a quantum phenomenon arising from emergent magnetic field generated by topological spin texture, is a key method for detecting non-coplanar spin structures like skyrmions in magnetic materials. Here, we investigate a bilayer structure of Pt and conducting ferrimagnet NiCo2O4 (NCO) of perpendicular magnetic anisotropy and demonstrate giant THE across a temperature range 2 - 350 K. The absence of THE in single-layer Pt and NCO, as well as in Pt/Cu/NCO, suggests its interfacial origin. The maximum THE occurring just before the NCO coercive field indicates its connection to magnetic nucleation centers, which are topologically equivalent to skyrmions. The large normalized THE, based on the emergent-field model, points to a high population density of small nucleation centers. This aligns with the unresolvable domain structures during magnetization reversal, even though clear domain structures are detected after zero-field cooling. These results establish heavy metal/NCO as a promising system for exploring topological spin structures.

Although topological spin textures are not commonly found in centrosymmetric magnetic systems, noncoplanar monodomain magnetic states such as flower and curling states do emerge due to the contribution of surfaces and edges in nanoparticles. In this work, we studied the topological nature of these intriguing noncoplanar spin textures and their manifestation in electric transport phenomena due to the Berry phase accumulation. Specifically, we calculated the topological charges $Q$ associated with these spin textures and the corresponding topological Hall effect. We assessed these spin textures across various particle sizes and along magnetic hysteresis loops and mapped the spin structures in confined geometries using magnetic force microscopy. We show that $Q$, as a fractional number, increases with particle size and saturates as the system transits from the flower state to the curling state. Along magnetic hysteresis loops, smaller particles that show flower states in zero field, exhibit a peak in $Q$ near the coercive field, a signature of the topological Hall effect demonstrated in other systems. In contrast, larger particles that show curling states during the magnetization reversal, exhibit transitions between the homogeneous state, flower state, and curling state, which generates jumps in $Q$ and the topological Hall effects. These results reveal the rich topological nature of centrosymmetric magnetic nanoparticles, offer control using magnetic field and probe using electric transport, suggesting promising potential applications.

Analytical calculations and micromagnetic simulations are used to determine the Berry curvature and topological Hall effect (THE) due to conduction electrons in small ferromagnetic particles. Our focus is on small particles of nonellipsoidal shapes, where noncoplanar spin structures yield a nonzero topological Hall signal quantified by the skyrmion number Q. We consider two mechanisms leading to noncoplanarity in aligned nanoparticles, namely flower-state spin configurations due to stray fields near corners and edges, and curling-type magnetostatic selfinteractions. In very small particles, the reverse magnetic fields enhance Q due to the flower state until the reversal occurs, whereas for particles with a radius greater than coherence radius Rcoh the Q jumps to a larger value at the nucleation field representing the transition from the flower state to the curling state. We calculate the Skyrmion density (average Berry curvature) from these spin structures as a function of particle size and applied magnetic field. Our simulation results agree with analytical calculations for both flower state and flux closure states. We showed the presence of Berry curvature in small particles as long as the size of the particle is less than the single domain limit. Using magnetic force microscopy (MFM), we also showed that in a nanodot of Co with a suitable size, a magnetic vortex state with perpendicular (turned-up) magnetization at the core is realized which can be manifested for Berry curvature and emergent magnetic field in confined geometries for single domain state at room temperature.

The exchange coupling between a hard magnetic layer MnBi and a soft magnetic layer Co-Fe has been found to significantly improve the maximum energy product. In this work, the spin structure of exchange-coupled MnBi:Co-Fe bilayers is experimentally investigated by X-ray magnetic circular dichroism (XMCD) and polarized neutron reflectometry (PNR). We find that the out-of-plane magnetization reversal process of the MnBi:Co-Fe bilayer structure involves formation of a curling-type twisting of the magnetization in the film plane at low or intermediate reversal fields. Micromagnetic simulations are further performed to provide a detailed view of the spins at the curling center. Reminiscent of chiral spin structures known as spin bobbers, this curling in the exchange-coupled hard-soft magnetic bilayers is a new type of skyrmionic spin structure and worth further investigation.

Topological phase in magnetic materials yields a quantized contribution to the Hall effect known as the topological Hall effect, which is often caused by skyrmions, with each skyrmion creating a magnetic flux quantum h/e. The control and understanding of topological properties in nanostructured materials is the subject of immense interest for both fundamental science and technological applications, especially in spintronics. In this work, the electron-transport properties and spin structure of exchange-coupled cobalt nanoparticles with an average particle size of 13.7 nm are studied experimentally and theoretically. Magnetic and Hall-effect measurements identify topological phase transitions in the exchange-coupled cobalt nanoparticles and were used to discover a qualitatively new type of hysteresis in the topological Hall effect namely, Berry-phase hysteresis. Micromagnetic simulations reveal the origin of the topological Hall effect namely, the chiral domains, with domain-wall chirality quantified by an integer skyrmion number. These spin structures are different from the skyrmions formed due to Dzyaloshinskii Moriya interactions in B20 crystals and multilayered thin films, and caused by cooperative magnetization reversal in the exchange-coupled cobalt nanoparticles. An analytical model is developed to explain the underlying physics of Berry-phase hysteresis, which is strikingly different from the iconic magnetic hysteresis and constitutes one aspect of 21st-century reshaping of our view on nature at the borderline of physics, chemistry, mathematics, and materials science.

Magnetic flux densities ( B-fields) and field intensities ( H-fields) in thin films are investigated from the viewpoints of Berry phase and topological Hall effect. The well-known origin of the topological Hall effect is an emergent B-field originating from the Berry phase of conduction electrons, but Maxwell’s equations predict the relevant perpendicular component Bz to be zero. This paradox is solved by treating the electrons as point-like objects in Lorentz cavities. These cavities can also be used to interpret magnetization measurements in the present and other contexts, but structural and magnetic inhomogeneities lead to major modifications of the Lorentz-hole picture.

Magnetotransport and ferromagnetism in thin films of ${\mathrm{Co}}_{2}\mathrm{Si}$ nanoclusters are investigated experimentally and theoretically. The nanoclusters are fabricated by an inert-gas condensation-type cluster-deposition method and have an average size of 11.3 nm. Unlike the bulk ${\mathrm{Co}}_{2}\mathrm{Si}$ that exhibits a very weak net magnetic moment only below 10 K, the nanoclusters exhibit room-temperature ferromagnetism with a substantial saturation magnetization. Key features of the system are its closeness to the Stoner transition, magnetic moments induced by spin polarization starting from surface atoms, and nonuniaxial anisotropy associated with the orthorhombic crystal structure of ${\mathrm{Co}}_{2}\mathrm{Si}$. A method is introduced to determine the effective anisotropy using the experimental magnetization data of this complex system and its relationship with the two lowest-order nonuniaxial anisotropy constants. On decreasing temperature from 300 K, the nanoclusters show electron-transport properties unusual for a ferromagnetic metal, including an increase of Hall resistivity and a nonmonotonic change of negative magnetoresistance with a peak at around 100 K. The underlying physics is explained on the basis of the large polarization of surface spins and variation in the degree of their misalignments due to temperature-dependent effective anisotropy.

Heusler compounds and alloys based on them are of great recent interest because they exhibit a wide variety of spin structures, magnetic properties, and electron-transport phenomena. Their properties are tunable by alloying and we have investigated L2(1)-orderd compound Ru2MnSn and its alloys by varying the atomic Mn:Sn composition. While antiferromagnetic ordering with a Neel temperature of 361 K was observed in Ru2MnSn, the Mnpoor Ru2Mn0.8Sn1.2 alloy exhibits properties of a diluted antiferromagnet in which there are localized regions of uncompensated Mn spins. Furthermore, a noncoplanar spin structure, evident from a topological Hall-effect contribution to the room-temperature Hall resistivity, is realized in Ru2Mn0.8Sn1.2. Our combined experimental and theoretical analysis shows that in the Ru2Mn0.8Sn1.2 alloy, the magnetic properties can be explained in terms of a noncoplanar antiferromagnetic scissor mode, which creates a small net magnetization in a magnetic field and subsequently yields a Berry curvature with a strong topological Hall effect.

The spin structure and transport behavior of B20-ordered CoSi nanomagnets are investigated experimentally and by theoretical calculations. B20 materials are of interest in spin electronics because their noncentrosymmetric crystal structure favors noncoplanar spin structures that yield a contribution to the Hall effect. However, stoichiometric bulk CoSi is nonmagnetic, and combining magnetic order at and above room temperature with small feature sizes has remained a general challenge. Our CoSi nanoclusters have an average size of 11.6 nm and a magnetic ordering temperature of 330 K. First-principle calculations and x-ray circular dichroism experiments show that the magnetic moment is predominantly confined to the shells of the clusters. The CoSi nanocluster ensemble exhibits a topological Hall effect, which is explained by an analytical model and by micromagnetic simulations on the basis of competing Dzyaloshinskii-Moriya and intra- and intercluster exchange interactions. The topological Hall effect is caused by formation of chiral spin textures in the shells of the clusters, which exhibit fractional skyrmion number and are therefore termed as paraskyrmions (closely related to skyrmion spin structures). This research shows how nanostructuring of a chiral atomic structure can create a spin-textured material with a topological Hall effect and a magnetic ordering temperature above room temperature.

In the first part, the scattering characteristics of an isolated dielectric coated conducting rod have been investigated. The types of considered coatings for the scattering analysis are realistic materials including barium strontium titanate, magnetodielectric, gallium arsenide, and silicon carbide. It is found that the gallium arsenide coating can be used to significantly reduce the scattering from a thin perfectly electric conducting cylindrical rod at specific observation angles. In the second part, the effective permittivity and permeability of metamaterials composed of two dimensional periodic arrangements of these dielectric coated conducting cylindrical rods have been studied. An increase in the double negative (DNG) bandwidth of a metamaterial composed of barium strontium titanate coated conducting rods has been observed in contrast to the corresponding bandwidth of a metamaterial composed of only barium strontium titanate material rods. Also an additional plasmonic epsilon negative (ENG) bandwidth has been found in case of a metamaterial composed of barium strontium titanate coated conducting rods. It is further studied that the widest ENG, mu negative, and DNG bandwidths exist for a metamaterial composed of gallium arsenide rods.

Magnets with chiral crystal structures and helical spin structures have recently attracted much attention as potential spin-electronics materials, but their relatively low magnetic-ordering temperatures are a disadvantage. While cobalt has long been recognized as an element that promotes high-temperature magnetic ordering, most Co-rich alloys are achiral and exhibit collinear rather than helimagnetic order. Crystallographically, the B20-ordered compound CoSi is an exception due to its chiral structure, but it does not exhibit any kind of magnetic order. Here, we use nonequilibrium processing to produce B20-ordered Co_{1+x}Si_{1-x} with a maximum Co solubility of x=0.043. Above a critical excess-Co content (x_{c}=0.028), the alloys are magnetically ordered, and for x=0.043, a critical temperature T_{c}=328  K is obtained, the highest among all B20-type magnets. The crystal structure of the alloy supports spin spirals caused by Dzyaloshinskii-Moriya interactions, and from magnetic measurements we estimate that the spirals have a periodicity of about 17 nm. Our density-functional calculations explain the combination of high magnetic-ordering temperature and short periodicity in terms of a quantum phase transition where excess-cobalt spins are coupled through the host matrix.

The effect of micromagnetic boundary conditions on the Berry curvature and topological Hall effect in granular nanostructures is investigated by model calculations. Both free surfaces and grain boundaries between interacting particles or grains affect the spin structure. The Dzyaloshinskii-Moriya interactions yield corrections to the Erdmann-Weierstrass boundary conditions, but the Berry curvature remains an exclusive functional of the local spin structure, which greatly simplifies the treatment of nanostructures. An explicit example is a model nanostructure with cylindrical symmetry whose spin structure is described by Bessel function and which yields a mean-field-type Hall-effect contribution that can be related to magnetic-force-microscopy images.

A nonequilibrium rapid-quenching method has been used to fabricate NiMnIn and NiMnGa alloys that are chemically and morphologically similar but crystallographically and physically very different. NiMnGa crystallizes in a Ni2In-type hexagonal structure, whereas NiMnIn is a cubic Heusler alloy. Both alloys yield a topological Hall effect contribution corresponding to bubble-type skyrmion spin structures, but it occurs in much lower magnetic fields in NiMnIn as compared to NiMnGa. The effect is unrelated to net Dzyaloshinskii-Moriya interactions, which are absent in both alloys due to their inversion-symmetric crystal structures. Based on magnetic-force microscopy, we explain the difference between the two alloys by magnetocrystalline anisotropy and uniaxial and cubic anisotropies yielding full-fledged and reduced topological Hall effects, respectively. Since NiMnIn involves small magnetic fields (0.02–0.3 kOe) at and above room temperature, it is of potential interest in spin electronics.

The relationship between quantum mechanics and nanoscale spin dynamics is investigated by analyzing past work in magnetism and beyond. Findings about magnetization dynamics, accumulated throughout the 20th century, are revisited from a unifying modern perspective and related to trends in other areas of physics and technology. Traditional topics, for example spin precession and thermally activated magnetization processes, are discussed with emphasis on characteristic times and length scales, showing that nanoscale magnetization dynamics is very different from atomic spin dynamics. It is shown how these topics are connected to more recent developments such as the Berry phase, the no-cloning theorem, quantum-spin fluctuations, and THz magnetization dynamics in antiferromagnets.