Geometrical frustration in magnetic materials often gives rise to exotic, low-temperature states of matter, such as the ones observed in spin ices. Here we report the imaging of the magnetic states of a thermally active artificial magnetic ice that reveal the fingerprints of a spin fragmentation process. This fragmentation corresponds to a splitting of the magnetic degree of freedom into two channels and is evidenced in both real and reciprocal space. Furthermore, the internal organization of both channels is interpreted within the framework of a hybrid spin–charge model that directly emerges from the parent spin model of the kagome dipolar spin ice. Our experimental and theoretical results provide insights into the physics of frustrated magnets and deepen our understanding of emergent fields through the use of tailor-made magnetism.

This Perspective surveys the state-of-the-art and future prospects of science and technology employing the nanoconfined light (nanophotonics and nanoplasmonics) in combination with magnetism. We denote this field broadly as nanoscale magnetophotonics. We include a general introduction to the field and describe the emerging magneto-optical effects in magnetoplasmonic and magnetophotonic nanostructures supporting localized and propagating plasmons. Special attention is given to magnetoplasmonic crystals with transverse magnetization and the associated nanophotonic non-reciprocal effects, and to magneto-optical effects in periodic arrays of nanostructures. We give also an overview of the applications of these systems in biological and chemical sensing, as well as in light polarization and phase control. We further review the area of nonlinear magnetophotonics, the semiconductor spin-plasmonics, and the general principles and applications of opto-magnetism and nano-optical ultrafast control of magnetism and spintronics.

The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order [1][2][3][4][5][6] , collective low-energy dynamics 7,8 and emergent magnetic properties 5,9,10 in, for example, artificial spin-ice structures. The common denominator of all these investigations is the use of Ising-like mesospins as building blocks, in the form of elongated magnetic islands. Here, we introduce a new approach: single interaction modifiers, using slave mesospins in the form of discs, within which the mesospin is free to rotate in the disc plane 11. We show that by placing these on the vertices of square artificial spin-ice arrays and varying their diameter, it is possible to tailor the strength and the ratio of the interaction energies. We demonstrate the existence of degenerate ice-rule-obeying states in square artificial spin-ice structures, enabling the exploration of thermal dynamics in a spin-liquid manifold. Furthermore, we even observe the emergence of flux lattices on larger length scales, when the energy landscape of the vertices is reversed. The work highlights the potential of a design strategy for two-dimensional magnetic nano-architectures, through which mixed dimensionality of mesospins can be used to promote thermally emergent mesoscale magnetic states.Lithographic techniques can be used to fabricate magnetic nanoarrays, in which the interaction between the elements can be chosen by, for example, the distance between the islands. This approach has been used in a number of previous works, addressing both the order and dynamics of magnetic nanostructures [1][2][3][4][5][6][7][8]12 . In the specific case of square artificial spin ice (SASI), this approach has even enabled tailoring of the thermal dynamics and relaxation 8,[13][14][15] , as well as experimental realizations 9 of the degenerate square-ice model 16 . The distance and thereby the coupling strength for nearest and nextnearest neighbours are different in SASI (d 1 ≠ d 2 ; see Fig. 1), resulting in the loss of degeneracy. As a consequence, the ice-rule-obeying vertices, with two islands pointing in-two islands pointing out, are split into two groups (T I and T II ) with different energies (E I < E II ). One way to remedy this shortcoming is to shift parts of the lattice in the third dimension 9,17,18 . An alternative way to modify the energy landscape is to introduce an interaction modifier, as illustrated in Fig. 1b. In these modified SASI (mSASI) arrays, all islands have the same distance, or gap G, to the interaction modifier. While a height offset might seem the obvious choice for manipulating the coupling strengths between the islands, the use of interaction modifiers at the vertices of artificial spin-ice structures is not only lithographically much easier to achieve, but also opens up completely new avenues for tailoring their energy landscapes. Instead of having a system consisting of only one type of island, we use two subsystems with widely different shape anisotropies a...

We have investigated the low-temperature thermodynamic properties of the dipolar kagome Ising antiferromagnet using at-equilibrium Monte Carlo simulations, in the quest for the ground-state manifold. In spite of the limitations of a single spin-flip approach, we managed to identify certain ordering patterns in the low-temperature regime and we propose a candidate for this unknown state. This novel configuration presents some intriguing features and passes several test-criteria, making it a very likely choice for the dipolar long-range order of this kagome Ising antiferromagnet.