Curvilinear magnetoelectrics with magnetic wires

Curvilinear magnetism emerged as an efficient approach to tailor magnetic chiral and anisotropic responses at the nanoscale. The effects of geometry on the statics and dynamics of magnetic textures in nanowires are already well understood, with many theoretical predictions being explored experimentally. The current focus of fundamental research is shifted to curvature and torsion effects in helimagnetic and (anti)ferromagnetic wires. Recent studies of these objects uncovered a possibility to design higher order magnetoelectric multipoles, including monopole, toroidal and quadrupole magnetoelectric moments. These moments are of paramount importance for the occurrence of linear magnetoelectric responses, which can be designed by a proper choice of the sample geometry. Magnetoelectric materials enable control of the nonvolatile magnetic order parameter using electric fields, which opens the way to energy-efficient magnetic memory and logic devices. In this chapter, we make the very first attempt to summarize current activities on curvilinear magnetoelectrics in wire-like geometries. Didactically, the chapter contains relevant background on magnetoelectricity as well as analytical geometry and curvilinear magnetism specific to nanowires, which is needed to understand the physics of curvilinear magnetoelectrics. The theoretical concepts discussed in this chapter can be used for the prediction and interpretation of magnetic responses of complex planar and 3D-shaped nanowires fabricated, e.g., via strain engineering or nanoscale 3D printing, as well as a broad class of molecular toroidal magnets revealing magnetoelectric properties.