Real-space anisotropic dielectric response in a multiferroic skyrmion lattice

Abstract

A magnetic skyrmion lattice is a microstructure consisting of hexagonally aligned skyrmions. While a skyrmion as a topologically protected carrier of information promises a number of applications, an easily accessible probe of the skyrmion and skyrmion lattice at mesoscopic scale is of significance. It is known that neutron scattering, Lorentz transmission electron microscopy, and spin-resolved STM as effective probes of skyrmions have been established. In this work, we propose that the spatial contour of dielectric permittivity in a skyrmion lattice with ferromagnetic interaction and in-plane (xy) Dzyaloshinskii-Moriya (DM) interaction can be used to characterize the skyrmion lattice. The phase field and Monte Carlo simulations are employed to develop the one-to-one correspondence between the magnetic skyrmion lattice and dielectric dipole lattice, both exhibiting the hexagonal symmetry. Under excitation of in-plane electric field in the microwave range, the dielectric permittivity shows the dumbbell-like pattern with the axis perpendicular to the electric field, while it is circle-like for the electric field along the z-axis. The dependences of the spatial contour of dielectric permittivity on external magnetic field along the z-axis and dielectric frequency dispersion are discussed.

Multiferroicity and skyrmions carrying electric polarization in GaV 4 S 8

“…Indeed, shortly after the first observation of skyrmions in multiferroic Cu 2 OSeO 3 (8), the electric-field control of the SkL has also been demonstrated in this compound (12,13). The dielectric response and emergent electrodynamics of skyrmions have also been extensively studied experimentally and theoretically both in itinerant and insulating magnets (5,7,14,15,16,17,18) Lacunar spinels, ternary chalcogenides of composition AM 4 X 8 (A = Ga and Ge; M = V, Mo, Nb, and Ta; X = S and Se), represent an interesting class of transition-metal compounds with weakly linked molecular units, cubane (M 4 X 4 ) n+ and tetrahedral (AX 4 ) n-, as structural building blocks (19,20,21,22). Recently, a plethora of correlation effects has been reported for AM 4 X 8 lacunar spinels, including pressure-induced superconductivity (23), bandwidthcontrolled metal-to-insulator transition (24,25), large negative magnetoresistance (26), a twodimensional topological insulating state (27), resistive switching via an electric-field induced transition (28,29,30), emergence of orbitally driven ferroelectricity (31), and, most interestingly, an extended Néel-type SkL phase (9).…”

“…Indeed, shortly after the first observation of skyrmions in multiferroic Cu 2 OSeO 3 (8), electric field control of SkLs in this compound was also demonstrated (12,13). The dielectric response and emergent electrodynamics of skyrmions have also been extensively studied, experimentally and theoretically, in both itinerant and insulating magnets (5,7,(14)(15)(16)(17)(18).…”

Unexpected observation of splitting of skyrmion phase in Zn doped Cu2OSeO3

“…The skyrmion lattice can be probed with several experimental methods, such as Lorentz transmission electron microscopy 11 , magnetic force microscopy 12 , spin-polarized scanning tunneling microscopy 13 and small angle neutron scattering 14 . The signature of skyrmion lattice can also be detected by relatively simple methods such as magnetic χ′ ac 15 , heat capacity 16 , topological Hall effect 17 and electrical polarization 18 19 20 .…”

Multiferroic materials and magnetoelectric physics: symmetry, entanglement, excitation, and topology

“…Based on this idea, Chu et al performed a simulation to show that the skyrmion lattice can be visualized using a microwave-frequency dielectric detection technique (see Fig. 41), which may provide an alternative method to monitor skyrmions in a noncollinear multiferroic [470]. In fact, experimentally, Okamura et al observed the microwave magnetoelectric effect via the skyrmion resonance modes with oscillating magnetic field at a frequency of 1 − 2 GHz in Cu 2 OSeO 3 [471].…”