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Real-space anisotropic dielectric response in a multiferroic skyrmion lattice.

Chu P, Xie YL, Zhang Y, Chen JP, Chen DP, Yan ZB, Liu JM - Sci Rep (2015)

Bottom Line: 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.The dependences of the spatial contour of dielectric permittivity on external magnetic field along the z-axis and dielectric frequency dispersion are discussed.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Solid State Microstructures and Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.

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.

No MeSH data available.


Related in: MedlinePlus

Simulated multiferroic domain structure, (a) spin configuration with Sz indicated by color, (b) spatial distribution of polarization magnitude, (c) Bragg intensity pattern of the spin configuration, and (d) the FE domain structure. Black arrows indicate the direction of dipoles in each domain, magnetic field is along the out-of-plane direction.
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f2: Simulated multiferroic domain structure, (a) spin configuration with Sz indicated by color, (b) spatial distribution of polarization magnitude, (c) Bragg intensity pattern of the spin configuration, and (d) the FE domain structure. Black arrows indicate the direction of dipoles in each domain, magnetic field is along the out-of-plane direction.

Mentions: Subsequently, we look at the spin SkX lattice and as-generated dielectric SkX lattice, as shown in Fig. 2 for Eext = 0 and Hz = 0.5(D2/J). As expected, the spin SkX lattice exhibits well-aligned hexagonal symmetry, as shown in Fig. 2(a), which is also identified by the Bragg pattern shown in Fig. 2(c). The simulated dielectric SkX lattice is plotted in Fig. 2(b), showing the hexagonal symmetry too although the electric dipoles are non-collinearly aligned. The orientation and magnitude of electric dipoles in each skyrmion are discussed in Fig. 1 and no detailed discussion is given. For reference, Fig. 2(d) presents the in-plane orientation of the electric dipoles over the whole lattice and a roughly hexagonal symmetry can be seen too. This one-to-one correspondence between the spin and dielectric lattices constitutes the basis for spatially resolved dielectric spectroscopy of the magnetic skyrmion lattice. It should be mentioned that the dielectric SkX lattice, similar to the case of a single dielectric skyrmion, shows no net macroscopic polarization if no electric bias is applied. However, for practical measurements, an electric poling is used and thus a small polarization will be observed, such as P ~ 16μC/m2 at 5 K for Cu2OSeO3, as revealed experimentally3. Obviously, the as-generated depolarization energy can be safely ignored in comparison with the magnetic interactions.


Real-space anisotropic dielectric response in a multiferroic skyrmion lattice.

Chu P, Xie YL, Zhang Y, Chen JP, Chen DP, Yan ZB, Liu JM - Sci Rep (2015)

Simulated multiferroic domain structure, (a) spin configuration with Sz indicated by color, (b) spatial distribution of polarization magnitude, (c) Bragg intensity pattern of the spin configuration, and (d) the FE domain structure. Black arrows indicate the direction of dipoles in each domain, magnetic field is along the out-of-plane direction.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4321174&req=5

f2: Simulated multiferroic domain structure, (a) spin configuration with Sz indicated by color, (b) spatial distribution of polarization magnitude, (c) Bragg intensity pattern of the spin configuration, and (d) the FE domain structure. Black arrows indicate the direction of dipoles in each domain, magnetic field is along the out-of-plane direction.
Mentions: Subsequently, we look at the spin SkX lattice and as-generated dielectric SkX lattice, as shown in Fig. 2 for Eext = 0 and Hz = 0.5(D2/J). As expected, the spin SkX lattice exhibits well-aligned hexagonal symmetry, as shown in Fig. 2(a), which is also identified by the Bragg pattern shown in Fig. 2(c). The simulated dielectric SkX lattice is plotted in Fig. 2(b), showing the hexagonal symmetry too although the electric dipoles are non-collinearly aligned. The orientation and magnitude of electric dipoles in each skyrmion are discussed in Fig. 1 and no detailed discussion is given. For reference, Fig. 2(d) presents the in-plane orientation of the electric dipoles over the whole lattice and a roughly hexagonal symmetry can be seen too. This one-to-one correspondence between the spin and dielectric lattices constitutes the basis for spatially resolved dielectric spectroscopy of the magnetic skyrmion lattice. It should be mentioned that the dielectric SkX lattice, similar to the case of a single dielectric skyrmion, shows no net macroscopic polarization if no electric bias is applied. However, for practical measurements, an electric poling is used and thus a small polarization will be observed, such as P ~ 16μC/m2 at 5 K for Cu2OSeO3, as revealed experimentally3. Obviously, the as-generated depolarization energy can be safely ignored in comparison with the magnetic interactions.

Bottom Line: 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.The dependences of the spatial contour of dielectric permittivity on external magnetic field along the z-axis and dielectric frequency dispersion are discussed.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Solid State Microstructures and Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.

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.

No MeSH data available.


Related in: MedlinePlus