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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

Snapshoted patterns of dielectric permittivity real part Re(ε) at different frequency, from top to bottom f = 30, 2, and 0.2τ−1.The left column (a)–(c) is under magnetic field Hz = 0.5D2/J, and right column (d)–(f) Hz = 0.7D2/J. Hereafter, E0 =  0.5/A1/P0 and magnetic field Hz is along out-of-plane direction.
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f4: Snapshoted patterns of dielectric permittivity real part Re(ε) at different frequency, from top to bottom f = 30, 2, and 0.2τ−1.The left column (a)–(c) is under magnetic field Hz = 0.5D2/J, and right column (d)–(f) Hz = 0.7D2/J. Hereafter, E0 = 0.5/A1/P0 and magnetic field Hz is along out-of-plane direction.

Mentions: Now we investigate the spatial dielectric permittivity patterns of the SkX lattice. The patterns of the real part Re(ε) for three different frequencies (three rows) at two magnetic field Hz (two columns) are shown in Fig. 4, given the Eext along the y-axis. Generally, the dielectric real part shows the dumbbell-like pattern with the two-fold symmetry along the x-axis, perpendicular to the direction of Eext. Each dumbbell is centered at one skyrmion center, giving the one-to-one correspondence. The effect of magnetic field Hz on the dielectric response pattern is associated with the stability of the SkX lattice, which is gradually destabilized by increasing Hz from 0.5D2/J to 0.7D2/J, resulting in the broken six-fold symmetry of the SkX lattice32. This consequence leads to the dumbbell distortion and gradual suppression of the dielectric response. As expected and shown in Fig. 3d, the dielectric real part is gradually suppressed with increasing frequency f, due to the well-known dispersion behavior.


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)

Snapshoted patterns of dielectric permittivity real part Re(ε) at different frequency, from top to bottom f = 30, 2, and 0.2τ−1.The left column (a)–(c) is under magnetic field Hz = 0.5D2/J, and right column (d)–(f) Hz = 0.7D2/J. Hereafter, E0 =  0.5/A1/P0 and magnetic field Hz is along out-of-plane direction.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: Snapshoted patterns of dielectric permittivity real part Re(ε) at different frequency, from top to bottom f = 30, 2, and 0.2τ−1.The left column (a)–(c) is under magnetic field Hz = 0.5D2/J, and right column (d)–(f) Hz = 0.7D2/J. Hereafter, E0 = 0.5/A1/P0 and magnetic field Hz is along out-of-plane direction.
Mentions: Now we investigate the spatial dielectric permittivity patterns of the SkX lattice. The patterns of the real part Re(ε) for three different frequencies (three rows) at two magnetic field Hz (two columns) are shown in Fig. 4, given the Eext along the y-axis. Generally, the dielectric real part shows the dumbbell-like pattern with the two-fold symmetry along the x-axis, perpendicular to the direction of Eext. Each dumbbell is centered at one skyrmion center, giving the one-to-one correspondence. The effect of magnetic field Hz on the dielectric response pattern is associated with the stability of the SkX lattice, which is gradually destabilized by increasing Hz from 0.5D2/J to 0.7D2/J, resulting in the broken six-fold symmetry of the SkX lattice32. This consequence leads to the dumbbell distortion and gradual suppression of the dielectric response. As expected and shown in Fig. 3d, the dielectric real part is gradually suppressed with increasing frequency f, due to the well-known dispersion behavior.

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