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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

(a) The ac electric field Eext as a function of time t at f = 0.3τ−1, (b) the total polarization as a function of time t, and (c) the x component and y component of magnetization as a function of time t. Simulated dielectric permittivity spectrum (d) real part and (e) image part around f = 1.0τ−1 given Hz = 0.3, 0.6, and 0.9D2/J along the out-of-plane direction. The ac electric filed Eω is along y-axis and E0 =  0.5/A1/P0.
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f3: (a) The ac electric field Eext as a function of time t at f = 0.3τ−1, (b) the total polarization as a function of time t, and (c) the x component and y component of magnetization as a function of time t. Simulated dielectric permittivity spectrum (d) real part and (e) image part around f = 1.0τ−1 given Hz = 0.3, 0.6, and 0.9D2/J along the out-of-plane direction. The ac electric filed Eω is along y-axis and E0 = 0.5/A1/P0.

Mentions: The above results appear to be the basis for investigating the dielectric response of the SkX lattice, to be discussed in details below. We simulate the responses of polarization P and dielectric permittivity ε(f) = Re(ε) + iIm(ε) to ac electric field Eext along a given direction in the microwave frequency range. Fig. 3(b) presents the simulated P as a function of time t for an Eext along the y-axis with E0 = 0.35/A1/P0 and f = 0.3τ−1. The simulated components of magnetization along the x-axis and y-axis, Mx and My, are plotted in Fig. 3(c). The instant response of the P is observed. For Eext along other directions, similar results can be observed. Furthermore, due to the ME coupling described by F(M, P) in Eq.(2), the instant response of Mx is identified too while My remains unchanged. Due to the dominated ferromagnetic arrangement along z-axis, component Mz is either insensitive to Eext. This ME coupling effect can also be characterized by the response of the dielectric frequency spectrum to varying magnetic field Hz. In Fig. 3(d) and Fig. 3(e) are plotted respectively the real part Re(ε) and imaginary part Im(ε) of the dielectric permittivity as a function of frequency f at three different Hz (in unit of D2/J). According to the phase diagram in Ref. 32, the spin SkX lattice can be stabilized for 0.23 < Hz < 0.78. In this case, the Re(ε) and Im(ε) are expected to exhibit remarkable frequency dispersion due to the existence of the dielectric SkX lattice, as confirmed by the data at Hz = 0.3 and 0.6. However, for Hz > 0.78, the ferromagnetic phase replacing the SkX phase is favored, implying the disappearance of magnetically induced electric dipoles and thus dielectric frequency dispersion. Indeed, the data at Hz = 0.9 shows no longer any dispersion. Here it should be mentioned that the high-f frequency dispersion at f ~ 100τ−1 is due to the electric field induced electric dipole fluctuations which have nothing to do with the SkX fluctuations resonated at f ~ 3τ−1.


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)

(a) The ac electric field Eext as a function of time t at f = 0.3τ−1, (b) the total polarization as a function of time t, and (c) the x component and y component of magnetization as a function of time t. Simulated dielectric permittivity spectrum (d) real part and (e) image part around f = 1.0τ−1 given Hz = 0.3, 0.6, and 0.9D2/J along the out-of-plane direction. The ac electric filed Eω is along y-axis and E0 =  0.5/A1/P0.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: (a) The ac electric field Eext as a function of time t at f = 0.3τ−1, (b) the total polarization as a function of time t, and (c) the x component and y component of magnetization as a function of time t. Simulated dielectric permittivity spectrum (d) real part and (e) image part around f = 1.0τ−1 given Hz = 0.3, 0.6, and 0.9D2/J along the out-of-plane direction. The ac electric filed Eω is along y-axis and E0 = 0.5/A1/P0.
Mentions: The above results appear to be the basis for investigating the dielectric response of the SkX lattice, to be discussed in details below. We simulate the responses of polarization P and dielectric permittivity ε(f) = Re(ε) + iIm(ε) to ac electric field Eext along a given direction in the microwave frequency range. Fig. 3(b) presents the simulated P as a function of time t for an Eext along the y-axis with E0 = 0.35/A1/P0 and f = 0.3τ−1. The simulated components of magnetization along the x-axis and y-axis, Mx and My, are plotted in Fig. 3(c). The instant response of the P is observed. For Eext along other directions, similar results can be observed. Furthermore, due to the ME coupling described by F(M, P) in Eq.(2), the instant response of Mx is identified too while My remains unchanged. Due to the dominated ferromagnetic arrangement along z-axis, component Mz is either insensitive to Eext. This ME coupling effect can also be characterized by the response of the dielectric frequency spectrum to varying magnetic field Hz. In Fig. 3(d) and Fig. 3(e) are plotted respectively the real part Re(ε) and imaginary part Im(ε) of the dielectric permittivity as a function of frequency f at three different Hz (in unit of D2/J). According to the phase diagram in Ref. 32, the spin SkX lattice can be stabilized for 0.23 < Hz < 0.78. In this case, the Re(ε) and Im(ε) are expected to exhibit remarkable frequency dispersion due to the existence of the dielectric SkX lattice, as confirmed by the data at Hz = 0.3 and 0.6. However, for Hz > 0.78, the ferromagnetic phase replacing the SkX phase is favored, implying the disappearance of magnetically induced electric dipoles and thus dielectric frequency dispersion. Indeed, the data at Hz = 0.9 shows no longer any dispersion. Here it should be mentioned that the high-f frequency dispersion at f ~ 100τ−1 is due to the electric field induced electric dipole fluctuations which have nothing to do with the SkX fluctuations resonated at f ~ 3τ−1.

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