Influence of magnetic field on electric polarization in small magnetic particles

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Within the framework of the phenomenological approach, we have obtained an inhomogeneous electric polarization associated with the appearance of an inhomogeneous magnetization distribution in the volume of small magnetic particles near the second-order phase transition from paramagnetic to ferromagnetic state. The temperature area of the existence of such inhomogeneous states for spherical shape particles of different sizes is determined. The change in the local electric polarization of small magnetic particles in an external magnetic field is considered.

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T. Shaposhnikova

Federal Research Centre Kazan Scientific Centre of the Russian Academy of Sciences

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Email: t_shap@kfti.knc.ru

Zavoisky Physical-Technical Institute

俄罗斯联邦, Kazan

R. Mamin

Federal Research Centre Kazan Scientific Centre of the Russian Academy of Sciences

Email: t_shap@kfti.knc.ru

Zavoisky Physical-Technical Institute

俄罗斯联邦, Kazan

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2. Fig. 1. Distributions of magnetization on the particle surface after the phase transition from the paramagnetic to the ferromagnetic state: for the case mr = mθ = 0, and mφ = mφ(r, φ) (5) at r = R, where R is the particle radius (a); for the case mr = mφ = 0 and mθ = mθ(r, φ) (7) at r = R (b). The arrows show the magnitudes and directions of the local magnetization vectors on the particle surface.

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3. Fig. 2. Distribution of local electric polarization inside a spherical particle in the plane z = 0 passing through the center of the particle, calculated using formula (9).

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4. Fig. 3. Phase diagram of the existence of an inhomogeneous vortex magnetic state and an inhomogeneous polar state for spherical nanoparticles in the coordinates of particle radius R — temperature T. The region of the inhomogeneous vortex state is shaded. Tc is the Curie temperature of the magnetic phase transition of the bulk material, Rc is the critical radius. At R < Rc, the spherical particle is uniformly magnetized. TCS = TC – ΔTS and TCV = TC – ΔTV are the temperature boundaries of the region of the inhomogeneous vortex state. At T > TCS, the homogeneous magnetic state becomes unstable with respect to the appearance of an inhomogeneous state (see text), since the energy of the inhomogeneous state becomes less than the energy of the homogeneous state.

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