Magnetoelectric effect in bismuth - neodymium ferrite - garnet films

The prehistory of the dielectric properties of bismuth – neodymium ferrite – garnet films on a Gd3Ga5O12 (111) substrate cooled in an electric and magnetic field were established. The dynamic characteristics of the electric polarization are studied at large times when the electric field is turned on and off. The influence of a magnetic field on the residual polarization was found. The dependence of the electric polarization on the electric field in a magnetic field is determined. Experimental data are explained in the Debye model.


Introduction
Multiferroics are characterized by a strong interrelation of the magnetic and electrical subsystems [1][2][3][4][5][6], which in single-phase ferromagnetic materials is realized due to the spin-lattice and electron-lattice interactions. Studies of single-phase materials are important for a deeper understanding of electromagnetic phenomena in solids and are of interest for the creation of a new generation of solidstate electronics devices.
Yttrium ferrite garnet has cubic symmetry with an inversion center [7] and at low temperatures (below 130 K) a structural transition with triclinic lattice distortion is detected [8,9]. The electric polarization may be caused by deformation of the structure, which leads to breaking of the center inversion as a result of epitaxial film stress on the substrate or cationic substitution on dodecahedral nodes; surface electron states, magnetic domain structure. In films (BiLu) 3 (FeGa) 5 O 12 thickness of 10 μm, grown by liquid phase epitaxy on a substrate Gd 3 Ga 5 O 12 with a substrate orientation (210) is found the electric polarization of the domain walls, which can be switched by the external magnetic field [10]. Electric polarization is absent on films with substrate (111) orientation. These effects can be explained due to inhomogeneous magnetoelectric interaction and changes the magnetic anisotropy of the electric field [11]. The last factor can be neglected using external magnetic field an order of magnitude greater than the saturation field.

Magnetostriction
The purpose of the research is to establish the mechanism of the magnetoelectric interaction in a strong magnetic field in bismuth -neodymium ferrites -garnets films deposited on a garnet substrate. The Nd 0.5 Bi 2.5 Fe 5 O 12 film (450 nm) was studied on a single-crystal substrate Gd 3 Ga 5 O 12 (GGG) in the (111) direction. The films were obtained by the method of epitaxial deposition [7].
The films have a maximum of magnetostriction and electrostriction at a temperature of 200 K. Expansion goes into compression of the film in a magnetic field at cooling . The experimental data are explained in terms of model of ferroelectric domains and the magnetoelectric interaction. The 2 maximum of magnetostriction is associated with the formation of a dipole glass and domain pinning [12].

Capacitance
Cooling the films in a magnetic field H = 12 kOe and in an electric field E = 400 V/cm from room temperature to T = 80 K leads to a decrease in capacitance within one percent. After cooling and further heating to T = 300 K film capacity decreases by (3-4) % (figure 1). The dependence of the dielectric constant on frequency at low temperatures is satisfactorily described in the Debye model with a relaxation frequency of 5 MHz. The dielectric relaxation in the low frequency region ω <300 Hz, is caused by electron jumps in the film defects Im(ε)~σ/ω [13][14][15]. At temperatures above room temperature, the diffusion contribution of the domain boundaries is added to the dielectric susceptibility in the form: Re(ε)=ε 0 +χ 0 /(1+(ωτ) 2 )-vlg (ω), Im(ε )= χ 0 ωτ/(1+(ωτ ) 2 )+σ/ω (1) where τ is the relaxation time, σ is the conductivity, v is the relaxation rate, χ 0 is the dielectric susceptibility in a constant field.

Remanent polarization
The dynamic characteristics of the electric polarization at large times is determined by measuring the charge when a rectangular voltage pulse is switched on with amplitude E = 400 V / cm with frequency ω = 0.01, 0.003 Hz (figure 2). The residual polarization found after turning off the field disappears at a temperature T = 300 K ( figure 3). The electric polarization depends on the direction of the magnetic field applied perpendicularly and parallel to the film. Coefficient magnetoelectric interaction is the secondrank tensor.   The electric polarization was found from the relation P=∫ when measuring the current in an external quasi-periodic field with a frequency w = 0.01 Hz with different orientations of the magnetic field [16][17][18]. Electric polarization versus the external field is shown in figure 4. The shift of polarization is caused by negatively charged defects in the vicinity of the interface. Hysteresis is observed in the region of large electric fields and is associated with the formation of an electric field at the interface of the substratefilm. When heated, the relative polarization bias is halved from T = 80 K to T = 300 K. In the general case, the polarization is determined by the field of charged defects, the interface field (P 0 ) P = P 0 + χαE. The dielectric susceptibility has a maximum at T = 280 K.

Conclusion
A decrease in the capacity of the film after cooling from room temperature to T = 80 K in an electric field is found. The frequency dependence of the film capacity is described in the Debye model, the relaxation time is found. The critical temperature of the disappearance of the residual polarization and the anisotropy of the electric polarization in a magnetic field are found. The temperature of the maximum dielectric constant is established.
The reported study was funded by Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science№ 18-42-240001 r_a, to the research project: «Inversion of the sign of the components of the magnetoelectric tensor on the temperature in films of bismuth garnet ferrite replaced by neodymium».