Integer Quantum Hall Effect, phase transition in researches of domain wall for data storage of thin Os_{x}Ra_{1-x}FeO_{3} nanofilms with channel of p-n junction

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The thin Os_{x}Ra_{1-x}FeO_{3} nanofilms have quasiparticle excitations that can be described by (2+1)-dimensional Dirac theory from developed a four-sublattice model (FSM) for the analytical description of A-cation displacements in (anti)ferroelectric-antiferrodistortive perovskites of ABO_{3} type. We have found that FSM explains the coexistence of rhombohedral (R), orthorhombic (O) and spatially modulated phases observed by atomic-resolution scanning transmission electron microscopy (STEM) in Os-doped RaFeO_{3}. Using this approach we atomically resolve the theoretical model of the sublattice asymmetry inherent to the case of the A-site Os/Ra cation sublattice in Os_{x}Ra_{1-x}FeO_{3} polymorphs. We have shown that this produces an unconventional form of the quantized Hall conductivity sigma_{xy}=-(2e^{2}/h)(2n+1) with n=0,1,2,... This unconventional quantization is caused by the analytical chirality of n=0 Landau level. In the article we have found the analytical chiral solutions of stationary Schrödinger boundary problem for domain wall for data storage of nanosize PmBaMn_{2}O_{6} ferroics with incommensurately modulated sinusoidal polarization waves Q_{T}, Q_{P}, Q_{b}. The computer solution of quantized energies or wave vectors of stationary inhomogeneous Schrödinger boundary problem for Q_{T}, Q_{P}, Q_{b} with sinusoidal depolarization waves for the thin PmBaMn_{2}O_{6} nanofilm are specified. We have presented the computation solutions of quantized normalized charges densities of the Eq. 96 stationary Schrödinger boundary problem for different thickness h of PmBaMn_{2}O_{6} ferroelectric (FE) nanofilms. We have found the computation solutions of order parameters of ferroelectric phase transition in the form of quantized hysteresis loops that were clearly visible like Fairy-tale Phoenix. We have found the quantized out-of-plane polarizations P_{3} dispersion for LSMO/BFO interface of polar-active ferroelectric nanofilm with semiconductor with different boundary parameters.

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