arXiv subjects

Xiao-Fan Zhang

Publications and source records attributed to Xiao-Fan Zhang.

4 recordsLinked to original sources

arXiv2026

Dielectric, magnetic, and magnetodielectric behaviors of BaFe12O19 hexaferrite modulated by Mn and Ti substitutions

We prepared Mn- and Ti mono-doped and co-doped BaFe12O19 hexaferrites via solid-state reaction to investigate the interplay between magnetic and dielectric properties. Mn2+ ions preferentially occupy the 4f2 and 2b sites, while Ti4+ ions mainly substitute the Fe3+ ions at 4f1 and 12k sites as revealed by the Raman spectroscopy and formation energy. Pure BaFe12O19 exhibits ferrimagnetism. The hexaferrites related to Ti doping have noncollinear longitudinal conical spin order at low temperatures, where BaFe6Mn3Ti3O19 retains this spin order up to room temperature. Ti4+ substitution at 4f1 and 12k sites plays a pivotal role in stabilizing the noncollinear conical spin order through adjusting the superexchange interactions and reducing the uniaxial magnetocrystalline anisotropy along the c-axis. The magnetic response exhibits two distinct transition temperatures because Ti4+ ions interrupt the magnetic superexchange interactions with two inequivalent exchange integrals. Pure BaFe12O19 presents a quantum paraelectric behavior at low temperatures, which is disrupted by Mn-Ti co-doping due to the decoupling of electric dipoles within the triangular bipyramid. Electron hopping and polaronic effects dominate the dielectric response at 10-50 K, while Maxwell-Wagner interfacial polarization and electron hopping contribute to dielectric dispersion at higher temperatures. The negative MD effect of pure BaFe12O19 and BaFe6Mn3Ti3O19 at 10 K originates from spin-phonon coupling and electric polarization induced by noncollinear spin order under magnetic field, respectively. The Mn-Ti co-doped samples achieve relatively higher MD responses at low magnetic fields. In higher temperatures, the MD effect arises mainly from the magnetic field modulation of the electron hopping with non-intrinsic interfacial polarization.

cond-mat.mtrl-sci↗

arXiv2021

Inverse scattering transform and dynamics of soliton solutions for nonlocal focusing modified Korteweg-de Vries equation

In this work, we mainly study the general $N$-soliton solutions of the nonlocal modified Korteweg-de Vries (mKdV) equation by utilizing the Riemann-Hilbert (RH) method. For the initial value belonging to Schwarz space, we firstly obtain the corresponding eigenfunctions and scattering data in the direct scattering process. Then we successfully establish a suitable RH problem of the nonlocal mKdV equation. The exact expression of the solution for the equation is derived via solving the RH problem. Using the symmetry of scattering data, the phenomena corresponding to different eigenvalues are analyzed, including bounded solutions, singular solutions, position solutions and kink solutions. Finally, the propagation path of the solution is observed, and the characteristic line is further used to analyze the continuity or other phenomena of the solution. The new dynamic behavior of the solution is observed by rotating the characteristic line at a certain angle.

nlin.SI↗

arXiv2021

Inverse scattering transform and multiple high-order pole solutions for the nonlocal focusing and defocusing modified Korteweg-de Vries equation with the nonzero boundary conditions

We extend the Riemann-Hilbert (RH) method to study the inverse scattering transformation and high-order pole solutions of the focusing and defocusing nonlocal (reverse-space-time) modified Korteweg-de Vries (mKdV) equations with nonzero boundary conditions (NZBCs) at infinity and successfully find its multiple soliton solutions with one high-order pole and multiple high-order poles. By introducing the generalized residue formula, we overcome the difficulty caused by calculating the residue conditions corresponding to the higher-order poles. In accordance with the Laurent series of reflection coefficient and oscillation term, the determinant formula of the high-order pole solution with NZBCs is established. Finally, combined with specific parameters, the dynamic propagation behaviors of the high-order pole solutions are further analyzed and some very interesting phenomena are obtained, including kink solution, anti kink solution, rational solution and breathing-soliton solution.

nlin.SI↗

arXiv2021

Inverse scattering transform of the coupled modified Korteweg-de Vries equation with nonzero boundary conditions

In this work, we extend the Riemann-Hilbert (RH) method in order to study the coupled modified Korteweg-de Vries equation (cmKdV) under nonzero boundary conditions (NZBCs), and successfully find its solutions with their various dynamic propagation behaviors. In the process of spectral analysis, it is necessary to introduce Riemann surface to avoid the discussion of multi-valued functions, and to obtain the analytical and asymptotic properties needed to establish the RH problem. The eigenfunction have a column that is not analytic in a given region, so we introduce the auxiliary eigenfunction and the adjoint matrix, which is necessary to derive the analytical eigenfunctions. The eigenfunctions have three kinds of symmetry, which leads to three kinds of symmetry of the scattering matrix, and the discrete spectrum is also divided into three categories by us. The asymptoticity of the modified eigenfunction is derived. Based on the analysis, the RH problem with four jump matrices in a given area is established, and the relationship between the cmKdV equation and the solution of the RH problem is revealed. The residue condition of reflection coefficient with simple pole is established. According to the classification of discrete spectrum, we discuss the soliton solutions corresponding to three kinds of discrete spectrum classification and their propagation behaviors in detail.

nlin.SI↗