A quantum hydrodynamical model of skyrmions with electrical dipole moments and novel magneto-electric skyrmion Hall effect

To introduce novel ways of manipulating the skyrmion dynamics we need to develop new fundamental models. Many-particle quantum hydrodynamics allows us to study inter-skyrmion interactions in the approximation of point-particle skyrmions, which were discovered in multiferroic insulators, where the spiral magnetic structure is accompanied by a finite electric dipole moment. We propose a new model of many-particle quantum hydrodynamics for dipolar skyrmions with dipole–dipole interaction, in the presence of electric and magnetic field gradients. Based on the developed model we find a new way to control the positions of skyrmions, using the crossed gradients of magnetic and electric fields or a novel magneto-electric Hall effect. We have shown that the influence of non-uniform magnetic field provides circular motion of the dipolar skyrmion in the plane with the frequency determined by the derivative of the external magnetic field and the amplitude of the dipole moment. We study the wave processes in the system of skyrmions. We investigate hydrodynamic waves in a skyrmion gas in crossed non-uniform electric and magnetic fields, and predict the generation of a new type of hydrodynamic waves and instabilities. Also, we predict a new type of polarization waves in a rigid skyrmion gas with the dipole–dipole interaction.