Linear magnetoelectric coupling and ferroelectricity induced by the flexomagnetic effect in ferroics

Анотація

We show that the flexomagnetic effect leads to new linear flexomagnetoelectric (FME) coupling in bulk and nanosized materials, where the polarization and (anti)magnetization vectors are spatially inhomogeneous due to external or internal forces. The linear FME coupling is proportional to the product of the gradients of (anti)magnetization, polarization, flexomagnetic, and flexoelectric tensors. Due to the gradient nature, the physical sources of the FME coupling are quite different from the well-known linear and quadratic magnetoelectric (ME) couplings. In nanosized systems with intrinsic spontaneous gradients of the (anti)magnetization and polarization the linear FME coupling induces the size-dependent linear ME coupling between the average polarization and magnetization. The linear ME coupling coefficient is inversely proportional to the characteristic size of the system (film thickness, particle radius, etc.), magnetization, and polarization extrapolation lengths. The flexomagnetic effect may lead to improper ferroelectricity in bulk and nanosized (anti)ferromagnetics via the new linear and nonlinear FME coupling. Thus we propose a new mechanism based of the flexomagnetic effect for creation of linear MEs, multiferroics, namely improper ferroelectrics-(anti)ferromagnetics. The FME coupling between the polarization and magnetization strongly influences the dielectric susceptibility and ME tunability of multiferroics. Using the symmetry theory we calculate the evident form of the flexomagnetic effect tensor for all 90 bulk magnetic classes and showed that 69 of them are flexomagnetic. Due to the symmetry lowering all 90 bulk magnetic classes become flexomagnetic in the vicinity of surfaces/interfaces. Consequently the flexomagnetic effect strongly increases the number of the ME multiferroic materials.