Theory of domain wall motion mediated magnetoelectric effects in a multiferroic composite

Abstract

A model is discussed for magnetoelectric (ME) interactions originating from the motion of magnetic domain walls (DWs) in a multiferroic composite of orthoferrites $R{\mathrm{FeO}}_{3}$ $(R\text{FO}$) with magnetic stripe domains and a piezoelectric such as lead magnesium niobate-lead titanate (PMN-PT). The DWs in $R\text{FO}$ can be set in motion with an ac magnetic field up to a critical speed of 20 km/s, the highest for any magnetic system, leading to the excitation of bulk and shear magnetoacoustic waves. Thus, the ME coupling will arise from flexural deformation associated with DW motion (rather than the Joule magnetostriction mediated coupling under a static or quasistatic condition). A $c$ plane orthoferrite with a single N\'eel-type DW in the $bc$ plane and an ac magnetic field $H$ along the $c$ axis is assumed. The deflection in the bilayer due to DW motion is obtained when the DW velocity is a linear function $H$ and the resulting induced voltage across PMN-PT is estimated. It is shown that a combination of spatial and time harmonics of the bending deformation leads to (i) a linear ME coefficient defined by ${\ensuremath{\alpha}}_{E}=E/H$ and (ii) a quadratic ME coefficient ${\ensuremath{\alpha}}_{\mathrm{EQ}}=E/{H}^{2}$. The model is applied to yttrium orthoferrites (YFO) and a PMN-PT bilayer since YFO has one of the highest DW mobility amongst the orthoferrites. The coefficient ${\ensuremath{\alpha}}_{E}$ is dependent on the DW position, and it is maximum when the DW equilibrium position is at the center of the sample. In YFO/PMN-PT the estimated low-frequency ${\ensuremath{\alpha}}_{E}$ \ensuremath{\sim} 30 mV/cm Oe and resonance value is 1.5 V/(cm Oe). Since orthoferrites (and PMN-PT) are transparent in the visible region and have a large Faraday rotation, the DW dynamics and the ME coupling could be studied simultaneously. The theory discussed here is of interest for studies on ME coupling and for applications such as magnetically controlled electro-optic devices.