  The theoretical description of the nanostructured
Pb(Fe1/2Ta1/2)x(Zr1/2Ti1/2)1-xO3 (PFTx-PZT(1-x)) and
Pb(Fe1/2Nb1/2)x(Zr1/2Ti1/2)1-xO3 (PFNx-PZT(1-x)) intriguing ferromagnetic,
ferroelectric and magnetoelectric properties at temperatures higher than 100 K
are absent to date. The goal of this work is to propose the theoretical
description of the physical nature and the mechanisms of the aforementioned
properties, including room temperature ferromagnetism, phase diagram dependence
on the composition x with a special attention to the multiferroic properties at
room temperature, including anomalous large value of magnetoelectric
coefficient. The comparison of the developed theory with experiments
establishing the boundaries between paraelectric, ferroelectric, paramagnetic,
antiferromagnetic, ferromagnetic and magnetoelectric phases, as well as the
characteristic features of ferroelectric domain switching by magnetic field are
performed and discussed. The experimentally established absence of
ferromagnetic phase in PFN, PFT and in the solid solution of PFN with PbTiO3
(PFNx-PT(1-x)) was explained in the framework of the proposed theory.
