  We propose experimental verification and theoretical explanation of magnetic
anomalies in the complex Fe-contained double perovskite multiferroics like
PbFe$_{1/2}$Nb$_{1/2}$O$_3$. The theoretical part is based on our model of
coexistence of long-range magnetic order and spin glass in the above
substances. In our model, the exchange interaction is anisotropic, coupling
antiferromagnetically $z$ spin components of Fe$^{3+}$ ions. At the same time,
the $xy$ components are coupled by much weaker exchange interaction of
ferromagnetic sign. In the system with spatial disorder (half of corresponding
lattice cites are occupied by spinless Nb$^{5+}$ ions) such frustrating
interaction results in the fact that antiferromagnetic order is formed by $z$
projection of the spins, while their $xy$ components contribute to spin glass
behaviour. Our theoretical findings are supported by the experimental evidence
of coexistence of antiferromagnetic and spin glass phases in chemically
disordered Fe-contained double perovskite multiferroics.
