  Structural, magnetic and multiferroic properties of single crystals of
Dy$_{1-x}$Ho$_x$MnO$_3$ ($x = 0, 0.2$) were investigated by the different
methods of polarized and classical neutron diffraction and macroscopic methods
in order to determine the effect of Ho doping on the magneto-electric behavior
of the title compounds. It is shown that substitution by Ho of 20% on the
position of Dy do not change overall crystal symmetry of compound. It remains
of Pnma type for both compositions down to the very low temperatures. Magnetic
ordering do not change the crystal structure. Precise magnetic order and it
detailed temperature and field evolution both in the pristine and substituted
compounds we determined using single crystal neutron diffraction and
magnetization measurements. The results show a complex interplay between
transition metal and rear earth magnetic sub lattices leading to so-called
"Mn-controlled" and "Dy-controlled" magnetic states. Using polarized neutron
diffraction 3D character of rear earth magnetic order in
Dy$_{0.8}$Ho$_{0.2}$MnO$_3$ in contract to DyMnO$_3$ and occurrence of the
chiral type magnetic structure on Mn subsystem could be revealed. The influence
of the external electric field on the magnetic chirality could be directly
evidenced, proving strong magneto-electric coupling in multiferroic phase. The
study of the electric polarization under similar temperatures and fields on the
same samples provides the direct correlation between the results of the
microscopic and macroscopic investigations.
