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Structural, magnetic and multiferroic properties of single crystals ofDy$_{1-x}$Ho$_x$MnO$_3$ ($x = 0, 0.2$) were investigated by the differentmethods of polarized and classical neutron diffraction and macroscopic methodsin order to determine the effect of Ho doping on the magneto-electric behaviorof the title compounds. It is shown that substitution by Ho of 20% on theposition of Dy do not change overall crystal symmetry of compound. It remainsof Pnma type for both compositions down to the very low temperatures. Magneticordering do not change the crystal structure. Precise magnetic order and itdetailed temperature and field evolution both in the pristine and substitutedcompounds we determined using single crystal neutron diffraction andmagnetization measurements. The results show a complex interplay betweentransition metal and rear earth magnetic sub lattices leading to so-called"Mn-controlled" and "Dy-controlled" magnetic states. Using polarized neutrondiffraction 3D character of rear earth magnetic order inDy$_{0.8}$Ho$_{0.2}$MnO$_3$ in contract to DyMnO$_3$ and occurrence of thechiral type magnetic structure on Mn subsystem could be revealed. The influenceof the external electric field on the magnetic chirality could be directlyevidenced, proving strong magneto-electric coupling in multiferroic phase. Thestudy of the electric polarization under similar temperatures and fields on thesame samples provides the direct correlation between the results of themicroscopic and macroscopic investigations.

Complex interplay between 3d and 4f magnetic systems and magnetic chirality in multiferroic Dy$_{1-x}$Ho$_x$MnO$_3$ ($x = 0, 0.2$)