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

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.