Magnetization dynamics and frustration in the multiferroic double perovskiteLu2MnCoO6

We investigate the magnetic ordering and the magnetization dynamics (from kHz to THz time scales) of the double perovskite ${\mathrm{Lu}}₂{\mathrm{MnCoO}}₆$ using elastic neutron diffraction, muon spin relaxation, and micro-Hall magnetization measurements. This compound is known to be a type II multiferroic with the interesting feature that a ferromagneticlike magnetization hysteresis loop couples to an equally hysteretic electric polarization in the bulk of the material despite a zero-field magnetic ordering of the type $\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\downarrow}$ along Co-Mn spin chains. Here we explore the unusual dynamics of this compound and find extremely strong fluctuations, consistent with the axial next-nearest-neighbor Ising (ANNNI) model for frustrated spin chains. We identify three temperature scales in ${\mathrm{Lu}}₂{\mathrm{MnCoO}}₆$ corresponding to the onset of highly fluctuating long-range order below ${T}_N=50\ifmmode\pm\else\textpm\fi{}3$ K identified from neutron scattering, the onset of magnetic and electric hysteresis, with change in kHz magnetic and electric dynamics below a 30 K temperature scale, and partial freezing of $\ensuremath{\sim}\mathrm{MHz}$ spin fluctuations in the muon spin relaxation data below $12\ifmmode\pm\else\textpm\fi{}3$ K. Our results provide a framework for understanding the multiferroic behavior of this compound and its hysteresis and dynamics.