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The ferroelectric phase of the multiferroic hexagonal manganites (h-ReMnO3)has been reported to undergo a series of magnetic transitions involvinglong-range ordering/reorientation of 4fRe3+ and/or 3dMn3+ spins below roomtemperature. These transitions have attracted a lot of attention in recentyears due to the geometrically frustrated nature of magnetic interactions. Wehave revisited these transitions in high quality single crystals of h-DyMnO3using dc and ac susceptibility measurements as a function of temperature (T),magnetic field (H) and frequency (w) supplemented by specific heatmeasurements. Taking h-DyMnO3 as an example, we show that the Dy3+ spins belowTN~68K are in a superferrimagnetic (SFIM) state whereas they undergo spin-glass(SG) transition below TDy3+~7K. Our observations demonstrate that neither theN\'eel transition at TN~68K nor the transition at TDy3+~7K is associated withlong-range ordered states of Dy3+ spins as believed so far in the literature.The SG state of h-DyMnO3 is quite exotic as it occurs in an ordered compoundpurely due to geometrical frustration without any random disorder. Further, itshows an interesting crossover from de Almeida-Thouless type exponent (m=2/3)to Gabay-Toulouse type (m=2) with increasing field which cannot be explained interms of the existing mean field theories of SG transition in Ising orHeisenberg systems but is expected for a vector X-Y SG system. Our observationscall for a systematic reinvestigation of the nature of magnetic transitionsinvolving Re3+ ions in other h-ReMnO3 also.

Evidence for superferrimagnetic clusters and spin-glass transition  involving 4f Dy3+ spins in h-DyMnO3: A new twist to 4f Re3+ spin ordering in  hexagonal manganites