Multiphase region of helimagnetic superlattices at low temperature in an extended six-state clock model

The variety of magnetic phases observed in rare-earth heterostructures at low temperatures (Jehan et al 1993 Phys. Rev. B 48 5594–606), such as Ho/Y, may be elucidated by an ANNNI-like model Hamiltonian. In previous work modelling bulk Ho (Seno, Rabson and Yeomans 1993 J. Phys. A: Math. Gen. 26 4887–905), such a Hamiltonian with a one-dimensional parameter space produced a single multiphase point. In contrast, the parameter space of the heterostructure model is three dimensional, and instead of an isolated multiphase point, we find two-dimensional multiphase regions. In an example of Villain’s ‘order from disorder’ (Villain, Bidaux, Carton and Conte 1980 J. Physique 41 1263–72; Pimpinelli, Uimin and Villain 1991 J. Phys.: Condens. Matter 3 4693–719), an infinitesimal temperature breaks the ground-state degeneracy. In first order of a low-temperature expansion, we find that the degeneracy is broken everywhere in a multiphase region except on a line. A segment of the line appears to remain multiphase to all orders in a lowtemperature expansion when the number L of magnetic layers between nonmagnetic spacers is 4 but not for other values of L. For L = 4, the hierarchy of phases more closely resembles that in the ANNNI model than in the bulk six-state clock model on which the present model is based. PACS numbers: 64.60.Cn, 05.50.+q, 75.70.Cn