Reentrant spin-flop transition in nanomagnets

An antiferromagnetic spin chain is known to undergo a transition from an anti-parallel to a spin-flop configuration when subjected to an increasing magnetic field. The transition arises from the competition between antiferromagnetic coupling and magnetic field, and connects an antiferromagnetic configuration with spins aligned along the field to a configuration where they are almost perpendicular to the field, with a small tilting angle producing a nonvanishing magnetization. In the thermodynamic limit, the spin-flop phase already occurs at infinitesimal field in the isotropic case, while a finite field is required in the presence of an easy-axis anisotropy favoring the field direction. If the spin chain is finite, a parity effect comes into play: if the number of spins is odd the antiferromagnetic configuration is favored because of the Zeeman energy gain from one unbalanced spin, and only beyond a finite field the spin-flop state appears, still in the isotropic case [1]. Moreover, in the presence of an anisotropy perpendicular to the field, the spin-flop state appears for both weak and strong field, the anti-parallel state appearing for intermediate fields [2]. In both transitions the configuration varies continuously with the field intensity. Such re-entrant transition is robust with respect to quantum fluctuations and it might be observed in atomic chains deposited on suitable substrates or in layered systems.[1] P. Politi and M. G. Pini, Phys. Rev. B 79 (2009) 012405[2] M. Crescioli, P. Politi, and R.Vaia. Phys. Rev. B 90 (2014) 100401 (R)