Ground states of the antiferromagnetic spin rings in strong magnetic fields

Antiferromagnetic (AFM) materials have distinct advances compared to ferromagnets, that allow to use them in variety of spintronic applications [1,2]. Antiferromagnetically coupled curvilinear spin chains are of fundamental interest as simplest systems possessing interplay between the geometry and magnetic subsystem [3].

In this work, we analyze the ground states of AFM ring-shaped spin chain with the nearest-neighbour Heisenberg exchange and single-ion anisotropy in presence of external magnetic field. The direction of magnetic field coincides with the symmetry axis of the ring. Collinear two-sublattice 1D curved AFM chain with even number of spins is considered, and the hard axis of anisotropy is oriented tangentially to the chain.

Within the classical continuum approach its magnetic state is described by two order parameters, the Néel and ferromagnetism vector fields. In the ground state, the Néel vector is oriented perpendicularly to the ring plane.

The magnetic field applied along the ring normal allows to observe spin-flop and spin-flip orientational phase transitions. We determine the dependency of spin-flop and spin-flip transition fields on the ring curvature and the critical curvature which separates two topologically different ground states above spin-flop transition. The first one with the Néel order parameter within the normal plane is mainly determined by the anisotropy at small curvatures. The second ground state at large curvatures is represented by onion ordering of the Néel vector. With the applied fields larger than critical spin-flip transition field Néel order parameter vanishes, which leads to ferromagnetic ground state. The phase diagram of AFM as a function of applied field intensity and the ring curvature is developed.