  Flexible ferromagnetic rings are spin-chain magnets, in which the magnetic
and mechanical subsystems are coupled. The coupling is achieved through the
tangentially oriented anisotropy axis. The possibility to operate the mechanics
of the nanomagnets by controlling their magnetization is an important issue for
the nanorobotics applications. A minimal model for the deformable curved
anisotropic Heisenberg ferromagnetic wire is proposed. An equilibrium phase
diagram is constructed for the closed loop geometry: (i) A vortex state with
vanishing total magnetic moment is typical for relatively large systems; in
this case the wire has the form of a regular circle. (ii) A topologically
trivial onion state with the planar magnetization distribution is realized in
small enough systems; magnetic loop is elliptically deformed. By varying
geometrical and elastic parameters a phase transition between the vortex and
onion states takes place. The detailed analytical description of the phase
diagram is well confirmed by numerical simulations.
