Chiral Effects in Curvilinear 1D Antiferromagnets

Spin-orbit phenomena enable new ways to manipulate magnetic ordering in low dimensional magnetism. In this respect, materials with antiferromagnetic (AFM) coupling attract significant attention providing higher eigenfrequencies, a rich diversity of material properties and perspectives of spatial scaling due to the absence of significant stray fields. Tailoring the geometry of AFM thin films and nanowires in planar or 3D architectures provides a possibility for changing magnetic responses by means of shape of the magnet [1,2]. 

In this presentation, we will discuss the recently discovered chiral and anisotropic effects peculiar for curvilinear 1D antiferromagnetic spin chains. 

A spin chain arranged along a space curve is a prototypical example of a curvilinear AFM whose shape is characterized by the curvature and torsion. In the absence of intrinsic anisotropy, the dipolar interaction renders the tangential direction as the hard axis of the anisotropy [3]. The competition of this geometry-tracking interaction with the nearest-neighbor exchange leads to the emergence of additional anisotropic and chiral energy terms, whose coefficients are determined by the curvature and torsion. The geometry-induced anisotropy is of easy-axis type and determines the direction of the AFM order parameter within the easy-plane enabled by the dipolar interaction. The geometry-induced inhomogeneous Dzyaloshinskii-Moriya interaction (DMI) renders the curvilinear spin chain acting as a chiral helimagnet. The latter leads to the geometrically-driven helimagnetic phase transition in helix-shaped AFM spin chains [3].

A local variation of the anisotropy axis can result in the non-collinearity of the neighboring spins in curvilinear spin chains. 1D AFMs exhibit the parity-breaking effect, which forbids exchanging sublattices once they are selected. This leads to the emergent magnetization at non-collinear AFM textures Therefore, in any spin chain arranged along a space curve, there is a weak ferromagnetism proportional to the curvature and torsion of the curve [4].

Spin chains arranged on a planar surface have the only ground state along the binormal direction [3]. In presence of an external magnetic field, their spin-flop state is dependent on geometrical parameters. The spin-reorientation transition is followed by the canted state for small enough rings due to the exchange-driven DMI. Furthermore, we will show that the curvature-induced DMI results in the hybridization of spin wave modes and enables a geometrically-driven local minimum of the low frequency branch, which opens exciting perspectives to study long-lived collective magnon states in AFMs [3]. This positions curvilinear 1D antiferromagnets as a novel platform for the realization of geometrically tunable chiral antiferromagnets for antiferromagnetic spinorbitronics and fundamental discoveries in the formation of coherent magnon condensates in the momentum space.