Effects of Geometry on Curvilinear Spin Chains

Curvilinear magnetism is of great fundamental and practical interest whose rapid development is inspired by novel experimental technologies and wide potential applications [1]. A general approach for description of curvilinear ferromagnets [2] has been recently developed and used for thin wires and shells uncovering magnetochiral effects in statics and dynamics [1,3]. Besides intensive research of ferromagnetic materials, their antiferromagnetically ordered (AFM) counterparts are promising candidates for spintronics applications by their low sensitivity to external fields and ultra high eigenfrequencies [4]. Here, we present a general approach for description of AFM textures in curvilinear spin chains [5]. We show that the magnetic dipole-dipole interaction in these systems can be reduced to a hard-axis anisotropy along the chain. Lagrangian of the curvilinear AFM spin chain in continuum limit corresponds to the biaxial chiral helimagnet. Helix geometry shows existence of two equilibrium magnetic states depending on values of curvature and torsion: (i) homogeneous state in the local reference frame, it is typical for helices with the curvature larger than torsion; and (ii) periodic state is quasi-homogeneous in the laboratory reference frame. For specific case of the AFM flat chain there is the only ground state, with the order parameter being oriented perpendicular to the chain plane. We show that in curvilinear system transverse and longitudinal magnon modes in the AFM helix and ring are coupled due to geometry-induced Dzyaloshinskii–Moriya interaction.

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