Exchange and anisotropy-driven effects in antiferromagnetic spin chains

Antiferromagnets (AFMs) represent a class of materials with complex magnetic subsystem involving more than one ferromagnetically ordered sublattice. Such properties as high resonance frequencies in THz range, negligible net magnetic moment and respective weak stray fields, strong spin-orbit interaction make them promising for applications. The field of curvilinear magnetism offers additional degrees of freedom to tailor chiral and anisotropic responses of magnets and is well-established for ferromagnetic materials. Curvilinear AFMs possess additional features, important for for spintronic and spin-orbitronic applications [1].

The simplest curvilinear AFM is a spin chain arranged along flat or space curve. This geometry is characterized by the scalar functions of curvature K(s) and torsion T(s) with s being a coordinate along the curve. In the absence of intrinsic anisotropy, the dipolar interaction renders the tangential direction as the hard axis of the anisotropy [2]. 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 K and T only. The geometry-driven anisotropic term brings about the easy axis determining direction of the order parameter within the dipole-driven easy-plane. The geometry-driven inhomogeneous Dzyaloshinskii-Moriya interaction (DMI) renders the curvilinear spin chain as a chiral helimagnet. For example, the spin chain along the helix with the given radius and pitch possesses one of two magnetic states depending on the geometrical parameters. For a dominating curvature K, the ground state is the homogeneous in the local reference frame, while for the dominating torsion T, the ground state is helicoidal. In contrast to ferromagnetic nanowires [3], there is no critical curvature, separating the ground states in the limiting case of small torsion. This reflects the presence of the only one ground state along the binormal direction for the spin chains along the flat curves [2].

The local variation of the anisotropy axis can result in the non-collinearity of the neighboring spins in curvilinear chains. 1D AFMs exhibit the parity-breaking effect, which forbids to exchange sublattices once they are selected. This leads to the emergent magnetization at non-collinear AFM textures [4]. Therefore, in any spin chain arranged along the space curve, there is a weak ferromagnetism proportional to the curvature and torsion of the curve [5].

In the presence of strong intrinsic anisotropy in AFM spin chain with the anisotropy axis following the tangential direction, one can observe the effects of geometry proportional to the anisotropy constant and curvature K [5]. Both models of the single- and inter-ion anisotropies lead to the tilt of the anisotropy axes, which is pronounced in the spin-flop phase. In addition, the single-ion anisotropy leads to the emergence of the additional anisotropic term of the homogeneous DMI symmetry. The latter is described by the tensor product of the ferro- and antiferromagnetic order parameters, which scales with K.

References

[1] V. Baltz, A. Manchon, M. Tsoi et al, Rev. Mod. Phys. Vol. 90, P. 015005 (2018); H. Yan, Z. Feng, P. Qin et al, Avd. Mat. Vol. 32, P. 1905603 (2020); D. D. Sheka, Appl. Phys. Lett. Vol. 118, P. 230502 (2021).
[2] O. V. Pylypovskyi, D. Y. Kononenko, K. V. Yershov et al, Nano Lett. Vol. 20, P. 8157 (2020).
[3] D. D. Sheka, V. P. Kravchuk, K. V. Yershov, Y. Gaididei, Phys. Rev. B Vol. 92, P. 054417 (2015).
[4] N. Papanicolaou, Phys. Rev. B Vol. 51, P. 15062 (1995); E. G. Tveten, T. Mueller, J. Linder et al, Phys. Rev. B Vol. 93, P. 104408 (2016).
[5] O. V. Pylypovskyi, Y. A. Borysenko, J. Fassbender et al, Appl. Phys. Lett., Vol. 118, P. 182405 (2021)