Magnetic Möbius stripe without frustration: Noncollinear metastable states

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

“…There are first steps in the understanding of curvilinear antiferromagnets, especially for spin chains. [444,446] It can be rigorously shown that in the absence of intrinsic anisotropy, K i = 0, the dipolar coupling between spins in Equation ( 32) leads to the effective hard axis anisotropy with the axis along the tangential direction. [444] This allows to present the linear density of Larganian Equation (33) for the intrinsically achiral and isotropic 1D spin chain in the long-wave approximation as [444]…”

“…[444] In the case of spin chains arranged along flat curves, this gives the antiferromagnetic ground state in the direction perpendicular to the chain plane determined by the geometrydriven easy axis anisotropy. [444] The latter can also contribute to the intrinsic anisotropy of spin-orbit origin, [446] observed, for example, in Cr wheels. [447,448] The interplay between the hard axis of dipolar-induced anisotropy with the extrinsic easy axis and chiral interaction stemming from the exchange interaction due to curvature renders intrinsically isotropic achiral spin chains as biaxial chiral helimagnets, see Figure 9b.…”

“…[445] Closed spin chains described by the Hamiltonian (Equation (32)) with A B = e e along the binormal direction exhibit a variety of long-living metastable states stabilized by the boundary conditions as well as interplay between the exchange, anisotropy, and dipolar interaction. [446] The number of spins in the ring brings about an additional degree of freedom for the magnetic sublattice. While even number of spins support the pure antiferromagnetic ordering, [444,446] the additional, odd magnetic moment breaks the antiferromagnetic state and leads to an appearance of the spiral ordering.…”

“…[446] The number of spins in the ring brings about an additional degree of freedom for the magnetic sublattice. While even number of spins support the pure antiferromagnetic ordering, [444,446] the additional, odd magnetic moment breaks the antiferromagnetic state and leads to an appearance of the spiral ordering. Figure 10a represents an example of the energy landscape for a chain consisting of four spins with a strong single-ion anisotropy and antiferromagnetic exchange.…”

“…Figure 10a represents an example of the energy landscape for a chain consisting of four spins with a strong single-ion anisotropy and antiferromagnetic exchange. The internal energy E in Equation ( 33) and the free energy G reads [446] The solid red (dashed green) line shows the helimagnetic phase transition between homogeneous and periodic ground states obtained by spin-lattice simulations (analytically). c) Example of spin wave dispersion in reduced units (left) for two antiferromagnetic helical chains (right).…”