Macroscopic quantum dynamics of toroidal moment in Ising-type rare-earth clusters

Abstract

We study the quantum dynamics of polygonal rare-earth molecular clusters with Ising-type ion magnetization. It is shown that the ground state of such systems is a non-magnetic quasi-doublet of states with oppositely twisted ion spins. The states differ in sign of toroidal moment, which is a natural physical quantity to characterize the spin chirality of the clusters. The possibility of macroscopic quantum tunneling of toroidal moment between the states is predicted. The effects of an external current is considered, both in equilibrium and in the frames of the Landau-Zener-Stückelberg tunneling model. The special treatment is given for the most important case of triangular rare-earth clusters.The model. -We consider a spin ring, a system of N non-Kramers rare-earth ions located in the apices of a regp-1 arXiv:1009.0371v2 [cond-mat.mes-hall]

Single-Molecule Toroic Design through Magnetic Exchange Coupling

“…[16][17][18] However, the molecular design for SMTs is very challenging, requiring the Ising-type on-site magnetic moments to be arranged in a vortex-like fashion from the proper molecular geometry and magnetic interactions. 11,13,19,20 Thus, the magnetic behavior of the first SMT, the {Dy 3 } triangle, 21 was initially defined as "unusual" until 2 years later, this "unusual" magnetic behavior was rationalized by theoretical calculations 22 and single-crystal experiments. 23 Both theory and experiments indicate that the {Dy 3 } triangle is interpreted within a non-collinear Ising model, together with a non-magnetic ground state and magnetic moments on the Dy III sites that are in almost perfect toroidal distribution, and coupled by Ising exchange interaction, confirming the observation of SMT behavior.…”

First Demonstration of Magnetoelectric Coupling in a Polynuclear Molecular Nanomagnet: Single‐Crystal EPR Studies of [Fe3O(O2CPh)6(py)3]ClO4⋅py under Static Electric Fields

“…In addition, those objects possess a rare quantum property, spin chirality, which derives from the simultaneous interplay of competing antiferromagnetic interactions and Dzyaloshinskii–Moriya interactions (DMI). Spin chirality has generated interest as it relates to diverse phenomena, such as orbital currents in Mott insulators, toroidal magnetic moments in Dy III 3 triangles, Berry phase in spin triangles, magnetic skyrmions and anomalous Hall effect in chiral magnets …”

Quantum magnetoelectric effect in the molecular crystal Dy3

“…Not only the mentioned current effect but also quantum dynamical effects are interesting in the context of magnetoelectricity. The slow quantum dynamics of the toroidal moment in SMTs [27] gives an intriguing possibility to observe non-equilibrium quantum MEE in a crystal of Ising-type rare-earth clusters, when the ground state is the doublet of states with energies (we imply ϕ = π 2 ) E = ±(3/4)j zz (∆/j zz ) 3 [27], where ∆ is the gap between the energy levels. The wave functions of the states in the doublet are very close to |ψ ± = (|τ z = +3 ±|τ z = −3 )/ √ 2.…”