Sequences of ground states and classification of frustration in odd-numbered antiferromagnetic rings

Abstract

The sequences of ground states in frustrated antiferromagnetic rings with odd number of local spins characterized by a single bond defect or by arbitrary uniform couplings to an additional spin located at the center are determined. The sequences provide firm constraints on the total ground-state quantum numbers, which are more stringent than those arising from the Lieb-Mattis theorem for bipartite quantum spin systems. Apart from their theoretical importance, they suggest the possibility of tailoring a given class of the molecular nanomagnets with desired ground-state properties by tuning the relevant couplings. In particular, they predict the spin S = 1/2 ground state for the centered rings composed of the half-integer spins with approximately uniform interactions. They confirm the applicability of the recent classification of spin frustration in both types of molecular nanomagnets. The classification is also discussed in the classical limit for the first class of the rings, providing a direct picture of frustration types. The Lieb-Mattis energy-level ordering and an analog of the Lande band, i.e., the energy spectra properties simplifying the characterization of the rings using the bulk magnetic or NMR measurements, are briefly discussed

Collinear and Non-Collinear Configurations in Classical Geometrically Frustrated Ring-Shaped Systems

“…Continuous changes of configurations start (and end, in the case of centered rings) at the well-determined critical value of α, independent on system size for centered rings. It should to be stressed that these obtained for the second of models, |α c | 4, are identical as those found in their quantum counterparts [16,19,20]. Basing on numerical results, it can be said that the first critical value for quantum rings with a defect bond tends to calculated here α c 1{pn¡1q (see Fig.…”

“…Moreover, these configurations are the same as these observed in the corresponding systems without frustration. Therefore, they can be considered as realizations of the third type frustration in classical systems [10,14,16]. Continuous changes of configurations start (and end, in the case of centered rings) at the well-determined critical value of α, independent on system size for centered rings.…”

“…The corresponding energies are ¡npα 2 {8 1q and ¡np|α|¡1q|, for |α| ¤ 4 and |α| ¥ 4, respectively. [16,19,20].…”

“…Hence, the energy function is written as number S{s in its quantum counterpart for s 10 and s 5{2; see also [14,16].…”

“…This problem has been studied recently in the context of magnetic molecules [9][10][11][12][13][14][15][16] and it has been shown that in a certain domain of the Hamiltonian parameters, a geometrically frustrated spin system with competing interactions has the unique ground state S-multiplet, with the same total spin number S as in the domain without frustration. This region was assigned to the third type of frustration, whereas the ground state multiplets with other values of S represent the second type of frustration.…”