Low-temperature properties of classical geometrically frustrated antiferromagnets

Abstract

We study the ground-state and low-energy properties of classical vector spin models with nearestneighbour antiferromagnetic interactions on a class of geometrically frustrated lattices which includes the kagome and pyrochlore lattices. We explore the behaviour of these magnets that results from their large ground-state degeneracies, emphasising universal features and systematic differences between individual models. We investigate the circumstances under which thermal fluctuations select a particular subset of the ground states, and find that this happens only for the models with the smallest ground-state degeneracies. For the pyrochlore magnets, we give an explicit construction of all ground states, and show that they are not separated by internal energy barriers. We study the precessional spin dynamics of the Heisenberg pyrochlore antiferromagnet. There is no freezing transition or selection of preferred states. Instead, the relaxation time at low temperature, T , is of orderh/kBT . We argue that this behaviour can also be expected in some other systems, including the Heisenberg model for the compound SrCr8Ga4O19.

Exotic topological order in fractal spin liquids

“…The following is a ground state: The Sierpinski triangle model has liquidlike order, but is different from conventional classical spin liquids such as antiferromagnetic Ising models on geometrically frustrated lattices. [28][29][30][31][32] Due to unconventional three-body interactions, the model does not have magnetic order at any temperature including T = 0. A zero-temperature thermodynamic entropy is large, but not extensive: S = √ N .…”

Spin correlations in the dipolar pyrochlore antiferromagnet Gd2Sn2O7

“…In most real materials, however, long-range magnetic order occurs at a measurable temperature T N , partially relieving this frustration. Even in these cases, however, materials often show a "cooperative paramagnet" regime over a wide temperature range T N < T θ CW , where frustration has the dominant effect on the magnetic properties [8]. Figure 1.…”

Spin-liquid phase and order by disorder of classical Heisenberg spins on the swedenborgite lattice

“…A famous example of this mechanism is provided by the classical kagome antiferromagnet where coplanar ground-state configurations are favored at low T [1], but other examples, also in higher dimensions, have been reported in the literature [9,12,13]. For other 3d systems, e.g., Heisenberg spins on the pyrochlore lattice, it was shown to be completely * Author to whom correspondence should be addressed: buhrandt@thp.uni-koeln.de absent, resulting in true classical spin liquids at T = 0 [3,14]. The factor responsible for presence or absence of order-bydisorder was identified to be the degree of degeneracy [3].…”

“…For other 3d systems, e.g., Heisenberg spins on the pyrochlore lattice, it was shown to be completely * Author to whom correspondence should be addressed: buhrandt@thp.uni-koeln.de absent, resulting in true classical spin liquids at T = 0 [3,14]. The factor responsible for presence or absence of order-bydisorder was identified to be the degree of degeneracy [3].…”

“…If the system does not have more degrees of freedom than constraints on the ground-state manifold (i.e., if the groundstate degeneracy is sufficiently small), it might show order-bydisorder. Otherwise, it remains disordered at all temperatures [3]. We have eight spins per unit cell with two angle degrees of freedom each and, consequently, 16 degrees of freedom, whereas Eq.…”