Ordering of the Antiferromagnetic Heisenberg Model on a Pyrochlore Slab

Abstract

Ordering of the geometrically frustrated two-dimensional Heisenberg antiferromagnet on a pyrochlore slab is studied by Monte Carlo simulations. The model is expected to serve as a reference system of SrCrGaO compound studied extensively. In sharp contrast to the kagomé Heisenberg antiferromagnet, the model exhibits locally non-coplanar spin structures at low temperatures, bearing nontrivial chiral degrees of freedom. We find that under certain conditions the model exhibits a novel Kosterlitz-Thouless-type transition at a finite temperature associated with these chiral degrees of freedom. Implications to experiments are discussed. This makes the spin ordering on these lattices a highly nontrivial issue. Triangles-or tetrahedrabased lattices might be classified into two categories: One is the tightly coupled lattice consisting of edge-sharing triangles or tetrahedra, and the other is the loosely-coupled lattice consisting of corner -sharing triangles or tetrahedra. Examples of the former are the triangular lattice in two dimensions (2D) and the stacked-triangular lattice in three dimensions (3D), while those of the latter are the 2D kagomé lattice and the 3D pyrochlore lattice. In earlier studies, emphasis was put on the former category. 2, 3) These studies revealed a variety of interesting ordering phenomena not encountered in standard unfrustrated magnets, e.g., novel universality classes, exotic phase transition such as chiral transition and new type of topological phase transition etc.Recently, interest has been focused more on the latter category, i.e., the 2D kagomé and 3D pyrochlore AFs. [4][5][6] Due to the looser coupling among the frustrating units, these systems often remain paramagnetic down to very low temperatures without any magnetic ordering. Indeed, various theoretical studies on the 2D kagomé and 3D pyrochlore AFs have revealed that these systems 1

Glassiness and exotic entropy scaling induced by quantum fluctuations in a disorder-free frustrated magnet

“…This rotation can be carried through entirely within the manifold of classical minimum energy spin configurations. On the classical level, such collective motions do not cost any energy, leading to an energy landscape with infinitely large flat bottom formed by collinear and coplanar state and thus, to low-temperature spin liquid behaviours 28 29 .…”

Power-law spin correlations in pyrochlore antiferromagnets

“…The basic results derived in this paper are transferable to other lattices in which the spins sit on the bonds of a bipartite lattice, and with antiferromagnetic interactions among all spins on bonds sharing a common end point, such that their sum is constrained to a fixed value. Besides the pyrochlore lattice, this class includes the kagomé lattice, the twodimensional "checkerboard" lattice, 19,20 the "sandwich" lattice modeling SrCr 8−x Ga 4+x O 19 and consisting of two kagomé layers linked by an additional triangular layer of spins, [22][23][24] and the garnet lattice. 25 The spin Hamiltonian, having only nearest-neighbor antiferromagnetic exchange, can be cast as a sum of squares…”

High Field ESR of the Frustrated Antiferromagnet Ba2Sn2Ga3ZnCr7O22on a Pyrochlore Slab

“…Theoretical studies on the magnet with pyrochlore slab have been reported. 14,15) Another well studied frustrating system is an insulating spinel ZnCr 2 O 4 . [8][9][10] The magnetic ions on the octahedral B sites of the cubic spinel structure form the pyrochlore lattice so that the spin frustration is expected if the dominant nearest-neighbor interactions are antiferromagnetic.…”