Kagomé antiferromagnet with defects: Satisfaction, frustration, and spin folding in a random spin system

Abstract

It is shown that site disorder induces noncoplanar states, competing with the thermal selection of coplanar states, in the nearest neighbor, classical Kagome Heisenberg antiferromagnet. For weak disorder, it is found that the ground state energy is the sum of energies of separately satisfied triangles of spins. This implies that disorder does not induce conventional spin glass behavior. A transformation is presented, mapping ground state spin configurations onto a folded triangular sheet (a new kind of "spin origami") which has conformations similar to those of tethered membranes.PACS numbers: 75.10.Nr, 75.10.Hk, 75.50.Ee It is well known that geometrical frustration in some nonbipartite lattices prevents long range magnetic order from being established and allows novel kinds of low temperature magnetic states to develop [1-3]. The Heisenberg Kagome antiferromagnet with nearest neighbor couplings is one of the most interesting of such systems. The classical system exhibits a rich, nontrivial ground state degeneracy, with both coplanar and noncoplanar states in the degenerate manifold. For the coplanar states, linear spin-wave theory yields one zero-energy mode for every point in the Brillouin zone [4,5]. All noncoplanar states have fewer zero modes, and, as a result, thermal effects select a nematiclike coplanar ground state [5], an example of the "order by disorder" effect [6,7]. Numerical studies have confirmed the tendency for thermal selection of the nematiclike state [5,8], and there is also evidence [4, 5, 8-10] for a tendency toward \/3 x \/3 ordering in the plane.By far the best-studied experimental Kagome system is the magnetoplumbite, SrCr9jr,Gai2-9pOi9 [11]. For p = 1, this system contains dense Kagome layers, separated by dilute triangular layers, of Cr. Although its CurieWeiss temperature 0cw (foi* P = 1) is over 500 K, no sublattice ordering is found down to helium temperature, where a spin glass, rather than an ordering transition is observed at a temperature T/. The ratio Qcw/Tf is about 130, at least for p > 0.5 [11][12][13]. T/ itself varies rapidly with doping [12,13], having its maximum value of about 4 K near p = 1, where one might expect structural disorder to be least important, and falling monotonically as p is reduced. These observations raise two questions:(1) Why is spin glass behavior, with a temperature scale of order J, not generated by nonmagnetic impurities at the 10% to 20% level and (2) what is the origin of the spin-glass-like behavior which is observed even foip^ 1? It is the first question which is addressed in this Letter, while the second is discussed briefly in our conclusions. Our main results are as follows:(1) Quite generally we find that disorder induces noncoplanarity in the ground state. At low temperatures, the nematiclike state, which is selected by thermal fluctuations, is overwhelmed by this tendency of disorder to induce noncoplanarity [14].(2) For a large class of distributions of spins of random magnitude, including dilute distributions of vacancies, the gro...

Impurity effects in highly frustrated diamond-lattice antiferromagnets

“…An impurity can then fix the spin configuration in its neighborhood, while constraining the spins outside of its vicinity very little. 13 Since each random impurity fixes a spin configuration in its neighborhood, roughly independently of the others, one may expect as a result a globally random ground state, i.e., a spin glass. In fact, the T > 0 dynamics of such defective pyrochlore and kagome systems is rather subtle, and the actual spin glass freezing temperature can sometimes be highly suppressed as a result.…”

Planar pyrochlore: A valence-bond crystal

“…It is a straightforward exercise to show that such ground-states have a continuous local degeneracy. Thermal fluctuations select planar spin configurations on the kagomé lattice [8,9], but are unable to build order from disorder in the pyrochlore lattice [10]. A simple Maxwellian counting has been done by the last authors: the number of degrees of freedom of N Heisenberg spins with a given length is F = 2N .…”

Order induced by dipolar interactions in a geometrically frustrated antiferromagnet

“…In real materials, several other types of interactions are present. Further neighbor exchange may be relevant 4 as may crystal field effects 10 , magnetic dipole interactions 9 or the effect of quenched disorder 3,11 .…”