Coulomb meets Néel

Monday, November 12, 2012

 Most physical systems tend to order at a low enough temperature, and there are very few exceptions to this rule. For magnetic compounds, such exceptions are called "spin liquids" and over the last two decades, much effort has been made to characterize such states, which would not break any symmetry.

It is widely believed that a good caricature of a spin liquid is given by a short-range Valence Bond wave function, a linear superposition of all coverings of a given lattice by two-site singlets (valence bonds) :

|\Psi_{\rm RVB}\rangle = \sum_c | c \rangle.

One particular covering of the square lattice is shown in the figure, where arrows represent two-spin singlets (|\!\!\uparrow \downarrow \rangle - | \!\!\downarrow \uparrow \rangle)/\sqrt{2}. The intuition behind this wave-function is two-fold :

  • short-range singlet pairing should inhibit formation of (Néel) long-range antiferromagnetic order,
  • the superposition over all coverings should forbid the crystallization of singlets into an ordered state.

Researchers at LPT had already shown (Phys. Rev. B 82, 180408(R) (2010)) that this intuition fails on the square lattice, as the four-point (Valence-Bond Valence-Bond) correlations turn out to be quasi-long range ordered and, therefore, very close to cristallisation. But still no long-range order is present.

A recent Physical Review Letters studied this RVB wave function on the cubic lattice and showed the situation to be even more surprising. Large-scale Monte Carlo simulations revealed two unintuitive behaviors :

  • Firstly and contrary to the naive expectation, this wave-function displays long-range antiferromagnetic order !
  • Secondly, the Valence-Bond correlations turn out to be dipolar (with an overall 1/r^3 decay, see figure above), in a surprising analogy with the Coulomb phase physics present e.g. in spin ice.

Further investigation is required to understand the generality of this new hybrid state of matter, which displays at once aspects of antiferromagnetism and of Coulomb physics.

To summarize, short-range Valence Bond wave functions (on bipartite lattices) are far from being featureless spin liquids !

Reference : Phys. Rev. Lett. 109, 147204 (2012), arXiv:1204.3195

Contact : Fabien Alet