Infinitesimal disorder in the Kagome lattice: Cluster spin glass

By Tom Sharp on April 18, 2017

How does weak bond disorder affect the classical spin liquid state in a geometrically frustrated Ising Kagome system? We find out from Mateus Schmidt, whose recent paper is available in Journal of Physics: Condensed Matter.

Geometrically frustrated magnets have been a central topic in condensed matter physics due to the possible realization of exotic states of matter, such as spin liquids (SL), a correlated paramagnetic state. In the quest for the experimental realization of these states, several geometrically frustrated magnets have been identified that exhibit a spin-glass behaviour in which the magnetic moments are frozen in random directions. Surprisingly, this spin-glass phase appears at very low levels of disorder or even, apparently, when disorder-free. The Kagome system Co₃Mg(OH)₆Cl₂ is particularly interesting, in which signatures of SL behaviour and spin freezing have been observed. However, the source of glassiness remains unclear and the freezing behaviour cannot be well described as a conventional spin glass. Moreover, experimental findings support the presence of small spin clusters. Therefore, the physical picture of this Kagome compound still lacks a proper explanation.

In our recent paper, we investigate the interplay of bond disorder and geometrical frustration in an Ising Kagome system. Since this problem requires a new mathematical and conceptual framework, we consider a new cluster method within the replica formalism. We apply this approach to a model with intercluster disorder (J) and short-range antiferromagnetic interactions (J₀) between Ising spins. For comparison, we also investigate the square lattice, in which geometrical frustration is absent.

Phase diagrams of T/J versus J0/J for the (a) square and (b) kagome lattices. taken from J.Phys. Cond. Mat. 165801 © IOP Publishing 2017.

We show that an infinitesimal disorder can drive a cluster spin-glass (CSG) ground-state below a SL regime in the geometrically frustrated Ising Kagome lattice. In the square lattice, a sufficiently strong antiferromagnetic coupling prevents the glassy state, introducing an antiferromagnetic long-range order. In our approach, a new degree of freedom – the cluster magnetic moment – is introduced by weak disorder. We find that geometrical frustration leads to uncompensated clusters potentiating the disorder effects. Therefore, we conclude that both clusters and geometrical frustration are the driving forces of glassy behaviour. As a consequence, in materials such as Co₃Mg(OH)₆Cl₂, glassiness is expected even at extremely low levels of disorder. However, further experimental and theoretical investigations are still needed to account for the nature of the glassy state in geometrically frustrated materials.

Our group is now exploring quantum fluctuation effects in the disordered Kagome system. These effects could be taken into account by considering transverse field and/or Heisenberg spins in the model under study, which may allow a more broadening picture of the interplay of disorder and geometrical frustration in Kagome lattices.

About the authors

Mateus Schmidt is a PhD student in the Condensed Matter Theory Laboratory at Universidade Federal de Santa Maria, studying the interplay of disorder and geometrical frustration in magnetic systems with focus on the onset of spin-glassbehaviour.

Fabio M Zimmer is an Associate Professor in Departamento de Física at Universidade Federal de Santa Maria. His team is currently interested in disordered quantum magnetism, focusing in spin-glass and geometrically frustrated systems

Sergio G Magalhaes is an Associate Professor in Instituto de Física at Universidade Federal do Rio Grande do Sul. His research interests are strongly correlated electron systems and disordered spin systems.

This work is licensed under a Creative Commons Attribution 3.0 Unported License