Emergent Potts order in the kagome <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> Heisenberg model
Vincent Grison, Pascal Viot, B. Bernu, Laura Messio
Abstract
Motivated by the physical properties of vesignieite ${\mathrm{BaCu}}_{3}{\mathrm{V}}_{2}{\mathrm{O}}_{8}{(\mathrm{OH})}_{2}$, we study the ${J}_{1}\ensuremath{-}{J}_{3}$ Heisenberg model on the kagome lattice, which is proposed to describe this compound for ${J}_{1}<0$ and ${J}_{3}\ensuremath{\gg}|{J}_{1}|$. The nature of the classical ground state and the possible phase transitions are investigated through analytical calculations and parallel tempering Monte Carlo simulations. For ${J}_{1}<0$ and ${J}_{3}>\frac{1+\sqrt{5}}{4}|{J}_{1}|$, the ground states are not all related by Hamiltonian symmetry. Order appears at low temperature via the order by disorder mechanism, favoring collinear configurations and leading to an emergent $q=4$ Potts parameter, that induces a finite temperature phase transition. For ${J}_{3}$ between $\frac{1}{4}|{J}_{1}|$ and $\frac{1+\sqrt{5}}{4}|{J}_{1}|$, the ground state goes through a succession of semispiral states, possibly giving rise to multiple phase transitions at low temperatures. The effects of quantum fluctuations are studied through linear spin-wave approximation and high-temperature expansions of the $S=1/2$ model.