Simultaneous Charge Ordering and Spin Dimerization in Quasi-Two-Dimensional Quarter-Filled Ladders

TL;DR

This paper investigates the interplay of charge ordering and spin dimerization in a quasi-two-dimensional ladder system, revealing a phase transition to a state with both charge order and a spin gap, influenced by inter-ladder coupling.

Contribution

It introduces a mean-field analysis of a coupled spin-pseudospin model for NaV2O5, showing how charge order and spin gaps coexist and how inter-ladder coupling affects quantum criticality.

Findings

Identification of two phases: charge-disordered and charge-ordered with spin gap.

The phase transition is second order, consistent with Landau theory.

Inter-ladder coupling destroys the quantum critical point, leading to exponential behavior of T_c.

Abstract

We study the spin-pseudospin Hamiltonian of the Ising Model in Transverse Field (IMTF) for pseudospins, coupled to the XY-spins on a triangular lattice. This model appears from analyses of the quarter-filled ladder compound $NaV_2O_5$, and pseudospins represent its charge degrees of freedom. In the molecular-field approximation we find that the model possesses two phases: charge-disordered without spin gap; and a low-temperature phase containing both the anti-ferroelectric (zigzag) charge order and spin dimerization (spin gap). The phase transition is of the second kind, and the calculated physical quantities are as those one expects from the Landau theory. One of particular features of the phase diagram is that the inter-ladder spin-pseudospin coupling, responsible for the spin gap generation, also destroys the IMTF quantum critical point, resulting in the exponential behavior of $T_c$ in the region of Ising's coupling where the IMTF is always disordered. We conclude that our mean-field results give a qualitatively correct description of the phase transition in $NaV_2O_5$, while a more sophisticated analysis is warranted in order to take into account the thermal fluctuations and, probably, the proximity of the IMTF quantum critical point.