Magnetic Order-Disorder Transitions on a 1/3 - Depleted Square Lattice

TL;DR

This paper investigates magnetic phase transitions on a one-third depleted square lattice using quantum Monte Carlo simulations, revealing quantum critical points and magnetic order in both localized and itinerant electron regimes.

Contribution

It provides the first detailed analysis of magnetic order-disorder transitions on a one-third depleted square lattice, including the location of quantum critical points and comparison with spin wave theory.

Findings

Identified the quantum critical point for antiferromagnetic order in the Heisenberg limit.

Determined the magnitude of the magnetic order parameter near the QCP.

Linked magnetic transitions to metal-insulator transitions in the itinerant case.

Abstract

Quantum Monte Carlo simulations are used to study the magnetic and transport properties of the Hubbard Model, and its strong coupling Heisenberg limit, on a one-third depleted square lattice. This is the geometry occupied, after charge ordering, by the spin-$\frac{1}{2}$ Ni$^{1+}$ atoms in a single layer of the nickelate materials La$_4$Ni$_3$O$_8$ and (predicted) La$_3$Ni$_2$O$_6$. Our model is also a description of strained graphene, where a honeycomb lattice has bond strengths which are inequivalent. For the Heisenberg case, we determine the location of the quantum critical point (QCP) where there is an onset of long range antiferromagnetic order (LRAFO), and the magnitude of the order parameter, and then compare with results of spin wave theory. An ordered phase also exists when electrons are itinerant. In this case, the growth in the antiferromagnetic structure factor coincides with the transition from band insulator to metal in the absence of interactions.