Effects of spin vacancies on magnetic properties of the Kitaev-Heisenberg model

TL;DR

This paper investigates how non-magnetic vacancies influence the magnetic phases and correlations in the Kitaev-Heisenberg model, revealing effects like symmetry breaking and potential spin-glass behavior through exact diagonalization studies.

Contribution

It provides a detailed analysis of vacancy effects on different magnetic phases, including the liquid and stripe phases, using exact diagonalization and perturbative methods.

Findings

Vacancies induce anisotropic magnetization patterns in the liquid phase.

Vacancies and small fields break symmetry and stabilize specific stripe patterns.

Vacancy-induced randomness may lead to spin-glass behavior.

Abstract

We study the ground state properties of the Kitaev-Heisenberg model in a magnetic field and explore the evolution of spin correlations in the presence of non-magnetic vacancies. By means of exact diagonalizations, the phase diagram without vacancies is determined as a function of the magnetic field and the ratio between Kitaev and Heisenberg interactions. We show that in the (antiferromagnetic) stripe ordered phase the static susceptibility and its anisotropy can be described by a spin canting mechanism. This accounts as well for the transition to the polarized phase when including quantum fluctuations perturbatively. Effects of spin vacancies depend sensitively on the type of the ground state. In the liquid phase, the magnetization pattern around a single vacancy in a small field is determined, and its spatial anisotropy is related to that of non-zero further neighbor correlations induced by the field and/or Heisenberg interactions. In the stripe phase, the joint effect of a vacancy and a small field breaks the six-fold symmetry of the model and stabilizes a particular stripe pattern. Similar symmetry-breaking effects occur even at zero field due to effective interactions between vacancies. This selection mechanism and intrinsic randomness of vacancy positions may lead to spin-glass behavior.