Quantum spin supersolid as a precursory Dirac spin liquid in a triangular lattice antiferromagnet

Abstract

Based on the recent experiments on the triangular lattice antiferromagnet <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>Na</a:mi><a:mn>2</a:mn></a:msub><a:mi>BaCo</a:mi><a:msub><a:mrow><a:mo>(</a:mo><a:msub><a:mi>PO</a:mi><a:mn>4</a:mn></a:msub><a:mo>)</a:mo></a:mrow><a:mn>2</a:mn></a:msub></a:mrow></a:math>, we propose the easy-axis XXZ spin-1/2 model on the triangular lattice, that exhibits a quantum spin supersolid, to be a precursory Dirac spin liquid. Despite the presence of a three-sublattice magnetic order as a spin supersolid, we suggest that this system is close to a Dirac spin liquid by exploring its spectroscopic response. The physical consequence is examined from the spectroscopic response, and we establish the continuous spectra near the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>M</b:mi></b:math> point in addition to the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>K</c:mi></c:math> point excitation from the spinon continuum on top of the three-sublattice order. Moreover, the satellite peaks were predicted at the mid-points connecting the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi mathvariant="normal">Γ</d:mi></d:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>K</f:mi></f:math> points. This proposal offers a plausible understanding of the recent inelastic neutron scattering measurement in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:msub><g:mi>Na</g:mi><g:mn>2</g:mn></g:msub><g:mi>BaCo</g:mi><g:msub><g:mrow><g:mo>(</g:mo><g:msub><g:mi>PO</g:mi><g:mn>4</g:mn></g:msub><g:mo>)</g:mo></g:mrow><g:mn>2</g:mn></g:msub></g:mrow></g:math> and could inspire further research in relevant models and materials, such as <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:msub><h:mi mathvariant="normal">K</h:mi><h:mn>2</h:mn></h:msub><h:mi>Co</h:mi><h:msub><h:mrow><h:mo>(</h:mo><h:msub><h:mi>SeO</h:mi><h:mn>3</h:mn></h:msub><h:mo>)</h:mo></h:mrow><h:mn>2</h:mn></h:msub></h:mrow></h:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:msub><j:mi>Rb</j:mi><j:mn>2</j:mn></j:msub><j:mi>Co</j:mi><j:msub><j:mrow><j:mo>(</j:mo><j:msub><j:mi>SeO</j:mi><j:mn>3</j:mn></j:msub><j:mo>)</j:mo></j:mrow><j:mn>2</j:mn></j:msub></j:mrow></j:math>, and even more anisotropic magnets like <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:msub><k:mi>PrMgAl</k:mi><k:mn>11</k:mn></k:msub><k:msub><k:mi mathvariant="normal">O</k:mi><k:mn>19</k:mn></k:msub></k:mrow></k:math>. Published by the American Physical Society 2024