Exploring <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-wave magnetism in cuprates from oxygen moments

The antiferromagnetic parent phase of high-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>T</a:mi><a:mi>c</a:mi></a:msub></a:math> cuprates has been established as a Néel state of copper moments, but early work pointed out the important role of ligand oxygen orbitals. Using the three-orbital Emery model, we explore how, and under which conditions, doping-induced antiferromagnetic ordering of weak magnetic moments on the oxygen sites can lead to unconventional <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>d</b:mi></b:math>-wave magnetism with spin-split electronic bands. The mechanism for forming such altermagnetic (AM) states in cuprates does not rely on a lowering of the crystal symmetry but rather on interaction-induced formation of magnetic moments on directional oxygen orbitals within the crystallographic unit cell. Therefore, we obtain two different types of AM, namely, a (0, 0)-AM and a (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>π</c:mi><c:mo>,</c:mo><c:mi>π</c:mi></c:mrow></c:math>)-AM. We explore different regimes and challenges for realizing oxygen AM supported by Hartree-Fock calculations and complementary exact diagonalization of small clusters. While the region of interacting parameters needed to realize these states may be difficult to achieve in known high-<d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>T</d:mi><d:mi>c</d:mi></d:msub></d:math> cuprates, we propose a scenario to realize AM induced by oxygen magnetic moments in a cuprate-based candidate compound using density functional theory and discuss experimental implications.