Fig. 2: Differences between a Haldane topological chain and an antiferromagnetic material.

a AKLT model representation of the Ni²⁺ spin-1 Haldane chain showing the antiferromagnetic coupling (gray oval) between two unpaired electrons (red and blue arrows) in the middle of the chain, leaving unpaired electrons (orange arrows) at ends of the chain. These two unpaired electrons may have antiparallel (shown) or parallel spins, giving singlet and triplet states, respectively, in Fig. 1. There is no magnetic unit cell in the Haldane system. b Schematic of the antiferromagnetic structure in NiO below its Néel temperature. The magnetic unit cell has twice the linear dimension of the crystal unit cell, as revealed by PND¹⁴. In the crystal unit cell, Ni²⁺ ions form a face-centered cubic cell with ferromagnetically coupled sheets that are anti-parallel with adjacent sheets. O²⁻ ions are shown as small gray cycles.