Weak Ferromagnetism in NiS${}_2$ under Nanocrystallization

Structurally well-ordered NiS${}_2$ nanocrystals with an average diameter of $27.0\pm 6.5$ nm retain the bulk-like two-step antiferromagnetic transitions, as shown by magnetization and heat-capacity measurements. Below the lower transition, the nanocrystals exhibit a hysteretic ferromagnetic response with large coercivity, exchange bias, and a vertical loop shift after field cooling, whereas the $M$-$H$ response just above the transition is nearly linear. These features are best explained by uncompensated surface moments generated where the low-temperature antiferromagnetic order terminates at the nanocrystal surface. The absence of a clear additional bulk-like weak-ferromagnetic component constrains homogeneous-canting models and indirectly favors a domain-wall scenario for the weak ferromagnetism of bulk NiS${}_2$.