  We experimentally demonstrate the strictly nonclassical behavior in a
many-atom system using a recently derived criterion [E. Kot et al., Phys. Rev.
Lett. 108, 233601 (2012)] that explicitly does not make use of quantum
mechanics. We thereby show that the magnetic moment distribution measured by
McConnell et al. [R. McConnell et al., Nature 519, 439 (2015)] in a system with
a total mass of $2.6\times 10^5$ atomic mass units is inconsistent with
classical physics. Notably, the strictly nonclassical behavior affects an area
in phase space $10^3$ times larger than the Planck quantum $\hbar$.
