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We investigate, using the density matrix renormalization group, the evolutionof the Nagaoka state with $t'$ hoppings that frustrate the hole kinetic energyin the $U=\infty$ Hubbard model on the anisotropic triangular lattice and thesquare lattice with second-nearest neighbor hoppings. We find that the Nagaokaferromagnet survives up to a rather small $t'_c/t \sim 0.2.$ At this criticalvalue, there is a transition to an antiferromagnetic phase, that depends on thelattice: a ${\bf Q}=(Q,0)$ spiral order, that continuously evolves with $t'$,for the triangular lattice, and the usual ${\bf Q}=(\pi,\pi)$ N\'eel order forthe square lattice. Remarkably, the local magnetization takes its classicalvalue for all considered $t'$ ($t'/t \le 1$). Our results show that therecently found classical kinetic antiferromagnetism, a perfect counterpart ofNagaoka ferromagnetism, is a generic phenomenon in these kinetically frustratedelectronic systems.

Evolution of Nagaoka phase with kinetic energy frustrating hoppings