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We show that the thermal entanglement in a spin system using only magneticsusceptibility measurements is restricted to the insulator materials. Wedevelop a generalization of the thermal entanglement witness that allows us toget information about the system entanglement with variable local spin lengthsthat can be used experimentally in conductor or insulator materials. As anapplication, we study thermal entanglement for the half-filled Hubbard modelfor linear, square and cubic clusters. We note that it is the itinerancy ofelectrons that favors the entanglement. Our results suggest a weak dependencebetween entanglement and external spin freedom degrees.

Thermal entanglement witness for materials with variable local spin lengths