(color online) The results of 〈 m d 2 〉 versus μ for various values of t₁ and t₃. The parameters are chosen as U = 1.6t, β = 40t⁻¹, V = 1.0t, and ε_d = −U/2. (a) For the “case A”, 〈 m d 2 〉 grows monotonically as t₁ increases, but decreases as t₃ increases in a wide range of μ. Inset shows the values of 〈 m d 2 〉 with respect to t₁ or t₃ for μ = 0. (b) For the “case B”, 〈 m d 2 〉 decreases as t₁ increases, and grows monotonically as t₃ increases. Inset shows the values of 〈 m d 2 〉 with respect to t₁ or t₃ for μ = 0. The inter-layer hoppings have the opposite effect on the local moment in comparison with “case A”. For all the cases, 〈 m d 2 〉 decreases as μ is lowered.