  We determine rigorously the effective permeability of magnetic metamaterials
composed of passive particles exhibiting magnetic resonances. The effective
permeability is expressed in terms of circuit parameters characteristic to
these particles (L, C, and R) and particle geometry. The derivation takes into
account the magnetic coupling between particles. We show that a bigger
concentration of particles leads to an improvement in the metamaterial
performances (such as bandwidth or loss tangent), but this effect saturates as
the particles are packed more tightly. The theory is validated through
numerical simulations of physically realizable metamaterials.
