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In a mean-field approximation, the susceptibility of a powdered sample is given approximately by Eq., with θ = (λ + 4 π / 3 - N) M s g μ B S / k B. Here, M s is the saturation magnetization per unit of volume and N is the demagnetizing factor of each grain of powder (Ref.). The effective mean-field parameter λ arises from a discrete sum over dipolar couplings with spins located inside the local sphere of a Lorentz construction while 4 π / 3 gives the contribution of the interaction with the rest, taken as a continuum. Considering nearly spherical grains is a reasonably good approximation in the case of very fine powdered samples. Then θ,λ M s g μ B S / k B. Dipolar couplings between pairs of molecular spins can favor either ferromagnetic or antiferromagnetic alignments of the spins, depending on the relative angle between the anisotropy axes and the relative position vector. For this reason, the sign of θ depends on the crystal's symmetry. It might be negative, as in the Mn 12 bz compound studied here, or positive, as in Mn 12 acetate (Refs.). The approximation employed in the calculations reported here amounts to setting the typical dipolar bias seen by a spin in a macroscopically demagnetized sample as equal to one half of the effective mean field λ M s in a magnetically saturated sample.
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As shown recently by Henderson (Ref.), the influence of transverse dipolar magnetic fields on the tunneling rates can be enhanced when excited states, associated to total S values different than 10, are coupled with the states of the ground multiplet. This effect cannot be treated within the "giant spin" model employed here. It might contribute to enhance further the magnetic relaxation of the amorphous material, which has a nearly isotropic distribution of dipolar fields, with respect to that of the crystal
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As shown recently by Henderson (Ref.), the influence of transverse dipolar magnetic fields on the tunneling rates can be enhanced when excited states, associated to total S values different than 10, are coupled with the states of the ground multiplet. This effect cannot be treated within the "giant spin" model employed here. It might contribute to enhance further the magnetic relaxation of the amorphous material, which has a nearly isotropic distribution of dipolar fields, with respect to that of the crystal.
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