Cobalt has Curie temperature and an atomic moment

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Magnetism in solids · Magnetism in solids

The Boundary-Value Problem, Ch Ferromagnetism: the Weiss field, domains, hysteresis and the magnetic circuit

Problem

Cobalt has Curie temperature TC=1388 KT_C = 1388\,\mathrm{K} and an atomic moment m=1.7 μBm = 1.7\,\mu_B, where μB=9.274×10−24 J T−1\mu_B = 9.274\times10^{-24}\,\mathrm{J\,T^{-1}} is the Bohr magneton. ((a)) Using μ0λWMs=3kBTC/m\mu_0\lambda_WM_s = 3k_BT_C/m, estimate the Weiss field that cobalt's Curie temperature requires. ((b)) Estimate the magnetic dipole field produced at one atomic site by a single neighbouring moment m=1.7 μBm=1.7\,\mu_B at a separation of 0.25 nm0.25\,\mathrm{nm}, using the on-axis dipole field magnitude Bdip=μ0m2πr3B_{\rm dip} = \dfrac{\mu_0 m}{2\pi r^3}. ((c)) State the ratio of the two fields and say what this ratio implies about the physical origin of ferromagnetic ordering in cobalt.

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