A single crystal of nickel

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Condensed Matter, Materials & Soft Matter · Magnetic materials

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

Problem

A single crystal of nickel, saturation magnetisation

M_s = 4.85\times10^5\,\mathrm{A\,m^{-1}}

, is grown as a cube of side

a = 2\,\mathrm{mm}

. If it were magnetised uniformly as a single domain along one axis, its demagnetising energy density would be

u_{\rm dem} = \tfrac12\mu_0 N_aM_s^2

with demagnetising factor

N_a = 1/3

. The domain wall energy of nickel is

\sigma_w = 1.0\times10^{-3}\,\mathrm{J\,m^{-2}}

. ((a)) Estimate

u_{\rm dem}

for the single-domain state. ((b)) Using the balance

n_d \approx \sqrt{u_{\rm dem}a/\sigma_w}

for the simplest structure of

n_d

alternating slab domains with the flux left open at the surface, estimate the number of domains and the width of each. ((c)) State briefly why real bulk domains in nickel are expected to be wider than this open-structure estimate.

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