Why is iron ferromagnetic?

Electron spin is one of the primary causes for elements to have magnetic character. Consider a block of pure iron \(\ce{ Fe }_{ 26 }^{ 56 }\) kept in a uniform magnetic field \(B\). Iron has electronic configuration \([\ce{Ar}] 4{ s }^{ 2 } 3{ d }^{ 6 }\) with 4 unpaired electrons.

Estimate the magnetic moment of this block per unit volume in S.I units at absolute temperature \(T\).

Details and Assumptions:

\( {\rho }_{ iron }= 7870kg\cdot { \text{ m} }^{ -3 } \)

\(T = 300 K\)

\(\left| B \right| =100\quad T\)

Consider spin only magnetic moment given by \(\sqrt{n(n+2)} { \mu }_{ B } \)

\( { \mu }_{ B }=9.27\times { 10 }^{ -24 }\quad \text{ J}{ \cdot T }^{ -1 } \)

\( { k }_{ \text{Boltzmann} }=1.38×{ 10 }^{ -23 } \text{ J}\cdot \text{ K}^{ -1 }\)

P.S.: Ferromagnetic character is caused by the formation of magnetic domains rather than just electron spin. However here we only consider electron spin.

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