1) Intro to magnetic materials

Lorentz force F =

qv x μ_0 H

What is a magnetic material

one that produces a magnetic field H without current flowing through it

Torque on magnetic moment τ =

μ_0 mH sin(θ) = (m x B)

What is a magnetic moment

vector describing the torque experienced by a magnetic dipole in an external field, units Am²

Dipole moment of a loop of current

m = IA

Magnetic moment due to orbital angular momentum

for an e in a state with l not=0 = e has non zero angular momentum which creates a magnetic moment; ml determines the alignment of the magnetic moment with the applied field

Magnetic moment due to electron spin

s=1/2: how much AM the e has due to spin (fixed);

m_s =+-1/2: AM vector can be spin up or spin down

Hunds rule

for partially filled shells:

first maximise S = Σ m_s ie align spins due to exchange energy

then maximise L = Σ m_l, e ‘orbit’ same direction so spend less time near each other reducing repulsion

Why are atoms magnetic

atoms total magnetic moment is due to the combination of orbital and spin magnetic moments; full shells have S=L=0; atoms in bonds or molecules are different as e behave differently

Equation for magnetisation

M = m/V; using of A/m = magnetic moment per unit volume

Magnetic flux density in materials

B = μ_0 (M + H) = total magnetic field due to both applied fields and magnetism from material

Magnetic flux density in free space

B = μ_0H; H is magnetic field intensity A/m, B in T (=kg/A/s²)

Magnetic susceptibility

how easy it is to magnetise a material with a given field; M = χH; differentiates different types of magnetic materials

Classes of magnetic material

Weak effects: diamagnets, paramagnets; Strong effects (magnetically ordered): ferromagnets, antiferromagnets, ferrimagnets

Diamagnetism

atoms have no net m; χ is small and negative; field induces a current in the atom producing an opposing field; over many atoms = net field in opposite direction; (classically need changing B field to induce current but no energy lost in atomic e so current remains)

Meissner effect

macroscopic induced currents in superconductors gives χ=-1 = perfect field cancellation

Paramagnetism

atoms have net magnetic moment; without field spins are disordered, M=0; external field aims to align spins while thermal energy produces disorder; χ is small and positive but varies with T and H; at high T and low H get Curie law χ=C/T

Ferromagnetism

adjacent spins align; M>0; Fe, Ni, Co (at RT) (ordering is spontaneous)

Antiferromagnetism

adjacent spins antialigned; M=0; Cr, MnO, CoO, NiO, FeMn;

Ferrimagnetism

adjacent spins align antiparallel but have different magentic moments; non zero M

Magnetic susceptibility of ferro and ferri magnets

spontaneous order gives them very high χ~10-100+

Magnetic hysterisis

M(H) is not single valued; depends on history of the field; Ms = saturation magnetisation; Mr = remanence; H_c = coercivity (field required to reverse magnetisation to 0)