1. P461 - magnetism1 Magnetic Properties of Materials H = magnetic field strength from macroscopic currents M = field due to charge movement and spin in atoms - microscopic can have residual magnetism: M not equal 0 when H=0 diamagnetic -> chi < 0. Currents are induced which counter applied field. Usually.00001. Superconducting chi = -1 (“perfect” diamagnetic)

2. P461 - magnetism2 Paramagnetism Atoms can have permanent magnetic moment which tend to line up with external fields if J=0 (Helium, filled shells, molecular solids with covalent S=0 bonds…) ---> chi = 0 assume unfilled levels and J>0 n = # unpaired magnetic moments/volume n+ = number parallel to B n- = number antiparallel to B n = n+ + n- moments want to be parallel as

3. P461 - magnetism3 Paramagnetism II Use Boltzman distribution to get number parallel and antiparallel where M = net magnetic dipole moment per unit volume can use this to calculate susceptibility(Curie Law)

4. P461 - magnetism4 Certain materials have very large chi (1000) and a non-zero B when H=0 (permanent magnet). Chi will go to 0 at critical temperature of about 1000 K (--> non ferromagnetic) 4s2: Fe26 3d6 Co27 3d7 Ni28 3d8 6s2: Gd64 4f8 Dy66 4f10 All have unfilled “inner” (lower n) shells. BUT lots of elements have unfilled shells. Why are a few ferromagnetic? Single atoms. Fe,Co,Ni D subshell L=2. Use Hund’s rules -> maximise S (symmetric spin) --> spatial is antisymmetric and electrons further apart. So S=2 for the 4 unpaired electrons in Fe Solids. Overlap between electrons --> bands but less overlap in “inner” shell overlapping changes spin coupling (same atom or to adjacent atom) and which S has lower energy. Adjacent atoms may prefer having spins parallel Ferromagnetism