Magnetism
Overview of magnetic materials
Magnetic objects
Magnetic field lines
Molecular magnetism, example 1 Paramagnets are attracted to magnetic fields
Paramagnetic gases
Organic radicals are magnetic
Zeeman splitting and NMR gap = g mz B g = Lande g-factor (~2 for eˉ) mz = magnetic moment B = magnetic field strength Nuclear gap energy corresponds to radio frequencies Certain nucleii have a magnetic spin, and are therefore active in NMR experiments
Metals Many metals have unpaired electrons due to the high d-orbital degeneracy. n = 3 unpaired spins S = 3/2 magnetic moment octahedral Cr3+ has 3 d-electrons
Metals Multiple spin arrangements (HS, LS) are possible for a given number of d-electrons (in this case, 7 valence electrons). n = 3 unpaired spins S = 3/2 magnetic moment n = 1 unpaired spins S = 1/2 magnetic moment halides < OHˉ < C2O42- < H2O < NCSˉ < py < NH3 < en < phen < NO2ˉ < CNˉ < CO
Zeeman splitting and NMR gap = g mz B g = Lande g-factor (~2 for eˉ) mz = magnetic moment B = magnetic field strength Nuclear gap energy corresponds to radio frequencies Certain nucleii have a magnetic spin, and are therefore active in NMR experiments
paramagnet (disordered spins) ferromagnet (co-aligned spins) antiferromagnet (anti-aligned spins)
Ferromagnets have a persistent moment, even without a magnetic field
cM vs T for ferromagnets ferromagnetic paramagnetic
The math of magnetism cM – Molar susceptibility meff – Effective moment mB – Bohr magneton
Useful experimental quantity Molar magnetic susceptibility, cM Magnetic susceptibility per mole Why use “molar” and not the “gram” susceptibility?
Moment per metal atom S = total spin (1/2 per e ˉ) n = # unpaired eˉ meff = moment in Bohr magnetons (mB) g = magnetogyric ratio (Landé g-facor, ~2) mB = 9.27 x 10-24 J / T
Magnetic susceptibility, cM (Curie Law – assumes no spin-spin interactions) cM = measurable quantity (M / H) Can calculate meff from cM Can calculate # of unpaired electrons from meff (units are slightly fudged)
Magnetic susceptibility, cM (Curie Law) Simple approximations break down when spins are not isolated from each other (Curie-Weiss law)