Kirchhoff-Institute for Physics

Think Abouts

Sketch the idea why magnetism is a completely QM phenomenon.
Why can the measured magnetisation depend on the shape of a sample? For which classes of magnetic materials is this relevant?
How does of the Hamiltonian of a free atom change in presence of magnetic fields?
Which are the three main contributions to magnetism in free atoms?
What is diamagnetism and why does it appear? Which temperature and magnetic field-dependence has it?

What is paramagnetism? How J (total magnetic moment) and m (magnetic moment) differ?
What is the Lande-factor?
What is a quantum number? Discuss magnetic quantum numbers.
Field and temperature dependence of paramagnets?
What is van Vleck paramagnetism and how large is it?
How to motivate the presence of spin-orbit coupling?
Why people discriminate LS- and jj-coupling?
What are Hund's rules and what is their physical origin?

What is a phase transition?
What are discontinuous and continuous phase transitions?
What is a Quantum Phase Transition?
Which symmetries are broken in a ferromagnetic phase?
Sketch the basics of the Landau model. What is it good for?
What is the mean field model of ferromagnetism? Which approximation does it employ?
What are Curie- and Curie-Weiss laws? Relevance?

What is a magnetic domain? Which energy contributions are to be considered to decide about domain sizes and domain wall widths?
Explain the hysteresis curve of a typical ferromagnet.
What is a magnon?
What is a Goldstone mode?
Which dispersion apply for FM/AFM magnons?
How to measure magnon dispersions?
What is Bloch's T^3/2-law?

How to prove the presence of AFM order?
What are spin-flop and spi-flip?
Sketch M vs T and M vs B of an AFM.
How strong a typical dipol-dipol interactions in solids?
What is "exchange hole" and how exchange interaction can be motivated?
Explain Pauli-susceptibility. Calculate it in the simplest model. What to extract from the experimental value of X_Pauli?
How to improve the model?
Why iron is ferromagnetic? Explain the Stoner model and derive Stoner's criterion.
What is Stoner's criterion?
What about materials which nearly fulfil Stoner's criterion?
How to perform XMCD experiments? What do these experiments yield?
What is the phenomenon of the Kondo effect? How to explain it?
What is the Kondo temperature?
What are Friedel oscillations?

Why electron energy levels form "Landau tubes" if magnetic field is applied?
Which trick is used to solve to Hamiltonian?
What are the quantum numbers and which are the related energies?
How does DOS change upon application of B-fields?
What is the De Hass van Alphen effect and what do we learn from the observed oscillations?
Shubnikov-De Haas effect?

What is "Crystal Field"?
Why crystal field effects are relevant for 3d ions but not for 4f-ions?
What means "Breaking of Hund's rules" and why does it happen?
Why one may to some extent neglect orbital momenta in 3d transition metal compounds?
Why t2g-level have a pseudo-orbital moment?
What is a spin-Hamiltonian and which information is in the value of the g-factor?
How to measure g-factors?
Explain the Jahn-Teller effect.

Write the 1-Band Mott-Hubbard Hamiltonian and explain the terms.
Why NiO is an insulator (and why it may be considered surprising)
What are Hubbard subbands?
Explain the bandwidth-controlled Mott-Hubbard transition
Why the Mott state is antiferromagnetic?
What is a charge-transfer-insulator as compared to a Mott-Hubbard one?
Extra question: How to explain the presence of p-metals?
Zaanen-Sawatzky-Allen schema?
Which are the excitations of Mott insulator
Explain PES.
Extra: What is a Zhang-Rice-Singlett? Why is it so stable?
Sketch the ingedrients of the 3-band Hubbard model
What is superexchange? How strong is it?
GKA rules: 180° exchange, 90° exchange
Kugel-Khomskii exchange
How to measure magnetic interactions (How does inelatic neutron scattering work)?
What is resonant X-ray diffraction and what can one learn from it?
What is double exchange and how to explain the CMR effect?

What are Ising and Heidenberg chains?
What are excitations and the excitation spectrum of the uniform Heisenberg chain?
Mermin Wagner theorem?
What about order in the Ising chain? At T=0 and T>0?
What is a Haldane chain and which are its main characteristics?
... how to measure them?
What is a Peierls transition?
And spin-Peierls? How to find it in the experiment?
What to learn from themal conductivity about magnetic excitations in 1D systems?
What is Bose-Einstein condensation of magnons?