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 XPauli?
  • 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 superparamagnetism? Phenomenolgically?
  • Why does it appear?
  • How to explain the critical size of a superparamagnet?
  • ... and of a single domain particle?
  • What is "blocking temperature"?
  • How does exchange bias show up? How to explain?

 

  • What is Magnetoresistance?
  • Why positive MR appears?
  • Explain negative MR in magnetically ordered materials.
  • What is AMR and how large it is? Explain qualitatively its presence.
  • What is GMR and why does it appear?
  • What is TMR and why does it appear?

 

  • 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?
 
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