Dzyaloshinskii-Moriya Interaction [1,2]

• Introduction, weak ferromagnetism
• Relativistic exchange interactions basic symmetry considerations
• Calculational methods:
  •  vector spin-density functional theory,
  •  spin-spiral calculations,
  •  Green's function methods
• Examples:
  •  magnetic domain walls, skyrmions,
  •  magneto-electric coupling
• Summary & outlook

[1] I. E. Dzialoshinskii, Sov. Phys. JETP 5, 1259 (1957) [2] T. Moriya, Phys. Rev. 120, 91 (1960)

Experimental techniques:  

• Magnetic susceptibility,
• Magnetisation,
• Heat capacity,
• NMR,
• MuSR,
• Neutron diffraction,
• Inelastic neutron scattering

Examples of experimental systems:

• Organic magnets
• Single molecule magnets
• Magnetism in competition with superconductivity
• Low-dimensional magnets
• Spin liquids
• Spin ice

• Dynamical Mean-Field Theory
• Instabilities and broken-symmetry phases in DMFT
• Magnetism in the Hubbard model
• Static vs dynamical mean-field
• DFT+DMFT, some examples on materials

• Introduction
  •  Mott insulator, Orbital degeneracy
  •  Spin-orbital exchange interactions

• Spin-orbit coupling
  •   Angular momentum, local electronic structure, g-factors
  •  Exchange interactions in j-basis

• Experimental implications
  •  j=1/2 systems: Iridates and Ruthenates
  •  j=3/2 systems: Vanadates, Molybdates,and Osmates

• Coulomb exchange & Hund’s rules
• Direct exchange
• Superexchange & Goodenough/Kanamori rules
• Double exchange
• Orbital exchange & orbital ordering

More details can be found in these lecture notes.

• Overview
  
  • Theory of magnetism: all problems solved? The most important temperature effects. Heisenberg versus Moriya. Fluctuations.
  • Trends in the Curie temperatures of Heusler compounds and applications in spintronics.
  • Antiferromagnets. Non-collinearity.

• Special topics:
  
  • Topology in magnetism - the Berry phase.
  • The anomalous Hall effect (AHE), perhaps also the  spin Hall effect.
  • The AHE in antiferromagnets.

• Stoner I as the DFT counterpart of Hubbard U (the spin-part therof) and Heisenberg J together. LDA+U and effective I in LDA+U.
• Andersen's extended Stoner theory for ferromagnetism in DFT. Application examples.
• Two sources of errors in DFT (w.r.t. magnetism): Hubbard U (examples) and Moria's zero-point fluctuations (examples). Applications and implementations of Moria's theory. "Poor man's Moria", a.k.a. renormalized Stoner theory.
• Basic magnetic interaction from the DFT point of view: (i) direct exchange (ii) superexchange (iii) FM superexchange (iv) FM direct (kinetic) exchange (v) double exchange (vi) RKKY
• An example of applications of (4): theory of dilute magnetic superconductors (Ba,K)(Zn,Mn)2As2.

• Basic ingredients
  • Ferroelectricity
  • Complex oxides
  • Symmetry Properties
  • Spin orbit coupling and Rashba effects

• Multiferroics
  • Different classifications (proper vs improper, bulk vs composite, etc)
  • Electronic ferroelectricity (spin, charge, orbital)
  • Different classes: oxides, organics and organic-inorganic hybrids

• Ferroelectric Rashba Semiconductors
  • Interplay between Rashba effect and ferroelectricity
  • Examples: GeTe, oxides, hyperferroelectrics

•  Summary

Basics of ab-initio superconductivity in the density functional way:  SC-DFT

• Functional construction and the effect of magnetism
• Pairing with spin fluctuations: Derivation of a Spin fluctuation effective electron-electron interaction from the magnetic susceptibility and the exchange-correlation kernel of TD-DFT.
• Its inclusion in SC-DFT
• Gap symmetry and renormalization in presence of overlapping pairing channels:
• phonons, spin fluctuations, plasmons ...

• Foundation of electron transport theory (non-equilibrium Green’s functions)
• Electron transport in magnetic system and heterostructures (the tunnelling problem)
• Giant magneto-resistance, tunnel magneto-resistance, spin-filtering at an interface
• Spin-transfer torque from DFT and non-equilibrium Green’s function methods
• Multi-scale approach to current-driven spin dynamics in heterostructures
• Overview of organic spintronics (spin-relaxation in organic materials, concept of spinterface)