#### Gustav Bihlmayer: Dzyaloshinskii-Moriya Interaction

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)

#### Stephen Blundell: Experimental overview

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

#### Luca de' Medici: Magnetism in Dynamical Mean Field Theory (DMFT)

- 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

#### George Jackeli: Spin-Orbit Mott Insulators: Magnetism, Order, and Excitations

- 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

#### Erik Koch: Exchange Mechanisms

- 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.

#### Juergen Kuebler: Overview and special topics in magnetism (theory)

- 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.

#### Igor Mazin: Density functional theory of magnetism: learn from successes and learn from failures

- 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.

#### Silvia Picozzi: Multiferroics

- 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

#### Antonio Sanna: Magnetism in Density Fuctional Theory for Superconductors

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 ...

#### Stefano Sanvito: Spintronics

- 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)

VIENNA COMPUTATIONAL MATERIALS LABORATORY

Sensengasse 8/12

A-1090 Vienna

AUSTRIA

T: +43-1-4277-51401

F: +43-1-4277-9514

E-Mail

Sensengasse 8/12

A-1090 Vienna

AUSTRIA

T: +43-1-4277-51401

F: +43-1-4277-9514