Order and Excitations in Condensed Matter (OECM | INU7016U)

Description: Syllabus

The allocation of topics to sessions is shown below. Each session is approximately three lectures.

Atomic Scale Structure of Material (session 1): The rich spectrum of condensed matter; Energy and time scales in condensed matter systems; Crystalline materials:
crystal structure as the convolution of lattice and basis; Formal introduction to reciprocal space.

Magnetism: Moments, Environments and Interactions (session 2) Magnetic moments and angular momentum; diamagnetism and paramagnetism; Hund's rule; Crystal fields; Exchange interactions

Order and Magnetic Structure (session 3) Weiss model of ferromagnetism and antiferromagnetism; Ferrimagnetism; Helical order; Spin Glasses; Magnetism in Metals; Spin-density waves; Kondo effect

Scattering Theory (sessions 4 and 5) X-ray scattering from a free electron (Thomson scattering); Atomic form factors; Scattering from a crystal lattice, Laue Condition and unit cell struture factors; Ewald construction; Dispersion corrections; QM derivation of cross-section; Neutron scattering lengths; Coherent and incoherent scattering

Excitations of Crystalline Materials (session 6) Dispersion curves of 1D monoatomic chain (revision); Understanding of dispersion curves in 3D materials; Examples of force constants in FCC and BCC lattices; Dispersion of 1D diatomic chain; Acoustic and Optic modes in real 3D systems; Phonons and second quantization; Anharmonic interactions

Magnetic Excitations (session 7) Excitations in ferromagnets and antiferromagnets; Magnons; Bloch T3/2 law; Excitations in 1, 2 and 3 dimension; Quantum phase transitions

Sources of X-rays and Neutrons (session 8) Full day visit to RAL. Neutron Sources and Instrumentation. Synchrotron Radiation. Applications of Synchrotron Radiation

Modern Spectroscopic Techniques (session 9)
Neutron scattering: triple-axis spectrometer, time-of-flight, polarized neutrons
X-ray scattering: X-ray magnetic circular dichroism, resonant magnetic scattering, reflectivity

Phase transitions and Critical Phenomena (session 10) Broken symmetry and order parameters in condensed matter. Landau theory and its application to structural phase transitions, ferromagnetism, etc. Ising and Heisenberg models. Critical exponents. Universality and scaling36

Local Order in Liquids and Amorphous Solids (session 11) Structure of simple liquids; Radial distribution function; Dynamics: viscosity, diffusion; Modelling; Glass formation; Simple and complex glasses; Quasi-crystals.

This module is taught by UCL.