Course outline: The outline can be downloaded here.
Class timings: 1:00 to 2:15 pm, Monday and Wednesday, Room: 301 SSE Complex.
Pre-mid term
To access the video recording, click on the numbered links below.
Origin of Magnetic Moments (2 Lectures)
1: Isolated magnetic moments and paramagnetism
- Magnetic moments
- Spin 1/2 particle, Spin j system
- Paramagnetism, Curie’s law, Brillouin function
- Slides on magnetic force microscopy
2: Forces and torques on magnetic moments
- Mott scattering (Supplementary information), Mott detector
- Bloch equation, Landau-Lifshitz-Gilbert equation
HW1: Isolated magnetic moments and paramagnetism (due date: Monday, 26 September, 1 pm)
- Example program (Matlab files)
- Dipolar interaction, exchange interaction
- Pauli’s equation, Pauli exclusion principle
- Ground and Excited state
- Heisenberg exchange Hamiltonian
- Ferromagnetism, antiferromagnetism
- Variational pricnciple
- Bonding and antibonding molecular orbitals
- Ionic bond, covalent bond
- Exchange degeneracy in the molecule causes singlet-triplet energies to be different
- London-Heitler approximation
- Direct exchange, Indirect exchange, Superexchange
- Heisenberg exchange Hamiltonian
- Example of finding energy splitting due to exchange Hamiltonian
8: Spin Orbit Interaction (SOI)
- Semi-classical treatment
- Quantum mechanical interpretation
- Helium (He) atom, Sodium (Na) doublet
- Multielectron Atom, L-S and j-j coupling
- Hund’s Rules:3d and 4f ions and their comparison
- Effective magnetic moments of 3d and 4f ions
HW2: Exchange Interaction (due date: Monday, 10 October, 12 pm)
- Orbital quenching
- 3d orbitals in Octahedral environment
- Crystal field splitting
- t2g and eg Orbitals
- 3d orbitals in tetrahedral environment
- Jahn-Teller Effect
- low spin and high spin configuration
11: Vibrating Sample Magnetometer
12: Diamagnetism of bound electrons and Pauli paramagnetism
- Bound electrons in a solid
- Canonical momentum
- Diamagnetism, Paramagnetism
- Van Vleck paramagnetism
- Fermi Dirac distribution, Density of states
- Spin split bands
- Pauli paramagnetism
HW3: Crystal field interactions, diamagnetism, Pauli paramagnetism (due date: Monday, 31 October, 10 am). Assistive Mathematica file.
- Spin-1/2 free electrons
- Landau Gauge
- Landau Quantization
- Landau levels for electrons in a solid
- Degeneracy of Landau levels
- k-space in a magnetic field
- Density of states (DOS) in a magnetic field
- Convolution of 1D and 2D DOS
- Van-Hove singularities
- Integrated density of states
- Change in Fermi level in a magnetic field
- De Haas-Van Alphen oscillations
- Magneto Oscillations (assistive files)
- Comparison between Pauli and Landau paramagnetism
- Magnetically ordered structures
- Ferromagnetism, antiferromagnetism, helimagnetism, conical magnetism
- Origin of mean-field theory
- Curie-Weiss law, Curie temperature
- Ferromagnetic (FM) ordering
- Spontaneous magnetization
HW4: Weiss molecular field theory and Ferromagnetism (due date: Monday, 21 November, 1 pm)
- Origin of Weiss molecular field
- Susceptibility of FM beyond critical temperature
- Antiferromagnetic ordering
- Neel Temperature
- Susceptibility of AF beyond Neel temperature
- Susceptibility of AF below Neel temperature
- Susceptibility parallel and perpendicular to B field
- Canted Spins in antiferromagnets
- Spin flip and Spin flop transitions (Assistive file)
- Magnetic excitations
- Dispersion relation for Spin waves
- Magnons
- Temperature dependence of magnon numbers
- Bloch Law, energy and heat capacity of magnons
HW5: Spin waves and magnons (due date: Monday, 28 November, 1 pm)
20: Quantum mechanical description of magnons
- Second quantization formalism
- Holstein-Primakoff transformations
- Mapping of exchange hamiltonian under Holstein-Primakoff transformations
- Tight Bonding Model
- Diagonalization of hamiltonian by Fourier transform
- Dispersion relation for magnons
HW6: Various aspects of quantum magnetism (due date: Monday, 12 December, 1 pm)
21: Landau theory of ferromagnetism
- Symmetry breaking and order parameter
- Power law for magnetization, phase transitions, critical exponents
- Experimental methods to determine the Curie temperature (Arott plot)
- Heat capacity of ferromagnet
- Ising interaction
- Role of entropy in ising chain
- Heat capacity of finite ising chain
- Tight binding inside a molecule (Hydrogen molecular ion)
- Tight bonding hamiltonian
- Bonding and antibonding molecular orbitals
- Tight binding chain
- Hubbard model: interplay of kinetic energies and Coulombic repulsion
- Stoner criterion, Susceptibility in Stoner model
- Qualitative analysis of ferromagnetism in 3d elements
- Rigid band model
- Weak and strong ferromagnets, Heusler alloys
- Superexchange interaction in MnO
- RKKY interaction