Magnetism 2016 - PhysLab

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Magnetism 2016

Home \ Class Teaching
41o2sx0zmcl-_sx383_bo1204203200_     images

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

sdTo 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)

3: Symmetrization Postulate

  • Dipolar interaction, exchange interaction
  • Pauli’s equation, Pauli exclusion principle

4: The Helium Atom

  • Ground and Excited state

5: Molecular Hydrogen Ion

  • Heisenberg exchange Hamiltonian
  • Ferromagnetism, antiferromagnetism
  • Variational pricnciple

6: The Hydrogen Molecule

  • Bonding and antibonding molecular orbitals
  • Ionic bond, covalent bond
  • Exchange degeneracy in the molecule causes singlet-triplet energies to be different
  • London-Heitler approximation

7: Exchange Interaction

  • 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)

9: Crystal Field Interaction

  • Orbital quenching
  • 3d orbitals in Octahedral environment
  • Crystal field splitting

10: Crystal Field Interaction

  • t2g and eg Orbitals
  • 3d orbitals in tetrahedral environment
  • Jahn-Teller Effect
  • low spin and high spin configuration

11: Vibrating Sample Magnetometer

  • VSM demonstration

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.

Assitive Mathematica File

13: Landau Levels

  • 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

14: Landau Levels

  • Density of states (DOS) in a magnetic field
  • Convolution of 1D and 2D DOS

15: Landau Diamagnetism

  • 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

16: Mean-Field theory

  • 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)

17: Ferromagnetism (FM)

  • Origin of Weiss molecular field
  • Susceptibility of FM beyond critical temperature

18: Antiferromagnetism (AF)

  • 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)

19: Spin Waves

  • 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

22: Ising chains

  • 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

23: Band magnetism

  • Tight binding chain
  • Hubbard model: interplay of kinetic energies and Coulombic repulsion

24: Stoner Model

  • 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

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  • Home
  • About Us
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    • Alumni
    • Open Positions
    • Muhammad Sabieh Anwar (Personal)
  • Academics
    • Lab Courses
    • Lab-I (ENGG-100/PHY-100/200)
    • Lab-II (PHY 300/500)
    • AstroLAB
    • Ibn Sahl Corner for Optics
    • Fast Optics
    • Smart Physics
    • Single Photon Quantum Mechanics Lab
    • Chasing Cosmic Ray Muons at Physlab
    • Stories
    • Physics Studio
    • Research Stories
    • Class Activities
    • Courses Taught
    • Class Demonstrations
    • PhysDiary
    • Health and Safety
    • Lab Safety
    • Workplace Organization
  • Research
    • Research Themes
    • Research Internships
    • Research Stories
    • Physics WorldCup
      • International Young Physicists’ Tournament (IYPT) 2019
      • International Young Physicists’ Tournament (IYPT) 2018
      • International Young Physicists’ Tournament (IYPT) 2016
    • Hunerkada
    • Grants
    • Theses and Reports
    • Scientific Publications
    • Invited Talks (Selected)
  • Outreach
    • Media
      • Lectures, Podcasts and Interviews
      • Videobytes
      • YouTube Channel
      • Visitors
      • Testimonials
    • The Scientific Mind Through the Eyes of a Physics Experimenter
    • National Laboratory Immersion Program
      • First Lahore 2012
      • Second Sukkur 2013
      • Third Lahore 2014
      • Fourth Lahore 2016
    • Labview Workshop 2016
    • Open house
      • 2009-2015
      • Open house 2023
    • Khwarizmi Science Society
    • Helping Pakistan’s Universities
      • National University of Technology (NUTECH) 2019
      • Pakistan Institute of Engineering and Applied Sciences
        (PIEAS) 2019 (Final Phase)
      • Pakistan Institute of Engineering and Applied Sciences
        (PIEAS) 2019 (Phase 2)
      • Pakistan Institute of Engineering and Applied Sciences
        (PIEAS) 2018 (Phase 1)
      • National University of Science & Technology 2016
      • Habib University 2014
      • Preston University 2013
      • Ghulam Ishaque Khan Institute of
        Engineering Sciences and Technology 2011
      • Institute of Space Technology 2010
    • The National STEM School
      • STEM School (2018 – 2019)
      • STEM school (2016 – 2017)
    • Abdus Salam Memorial Lecture Series
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      • PhysPlot
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      • Phystrack
    • Mechanical Workshop
    • Inventory
    • 3D Printed Galleria
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    • Equipment Howto’s
  • PhysGPT
  • Contact Us