Course Unit Page

  • Teacher Samuele Sanna

  • Credits 6

  • SSD FIS/03

  • Teaching Mode Traditional lectures

  • Language English

  • Campus of Bologna

  • Degree Programme Second cycle degree programme (LM) in Physics (cod. 9245)

  • Teaching resources on Virtuale

Academic Year 2020/2021

Learning outcomes

At the end of the course the student will learn the basic quantum phenomena occurring in magnetic and superconducting materials and several experimental techniques employed to study these properties at both macroscopic and microscopic scale. The student will become familiar with several magnetic and superconducting materials and with their importance for current research and technological applications.

Course contents


-> Introduction:

magnetic moments and quantum mechanics; the coupling of two spins.

-> Isolated magnetic moments:

Hamiltonian of an isolated atom in a magnetic field; Larmor diamagnetism; paramagnetism and Brillouin theory; the Curie law vs. ground state of ions and their fine structure; comparison with experiments and Crystal field contribution; Van Vleck Paramagnetism. Applications of diamagnetic and paramagnetic materials: how to reach very low temperature by using the adiabatic demagnetization. Nuclear spins and hyperfine structure.

-> Ordered and Magnetic structures:

Summary of Interactions (Dipolar, exchange); Ferromagnetism, Antiferromagnetism and Ferrimagnetism: The Weiss model and the quantum origin of the molecular field. Applications of Ferromagnetic materials.

-> Magnetism in metals:

Pauli paramagnetism; Landau levels and Landau diamagnetism.

-> Additionally, brief introduction also to concepts of:

order broken symmetry and phase transitions (Landau theory); excitations and magnons; domain walls and magnetocrystalline anisotropy.

-> Experimental methods to measure magnetic moment and susceptibility of materials.

-> Principle and applications of magnetic resonance techniques:

Nuclear magnetic resonance and Magnetic Resonance Imaging (classical and quantum approach); Electron spin resonance; Mossbauer spectroscopy; Muon spin spectroscopy.



-> Introduction of superconductivity: main properties, materials and their characteristic parameters and application.

->Thermodynamic properties of superconductors:

Free Energy and thermodynamic field; entropy and specific heat.

-> Perfect diamagnetism: The Meissner effect and the magnetic levitation; The London model.

-> Type-I and type-II superconductors: critical magnetic fields vs characteristic parameters.

-> Microscopic description of the superconducting condensate: Cooper pairs; introduction to BCS model; the superconducting gap; comparison with experiments: isotopic mass effect and different confirmations of the Cooper pairs formation.

-> Quantization of magnetic flux in a superconducting ring.

-> Josephson effects and superconducting quantum interference device. Application of Josephson devices.

-> Ginzburg-Landau theory of superconductivity.


[1] Steve Blundell, Magnetism in Condensed Matter (Oxford University Press).

[2] J. M. D. Coey, Magnetism and Magnetic Materials (Cambridge University Press).

[3] M. Cyrot and D. Pavuna, Introduction to Superconductivity and High-Tc Materials (World Scientific Publ. Co.).

[4] Lecture notes.

Teaching methods

Frontal lectures using the blackboard for the demonstrations and a slide projector for viewgraphs and graphic renderings.

Assessment methods

Oral examination.

Teaching tools

Blackboard, overhead projection.

Office hours

See the website of Samuele Sanna