Course Unit Page

Academic Year 2021/2022

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


Scientific and technological progress rely on the ability of analyse and manipulate physical systems at quantum level. Novel quantum technologies, based on the quantum principles of superposition and entanglement, are emerging in a number of sectors, namely communication, computing, sensing and measuring. Most of them are based on the use of quantum materials, namely materials which display collective quantum phenomena, also called emergent phenomena, emerging from the many-body interaction of different physical entities such as spin, charge, phonon, orbital…

Magnetic and superconducting materials are among the prototypes of quantum materials for most prominent quantum technologies, such as quantum computing and sensing. These technologies often make use of magnetic resonant techniques for the manipulation of the quantum states.

In this course a basic introduction to magnetism and superconductivity and to magnetic resonant techniques is provided by combining theoretical and experimental/phenomenological approach.



-> 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 temperatures 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.

-> use of magnetic resonances for quantum computing and sensing

creation of qubits, quantum entanglement and quantum gates

a prototype of quantum sensor: nitrogen-vacancy centers in diamond


-> 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.

-> Use of superconductors for quantum computing and sensing


Comments from the student's anonimous evaluation form of my lectures


[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.

Links to further information


Office hours

See the website of Samuele Sanna