# QUANTUM MAGNETISM AND SUPERCONDUCTIVITY - 2023/4

Module code: PHYM062

## Module Overview

This module is designed to provide an introduction to the theory and applications of quantum magnetism and superconductivity and their applications in modern science and technology. Both superconductivity and magnetism are manifestations of electronic charge and spin, and constitute prime examples of phase transitions in metals. A range of phenomena that are resulting from these phase transitions is surveyed. A significant part of the module is devoted to modern technological applications in magnetometry, spintronics, and quantum information processing.

### Module provider

Mathematics & Physics

### Module Leader

GINOSSAR Eran (Maths & Phys)

### Number of Credits: 15

### ECTS Credits: 7.5

### Framework: FHEQ Level 7

### JACs code: F342

### Module cap (Maximum number of students): N/A

## Overall student workload

Independent Learning Hours: 107

Tutorial Hours: 11

Guided Learning: 10

Captured Content: 22

## Module Availability

Semester 2

## Prerequisites / Co-requisites

The module will assume prior knowledge equivalent to the following modules. You are required to take Advanced Quantum Physics (PHY3044) before you take this module. Also, if you have not taken the following modules you should consult the module descriptors - Quantum Physics (PHY2069). Solid State Physics (PHY2068) & From atoms to Lasers (PHY2062).

## Module content

__Superconductivity__

- Electrodynamics of superconductors

- The London equations
- Meissner effect, Vortices
- Drude model
- Finite frequency response
- Type I/II superconductivity.

- Cooper pairs and introduction to microscopic theory
- Quantum circuits

- Josephson effect
- The dc SQUID
- Superconducting circuits.

- The Ginzburg-Landau theory*

__Magnetism__ - Diamagnetism & Paramagnetism

- Quantum and classical explanation of diamagnetism
- Quantum mechanical (Brillouin) theory of paramagnetism
- The Brillouin function

- Ferromagnetism

- Origin of ferromagnetism – the exchange interaction
- Direct and indirect exchange interaction – anti-ferromagnetism
- Characteristics of ferromagnetism

- Magnetism in metals

- Density of states at the Fermi energy
- Pauli paramagnetism
- Ferromagnetic metals

- Domains

- Domain walls – Bloch and Néel domain walls
- Magnetocrystalline anisotropy
- Domain formation and magnetisation
- Applications of soft and hard magnetic materials

- Metal Spintronics

- Magnetoresistance
- The Spin-Valve

- Semiconductor Spintronics

- The Spin Transistor
- Spin dynamics in semiconductors
- Spin control in semiconductors
- Spin lifetime in semiconductors

- Advanced Topics*

- Broken symmetry & phase transitions
- Landau theory of ferromagnetism
- Spin Waves
- Quantum computing with spins – The two spin quibit

## Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

Coursework | COURSEWORK ASSIGNMENT I | 15 |

Coursework | COURSEWORK ASSIGNMENT II | 15 |

Examination | End of Semester Examination - 2 hours | 70 |

## Alternative Assessment

None.

## Assessment Strategy

__Assessment Strategy__

- analytical ability by solution of unseen problems in both coursework and exam

subject knowledge by recall of both “textbook” theory and important research articles in the exam

ability to generalize text-book theory by open-ended research component in the coursework

Thus, the

__summative assessment__for this module consists of:

2 hour written exam with 2 sections: Section A (compulsory) Magnetism: 20 marks, Superconductivity 20 marks. Section B (1 of 2) Magnetism 20 marks or Superconductivity 20 marks., weighted at 70%

2 assignments on specials topics, which will take a total of 40 hours of effort, each weighted at 15% - a total of 30

__Formative assessment and feedback__

Students will receive verbal feedback on progress with problems in tutorials and model solutions to the tutorial questions.

## Module aims

- This module aims to: To provide an introduction to the important role that electronic interaction plays in solid-state physics leading to phase transitions in electronic systems. To provide an introduction to microscopic theory and phenomenology of both quantum magnetic phenomena and superconductivity. Introduction to applications of solid-state physics to micro-electronics and metrology.

## Learning outcomes

Attributes Developed | ||

001 | Describe the electromagnetic behaviour of Type I superconductors in electromagnetic fields, and the London theory. | KC |

002 | Exhibit an understanding of the topic of Cooper pairs and how its predictions relate to experimental observations | KC |

003 | Exhibit an understanding of the topic of Ginzburg-Landau theory and how its predictions relate to experimental observations | KC |

007 | Apply the principles of exchange interactions to determine magnetic ordering in materials. | KC |

011 | Evaluate spin diffusion and lifetimes. | KC |

009 | Determination of domain wall formation using energy considerations | KC |

010 | Determination of magnetoresistances based on material parameters and structure. | KC |

004 | Explain the quantum origin of diamagnetism and paramagnetism. | K |

005 | Determination of magnetic properties such as susceptibility and Curie temperature using observed magnetic behaviour. | KC |

012 | Explain and compare simple models of magnetism, including Landau theory of ferromagnetism, Heisenburg model and Ising models. | KC |

013 | Explain the origin of spin waves, including deriving their energy dispersion and their role in magnetic behaviour at low temperatures (Bloch T3/2 law). | KC |

014 | Explain the principle and determine the parameters for the initialisation, control and readout of a two-spin quibit. | KC |

006 | Demonstrate application of Brillouin function in determining paramagnetic behaviour, including incorporating a molecular field to describe ferromagnetism. | KC |

008 | Demonstrate application of the density of states in metals to describe paramagnetic and ferromagnetic behaviour. | KC |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

## Methods of Teaching / Learning

The __learning and teaching__ strategy is designed to provide:

- a comprehensive theoretical treatment for the subject knowledge
- practice in problem solving for the cognitive skills

The

__learning and teaching__methods include:

- “chalk and talk” lectures (total of 22 hours) backed up with a guided study to stimulate uptake of subject knowledge Lectures will be recorded and made available on Ponopto.
- * Self-guided study on advanced topics using provided notes, recommended reading and supported by additional tutor drop-in sessions.
- tutorial demonstration of solutions to key problems after students have attempted them for formative feedback (1 hour per week x 11)

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

## Reading list

https://readinglists.surrey.ac.uk

Upon accessing the reading list, please search for the module using the module code: **PHYM062**

## Programmes this module appears in

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

Physics MSc | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics with Nuclear Astrophysics MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics with Astronomy MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics with Quantum Technologies MPhys | 2 | Compulsory | A weighted aggregate mark of 50% is required to pass the module |

Physics MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2023/4 academic year.