# Introduction to Magnetism HS22

**Teaching Assistant**: Laura van Schie

# Preface

The lecture *Introduction to Magnetism* is the regular course on magnetism for the MSc curriculum of the Department of Physics of ETH Zurich. Contents and learning objectives of this course have been defined with the help of 15 professors who perform research on magnetism and related fields, such as multiferroicity and superconductivity.
The result is a lecture that addresses fundamental aspects of magnetism which are rarely spelled out comprehensively in basic courses of solid-state physics. We will start reviewing the basic mechanisms from which atomic magnetic moments and their reciprocal coupling arise. We will then learn that thermal fluctuations play a remarkable role in determining the degree of (bi-)stability of a magnet. Theoretical concepts will be applied to few selected nano-sized magnets, which will serve as clean reference systems.

Students are assumed to possess a basic background knowledge in quantum mechanics, solid-state and statistical physics as well as classical electromagnetism.

## Learning goals of the course

At the end of this course students should have acquired the basic knowledge needed to develop a research project in the field of magnetism or to attend effectively more advanced courses on this topic.

In particular, they should be able to

- Apply concepts of quantum-mechanics to estimate the strength of atomic magnetic moments and their interactions.
- Identify the mechanisms from which exchange interaction originates in solids (itinerant and local-moment magnetism).
- Relate the type of magnetic ordering to the type of excitations that destroy ferromagnetism at finite temperature in different systems.

- Assess the origin of bistability in realistic magnets.

## Learning material

Since the covid pandemic we have decided to make all the learning material available through a RStudio Sever. Throughout the course this document will be updated to build up the eBook of the lecture notes, publicly available. From the proper icon on the top bar you will be able to download the pdf version of the lecture notes *Introduction_to_Magnetism_HS22.pdf*, which will also be updated every week.
Clicking on the next link you will access the **private** section of the RStudio Server, using the **personal credentials** that were given at the beginning of the course. From there you can complete and upload assignments as well as receive feedback from us, through the `AssignmentMailbox`

. Moreover, you will have access to the folder `CourseLibrary`

, containing some literature and additional learning material.

Notes hand-written during the lecture will be distributed by updating the links in the table Lecture plan below.

Moodle will only be used as a backup support.

## Live streaming and office hours

The current guidelines of the *Rektorat* encourage to attend lectures in person. Nevertheless, we are considering to give you the opportunity to attend them also in live streaming joining this Zoom meeting:

**Meeting ID**: 635 5619 6921

**Password**: 401717

During the semester Laura and I will be available for **office hours** every **Thursday** at **14:15**. This event will take place via Zoom using the same link.

## Lecture plan

Below you can find a tentative timetable of the course:

week | Lecture | assignment |
---|---|---|

week 1 | The electron in a static electromagnetic field | Solution |

week 2 | Magnetic moment of the free ion | Solution |

week 3 | Crystal-field theory for transition metals | Solution |

week 4 | Transition-metals versus rare-earth ions | Solution |

week 5 | The single-ion spin Hamiltonian | Solution |

week 6 | Interatomic exchange interaction | Solution |

week 7 | Ferromagnetism in metallic Fe | Solution |

week 8 | Thermodynamics and statistical mechanics | Solution |

week 9 | The Ising model | Solution |

week 10 | The XY model | Solution |

week 11 | The Heisenberg model | Solution |

week 12 | Domain walls in the Heisenberg model | Solution |

week 13 | Elements of spin dynamics |

## Formative assessment

Formative assessment will be implemented both with classroom activities and assignments. Students are expected to complete the assignments directly on the RStudio Server, as will be explained during the first lecture. Handing in assignments is **not a prerequisite** to be admitted to the **exam**. However, since exam questions and formative assessments share the same spirit, it is in your own interest to complete and hand in assignments. **Every Friday at 23:59 pm** we will collect automatically and review your assignments. Depending on the type of assignment the feedback can be provided differently. During each lecture some time we will be devoted to let you do part of the assignments on your own and pose questions to Laura and myself. When meaningful, solutions to the assignments will be distributed through the table Lecture plan above.

**Attendance certificate**

Should you need an attendance certificate for the course you must have handed-in at least **10** out of 12 assignments **by Monday 19th of December** and receive a positive evaluation on them.

## General readings

The reader who is interested in deepening his/her knowledge on the topics covered in this lecture, and not only, is addressed to the following books:

- Quantum Theory of Magnetism, R. M. White (1970).
- Molecular Nanomagnets, D. Gatteschi, R. Sessoli, and J. Villain (2005).
- Molecular Magnetism, O. Kahn (1993).
- Magnetism: From Fundamentals to Nanoscale Dynamics, J. Stöhr and H.C. Siegmann (2006).

Some selected chapters of these books are also available in the folder `CourseLibrary`

or in Moodle.

## Acknowledgments

This course most probably would have not existed if Prof. Danilo Pescia had not trusted me and introduced me to the exciting experience of teaching Magnetism. The current version of the course is a development of a previous one – called *Magnetism I: From the Atom to Solid State* – that Prof. Danilo Pescia kindly invited me to teach together with him back in 2009. Since then, the spectrum of topics discussed in the course has broaden at some inevitable expenses: I hope that the original spirit has been preserved as well as the take-home messages grounded on basic principles. Thank you Danilo for this opportunity and for having taught me to hunt for fundamental principles in Physics.

I am indebted to Fernando Pedraza for having initiated me to the use of RMarkdown in university teaching and for the support he provided to solve several technical issues.

A special thank goes to Dr. Diane Lançon, a former teaching assistant, for helping me improve the description of itinerant magnetism and writing parts of the lecture notes.

Previous years’ assistants, Luca Marini and Dominik Nowak, are acknowledged for the energies and dedication they put to facilitate the communication with students when distant learning was imposed by the covid pandemic. Many innovative ideas for formative assessments and personalized feedback to students were proposed by them.

Last but note least, I would like to acknowledge our Teaching Assistant, Laura, who promptly jumped into this project to support me in the coordination and correction of the formative assessments.

Zurich, September 2022

Alessandro Vindigni