# Introduction to Magnetism HS21

**Teaching Assistant**: Dominik Nowak

# 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).
- Evaluate the consequences of the interplay between competing interactions and thermal energy.
- Apply general concepts of statistical physics to assess the origin of bistability in realistic magnets.
- Discriminate the dynamic responses of a magnet to different external stimuli.

## Technical aspects

Since last year, in response to the covid pandemic, we have chosen to make all the learning material available through a RStudio Sever, on which you can login with credentials that will be given at the beginning of the course. According to the current guidelines of the *Rektorat* “all courses should also be offered remotely if this is technically and organisationally possible”. Details to attend the class via Zoom can be found in the password-protected area of the RStudio Server. In addition, recorded videos of the lectures will be made available. However, we strongly recommend to follow in presence or in live streaming because the lecture quality always benefit from your contribution.

Moodle will only be used as a backup support.

## Lecture plan

Below you can find the final timetable of the course:

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

week 1 | Orbital contribution to atomic magnetic moments | solution |

week 2 | Magnetic moments of free-ions and the role of spin | solution |

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

week 4 | The single-ion spin Hamiltonian | solution |

week 5 | Interatomic exchange coupling | solution |

week 6 | Itinerant vs local-moment magnetism | solution |

week 7 | RKKY interaction and cooperative models of magnetism | solution |

week 8 | The Ising model | solution |

week 9 | The XY model | solution |

week 10 | The Heisenberg model | solution |

week 11 | Domain walls in the Heisenberg model | solution |

week 12 | Spin precession and quantum tunneling | solution |

week 13 | Thermal equilibrium and superparamagnetism |

## Working settings

The recorded videos of the lectures and the notes will be distributed by updating the links in the table above. On a weekly basis, we will update the folders eBook (containing the lecture notes) and Assignments in your home directory. The file *Introduction_to_Magnetism_HS21.pdf*, available under the folder *eBook*, contains a pdf of the lecture notes up to the topic discussed on the current week. This pdf file can also be viewed by simply clicking on the proper icon on the html file, as shown in this video. Note that we **will not** distribute the complete lecture notes at the beginning of the course and that the file *Introduction_to_Magnetism_HS21.pdf* will be overwritten every week. Therefore, if you plan on learning on the **pdf** version (e.g. to take notes or highlight some parts), you should **download the newly distributed material and split it** from the old parts (otherwise your notes will be overwritten).

## Zoom meeting

You will be able to attend classes from remote joining this Zoom meeting:

**Meeting ID**: 635 5619 6921

**Password**: 401717

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

## Formative assessment

Formative assessment will be implemented both with classroom activities and assignments. Students are expected to complete the assignments directly in the RMarkdown interactive environment, as will be explained during the first lecture. Handing in assignments is **mandatory** to obtain the **attendance certificate** (see next session) but is **not a prerequisite** to be admitted to the **exam**. However, since exam questions and formative assessment share the same spirit, it is in your own interest to complete and hand in assignments. **Every Saturday at 1:00 pm** we will collect automatically and review your assignments. Depending on the type of assignment the feedback can be provided differently. In general, assignments or questions you pose in your submission will be discussed in plenum during the class on the following Monday. When meaningful, a solution to the assignment will be distributed through the table above.

## Attendance certificate

To obtain the attendance to the course a student must hand-in **by Saturday 18th of December** and receive a positive evaluation on **10** out of 12 assignments.

## General readings

The reader who is interested 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 `CourseLibraty`

, on this link 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 initiating me to the use of RMarkdown and Shiny App in university teaching. I am enthusiastic about exploring the potential of these technologies and hope that the final judgment of students will be that they, indeed, facilitate learning. Many thanks Fernando!

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.

Last year’s assistant Luca Marini is acknowledged for the energies and dedication he put to facilitate the communication and exchange with students during the time of distant learning, imposed by the covid pandemic. Many technical implementations and ideas for formative assessments were proposed by Luca or emerged from our discussions.

Last but note least, I would like to acknowledge our Teaching Assistant, Dominik, who promptly jumped into this project to support me in the material preparation and in the revision of students’ contributions as well as in the final assessment. Thank you very much Dominik for your enthusiasm for Magnetism!