# Magnetism in 2D¶

This exercise investigates magnetic order in 2D. While, a magnetic ground state may be found for a 2D material using DFT, magnetic order at finite temperatures requires spin-orbit coupling and magnetic anisotropy.

The exercise will teach you how to extract magnetic exchange and anisotropy
parameters from first principles calculations. It will also touch upon the
Mermin-Wagner theorem and show why anisotropy is crucial for magnetic order in
2D. The first part shows how to calculate the Curie temperature in CrI_{3}. In
the second part you you investigate VI_{2}, which has anti-ferromagnetic
coupling and non-collinear order. In the third part you will search for a new
2D material with large critical temperature based on a database of 2D
materials.

## Part 1: Critical temperaure of CrI_{3}¶

The notebook `magnetism1.ipynb`

shows how to set up a monolayer of CrI_{3} and
calculate the critical temperature

- Set up a the structure and optimize the geometry of CrI
_{3} - Calculate the exchange parameter from a total energy mapping analysis
- Derive the instability of the magnetic ground state when anisotropy is neglected (The Mermin-Wagner theorem)
- Calculate the magnetic anisotropy and critical temperature

## Part 2: Non-collinear magnetism - VI_{2}¶

If the magnetic atoms form a hexagonal lattice and the exchange coupling is
anti-ferromagnetic, the ground state will have a non-collinear structure. In
the notebook `magnetism2.ipynb`

you will

- Relax the atomic postions of the material
- Compare a collinear anti-ferromagnetic structure with the ferromagnetic state
- Obtain the non-collinear ground state
- Calculate the magnetic anisotropy and discuss whether or not the mateerial will exhibit magnetic order at low temperature

## Part 3: Find a new 2D material with large critical temperature¶

In this last part you will search the database and pick one material you
expect to have a large critical temperature. The total energy mapping analysis
is carried out to obtain exchange coupling parameters and a first principles
estimate of the critical temperature. The guidelines for the analysis is found
in the notebook `magnetism3.ipynb`

.