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 CrI3. In the second part you you investigate VI2, 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 CrI3¶
The notebook magnetism1.ipynb
shows how to set up a monolayer of CrI3 and
calculate the critical temperature
Set up a the structure and optimize the geometry of CrI3
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 - VI2¶
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
.