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.