# How accurately are magnetic effects treated in *ab initio* methods?

I am a condensed matter theorist and I mostly use quantum Monte Carlo methods. I use models like the Heisenberg model, an represent an extreme simplification of real materials to just localized spin degrees of freedom (no electrons, orbitals, etc).

The advantage of this extreme simplification is it allows much more precise studies of the underlying physics. The disadvantage is that it can be difficult to make direct connections to experiments.

I know very little about how ab initio methods work and even less about how they treat magnetism. I would like to have a better sense of the capabilities of these methods.

1. Is it possible to model strong magnetic correlations or magnetic phase transitions?
2. Can ab initio methods be used to calculate exchange parameters (like the Heisenberg $$J$$)?
• Spin-spin can be treated an-initio (Boris Minaev did it for Li$_2$). External magnetic fields can certainly be included. Heisenberg's J can be estimated I believe (see the most cited paper by Steve Winter). I'm sure they can be used to study magnetic phase transitions but I don't know any examples. However I don't know how to answer #3: I only ever calculated spin-orbit interactions, and they tend to be hard, but I lack experience with others so I can't compare 😂 – Nike Dattani May 26 '20 at 13:24
• Just a piece of general advice: asking 5 questions at the same time is not the best idea. The question is already extremely broad (what methods? what systems? how do you deal with spin-orbit coupling? etc), maybe you one to focus on one main question of it. – Greg May 27 '20 at 10:41
• That's fair, I'll edit it to make it simpler. – taciteloquence May 27 '20 at 10:44
• Thank you for the clarification. I have one more question: what do you mean that it is difficult to make a connection with experiments? You mean you have to know J, D etc to have good simulation? Experiments generally give thermal expectation values of different properties, not J such. Ab initio methods in that sense are even harder t compare to experiments as they give only energies of different spin-configurations, you still have to make a thermodynamic model on the top of it, calculate thermal occupations etc. – Greg May 28 '20 at 3:02
• To connect to experiments you have to make guesses at J, D, etc, but more importantly, you have to know what the interactions look like in the first place. Are the spins localized? How do they interact with their neighbors and next nearest neighbors, etc? Are those interactions isotropic, etc? If there are any moving electrons or holes (or any interactions that don't involve spin), then accounting for those can be very difficult. – taciteloquence May 28 '20 at 3:23