# What are examples of materials that closely correspond to the Heisenberg model?

I use the antiferromagnetic Heisenberg model all the time:

$$H = J \sum \limits_{\langle i,j \rangle} \vec S_i \cdot \vec S_j$$

What are some examples of materials that are well-described by this model in 3D? What about in 1D and 2D?

• I love this question! – Nike Dattani May 12 at 15:44
• It's unfortunately not something that I have (yet) the knowledge to answer. I do want the most to be achieved from this bounty though, and with 23 hours left I have started to look up authors who might have written papers on this Hamiltonian. I found this book chapter: link.springer.com/chapter/10.1007/978-3-540-85416-6_7 and will try to contact the authors tomorrow (it's almost 1am here and I'm heading to bed soon!). If others are able to help do the same it would be appreciated, as I truly think this question needs more attention from experts in the field. – Nike Dattani May 20 at 4:55

A famous example of a nearly ideal spin-$$1/2$$ isotropic Heisenberg antiferromagnetic chain (1D) system is copper pyrazine dinitrate [Cu(C$$_4$$H$$_4$$N$$_2$$)(NO$$_3$$)$$_2$$], which was discussed in Hammar et al. Phys. Rev. B 59, 1008 (1999) [arXiv link]. Another excellent realizations include KCuF$$_3$$, which has stronger (but still low) interchain coupling, and orders at low temperatures. However, the spectrum of magnetic excitations above $$\sim J/10$$ matches DMRG and Bethe Ansatz calculations very closely. See e.g. Lake et al. Phys. Rev. Lett. 111, 137205 (2013) [arXiv link]. A third example is CuSO$$_4\cdot 5$$D$$_2$$O, see Mourigal et al. Nature Physics 9, 435 (2013) [arXiv link].