# How to choose the values of J and spin parameters in a heterogeneous spin system?

In this work, graphene-based systems that are described by mixed spin-3/2 and spin-5/2 are studied using the . A diagram of the structure is shown bellow:

The Hamiltonian used is:

$$$$\tag{1} {H_I} = - J\sum\limits_{\left\langle {i,j} \right\rangle } {{S_i}{\sigma _j}} - {J_\sigma }\sum\limits_{\left\langle {i,j} \right\rangle } {{\sigma _i}{\sigma _j}} - {J_S}\sum\limits_{\left\langle {i,j} \right\rangle } {{S_i}{S_j}} - {K_v}\left( {\sum\limits_i {S_i^2} + \sum\limits_j {\sigma _j^2} } \right).$$$$

Here $$\left\langle {i,j} \right\rangle$$ refers to the sum over the nearest neighbors pairs, $$\left[ i,j \right]$$ means sum over the next-nearest neighbors pairs, $$J$$, $$J_\sigma$$ and $$J_S$$ are the exchange interaction constants between sites $$\sigma−S$$, $$\sigma−\sigma$$ and $$S−S$$, respectively (see diagram above), and $$K_v$$ is the crystal field anisotropy constant. The spins moments can take values $$\sigma = ±3/2,±1/2$$ and $$S=±5/2,±3/2,±1/2$$.

### How are $$J$$, $$J_\sigma$$, $$J_S$$, $$\sigma$$ and $$S$$ chosen?

• It depends what behavior you are interested in. Are you comparing to an experimental system? Another numerical model? – taciteloquence Mar 23 at 17:55
• You would consider S to be the number of unpaired electron on your magnetic atom, typically. For eg, if you have an Fe atom with a moment of 3 bohr magneton, S would just be 3*(1/2). If you can't eyeball 'S', you can simply infer it from your DFT calculation. All other parameters in your question can be estimated through first-principles, through DFT. I just answered a question regarding the calculation of Js, hopefully that points you in the right direction: mattermodeling.stackexchange.com/questions/1548/… – Xivi76 Mar 23 at 20:23
• @Xivi76 As this is one of our longest standing unanswered questions, do you think you'd be able to turn this into an answer at some point (if you have time)? – Nike Dattani Apr 18 at 2:59