Previous questions (here, here and here) were about modeling magnetic homogeneous systems using Heisenberg and/or Ising hamiltonians:

\begin{equation} \tag{Heisenberg} \hat{H}_H=-\sum_{\langle i j\rangle}J\hat{S}_i\hat{S}_j \end{equation}

\begin{equation} \tag{Ising} \hat{H}_I=-\sum_{\langle ij\rangle}J\hat{S}_i^z\hat{S}_j^z \end{equation}

In this work1 (free access), graphene-based systems described by mixed spin-3/2 and spin-5/2 are studied using Ising Hamiltonian. A diagram of the structure is shown bellow (image linked from original address):

The Hamiltonian used is:

\begin{equation} \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) \end{equation}

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 $S=±5/2,±3/2,±1/2$.

My questions are:

  • What are the physical justification in setting the values for the exchange interaction constants $J$, $J_\sigma$ and $J_S$?
  • What are the physical justifications setting the values of $\sigma$ and $S$?
  1. J.D.Alzate-Cardona, D.Sabogal-Suárez, E.Restrepo-Parra, Critical and compensation behavior of a mixed spin-3/2 and spin-5/2 Ising ferrimagnetic system in a graphene layer. J. Mag. Mag. Matt. 429 34–39 (2017) (DOI: 10.1016/j.jmmm.2017.01.004)

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