Question

Let's consider the case in 1D only for simplicity.

As we know in Density functional theory (DFT), we start the calculation by giving the crystal structure, and element details of materials. Well, Good Enough!

Whereas I have seen papers on low-dimensional magnetic materials (spin chain), they consider the models to have only exchange interaction constants. Is that enough?

How we can arrive at the effective spin chain model/hamiltonian for the corresponding low-dimensional spin chain material?

Answer 1

To arrive at an effective spin chain model for a low-dimensional spin chain material, one primarily focuses on exchange interaction constants which define a simplified spin chain Hamiltonian. DFT and empirical data from experiments, such as inelastic neutron scattering, are used to determine these exchange constants. Crystal Field Theory can also provide insights into the energies of electronic states in related transition metal complexes.

Step-by-step explanation:

Low-dimensional spin chain materials in density functional theory (DFT) are often studied using simplified models that feature exchange interaction constants. To develop an effective spin chain model for simulating a one-dimensional spin chain material, the exchange interactions between adjacent magnetic moments or spins are the main focus. These exchange interactions are typically quantified by the exchange constants (J) in a Hamiltonian formalism. In the context of DFT, the spin chain is an abstraction that simplifies the complex electron-electron interactions and crystal structure into a model concerned primarily with magnetic interactions.

The transition from a real material to an effective spin chain model involves mapping out the magnetic interactions that dominate at low dimensions, ignoring other complexities. This process requires a detailed understanding of the material's electronic structure, which can be informed by both DFT calculations and experimental results. While DFT provides detailed insights into the material's electronic properties and can hint at the magnetic interactions present, empirical data from experiments such as inelastic neutron scattering are crucial to accurately determine the exchange constants that define the spin chain Hamiltonian.

In addition, Crystal Field Theory (CFT) can play a role in understanding the energies of electronic states in transition metal complexes, which may contribute to the overall magnetic properties modeled by the Hamiltonian. However, in a strictly one-dimensional case, those detailed electron-ligand interactions may be less significant compared to the direct spin-spin exchange interactions.