# Condensed Matter Theory

#### Research by Professor J. Garner

Dr. Garner is doing work on computer modeling of interacting magnetic spins in host media. The spins’ magnetic moments arise from unfilled valence shells and are therefore due to both orbital and intrinsic electron motions.

The crystal host medium does not contribute directly to the magnetization of the materials, however the host perturbs the valence electron energy levels.

In the first order approximation we neglect all spin interactions; this is called the *singlet model*. The valence electrons experience perturbations due to the host (crystal field), spin-orbit interactions, an internal spin interaction and finally, the Zeeman coupling of the electrons to an externally applied magnetic field.

The magnetization is computed from the dependence of the electron’s energy levels on the field and specific heat is found from the dependence on temperature.

In the second order, the doublet model, we assume every spin is coupled to a near-neighbor spin.

The coupling is due to an exchange or superexchange mechanism. We have considered both ferro- and anti-ferromagnetic couplings.

Currently, we are working on the third order (*triplet model*) where it is assumed every valence electron is part of a triplet of interacting spins. This work requires the expertise of collaborators in parallel computing since the diagonalization of the hamiltonian matrix to get the energy levels is very time-consuming. Without parallel computers this calculation is not feasible.

All of the above models are being compared to experimental magnetization and specific heat measurements on diluted magnetic semiconductors, such as III-VI systems. We are especially excited about what we will find in the triplet model since this is the first model where the phenomenon of frustration can be present which is one of the hallmarks of spin glass physics. How close our simple models will come to real materials is still to be seen.