Invited
Theory and modelling: Effective hamiltonian approaches

Here, we will focus on effective Hamiltonian techniques, in order to understand ferroelectricity at a microscopic level. The first microscopic, effective Hamiltonian approach of ferroelectric materials was developed in the mid-nineties. Since then, it has achieved great successes in describing various ferroelectric materials. In a nutshell, effective Hamiltonian methods first identify the most important degrees of freedom in a ferroelectric material, and then, based on symmetry arguments, constructs the internal energy of the system as a function of these degrees of freedom and their interactions. The coefficients entering the effective Hamiltonian energy are typically obtained from ab-initio computations. These techniques are then used into Monte-Carlo and molecular dynamics simulation to determine static and dynamical properties at finite temperature, respectively.

Initially, only the so-called local modes and strains of simple bulk systems were included into effective Hamiltonian schemes. However, later on, alloy effects, oxygen octahedral tiltings and magnetic degrees of freedom were added into effective Hamiltonian approaches, and nanostructures were also investigated thanks to these techniques.

Technical details about effective Hamiltonians will be reported. The understanding of complex properties and discoveries of novel effects arising from the use of these Hamiltonians will also be discussed.

These works are supported by the Arkansas Research Alliance (ARA), ARO Grants No. W911NF-21-1-0113 and No. W911NF-21-2-0162 (ETHOS), ONR Grant No. N00014-21-1-2086, the Vannevar Bush Faculty Fellowship (VBFF) Grant No. N00014-20-1-2834 from the Department of Defense, and the MonArk NSF Quantum Foundry supported by the National Science Foundation Q-AMASE-I program under NSF award No. DMR-1906383.