Multipolar ordering in electro- and magnetostatic coupled nanosystems.

Area of Science:

• Physics
• Chemistry
• Materials Science

Background:

• Electric and magnetic multipole moments are crucial for understanding intermolecular forces, optical phenomena, and potentials.
• Experimental determination of multipole moments is challenging, necessitating accurate theoretical predictions.
• Diverse definitions of multipole moments and interactions in literature complicate the use of published results.

Purpose of the Study:

• To provide a comprehensive overview of mathematical definitions for multipole expansion and their interrelations.
• To present a general theoretical framework for multipolar ordering on periodic two-dimensional lattices.
• To review numerical methods for calculating multipolar ground states and discuss applications in nanomagnetism.

Main Methods:

• Review of static multipole expansion in Cartesian and spherical coordinates, including coordinate transformations.
• Summary of multipole moments for various symmetric charge distributions.
• Review of Monte Carlo simulations for calculating multipolar ground states, with emphasis on odd and even order moments.
• Discussion of magnetic multipole-multipole interactions in nanomagnetic arrays.

Main Results:

• Consolidation of various mathematical definitions of multipole expansion and their relationships.
• Theoretical description of multipolar ordering on 2D lattices.
• Overview of multipole moments for symmetric charge distributions.
• Review of Monte Carlo methods for ground state calculations.
• Analysis of magnetic multipole interactions in nanomagnetic systems.

Conclusions:

• The review provides a unified perspective on multipole moment definitions and theoretical frameworks.
• It highlights the importance of multipole moments in diverse physical phenomena, from intermolecular forces to nanomagnetism.
• The study facilitates the use of published results and guides future theoretical and experimental investigations.