High School Students Simulate Domains in Random Magnets

The field of magnetic materials is amongst the most rapidly evolving areas of condensed matter physics, and has tremendous technological relevance. For example, the importance of the discovery of giant magnetoresistance materials, and their incorporation into modern electronics, was summarized in the 2007 New York Times headline “Physics of the iPod awarded Nobel Prize.” The objectives of the core research in the SSAA project of Profs. Curro, Pickett, and Scalettar (UC Davis, Physics) concern an investigation of several classes of magnetic materials- rare earths and their compounds, heavy fermions, and iron-pnictide superconductors. One project emphasis is on the effects of disorder.

In Summer 2018, eleven students in the class of Mr. Dubarrie Fagout of River City High School in West Sacramento, participated in this research in a paid internship in the Physics Department at UC Davis, under the sponsorship of the DOE SSAAP program and the Oak Ridge Institute for Science Education. Their goal was to develop codes, written in python, which examined the formation of magnetic regions around defects in a solid, and determine how those regions develop as the temperature is lowered and the strength and type of disorder are varied. The project began with tutorials on the python programming language and on the physics of magnetism led by UCD undergraduate students Miguel Alba and Mayra Sandoval.

One warm-up problem was the implementation of Conway’s ‘Game of Life’ in python. This game is the realization of Stanislaw Ulam and John von Neumann’s idea of cellular automata- iterative procedures which exhibit patterns with unpredictable emergent patterns. The programming of this problem has close algorithmic connections- the presence of a two dimensional grid of sites on which reside degrees of freedom which evolve in time under the influence of nearby sites- to the magnetic simulations which were the ultimate goal of the research project.

River City High School students Flora Cox, Xavier Garces, Ikaika Griffith, Naomi Mihov, Lucas Monteros, Tatiana Nikolaeva, Kevin Potesta, Aaron Quock, Haydee Vazquez Solorio, Alisha Vikash, and Anika Vikash were interns in the program.

The students’ computational approach to disordered magnetic materials involved setting up an inital array of magnetic moments, and then determining new directions on each site, based on the ‘exchange energies’ to its neighbors. Student-written python programs solved for the system’s properties by iterating the calculation of the new directions repeatedly. With these codes, the students were able to observe local magnetic “puddles” form in regions where the interactions between the moments are large, and then model how these puddles grow and merge as the temperature is reduced. Connections to current experiments on heavy fermion materials were emphasized. The figure below shows two snapshots of one of the interns’ simulations. At left, an initial random configuration is shown. Red squares denote strong ‘north poles’ (magnetic moments in the positive z direction) and blue squares strong ‘south poles (magnetic moments in the negative z direction). Other colors are intermediate values. By the end of the simulation (right) two large puddles dominate the magnetic landscape.

A full student-produced movie showing magnetic domain formation at one particular temperature and degree of disorder, starting from a random state, is available here: http://scalettar.physics.ucdavis.edu/magnetmovieT2dis01mix020.gif

As part of the internship, the students visited four UCD condensed matter laboratories: nuclear magnetic resonance (Prof. Curro), crystal growth (Prof. Taufour), photoemission spectroscopy (Prof. Vishik), and scanning tunneling microscopy (Prof. da Silva Neto). The host faculty emphasized connections of the interns’ project to modern magnetism research.

The program finished with a closing ceremony involving the students’ families and friends at which they presented the background, results and significance of their research.

We are especially grateful to Terri Stone and Marie Westfall for helping shepherd this program through the DOE educational offices.