Undergraduate Research

Magnetic Behavior of Diluted Hexaferrites

Dr. Thomas Vojta & Dr. Julia Medvedeva · August 2017 – May 2019

Hexaferrites such as BaFe₁₂O₁₉, SrFe₁₂O₁₉, and PbFe₁₂O₁₉ are ferrimagnets with Néel temperatures around 720 K, used in everything from magnetic stripes and barcodes to small motors and microwave devices. Substituting non-magnetic gallium for iron in PbFe_12−xGa_xO₁₉ suppresses the ordering temperature, and experiments show it following a 2/3 power law, T_N ∼ (1 − x/x_c)^2/3, over the entire temperature range, which is unexpected. Our goal was to understand where the shape of this phase boundary comes from.

What I did

• Performed realistic Monte Carlo simulations of diluted hexaferrites: a Heisenberg model on the real crystal structure, with exchange interactions calculated from first principles, using Wolff and Metropolis updates.
• Programmed parallelized code to run large-scale simulations, up to 40³ double unit cells (1,536,000 spins), averaged over many disorder configurations.
• Located the critical temperatures from Binder cumulant crossings and mapped the ferrimagnetic–paramagnetic phase boundary.
• Compared against a simple site-diluted cubic lattice model (up to 80³ = 512,000 spins).

What we found

The critical concentration x_c agrees with percolation theory. But neither the leading, unfrustrated interactions nor added sub-leading, frustrated interactions reproduce the experimental 2/3 power law, and on the cubic lattice we found an exponent close to 1. A simple magnetic percolation picture doesn't explain the phase boundary, which leaves room for other effects: a non-uniform distribution of the Ga ions, interplay between magnetism and ferroelectricity, or dilution-dependent interactions.

Presentations & awards

• APS March Meeting 2018 (Los Angeles) and 2019 (Boston)
• Missouri Undergraduate Research Day at the Capitol, 2019: presented "Disorder and Dynamics of Quantum Materials" to state legislators
• Missouri S&T Fuller Poster Competition: 1st place (47th annual) and runner-up (48th annual)

Publications

• L. Sowadski, S. Anderson, C. Lerch, J. Medvedeva, T. Vojta, "Magnetic Properties of Diluted Hexaferrites," Phys. Rev. B 110, 014432 (2024)
• G. Khairnar, C. Lerch, T. Vojta, "Phase Boundary Near a Magnetic Percolation Transition," Eur. Phys. J. B 94, 43 (2021)

Diffraction Gratings and the Orbital Angular Momentum of Light

Dr. Daniel Fischer · Laboratory for Atomic, Molecular, and Optical Research (LAMOR) · January 2017 – May 2018

• Worked with Dr. Fischer on a variety of research in his Laboratory for Atomic, Molecular, and Optical Research.
• Gained hands-on experience with high-powered lasers and optics.
• Investigated orbital angular momentum and how this optical property could be used in other areas of Dr. Fischer's research.
• Used a laser, a light modulator, a camera, and various optics to measure how different diffraction gratings affected the output intensity and beam profile of the laser light.
• Used MATLAB to generate and fine-tune the diffraction gratings displayed on the light modulator.

Superfluid Density and Compressibility at the Superfluid–Mott Glass Transition

Dr. Thomas Vojta · August 2016 – August 2017

• Assisted Dr. Vojta with his research on quantum phase transitions, focusing on the transition from an insulator to a superfluid.
• Incorporated the stiffness parameter into several existing models of this phase transition.
• Used the Pegasus IV high-performance cluster to run large system sizes and generate data.
• Plotted and fit the data in gnuplot to extract the value of the stiffness.

Publications & presentations

• C. Lerch, T. Vojta, "Superfluid Density and Compressibility at the Superfluid–Mott Glass Transition," Eur. Phys. J. Special Topics 227, 2275 (2019)
• J. Crewse, C. Lerch, T. Vojta, "Quantum Critical Behavior of a Three-Dimensional Superfluid–Mott Glass Transition," Phys. Rev. B 98, 054514 (2018)
• APS March Meeting 2018, Los Angeles