Welcome to the Frandsen Group!

About the Group

We are an experimental condensed matter physics group focused on investigating the structure and magnetism of fascinating--and often technologically promising--materials, such as superconductors, strongly correlated electron systems, multiferroics, magnetocalorics, molten salts for nuclear reactors, and more. We use beams of neutrons, x-rays, and muons produced at large-scale accelerator facilities to probe the atomic and magnetic correlations in these materials, together with advanced computational modeling to gain quantitative insight into the spatial arrangement of atoms and spins in a given material. Specific techniques include atomic and magnetic pair distribution function (PDF) analysis of neutron/x-ray total scattering data and muon spin relaxation/rotation (μSR). Interested and motivated undergraduate and prospective graduate students are encouraged to reach out to learn more about our research and find opportunities to participate.

Research Projects

Thermoelectrics, Magnetocalorics, and Multiferroics--Oh My!

This project focuses on the connection between the local atomic and magnetic structure and the energy-relevant properties of magnetocaloric, thermoelectric, and multiferroic materials. Magnetocaloric materials exhibit large temperature changes with the application and removal of a magnetic field, offering promising applications in solid-state refrigeration and waste heat harvesting. Thermoelectric materials experience an electrical voltage when subjected to a temperature gradient or vice versa, also providing novel routes for energy-efficient cooling and waste heat harvesting. Multiferroic materials show cross-order coupling between electric polarization and magnetic order, potentially enabling unique functionalities for energy transformation, information science, and signal processing. We are using combined atomic and magnetic pair distribution function analysis, together with muon spin spectroscopy, to establish the local atomic and magnetic structure of representative compounds for these material classes and better understand the origin of their outstanding properties. In the process, we are developing new experimental and computational methods for magnetic pair distribution function analysis, which will be widely applicable to many other materials, as well. Funding: US Department of Energy, Early Career program.

Molten Salts For Improved Nuclear Reactors

Molten salt reactors (MSRs) are a promising nuclear reactor design concept in which molten ionic salts function as the coolant and/or fuel source in the reactor. MSRs have many potential advantages over standard designs in commercial use today, including greatly enhanced safety/security and the ability to produce critical medical radioisotopes in addition to vast amounts of carbon-free electricity. To make MSRs a reality, it is necessary to understand and predict the behavior of the salts in operating conditions. Gaining a detailed knowledge of the local structure of the molten salts on the atomic scale is an essential step in this direction, since the local interactions between constituent atoms determine the macroscopic properties. In this project, we use cutting-edge neutron and x-ray total scattering and computational modeling techniques to establish the structure of relevant molten salts. We work closely with collaborators in BYU Chemical Engineering. Funding: US Department of Energy, Nuclear Energy University Program (pending).

Superconductors, Geometrically Frustrated Magnets, Magnetic Nanoparticles, and More

We maintain broad interest and involvement in structural studies of numerous material systems where knowledge of the local atomic and magnetic structure can add value. We have ongoing projects on iron-based superconductors, geometrically frustrated triangular lattice antiferromagnets, magnetic nanoparticles, Mott insulator systems, high-entropy alloys and oxides, and more. We are always open to collaborations on interesting material systems.

Selected Publications

Local and long-range atomic/magnetic structure of non-stoichiometric spinel iron oxide nanocrystallites

BYU Authors: Benjamin A. Frandsen, published in IUCrJ

Spinel iron oxide nanoparticles of different mean sizes in the range 10–25 nm have been prepared by surfactant-free up-scalable near- and super-critical hydrothermal synthesis pathways and characterized using a wide range of advanced structural characterization methods to provide a highly detailed structural description. The atomic structure is examined by combined Rietveld analysis of synchrotron powder X-ray diffraction (PXRD) data and time-of-flight neutron powder-diffraction (NPD) data. The local atomic ordering is further analysed by pair distribution function (PDF) analysis of both X-ray and neutron total-scattering data. It is observed that a non-stoichiometric structural model based on a tetragonal γ-Fe2O3 phase with vacancy ordering in the structure (space group P43212) yields the best fit to the PXRD and total-scattering data. Detailed peak-profile analysis reveals a shorter coherence length for the superstructure, which may be attributed to the vacancy-ordered domains being smaller than the size of the crystallites and/or the presence of anti-phase boundaries, faulting or other disorder effects. The intermediate stoichiometry between that of γ-Fe2O3 and Fe3O4 is confirmed by refinement of the Fe/O stoichiometry in the scattering data and quantitative analysis of Mössbauer spectra. The structural characterization is complemented by nano/micro-structural analysis using transmission electron microscopy (TEM), elemental mapping using scanning TEM, energy-dispersive X-ray spectroscopy and the measurement of macroscopic magnetic properties using vibrating sample magnetometry. Notably, no evidence is found of a Fe3O4/γ-Fe2O3 core-shell nanostructure being present, which had previously been suggested for non-stoichiometric spinel iron oxide nanoparticles. Finally, the study is concluded using the magnetic PDF (mPDF) method to model the neutron total-scattering data and determine the local magnetic ordering and magnetic domain sizes in the iron oxide nanoparticles. The mPDF data analysis reveals ferrimagnetic collinear ordering of the spins in the structure and the magnetic domain sizes to be ∼60–70% of the total nanoparticle sizes. The present study is the first in which mPDF analysis has been applied to magnetic nanoparticles, establishing a successful precedent for future studies of magnetic nanoparticles using this technique.

Spin dynamics and a nearly continuous magnetic phase transition in an entropy-stabilized oxide antiferromagnet

BYU Authors: Benjamin A. Frandsen, K. Alec Petersen, Nicolas A. Ducharme, Alexander G. Shaw, and Ethan J. Gibson, published in Phys. Rev. Materials

The magnetic order and the spin dynamics in the antiferromagnetic entropy-stabilized oxide (Mg_0.2Co_0.2Ni_0.2Cu_0.2Zn_0.2)O (MgO-ESO) have been studied using muon spin relaxation (μ SR) and inelastic neutron scattering. We find that antiferromagnetic order develops gradually in the sample volume as it is cooled below 140 K, becoming fully ordered around 100 K. The spin dynamics show a critical slowing down in the vicinity of the transition, and the magnetic order parameter grows continuously in the ordered state. These results indicate that the antiferromagnetic transition is continuous but proceeds with a Gaussian distribution of ordering temperatures. The magnetic contribution to the specific heat determined from inelastic neutron scattering likewise shows a broad feature centered around 120 K. High-resolution inelastic neutron scattering further reveals an initially gapped spectrum at low temperature which sees an increase in a quasielastic contribution upon heating until the ordering temperature.

Structural, magnetic, and electronic evolution of the spin-ladder system BaFe₂S_3−xSe_x with isoelectronic substitution

BYU Authors: Benjamin A. Frandsen, published in Phys. Rev. B

We report experimental studies of a series of BaFe₂S_3−xSe_x (0≤x≤3) single crystals and powder specimens using x-ray diffraction, neutron-diffraction, muon-spin-relaxation, and electrical transport measurements. A structural transformation from Cmcm (BaFe₂S₃) to Pnma (BaFe₂Se₃) was identified around x=0.7−1. Neutron-diffraction measurements on the samples with x=0.2, 0.4, and 0.7 reveal that the Néel temperature of the stripe antiferromagnetic order is gradually suppressed from ∼120 to 85 K, while the magnitude of the ordered Fe²⁺ moments shows very little variation. Similarly, the block antiferromagnetic order in BaFe₂Se₃ remains robust for 1.5≤x≤3 with negligible variation in the ordered moment and a slight decrease of the Néel temperature from 250 K (x=3) to 225 K (x=1.5). The sample with x=1 near the Cmcm and Pnma border shows coexisting, two-dimensional, short-range stripe- and block-type antiferromagnetic correlations. The system remains insulating for all x, but the thermal activation gap shows an abrupt increase when traversing the boundary from the Cmcm stripe phase to the Pnma block phase. The results demonstrate that the crystal structure, magnetic order, and electronic properties are strongly coupled in the BaFe₂S_3−xSe_x system.

Nonsuperconducting electronic ground state in pressurized BaFe₂S₃ and BaFe₂S_2.5Se_0.5

BYU Authors: Benjamin A. Frandsen, published in Phys. Rev. B

We report a comprehensive study of the spin ladder compound BaFe₂S_2.5Se_0.5 using neutron diffraction, inelastic neutron scattering, high pressure synchrotron diffraction, and high pressure transport techniques. We find that BaFe₂S_2.5Se_0.5 possesses the same C_mcm structure and stripe antiferromagnetic order as does BaFe₂S₃, but with a reduced Néel temperature of T_N=98 K compared to 120 K for the undoped system, and a slightly increased ordered moment of 1.40μB per iron. The low-energy spin excitations in BaFe₂S_2.5Se_0.5 are likewise similar to those observed in BaFe₂S₃. However, unlike the reports of superconductivity in BaFe₂S₃ below Tc∼14 K under pressures of 10 GPa or more, we observe no superconductivity in BaFe₂S_2.5Se_0.5 at any pressure up to 19.7 GPa. In contrast, the resistivity exhibits an upturn at low temperature under pressure. Furthermore, we show that additional high-quality samples of BaFe₂S₃ synthesized for this study likewise fail to become superconducting under pressure, instead displaying a similar upturn in resistivity at low temperature. These results demonstrate that microscopic, sample-specific details play an important role in determining the ultimate electronic ground state in this spin ladder system. We suggest that the upturn in resistivity at low temperature in both BaFe₂S₃ and BaFe₂S_2.5Se_0.5 may result from Anderson localization induced by S vacancies and random Se substitutions, enhanced by the quasi-one-dimensional ladder structure.

The structure of molten FLiNaK

BYU Authors: Benjamin A. Frandsen, Stella D. Nickerson, Austin D. Clark, Andrew Solano, Raju Baral, Johnny Williams, and Matthew Memmott, published in J. Nucl. Mater.

The structure of the molten salt (LiF)0.465(NaF)0.115(KF)0.42 (FLiNaK), a potential coolant for molten salt nuclear reactors, has been studied by ab initio molecular dynamics simulations and neutron total scattering experiments. We find that the salt retains well-defined short-range structural correlations out to approximately 9 Å at typical reactor operating temperatures. The experimentally determined pair distribution function can be described with quantitative accuracy by the molecular dynamics simulations. These results indicate that the essential ionic interactions are properly captured by the simulations, providing a launching point for future studies of FLiNaK and other molten salts for nuclear reactor applications.

Observation of a C -type short-range antiferromagnetic order in layer spacing expanded FeS

BYU Authors: Benjamin A. Frandsen, published in Phys. Rev. Materials

We report neutron diffraction studies of FeS single crystals obtained from Rb_xFe₂−yS₂ single crystals via a hydrothermal method. While no √5×√5 iron vacancy order or block antiferromagnetic order typical of Rb_xFe_2−yS₂ is found in our samples, we observe C-type short range antiferromagnetic order with moments pointed along the c-axis hosted by a new phase of FeS with an expanded inter-layer spacing. The N'{e}el temperature for this magnetic order is determined to be 170±4 K. Our finding of a variant FeS structure hosting this C-type antiferromagnetic order demonstrates that the known FeS phase synthesized in this method is in the vicinity of a magnetically ordered ground state, providing insights into understanding a variety of phenomena observed in FeS and the related FeSe_1−xS_x iron chalcogenide system.