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.

Promoting Many-Body Quantum Entanglement in Geometrically Frustrated Magnets with Disorder

Quantum information technologies rely on quantum entanglement, or the intrinsic linking of one quantum object to another. An important research objective is to gain a fundamental understanding of many-body quantum entanglement involving large numbers of quantum objects. Certain magnetic materials known as geometrically frustrated magnets provide a valuable platform for this topic of study because they may exhibit many-body-entanglement at low temperature. This project advances the search for promising quantum-entangled frustrated magnets through a systematic investigation of the role of atomic-scale disorder in promoting or hindering many-body entanglement. The results illuminate strategies for utilizing disorder to promote quantum-entangled ground states and contribute to a deeper understanding of many-body quantum entanglement in general. Funding: US National Science Foundation LEAPS Program.

Novel magnets, Magnetic Nanoparticles, Metal-Insulator Transitions, High-Entropy Materials, 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 novel magnets such as altermagnets and low-dimensional magnets, magnetic nanoparticles, Mott insulator systems and materials with metal-insulator transitions, high-entropy alloys and oxides, and more. We are always open to collaborations on interesting material systems.

Selected Publications

Widespread orthorhombic fluctuations in the (Sr,Na)Fe₂As₂ family of superconductors

Benjamin A. Frandsen (et al.)

We report comprehensive pair distribution function measurements of the hole-doped iron-based superconductor system Sr_1−xNa_xFe₂As₂. Structural refinements performed as a function of temperature and length scale reveal orthorhombic distortions of the instantaneous local structure across a large region of the phase diagram possessing average tetragonal symmetry, indicative of fluctuating nematicity. These nematic fluctuations are present up to high doping levels (x ≳ 0.48, near optimal superconductivity) and high temperatures (above room temperature for x = 0, decreasing to 150 K for x = 0.48), with a typical length scale of 1–3 nm. This work highlights the ubiquity of nematic fluctuations in a representative iron-based superconductor and provides important details about the evolution of these fluctuations across the phase diagram.

Gradual enhancement of stripe-type antiferromagnetism in the spin-ladder material BaFe₂S₃ under pressure

Benjamin A. Frandsen (et al.)

We report pressure-dependent neutron diffraction and muon spin relaxation/rotation measurements combined with first-principles calculations to investigate the structural, magnetic, and electronic properties of BaFe₂S₃ under pressure. The experimental results reveal a gradual enhancement of the stripe-type ordering temperature with increasing pressure up to 2.6 GPa and no observable change in the size of the ordered moment. The ab initio calculations suggest that the magnetism is highly sensitive to the Fe-S bond lengths and angles, clarifying discrepancies with previously published results. In contrast to our experimental observations, the calculations predict a monotonic reduction of the ordered moment with pressure. We suggest that the robustness of the stripe-type antiferromagnetism is due to strong electron correlations not fully considered in the calculations.

Spectral Evidence for Emergent Order in Ba_1−xNa_xFe₂As₂

B. A. Frandsen (et al.)

We report an angle-resolved photoemission spectroscopy study of the iron-based superconductor family, Ba1−xNaxFe2As2. This system harbors the recently discovered double-Q magnetic order appearing in a reentrant C4 phase deep within the underdoped regime of the phase diagram that is otherwise dominated by the coupled nematic phase and collinear antiferromagnetic order. From a detailed temperature-dependence study, we identify the electronic response to the nematic phase in an orbital-dependent band shift that strictly follows the rotational symmetry of the lattice and disappears when the system restores C4 symmetry in the low temperature phase. In addition, we report the observation of a distinct electronic reconstruction that cannot be explained by the known electronic orders in the system.

μSR study of spin freezing and persistent spin dynamics in NaCaNi₂F₇

B A Frandsen (et al.)

A new pyrochlore compound, NaCaNi2F7, was recently synthesized and has a single magnetic site with spin-1 Ni2+ . We present zero field and longitudinal field muon spin rotation (μSR) measurements on this pyrochlore. Density functional theory calculations show that the most likely muon site is located between two fluorine ions, but off-centre. A characteristic F-μ-F muon spin polarization function is observed at high temperatures where Ni spin fluctuations are sufficiently rapid. The Ni2+ spins undergo spin freezing into a disordered ground state below 4 K, with a characteristic internal field strength of 140 G. Persistent Ni spin dynamics are present to our lowest temperatures (75 mK), a feature characteristic of many geometrically frustrated magnetic systems.

Disentangling superconducting and magnetic orders in NaFe_1−xNi_xAs using muon spin rotation

Benjamin A. Frandsen (et al.)

Muon spin rotation and relaxation studies have been performed on a “111” family of iron-based superconductors,
NaFe1−xNixAs, using single crystalline samples with Ni concentrations x = 0, 0.4, 0.6, 1.0, 1.3, and
1.5%. Static magnetic order was characterized by obtaining the temperature and doping dependences of the local
ordered magnetic moment size and the volume fraction of the magnetically ordered regions. For x = 0 and 0.4%,
a transition to a nearly-homogeneous long range magnetically ordered state is observed, while for x 0.4%
magnetic order becomes more disordered and is completely suppressed for x = 1.5%. The magnetic volume
fraction continuously decreases with increasing x.Development of superconductivity in the full volume is inferred
fromMeissner shielding results for x 0.4%.The combination ofmagnetic and superconducting volumes implies
that a spatially-overlapping coexistence of magnetism and superconductivity spans a large region of the T -x
phase diagram for NaFe1−xNixAs. A strong reduction of both the ordered moment size and the volume fraction is
observed below the superconducting TC for x = 0.6, 1.0, and 1.3%, in contrast to other iron pnictides in which one
of these two parameters exhibits a reduction below TC, but not both. The suppression of magnetic order is further
enhanced with increased Ni doping, leading to a reentrant nonmagnetic state belowTC for x = 1.3%. The reentrant
behavior indicates an interplay between antiferromagnetism and superconductivity involving competition for the
same electrons. These observations are consistent with the sign-changing s
± superconducting state, which is
expected to appear on the verge of microscopic coexistence and phase separation with magnetism. We also
present a universal linear relationship between the local ordered moment size and the antiferromagnetic ordering
temperature TN across a variety of iron-based superconductors.We argue that this linear relationship is consistent
with an itinerant-electron approach, in which Fermi surface nesting drives antiferromagnetic ordering. In studies
of superconducting properties, we find that the T = 0 limit of superfluid density follows the linear trend observed
in underdoped cuprates when plotted against TC. This paper also includes a detailed theoretical prediction of the
muon stopping sites and provides comparisons with experimental results.

Real-space investigation of short-range magnetic correlations in fluoride pyrochlores NaCaCo₂F₇ and NaSrCo₂F₇ with magnetic pair distribution function analysis

Benjamin A. Frandsen (et al.)

We present time-of-flight neutron total scattering and polarized neutron scattering measurements of the magnetically frustrated compounds

{NaCaCo}_{2} F_{7}

and

{NaSrCo}_{2} F_{7}

, which belong to a class of recently discovered pyrochlore compounds based on transition metals and fluorine. The magnetic pair distribution function (mPDF) technique is used to analyze and model the total scattering data in real space. We find that a previously proposed model of short-range XY-like correlations with a length scale of 10–15 Å, combined with nearest-neighbor collinear antiferromagnetic correlations, accurately describes the mPDF data at low temperature, confirming the magnetic ground state in these materials. This model is further verified by the polarized neutron scattering data. From an analysis of the temperature dependence of the mPDF and polarized neutron scattering data, we find that short-range correlations persist on the nearest-neighbor length scale up to 200 K, approximately two orders of magnitude higher than the spin freezing temperatures of these compounds. These results highlight the opportunity presented by these new pyrochlore compounds to study the effects of geometric frustration at relatively high temperatures, while also advancing the mPDF technique and providing an opportunity to investigate a genuinely short-range-ordered magnetic ground state directly in real space.