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.

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.

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).

Selected Publications

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Disentangling superconducting and magnetic orders in NaFe1−xNixAs using muon spin rotation
Abstract: 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.
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Real-space investigation of short-range magnetic correlations in fluoride pyrochlores NaCaCo2F7 and NaSrCo2F7 with magnetic pair distribution function analysis
Abstract: We present time-of-flight neutron total scattering and polarized neutron scattering measurements of the magnetically frustrated compounds NaCaCo2F7 and NaSrCo2F7, 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.
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Local Orthorhombicity in the Magnetic C4 Phase of the Hole-Doped Iron-Arsenide Superconductor Sr1−xNaxFe2As2
Abstract: We report on temperature-dependent pair distribution function measurements of 
Sr
1
−
x
Na
x
Fe
2
As
2
, an iron-based superconductor system that contains a magnetic phase with reentrant tetragonal symmetry, known as the magnetic 
C
4
 phase. Quantitative refinements indicate that the instantaneous local structure in the 
C
4
 phase comprises fluctuating orthorhombic regions with a length scale of 
∼
2
 
 
nm
, despite the tetragonal symmetry of the average static structure. Additionally, local orthorhombic fluctuations exist on a similar length scale at temperatures well into the paramagnetic tetragonal phase. These results highlight the exceptionally large nematic susceptibility of iron-based superconductors and have significant implications for the magnetic 
C
4
 phase and the neighboring 
C
2
 and superconducting phases.
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Signatures of the topological s+− superconducting order parameter in the type-II Weyl semimetal Td-MoTe2
By B. A. Frandsen (et al.)
Abstract: In its orthorhombic T d polymorph, MoTe2 is a type-II Weyl semimetal, where the Weyl fermions emerge at the boundary between electron and hole pockets. Non-saturating magnetoresistance and superconductivity were also observed in T d-MoTe2. Understanding the superconductivity in T d-MoTe2, which was proposed to be topologically non-trivial, is of eminent interest. Here, we report high-pressure muon-spin rotation experiments probing the temperature-dependent magnetic penetration depth in T d-MoTe2. A substantial increase of the superfluid density and a linear scaling with the superconducting critical temperature T c is observed under pressure. Moreover, the superconducting order parameter in T d-MoTe2 is determined to have 2-gap s-wave symmetry. We also exclude time-reversal symmetry breaking in the superconducting state with zero-field μSR experiments. Considering the strong suppression of T c in MoTe2 by disorder, we suggest that topologically non-trivial s +− state is more likely to be realized in MoTe2 than the topologically trivial s ++ state.
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Pressure tuning of structure, superconductivity, and novel magnetic order in the Ce-underdoped electron-doped cuprate T′−Pr1.3−xLa0.7CexCuO4 (x=0.1)
By B. A. Frandsen (et al.)
Abstract: High-pressure neutron powder diffraction, muon-spin rotation, and magnetization studies of the structural, magnetic, and the superconducting properties of the Ce-underdoped superconducting (SC) electron-doped cuprate system with the 
Nd
2
CuO
4
 (the so-called 
T
′
) structure 
T
′
−
Pr
1.3
−
x
La
0.7
Ce
x
CuO
4
 with 
x
=
0.1
 are reported. A strong reduction of the in-plane and out-of-plane lattice constants is observed under pressure. However, no indication of any pressure-induced phase transition from 
T
′
 to the 
K
2
NiF
4
 (the so-called T) structure is observed up to the maximum applied pressure of 
p
 = 11 GPa. Large and nonlinear increase of the short-range magnetic order temperature 
T
so
 in 
T
′
−
Pr
1.3
−
x
La
0.7
Ce
x
CuO
4
 (
x
=
0.1
) was observed under pressure. Simultaneous pressure causes a nonlinear decrease of the SC transition temperature 
T
c
. All these experiments establish the short-range magnetic order as an intrinsic and competing phase in SC 
T
′
−
Pr
1.3
−
x
La
0.7
Ce
x
CuO
4
 (
x
=
0.1
). The observed pressure effects may be interpreted in terms of the improved nesting conditions through the reduction of the in-plane and out-of-plane lattice constants upon hydrostatic pressure.
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Uniaxial pressure effect on the magnetic ordered moment and transition temperatures in BaFe2−xTxAs2 (T=Co,Ni)
Abstract: We use neutron diffraction and muon spin relaxation to study the effect of in-plane uniaxial pressure on the antiferromagnetic (AF) orthorhombic phase in 
BaFe
2
As
2
 and its Co- and Ni-substituted members near optimal superconductivity. In the low-temperature AF ordered state, uniaxial pressure necessary to detwin the orthorhombic crystals also increases the magnetic ordered moment, reaching an 11% increase under 40 MPa for 
BaFe
1.9
Co
0.1
As
2
, and a 15% increase for 
BaFe
1.915
Ni
0.085
As
2
. We also observe an increase of the AF ordering temperature (
T
N
) of about 0.25 K/MPa in all compounds, consistent with density functional theory calculations that reveal better Fermi surface nesting for itinerant electrons under uniaxial pressure. The doping dependence of the magnetic ordered moment is captured by combining dynamical mean field theory with density functional theory, suggesting that the pressure-induced moment increase near optimal superconductivity is closely related to quantum fluctuations and the nearby electronic nematic phase.