Abstract
This thesis presents work done during my PhD jointly at the Niels Bohr Institute and
the European Spallation Source. The thesis can be divided into four parts: introduction,
magnetic nanoparticles, frustrated materials and superconductivity.
The rst part is an introduction to magnetism and neutron scattering. Here, the most
common types of magnetic order are described, and a short introduction to magnetic
frustration is given. Frustration occurs when the exchange interactions in a material cannot
be simultaneously satised, as is e.g. the case for a triangle of antiferromagnetically
coupled spins. This leads to absence of long range order even at very low temperatures
and to fascinating new states of matter.
Neutron scattering is the main experimental tool used in this thesis. The advantage
of neutron scattering is that the neutron is sensitive to both magnetic order and magnetic
dynamics, and it is thus perfect for studying magnetic materials.
Magnetic nanoparticles have properties that are quite dierent from their bulk counterparts.
The spin waves are quantized, so that only the lowest excitation, having q = 0,
is excited. This leads to phenomena such as superparamagnetism, in which all the spins
in the nanoparticle move coherently. One part of the thesis explores the structure and
dynamic of magnetic nanoparticles, with emphasis being placed on hematite. Hematite
has easy-axis and in-plane anisotropy, as well as being strongly antiferromagnetic. The
excitation energies have been derived analytically and compared with neutron scattering
experiments on 8 nm and 16 nm particles, validating the theory and determining the
magnitude of the anisotropy constants. In addition, the temperature dependence of the
excitations and of the superparamagnetism are explored using numerical simulations.
Through these simulations, a new mode, labeled the rotor mode, was discovered.
Goethite nanoparticles have only uniaxial anisotropy. Their magnetic dynamics were
explored using neutron scattering, and the anisotropy constant was determined.
Furthermore, the structure of NiO particles of various sizes was explored using polarized
neutron scattering. They are found to cant away from the (111) direction along
which bulk NiO orders.
Two magnetically frustrated compounds have been investigated in this thesis: Gd3Ga5O12
(GGG) and Gd3Al5O12 (GAG). They are structurally similar, but have slightly dierent
lattice spacing, leading to slightly dierent exchange and dipole interactions between the
spins. On both materials the magnetism rests on the s = 7=2 Gd3+ ions, which order
in two interpenetrating hyperkagome lattices. The hyperkagome lattice can be seen as
a three-dimensional analogue of the kagome lattice, as both consist of corner-sharing
triangles.
The phase diagram of GGG was explored using susceptibility measurements and
polarized neutron scattering. Several new phases were discovered, and their neutron
scattering signature determined. The zero eld structure was given particular attention
with the discovery of a hidden long range order, resting on loops of 10 spins. This
hidden order is quite unusual, as only groups of spins order, while individual spins
remain correlated only over short distances. The hidden order has been shown to also
be present in GAG, although the magnitude of the order parameter is smaller here.
The magnetic dynamics of GAG as function of applied magnetic eld were measured
using inelastic neutron scattering. The data showed the existence of a low energy mode
in zero eld, similar to what was discovered in GGG earlier. An applied magnetic eld
was found to sharpen the excitations, nally inducing a gap when the sample enters the
ferromagnetic state.
The dynamics of GGG were measured on the eV scale, showing how the spin
uctuations slow down with decreasing temperature, in agreement with previously published
Mossbauer spectroscopy measurements. The uctuations were found to be dispersionless,
which is indicative of the lack of conventional long range order in GGG.
Several members of the La2􀀀xSrxCuO4+y cuprate family of high-temperature superconductors
were investigated using neutron scattering. In La2􀀀xSrxCuO4 with x = 0:12
the correlations along the c-axis were investigated. It was found that quickly cooling the
sample (quenching) induced the same kind of short range correlations along the c-axis
as a strong applied magnetic eld.
Underdoped La2􀀀xSrxCuO4 with x = 0:07 was measured with a range of neutron
scattering instruments, investigating both the magnetic and nuclear dynamics. The
magnetic uctuations were found to be gapless, consistent with a pair-density-wave
type of order. Furthermore, measurements of the phonons indicated a lowering of the
symmetry from the low temperature orthorhombic phase to the low temperature less
orthorhombic phase.
A theoretical study of the pair-density-wave state was conducted and compared
to regular d-wave superconductivity. It was found that the pair-density-wave state
would have no superconducting resonance in neutron scattering experiments, thereby
conrming earlier experimental observations.
Several neutron scattering experiments on oxygen doped La2CuO4+y were performed,
with a number of interesting results. There was evidence of a small gap below 0.5 meV,
and the intensity of the uctuations above this energy was found to decrease with increasing
applied magnetic eld, contrary to expectations. The most likely explanation
is that the magnetic eld increases the correlations in the sample, thereby sharpening
the peaks. If the measurements were not at the center of the peaks, this eect would
lead to an apparent decrease in the peak intensity.
This experiment indicated that the inelastic peaks moved away from the positions of
the elastic peaks, which was conrmed with further neutron scattering experiments. An
apparent discontinuity in the dispersion of the dynamic stripes in the limit of vanishing
energy transfer was found in violation of Goldstone's theorem. Detailed simulations of
the experiment showed that this eect could not be explained by experimental nonidealities,
and must therefore be real. It was therefore concluded that the dynamic stripes are not the Goldstone modes associated with the broken symmetry of the static stripes. In other words, the dynamic and static signals originate in two dierent phases of the sample. This has wide-ranging consequences, as the Goldstone assumption is fundamental in most theoretical studies of spin dynamics in cuprate superconductors including the study mentioned above.
the European Spallation Source. The thesis can be divided into four parts: introduction,
magnetic nanoparticles, frustrated materials and superconductivity.
The rst part is an introduction to magnetism and neutron scattering. Here, the most
common types of magnetic order are described, and a short introduction to magnetic
frustration is given. Frustration occurs when the exchange interactions in a material cannot
be simultaneously satised, as is e.g. the case for a triangle of antiferromagnetically
coupled spins. This leads to absence of long range order even at very low temperatures
and to fascinating new states of matter.
Neutron scattering is the main experimental tool used in this thesis. The advantage
of neutron scattering is that the neutron is sensitive to both magnetic order and magnetic
dynamics, and it is thus perfect for studying magnetic materials.
Magnetic nanoparticles have properties that are quite dierent from their bulk counterparts.
The spin waves are quantized, so that only the lowest excitation, having q = 0,
is excited. This leads to phenomena such as superparamagnetism, in which all the spins
in the nanoparticle move coherently. One part of the thesis explores the structure and
dynamic of magnetic nanoparticles, with emphasis being placed on hematite. Hematite
has easy-axis and in-plane anisotropy, as well as being strongly antiferromagnetic. The
excitation energies have been derived analytically and compared with neutron scattering
experiments on 8 nm and 16 nm particles, validating the theory and determining the
magnitude of the anisotropy constants. In addition, the temperature dependence of the
excitations and of the superparamagnetism are explored using numerical simulations.
Through these simulations, a new mode, labeled the rotor mode, was discovered.
Goethite nanoparticles have only uniaxial anisotropy. Their magnetic dynamics were
explored using neutron scattering, and the anisotropy constant was determined.
Furthermore, the structure of NiO particles of various sizes was explored using polarized
neutron scattering. They are found to cant away from the (111) direction along
which bulk NiO orders.
Two magnetically frustrated compounds have been investigated in this thesis: Gd3Ga5O12
(GGG) and Gd3Al5O12 (GAG). They are structurally similar, but have slightly dierent
lattice spacing, leading to slightly dierent exchange and dipole interactions between the
spins. On both materials the magnetism rests on the s = 7=2 Gd3+ ions, which order
in two interpenetrating hyperkagome lattices. The hyperkagome lattice can be seen as
a three-dimensional analogue of the kagome lattice, as both consist of corner-sharing
triangles.
The phase diagram of GGG was explored using susceptibility measurements and
polarized neutron scattering. Several new phases were discovered, and their neutron
scattering signature determined. The zero eld structure was given particular attention
with the discovery of a hidden long range order, resting on loops of 10 spins. This
hidden order is quite unusual, as only groups of spins order, while individual spins
remain correlated only over short distances. The hidden order has been shown to also
be present in GAG, although the magnitude of the order parameter is smaller here.
The magnetic dynamics of GAG as function of applied magnetic eld were measured
using inelastic neutron scattering. The data showed the existence of a low energy mode
in zero eld, similar to what was discovered in GGG earlier. An applied magnetic eld
was found to sharpen the excitations, nally inducing a gap when the sample enters the
ferromagnetic state.
The dynamics of GGG were measured on the eV scale, showing how the spin
uctuations slow down with decreasing temperature, in agreement with previously published
Mossbauer spectroscopy measurements. The uctuations were found to be dispersionless,
which is indicative of the lack of conventional long range order in GGG.
Several members of the La2􀀀xSrxCuO4+y cuprate family of high-temperature superconductors
were investigated using neutron scattering. In La2􀀀xSrxCuO4 with x = 0:12
the correlations along the c-axis were investigated. It was found that quickly cooling the
sample (quenching) induced the same kind of short range correlations along the c-axis
as a strong applied magnetic eld.
Underdoped La2􀀀xSrxCuO4 with x = 0:07 was measured with a range of neutron
scattering instruments, investigating both the magnetic and nuclear dynamics. The
magnetic uctuations were found to be gapless, consistent with a pair-density-wave
type of order. Furthermore, measurements of the phonons indicated a lowering of the
symmetry from the low temperature orthorhombic phase to the low temperature less
orthorhombic phase.
A theoretical study of the pair-density-wave state was conducted and compared
to regular d-wave superconductivity. It was found that the pair-density-wave state
would have no superconducting resonance in neutron scattering experiments, thereby
conrming earlier experimental observations.
Several neutron scattering experiments on oxygen doped La2CuO4+y were performed,
with a number of interesting results. There was evidence of a small gap below 0.5 meV,
and the intensity of the uctuations above this energy was found to decrease with increasing
applied magnetic eld, contrary to expectations. The most likely explanation
is that the magnetic eld increases the correlations in the sample, thereby sharpening
the peaks. If the measurements were not at the center of the peaks, this eect would
lead to an apparent decrease in the peak intensity.
This experiment indicated that the inelastic peaks moved away from the positions of
the elastic peaks, which was conrmed with further neutron scattering experiments. An
apparent discontinuity in the dispersion of the dynamic stripes in the limit of vanishing
energy transfer was found in violation of Goldstone's theorem. Detailed simulations of
the experiment showed that this eect could not be explained by experimental nonidealities,
and must therefore be real. It was therefore concluded that the dynamic stripes are not the Goldstone modes associated with the broken symmetry of the static stripes. In other words, the dynamic and static signals originate in two dierent phases of the sample. This has wide-ranging consequences, as the Goldstone assumption is fundamental in most theoretical studies of spin dynamics in cuprate superconductors including the study mentioned above.
| Original language | English |
|---|
| Publisher | The Niels Bohr Institute, Faculty of Science, University of Copenhagen |
|---|---|
| Publication status | Published - 2016 |