TY - BOOK

T1 - Complex Magnetic Systems Studied with Neutron Scattering

AU - Jacobsen, Henrik

PY - 2016

Y1 - 2016

N2 - This thesis presents work done during my PhD jointly at the Niels Bohr Institute andthe 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 mostcommon types of magnetic order are described, and a short introduction to magneticfrustration is given. Frustration occurs when the exchange interactions in a material cannotbe simultaneously satised, as is e.g. the case for a triangle of antiferromagneticallycoupled spins. This leads to absence of long range order even at very low temperaturesand to fascinating new states of matter.Neutron scattering is the main experimental tool used in this thesis. The advantageof neutron scattering is that the neutron is sensitive to both magnetic order and magneticdynamics, 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 spinsin the nanoparticle move coherently. One part of the thesis explores the structure anddynamic of magnetic nanoparticles, with emphasis being placed on hematite. Hematitehas easy-axis and in-plane anisotropy, as well as being strongly antiferromagnetic. Theexcitation energies have been derived analytically and compared with neutron scatteringexperiments on 8 nm and 16 nm particles, validating the theory and determining themagnitude of the anisotropy constants. In addition, the temperature dependence of theexcitations 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 wereexplored using neutron scattering, and the anisotropy constant was determined.Furthermore, the structure of NiO particles of various sizes was explored using polarizedneutron scattering. They are found to cant away from the (111) direction alongwhich 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 dierentlattice spacing, leading to slightly dierent exchange and dipole interactions between thespins. On both materials the magnetism rests on the s = 7=2 Gd3+ ions, which orderin two interpenetrating hyperkagome lattices. The hyperkagome lattice can be seen asa three-dimensional analogue of the kagome lattice, as both consist of corner-sharingtriangles.The phase diagram of GGG was explored using susceptibility measurements andpolarized neutron scattering. Several new phases were discovered, and their neutronscattering signature determined. The zero eld structure was given particular attentionwith the discovery of a hidden long range order, resting on loops of 10 spins. Thishidden order is quite unusual, as only groups of spins order, while individual spinsremain correlated only over short distances. The hidden order has been shown to alsobe 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 measuredusing inelastic neutron scattering. The data showed the existence of a low energy modein zero eld, similar to what was discovered in GGG earlier. An applied magnetic eldwas found to sharpen the excitations, nally inducing a gap when the sample enters theferromagnetic 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 publishedMossbauer 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 superconductorswere investigated using neutron scattering. In La2􀀀xSrxCuO4 with x = 0:12the correlations along the c-axis were investigated. It was found that quickly cooling thesample (quenching) induced the same kind of short range correlations along the c-axisas a strong applied magnetic eld.Underdoped La2􀀀xSrxCuO4 with x = 0:07 was measured with a range of neutronscattering instruments, investigating both the magnetic and nuclear dynamics. Themagnetic uctuations were found to be gapless, consistent with a pair-density-wavetype of order. Furthermore, measurements of the phonons indicated a lowering of thesymmetry from the low temperature orthorhombic phase to the low temperature lessorthorhombic phase.A theoretical study of the pair-density-wave state was conducted and comparedto regular d-wave superconductivity. It was found that the pair-density-wave statewould have no superconducting resonance in neutron scattering experiments, therebyconrming 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 increasingapplied magnetic eld, contrary to expectations. The most likely explanationis that the magnetic eld increases the correlations in the sample, thereby sharpeningthe peaks. If the measurements were not at the center of the peaks, this eect wouldlead to an apparent decrease in the peak intensity.This experiment indicated that the inelastic peaks moved away from the positions ofthe elastic peaks, which was conrmed with further neutron scattering experiments. Anapparent discontinuity in the dispersion of the dynamic stripes in the limit of vanishingenergy transfer was found in violation of Goldstone's theorem. Detailed simulations ofthe 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.

AB - This thesis presents work done during my PhD jointly at the Niels Bohr Institute andthe 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 mostcommon types of magnetic order are described, and a short introduction to magneticfrustration is given. Frustration occurs when the exchange interactions in a material cannotbe simultaneously satised, as is e.g. the case for a triangle of antiferromagneticallycoupled spins. This leads to absence of long range order even at very low temperaturesand to fascinating new states of matter.Neutron scattering is the main experimental tool used in this thesis. The advantageof neutron scattering is that the neutron is sensitive to both magnetic order and magneticdynamics, 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 spinsin the nanoparticle move coherently. One part of the thesis explores the structure anddynamic of magnetic nanoparticles, with emphasis being placed on hematite. Hematitehas easy-axis and in-plane anisotropy, as well as being strongly antiferromagnetic. Theexcitation energies have been derived analytically and compared with neutron scatteringexperiments on 8 nm and 16 nm particles, validating the theory and determining themagnitude of the anisotropy constants. In addition, the temperature dependence of theexcitations 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 wereexplored using neutron scattering, and the anisotropy constant was determined.Furthermore, the structure of NiO particles of various sizes was explored using polarizedneutron scattering. They are found to cant away from the (111) direction alongwhich 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 dierentlattice spacing, leading to slightly dierent exchange and dipole interactions between thespins. On both materials the magnetism rests on the s = 7=2 Gd3+ ions, which orderin two interpenetrating hyperkagome lattices. The hyperkagome lattice can be seen asa three-dimensional analogue of the kagome lattice, as both consist of corner-sharingtriangles.The phase diagram of GGG was explored using susceptibility measurements andpolarized neutron scattering. Several new phases were discovered, and their neutronscattering signature determined. The zero eld structure was given particular attentionwith the discovery of a hidden long range order, resting on loops of 10 spins. Thishidden order is quite unusual, as only groups of spins order, while individual spinsremain correlated only over short distances. The hidden order has been shown to alsobe 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 measuredusing inelastic neutron scattering. The data showed the existence of a low energy modein zero eld, similar to what was discovered in GGG earlier. An applied magnetic eldwas found to sharpen the excitations, nally inducing a gap when the sample enters theferromagnetic 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 publishedMossbauer 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 superconductorswere investigated using neutron scattering. In La2􀀀xSrxCuO4 with x = 0:12the correlations along the c-axis were investigated. It was found that quickly cooling thesample (quenching) induced the same kind of short range correlations along the c-axisas a strong applied magnetic eld.Underdoped La2􀀀xSrxCuO4 with x = 0:07 was measured with a range of neutronscattering instruments, investigating both the magnetic and nuclear dynamics. Themagnetic uctuations were found to be gapless, consistent with a pair-density-wavetype of order. Furthermore, measurements of the phonons indicated a lowering of thesymmetry from the low temperature orthorhombic phase to the low temperature lessorthorhombic phase.A theoretical study of the pair-density-wave state was conducted and comparedto regular d-wave superconductivity. It was found that the pair-density-wave statewould have no superconducting resonance in neutron scattering experiments, therebyconrming 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 increasingapplied magnetic eld, contrary to expectations. The most likely explanationis that the magnetic eld increases the correlations in the sample, thereby sharpeningthe peaks. If the measurements were not at the center of the peaks, this eect wouldlead to an apparent decrease in the peak intensity.This experiment indicated that the inelastic peaks moved away from the positions ofthe elastic peaks, which was conrmed with further neutron scattering experiments. Anapparent discontinuity in the dispersion of the dynamic stripes in the limit of vanishingenergy transfer was found in violation of Goldstone's theorem. Detailed simulations ofthe 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.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99121947995305763

M3 - Ph.D. thesis

BT - Complex Magnetic Systems Studied with Neutron Scattering

PB - The Niels Bohr Institute, Faculty of Science, University of Copenhagen

ER -