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Abstract
In this thesis the magnetic excitations in six low dimensional quantum magnets are investigated using inelastic neutron scattering complemented with thermodynamic measurements, such as magnetic susceptibility and specific heat.
•Cu(DCOO)2•4D2O (CFTD) is a twodimensional S = 1/2 antiferromagnet on a square lattice. It is well established that in the lowtemperature limit CFTD exhibits an anomaly in its spin excitation spectrum at short wavelengths on zone boundary. In the vicinity of the (π; 0) the onemagnon excitation exhibits depression in energy, is strongly damped and attenuated. In particular, the attenuated spectral weight is transferred to an isotropic continuum of excitations extending to high energies. The origin of the anomaly is still under debate, particularly in relation to the existence of spinons in two dimensions. Here we present a study on the thermal evolution of the (π; 0) anomaly up to finite temperatures T/J ∼ 2/3. Our data reveal that the anomaly survives even in the absence of longrange, threedimensional order and that it is thus a feature closely related to the twodimensional S = 1/2 antiferromagnet on a square lattice. With further increase of temperature, the (π; 0) anomaly is washed out as the zoneboundary excitations gradually softens and dampens. This is confirmed by a comparison of our data with a finite temperature Quantum Monte Carlo calculation where a good accord is found.•It is wellestablished that, theoretically, magnons in a twodimensional antiferromagnet on a square lattice exhibit spontaneous decays at high fields due to the nonzero interaction between the onemagnon branch and the twomagnon continuum. Such a decay of magnons has already been observed in a classical spin system. But the experimental evidence for magnon decays in a quantum case S = 1/2 is absent. Here we present the results of inelastic neutron scattering experiments and higherorder spin wave calculations on (5CAP)_{2}CuCl_{4} (CAPCC), a quasitwodimensional S = 1/2 antiferromagnet on a square lattice with finite interlayer coupling, designed to study the field evolution of its spin excitations. Our data reveal that the one magnon response at vicinities close to (π/2; π/2) dampens more heavily compared to (π; 0) with an increasing field, in particular when the field approaches the saturation field of the system. Such an observation agrees with theoretical predictions. Compared to the higherorder spin wave results, the decays of onemagnon response are more pronounced in the experimental data. Such a discrepancy might due to the existence of other exchange interactions in the system. Nevertheless, our results provide the first experimental evidence for magnon decays in the twodimensional S = 1/2 antiferromagnet on a square lattice.•The quasitwodimensional honeycomb lattice antiferromagnet Na_{2}Co_{2}TeO_{6} is proposed to be a possible platform for hosting Kitaev related physics. Here we present the results of inelastic neutron powder scattering experiments, designed to study the crystal field and spin excitations in Na_{2}Co_{2}TeO_{6}. Our analysis on the crystal field excitations reveals that the singleion ground state for Co (II) is a spinorbit mixed Kramers doublet characterized by an effective spin angular momentum S_{eff} = 1/2. Given the CoO_{6} octahedra are arranged in an edgesharing fashion, this confirms the potential of Na_{2}Co_{2}TeO_{6} being a Kitaev material. The analysis of the spin excitations reveals that the Hamiltonian of Na_{2}Co_{2}TeO_{6} deviates from a simple Heisenberg model. In particular, strong anisotropies are required to qualitatively explain the observed spectra. We analyzed the possibility of the spectra resembling a HeisenbergKitaev Hamiltonian. The result shows that the nearest neighbor inplane Heisenberg interaction is heavily suppressed and significantly smaller than a dominant ferromagnetic Kitaev interaction. This is in accord with theoretical predictions. In contrast to other similar studies, we present a complete analysis on the crystal field excitations. •The magnetic properties of three metalorganic framework compounds, CrI_{2}(pyrazine)_{2}, GaCl_{2}(pyrazine)_{2} and CrCl_{2}(pyrazine)_{2} (pyrazine: C_{4}H_{4}N_{2}) are investigated. Despite the isostructural relation, their electronic and magnetic properties vary substantially. CrI_{2}(pyrazine)_{2} is a twodimensional S = 2 antiferromagnet on a square lattice. The results of an inelastic neutron powder scattering experiment reveal that a gap ∼ 0:1 meV is present in the spin wave spectrum and the data are best described by a J_{1}—J_{2 }Heisenberg Hamiltonian with an easyaxis singleion anisotropy. Unlike CrI2(pyrazine)2, magnetism in GaCl_{2}(pyrazine)_{2} arises from the unpaired electrons on pyrazines. For every formula unit of GaCl_{2}(pyrazine)_{2}, an electron is transferred from Ga to one of the pyrazine ligands. Therefore GaCl_{2}(pyrazine)_{2} manifests itself as a S = 1/2 system, which is supported by it magnetic susceptibility. Specific heat measurements reveal no formation of longrange order down to 2 K. The results of a polarized neutron powder diffraction experiment reveal that the total spin angular momentum S(S+1) is in good accord with the S = 1/2 oneelectron scenario. More rapid decay of the extracted magnetic form factor compared to 3d transition metals indicates the electron is spatially delocalized. This is consistent with the having electrons on pyrazine ligands picture. Both CrI_{2}(pyrazine)_{2} and GaCl_{2}(pyrazine)_{2} are well placed in an insulating limit. In contrast CrCl_{2}(pyrazine)_{2} is electrically conductive at room temperature. Similar to GaCl_{2}(pyrazine)_{2}, the two pyrazine ligands in one formula unit of CrCl_{2}(pyrazine)_{2} takes an electron away from the Cr ion. This gives rise to antiferromagnetically coupled Cr (III) and pyrazine spins. Below 55 K. the uncompensated S = 1 degree of freedoms are ferromagnetically coupled leading to a ferrimagnetic order. Results from inelastic neutron powder scattering reveal the only magnetic excitations of the system are below 1 meV. Compared to CrI_{2}(pyrazine)_{2}, the intensity of the excitations is significantly depressed. By tracking the Qdependence of the excitation energy, a }!/ Q2 relation is obtained. This is consistent with the ferromagnetic coupled S = 1 picture.
•Cu(DCOO)2•4D2O (CFTD) is a twodimensional S = 1/2 antiferromagnet on a square lattice. It is well established that in the lowtemperature limit CFTD exhibits an anomaly in its spin excitation spectrum at short wavelengths on zone boundary. In the vicinity of the (π; 0) the onemagnon excitation exhibits depression in energy, is strongly damped and attenuated. In particular, the attenuated spectral weight is transferred to an isotropic continuum of excitations extending to high energies. The origin of the anomaly is still under debate, particularly in relation to the existence of spinons in two dimensions. Here we present a study on the thermal evolution of the (π; 0) anomaly up to finite temperatures T/J ∼ 2/3. Our data reveal that the anomaly survives even in the absence of longrange, threedimensional order and that it is thus a feature closely related to the twodimensional S = 1/2 antiferromagnet on a square lattice. With further increase of temperature, the (π; 0) anomaly is washed out as the zoneboundary excitations gradually softens and dampens. This is confirmed by a comparison of our data with a finite temperature Quantum Monte Carlo calculation where a good accord is found.•It is wellestablished that, theoretically, magnons in a twodimensional antiferromagnet on a square lattice exhibit spontaneous decays at high fields due to the nonzero interaction between the onemagnon branch and the twomagnon continuum. Such a decay of magnons has already been observed in a classical spin system. But the experimental evidence for magnon decays in a quantum case S = 1/2 is absent. Here we present the results of inelastic neutron scattering experiments and higherorder spin wave calculations on (5CAP)_{2}CuCl_{4} (CAPCC), a quasitwodimensional S = 1/2 antiferromagnet on a square lattice with finite interlayer coupling, designed to study the field evolution of its spin excitations. Our data reveal that the one magnon response at vicinities close to (π/2; π/2) dampens more heavily compared to (π; 0) with an increasing field, in particular when the field approaches the saturation field of the system. Such an observation agrees with theoretical predictions. Compared to the higherorder spin wave results, the decays of onemagnon response are more pronounced in the experimental data. Such a discrepancy might due to the existence of other exchange interactions in the system. Nevertheless, our results provide the first experimental evidence for magnon decays in the twodimensional S = 1/2 antiferromagnet on a square lattice.•The quasitwodimensional honeycomb lattice antiferromagnet Na_{2}Co_{2}TeO_{6} is proposed to be a possible platform for hosting Kitaev related physics. Here we present the results of inelastic neutron powder scattering experiments, designed to study the crystal field and spin excitations in Na_{2}Co_{2}TeO_{6}. Our analysis on the crystal field excitations reveals that the singleion ground state for Co (II) is a spinorbit mixed Kramers doublet characterized by an effective spin angular momentum S_{eff} = 1/2. Given the CoO_{6} octahedra are arranged in an edgesharing fashion, this confirms the potential of Na_{2}Co_{2}TeO_{6} being a Kitaev material. The analysis of the spin excitations reveals that the Hamiltonian of Na_{2}Co_{2}TeO_{6} deviates from a simple Heisenberg model. In particular, strong anisotropies are required to qualitatively explain the observed spectra. We analyzed the possibility of the spectra resembling a HeisenbergKitaev Hamiltonian. The result shows that the nearest neighbor inplane Heisenberg interaction is heavily suppressed and significantly smaller than a dominant ferromagnetic Kitaev interaction. This is in accord with theoretical predictions. In contrast to other similar studies, we present a complete analysis on the crystal field excitations. •The magnetic properties of three metalorganic framework compounds, CrI_{2}(pyrazine)_{2}, GaCl_{2}(pyrazine)_{2} and CrCl_{2}(pyrazine)_{2} (pyrazine: C_{4}H_{4}N_{2}) are investigated. Despite the isostructural relation, their electronic and magnetic properties vary substantially. CrI_{2}(pyrazine)_{2} is a twodimensional S = 2 antiferromagnet on a square lattice. The results of an inelastic neutron powder scattering experiment reveal that a gap ∼ 0:1 meV is present in the spin wave spectrum and the data are best described by a J_{1}—J_{2 }Heisenberg Hamiltonian with an easyaxis singleion anisotropy. Unlike CrI2(pyrazine)2, magnetism in GaCl_{2}(pyrazine)_{2} arises from the unpaired electrons on pyrazines. For every formula unit of GaCl_{2}(pyrazine)_{2}, an electron is transferred from Ga to one of the pyrazine ligands. Therefore GaCl_{2}(pyrazine)_{2} manifests itself as a S = 1/2 system, which is supported by it magnetic susceptibility. Specific heat measurements reveal no formation of longrange order down to 2 K. The results of a polarized neutron powder diffraction experiment reveal that the total spin angular momentum S(S+1) is in good accord with the S = 1/2 oneelectron scenario. More rapid decay of the extracted magnetic form factor compared to 3d transition metals indicates the electron is spatially delocalized. This is consistent with the having electrons on pyrazine ligands picture. Both CrI_{2}(pyrazine)_{2} and GaCl_{2}(pyrazine)_{2} are well placed in an insulating limit. In contrast CrCl_{2}(pyrazine)_{2} is electrically conductive at room temperature. Similar to GaCl_{2}(pyrazine)_{2}, the two pyrazine ligands in one formula unit of CrCl_{2}(pyrazine)_{2} takes an electron away from the Cr ion. This gives rise to antiferromagnetically coupled Cr (III) and pyrazine spins. Below 55 K. the uncompensated S = 1 degree of freedoms are ferromagnetically coupled leading to a ferrimagnetic order. Results from inelastic neutron powder scattering reveal the only magnetic excitations of the system are below 1 meV. Compared to CrI_{2}(pyrazine)_{2}, the intensity of the excitations is significantly depressed. By tracking the Qdependence of the excitation energy, a }!/ Q2 relation is obtained. This is consistent with the ferromagnetic coupled S = 1 picture.
Original language  English 

Publisher  Department of Physics, Technical University of Denmark 

Number of pages  173 
Publication status  Published  2021 
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 1 Finished

Macroscopic Quantum States in LowDimensional Materials
Wan, W., Christensen, N. B., Pedersen, K. S., Haldrup, K., Deen, P. P. M., Quintero, D. L. C. & Rønnow, H. M.
Technical University of Denmark
01/08/2018 → 11/02/2022
Project: PhD