Nanomagnets: Magnetic Properties and Inelastic Neutron Scattering Studies

In this thesis, small quantum spin systems, known as nano-magnets or molecular magnets, have been investigated. This is an area of great interest in the development of nanotechnology and quantum computers. Previous research on molecular magnets has concentrated on large, complex materials, which have many magnetic ions competing for superexchange pathways. Due to the large number of magnetic ions, the Hamiltonians resulted in very large Hilbert spaces, which makes it difficult for the magnetic interactions to be characterized and analyzed. Through the analysis of smaller and simpler magnetic clusters, insight can be gained from the interactions of the magnetic ions in these systems. Because many quantum spin systems can be accurately modeled using an antiferromagnetic Heisenberg Hamiltonian, we will assume this as a starting point for the theoretical description of molecular magnets. Our previous work on these systems considered only clusters of S=1/2 ions. Here, we derived closed form results for the magnetothermal properties and inelastic neutron scattering structure factors for dimers, trimers, and tetramers in various geometries, and in several cases were able to compare these calculations to known molecular magnets, and assist in the identification of the dominant magnetic interaction pathways. Using similar methods, these results are extended to clusters of two to six ions of spin S. An analysis of magnetic properties and observables for these clusters reveal a distinct pattern for that may be useful for the understanding of large clusters that cannot be determined analytically. From the specific case examined, the analysis of data from experiments on some magnetic materials shows the use and need for these calculations. This study of magnetic interactions in small quantum magnets develops clearer insight into the nature of excitations of larger, more complicated systems, which at present can only be investigated phenomenologically or through the use of numerical methods

2D spin-orbit-coupled frustrated magnets

The dissertation presents the complete way from the synthesis over the structural characterization to the thermodynamic properties of two compounds based on Ru, Na2RuO3 and Na3RuO4, and of two compounds based on Co, Na2BaCo(PO4)2 and Na2SrCo(PO4)2. The individual interplay of Hund’s coupling, spin-orbit coupling, and crystal field effects governs the magnetism in these compounds. In Na2RuO3 the Ru ions form a honeycomb lattice. Temperature dependent heat capacity and magnetization measurements point towards a spin-orbit entangled J=0 ground state. Excitations from the non-magnetic ground state to higher lying J levels were spectroscopically detected. In Na3RuO4 triangular features are found on two different length scales. The edge-shared RuO6 octahedra form tetramers which are composed of two triangles and the tetramers form a secondary triangular lattice. With neutron diffraction it was shown that the tetramers are antiferromagnetic units and competing exchange interactions on the secondary triangular lattice lead to an incommensurately modulated magnetic structure. The Co ions with effective spin 1/2 in Na2BaCo(PO4)2 form a direct triangular lattice. The compound was presented as quantum spin liquid candidate in the literature. However, the data shown in this work reveal a phase transition at around 150 mK and heat capacity and direction dependent magnetization data are accurately described with the nearest neighbor XXZ model. Based on the analysis of the temperature dependent synchrotron powder diffraction data the space group was revised to P-3 and structural dynamics were shown to be present. This was confirmed by NMR measurements. The compound was further compared to Na2SrCo(PO4)2 with a monoclinic symmetry and the structural differences were directly related to the differences of the thermodynamic properties.Die Doktorarbeit präsentiert den Weg von der Synthese über die strukturelle Charakterisierung zu den thermodynamischen Eigenschaften zweier Verbindungen basierend auf Ru, Na2RuO3 und Na3RuO4, und zweier Verbindungen basierend auf Co, Na2BaCo(PO4)2 und Na2SrCo(PO4)2. Das individuelle Zusammenspiel von Hundscher Kopplung, Spin-Bahn-Kopplung und Kristallfeldeffekten bestimmt den Magnetismus in diesen Verbindungen. In Na2RuO3 formen die Ru Ionen ein Honigwabengitter. Temperaturabhängige Wärmekapazitäts- und Magnetisierungsmessungen deuten einen Spin-Bahn gekoppelten J=0 Grundzustand an. Anregungen vom nicht magnetischen Grundzustand zu energetisch höher gelegenen J Niveaus wurden spektroskopisch nachgewiesen. In Na3RuO4 ist das Motiv des Dreiecks auf zwei Längenskalen zu finden. Die über die Kanten verknüpften RuO6 Oktaeder formen Tetramere, die aus zwei Dreiecken zusammengesetzt sind. Die Tetramere bilden ein sekundäres Dreiecksgitter. Mit Hilfe von Neutronendiffraktometrie wurde gezeigt, dass die Tetramere antiferromagnetische Einheiten sind und dass konkurrierende Wechselwirkungen auf dem sekundären Dreiecksgitter zu einer inkommensurablen magnetischen Struktur führen. In Na2BaCo(PO4)2 formen die Co Ionen mit effektivem Spin 1/2 ein direktes Dreiecksgitter. Die Verbindung wurde als Quantenspinflüssigkeit in der Literatur vorgestellt. Allerdings zeigen die Daten, die in dieser Arbeit präsentiert werden, einen Phasenübergang bei einer Temperatur von circa 150 mK. Die Daten aus Wärmekapazitäts- und richtungsabhängigen Magnetisierungsmessungen können mit dem XXZ Model für nächste Nachbarn beschrieben werden. Die Analyse der Daten aus Pulver-Synchrotron Messungen ergab, dass die Raumgruppe zu P-3 revidiert werden muss und es wurde gezeigt, dass strukturelle Dynamiken vorliegen. Dies wurde durch NMR Messungen bestätigt. Die Verbindung wurde außerdem mit Na2SrCo(PO4)2 verglichen. Na2SrCo(PO4)2 hat eine monokline Symmetrie und die strukturellen Unterschiede wurden direkt mit den Unterschieden der thermodynamischen Eigenschaften in Verbindung gebracht

Spin-lozenge thermodynamics and magnetic excitations in Na3RuO4

We report inelastic and elastic neutron scattering, magnetic susceptibility, and heat capacity measurements of polycrystalline sodium ruthenate (Na$_3$RuO$_4$). Previous work suggests this material consists of isolated tetramers of $S=3/2$ Ru$^{5+}$ ions in a so-called "lozenge" configuration. Using a Heisenberg antiferromagnet Hamiltonian, we analytically determine the energy eigenstates for general spin $S$. From this model, the neutron scattering cross-sections for excitations associated with spin-3/2 spin-tetramer configurations is determined. Comparison of magnetic susceptibility and inelastic neutron scattering results shows that the proposed "lozenge" model is not distinctly supported, but provides evidence that the system may be better described as a pair of non-interacting inequivalent dimers, \textit{i.e} double dimers. However, the existence of long-range magnetic order below $T_c \approx 28$ K immediately questions such a description. Although no evidence of the lozenge model is observed, future studies on single crystals may further clarify the appropriate magnetic Hamiltonian.Comment: 11 Pages, 10 Figures, Submitted to Phys. Rev.