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Unlike conventional magnets where the magnetic moments are partially or completely static in the ground state, in a quantum spin liquid they remain in collective motion down to the lowest temperatures. The importance of this state is that it is coherent and highly entangled without breaking local symmetries. In the case of magnets with isotropic interactions, spin-liquid behaviour is sought in simple lattices with antiferromagnetic interactions that favour antiparallel alignments of the magnetic moments and are incompatible with the lattice geometries. Despite an extensive search, experimental realizations remain very few. Here we investigate the novel, unexplored magnet Ca 10 Cr 7 O 28 , which has a complex Hamiltonian consisting of several different isotropic interactions and where the ferromagnetic couplings are stronger than the antiferromagnetic ones. We show both experimentally and theoretically that it displays all the features expected of a quantum spin liquid. Thus spin-liquid behaviour in isotropic magnets is not restricted to the simple idealized models currently investigated, but can be compatible with complex structures and ferromagnetic interactions. A detailed and systematic study of Ca 10 Cr 7 O 28 reveals all the hallmarks of spin-liquid behaviour, in spite of the compound’s unusually complex structure.

We combine ultra-high-resolution inelastic neutron scattering and quantum Monte Carlo simulations to study thermodynamics and spin excitations in the spin-supersolid phase of the triangular lattice XXZ antiferromagnet K 2 Co(SeO 3 ) 2 under zero and non-zero magnetic field. BKT transitions signaling the onset of Ising and supersolid order are clearly identified, and the Wannier entropy is experimentally recovered just above the supersolid phase. At low temperatures, with an experimental resolution of about 23 μeV, no discrete coherent magnon modes are resolved within a broad scattering continuum. Alongside gapless excitations, a pseudo-Goldstone mode with a 0.06 meV gap is observed. A second, higher-energy continuum replaces single-spin-flip excitations of the Ising model. Under applied fields, the continuum evolves into coherent spin waves, with Goldstone and pseudo-Goldstone sectors responding differently. The experiments and simulations show excellent quantitative agreement.

In the rapidly expanding field of topological materials there is growing interest in systems whose topological electronic band features can be induced or controlled by magnetism. Magnetic Weyl semimetals, which contain linear band crossings near the Fermi level, are of particular interest owing to their exotic charge and spin transport properties. Up to now, the majority of magnetic Weyl semimetals have been realized in ferro- or ferrimagnetically ordered compounds, but a disadvantage of these materials for practical use is their stray magnetic field which limits the minimum size of devices. Here we show that Weyl nodes can be induced by a helical spin configuration, in which the magnetization is fully compensated. Using a combination of neutron diffraction and resonant elastic x-ray scattering, we find that below TN = 14.5 K the Eu spins in EuCuAs develop a planar helical structure which induces two quadratic Weyl nodes with Chern numbers C = ±2 at the A point in the Brillouin zone.

The celebrated Kitaev quantum spin liquid (QSL) is the paradigmatic example of a topological magnet with emergent excitations in the form of Majorana Fermions and gauge fluxes. Upon breaking of time-reversal symmetry, for example in an external magnetic field, these fractionalized quasiparticles acquire non-Abelian exchange statistics, an important ingredient for topologically protected quantum computing. Consequently, there has been enormous interest in exploring possible material realizations of Kitaev physics and several candidate materials have been put forward, recently including α-RuCl 3 . In the absence of a magnetic field this material orders at a finite temperature and exhibits low-energy spin wave excitations. However, at moderate energies, the spectrum is unconventional and the response shows evidence for fractional excitations. Here we use time-of-flight inelastic neutron scattering to show that the application of a sufficiently large magnetic field in the honeycomb plane suppresses the magnetic order and the spin waves, leaving a gapped continuum spectrum of magnetic excitations. Our comparisons of the scattering to the available calculations for a Kitaev QSL show that they are consistent with the magnetic field induced QSL phase. Condensed Matter Physics: magnetic field drives spins to a liquid A sufficiently large magnetic field suppresses long-range magnetic order in α-RuCl 3 , leaving a disordered state with a gapped continuum spectrum of magnetic excitations, similar to that expected for the famous Kitaev quantum spin liquid. An international team led by Stephen E. Nagler from Oak Ridge National Laboratory in the USA performed time-of-flight neutron scattering to study low energy magnetic excitations of α-RuCl 3 . They observed that the application of a sufficiently large magnetic field to this material suppressed spin waves associated with the long-range order, and drove it to an unusual excited state. By comparison with calculations, these results are consistent with the Kitaev quantum spin liquid state in a magnetic field. The results provide important information of a possible route to producing gapped excitations related to magnetic Majorana Fermions towards topologically protected quantum computation.

Die vorliegende Doktorarbeit beschäftigt sich mit der Untersuchung der magnetischen Isolatoren Ca10Cr7O28 und (NO)[Cu(NO3)3]. Die magnetischen Eigenschaften basieren auf den Spin-1/2 3d Übergangsmetallen Cr5+ und Cu2+, welche ein ausgelöschtes Bahnmoment aufweisen, was magnetisch zu einem reinen Spinmoment führt. Der erste Teil dieser Arbeit handelt von dem zweidimensionalen und frustrierten Magnet Ca10Cr7O28. Die detaillierte Analyse der Kristallstruktur und der magnetischen Eigenschaften zeigen die Abwesenheit von langreichweitiger Ordnung bis zu den tiefsten erreichbaren Temperaturen und die Präsenz von langsamen Fluktuationen. Die magnetischen Anregungen sind diffus und auch bei tiefster Temperatur und im Nullfeld ohne Energielücke, was konsistent mit einem Spinflüssigkeits-Grundzustand ist. In der langreichweitig geordneten Phase unter externem Magnetfeld bilden die Anregungen jedoch definierte Spinwellen, woraus die Wechselwirkungsparameter durch Fitten der Spektra mit linearer Spinwellen-Theorie extrahiert werden konnten. Die resultierenden Wechselwirkungen ergeben eine neuartige, frustrierte Struktur basierend auf ferromagnetischen und antiferromagnetischen Doppeldreiecken, welche in einem zweidimensionalen Kagomegitter gekoppelt sind. (NO)[Cu(NO3)3] ist eine eindimensionale, antiferromagnetisch gekoppelte Spin- 1/2 Heisenberg-Kette mit frustrierten Wechselwirkungen zwischen den Ketten, was dem Nersesyan-Tsvelik Modell entspricht. Konkurrierende nächste und übernächste Nachbar-Wechselwirkungen zwischen den Ketten entkoppeln diese und verstärken die niedrige Dimensionalität. Dies wird bestätigt durch das ideale eindimensionale Verhalten, welches hinunter bis zu niedrigen Energien und Temperaturen beobachtet wurde. (NO)[Cu(NO3)3] entwickelt langreichweitige magnetische Ordnung mit einer inkommensurablen Struktur in Form einer Spindichtewelle bei einer stark reduzierten Néel-Temperatur, was mit dem Vorhandensein von Frustration zu erklären ist. Der Phasenübergang wird analysiert und das magnetische Anregungsspektrum wird mit aktuellen theoretischen Modellen für antiferromagnetische Spin-1/2 Heisenberg-Ketten verglichen. Zusammen zeigen diese beiden Materialien, wie Frustration und niedrige Dimensionalität zu komplexem magnetischen Verhalten, sowie zu unkonventionellen magnetischen Grundzuständen führen können.

Aimed at a more realistic classical description of natural quantum systems, we present a two-dimensional tensor network algorithm to study finite temperature properties of frustrated model quantum systems and real quantum materials. For this purpose, we introduce the infinite projected entangled simplex operator ansatz to study thermodynamic properties. To obtain state-of-the-art benchmarking results, we explore the highly challenging spin-1/2 Heisenberg anti-ferromagnet on the Kagome lattice, a system for which we investigate the melting of the magnetization plateaus at finite magnetic field and temperature. Making close connection to actual experimental data of real quantum materials, we go on to studying the finite temperature properties of Ca\\(_{10}\\)Cr\\(_7\\)O\\(_{28}\\). We compare the magnetization curve of this material in the presence of an external magnetic field at finite temperature with classically simulated data. As a first theoretical tool that incorporates both thermal fluctuations as well as quantum correlations in the study of this material, our work contributes to settling the existing controversy between the experimental data and previous theoretical works on the magnetization process.

We report high-resolution inelastic neutron scattering measurements of the excitation spectrum in large single crystals of the spin-1/2 triangular lattice Ising-like antiferromagnet Na2BaCo(PO4)2 in magnetic fields applied transverse to the Ising axis. In the high-field polarized phase above a critical field \\(B_{C}\\) we observe sharp magnons, as expected in the case of no exchange disorder. Through simultaneous fits to the dispersions including data in polarizing field along the Ising axis, we obtain an excellent match to an Ising-like XXZ Hamiltonian and rule out previously proposed Kitaev exchanges. In the intermediate-field phase below \\(B_{C}\\), we observe three dispersive modes, out of which only the lowest energy one is sharp and the others are broad and overlap with continuum scattering. We propose that the broadening effects are due to magnon decays into two-magnon excitations and confirm that such processes are kinematically allowed. The continuum scattering becomes progressively stronger upon lowering field and, at 0.25 T and zero field, it dominates the complete spectrum with no clear evidence for even broadened magnon modes. We discuss the relevance of the continuous manifold of mean-field degenerate ground states of the refined Hamiltonian for capturing the observed spectrum in zero field, and compare the data with the one- and two-magnon spectrum averaged over this manifold. We also propose a model of the interlayer couplings to explain the observed finite interlayer magnetic propagation vector of the zero-field magnetic order; this requires the breaking of the mirror symmetry in the nominal P-3m1 space group and through refinement of x-ray diffraction data on an untwinned single crystal, we indeed confirm a rotation of the CoO6 octahedra around the c-axis, which lowers the symmetry to P-3.

The honeycomb magnet \\(\\alpha\\)-RuCl\\(_{3}\\) has been a leading candidate for realizing the Kitaev quantum spin liquid (QSL), but its intrinsic spin dynamics have remained obscured by crystal twinning. Here we apply biaxial anisotropic strain to detwin \\(\\alpha\\)-RuCl\\(_{3}\\) single crystals and directly visualize the intrinsic magnetic excitations using inelastic neutron scattering. We discover that the low-energy spin waves emerge from the \\(M\\) points -- transverse to the magnetic Bragg peaks -- providing direct evidence of anisotropic magnetic interactions in \\(\\alpha\\)-RuCl\\(_{3}\\). The intrinsic spin-wave spectrum imposes stringent constraints on the extended Kitaev Hamiltonian, yielding a refined, quantitatively consistent set of exchange couplings for the zigzag ground state and its low-energy dynamics. Above the magnon band, we uncover broad excitation continua: while a twofold-symmetric feature near 6 meV at \\(\\Gamma\\) is consistent with bimagnon scattering, the dominant spectral weight forms a sixfold-symmetric continuum extending up to \\(\\sim 16\\) meV that cannot be explained by conventional magnons. This strongly supports the presence of fractionalized excitations-a hallmark of Kitaev QSL physics. Our findings establish biaxial strain as a powerful symmetry-breaking probe to access the intrinsic spin dynamics of Kitaev materials and provide critical benchmarks for refining theoretical models of quantum magnetism in \\(\\alpha\\)-RuCl\\(_{3}\\).

We combine ultra-high-resolution inelastic neutron scattering and quantum Monte Carlo simulations to study thermodynamics and spin excitations in the spin-supersolid phase of the triangular lattice XXZ antiferromagnet K\\(_2\\)Co(SeO\\(_3\\))\\(_2\\) under zero and non-zero magnetic field. BKT transitions signaling the onset of Ising and supersolid order are clearly identified, and the Wannier entropy is experimentally recovered just above the supersolid phase. At low temperatures, with an experimental resolution of about 23 \\(\\)eV, no discrete coherent magnon modes are resolved within a broad scattering continuum. Alongside gapless excitations, a pseudo-Goldstone mode with a 0.06 meV gap is observed. A second, higher-energy continuum replaces single-spin-flip excitations of the Ising model. Under applied fields, the continuum evolves into coherent spin waves, with Goldstone and pseudo-Goldstone sectors responding differently. The experiments and simulations show excellent quantitative agreement.

We present an X-band and tunable high-frequency/high-field electron spin resonance (HF-ESR) study of single-crystalline Ca\\(_10\\)Cr\\(_7\\)O\\(_28\\), which constitutes alternating antiferromagnetic and ferromagnetic kagome bilayers. At high temperatures, a phonon-assisted relaxation process is evoked to account for the pronounced increase of the linewidth in an exchange-narrowing regime (\\(k_ BT J\\)). In contrast, at low temperatures (\\(k_ BT J\\)), a power-law behavior in line narrowing is observed. Our data reveal two distinct power-law regimes for the linewidth which crossover at \\(T^* 7.5\\)~K. Notably, the intriguing evolution of the ESR linewidth in this alternating kagome bilayer system with opposite sign of exchange interactions highlights distinct spin dynamics compared to those in a uniform kagome antiferromagnet.