Quantum magnetism and quantum phase transitions

Abstract:

CuLa2Ge2O8 forms a distorted triangular lattice of quantum spin-1/2 Cu²⁺ ions. A crystal growth method was developed using the traveling-solvent floating zone technique, resulting in the synthesis of a large single crystal (4mm×4mm×10 mm). The crystal was characterized with regard to phase purity and crystallinity using powder x-ray diffraction, energy dispersive x-ray analysis, and Laue diffraction, and found to be of excellent quality. The magnetic properties were characterized using dc-susceptibility, magnetization, and heat capacity measurements, which revealed weak magnetic frustration with long-range magnetic order occurring below TN=1.14(1) K. The magnetic structure determined using neutron powder diffraction is a commensurate, noncollinear antiferromagnetic structure, different from the 120^∘ order of an equilateral triangular antiferromagnet. The ordered moments lie in the bc-plane, with components mb=0.50(3) µB and mc=0.73(5) µB along the b- and c-axes respectively, giving a total ordered moment of Mtotal=0.89(6)µB/Cu²⁺ at 20 mK.

Abstract:

Muon spin rotation (μSR) measurements of internal magnetic field shifts, known as the muon Knight shift, are used for determining pairing symmetries in superconductors. While this technique has been especially effective for f-electron-based heavy-fermion superconductors, it remains challenging in d-electron-based superconductors such as Sr_{2}RuO_{4}, where the Knight shift is intrinsically small. Here, we report high-precision muon Knight shift measurements of superconducting Sr_{2}RuO_{4}. We observe that using multiple pieces of crystals, a common practice in μSR measurements, induces a substantial paramagnetic shift below the superconducting transition temperature, T_{c}, when a weak magnetic field is applied. We attribute such an unresolved paramagnetic shift to stray fields generated by neighboring diamagnetic crystals. To avoid this, one piece of crystal was used in this Letter. We experimentally determine the muon Knight shift of Sr_{2}RuO_{4} in the normal state to be -116±7  ppm. By combining the observed muon Knight shift with independently determined bulk magnetization data from the same crystal used in μSR and carefully separating various contributions to the shift, we confirm a significant reduction in the spin Knight shift below T_{c}, consistent with spin-singlet-like pairing. This result constitutes the precise muon Knight shift measurement in a d-electron-based superconductor. Our results highlight the potential of μSR as a powerful complementary technique to the established method of nuclear magnetic resonance for probing the spin susceptibility in superconductors.

Abstract:

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 ${\mathrm{Na}}_2\mathrm{BaCo}{\left({\mathrm{PO}}_4\right)}_2$ in magnetic fields applied transverse to the Ising axis. In the high-field polarized phase above a critical field $B_{\mathrm{C}}$ , we observe sharp magnons, as expected in the case of no exchange disorder. Through simultaneous fits to the dispersions including data in a 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 $B_{\mathrm{C}}$ , 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 the field and, at 0.25 T and zero field, it dominates the entire 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 $P\overline{3}m1$ space group and through refinement of x-ray diffraction data on an untwinned single crystal, we indeed confirm a rotation of the ${\mathrm{CoO}}_6$ octahedra around the $c$ axis, which lowers the symmetry to $P\overline{3}$ .