The emergence of Dirac/Weyl fermions in condensed matter systems is intimately related to symmetry-protected crystal states. Quasi-two dimensional Weyl semimetal MoTe$_{2}$ shows a non-trivial topologically protected phase upon cooling from the monoclinic (1T$^{\prime }$-P2$_{1}/m$) to the orthorhombic (T$_{d}$-Pnm2$_{1}$) phase. Using single crystal neutron diffraction, we determined that the high temperature 1T$^{^{\prime }}$ lacks inversion and the symmetry is P2$_{1}$ instead, but is devoid of Weyl nodes. The structural transition from the T$_{d}$, with AAAA layer ordering to the 1T$^{\prime }$ with ABAB stacking occurs via continuous shifts of layers, evidenced by the diffuse scattering in the out-of-plane direction. These shifts also lead to Weyl node annihilation as the tilting angle beta changes away from 90 degrees.
Electronic tunability in crystals with weakly bound layers can be achieved through layer stacking order. One such example is ${\mathrm{MoTe}}_{2}$, where the low-temperature orthorhombic ${T}_{d}$ phase is topological and host to Weyl quasiparticles. The transition mechanism to the nontrivial topology is elucidated by single-crystal neutron diffraction. Upon cooling from the monoclinic $1{T}^{\ensuremath{'}}$ to the ${T}_{d}$ phase, diffuse scattering accompanies the transition, arising from random, in-plane layer displacements, and dissipates upon entering the ${T}_{d}$ phase. Diffuse scattering is observed only in the $H0L$ plane due to irreversible layer shifts along the $c$ axis that break the centrosymmetry of the monoclinic lattice.
The role of phase separation and the effect of Fe-vacancy ordering in the emergence of superconductivity in alkali metal doped iron selenides ${\mathrm{A}}_{x}{\mathrm{Fe}}_{2\ensuremath{-}y}{\mathrm{Se}}_{2}$ (A = K, Rb, Cs) is explored. High energy x-ray diffraction and Monte Carlo simulation were used to investigate the crystal structure of quenched superconducting (SC) and as-grown nonsuperconducting (NSC) ${\mathrm{K}}_{x}{\mathrm{Fe}}_{2\ensuremath{-}y}{\mathrm{Se}}_{2}$ single crystals. The coexistence of superlattice structures with the in-plane $\sqrt{2}\ifmmode\times\else\texttimes\fi{}\sqrt{2}$ K-vacancy ordering and the $\sqrt{5}\ifmmode\times\else\texttimes\fi{}\sqrt{5}$ Fe-vacancy ordering were observed in both the SC and NSC crystals alongside the I4/mmm Fe-vacancy-free phase. Moreover, in the SC crystals, an Fe-vacancy-disordered phase is additionally proposed to be present. Monte Carlo simulations suggest that it appears at the boundary between the I4/mmm vacancy-free phase and the I4/m vacancy-ordered phases ($\sqrt{5}\ifmmode\times\else\texttimes\fi{}\sqrt{5}$). The vacancy-disordered phase is nonmagnetic and is most likely the host of superconductivity.
Quantum spin liquid (QSL) is a disordered state of quantum-mechanically entangled spins commonly arising from frustrated magnetic dipolar interactions. However, QSL in some pyrochlore magnets can also come from frustrated magnetic octupolar interactions. Although the key signature for both dipolar and octupolar interaction-driven QSL is the presence of a spin excitation continuum (spinons) arising from the spin quantum number fractionalization, an external magnetic field-induced ferromagnetic order will transform the spinons into conventional spin waves in a dipolar QSL. By contrast, in an octupole QSL, the spin waves carry octupole moments that do not couple, in the leading order, to the external magnetic field or to neutron moments but will contribute to the field dependence of the heat capacity. Here we use neutron scattering to show that the application of a large external magnetic field to Ce2Zr2O7, an octupolar QSL candidate, induces an Anderson-Higgs transition by condensing the spinons into a static ferromagnetic ordered state with octupolar spin waves invisible to neutrons but contributing to the heat capacity. Our theoretical calculations also provide a microscopic, qualitative understanding for the presence of octupole scattering at large wavevectors in Ce2Sn2O7 pyrochlore, and its absence in Ce2Zr2O7. Therefore, our results identify Ce2Zr2O7 as a strong candidate for an octupolar U (1) QSL, establishing that frustrated magnetic octupolar interactions are responsible for QSL properties in Ce-based pyrochlore magnets.
Magnetic order in most materials occurs when magnetic ions with finite moments in a crystalline lattice arrange in a particular pattern below the ordering temperature determined by exchange interactions between the ions. However, when the crystal electric field (CEF) effect results in a spin-singlet ground state on individual magnetic sites, the collective ground state of the system can either remain non-magnetic, or more intriguingly, the exchange interactions between neighboring ions, provided they are sufficiently strong, can admix the excited CEF levels, resulting in a magnetically ordered ground state. The collective magnetic excitations in such a state are so-called spin excitons that describe the CEF transitions propagating through the lattice. In most cases, spin excitons originating from CEF levels of a localized single ion are dispersion-less in momentum (reciprocal) space and well-defined in both the magnetically ordered and paramagnetic states. Here we use thermodynamic and neutron scattering experiments to study stoichiometric Ni2Mo3O8 without site disorder, where Ni2+ ions form a bipartite honeycomb lattice comprised of two triangular lattices, with ions subject to the tetrahedral and octahedral crystalline environment, respectively. We find that in both types of ions, the CEF excitations have nonmagnetic singlet ground states, yet the material has long-range magnetic order. Furthermore, CEF spin excitons from the triangular-lattice arrangement of tetrahedral sites form, in both the antiferromagnetic and paramagnetic states, a dispersive diffusive pattern around the Brillouin zone boundary in reciprocal space. The present work thus demonstrates that spin excitons in an ideal triangular lattice magnet can have dispersive excitations, irrespective of the existence of static magnetic order, and this phenomenon is most likely due to spin entanglement and geometric frustrations.
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