Composite spin and quadrupole wave in the ordered phase of Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$

Abstract

The hidden ordered state of the frustrated pyrochlore oxide Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$ is possibly one of the two electric multipolar, or quadrupolar, states of the effective pseudospin-1/2 Hamiltonian derived from crystal-field ground state doublets of non-Kramers Tb${}^{3+}$ ions. These long-range orders are antiparallel or parallel alignments of transverse pseudospin components representing electric quadrupole moments, which cannot be observed as magnetic Bragg reflections by neutron scattering. However pseudospin waves of these states are composite waves of the magnetic-dipole and electric-quadrupole moments, and can be partly observed by inelastic magnetic neutron scattering. We calculate these spin-quadrupole waves using linear spin-wave theory and discuss previously observed low-energy magnetic excitation spectra of a polycrystalline sample with $x=0.005$ ($T_{\text{c}}=0.5$ K).

arXiv comment7 pages, 5 figures; Eqs. (1), (6), and (7) are corrected (v5)

References in corpus (24)

• Spin Ice State in Frustrated Magnetic Pyrochlore Materials
• Magnetic Monopoles in Spin Ice
• Magnetic Pyrochlore Oxides
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets
• Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets
• Coulombic Quantum Liquids in Spin-1/2 Pyrochlores
• Magnetic and Thermodynamic Properties of the Collective Paramagnet-Spin Liquid Pyrochlore Tb2Ti2O7
• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
• Seeing the light : experimental signatures of emergent electromagnetism in a quantum spin ice
• Generic quantum spin ice
• Why spin ice obeys the ice rules
• Higgs transition from a magnetic Coulomb liquid to a ferromagnet in Yb_2Ti_2O_7
• Quantum fluctuations in the effective pseudospin-1/2 model for magnetic pyrochlore oxides
• Description of Multipole in f-Electron Systems
• Magnetoelastic excitations in the pyrochlore spin liquid Tb${}_2$Ti${}_2$O${}_7$
• Long-range order and spin-liquid states of polycrystalline Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Understanding Paramagnetic Spin Correlations in the Spin-Liquid Pyrochlore Tb2Ti2O7
• Antiferromagnetic Spin Ice Correlations at (1/2,1/2,1/2) in the Ground State of the Pyrochlore Magnet Tb2Ti2O7
• Spin liquid correlations, anisotropic exchange and symmetry breaking in Tb2Ti2O7
• Quantum spin fluctuations in the spin liquid state of Tb2Ti2O7
• Neutron spectroscopic study of crystal field excitations in Tb2Ti2O7 and Tb2Sn2O7
• Spin dynamics in the ordered spin ice Tb${}_2$Sn${}_2$O${}_7$
• Temperature and Magnetic Field Dependence of Spin Ice Correlations in the Pyrochlore Magnet Tb2Ti2O7

Cited by in corpus (16)

• Frustrated quantum rare-earth pyrochlores
• Anisotropic exchange within decoupled tetrahedra in the quantum breathing pyrochlore Ba3Yb2Zn5O11
• A spin liquid with pinch-line singularities on the pyrochlore lattice
• Crystal field parameters of the rare earth pyrochlores $R_2$Ti${}_2$O${}_7$ ($R$ = Tb, Dy, Ho)
• Quadrupole Order in the Frustrated Pyrochlore Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Sample independence of magnetoelastic excitations in the rare earth pyrochlore Tb2Ti2O7
• Quantum spin liquid and electric quadrupolar states of single crystal Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Competing Gauge Fields and Entropically-Driven Spin Liquid to Spin Liquid Transition in non-Kramers Pyrochlores
• Continuum excitation and pseudospin wave in quantum spin-liquid and quadrupole ordered states of Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Spin correlations of quantum-spin-liquid and quadrupole-ordered states of Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Quadrupole order in the frustrated pyrochlore magnet Tb${}_2$Ti${}_2$O${}_7$
• Field-Tuned Quantum Effects in a Triangular-Lattice Ising Magnet
• Thermodynamic properties of quadrupolar states in the frustrated pyrochlore magnet Tb${}_2$Ti${}_2$O${}_7$
• Dimensional change of quadrupole orders in pseudospin-$\frac{1}{2}$ pyrochlore magnets under [111] field
• Traversing the pyrochlore stability diagram; microwave-assisted synthesis and discovery of mixed B-site Ln${}_2$InSbO${}_7$ family
• Spin and quadrupole correlations by three-spin interaction in the frustrated pyrochlore magnet Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$