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).

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

References in corpus (5)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
• Why spin ice obeys the ice rules
• 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

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${}_{7+y}$