Composite Spin and Quadrupole Wave in the Ordered Phase ofTb_2+xTi_2-xO_7+y

Abstract

The hidden ordered state of the frustrated pyrochlore oxide Tb2+xTi2−xO7+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 electricquadrupole 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 (Tc = 0.5 K).

Quadrupole Order in the Frustrated PyrochloreTb2+xTi2−xOTakatsu1, Onoda2, Kittaka3 et al. 2016Phys. Rev. Lett.Self Cite57158901View full textAdd to dashboardCite

“…(1), σ r are the Pauli matrices (pseudospin) at a site r, σ ± r ≡ (σ x r ± iσ y r )/2, and φ r,r ′ = ± 2π 3 , 0 [11,37]. The magnetic dipole moment µ eff σ z r is parallel to the local 111 axis e z r [37].…”

“…The magnetic dipole moment µ eff σ z r is parallel to the local 111 axis e z r [37]. The first three terms of Eq.…”

“…(1) represents the quadrupole interaction H q . We note that the transverse components (σ x r , σ y r ) of the pseudospin represent electric quadrupole (and 16-, 64-pole) moments [11,37]. Note that QMC simulations of the model Eq.…”

“…This experimental behavior can be described in terms of pseudospin waves in the PAF and PF phases, as discussed in Ref. [37]. The powder-averaged dynamical magnetic structure factor S (|Q|, E) is calculated within the MF-RPA [37], which can correctly describe the spectrum in an ordered state within the linear spin-wave approximation.…”

“…[37]. The powder-averaged dynamical magnetic structure factor S (|Q|, E) is calculated within the MF-RPA [37], which can correctly describe the spectrum in an ordered state within the linear spin-wave approximation. Extensive calculations in a wide range of the parameters (δ, q) show that reasonable agreements are obtained in the PAF phase with (δ, q) = (0.0 ± 0.4, 0.8 ± 0.3) [Fig.…”