Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7

Here we establish the systematic existence of a U(1) degeneracy of all symmetry-allowed Hamiltonians quadratic in the spins on the pyrochlore lattice, at the mean-field level. By extracting the Hamiltonian of Er2Ti2O7 from inelastic neutron scattering measurements, we then show that the U(1)-degenerate states of Er2Ti2O7 are its classical ground states, and unambiguously show that quantum fluctuations break the degeneracy in a way which is confirmed by experiment. This is the first definitive observation of order-by-disorder in any material. We provide further verifiable consequences of this phenomenon, and several additional comparisons between theory and experiment.Comment: 4.5 pages, 3 figures, 7.5 pages of Supplemental Material, 8 supplemental figure

Singlet-Triplet Excitations in the Unconventional Spin-Peierls System TiOBr

We have performed time-of-flight neutron scattering measurements on powder samples of the unconventional spin-Peierls compound TiOBr using the fine-resolution Fermi chopper spectrometer (SEQUOIA) at the SNS. These measurements reveal two branches of magnetic excitations within the commensurate and incommensurate spin-Peierls phases, which we associate with n = 1 and n = 2 triplet excitations out of the singlet ground state. These measurements represent the first direct measure of the singlet-triplet energy gap in TiOBr, which is determined to be Eg = 21.2 +/- 1.0 meV.Comment: 5 pages, 4 figures, submitted for publicatio

Neutron spectroscopic study of crystal field excitations in Tb2Ti2O7 and Tb2Sn2O7

We present time-of-flight inelastic neutron scattering measurements at low temperature on powder samples of the magnetic pyrochlore oxides Tb2Ti2O7 and Tb2Sn2O7. These two materials possess related, but different ground states, with Tb2Sn2O7 displaying "soft" spin ice order below Tn~0.87 K, while Tb2Ti2O7 enters a hybrid, glassy spin ice state below Tg~0.2 K. Our neutron measurements, performed at T=1.5 K and 30 K, probe the crystal field states associated with the J=6 states of Tb3+ within the appropriate Fd\bar{3}m pyrochlore environment. These crystal field states determine the size and anisotropy of the Tb3+ magnetic moment in each material's ground state, information that is an essential starting point for any description of the low-temperature phase behavior and spin dynamics in Tb2Ti2O7 and Tb2Sn2O7. While these two materials have much in common, the cubic stanate lattice is expanded compared to the cubic titanate lattice. As our measurements show, this translates into a factor of ~2 increase in the crystal field bandwidth of the 2J+1=13 states in Tb2Ti2O7 compared with Tb2Sn2O7. Our results are consistent with previous measurements on crystal field states in Tb2Sn2O7, wherein the ground state doublet corresponds primarily to m_J=|\pm 5> and the first excited state doublet to mJ=|\pm 4>. In contrast, our results on Tb2Ti2O7 differ markedly from earlier studies, showing that the ground state doublet corresponds to a significant mixture of mJ=|\pm 5>, |\mp 4>, and |\pm 2>, while the first excited state doublet corresponds to a mixture of mJ=|\pm 4>, |\mp 5>, and |\pm 1>. We discuss these results in the context of proposed mechanisms for the failure of Tb2Ti2O7 to develop conventional long-range order down to 50 mK.Comment: 12 pages, 6 figures. Version is the same as the published one, except for figure placement on page

Quenched crystal field disorder and magnetic liquid ground states in Tb2Sn2-xTixO7

Solid-solutions of the "soft" quantum spin ice pyrochlore magnets Tb2B2O7 with B=Ti and Sn display a novel magnetic ground state in the presence of strong B-site disorder, characterized by a low susceptibility and strong spin fluctuations to temperatures below 0.1 K. These materials have been studied using ac-susceptibility and muSR techniques to very low temperatures, and time-of-flight inelastic neutron scattering techniques to 1.5 K. Remarkably, neutron spectroscopy of the Tb3+ crystal field levels appropriate to at high B-site mixing (0.5 < x < 1.5 in Tb2Sn2-xTixO7) reveal that the doublet ground and first excited states present as continua in energy, while transitions to singlet excited states at higher energies simply interpolate between those of the end members of the solid solution. The resulting ground state suggests an extreme version of a random-anisotropy magnet, with many local moments and anisotropies, depending on the precise local configuration of the six B sites neighboring each magnetic Tb3+ ion.Comment: 6 pages, 6 figure