Intrinsic quantum disorder in Yb2Ti2O7 and the quantum S=1/2 pyrochlore phase diagram

TL;DR

The study investigates intrinsic quantum disorder in Yb2Ti2O7 by combining inelastic neutron scattering under magnetic fields with multiple magnon theories and exact diagonalization. A low-energy $dipolar$ spin Hamiltonian with fitted exchange parameters is used to connect spectroscopic data to a quantum phase diagram, revealing an emergent quantum phase near the FM–AFM boundary and magnon breakdown as the system is tuned toward zero field. The results show that magnon broadening is intrinsic, not domain-related, and that Yb2Ti2O7 exhibits quantum-critical-like behavior with field-tunable transitions from coherent magnons to a nontrivial quantum ground state. This work highlights quantum criticality as a generic feature of dipolar pyrochlore systems and provides a benchmark for many-body methods and future explorations of related materials.

Abstract

We present an experimental and theoretical study of the anisotropic pyrochlore phase diagram. Inelastic field-dependent neutron scattering on Yb$_2$Ti$_2$O$_7$ shows intrinsic broadening and a flat low-energy magnon mode which is partially captured by interacting magnon models. Exact diagonalization reveals the existence of an emergent quantum phase between ferromagnetism and antiferromagnetism, in which Yb$_2$Ti$_2$O$_7$ Hamiltonian potentially resides. This behavior matches the phenomenology of quantum criticality in heavy fermion systems, and shows Yb$_2$Ti$_2$O$_7$ is a clean system which can be field-tuned from well-defined magnons to a nontrivial quantum ground state. This suggests that quantum criticality is a generic feature of the dipolar phase diagram.

Figures (27)

• Figure 1: (a) Pyrochlore unit cell of corner sharing tetrahedra, with the nearest neighbor exchange matrix Ross_Hamiltonian. (b) Classical phase diagram Yan2017. (c) Quantum phase diagram from this study, where the white stars indicate phase boundaries from exact diagonalization. White regions are the emergent quantum phases surrounding classical degeneracies.
• Figure 2: Yb2Ti2O7 inelastic neutron scattering along high symmetry directions $\Gamma (000) \rightarrow K (220) \rightarrow X (200) \rightarrow \Gamma$ at $T=0.15$ K at various fields between 0 T and 2 T along [001]. Panels (a)-(g) show experimental data. At 0 T the excitations are very broad and are most intense around $K$, but the smallest field completely suppresses the $K$-point low-energy scattering. As field increases, the modes gradually become sharper and less diffuse. Panels (h)-(n) show linear spin wave theory (LSWT) calculations of the inelastic spectrum using the Hamiltonian in Ref. Thompson_2017. Panels (o)-(u) show nonlinear spin wave theory (NLSWT) calculations using the same Hamiltonian (the zero field calculations around the $K$-point are unstable, and are shown by a grey region). Panels (v)-(bb) show the THED calculations with the same Hamiltonian. At zero field the THED calculations are unstable, but at finite fields they show a significant amount of broadening.
• Figure 3: Calculated pyrochlore phase diagram assuming $J_3=-0.272$ meV, $J_4=0.049$ meV (the Yb2Ti2O7 parameters in Ref. Thompson_2017). Panel (a) shows the phases determined by Pearson R correlations. Panel (b) shows the size of the ordered moment, calculated as the covariance with the reference $S({\bf Q})$. The black circles in panels (a) and (b) indicate parameters which were explicitly calculated; regions in between were interpolated. Panels (c)-(e) show the reference $S({\bf Q})$ for FM ($J = [-0.5,-0.5,J_3,J_4]$), $\Psi_4$ ($J = [0,0.5,J_3,J_4]$), and $\Psi_3/\Psi_2$ ($J = [0.5,-0.5,J_3,J_4]$). Panel (f) shows the structure factor for the center of the phase diagram, $J = [-0.05,0.0,J_3,J_4]$. Panel (g) shows the structure factor for the Heisenberg quantum spin liquid region $J = [0.5,0.5,J_3,J_4]$.
• Figure 4: Line scans obtained by ED calculations using 32 sites through the phase boundaries in the $J_3=-0.272$ meV, $J_4=0.049$ meV phase diagram (Fig. \ref{['fig:PhaseDiagramJ_YTO']}). The top row (a)-(c) shows phase correlation with the three ordered phases. The second row (d)-(f) shows the ground state energy (in arbitrary units) across the line scan. The third row (g)-(i) show the first derivative in energy, while the fourth row (j)-(l) shows the second derivative in energy. The boundary between $\Psi_4$ and $\Psi_3/\Psi_2$ is very clearly first-order with an abrupt transition and a discontinuity in the first derivative. However, the boundary between FM and both AFM phases involves two distinct transitions with an intermediate phase in between. The FM-$\Psi_3/\Psi_2$ boundary appears to involve one second order transition and one weakly first-order transition, whereas the FM-$\Psi_4$ boundary involves two second order transitions. The discontinuities of the phase boundaries are also visible in the phase correlation scans.
• Figure 5: The gap at the $X$ point to the intense flat mode versus [001] magnetic field for Yb2Ti2O7, the THED calculation, the NLSWT calculation, and the LSWT model.