Phase Transition and Thermal Order-by-Disorder in the Pyrochlore Quantum Antiferromagnet Er2Ti2O7: a High-Temperature Series Expansion Study

Abstract

Several rare earth magnetic pyrochlore materials are well modeled by a spin-1/2 quantum Hamiltonian with anisotropic exchange parameters Js. For the Er2Ti2O7 material, the Js were recently determined from high-field inelastic neutron scattering measurements. Here, we perform high-temperature (T) series expansions to compute the thermodynamic properties of this material using these Js. Comparison with experimental data show that the model describes the material very well including the finite temperature phase transition to an ordered phase at Tc~1.2 K. We show that high temperature expansions give identical results for different q=0 xy order parameter susceptibilities up to 8th order in β=1/T (presumably to all orders in β). Conversely, a non-linear susceptibility related to the 6th power of the order parameter reveals a thermal order-by-disorder selection of the same non-colinear ψ_2 state as found in Er2Ti2O7.

12 pages, 4 figures

References in corpus (9)

• Why spin ice obeys the ice rules
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Quantum order by disorder and accidental soft mode Er2Ti2O7
• Lightly stuffed pyrochlore structure of single-crystalline Yb2Ti2O7 grown by the optical floating zone technique
• Is the Yb2Ti2O7 pyrochlore a quantum spin ice?
• Ground State Phase Diagram of Generic XY Pyrochlore Magnets with Quantum Fluctuations
• Magnetic order, magnetic correlations and spin dynamics in the pyrochlore antiferromagnet Er2Ti2O7
• Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet

Cited by in corpus (42)

• Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets
• Frustrated quantum rare-earth pyrochlores
• Theory of multiple--phase competition in pyrochlore magnets with anisotropic exchange, with application to Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7
• Living on the edge : ground-state selection in quantum spin-ice pyrochlores
• Frustration and anisotropic exchange in ytterbium magnets with edge-shared octahedra
• Are multiphase competition & order-by-disorder the keys to understanding Yb2Ti2O7?
• Experimental Insights into Ground State Selection of Quantum XY Pyrochlores
• Magnetic Frustration in Lead Pyrochlores
• Liquid-like correlations in single crystalline Y2Mo2O7: an unconventional spin glass
• Anisotropic exchange within decoupled tetrahedra in the quantum breathing pyrochlore Ba3Yb2Zn5O11
• Order by Disorder Spin Wave Gap in the XY Pyrochlore Magnet Er2Ti2O7
• Refrustration and competing orders in the prototypical Dy2Ti2O7 spin ice material
• Single-ion properties of the $S_{eff}$ = 1/2 XY antiferromagnetic pyrochlores, Na$A^{\prime }$Co${}_2$F${}_7$ ($A^{\prime }=$ Ca${}^{2+}$, Sr${}^{2+}$)
• Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid
• Order by Disorder and Energetic Selection of the Ground State in the XY Pyrochlore Antiferromagnet Er2Ti2O7. An Inelastic Neutron Scattering Study
• Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets
• Static and dynamic XY-like short-range order in a frustrated magnet with exchange disorder
• Nature of finite-temperature transition in anisotropic pyrochlore Er2Ti2O7
• Effect of Chemical Pressure on the Crystal Electric Field States of Erbium Pyrochlore Magnets
• Order-by-disorder near criticality in $XY$ pyrochlore magnets
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: the Case of Multiple-k Partial Order on the Pyrochlore Lattice
• Competing orders in pyrochlore magnets from a ${\mathbb{Z}}_2$ spin liquid perspective
• Order Induced by Dilution in Pyrochlore XY Antiferromagnets
• Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions
• High temperature spin-freezing transition in Pyrochlore Eu2Ti2O7: A new observation from ac-susceptibility
• Spin freezing in the disordered pyrochlore magnet NaCaCo${}_2$F${}_7$: NMR studies and Monte-Carlo simulations
• Magnetic dilution and domain selection in the XY pyrochlore antiferromagnet Er${}_2$Ti${}_2$O${}_7$
• Understanding Reentrance in Frustrated Magnets: the Case of the Er${}_2$Sn${}_2$O${}_7$ Pyrochlore
• Absence of moment fragmentation in the mixed $B$-site pyrochlore Nd${}_2$GaSbO${}_7$
• Competeing orders in spin-1 and spin-3/2 XXZ Kagome antiferromagnets: A series expansion study
• Control of effective free energy landscape in a frustrated magnet by a field pulse
• Field induced phase diagram of the XY pyrochlore antiferromagnet Er${}_2$Ti${}_2$O${}_7$
• Experimental evidence for field induced emergent clock anisotropies in the XY pyrochlore Er${}_2$Ti${}_2$O${}_7$
• Order-by-disorder without quantum zero-point fluctuations in the pyrochlore Heisenberg ferromagnet with Dzyaloshinskii-Moriya interactions
• Electronic structure by X-ray absorption spectroscopy and observation offield induced unusually slowspin relaxation from magnetic properties in pyrochlore Eu${}_{2-x}$Fe${}_x$Ti${}_2$O${}_7$
• Holographic antiferromganetic quantum criticality and AdS${}_2$ scaling limit
• Phase diagram of the frustrated quantum-XY model on the honeycomb lattice studied by series expansions: Evidence for proximity to a bicritical point
• Higher-Rank Spin Liquids and Spin Nematics from Competing Orders in Pyrochlore Magnets
• Beyond Single Tetrahedron Physics of Breathing Pyrochlore Compound Ba3Yb2Zn5O11
• Monte Carlo study on the detection of classical order by disorder in real antiferromagnetic Ising pyrochlores
• Thermodynamically Induced Particle Transport: Order-by-Induction and Entropic Trapping at the Nano-Scale