[Paper Review] Antiferromagnetic Spin Ice Correlations at (1/2,1/2,1/2) in the Ground State of the Pyrochlore Magnet Tb2Ti2O7

Katharina Fritsch, Kate A. Ross+6 more|arXiv (Cornell University)|Oct 3, 2012

Advanced Condensed Matter Physics4 citations

TL;DR

This study reveals short-range antiferromagnetic spin ice correlations in Tb₂Ti₂O₇ at 70 mK, with diffuse elastic scattering centered at (1/2,1/2,1/2) in reciprocal space, indicating two-in, two-out spin configurations over ~2 conventional unit cells. The signal is separated from low-energy inelastic scattering by a 0.06–0.08 meV gap and is suppressed by small magnetic fields, supporting a quantum spin ice ground state with spin canting of ~12° from <111> axes.

ABSTRACT

We present high-resolution single crystal time-of-flight neutron scattering measurements on the candidate quantum spin liquid pyrochlore Tb2Ti2O7 at low temperature and in a magnetic field. At ~70 mK and in zero field, Tb2Ti2O7 reveals diffuse magnetic elastic scattering at (1/2,1/2,1/2) positions in reciprocal space, consistent with short-range correlated regions based on a two-in, two-out spin ice configuration on a doubled conventional unit cell. This elastic scattering is separated from very low-energy magnetic inelastic scattering by an energy gap of ~0.06-0.08 meV. The elastic signal disappears under the application of small magnetic fields and upon elevating temperature. Pinch-point-like elastic diffuse scattering is observed near (1,1,1) and (0,0,2) in zero field at ~70 mK, in agreement with Fennell et al. (Ref. 1), supporting the quantum spin ice interpretation of Tb2Ti2O7.

Motivation & Objective

• To resolve the nature of the ground state in the pyrochlore magnet Tb₂Ti₂O₇, which exhibits no long-range magnetic order down to 50 mK despite strong geometric frustration.
• To investigate whether short-range antiferromagnetic spin ice correlations exist at low temperatures, particularly at (1/2,1/2,1/2) in reciprocal space.
• To determine the origin of diffuse elastic scattering and its suppression under magnetic fields, distinguishing it from inelastic excitations and crystal-field effects.
• To test the quantum spin ice scenario by identifying pinch-point-like scattering and energy gaps consistent with emergent gauge structure.
• To quantify spin correlations via a 128-spin model on a doubled unit cell, fitting observed intensities to infer spin canting angles.

Proposed method

• High-resolution single-crystal time-of-flight neutron scattering was performed at the DCS and LET instruments at ISIS and NIST, respectively, at temperatures as low as 70 mK.
• Elastic and inelastic scattering intensities were measured across multiple energy transfers (E = -0.1 to 1.8 meV), with data corrected for detector efficiency and background from an empty can.
• A 128-spin model on a doubled conventional unit cell was used to simulate the two-in, two-out spin ice configuration with spin canting of ~12° from <111> axes.
• Diffuse scattering patterns were analyzed in reciprocal space, particularly in the (H,H,L) plane and along <0,0,L> and <H,H,H> directions, to identify pinch-point features.
• Magnetic field dependence was probed by applying fields up to 4 T along high-symmetry directions, with scattering monitored at (1/2,1/2,1/2) and (0,0,2).
• Data were reduced using DAVE and Mantid, and analyzed with the HORACE software package to extract intensity maps and energy-dependent scattering.

Experimental results

Research questions

• RQ1 Does Tb₂Ti₂O₇ exhibit short-range antiferromagnetic spin ice order at (1/2,1/2,1/2) in reciprocal space at ultra-low temperatures?
• RQ2 Is the observed elastic scattering at (1/2,1/2,1/2) separated from inelastic excitations by a distinct energy gap, and what does this imply for the ground state?
• RQ3 How does the application of small magnetic fields affect the (1/2,1/2,1/2) elastic signal, and what does this reveal about the stability of the spin ice correlations?
• RQ4 Are the diffuse scattering features near (0,0,2) and (1,1,1) consistent with pinch-point behavior expected in quantum spin ice systems?
• RQ5 Can the observed elastic scattering be quantitatively explained by a two-in, two-out spin ice model with spin canting, and what is the inferred canting angle?

Key findings

• Diffuse elastic scattering at (1/2,1/2,1/2) is observed at 70 mK in zero field, indicating short-range antiferromagnetic spin ice correlations extending over approximately two conventional pyrochlore unit cells.
• This elastic scattering is separated from low-energy inelastic scattering by a clear energy gap of ~0.06–0.08 meV, consistent with a gapped spin liquid or quantum spin ice ground state.
• The (1/2,1/2,1/2) signal vanishes under small magnetic fields (2–4 T) applied along high-symmetry directions, indicating sensitivity to field-induced lifting of spin ice degeneracy.
• Pinch-point-like diffuse elastic scattering is observed near (0,0,2) and (1,1,1), characteristic of Coulombic spin ice correlations, supporting a quantum spin ice interpretation.
• A 128-spin model on a doubled unit cell fits the observed peak intensities, yielding a spin canting angle of ~12° from the local <111> axes in the two-in, two-out configuration.
• High-energy inelastic scattering at 0.8–2.0 meV is dominated by crystal-field excitations, consistent with earlier studies of Tb³⁺ ion states.