Experimental evidence for field induced emergent clock anisotropies in the XY pyrochlore Er$_2$Ti$_2$O$_7$
Bibliographic record
Abstract
The XY pyrochlore antiferromagnet Er$_2$Ti$_2$O$_7$ exhibits a rare case of $Z_6$ discrete symmetry breaking in its $ψ_2$ magnetic ground state. Despite being well-studied theoretically, systems with high discrete symmetry breakings are uncommon in nature and, thus, Er$_2$Ti$_2$O$_7$ provides an experimental playground for the study of broken $Z_n$ symmetry, for $n>2$. A recent theoretical work examined the effect of a magnetic field on a pyrochlore lattice with broken $Z_6$ symmetry and applied it to Er$_2$Ti$_2$O$_7$. This study predicted multiple domain transitions depending on the crystallographic orientation of the magnetic field, inducing rich and controllable magnetothermodynamic behavior. In this work, we present neutron scattering measurements on Er$_2$Ti$_2$O$_7$ with a magnetic field applied along the [001] and [111] directions, and provide the first experimental observation of these exotic domain transitions. In a [001] field, we observe a $ψ_2$ to $ψ_3$ transition at a critical field of 0.18$\pm$0.05T. We are thus able to extend the concept of the spin-flop transition, which has long been observed in Ising systems, to higher discrete $Z_n$ symmetries. In a [111] field, we observe a series of domain-based phase transitions for fields of 0.15$\pm$0.03T and 0.40$\pm$0.03T. We show that these field-induced transitions are consistent with the emergence of two-fold, three-fold and possibly six-fold Zeeman terms. Considering all the possible $ψ_2$ and $ψ_3$ domains, these Zeeman terms can be mapped onto an analog clock - exemplifying a literal clock anisotropy. Lastly, our quantitative analysis of the [001] domain transition in Er$_2$Ti$_2$O$_7$ is consistent with order-by-disorder as the dominant ground state selection mechanism.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".