Assessment of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>RE</mml:mi><mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>OH</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>Ising magnetic materials as possible candidates for the study of transverse-field-induced quantum phase transitions
Bibliographic record
Abstract
The ${\text{LiHo}}_{x}{\text{Y}}_{1\ensuremath{-}x}{\text{F}}_{4}$ Ising magnetic material subject to a magnetic field perpendicular to the ${\text{Ho}}^{3+}$ Ising direction has shown over the past 20 years to be a host of very interesting thermodynamic and magnetic phenomena. Unfortunately, the availability of other magnetic materials other than ${\text{LiHo}}_{x}{\text{Y}}_{1\ensuremath{-}x}{\text{F}}_{4}$ that may be described by a transverse-field Ising model remains very much limited. It is in this context that we use here a mean-field theory to investigate the suitability of the $\text{Ho}{(\text{OH})}_{3}$, $\text{Dy}{(\text{OH})}_{3}$, and $\text{Tb}{(\text{OH})}_{3}$ insulating hexagonal dipolar Ising-type ferromagnets for the study of the quantum phase transition induced by a magnetic field, ${B}_{x}$, applied perpendicular to the Ising spin direction. Experimentally, the zero-field critical (Curie) temperatures are known to be ${T}_{c}\ensuremath{\approx}2.54$, 3.48, and 3.72 K, for $\text{Ho}{(\text{OH})}_{3}$, $\text{Dy}{(\text{OH})}_{3}$, and $\text{Tb}{(\text{OH})}_{3}$, respectively. From our calculations we estimate the critical transverse field, ${B}_{x}^{c}$, to destroy ferromagnetic order at zero temperature to be ${B}_{x}^{c}=4.35$, 5.03, and 54.81 T for $\text{Ho}{(\text{OH})}_{3}$, $\text{Dy}{(\text{OH})}_{3}$, and $\text{Tb}{(\text{OH})}_{3}$, respectively. We find that $\text{Ho}{(\text{OH})}_{3}$, similarly to ${\text{LiHoF}}_{4}$, can be quantitatively described by an effective $S=1/2$ transverse-field Ising model. This is not the case for $\text{Dy}{(\text{OH})}_{3}$ due to the strong admixing between the ground doublet and first excited doublet induced by the dipolar interactions. Furthermore, we find that the paramagnetic (PM) to ferromagnetic (FM) transition in $\text{Dy}{(\text{OH})}_{3}$ becomes first order for strong ${B}_{x}$ and low temperatures. Hence, the PM to FM zero-temperature transition in $\text{Dy}{(\text{OH})}_{3}$ may be first order and not quantum critical. We investigate the effect of competing antiferromagnetic nearest-neighbor exchange and applied magnetic field, ${B}_{z}$, along the Ising spin direction $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ on the first-order transition in $\text{Dy}{(\text{OH})}_{3}$. We conclude from these preliminary calculations that $\text{Ho}{(\text{OH})}_{3}$ and $\text{Dy}{(\text{OH})}_{3}$ and their ${\text{Y}}^{3+}$ diamagnetically diluted variants, ${\text{Ho}}_{x}{\text{Y}}_{1\ensuremath{-}x}{(\text{OH})}_{3}$ and ${\text{Dy}}_{x}{\text{Y}}_{1\ensuremath{-}x}{(\text{OH})}_{3}$, are potentially interesting systems to study transverse-field-induced quantum fluctuations effects in hard axis (Ising-type) magnetic materials.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.002 | 0.003 |
| Meta-epidemiology (broad) | 0.001 | 0.004 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.003 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.414 | 0.001 |
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; both teacher heads agree on what is shown here.
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".