# Field-induced magnetic states in geometrically frustrated SrEr2O4

### Submission summary

 As Contributors: Oleg Petrenko Preprint link: scipost_202103_00006v1 Date submitted: 2021-03-04 00:22 Submitted by: Petrenko, Oleg Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Experiment Approach: Experimental

### Abstract

We report an unusual in-field behaviour of SrEr2O4 for a magnetic field applied along two high-symmetry directions, the a and c axes. This geometrically frustrated magnet hosts two crystallographically inequivalent Er ions, Er1 and Er2, that are both located on triangular zigzag ladders, but only one site, Er1, forms a long-range magnetic order at low temperatures in a zero field. We follow the sequence of peculiar field induced states in SrEr2O4 with detailed single-crystal magnetisation and neutron diffraction experiments. On appli- cation of an external field along the c axis, the long-range antiferromagnetic order of the Er1 ions is rapidly destroyed and replaced in fields between 2 and 5 kOe by a state with shorter-range correlations. The change in correlation length coincides with a fast increase in magnetisation during the metamagnetic transition above which a long-range order is reestablished and maintained into the high fields. The high-field ferromagnet-like order is characterised by sig- nificantly different magnetic moments on the two Er sites with the Er1 site dominating the magnetisation process. For the field applied parallel to the a axis, in the field range of 4 to 12 kOe, the planes of diffuse magnetic scat- tering observed in zero field due to the one-dimensional correlations between the Er2 moments are replaced by much more localised but still diffuse features corresponding to the establishment of an up-up-down structure associated with a one-third magnetisation plateau. Above 14 kOe a ferromagnet-like high-field order is induced following another phase transition. For this direction of the field, the Er2 moments dictate the succession of transitions while the Er1 mo- ments remain significantly less polarised. A complete field polarisation of both Er sites is not achieved even at 50 kOe for either field direction, reflecting the strongly anisotropic nature of magnetisation process in SrEr2O4.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission scipost_202103_00006v2 on 9 June 2021

Submission scipost_202103_00006v1 on 4 March 2021

## Reports on this Submission

### Strengths

Thorough inelastic neutron-scattering study of single crystals of SrEr$_2$O$_4$ in an external magnetic field.

### Weaknesses

1- Some figures lack clarity.
2- Missing bridge to Ising model description.

### Report

The manuscript reports an unusual in-field behavior of SrEr$_2$O$_4$. This geometrically frustrated magnet hosts two crystallographically inequivalent Er ions that are both located on triangular zigzag ladders forming a honeycomb network, but only one site orders magnetically at low temperatures in zero magnetic field. The authors follow the sequence of peculiar field-induced states with detailed single-crystal magnetization and inelastic neutron scattering experiments. Among other phases, for the field applied parallel to the $a$ axis, an up-up-down structure is established in an intermediate field range.

This appears to be solid and interesting experimental work that in principle should be suitable for publication in SciPost Physics. However, some revisions may be appropriate before acceptance.

Apart from a list of suggested smaller changes (see below), I feel that a more detailed discussion of the magnetic Er$^{3+}$ ions in the present compound and their crystal-field level scheme would be helpful to close the gap to the Ising model, in particular in the discussion of section 4. For example, the magnetization data in Fig. 4(d) demonstrates that these are clearly not spin-1/2 Ising spins, at least not with a free-electron $g \approx 2$. It might also be helpful to discuss the local anisotropy axes. For example, if the Er1 and Er2 sites have different anisotropy axes, a transverse field component at least on one site could never be avoided such that there would always be some smearing expected. Such remarks may also help to elucidate the last sentence of the abstract where the authors state that full polarization of both Er sites is not achieved even in fields of 50 kOe.

Another global comment is that 2D color maps are esthetically nice ways of presenting data, but it is difficult to extract quantitative information from them. Thus, Figs. 2, 5, and A1-A6 may be a case for following the recommendation of publication of the underlying data, see item 5 of "General acceptance criteria" at https://scipost.org/SciPostPhys/about, preferably both the raw data as well as the background-subtracted data.

### Requested changes

In addition to the revisions suggested in the Report, I have a few minor requests for changes:
A- Appendixes should be cited as such in the text and not as "Sec"tions.
B- In the fourth paragraph of the section "2 Experimental details" something is missing between "along the $a$, $b$ and $c$" and "respectively".
C- Figure 2 has low quality, in particular fonts are fuzzy.
D- The axis labels of Figs. 2 and A1-A6 are strange; I consider the notation of Fig. 5 to designate the coordinates -in this case $(hk0)$- preferable.
E- The text used to label Fig. 6 is a bit small.
F- Figures A1-A6 lack clarity (e.g., the intensity scale is difficult to read).
G- "Ising" and "Kastelyn" are names and should thus start with a capital letter in the titles of Refs. [35,36] and [37], respectively.

• validity: high
• significance: good
• originality: good
• clarity: high
• formatting: good
• grammar: excellent

### Strengths

solid and very detailed experiments
careful analysis

### Weaknesses

presentation somewhat hard to follow
figures mostly too crowded, insets too small, color coding doesn't very well

### Report

The authors present a detailed study of a frustrated magnet, SrEr2O4, by means of magnetization and neutron diffraction in magnetic fields. In this material, the two crystallographically inequivalent Er sites also behave differently with respect to magnetic order: while the Er(1) site exhibits long-range magnetic order below 0.75K, for the Er(2) only short-order signatures have been reported. In the present manuscript, the in-field response along certain crystallographic directions of this of mixed magnetic order is reported and discussed. Most importantly, this study reveals a very different field response of the two Er sites and for the different crystallographic directions.

Overall, this is a very sound experimental study, with a very careful analysis of the experimental data. The conclusions reveal yet another highly unusual response to - in this case - magnetic fields as result of magnetic frustration. Altogether, I therefore conclude that in principle the paper meets the criteria for publication in terms of novelty and scientific soundness. Only, the presentation of the work, in particular regarding the figures in the manuscript, needs improvement (see requested changes). Only after these changes the paper maybe accepted for publication.

### Requested changes

Figures are mostly too small, with various panels crammed together in one figure (example: figure 2, figures in appendix), various insets too small to read the numbers (figure 6), data points almost not visible (red crosses in figure 6), color coding inappropriate (figure 3c: dark purple vs. black as difference between (0 3 1/3) and (0 3 -1/3), intensity maps being basically black with some color spots visible to the trained eye only (figures in appendix). It makes the paper very hard to read ... the authors should optimize the figure presentation to the effect that it is not necessary to zoom in to 300%, and correspondingly modify the text as necessary.

• validity: high
• significance: good
• originality: good
• clarity: ok
• formatting: below threshold
• grammar: good