# Breathing distortions in the metallic, antiferromagnetic phase of LaNiO$_3$

### Submission summary

 As Contributors: Alaska Subedi Arxiv Link: https://arxiv.org/abs/1708.08899v2 Date accepted: 2018-08-27 Date submitted: 2018-07-16 Submitted by: Subedi, Alaska Submitted to: SciPost Physics Discipline: Physics Subject area: Condensed Matter Physics - Theory Approaches: Theoretical, Computational

### Abstract

I study the structural and magnetic instabilities in LaNiO$_3$ using density functional theory calculations. From the non-spin-polarized structural relaxations, I find that several structures with different Glazer tilts lie close in energy. The $Pnma$ structure is marginally favored compared to the $R\overline{3}c$ structure in my calculations, suggesting the presence of finite-temperature structural fluctuations and a possible proximity to a structural quantum critical point. In the spin-polarized relaxations, both structures exhibit the $\uparrow\!\!0\!\!\downarrow\!\!0$ antiferromagnetic ordering with a rock-salt arrangement of the octahedral breathing distortions. The energy gain due to the breathing distortions is larger than that due to the antiferromagnetic ordering. These phases are semimetallic with small three-dimensional Fermi pockets, which is largely consistent with the recent observation of the coexistence of antiferromagnetism and metallicity in LaNiO$_3$ single crystals by Guo \textit{et al.} [Nat. Commun. 9, 43 (2018)].

### Ontology / Topics

See full Ontology or Topics database.

Published as SciPost Phys. 5, 020 (2018)

I thank the anonymous referee and Prof. Aichhorn for the review and their positive evaluation. I also thank them for suggestions for changes. I have addressed their issues, which I detail below.

Anonymous referee:
1 - add the comment on the DFT+DMFT calculation.
I have added a reference to the mentioned DFT+DMFT calculations.

Prof. Aichhorn:
1) Some discussion on the numerical accuracy of the total energies.
A new paragraph is added discussing the numerical accuracy.

2) Some rewriting, in particular in section 3.2, to make the main points clearer.
Section 3.2 has been reorganized. A paragraph has been deleted and subsections have been added.

3) It would be nice if Alaska could clarify if a disproportionated state exists without magnetic ordering.
I have clarified this.

### List of changes

List of changes:

1) The arXiv link to the original experimental paper has been updated with the reference to the published paper.

2) Ref. 41, Parragh et al. [PRB 88, 195116 (2013)] has been added in page 4.

3) I have added a following paragraph at the end of Methods section:

"To check convergence with respect to the planewave cut-off, I repeated
the structural relaxations of the various Glazer tilts for a cut-off
value of 60 Ry. Same energetic rankings were obtained. I also did some
calculations with larger $k$-point meshes, and this did not change the
results in a meaningful way. Note that the meshes used in this work
are denser than those used in two recent DFT studies on the rare-earth
niclelates \cite{Varignon2017,Hampel2017}."

4) The imaginary i have been added for the imaginary frequencies in page 6.

5) The a+b-c- tilt is not stabilized for YNiO3, and the corresponding entry in Table I is changed to "---".

6) Section 3.2 is split into two sections:
3.2.1 Spin-polarized structural relaxations in $R\overline{3}c$ LaNiO$_3$
3.2.2 Spin-polarized structural relaxations in $Pnma$ LaNiO$_3$

7) The paragraph "An intriguing aspect of..." near the beginning of section 3.2 has been completely removed to increase clarity.

8) Motivation for the multitude of the spin-polarized calculations have been provided by adding the following paragraph in page 8:

"To understand the nature of magnetic instabilities, if there are any,
in LaNiO$_3$ and possible competition between different magnetic
interactions, I extensively studied the stability of diverse magnetic
ordering phases in several supercells of $R\overline{3}c$ and $Pnma$
structures using spin-polarized DFT calculations within the PBE GGA."

9) The negligence of the matrix element in the Lindhard susceptibility is discussed and justified in futher detail in page 10:

"The negligence of the matrix element changes the relative intensities of
the peaks in the susceptibility \cite{Heil2014}. However, major
features remain the same and qualitative understanding can still be
gleaned off from such an approximation. I note that a previous
discussion of the magnetic susceptibility in the nickelates has also

11) I have added the following sentence at the end of section 3.2:

"This is also supported by the fact that I
was not able to stabilize breathing distortions in the
non-spin-polarized calculations."

10) In Fig. 7, the "L-AFM" and "T-AFM" have been changed to "R-AFM" and "P-AFM", respectively.

11) The last two paragraphs in page 13 have been slightly reworked to improve readability.

### Submission & Refereeing History

Resubmission 1708.08899v2 on 16 July 2018
Submission 1708.08899v1 on 30 August 2017