# Momentum-space and real-space Berry curvatures in Mn$_{3}$Sn

### Submission summary

 As Contributors: Kamran Behnia · Alaska Subedi · Zengwei Zhu Arxiv Link: https://arxiv.org/abs/1802.00277v4 Date accepted: 2018-11-29 Date submitted: 2018-11-07 Submitted by: Behnia, Kamran Submitted to: SciPost Physics Domain(s): Experimental Subject area: Condensed Matter Physics - Experiment

### Abstract

Mn$_{3}$X (X= Sn, Ge) are noncollinear antiferromagnets hosting a large anomalous Hall effect (AHE). Weyl nodes in the electronic dispersions are believed to cause this AHE, but their locus in the momentum space is yet to be pinned down. We present a detailed study of the Hall conductivity tensor and magnetization in Mn$_{3}$Sn crystals and find that in the presence of a moderate magnetic field, spin texture sets the orientation of the $k$-space Berry curvature with no detectable in-plane anisotropy due to the $Z_6$ symmetry of the underlying lattice. We quantify the energy cost of domain nucleation and show that themultidomain regime is restricted to a narrow field window. Comparing the field dependence of AHE and magnetization, we find that there is a distinct component in the AHE which does not scale with magnetization when the domain walls are erected. This so-called `topological' Hall effect provides indirect evidence for a non-coplanar spin components and real-space Berry curvature in domain walls.

### Ontology / Topics

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Resubmission Comment
We are grateful to both referees for their insightful comments, which helped us to improve the manuscript. We agree with the second point raised by referee 2 that noncoplanar spin texture has implications for components of the Hall conductivity besides those discussed here. But, this is not the subject of the present already lengthy communication.

### List of changes

Following referees’ recommendations, here are the changes in the new version:
1. We have deleted the statement "the U(1) symmetry is not broken to a Z6 anisotropy." We have detailed our discussion of single-ion-anisotropy and included a reference to an angle-dependent torque magnetometry study, in agreement with what is implied by our angle-dependent measurements of Hall conductivity.
2. We have made a more precise statement regarding the link between equilibrium and sweeping rate, by adding: “In other words, the time scale of all detectable dynamic phenomena remains faster than our sweeping rates.”
3. We have clarified the distinction and the links between ‘topological’ Hall effect, out-of-plane spin component and skyrmionic number. We specified that skyrmionic number can be finite even in absence of a skyrmion lattice.
4. We removed grammatical and spelling mistakes, which we could identify.

### Submission & Refereeing History

Resubmission 1802.00277v4 on 7 November 2018
Submission 1802.00277v3 on 31 August 2018

## Reports on this Submission

### Report

I am satisfied with the revised manuscript and suggest the publication in current form.

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