# Electric manipulation of domain walls in magnetic Weyl semimetals via the axial anomaly

### Submission summary

 As Contributors: Jens H Bardarson · Yago Ferreiros · Julia Hannukainen Preprint link: scipost_202101_00004v2 Date submitted: 2021-04-07 16:29 Submitted by: Hannukainen, Julia Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Approach: Theoretical

### Abstract

We show how the axial (chiral) anomaly induces a spin torque on the magnetization in magnetic Weyl semimetals. The anomaly produces an imbalance in left- and right-handed chirality carriers when non-orthogonal electric and magnetic fields are applied. Such imbalance generates a spin density which exerts a torque on the magnetization, the strength of which can be controlled by the intensity of the applied electric field. We show how this results in an electric control of the chirality of domain walls, as well as in an improvement of the domain wall dynamics, by delaying the onset of the Walker breakdown. The measurement of the electric field mediated changes in the domain wall chirality would constitute a direct proof of the axial anomaly. Additionally, we show how quantum fluctuations of electronic Fermi arc states bound to the domain wall naturally induce an effective magnetic anisotropy, allowing for high domain wall velocities even if the intrinsic anisotropy of the magnetic Weyl semimetal is small.

###### Current status:
Editor-in-charge assigned

We thank the referees for their careful reading of our manuscript, and their constructive comments. We address their comments separately in a response to each report.

### List of changes

Section I:

Redefined the constants of three inline equations in the paragraph following Eq. 1.

Section II.

Added a term to Eq. 12, and described it in the text below this equation together with a reference.

Section III.

Rewritten the section describing the origin of $L_{\mu_5}$. This section starts at the next new paragraph following Eq. 26, and ends with Eq. 28.

Added an equation for the spin Torque; Eq. 30.

Added a paragraph directly after Eq. 30 describing a term due to the chiral separation effect, and why it is neglected.

Added a paragraph in the end of the section describing why we do not capture the term in Eq. 4.

Section IV.

Added a comment on the resulting chiralities; first paragraph in the section, sentence starting with: "Intuitively, the effect can be understood..."

Subsection A.
Rewritten the paragraph following Eq. 42, describing the minimum energy configuration due the field $E_y$.

Subsection B.

First paragraph: Added a description of the choice of magnetic field.

Eq. 44: Rewrote the scalar product in terms of the only non-zero term: $E_zB_z$

Last part of the paragraph after Eq. 45: added a section comparing the value of the velocity due to the effect from the Fermi-arcs, to typical domain wall velocities in nanowires.

Appendix.

After equation A2. Added a sentence explaining that the chemical potential is taken to be zero.

Directly following equation A9: Added a comment on additional gapped bound states.

Typos:

Caption in Figure 3: Changed $B_x$ to $B_y$.
Changed sign of $\gamma^5$ in Eq. 24 and Eq. A2.
Changed $\gamma_5$ to $\gamma^5$ in Eq. A.16.

### Submission & Refereeing History

Resubmission scipost_202101_00004v2 on 7 April 2021
Submission scipost_202101_00004v1 on 8 January 2021

## Reports on this Submission

### Weaknesses

1 - The derivation procedure of the effective Lagrangian in Section 3 may still appear confusing to some readers. The authors insist that the effective Lagrangian is derived by integrating out the fermionic degrees of freedom from the microscopic Weyl Hamiltonian [Eqs.(23) and (24)]. The terms $L_{\mathrm{bound}}$ and $L_{\mathrm{CS}}^5$ are derived in this way in Appendix A. However, as far as I can see from this manuscript, the term $L_{\mu_5}$ is not derived from path integral, but from the form of the axial separation current phenomenologically. While I have no doubt about this derivation process, I encourage the authors to mention that its derivation process is somewhat different from the other parts of the Lagrangian.

### Report

In the revised manuscript, the authors have considered all the suggestions and criticisms raised by the referees, and have significantly improved their presentation. I find that those changes overcome most of the weaknesses pointed out by the referees, except for one raised in this report. I thus believe that this manuscript is worth being published after making some revision.

### Requested changes

1 - In the left column of page 7, I find the word "Block" twice, which may be typos for "Bloch".

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