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Electric manipulation of domain walls in magnetic Weyl semimetals via the axial anomaly
by Julia D. Hannukainen, Alberto Cortijo, Jens H. Bardarson, Yago Ferreiros
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users):  Jens H Bardarson · Yago Ferreiros · Julia Hannukainen 
Submission information  

Preprint Link:  scipost_202101_00004v2 (pdf) 
Date accepted:  20210428 
Date submitted:  20210407 16:29 
Submitted by:  Hannukainen, Julia 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

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 righthanded chirality carriers when nonorthogonal 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.
Author comments upon resubmission
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 nonzero 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 Fermiarcs, 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.
Published as SciPost Phys. 10, 102 (2021)
Reports on this Submission
Anonymous Report 2 on 2021421 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202101_00004v2, delivered 20210421, doi: 10.21468/SciPost.Report.2817
Report
In their resubmission authors have addressed well all the point raised in my first report, and I think the manuscript makes for a clear and interesting read, to which I have no further remarks. I stand by my earlier assessment that the paper satisfies all the general acceptance criteria of the journal and expectation 3: "Open a new pathway in an existing or a new research direction, with clear potential for multipronged followup work", as I justified in the previous report. Therefore, I recommend the manuscript for publishing in SciPost Physics.
Anonymous Report 1 on 2021414 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202101_00004v2, delivered 20210414, doi: 10.21468/SciPost.Report.2793
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".
Author: Julia Hannukainen on 20210428 [id 1387]
(in reply to Report 1 on 20210414)We thank the referee for their report. We address the points raised by the referee:
"1The 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 $L_{bound}$ and $L_{5CS}$ 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."
We will update the manuscript by adding the sentence: "The derivation of the second contribution to the effective Lagrangian, $L_{\mu_5}$, differs from the derivation of $L_{\rm{bound}}$; rather than starting from the Weyl Lagrangian in Eq.(23), the existence and specific form of $L_{\mu_5}$ are instead derived from the axial separation effect.", at the beginning of the section deriving $L_{\mu_5}$, in the main text.
"2 In the left column of page 7, I find the word "Block" twice, which may be typos for "Bloch"."
These are indeed typos and will be corrected in the updated manuscript.