Simulating Domain Walls in Weyl 

Semimetals to Study the Effects of 

Weyl Fermions on Magnetic Behavior

Patrick Chen

Lab: NIST Center for Neutron Research(NCNR)

Mentors: Jonathan Gaudet, Michael Donahue(ITL)

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Goal

Accurately model the magnetic behavior in 

Weyl semimetals to explore novel behaviors 

caused by the influence of Weyl electrons.

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Background Information

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Spin and Magnetism ● Spin is an inherent property 

of elementary particles ○ Can be thought of as a “tiny 

magnet” for the purposes of 

this presentation

● Large regions of aligned spin 

are called ferromagnetic 

domains and result in a net 

magnetization

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Domain Walls and Magnetic Interactions

Exchange - Local interaction 

of neighboring atoms 

through overlapping 

wavefunctions

Dipole/Demagnetization -

Long range effect due to the 

net magnetization

Anisotropy - Preferred axis of 

alignment

Ferromagnetic

Preferred axis

or

Antiferromagnetic

Domain Wall

● A single crystal can have multiple 

domains of differing alignments. 

○ Transition region is called a 

domain wall

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What is special about Weyl semimetals?

● Weyl electrons

○ “Massless” - highly mobile

○ Chiral - “handedness”

○ Mediates the DzyaloshinskiiMoriya(DM) interaction that 

tends to misalign neighboring 

spins

Direction of Propagation

Weyl electrons

Local spin 6

CeAlSi
Neutron Scattering

● Why is it useful?

○ Measures magnetic and 

structural properties

○ Highly penetrating, so it is 

able to measure bulk

properties

○ Sensitive on nanometer

and micron length 

scales(for Small Angle 

Neutron Scattering(SANS))

https://www.nist.gov/image/scatteringgif-0

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High-q Low-q
Comparison to Neutron Scattering Data

Simulated Scattering of Bilayer 

Striped Domains

Measured Scattering Data

Figure in progress

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CeAlSi
Creating the Model

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OOMMF Toolkit and Procedures

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● Initiate from a 

random configuration 

of spins

● “Solves” the spin 

configuration by 

minimizing energy

● Should be thought of 

as a small part of a 

larger crystal
Verification of the OOMMF Simulation

● Includes only the exchange, 

anisotropy and dipole interactions 

which are well understood. 

○ Expect domain wall to process 

along the in/out-of-plane direction.

y

z

x

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Modeling the DM Interaction

y

z

x

Without DM

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With DM

● Expectations

○ More domains, leading to stripes

○ Chiral domain wall transitions Red - Out of Plane(+x)

Blue - Into Plane(-x)
Conclusion and Future Direction

Results

● Model successfully 

incorporates the DM 

interaction

● Observed chiral stripes in 

simulated Weyl semimetal

○ Connects the theory for 

DM to observed scattering 

data

Future Direction

● Tune parameters to correlate 

more closely with real world 

measurements

● Generate scattering profiles of 

these simulations

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Acknowledgments

● Jonathan Gaudet

● Michael Donahue

● Summer Undergraduate Research 

Fellowship(SURF)

○ Cara O’Malley

○ Julie Borchers

○ Susana Teixeira

○ Leland Harriger

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The Center for High Resolution Neutron Scattering (CHRNS) is a national user 

facility jointly funded by the NIST Center for Neutron Research (NCNR) and the 

National Science Foundation (NSF) under Agreement No. DMR-2010792
Questions?

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R = Nd, 

Sm, or Ce

Al

X=Si or Ge

RAlX

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Exchange DM

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Elias, Nature Physics 7, 701-704 (2011) S. Nakatsuji and N. Kiyohara, Nature 527.7577 (2015)

Break inversion symmetry

Break time-reversal 

symmetry(magnetism)

and/or

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Magnetic Paramagnetic

Multi-domain Single-domain

2 K
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