A55.007: Room 305, Mon. March 6

Skyrmions in van der Waals centrosymmetricmaterials
Hung Ba Tran1,2,*, Yu-ichiro Matsushita1,2,3
1Tokyo Institute of Technology, Japan
2Quemix Inc., Tokyo, Japan
3
QST, Tokyo, Japan

Email: tran.h.ag@m.titech.ac.jp1Introduction
Noncentrosymmetric vs Centrosymmetric

Searching new mechanism to stabilize skyrmions in centrosymmetric lattice is urgent task
Chem. Rev. 121, 2857 (2021)

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Introduction
Target materials
MX3
M: V, Cr, Fe, Mn
X: Cl, Br, I!
R𝟑bccaDzyaloshinskii-Moriya interactions of2nd NN can be finiteab
Purpose: To investigate the effect of Dzyaloshinskii-Moriya interactions on magnetic
properties of van der Waals centrosymmetric MX3

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Methods
Classical Heisenberg model with Dzyaloshinski-Moriya interaction
𝟐𝑯𝐇𝐞𝐢𝐬 = − $ 𝑱𝒎
𝒊𝒋 𝑺𝒊 ' 𝑺𝒋 − $ 𝑫𝒊𝒋 ' (𝑺𝒊 ×𝑺𝒋 ) − $ 𝒌𝐮 (𝒆𝒖 ' 𝑺𝒊 ) − 𝒈𝝁𝐁 $ 𝑯𝐞𝐱𝐭 ' 𝑺𝒊!𝒊𝒋$!𝒊𝒋$𝒊

Isotropic
exchange

Antisymmetricexchange𝒊Uniaxial
anisotropy

ZeemanResults and Discussions
Isotropic exchange coupling constant Jij of CrX 3
MAE 0.034 (meV/Cr-atom)
8
Cr−CrCrCl3420−20.4

MAE 0.590 (meV/Cr-atom)
Cr−Cr

6Jij (meV)

Jij (meV)

68CrI34200.8
1.2
distance d/a

1.6

−20.4

0.8
1.2
distance d/a

1.6

We use classical Heissenberg model with isotropic exchange, antisymmetric exchangeor DMI, uniaxial anisotropy, and Zeeman term. All parameters of Monte Carlosimulations are obtained from first principles calculations.
First we consider the magnetic exchange coupling constants Jij in CrX3. When Xchange from Cl to I, the magnetocrystalline anisotropy increase from 0.034 to 0.590
meV/ Cr-atom. The positive value of MAE mean the easy axis is out of plane, the cdirection. In additions, the interlayer exchange coupling constant in CrCl3 is positive.
So it does not support the in plane AFM in experimental paper.

4Dij length and magnetization of CrX330
20DMI on 40

230
201

1

10

100.2

50

100T (K)15000200050

3DMI off 40

230
20100T (K)150

3DMI on 40

230
201

1

101000.4

0.8
1.2
distance d/a1.6

00200
5050

CrI30.40χ (a.u)

Cr−Cr01.6M (µB/f.u)|Dij| (meV)

0.6

0.8
1.2
distance d/a

M (µB/f.u)

00.4

χ (a.u)23

χ (a.u)0.2

DMI off 40
χ (a.u)0.4

M (µB/f.u)|Dij| (meV)

CrCl35050

3M (µB/f.u)

SPR-KKR (LDA-wSOC) and Vasp (optB86b-vdw-wSOC)
0.6 Cr−Cr

050

100T (K)

150

0200

0050

100
T (K)

1500200

Then we consider the DMI in first principles calculations. The DMI of second nerest
neighbor of intralayer is finite and quite large even in CrCl3. As point out in previous
slide, the results of MAE and Jij in CrCl3 does not suport the inplane AFM inexperimental works. And if we calculated the magnetization with switch off DMI, all
CrX3 shows clear FM-PM transition with the ground state being FM.
But if we include the DMI in simulations, the FM in CrCl3 is disappeared while theFM-PM transition is maintained in CrBr3 and CrI3 due to high MAE. So with the DMIin simulation, we can get zero magnetization and magnetic susceptibility in CrCl3,similar behavior with experimental of inplane AFM order.

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Comparison of magnetic phase diagram of CrCl3high

1m (a.u)

H (kOe)

100.1

0.01

low
204060

80

100

T (K)
Phys. Rev. Mater. 1, 014001 (2017)

Then we calculate the magnetic phase diagram of CrCl3. the blue color means
magnetization is small, it is AFM or PM in experimental phase diagram. The red color
means the magnetization is high, it is FM in experimental. Here at this temperature,
the red region is expand in low magnetic field region. We got a good agreement withexperimetal study.

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Magnetic phase diagram in CrCl3

1010860
50840306201040@10K-4T−102 −40−30−20−10 0 10 20 30 40 50 60 70

FM6𝜒(a. u)

H (T)@10K-0T
Incommensurate

PM4SkL
2020

7.68
7.68
7.68
7.68
7.68
−z
7.68

Skyrmion lattice

IC0+z7.68

4060
T (K)

80

1000D≅2nmbc

aThen we check the snapshot of Monte Carlo simulations for making the magnetic
phase diagram in magnetic susceptibility. At 10 K and 0 T, the magnetic phase isincomensurate with broken of long range order. If we apply magnetic field like 4 T, wecan get the skyrmion lattice in CrCl3.

7108FM

66PM44SkL

202IC0204060T (K)8010020

2.35 degree

5bca02SkL

VCl3
0050

VCl3-@10K-6T

10 nm

10 nm

7.68+z7.68
7.68
7.68
7.68
7.68
7.68

−z1IC

CrCl3-@10K-4T

60
50
4030b20
100ca−10−40−30−20−10 0 10 20 30 40 50 60 70

3PM

105CrCl3

4FM15

𝜒(a. u)H (T)86.69 degree

𝑫𝑴H (T)10𝜒(a. u)

Skyrmion in CrCl3 and VCl3100T (K)60
5040b3020100ca−10−40−30−20−10 0 10 20 30 40 50 60 70

15020007.68
+z
7.68
7.68
7.68
7.68
7.68
7.68

−z

We also found that VCl3 also have similar magnetic phase diagram as CrCl3. However,the DM vector of VCl3 is nearly opposite with CrCl3. It leads to two type of skyrmion
with diferent helicity. If we can control the electron or hole dope in multilayer, wemight control the helicity of the materials. Note that the skyrmion diameter is quitesmall, about 2 nm due to the centrosymmetric materials.

810 nmMeron and AFM skyrmion in
MnCl3 and FeCl3

Meron in
MnCl3

105Jij (meV)0−10−15V−VCr−CrMn−Mn
Fe−Fe−20−250.4|Dij| (meV)

60504030
2010b0−10−40−30−20−10 0 10 20 30 40 50 60 70

−50.6

1V−V
0.9
Cr−Cr0.8 Mn−Mn
Fe−Fe0.7
0.6
0.5
0.4
0.3
0.2
0.1
00.4 0.6

0.8

11.2 1.4
distance d/a1.6

1.8

c+z7.68

7.68
7.68
7.68
7.68
7.68
−z7.68a10 nm

AFM Skyrmion in FeCl3

0.8

11.2 1.4
distance d/a1.6

1.8

60
5040b30
2010a0c−10−40−30−20−10 0 10 20 30 40 50 60 70+z7.68
7.68
7.68
7.68
7.68
−z7.68
7.68

We also found the Meron in MnCl3 and AFM skyrmion in FeCl3. In MnCl3, themagnetic anisotropy is easy plane with ab plane, it leads to the formation of Meronat zero external magnetic field.
In FeCl3, the magnetic exchange coupling constants is negative, so it prefer AFMorder. The AFM skyrmion has advantage that the hall velocity is approximately equal
to zero, so it can survivor for long time.

9Summary
New mechanism to stabilize skyrmions invan der Waals centrosymmetric material

Not only skyrmions but also meron andantiferromagnetic skyrmions are observed

VCl3 and CrCl3 shows posibility to control
helicity by heterostructure and electric field

H. B. Tran, Y. Matsushita, arXiv:2209.02333(2022)

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Thank you so much for kind attentions!

That all for our talk today, thank you so much for kind attentions.

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