Proximity-Induced Magnetic Phases in CrI3 Monolayers Coupled to WTe2

Eötvös Loránd University

Centre For Energy Research

Zoltán Tajkov

The Team

  • László Oroszlány, Zoltán Tajkov, János Koltai, Dániel Pozsár, Andor Kormányos, András Balogh, Tamás Véber, Marcell Sipos
     
  • Jaime Ferrer, Amador Garcia Fuente, Gabriel Martinez-Carracedo, Aurelio Hierro Rodriguez, Balázs Nagyfalusi, Rosa Eulalia González Ferreras
     
  • Felix Büttner, Kai Litzius, Steffen Wittrock
     
  • Efren Navarro-Moratalla, Marta Galbiati, Jose Joaquin Perez Grau
     
  • László Szunyogh, László Udvardi, Bendegúz Nyári, Anjali Jyothi Bhasu 
\mathcal{H}=-\frac{1}{2}\displaystyle\sum_{i\ne j}J_{ij}\,\vec{e}_{i}\vec{e}_{j}
E_{ij}^{\mathrm{int}}=\delta E(\vec{e}_{i},\vec{e}_{j})-\delta E(\vec{e}_{i})-\delta E(\vec{e}_{j})=-J_{ij}\,\delta\vec{e}_{i}\delta\vec{e}_{j}
\delta E_{\text{KS},ij}=\frac{1}{\pi}\displaystyle\int\limits _{-\infty}^{\varepsilon_\text{F}}\mathrm{d}\varepsilon\,\text{ImTr}\left(\delta\hat{V_i}\hat{G}(\varepsilon)\delta\hat{V_j}\hat{G}(\varepsilon)\right)

Heisenberg model and DFT perturbation theory

DFT through

RKKR

&

Liechtenstein, Katsnelson , Antropov,  Gubanov

J. Magn. Magn. Mater. 67 65 (1987)

 

Oroszlány, Ferrer, Deák, Udvardi, Szunyogh
Phys. Rev. B 99, 224412  (2019)

What is \(\delta \hat{V}_i\) ?

1) We need to rotate the magnetic moment!

2) We need to identify the magnetic entity!

Could be:

  • Single atom
  • Cluster of atoms
  • Certain orbitals inside an atom

Relativistic magnetic model parameters

\mathcal{H}=\frac{1}{2}\sum_{i\neq j}J_{ij}^{H}\boldsymbol{e}_{i}\cdot\boldsymbol{e}_{j}+\frac{1}{2}\sum_{i\neq j}\boldsymbol{e}_{i}\hat{J}_{ij}^{S}\boldsymbol{e}_{j}+\frac{1}{2}\sum_{i\neq j}\boldsymbol{D}_{ij}\cdot\left(\boldsymbol{e}_{i}\times\boldsymbol{e}_{j}\right)+\sum_{i}\boldsymbol{e}_{i}\hat{K}_{i}\boldsymbol{e}_{i}

Udvardi, Szunyogh, Palotás, Weinberger

Phys. Rev. B 68, 104436 (2003)

 

Martínez-Carracedo, Oroszlány, García-Fuente, Nyári, Udvardi, Szunyogh, Ferrer
Phys. Rev. B 108, 214418  (2023)

Istropic

exchange

Symmetric  traceless exchange

Dzyaloshinskii - Moriya vector

On-site

anisotropy

Grogu

State of GROGU

\mathcal{H}=\frac{1}{2}\sum_{i\neq j}J_{ij}^{H}\boldsymbol{e}_{i}\cdot\boldsymbol{e}_{j}+\frac{1}{2}\sum_{i\neq j}\boldsymbol{e}_{i}\hat{J}_{ij}^{S}\boldsymbol{e}_{j}+\frac{1}{2}\sum_{i\neq j}\boldsymbol{D}_{ij}\cdot\left(\boldsymbol{e}_{i}\times\boldsymbol{e}_{j}\right)+\sum_{i}\boldsymbol{e}_{i}\hat{K}_{i}\boldsymbol{e}_{i}

Udvardi, Szunyogh, Palotás, Weinberger

Phys. Rev. B 68, 104436 (2003)

 

Martínez-Carracedo, Oroszlány, García-Fuente, Nyári, Udvardi, Szunyogh, Ferrer
Phys. Rev. B 108, 214418  (2023)

Grogu

  • Full SIESTA support
  • GPU support
  • Relativstic parameters
  • Flexible API to set up more complicated systems with complex magnetic entities
  • Command line interface to extract and visualize the magnetic parameters
  • Multiple output formats for atomistic spin dynamics softwares

Coming soon:

  • Wannier90 support
  • OpenMX support
  • Higher order interaction 

Showcase: CrI3 monolayer

Cr

I

  • Semiconductor
  • Experimental \( T_C \) is around 45 K
  • Superexchange
  • Hubbard-U, U=3eV needed!

Showcase: CrI3 monolayer

d=1.62 \( \AA \)

Unit cell length: 7.13 \( \AA \)

Exchange parameters [meV]:

Calculated \( T_C \) is around 23 K

VAMPIRE 7

J_\mathrm{iso}^{1^{st}}

-1.14

J_\mathrm{iso}^{2^{nd}}

-0.93

J_\mathrm{iso}^{3^{rd}}

-0.02

|DM|^{2^{nd}}

0.15

D. Wang, Journal of Physical Chemistry C 125, 18467, 2021

Showcase: CrI3 monolayer + WTe2

Exchange parameters [meV]:

Cr

I

W

Te

d \( = 1.64  \AA \)

Unit cell length: 7.13 \( \AA \)

d\(_\mathrm{vdW} = 4.28 \AA\)  

Small, > 0.15% strain

J_\mathrm{iso}^{1^{st}}

-1.14

-1.16

J_\mathrm{iso}^{2^{nd}}

-0.93

-1.03

J_\mathrm{iso}^{3^{rd}}

-0.02

-0.05

|DM|^{2^{nd}}

0.15

0.38

Pure CrI3

With WTe2

Showcase: CrI3 monolayer + WTe2

Exchange parameters [meV]:

J_\mathrm{iso}^{1^{st}}

-1.14

-1.16

J_\mathrm{iso}^{2^{nd}}

-0.93

-1.03

J_\mathrm{iso}^{3^{rd}}

-0.02

-0.05

|DM|^{2^{nd}}

0.15

0.38

  • Tc for pure CrI3:       23 K     Pure CrI3
  • Tc for CrI3+WTe2:    32 K     With WTe2

VAMPIRE 7

40% increase

Pure CrI3

With WTe2

Showcase: CrI3 monolayer + WTe2

\vec{E}_\text{ext}

Modest external electric field  boosts Tc up to 33% 

VAMPIRE 7

Relativistic magnetic interactions

  • https://github.com/danielpozsar/grogu
  • Single DFT calculation
  • Pair creation is extremely cheap
  • parallel BZ integral with MPI or CUDA
  • Generalised Heisenberg model
H(\{\mathbf{S}_i\}) = \frac{1}{2} \sum_{i \neq j} \mathbf{S}_i \mathcal{J}_{ij} \mathbf{S}_j + \sum_i \mathbf{S}_i K_i \mathbf{S}_i

UNDER 1 Hour on 8 GPUs