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
DPG 2026
By novidad21
