Proximity-Induced Magnetic Phases in CrI3 Monolayers Coupled to WSe2
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 \(\delta \hat{V}_i\) ?
\left(\begin{array}{cc}
V_{AA} & 0\\
0 & 0
\end{array}\right),\ \text{vs.}\ \left(\begin{array}{cc}
V_{AA} & V_{AR}/2\\
V_{RA}/2 & 0
\end{array}\right)
3) The definition of local operator in a non-orthogonal basis needs a pragmatic choice!
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
Showcase: CrI3 monolayer
d=1.59 \( \AA \)
Unit cell length: 7.06 \( \AA \)
Exchange parameters [meV]:
J_\mathrm{iso}^{1^{st}}
-0.4
J_\mathrm{iso}^{2^{nd}}
-1.0
J_\mathrm{iso}^{3^{rd}}
0.2
DM_z^{2^{nd}}
0.0
|DM|^{2^{nd}}
0.14
Calculated \( T_C \) is around 45 K
Uppsala Atomistic Spin Dynamics software
K
0.47
Showcase: CrI3 monolayer + WSe2
NO WSe2
Exchange parameters [meV]:
J_\mathrm{iso}^{1^{st}}
-0.4
1.7
J_\mathrm{iso}^{2^{nd}}
-1.0
-1.4
0.5
DM_z^{2^{nd}}
0.0
0.16
|DM|^{2^{nd}}
0.14
0.21
K
0.47
0.61
Cr
I
W
Se
d \( = 1.64 \AA \)
Unit cell length: 6.74 \( \AA \)
d\(_\mathrm{vdW} = 4.23 \AA\)
YES WSe2
Large, 5% strain
J_\mathrm{iso}^{3^{rd}}
0.2
Showcase: CrI3 monolayer + WSe2
NO WSe2
Exchange parameters [meV]:
J_\mathrm{iso}^{1^{st}}
-0.4
1.7
1.9
J_\mathrm{iso}^{2^{nd}}
-1.0
-1.4
-1.5
0.5
0.6
DM_z^{2^{nd}}
0.0
0.16
0.14
|DM|^{2^{nd}}
0.14
0.21
0.22
K
0.47
0.61
N.A.
Unit cell length: 6.74 \( \AA \)
YES WSe2
Large, 5% strain
J_\mathrm{iso}^{3^{rd}}
0.2
NO WSe2
-5% strain
missing
Showcase: CrI3 monolayer + WSe2
NO WSe2
Exchange parameters [meV]:
J_\mathrm{iso}^{1^{st}}
-0.4
1.7
1.9
J_\mathrm{iso}^{2^{nd}}
-1.0
-1.4
-1.5
0.5
0.6
Unit cell length: 6.74 \( \AA \)
YES WSe2
Large, 5% strain
J_\mathrm{iso}^{3^{rd}}
0.2
NO WSe2
-5% strain
We need better twist angle!
-3.2
-0.2
0.1
YES WSe2
NO RELAX
Not insulator anymore!
DM_z^{2^{nd}}
0.0
0.16
0.14
0.0
|DM|^{2^{nd}}
0.14
0.21
0.22
0.14
K
0.47
0.61
N.A.
0.81
Showcase: CrI3 monolayer + WSe2
Exchange parameters [meV]:
NO WSe2
YES WSe2
NO WSe2 , -5% strain
J_\mathrm{iso}^{1^{st}}
-0.4
1.7
1.9
J_\mathrm{iso}^{2^{nd}}
-1.0
-1.4
-1.5
0.5
0.6
DM_z^{2^{nd}}
0.0
0.16
0.14
|DM|^{2^{nd}}
0.14
0.21
0.22
K
0.47
0.61
N.A.
J_\mathrm{iso}^{3^{rd}}
0.2
The servers are down...
-3.2
-0.2
0.1
0.0
0.14
0.81
YES WSe2 NO RELAX
0.81
Showcase: CrI3 monolayer + WSe2
Exchange parameters [meV]:
NO WSe2
YES WSe2
NO WSe2 , -5% strain
J_\mathrm{iso}^{1^{st}}
-0.4
1.7
1.9
J_\mathrm{iso}^{2^{nd}}
-1.0
-1.4
-1.5
0.5
0.6
DM_z^{2^{nd}}
0.0
0.16
0.14
|DM|^{2^{nd}}
0.14
0.21
0.22
K
0.47
0.61
N.A.
J_\mathrm{iso}^{3^{rd}}
0.2
Preliminary results!
GROGU is a post processing tool
The results are as good as your DFT
-3.2
-0.2
0.1
0.0
0.14
YES WSe2 NO RELAX
0.81
Relativistic magnetic interactions
- Very early release !!
- 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
BME 2025
By novidad21
