structure

Bulk experimentally synthesized*

*Ref: Monohalogenide der Lanthanoide, Hj. Mattausch, et.al, ZAAC, 1980

E_{\text{bind}} =\frac{(E_{\text{full layer}} - 2 \times E_{\text{half layer}})}{A_{\text{contacting}}}

E_{\text{bind}} =\frac{(E_{\text{full layer}} - 2 \times E_{\text{half layer}})}{A_{\text{contacting}}}

FM

AFM

Spacegroup:
Binding energy:

0.11 \mathrm{eV/ Å^{2}}

0.11 \mathrm{eV/ Å^{2}}

\mathrm{P\bar{3}m1}

\mathrm{P\bar{3}m1}

MagnetiC site

Spin density ( )

\rho_{\uparrow} - \rho_{\downarrow}

\rho_{\uparrow} - \rho_{\downarrow}

FM

Off atom electrons contributes the most!

AFM

Monolayer LaBr is an 2D magnetic material with a magnetic moment of

1.7 \mu_B .

1.7 \mu_B .

Dice Model

The Dice model:
- Sites arranged in a triangle lattice.
- One possible hopping quenched (here, $t_{23}$ ).
- The remaining hoppings cause destructive interference.

Wavefunction plot for the middle band @ Gamma

Flat band!

Extended Hubbard Model

To understand the underlying mechanism of magnetism relating to the flat band, we employed extended Hubbard model.
The electron-electron interaction is taken into consideration in a mean-field self-consistent fashion.

\begin{aligned} \mathcal{H}=&-t \sum_{\langle ij\rangle} \sum_{\sigma}\left(c_{i \sigma}^{\dagger} c_{j \sigma}+c_{j \sigma}^{\dagger} c_{i \sigma}\right) \\ \end{aligned}

\begin{aligned} \mathcal{H}=&-t \sum_{\langle ij\rangle} \sum_{\sigma}\left(c_{i \sigma}^{\dagger} c_{j \sigma}+c_{j \sigma}^{\dagger} c_{i \sigma}\right) \\ \end{aligned}

\begin{aligned} &+U \sum_{i} n_{i \uparrow} n_{i \downarrow}+X \sum_{\langle ij \rangle} \sum_{\sigma}\left(c_{i \sigma}^{\dagger} c_{j \sigma}+c_{j \sigma}^{\dagger} c_{i \sigma}\right)\left(n_{i,-\sigma}+n_{j,-\sigma}\right) \\ &+J \sum_{\langle ij \rangle} \left(\frac{1}{2}\sum_{\alpha,\beta} c_{i\alpha}^{\dagger} \sigma_{\alpha\beta} c_{i\beta}\right) \left(\frac{1}{2}\sum_{\alpha,\beta} c_{j\alpha}^{\dagger} \sigma_{\alpha\beta} c_{j\beta}\right) \end{aligned}

\begin{aligned} &+U \sum_{i} n_{i \uparrow} n_{i \downarrow}+X \sum_{\langle ij \rangle} \sum_{\sigma}\left(c_{i \sigma}^{\dagger} c_{j \sigma}+c_{j \sigma}^{\dagger} c_{i \sigma}\right)\left(n_{i,-\sigma}+n_{j,-\sigma}\right) \\ &+J \sum_{\langle ij \rangle} \left(\frac{1}{2}\sum_{\alpha,\beta} c_{i\alpha}^{\dagger} \sigma_{\alpha\beta} c_{i\beta}\right) \left(\frac{1}{2}\sum_{\alpha,\beta} c_{j\alpha}^{\dagger} \sigma_{\alpha\beta} c_{j\beta}\right) \end{aligned}

Main Takeaways

Methods

structure

Flat band

Controlling Flat band

MagnetiC site

Interstitial sites

ELECTRIDES!

Dice Model

Extended Hubbard Model

results

Summary

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