# L edge XAS including rare earth 5d orbital with elliptic DOS

asked by Ruiwen Xie (2021/12/05 22:16)

Dear Quanty Developer,

For the L-edge XAS of CeFe2, if the Hamiltonian is defined as $$ \begin{eqnarray} H=\sum_{\nu}(\epsilon_{f,\nu}-g_j \mu_B j_z h)f^{\dagger}_{\nu}f_{\nu} + \sum_{\mu}\epsilon_{p,\mu}p^{\dagger}_{\mu}p_{\mu} + \sum_{k,\xi}\epsilon_{k,\xi}d^{\dagger}_{k,\xi}d_{k,\xi} + \sum_{\nu}\epsilon_{a,\nu}a^{\dagger}_{\nu}a_{\nu} + \sum_{\nu}(Va^{\dagger}_{\nu}f_{\nu} + V^{*}f^{\dagger}_{\nu}a_{\nu}) + U_{ff}\sum_{\nu>\nu^{\prime}}f^{\dagger}_{\nu}f_{\nu}f^{\dagger}_{\nu^{\prime}}f_{\nu^{\prime}} - U_{fc}\sum_{\nu,\mu}f^{\dagger}_{f,\nu}f_{f,\nu}(1-p^{\dagger}_{p,\mu}p_{p,\mu}) \end{eqnarray} $$ Here, the 5d orbital of the rare earth (third term) is dispersive and the density of states for this 5d band is assumed to be elliptic $$ \begin{equation} \rho_d(\epsilon) = (\frac{2}{\pi W^2})\sqrt{W^2-(\epsilon-E_d)^2}, \end{equation} $$

where E_d is the center of 5d band and there exists spin splitting for 5d band due to 5d(Ce)-3d(Fe) spin polarization. The Fermi level is determined so that the 5d occupancy is 1. Then the 2p state is restricted to be excited only to the unoccupied 5d state.

So, my question is, in Quanty, how should I describe the band-like feature of 5d orbitals? Is it similar to the discretization of ligand orbital (but here only with different on-site energies for different energy levels)? However, since 5d orbital is partially filled, how should I impose the restrictions when solving the eigenstates of Hamiltonian with several discretized energy levels?

I would be very appreciated if you could also share with me some tutorial script (if you have any) regarding my question.

Thanks a lot for your time!

Best Regards, Ruiwen Xie

## Answers

I forgot to mention that I am interested in XMCD, that is why I care about spin splitting of 5d orbital. Thanks again.