https://www.quanty.org/ 2026-04-29T06:50:49+00:00 https://www.quanty.org/ https://www.quanty.org/_media/wiki/dokuwiki.svg text/html 2025-11-20T02:29:44+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/density_matrix_plot?rev=1763605784&do=diff Density matrix plot An intuitive way to look at eigenstates is to plot the charge density. For multi-electron wave-functions one can not plot the wave-function (it depends on $3\times n$ coordinates) but the charge density is a well defined simple quantity. We here use the rendering options of \textit{Mathematica} in combination with the package for \textit{Mathematica} (Quanty.nb) to plot the density matrix of the lowest three eigenstates in NiO.$S_z=-1$$S_z=0$$S_z=1$$x^2-y^2$$z^2$$S_z=0$nio_cr… text/html 2025-11-20T02:29:46+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/energy_level_diagram?rev=1763605786&do=diff Energy level diagram In order to do temperature averaging it is important to understand the number of excited states that are important. One can learn a lot by looking at the energy level diagram. Here we plot one for Ni$^{2+}$.The input file is: -- For NiO we know that 10Dq=1.1 eV, however if you have a new compound you might roughly -- know these values, but never exactly. It is then nice to see how the eigen-state -- energies change as a function of 10Dq. -- plots were one shows the eigen-… text/html 2025-11-20T02:29:44+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/fy_l23m1?rev=1763605784&do=diff FY $L_{2,3}M_{1}$ In Fluoressence Yield spectroscopy one can focus on different decay channels. Each of them will yield a different spectrum. For a $2p$ to $3d$ excitation one can look at the $3s$ to $2p$ decay. The edge measured is thus the $L_{2,3}M_{1}$ edge.The corresponding input file is:$L_{2,3}M_{45}$nio_crystal_field index text/html 2025-11-20T02:29:45+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/fy_l23m45?rev=1763605785&do=diff FY $L_{2,3}M_{4,5}$ The absorption cross section is in principle measured using transmission. Transmission experiments in the soft-x-ray regime can be difficult as the absorption is quite high. Alternatively one can measure the reflectivity, which allows one to retrive the complete conductivity tensor using ellipsometry. As the x-ray wave-length is not large compared to the sample thickness this does not return the average sample absorption, but gives spatial information as well. Known as resona… text/html 2025-11-20T02:29:44+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/groundstate?rev=1763605784&do=diff Groundstate The first example looks at the ground-state of NiO. Ni in NiO is $2+$ and thus has locally $8$ electrons in the Ni $d$-shell. The lowest state has two holes in the $e_g$ orbitals with $S=1$ ($\langle S^2\rangle=1(2+1)=2$). The output of this example shows several expectation values of the $45$$d^8$nio_crystal_field index text/html 2025-11-20T02:29:45+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/nixs_l23?rev=1763605785&do=diff nIXS $L_{2,3}$ Besides low energy transitions nIXS can be used as a core level spectroscopy technique. One then measures resonances with non-resonant inelastic x-ray scattering :-).The input script: -- using inelastic x-ray scattering one can not only measure low energy excitations, -- but equally well core to core transitions. This allows one to probe for example -- 3p to 3d transitions using octupole operators. -- We set the output of the program to a minimum Verbosity(0) -- we need a 2p … text/html 2025-11-20T02:29:45+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/nixs_m45?rev=1763605785&do=diff nIXS $M_{4,5}$ ($d$-$d$ excitations) Inelastic x-ray scattering IXS (non-resonant) nIXS or x-ray Raman scattering allows one to measure non-dipolar allowed transitions. A powerful technique to look at even $d$-$d$ transitions with well defined selection rules \cite{Haverkort:2007bv, vanVeenendaal:2008kv, Hiraoka:2011cq}, but can also be used to determine orbital occupations of rare-earth ions that are fundamentally not possible to determine using dipolar spectroscopy \cite{Willers:2012bz}.$d$$d$… text/html 2025-11-20T02:29:44+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/rixs_l23m1?rev=1763605784&do=diff RIXS $L_{2,3}M_{1}$ Instead of looking at low energy excitations one can use RIXS to look at core-core excitations. A powerful technique comparable to other core level spectroscopies like x-ray absorption and core-level photoemission at once.Here a script to calculate the Ni $2p$$3d$$L_{2,3}$$3s$$2p$$M_{1}$$L_{2,3}M_{4,5}$nio_crystal_field index text/html 2025-11-20T02:29:45+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/rixs_l23m45?rev=1763605785&do=diff RIXS $L_{2,3}M_{4,5}$ Using the function ResonantSpectra we can calculate inelastic x-ray scattering. (or other second order processess) Here we show the example of $d$-$d$ excitations in NiO using RIXS. Due to an ever increasing resolution this method gains rapidly in popularity and impact. See for example the combined work of Ghiringhelli \textit{et al.} For NiO see \cite{Ghiringhelli:2005kp}.$d$$d$nio_crystal_field index text/html 2025-11-20T02:29:46+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/start?rev=1763605786&do=diff NiO crystal field This tutorial shows several calculations of NiO in the crystal-field approximation. Within the crystal-field approximation the solid is approximated by a single atom in an effective electric potential. This is a huge simplification and for many properties not valid. One should not confuse the crystal field potentials with real potentials. They are introduced to mimic the bonding in a crystal. Non-the-less it is a rather useful approximation for many local properties of a solid.… text/html 2025-11-20T02:29:44+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/temperature?rev=1763605784&do=diff Temperature The effect of temperature can be added by calculating excited states and expectation values of excited states. The temperature dependent expectation value is then created using Boltzmann statistics.A small example: -- Sofar we calculated eigenstates and expectation values (or spectra) of these -- eigenstates. At 0 K one would measure the expectation value of the lowest eigenstate -- at finite temperature one would measure an average over several states weighted by -- Boltzmann stat… text/html 2025-11-20T02:29:44+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/xas_l23_as_conductivity_tensor?rev=1763605784&do=diff XAS $L_{2,3}$ as conductivity tensor Absorption spectra are polarization dependent. In principle one can choose an infinite different number of polarizations. Calculating for each different experimental geometry (or polarization) a new spectrum is cumbersome and not needed. The material properties are given by the conductivity tensor. For dipole transitions a 3 by 3 matrix. The absorption spectra for a given experiment are then found by the relation:\begin{equation} I(\omega,\epsilon) = -\mathrm… text/html 2025-11-20T02:29:46+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/xas_l23_partial_excitations?rev=1763605786&do=diff XAS $L_{2,3}$ partial excitations In order to understand where a particular peak originates from one can look at the character of the excited state. Quanty works with Green's functions and we can not just look at the excited eigen-states as these are not really calculated. We can however modify the transition operator in order to understand where the spectra come from. The example below looks at excitations into the $t_{2g}$$e_g$$d$$j=1/2$$j=3/2$$2p$$2p$$3d$$e_g$$t_{2g}$$2p_{j=1/2}$$2p_{j=3/2}$n… text/html 2025-11-20T02:29:45+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/tutorials/nio_crystal_field/xas_l23?rev=1763605785&do=diff XAS $L_{2,3}$ Once the ground-state is calculated one can calculate the spectra. This example shows the Ni $2p$ to $3d$ excitations in NiO. Note that these excitations have an energy of more than 800 electron Volt, which is much higher than the chemically relevant energy scales. Non-the-less these kind of spectroscopy contain useful information on the local ground-state wave-function and the low energy effective Hamiltonian. nio_crystal_field index