Ab initio calculations of X-ray magnetic circular dichroism spectra within the projector augmented wave method: An implementation into the VASP code

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• 作者：Anant Dixit¹ ; ^{dixit@ipcms.unistra.fr" class="auth_mail" title="E-mail the corresponding author} ; M. Alouani ; ^{mea@ipcms.unistra.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Ab-initio ; First-principles ; DFT ; XAS ; XMCD ; PAW ; VASP
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：207
• 期：Complete
• 页码：136-144
• 全文大小：573 K

文摘

X-ray absorption and X-ray magnetic circular dichroism (XMCD) are very powerful tools for probing the orbital and spin moments of each atomic species orbital of magnetic materials. In this work, we present the implementation of a module for computing the X-ray absorption and XMCD spectra into the VASP code. We provide a derivation of the absorption cross-section in the electric dipole approximation. The matrix elements, which make up the X-ray absorption cross-section for a given polarization of light, are then computed using either the momentum operator class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301461&_mathId=si22.gif&_user=111111111&_pii=S0010465516301461&_rdoc=1&_issn=00104655&md5=b3256d39fc63d5b5ac366cd07da4500f">class="imgLazyJSB inlineImage" height="9" width="11" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516301461-si22.gif">class="mathContainer hidden">class="mathCode">$p$ or the position operator class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301461&_mathId=si23.gif&_user=111111111&_pii=S0010465516301461&_rdoc=1&_issn=00104655&md5=5ce2c69e83342178308a176431ecd898">class="imgLazyJSB inlineImage" height="6" width="9" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516301461-si23.gif">class="mathContainer hidden">class="mathCode">$r$, within the projector augmented wave method. The core electrons are described using the relativistic basis-set whereas for the valence electrons, the spin–orbit coupling is added perturbatively to the semi-relativistic Hamiltonian. We show that both the class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301461&_mathId=si22.gif&_user=111111111&_pii=S0010465516301461&_rdoc=1&_issn=00104655&md5=b3256d39fc63d5b5ac366cd07da4500f">class="imgLazyJSB inlineImage" height="9" width="11" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516301461-si22.gif">class="mathContainer hidden">class="mathCode">$p$ and the class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301461&_mathId=si23.gif&_user=111111111&_pii=S0010465516301461&_rdoc=1&_issn=00104655&md5=5ce2c69e83342178308a176431ecd898">class="imgLazyJSB inlineImage" height="6" width="9" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516301461-si23.gif">class="mathContainer hidden">class="mathCode">$r$ implementations lead to the same results. The results for the K-edge and L₂₃-edges of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516301461&_mathId=si1.gif&_user=111111111&_pii=S0010465516301461&_rdoc=1&_issn=00104655&md5=ea273b9508295668bb8c111a3e14ed1c" title="Click to view the MathML source">bccclass="mathContainer hidden">class="mathCode">$bcc$-iron are then computed and compared to experiment.