Magnetic anisotropy and intermediate valence in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>CeCo</mml:mi> <mml:mn>5</mml:mn> </mml:msub> </mml:math> ferromagnet

The intermediate valence of Ce in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>CeCo</a:mi> <a:mn>5</a:mn> </a:msub> </a:math> challenges standard density functional theory (DFT) and static <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>DFT</b:mi> <b:mo>+</b:mo> <b:mi>U</b:mi> </b:mrow> </b:math> approaches, which fail to capture its magnetic properties. By combining <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>DFT</c:mi> <c:mo>+</c:mo> <c:mi>U</c:mi> </c:mrow> </c:math> with exact diagonalization of the Anderson impurity model for the Ce <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mn>4</d:mn> <d:mi>f</d:mi> </d:mrow> </d:math> shell, we find a substantial reduction of Ce spin and orbital moments, consistent with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>DFT</e:mi> <e:mo>+</e:mo> <e:mi>DMFT</e:mi> </e:mrow> </e:math> (dynamical mean-field theory), arising from <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msup> <f:mrow> <f:mi>Ce</f:mi> </f:mrow> <f:mrow> <f:mn>4</f:mn> <f:mo>+</f:mo> </f:mrow> </f:msup> <f:mo>−</f:mo> <f:msup> <f:mrow> <f:mi>Ce</f:mi> </f:mrow> <f:mrow> <f:mn>3</f:mn> <f:mo>+</f:mo> </f:mrow> </f:msup> </f:math> valence fluctuations. The total magnetic moment of 6.70 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msub> <g:mi>µ</g:mi> <g:mi>B</g:mi> </g:msub> </g:math> agrees with experiment, and the calculated <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mn>4</h:mn> <h:mi>f</h:mi> </h:mrow> </h:math> density of states reproduces photoemission and bremsstrahlung isochromat spectra. The uniaxial magnetic anisotropy energy reaches 4.8 meV/f.u. when Coulomb correlations on both Ce <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mn>4</i:mn> <i:mi>f</i:mi> </i:mrow> </i:math> and Co <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mn>3</j:mn> <j:mi>d</j:mi> </j:mrow> </j:math> shells are included, in very good agreement with experimental data. These results highlight the importance of dynamical correlations and provide guidance for exploring high-performance, low-rare-earth-content permanent magnets.