Element-specific insight into ferromagnetic stability in UCoGe revealed by soft x-ray magnetic circular dichroism

We investigated the element-specific electronic states and magnetic properties of ferromagnetic superconductor UCoGe and Ru-substituted $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$ using soft x-ray magnetic circular dichroism (XMCD) experiments at the absorption edges of U $N_{4,5}$, Co $L_{2,3}$, and Ge $L_{2,3}$. YCoGe, a nonmagnetic compound without the $5f$ electrons, was also examined as a reference material. The shapes of the XMCD spectra of UCoGe at the U $N_5$ and Ge $L_{2,3}$ edges are indistinguishably similar to those of $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$. On the other hand, the XMCD spectral shape at the Co $L_2$ edge is very peculiar and is changed by the presence of the U $5f$ electrons and the Ru substitution. From the sum rule analysis for the XMCD spectra, it was found that the magnetic moments of the U $5f$ and Co $3d$ electrons in UCoGe and $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$ are aligned in the same direction under the present experimental conditions: $T$ = 5.5–50 K and ${\mu }_{0}H$ = 0–10 T. Furthermore, not only in UCoGe and $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$ but even in the case of YCoGe, the Co $3d$ electrons have a large orbital magnetic moment, suggesting that the Co $3d$ electrons in these compounds are in a low-symmetry electronic environment originally. Through the $T$ and ${\mu }_{0}H$ dependence of the XMCD intensity, it was revealed that the magnetic properties at the Co site are not simply induced by the magnetism at the U site and that the Co $3d$ electrons play an important role in the stability of ferromagnetism. The present findings clearly demonstrate that the contribution of not only the U $5f$ electrons but also the Co $3d$ electrons is very crucial to understanding the complex physical properties of the $\mathrm{U}\left({\mathrm{Co}}_{1-x}{\mathrm{Ru}}_x\right)\mathrm{Ge}$ system.

Figure 1

Experimental XAS and XMCD spectra of UCoGe, $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$. (a) XAS spectra of UCoGe and $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$ at U-$N_{4,5}$ and Co-$L_{2,3}$ measured at $T$ = 5.5 K and $H$ = 10 T. (b) XMCD spectra of UCoGe at $T$ = 5.5 K and $H$ = 3, 5, and 10 T. (c) XMCD spectra of $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$. The upper spectra were measured at $T$ = 5.5 K and $H$ = 3 and 10 T. The lower spectrum was done at $T$ = 15 K and $H$ = 10 T. Right and left insets of panels (b) and (c) show enlarged plots at U-$N_5$ and Co-$L_2$, which are normalized to overlap each other, respectively. The purple arrows in the insets indicate the photon energy at which the XMCD-$H$ curves were measured, as shown in Fig. 4. See text for the black arrows in panels (b) and (c), and the red arrow in the left inset of panel (c).

Figure 2

Experimental XAS and XMCD spectra of UCoGe and U(CoRu)Ge at Ge-$L_{2,3}$ measured at $T$ = 5.5 K and $H$ = 10 T. (a) XAS spectra and (b) XMCD spectra. Inset shows the XMCD-$H$ curve of U(CoRu)Ge at Ge-$L_3$ measured at $T$ = 5.5 K. The purple arrow in panel (b) indicates the photon energy at which the XMCD-$H$ curve was measured, as shown in the inset.

Figure 3

Experimental XAS and XMCD spectra of YCoGe, and comparison of XMCD spectra of YCoGe and Co metal. (a) XAS spectrum of YCoGe at Co-$L_{2,3}$ measured at $T$ = 10 K and $H$ = 10 T. (b) XMCD spectra of YCoGe at $T$ = 10 K and $H$ = 5 and 10 T. Inset shows the XMCD-$H$ curve at Co-$L_3$ (indicated by the purple arrow) measured at $T$ = 10 K. (c) XAS spectrum of Co metal at Co-$L_{2,3}$ measured at $T$ = 300 K (RT) and $H$ = 2 T. (d) XMCD spectrum of Co metal at RT and $H$ = 2 T. (e) Comparison of XMCD spectra of YCoGe and Co metal. The width of the XMCD spectrum of YCoGe at Co-$L_3$ is narrower than that of Co metal. Inset shows enlarged spectra of YCoGe around Co-$L_2$.

Figure 4

$H$ dependence of the XMCD intensity (XMCD-$H$ curve) at several $T\mathrm{s}$. Panels (a) and (b) show XMCD-$H$ curves of UCoGe at U-$N_5$ and Co-$L_2$, respectively. These are measured at $T$ = 5.5, 10, 20, 25, 30, 40, and 50 K. Panels (c) and (d) show XMCD-$H$ curves of $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$ at U-$N_5$ and Co-$L_2$ edge, respectively. These are measured at $T$ = 5.5 and 15 K. In the insets, the enlarged XMCD-$H$ curves in the range $H$ = $\pm 0.5\mathrm{T}$ are shown.

Figure 5

Comparison of magnetic properties of UCoGe and $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$. (a) The $T$ dependence of XMCD intensity divided by $H$ strength (XMCD/$H$) of UCoGe at $H$ = 2, 5, and 10 T. (b) The $T$ dependence of the XMCD-$H$ curves of $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$. (c, d) The comparison of the XMCD-$H$ curves of UCoGe and $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$ at $T$ = 5.5 K. Panels (c, d) are the comparison at the U $N_5$ and Co $L_2$ edges, respectively. In these panels, the normalization is done by adjusting the ranges of the left and right vertical axes (see text).

Figure 6

Analysis using the sum rules [36, 37] at Co-$L_{2,3}$. (a) Integrals of the XMCD spectra of UCoGe ($T$ = 5.5 K, $H$ = 10 T), $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$ ($T$ = 5.5 K, $H$ = 10 T), YCoGe ($T$ = 10 K, $H$ = 10 T). The integral of YCoGe is multiplied by 10, displayed in the right vertical axis. The red and blue horizontal dotted lines show the U-$N_{4,5}$ integral of UCoGe and $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$, respectively, deduced from the result of the XMCD spectrum at U-$M_{4,5}$ [25] (see text). The green (brown) vertical line and arrow show the photon energy position where $p$, the Co-$L_3$ integral ($q$, Co-$L_{2,3}$ integral) is taken. For example, the $q$ value (Co-$L_{2,3}$ integral) is obtained as displayed with a black close brace. (b) $T$ and $H$ dependence of the values of $\delta$ for UCoGe, $\mathrm{U}\left({\mathrm{Co}}_{0.88}{\mathrm{Ru}}_{0.12}\right)\mathrm{Ge}$, YCoGe, and Co metal.