Composition and temperature dependence of the Yb valence in ${\text{YbMn}}_6{\text{Ge}}_{6-x}{\text{Sn}}_x$ studied by RIXS

We investigate the composition and temperature (10–450 K) dependence of the Yb valence in ${\mathrm{YbMn}}_6{\mathrm{Ge}}_{6-x}{\mathrm{Sn}}_x$ ($x=0.0$, 3.8, 4.2, 4.4, and 5.5) using resonant inelastic x-ray scattering (RIXS). The observed change in the Yb valence with composition (from $\upsilon \sim 3$ for $x=0$ to $\upsilon \sim 2.7$ for $x=5.5$) is likely driven by negative chemical pressure effects due to the Sn for Ge substitution. While Yb is nonmagnetic in ${\mathrm{YbMn}}_6{\mathrm{Ge}}_{0.5}{\mathrm{Sn}}_{5.5}$, intermediate valent Yb magnetically orders at unexpectedly high temperature (up to 90 K) in the alloys with $x=3.8$, 4.2, and 4.4. The three latter alloys further exhibit an increase in the Yb valence upon cooling, which is opposite to the usual behavior. Interactions with the magnetically ordered Mn sublattice are invoked to account for these unprecedented phenomena through a simplified model based on an Anderson Hamiltonian with a Zeeman term mimicking the Mn-Yb exchange interactions. We further show that the Yb magnetic behavior in this series can be interpreted based on Doniach's picture. Compared with standard intermediate valent materials where Yb is embedded in a nonmagnetic matrix, the strong Mn-Yb exchange interaction enhances the intermediate valent Yb magnetic ordering temperature and allows for extending the stability domain of the Yb magnetic order towards lower Yb valence.

Figure 1

Room-temperature RIXS (a) and PFY XAS (b) spectra for the alloys with $x=0.0$, 3.8, 4.2, 4.4, and 5.5.

Figure 2

(a) Variation of the room-temperature cell volume with the Sn content. The continuous line marks volumes expected for a fully trivalent Yb: it joins the cell volume of ${\mathrm{YbMn}}_6{\mathrm{Ge}}_6$ with that of ${\mathrm{LuMn}}_6{\mathrm{Sn}}_6$ (data from Ref. [28]). The dotted line, which links the cell volume of ${\mathrm{YbMn}}_6{\mathrm{Ge}}_6$ with that of ${\mathrm{YbMn}}_6{\mathrm{Sn}}_6$ (data from Ref. [20]), corresponds to a simple linear variation of the cell parameters. (b) Variation of the room-temperature Yb valence with the Sn content. The shaded areas mark the miscibility gaps [19].

Figure 3

RIXS spectra for $x=0.0$ and 5.5 at 300 K and 10 K. RIXS spectra for $x=4.4$ between 450 and 8 K.

Figure 4

Thermal dependence of the Yb valence in ${\mathrm{YbMn}}_6{\mathrm{Ge}}_{6-x}{\mathrm{Sn}}_x$ ($x=0.0$, 3.8, 4.2, 4.4, and 5.5).

Figure 5

Thermal dependence of the magnetization of ${\mathrm{YbMn}}_6{\mathrm{Ge}}_{6-x}{\mathrm{Sn}}_x$ ($x=3.8$, 4.2, 4.4, and 5.5) in an applied field of 500 Oe. The weak ferromagnetic component seen on the curve of $x=3.8$ below $\sim 300$ K is due to the magnetic ordering of the ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ impurity. The data for $x=0.0$ are not shown: the Mn sublattice antiferromagnetically orders above 350 K (the highest temperature of the experiment) and the low-temperature behavior is overshadowed by the ferromagnetic ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ impurity.

Figure 6

Calculated temperature dependence of the Yb valence obtained for several $r={\mu }_{B}B/\delta$ parameters. The $r\gg 1$ corresponds to the $x=0$ sample $\left(\upsilon \sim 3\right)$, whereas the Yb valence in the $x=4.4$ and 5.5 alloys can be described with $r=1.25$ and $r=0.15$, respectively.

Figure 7

Thermal dependence of the reduced volume $V/V_0$ ($V_0$ is the room-temperature volume) of ${\mathrm{YbMn}}_6{\mathrm{Ge}}_{6-x}{\mathrm{Sn}}_x$ ($x=3.8$, 4.2, 4.4, and 5.5) between 300 K and 10 K. The inset shows the thermal variation of the cell volume for $x=4.2$ and 4.4.

Figure 8

Composition dependence of the Yb ordering temperature (green circles, left scale) and Yb magnetic moment (red squares, right scale). Data in open symbols are taken from Ref. [19]. The lines are guides to the eye.

Figure 9

Hysteresis loops of $x=4.4$ and $x=5.5$ at 5 K in field up to 90 kOe.