Role of Ge in Bridging Ferromagnetism in the Giant Magnetocaloric ${\mathrm{Gd}}_5({\mathrm{Ge}}_{1-x}{\mathrm{Si}}_x{)}_4$ Alloys

X-ray magnetic circular dichroism (XMCD) measurements and density functional theory (DFT) are used to study the electronic conduction states in ${\mathrm{Gd}}_5({\mathrm{Ge}}_{1-x}{\mathrm{Si}}_x{)}_4$ materials through the first-order bond-breaking magnetostructural transition responsible for their giant magnetocaloric effect. Spin-dependent hybridization between Ge $4p$ and Gd $5d$ conduction states, which XMCD senses through the induced magnetic polarization in Ge ions, enables long-range Ruderman-Kittel-Kasuya-Yosida ferromagnetic interactions between Gd $4f$ moments in adjacent Gd slabs connected by Ge(Si) bonds. These interactions are strong below but weaken above the Ge(Si) bond-breaking transition that destroys 3D ferromagnetic order.

Figure 1

Top panel: Gd $L_3$ and Ge $K$ edge-jump normalized XMCD data for $x=0.5$ at $H=2\mathrm{T}$. The helicity-independent absorption coefficient (scaled to fit) is shown with solid lines. Results from DFT calculations are superimposed (dashed lines). At this field XMCD is half its saturation value, and calculations were scaled accordingly. Lower panel: temperature dependence of Ge and Gd XMCD signals together with SQUID bulk-magnetization data ($H=2\mathrm{T}$) for $x=0.125$, 0.5 samples. Vertical dashed lines indicate the centroids of the bond-breaking structural transition.

Figure 2

Far right: schematic of the structure showing slab-connecting Ge(Si)-Ge(Si) bonds. Gd also occupies sites at the slabs’ edges and Ge(Si) also occupies sites near the center of the slabs [3]. (a) Magnitude of complex Fourier transform (FT) of Ge $K$-edge XAFS data in the $k=[2,13]{\AA }^{-1}$ range for $x=0.125$ (lines) and representative fits (points) using the known low temperature (LT) and high temperature (HT) crystal structures [21]. $k$ is photoelectron wave number. Peaks in the FT are shifted toward shorter distances by $\approx 0.35\AA$ due to photoelectron scattering phase shifts. Vertical lines delimit the fitted region with corresponding back-Fourier transformed data and fits shown in (b). A large misfit is obtained when short (long) bonds are forced to be present in HT (LT) phases (dashed lines).

Figure 3

Left panel: spin-density contour plots of the ($a$, $b$, 0.5) plane for $O$ and $M$ structures ($x=0.5$). The atoms are slightly off the plane (about 0.28 Å for ${\mathrm{Ge}}_2$ in the $M$ structure). The distance between ${\mathrm{Ge}}_2$ atoms is about 2.6 Å and 3.5 Å in $O$ and $M$ structures, respectively. The spin density (in $e/a_0^3$ units, $a_0$ Bohr radius) includes states extending from $-1.5\mathrm{eV}$ to 0 eV ($E_F$). Right panel: projected density of $4p$ states at bond-breaking ${\mathrm{Ge}}_2$ sites and $5d$ states on the nearest Gd site at the slab’s edge ($\sim 2.5\AA$ off the plane in contour plots). Hatched regions show the spin-down states that develop in the $M$ structure.