Coexisting Kondo hybridization and itinerant $f$-electron ferromagnetism in ${\mathrm{UGe}}_2$

Kondo hybridization in partially filled $f$-electron systems conveys a significant amount of electronic states sharply near the Fermi energy leading to various instabilities from superconductivity to exotic electronic orders. ${\mathrm{UGe}}_2$ is a $5f$ heavy fermion system, where the Kondo hybridization is interrupted by the formation of two ferromagnetic phases below a second order transition $T_c\sim 52\mathrm{K}$ and a crossover transition $T_x\sim 32\mathrm{K}$. These two ferromagnetic phases are concomitantly related to a spin-triplet superconductivity that only emerges and persists inside the magnetically ordered phase at high pressure. The origin of the two ferromagnetic phases and how they form within a Kondo-lattice remain ambiguous. Using scanning tunneling microscopy and spectroscopy, we probe the spatial electronic states in the ${\mathrm{UGe}}_2$ as a function of temperature. We find a Kondo resonance and sharp $5f$-electron states near the chemical potential that form at high temperatures above $T_c$ in accordance with our density $\mathrm{functional}\mathrm{theory}+\mathrm{Gutzwiller}$ calculations. As temperature is lowered below $T_c$, the resonance narrows and eventually splits below $T_x$ dumping itinerant $f$-electron spectral weight right at the Fermi energy. Our findings suggest a Stoner mechanism forming the highly polarized ferromagnetic phase below $T_x$ that itself sets the stage for the emergence of unconventional superconductivity at high pressure.

Figure 1

(a), (b) Topographic image of cleaved ${\mathrm{UGe}}_2$ revealing subatomic terraces with alternating chemically different surface terminations, one of which undergoes a surface reconstruction. (c) Comparison of the terrace heights extracted from the blue line cut in (b) with the crystal structure of ${\mathrm{UGe}}_2$ suggesting the breaking of a single bond (U-Ge2) that exposes the reconstructed Ge2 surface ($B$) and U surface ($A$). (d),(e) STM $dI$/$dV$ spectra on the two surfaces at high (d) and low (e) temperatures. Note that the data in (d) and (e) are not taken on the same spatial location. (f) $\mathrm{DFT}+\mathrm{Gutzwiller}$ calculation of the electronic density of states in ${\mathrm{UGe}}_2$ in the nonmagnetic phase. Note that U $5f_{7/2}$ due to spin-orbit coupling are at much higher energies (1–2 eV).

Figure 2

STM spectra taken at different locations on surfaces $A$ (a) and $B$ (b) at 8 K. The spectra in (a) reveal spatial uniformity, whereas those in (b) are spatially inhomogeneous due to the surface inhomogeneity. The lines correspond to the energies of the observed peaks that are similar on both surfaces.

Figure 3

(a), (b) STM spectroscopy on surface $A$ as a function of temperature with two different experimental settings described in the text. The spectra reveal a Fano line shape ($E_2$ resonance) located above the chemical potential. As temperature is lowered below $T_c$, a second resonance emerges near the Fermi energy ($E_1$ resonance) below $\sim 35\mathrm{K}$. (c), (d) Second derivative of the spectra in (a) and (b) showing the evolution of the $E_1$ and $E_2$ resonances as a function of temperature. (e) Fitting of the data in (b) to a single Fano line shape. The spectrum above $T_c$ can be explained by a single resonance, while at lower temperatures, the data deviate from a single Fano line shape.

Figure 4

(a) STM spectroscopy and corresponding two Fano–line-shape model fit at different temperatures. (b)–(d) extracted Fano amplitude, width, and energy as a function of temperature. Red data points correspond to the $E_1$ resonance near $E_{\mathrm{F}}$ whereas the blue data points correspond to the $E_2$ resonance above the chemical potential. The lines in (c) represent Γ($T$) for a $T_K$ of 110 K (blue) and $T_K$ of 55 K (red).