Fermi liquid breakdown and evidence for superconductivity in YFe$_2$Ge$_2$
In the d-electron system YFeGe, an unusually high and temperature dependent Sommerfeld ratio of the specific heat capacity and an anomalous power law temperature dependence of the electrical resistivity signal Fermi liquid breakdown, probably connected to a close-by quantum critical point.Full resistive transitions, accompanied by DC diamagnetic screening fractions of up to 80% suggest that pure samples of YFeGe superconduct below .
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The threshold of magnetism in transition metal compounds is frequently associated with anomalous low temperature properties, such as the robust power-law resistivity observed in MnSi , ZrZn [2, 3] and NbFe . Quantum critical phenomena associated with incipient antiferromagnetic or spin density wave order remain comparatively underexplored in this material class. The close association of superconductivity with the border of antiferromagnetism in a large number of iron pnictide and chalcogenide compounds further motivates the search for suitable candidate materials among transition metal intermetallics.
The (Y/Lu)FeGe system offers such an opportunity to study a spin density wave quantum phase transition in a transition metal composition series. LuFeGe crystallizes in the ThCrSi structure () and exhibits spin density wave order below [5, 6]. Electron counting places Fe in (Y/Lu)FeGe at the same valence as in the isostructural superconductors (K, Rb, Cs)FeAs, but the magnetic order in LuFeGe differs from that of the iron arsenides: the Fe moments align ferromagnetically within the basal plane and couple antiferromagnetically to their neighbours along the crystallographic direction, corresponding to an ordering wavevector . Applied hydrostatic pressure raises . Partial substitution of Lu by Y expands the unit cell and suppresses  at a critical composition of LuYFeGe.
Here, we concentrate on the end member of the series, YFeGe, which is paramagnetic at ambient pressure and displays an unusually high Sommerfeld coefficient of the specific heat capacity . Our low temperature measurements reveal hallmarks of Fermi liquid breakdown, such as an anomalous power law form of the electrical resistivity and a strongly temperature dependent at low , as well as full resistive superconducting transitions and large diamagnetic screening fractions consistent with bulk superconductivity below an onset .
Single crystals of YFeGe were grown from tin flux following published methods , and polycrystals were obtained by radio frequency melting of the elements (Y 3N, Fe 4N, Ge 6N) on a water-cooled copper boat, followed by annealing in vacuum at for 7 days. The residual resistivity ratios () obtained from flux growth were typically about 10, whereas annealed polycrystals reached resistivity ratios of up to 50. The electrical resistivity and the magnetic susceptibility were measured in an adiabatic demagnetisation refrigerator to below , and the specific heat capacity was measured in a Quantum Design Physical Properties Measurement System with a He insert to below . The magnetisation data was acquired in a Cryogenic SQUID magnetometer with a He insert to below . X-ray studies confirmed the quality and composition of our samples, giving the lattice parameters , and the conventional unit cell volume . Our samples were found to be at least phase pure, and the only impurity phase which could be identified in some of the polycrystals is a ferromagnetic Fe/Ge alloy.
At elevated temperatures , our findings are consistent with those reported previously : The magnetic susceptibility is small and weakly temperature dependent, the resistivity is metallic (inset of Fig. 1), and the Sommerfeld coefficient of the specific heat capacity, is surprisingly high, reaching values near at (Fig. 1).
Extending the measurements to lower reveals a gradual further increase of (Fig. 1), and the electrical resistivity displays an unusual power-law temperature dependence of the form up to temperatures of the order of (Fig. 2). These findings suggest Fermi liquid breakdown similar to that observed in other transition metal compounds, such as MnSi, ZrZn and NbFe [1, 2, 3, 4]. In contrast to the latter, which are close to the threshold of ferromagnetism, the weak -dependence and comparatively small magnitude of the magnetic susceptibility in YFeGe  suggests a different scenario. Electronic structure calculations [9, 10] indicate that ferromagnetism and various antiferromagnetic states compete in YFeGe. However, they find a significant energy advantage for order, which is indeed observed in LuFeGe. This would be consistent with the interpretation that the low temperature properties of YFeGe are affected by a nearby antiferromagnetic (or spin density wave) quantum critical point. Proximity to a magnetic quantum critical point could also explain one of the central puzzles in YFeGe, namely the 10-fold enhancement of the heat capacity over the band structure value of [9, 10]. However, stoichiometric YFeGe is sufficiently far removed from the critical composition found in the (Y/Lu)FeGe composition series  to leave open alternative possibilities.
Below , superconducting transitions are apparent in the electrical resistivity (Fig. 2) as well as in the DC magnetisation (Fig. 3). While the onset of the resistive transition is observed at ( point at ), the onset of superconductivity is apparent in DC magnetisation measurements only below . This suggests that varies across the sample. For the sample shown, the superconducting volume fraction extracted from the magnetisation measurement (Fig. 3) amounts to at least .
Comparing polycrystals with different residual resistance ratios, we find a clear correlation between sample purity and both the size of the superconducting jump and the value of observed in resistivity measurements. Full superconducting transitions are obtained in polycrystalline samples with , while unannealed polycrystals with lower RRR as well as the flux-grown single crystals with only show partial transitions.
Heat capacity measurements down to have not revealed a clear anomaly associated with the superconducting transition. This might result from an intrinsically interesting mechanism, such as an anomalously reduced superconducting gap. However, at this stage it could equally be attributed to the broad nature of the transition, or it could suggest that despite the large diamagnetic screening signal superconductivity is confined to small fractions of the sample. A comprehensive study on high quality flux-grown crystals  also remarked on the absence of a heat capacity anomaly near , whereas a superconducting heat capacity anomaly was reported by a third group . This indicates that if alien phases can be ruled out, slight variations in the stoichiometry might play a role in establishing bulk superconductivity in YFeGe.
The initial slope of the resistive upper critical field is (inset of Fig. 2). This corresponds to an extrapolated clean-limit weak-coupling orbital-limited critical field . This value significantly exceeds the observed critical field in the low temperature limit of , suggesting that the low temperature critical field is Pauli limited. In the standard treatment (e.g. ), the extrapolated orbital-limited critical field corresponds to a superconducting coherence length , where is the quantum of flux. Such a short coherence length is roughly consistent with the enhanced quasiparticle mass and consequently low Fermi velocity indicated by the high Sommerfeld coefficient of the specific heat capacity: we estimate the BCS coherence length from [14, 15], where is the Fermi velocity and is the superconducting gap, approximated as . Representing the electronic structure of YFeGe by one or two spherical Fermi surface sheets with radius (corresponding to half-filled bands) in order to extract from , we would expect for a single sheet or for two sheets, in rough agreement with obtained above. The mean free path in our samples can likewise be estimated (e.g. ) from , where is the residual resistivity, to be about () for the highest quality samples, when one (two) Fermi surface sheets are assumed. This indicates that indeed exceeds , so that an anisotropic order parameters is not ruled out by disorder scattering.
We thank C. Geibel, P. Niklowitz, S. Friedemann, M. Gamza and G. G. Lonzarich for helpful discussions. This work was supported by EPSRC UK and Trinity College Cambridge.
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