Dans le document The nature of Fermi-liquids, an optical perspective (Page 168-177)

4.7 Phonon splitting in the c-axis spectra of Sr 2 RuO 4

4.7.3 Characterization Magnetometry

The susceptibility measurement have been achieved in two different setups. First the low temperature superconducting transition of sample Tc134 and Tc128 were measured in Salerno by Fittipaldi and co-workers. With a temperature range of 343 mK to 2 K, the susceptibility is shown in the inset of Figure 4.44. The normal state is shown in the two main graphs of Figure 4.44, was measured in Geneva both in field cooling (FC) and zero field cooling (ZFC), from room temperature to 1.8 K. In order to allow a better comparison of the phenomenon, the data were scaled in order to obtain the same magnetization at high temperature. For comparison, the data of Maenoet al.[290]is added in Figure 4.44 whose temperature dependence (without

0 3 6 9 12

Figure 4.42: Scanning electron microscope surface topography of the Tc128 and C362 Sr2RuO4 samples.(a)Line scan taken at positionp1of sample C362. The data are shown in weight percentage along the line crossing a pure ruthenium inclusion in yellow in(b). Error bars are shown as light color areas. The color dashed lines show the expected weight for Sr2RuO4. The grey dotted line are for the expectation values of Sr3Ru2O7. (c)and(d)Similar scan at positionp2, crossing small rutheniumµm-sized dots. (e)Surface scan. The composition homogeneity of the Tc128 sample at positionp1. The darker the pixel is the higher the proportion of the element. (f)Overall secondary electrons scan of sample Tc128. An extensive analysis was achieved for three position (yellow).

The remaining surface was qualitatively checked for other different inclusions. No trace of pure ruthenium is observed.(g)and(h)Same analysis for positionp1 of sample C362. Trace of pure ruthenium are observed as small round shaped area.

13.90 25.96(006) 27.99 31.75(?) 34.41(008) 36.24? 37.77? 42.5343.63(0010) 52.97(0012) 57.83 62.68(0014) 74.36

10 20 30 40 50 60 70 80

2θ (degree) 100

101 102 103 104


100 101 102 103 104


Tc134 (00L)φ=90 Sr2RuO4

Sr3Ru2O7 unknown (c)

1 2 3 4 5 6 7 8 /2 (nm)

0 0.4 0.8

sin(θ) c=12.7502(5) (nm)

(a) 21.8 21.9 22


0 0.3 0.6 0.9


(006) φ=90


Figure 4.43: X-ray diffraction pattern of the Tc134 sample. The indexed peaks in red correspond to Sr2RuO4; in green to Sr3Ru2O7and the remaining peak are unknown(a)Linear fit of the (00L) peaks of the diffractogram. (c)ωscan of the (006) peak.

0 50 100 150 200 250

Figure 4.44: Susceptibility measurement of the Tc134 Sr2RuO4sample for different applied fields along thec-axis. (a)Field cooling and(b)zero field cooling. The data of Maenoet al. is reproduced from[290]. The data are scaled in order to obtain the same magnetization at high temperature.

(c)Temperature derivative of the field cooled magnetization curves. The onset of the transition at about 93 K and 161 K is defined by the average ofT1and T2. (d)Magnetic field dependance of the

18 K maximum temperature peak for both field cooling and zero field cooling measurement.

magnetic impurities) is very small such that the spin susceptibilityχspincan easily be extracted and estimated to be 0.9×10−3emu/mol. The Ruddlesden-Popper series have different magnetic structures happening at different temperatures so that it is easy to determine the impurities present in the material, the double and triple layer, but also the last element of the series (SrRuO3) is present. Moreover, it is possible to determine the percentage of present impurities in the crystals. The data of different Ruddlesden-Popper series is taken from the literature: The double layer data are from[291], the third layer from[292]and SrRuO3 from[293]. All the contribution are summed up with a weighting factor in order to reproduce the field cooling magnetization data at 100 Oe. The artificially reproduced curve is shown as the purple dashed line in Figure 4.44(a). Taking into account the magnetic response of the impurity phase allows to match exactly the single layer magnetization at high temperature. From room temperature to low temperature, the first feature is the ferromagnetic transition of SrRuO3 which is only accounting for 12.5 ppm of entire crystal in weight. The second transition is attributed to Sr4Ru3O10present at 448 ppm. The last feature is clearly attributed to Sr3Ru2O7 and with 4 % in weight is the most abundant impurity.

The different transition temperatures were determined by taking the temperature derivative of the magnetization d(M/H)/dT shown in Figure 4.44 (c). A constant fit was applied in the almost flat region before and after the transition In between these regions a linear fit was applied and the minimum and maximum temperatures were determined at the intersection point of the adjacent lines. The critical temperature is defined as the average ofT1andT2[294]. The ferromagnetic transition of SrRuO3is found at 161.0(5)K. However, it was shown that this material undergoes a structural phase transition driven by biaxial strain imposed by substrate mismatch on which the material is grown [295]. With that strain, the SrRuO3 structure is changing from orthorhombic to tetragonal, which affects its electronic properties, notably its ferromagnetic transition that tends to increase upon reducing thec-axis lattice parameter[294]. In such a case, the lattice parameter is found to be 3.917(5)Å, which shows that the material is probably present at the interface with Sr4Ru3O10. this also suggests that the impurity layers are stacked together as suggested in the previous sections. The magnetic transition of Sr4Ru3O10is found at 93.5(5)K which is different from the value 105 K found in the literature[192], this suggest as well that this material is strained in the main Sr2RuO4 lattice.

Another interesting aspect is the emergence of short-range antiferromagnetic correlations below approximatively 20 K [291]. The maximum of susceptibility at low temperature is attributed to Sr3Ru2O7 and its temperature dependence is shown in Figure 4.44 (d). Also shown in[291], this peak shifts with temperature, but seems to stabilize at high field while it is suppressed down to temperatures below 5 K above 6 T for very pure Sr3Ru2O7 samples[198].

Finally based on the onset of a very small decrease of the susceptibility above 1.5 K the pure ruthenium volume fraction in the Tc134 is very roughly estimated to be 5 ppm to 50 ppm. Discussion

In this section the splitting of the optical phonon were reviewed through different scenario. The impact was shown to be different for all the samples, even between two sample coming from the same batch (Tc134 and Tc128). Surprisingly, this effect is not affecting Tc, which indicated that the interpretation from impurities coming from the precursor material was not valid. The strength of the splitted phonon peaks is almost evenly distributed so that a scenario with a mix of two different phases could in be principle be also rejected. The remaining scenario is relying on strain effects which would slightly lower the symmetry of the crystal. In this case the idea of having a tilt of the ruthenium octahedron is the most probable scenario which could be involved by a lattice strain from the Sr3Ru2O7 impurity layers.

4.8 Conclusions

In this chapter, the Fermi-liquid Sr2RuO4was heralded as the first material showing the expected relation between energy and temperature in the optical scattering rate withp=2. Despite being a multi-band system the electrical resistivity was described using a simple Fermi-liquid pointing to two different energy scales, a low temperature Fermi-liquid and a second component in parallel which could be described by standard electron-electron interaction in a 3D Fermi-liquid or any 2D modes with a linear dispersion. Numerical calculation through DFT+DMFT were carried out, which in combination with the optical data allowed to demonstrate the existence of high-energy and temperature resilient particle-hole excitation. Finally reflectivity measurements on theac-plane of the material showed a sample dependent splitting of the c-axis phonon.

Extensive research is still needed but the scenario of a internal stress due to the presence of layers of Sr3Ru2O7 in the crystal was put forward. That scenario is compatible with the various bulk characterization measures that have been undertaken.




Fermi-liquid like properties in the pseudogap phase of the cuprates

A.1 Fermi-liquid fit of the reflectivity

The reflectivity of any Fermi-liquid can be fitted using the Fermi-liquid model instead of the standard Drude formula. As shown in Figure A.1, the low energy reflectivity is correctly reproduced by the model and its extrapolation down to zero can be used during the Kramers-Kronig analysis.

0 10 20 30 40 50 60 70

Photon energy (meV) 0.8

0.9 1



380 K 340 K 300 K 260 K 220 K 180 K 140 K 100 K 70 K

Figure A.1: Fermi-liquid model fitted to the FIR reflectivity of HgBa2CuO4+x UD67. The fit was done at selected temperature above Tc. The fitting extend up to 70 meV and except the sharp phonons, the fit quality is excellent up to 60 meV. The fitting procedure uses the temperature as a fixed parameter while finding the best Fermi-liquid parameters : T0,(0)andZΓ.

Dans le document The nature of Fermi-liquids, an optical perspective (Page 168-177)