Discussion and conclusions

The hysteresis analysis with the help of the Hall sensor, as presented in sec- tion 5.3.1, suggests that at low temperatures both the phase transition on the left hand side of of the AFM-B phase and the one on the right hand side of it, are accompanied by weak but noticeable hysteresis in resistivity. However the temperature dependence of the hysteresis for the two phase transition lines is dif- ferent. For the one to the left of the AFM-B phase, the hysteresis persists as the temperature increases until the transition line merges with the antiferromagnetic- paramagnetic phase transition line (at approximately 6 K for my samples). For the antiferromagnetic-paramagnetic phase transition, as the temperature increases the magnitude of the hysteresis in resistivity is quickly suppressed and becomes unresolvable at approximately 3.5K. So overall it seems that the AFM-B phase is surrounded by two first order phase transition lines on the two sides and one second order phase transition line on the dome.

If the antiferromagnetic-paramagnetic phase transition is second order at rela- tively high temperature (≥3.5 K to TN) and becomes first order as the transition temperature is suppressed towards zero, questions about whether there are really quantum fluctuations in this material will arise.

In my work, I also found hysteresis in resistivity between the field sweeping up and the field sweeping down curves in both the AFM-B phase and the AFM-A phase. In contrast to the finding of Balicas et al. [7], where resistivity hysteresis was only found in the AFM-B and not reproduced in all their samples, the resistivity hysteresis discovered in our samples turned out to be highly reproducible.

Based on the magneto-resistivity measurements I constructed a 3D phase diagram of fl-T-H which showed the details of the evolution of fl of CeAuSb2 in magnetic

fields and at different temperatures. This helped to clarify the boundary of the AFM-B phase, which one of the things that I planned to do. The angle dependent electrical transport measurements revealed that, as the magnetic field was turned from the c-axis towards the basal plane, the magneto-resistivity of flCeAuSb2 was controlled by the c-axis projection of the field. The effects of tilting the field from

the c-axis towards the basal plane was basically just to push the two transitions

to higher fields.

The torque magnetometry measurements have yielded results that are consistent with those of the electrical transport. At the positions where the transitions were observed in resistivity, two metamagnetic transitions were observed and they were also pushed to higher fields when the field direction is tilted from thec-axis towards

the basal plane.

The last thing to mention is that no evidence of further transition splitting has been found at either of the two phase transitions even at temperatures well below 1 K (neither in magneto-resistivity nor torque magnetometry measurements).

Chapter 6

Conclusions and future work

I have presented in this thesis the experimental work that I have performed on two strongly correlated materials, Sr2RuO4 and CeAuSb2, and the corresponding

results. Here I give a short summary to the work and the results, and then point out some potential work that might be meaningful for future research.

6.1 Sr

RuO

To investigate the superconducting properties of Sr2RuO4, I tried to traverse its

“-band VHS with piezo-electric based uniaxial strain methods, and studied the superconducting transition temperature dependence on uniaxial strain along the [100] direction and the relationship between the transition temperature and the c-

axis upper critical fieldHc2. Simulation results suggest that to traverse the“-band VHS, the strain scale needed would be between 0.5% and 1.0%. The experimental results showed that, for a sample whose transition temperatureTc is 1.45 K under zero strain, by applying a uniaxial strain Á100 of approximately 0.92%, Tc could be enhanced by a factor of 230%, to ≥3.4 K, and it seemed that Tc could not be enhanced further with higher strain. At the same time, the upper critical fieldHc2 showed an enhancement that was larger than T_c2. These results, when considered

together with the simulation results, indicate that“-band VHS has very likely been successfully transversed, without destroying the material’s superconductivity. Technically, results presented in this work have manifested the big advantage of the piezo-electric based uniaxial stain methods in achieving highly homogeneous strain. The superconducting transition reflected in the AC susceptibility signal was neat and was only broadened by a limited amount even when the sample was considerably strained. The strain homogeneity was also high enough to guarantee successful measurements on the upper critical field Hc2. Close to the highest applied strain the sharpening of the onset of the superconducting transition gave rise to a well defined Tc.

Regarding the pairing symmetry of Sr2RuO4, although in a naive BCS picture the

results do not seem to favour the chiralp-wave scenario, it is difficult draw a clear

conclusion at this point. The results presented here need proper interpretation based on careful theoretical calculations. This work, I believe, is only a starting point for the study with uniaxial strain methods on superconductivity of Sr2RuO4

from the perspective of approaching a VHS.

What is desirable next is not only theoretical calculations but also more experi- mental work. From the experimental point of view, it will be interesting to combine the uniaxial strain methods with more probing methods (A) to directly verify that the “-band VHS has indeed been traversed, and (B) to study other equilibrium properties of Sr2RuO4 under uniaxial strain. For the former, ARPES is probably

the most evident option, especially considering its previous successful application in studying the VHS of chemically doped Sr2RuO4 [47] [171]. Technically it is

possible because a considerable section of the top surface of the sample is open to spectroscopy in piezo-electric based uniaxial strain methods. For the latter, data on for example specific heat or electrical resistivity will be useful to obtain better understanding on the change in physics when the sample is strained. Tak- ing the specific heat for example, one may see the effects of enhancement of the DOS as the sample is strained, and if the chiral p-wave proposal were true and

the experimental resolution were high enough, one might expect to see two tran- sitions in series as the strained sample is cooled from its normal state to the deep superconducting state.