Valores

I hope that during the course of this thesis I have demonstrated that the new uniaxial stress technique that I describe is now coming out of its infancy. The first successful adaptation of the device by another group has now been reported, and used by Sternet al. [249] to study SmB6 under strain. I know that a number of other groups world-wide are also working on implementing the technique, and versions of the Hicks design are now being sold commercially by Razorbill Instruments.

I would like to conclude by summarising how the uniaxial stress technique has developed and what I envision for the future; what physics it can help tackle and some key directions for further techni- cal development. For the scientific conclusions regarding Sr2RuO4 and Sr3Ru2O7, the reader is referred back to the conclusions at the end of each of the respective chapters.

The work in this thesis has hopefully demonstrated that the device as it stands now is already a powerful tool for condensed matter physics research. Two of its key uses have been demon- strated; its brute force is useful for Van Hove singularity tuning, and its fine precision is useful for controlled symmetry breaking. I would like to reiterate once more the significance of the energy changes possible with this technique. We are now quite routinely able to reach strains of 1 %, but to put it in perspective it is useful to compare to more common energy scales. Roughly, one can say that a strain of 1 % can change the Fermi level by approximately 1 % of the band width. For Sr₂RuO₄ the band width of theγband

along the [100] direction is∼3 eV, so a 1 % change of strain along

the [100] direction is equivalent to a temperature change of∼300 K

or the Zeeman splitting from a magnetic field of∼600 T.

I have looked mainly at ruthenates using both resistivity and magnetic susceptibility but this uniaxial stress technique is applica- ble in principle to a far wider range of materials and experimental techniques. As outlined in chapter 2, techniques such as heat ca- pacity, thermal conductivity, Seebeck and Nernst effect, nuclear magnetic resonance (NMR), and many more, are all in principle possible. Additionally, since the upper face of the sample remains exposed, even techniques like angle-resolved photoemission spec- troscopy (ARPES) and scanning tunnelling microscopy (STM) may be possible. Even if experiment specific restraints impose a smaller strain range, quite significant changes have still been demonstrated at lower strains, and integrating these techniques with uniaxial

140 Conclusions and Outlook

stress will open up a whole host of new experimental possibilities. Much novel physics will benefit from the new perspective of uniaxial stress. For example, in the high temperature cuprate superconductors the proximity of a Van Hove singularity to the Fermi level is well-established [250–253]. If possible, tuning through this Van Hove singularity with uniaxial pressure may provide a novel way to explore the phase diagram with more control and less disorder than chemical doping. Uniaxial pressure may also be useful for more direct investigations into the superconductivity and competing instabilities. It is well-established in certain regions of the phase diagram that charge order is stabilised [254, 255], and nematic fluctuations are reported in certain regions of the phase diagram too [256, 226, 257]. Both these phenomena may have a strong coupling to uniaxial pressure and thus could reveal further insights into the cuprates. For example, in rare-earth doped La₂₋xSrxCuO4, a system with an analogous stripe phase tox=1/8

doped La₂₋xBaxCuO4, uniaxial pressure applied at a 45° to the

Cu-O-Cu bond direction has been demonstrated to rapidly enhance

Tc by almost a factor of 2, and was attributed to a suppression of

the competition with stripe ordering [42,258].

Many other novel superconductors would also be suitable for uniaxial stress measurements. The multiple superconducting phases of UPt3are known to respond differently and anisotropically under uniaxial stress [259–261]. A reinvestigation with higher homo- geneity, precision and range could be quite fruitful. So too could investigations on another possible time-reversal symmetry-breaking superconductor PrOs₄Sb₁₂ [262], and on the strongly nematic iron- based superconductors [227,56].

Other puzzles such as the hidden order parameter in URu2Si2 might also be amenable to study under high uniaxial pressure, but hopefully this technique can find uses across a far wider range of fields than the quite closely related examples suggested here.

As already discussed, we are now routinely capable of reaching 1 % level strains. The yield strain of some materials, however, can be much higher still and a key direction for future developments will be to see how much higher we can push this. Single crystal silicon and several other silicon containing ceramics have yield strains greater than 3 % [263] andab initiocalculations for pristine silicon nitride suggest this could even be in excess of 10 % for higher purity samples [264]. As part of this development process, two key aspects should be the development of controlled stress rather than controlled strain devices and miniaturisation.

Currently the largest uncertainty in determining the sample strain comes from the epoxy. This rather imprecise strain scale means it is not possible to compare subtle differences between many samples. In a device where stress rather than strain is applied and

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controlled, the relatively softer epoxy does not hinder the accuracy, since all the force applied to the epoxy must also be transmitted through the sample. Controlling the applied stress is beneficial for other reasons too. It simplifies identifying zero strain and eliminates the complications that arise from differential thermal expansion in the controlled strain devices. Additionally the range of materials that can be measured is expanded. Materials which undergo struc- tural changes involving a large change in lattice constant between the mounting temperature and measuring temperature would now be suitable for study, avoiding the complications that could arise when the sample length is held constant in a controlled strain device.

For a truly controlled stress device the spring constant of the device must be lower than that of the sample. Inherently this requires the device to produce a much larger displacement in order to apply the force to the sample, for instance, by pushing on one end of a soft spring. To facilitate this a purely mechanical solution may be needed or perhaps some form of mechanical amplification for the piezo actuators.

Miniaturisation would also be useful on many fronts. Currently there are rather stringent requirements on sample size, with a min- imum sample length of approximately 1 mm. For many interesting samples it is simply not possible to grow samples big enough for this method and routes to expand the capability, for instance by mounting samples to a platform that is then strained, should be explored. The upper limits of strain will also be limited by the quality of the sample’s surface. Currently all samples are prepared with mechanical cutting and polishing but more pristine surfaces and geometries may be possible using new fabrication techniques such as xenon plasma or liquid gallium focused ion beam milling. However, restrictions on reasonable cutting time limit the overall size of samples that can be prepared in this way. In the current device the achievable strain range is also limited by the strength of the epoxy holding the sample between the sample plates. By reduc- ing the thickness of the sample, the force required and therefore the shear stress in the epoxy can also be reduced. However, the length of the sample must also be reduced proportionally for the same buckling limit to be maintained. The highest ultimate strain may therefore come by utilising a combination of these ideas.

Overall we are still at an early stage in terms of the expected development of the uniaxial pressure technique, and there is still plenty of room for advancement as well as exciting opportunities for measurements to come. I hope then that the work presented in this thesis provides strong motivation for tackling these new challenges and experimental frontiers.