Nivel de la investigación: Descriptivo, transversal

One question which previous experiments have been unable to answer is whether Sr3Ru2O7’s phase, in the absence of any symmetry-breaking fields, breaks the four-

fold rotational symmetry of the crystal lattice or not. Indeed, the state with reduced symmetry, seen for instance by a large in-plane resistive anisotropy [4], has only been observed with an applied in-plane magnetic field. With our experiment we have shown that in-plane strain can also induce a strong in-plane anisotropy. It is therefore possible that the underlying state is C4 symmetric with a strong suscep-

tibility to symmetry-breaking fields, rather thanC2 symmetric. Understanding the

symmetry of the phase is vital in terms of determining its order parameter. Let us briefly explore the expected behaviour for aC2andC4symmetric phase respectively.

If we associate an enhanced resistivity in the phase along a and b with an or- der parameter ∆a and ∆b respectively, two scenarios can be put forward. In the

first, the phase is locallyC2 symmetric. The degeneracy of ∆a and ∆b implies the

formation of domains in the absence of any symmetry-breaking fields, where the order parameter is rotated by 90° between domains. Under zero strain and with no in-plane field the measured response would be isotropic, as the signal would be averaged over a large number of domains. The effect of a symmetry-breaking field would be lift the degeneracy between the two order parameters. In the second sce- nario, the phase is locally C4 symmetric, meaning that the components alongaand

bdo not compete strongly and can coexist locally. In this case a symmetry-breaking field would continuously suppress one order parameter whilst enhancing the other, with the two orders coexisting over a finite range. Both of these scenarios corre- spond to particular limits of the Ginzburg Landau model for a two component order parameter discussed in relation to Sr2RuO4 in Section 3.5.4. For the first scenario,

the interaction term βI between the order parameters is very large and prevents

coexistence of the two orders, whilst for the second,βI is much smaller. The phase

diagrams for the two scenarios are sketched in Figure 6.17.

In these phase diagrams we have neglected the first order metamagnetic tran- sitions and drawn the phase boundaries as second order transitions. Evidence of symmetry-breaking inside the phase was found by Lester et al. [44], who showed that it was host to a SDW. Only the transition atf = 0 in the left-hand panel is first order, as it takes place when theC4 symmetry is already broken. In Sr3Ru2O7 some

coupling must occur between the second order transitions and the metamagnetism to make some of the observed transitions first order: those bounding the A-phase for instance are distinctly first order [33].

Our data appear qualitatively much closer to the second scenario, where both types of order coexist microscopically in the region around zero strain. This can be seen by comparing the right-hand panel of Figure 6.17 with Figure 6.5C, where the outlines of the regions of enhanced ρaa and ρbb are plotted. As noted previously,

B

B

f

f

0

0

Δ

or Δ

Δ

or Δ

Δ

or Δ

Δ

or Δ

Δ

and Δ

Figure 6.17: Phase diagrams for two different scenarios in Sr3Ru2O7. f is a

symmetry-breaking field, either magnetic field or strain. Left: Strong competi- tion between the order parameters causes domain formation at f = 0 where they are degenerate, with the degeneracy being lifted by non-zero f. The thick black line denotes a first order transition, whilst all of the other boundaries denote second order transitions. Right: Order along aand b do not compete strongly and coexist over a range off.

and has a field dependent width in strain. These observations are consistent with the qualitative predictions made for the second scenario. Is it possible however that domains of locally C2 symmetric order could be stabilized over a finite region in

strain, giving the appearance of coexistence andC4 symmetry?

It is plausible for instance that domains could be stable over a finite strain range if there is an inhomogeneous strain field within the sample. Strain inhomogeneity could be due to a random distribution of defects within the sample, or dislocations along the edge caused by the wire saw. The main source of inhomogeneity in our experiment is most likely due to bending of the sample, which as discussed in Section 6.2.5 gave rise to ∼ 0.02% inhomogeneity for sample #1 and less than 0.01% for samples #2 and #3. The width of the coexistence region is however∼0.08%, larger than the inhomogeneity in any of the samples. Moreover, if this region were being broadened by strain inhomogeneity, one would not expect its width in strain to be field-dependent, as was observed. We therefore argue that the coexistence region measured in our samples is not a consequence of strain inhomogeneity. Additionally, we should emphasize that the data were collected by repeatedly ramping B k c

through the phase at a series of steps in strain. Hence the overlap region is not a result of latency across the first order line shown in the left-hand panel of Figure 6.17.

Long-range elastic or ferromagnetic interactions between domains could in theory cause them to become stabilized over a finite strain range. A lattice deformation of the order of 10−6 was measured upon entering the phase under an applied in- plane field [41]. This is much smaller than the 0.08% strain width of the coexistence region, so it does not seem plausible that long-range elastic interactions are causing

a domain structure to stabilize. Domain stabilization via ferromagnetic interactions also appears unlikely, as the coexistence region extends over a field range of∼1 T. The metamagnetic jump at 7.85 T, which is the larger of the two, is by comparison only µ0∆M = 0.008 T [36], indicating that internal fields in the sample are likely

much smaller than the width of the coexistence region.

A signature of domains in the sample would be the observation of hysteresis. Indeed, domains tend to become pinned around local defects in the lattice, so that a finite amount of energy is required to change their size and alignment. In the case of a ferromagnet, hysteresis is observed by measuring magnetization as a function of field which produces a hysteresis loop as the field is ramped up and then back down again. A similar effect was previously searched for in Sr3Ru2O7during a series

of experiments performed with a vector-magnetic field [121]. In these the magnetic field parallel to a was slowly swept up and then back down, whilst controlling the field alongc to always remain within the phase. No sign of hysteresis was observed between the up- and down-ramps, indicating that if domains do exist they must be extremely weekly pinned.

Our data, combined with the lack of evidence for domains, strongly suggest that the phase is C4 symmetric with a high susceptibility to in-plane fields. The

question of how to explain the magnitude of the enhancement in resistivity in the phase however remains. Indeed, one of the primary explanations for the increase in resistivity has been domain wall scattering. Locally C2 symmetric order aligned

along a or b would tend to favour domain formation along the h110i directions, similar to twin boundaries [47]. The resistive anisotropy is however aligned along the in-plane axes, which also indicates that domains do not play a role in the resistivity enhancement.