3.5 dHvA in the nematic phase
3.5.2 Angular dependence of the oscillations
dHvA oscillations were measured at a base temperature of 25 mK, at 16 different angles between 0◦ and 25◦ for sample C698I, and between -14◦ and 16◦ for sample
C698A, with an angle step of about 1.6◦. The difference in angle spans originated from
a misalignment of the samples with respect to the field (see section 3.3 for details). Figure 3.20 presents the angular dependence of dHvA obtained on both samples. The top left plot presents data from C698I, where the magnetic field was rotated from c-axis towards [110], while the top right plot relates to C698A, where the field was rotated towards [100]. We observed that the oscillations were only present near 0◦, and
were significantly suppressed as we rotated away the magnetic field, where effectively, dHvA vanished at an angle of about 5-6◦. In order to emphasise this observation,
we performed Fourier transforms using the same background substraction method as described previously, shown in the bottom plots. Both peaks at 1.0 and 2.3 kT decreased in intensity as we rotated away from c-axis.
Although the temperature dependence and the frequency values for the dHvA peaks that we found in the nematic phase lead us to associate these to the low field side dHvA spectra of Sr3Ru2O7, this strong angular dependence could be related to
the high field dHvA, where we observed that frequencies disappear and appear as a
22This was done for the same considerations as in the previous section regarding low temperature
7.4 7.6 7.8 8 8.2 −1 0 1 2 3 4 5 6 7 8 9 Magnetic Field ( T ) V ( mV ) 10° 8° 6° 4° 2° 1° 0° 0 2 4 6 8 10 12 14 0 1 2 3 4 5 Amplitude ( µ V / T 1 /2 ) Frequency ( kT ) 6° 4° 2° 0° 7.4 7.6 7.8 8 8.2 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 Magnetic Field ( T ) V ( mV ) −7° −5° −3° −1° 1° 3° 5° 7° 0 2 4 6 8 10 12 14 0 0.5 1 1.5 2 2.5 3 Amplitude ( µ V / T 1 /2 ) Frequency ( kT ) −7° −5° −3° 1°
Figure 3.20: T op lef tRaw second harmonic data taken on sample C698I, as a function of the angle between its c-axis and the magnetic field, at a temperature of 25 mK. The field is rotated in the crystallographic direction of [110]. T op right Same type of data taken on C698A, and the rotation is performed towards [100]. Bottom Fourier transforms of the data in the nematic phase as a function of angle for sample C698I (lef t) and C698A (Bottom).
function of angle. If the peak at 2.3 or 2.5 kT really corresponds to the 1.8 - 1.6 kT frequency, then it is consistent to find that it vanishes as a function of angle inside the nematic phase. It is not the same for the peak at 1.0 kT, since we know that in the high field side, it is not present around the c-axis, but appears at around 5◦ (see
figure 3.11). It is then, at this point, difficult understand what we observed inside the nematic phase.
Discussion
We present in this chapter an analysis and an interpretation of the data presented in the preceding chapter. We provide a complete model for the Fermi surface of Sr3Ru2O7, as well as a an interpretation of its properties near the QCEP at the meta-
magnetic transition. With our data alone, we could not produce a unique model for the FS, but this has become possible by the use of a combination of our data, ARPES measurements that were performed by A. Tamai et al. and magnetocaloric oscillations experiments carried out by A. Rost [36, 62]. The model introduced by A. Tamai et al. suggests that metamagnetism may be produced by a peak in the DOS situated near a new small FS pocket which was subsequently discovered by A. Rost in magnetocaloric oscillations. This suggestion is consistent with our data showing that no quasiparticle mass enhancement is present for any of the previously known FS pockets. We unfortunately provide no definite proof but only partial evidence in- dicating that the new FS pocket is responsible for metamagnetism and the previously observed quantum critical properties.
We moreover make use of various models in order to interpret some unusual prop- erties of our dHvA data, the anomalous beat patterns in the low field side and the highly split spectra in the high field side. For the first problem, we introduce a simple generic model of metamagnetism that features a peak in the DOS, which we use to simulate the field and angle dependence of the amplitude of the 1.8 kT frequency. We obtain only partial agreement with the data, which indicates that the physics taking place are more complex. For the second problem, we use the theory for magnetic breakdown in order to show that a large number of almost degenerate orbits can arise from only a few symmetrical breakdown points in the BZ. We provide there the most probable hot spots in the BZ where magnetic breakdown could occur, and calculate the size of the new expected cyclotron orbits. The two models presented are far from exact. They were only developed to point to probable sources for these anomalous properties; detailed calculations are beyond the scope of this thesis.
Finally, we discuss the absence of an enhancement of the quasiparticle masses near the QCEP and the appearance of dHvA inside the nematic phase. For the first of these phenomena, we provide a mechanism which was probably responsible for producing spurious mass enhancements through systematic errors in the non- linear LK fits of the previous work of Borzi et al. [40]. We give examples of an artificial mass enhancement, but we provide detailed evidence in appendix F using numerical simulations. We furthermore discuss the implication of the absence of a mass enhancement by comparing with electronic specific heat data and measurements of the A coefficient of the resistivity. Regarding the nematic phase oscillations, we provide an interpretation for their presence, and argue that their suppression with angle may be related to putative nematic domains.
4.1
Zero field Fermi surface
In a dHvA experiment on a two-dimensional material, one cannot determine the in- plane shape of the FS (see section 1.3.4). In such a case, one knows the sizes of the various FS pockets, but not their position in k-space or their form and orientation (the terms with µ 6= 0 in the expansion of eq. 1.21), nor whether they consist of electrons or holes. In order to orient ourselves in this respect, ARPES experiments were highly desirable.
Such experiments were performed by Tamai and co-workers at the Stanford Syn- chrotron Radiation Laboratory, using single crystals of Sr3Ru2O7 provided by the
author, originating from the ensemble studied in section 2.4 [36]. High quality data were obtained, and a complete interpretation of the low field side FS was constructed, using both ARPES and dHvA data from this work. These results are part of this thesis work only inasmuch as they used low field dHvA frequencies and quasiparticle masses from this project, which had first been measured by Borzi et al. [40], and subsequently remeasured with more precision by the author. They are presented here for the reason that they are essential to the interpretation of the main results of this project. We present in this section the photoemission data and its interpretation, along with a comparison to dHvA data.
Moreover, quantum oscillations in the magnetocaloric effect were discovered in Sr3Ru2O7 by A. Rost[62], featuring an additional low frequency orbit that was not
detected by the author of this work using dHvA, due to lack of sensitivity in this frequency region1. This information has been important for the interpretation of
our results and is presented as well. Therefore, we first describe the measurements
1
Second harmonic dHvA possesses a sensitivity that vanishes at zero frequency asF2
, while the magnetocaloric oscillations feature good sensitivity at low, but not at high frequencies.
0 500 1000 1500 2000 Frequency [T] Amplitude [a.u.] 0 50 100 150 200 250 300 T S [mK] Amplitude [a.u.] FFT Data LK: m=9.8 ±0.6
Figure 4.1: Quantum oscillations in the magnetocaloric effect. Lef tFourier transform of the oscillations between 4 and 7 T.RightTemperature dependence of the amplitude of the peak at 110 T, circles, along with a fit of ∂LK(T)/∂T, solid line. Taken from A. Rost [62].
performed with the magnetocaloric effect, followed by those using ARPES. We then introduce the model constructed by A. Tamaiet al.and an interpretation for the zero field FS of Sr3Ru2O7.