SISTEMAS TECNOLÓGICOS DE LA CMAC AREQUIPA

There are several different field orientations at which Shubnikov-de Haas oscillations can be seen. Near the moment rotation transition, the extremal area associated with the only observable fre-

quencies is field dependent, indicating that the bands being probed are involved in the magnetism. Given the relatively few frequencies observed, the limited angle ranges, and the undetermined linear part of the field dependent frequencies, it is difficult to draw any robust conclusions about the shape and size of the Fermi surface pockets which contribute the observed frequencies. As noted in section4.5.1, two frequencies are field independent by virtue of being observed well away from the moment rotation transition. The observations are consistent with spherical pockets, oblate or prolate spheroids or, less likely, more complex geometries. The two frequencies are probably from different pockets, and, if spherical would enclose 1.7% and 2.4% of the Brillouin zone volume. Of course symmetry allows there to be several copies of each pocket in the zone, so integer multiples of these values are also possible. The mass of one pocket has been observed to be 75±20 me, the other has too poor signal to noise to estimate a mass. The former then, if

spherical, contributesγpocket= kB2

6~2m

∗p

A/πper unit volume, or 12 mJmol−1_K−2_{, to the specific}

heatγ. This value is again multiplied by the number of pockets in the zone. ForB_kb, the mass is known, but the exact area is not. Assuming 200 T andm∗_{= 8mefor the high-field pocket, it} encloses less than 0.2% of the zone and contributes an almost negligible 0.5 mJmol−1_K−2 _toγ.

The measured zero field gamma is 160 mJmol−1_K−2_{[27,25]. The only high field measurements}

are those reported by Prok´es[27], which has an erratum[26] reporting some of the samples were misaligned. The erratum does not indicate that the specific heat results were affected, but the resistivity results were also not listed as affected by the erratum, but are different resistivity from those measured here. Nevertheless, they showγ is field independent forB_ka, and drops quickly before saturating at about 130 mJmol−1K−2 for both of the other field directions. Magnetization measurements in the same paper and elsewhere[29] indicate that the response to field alongais much less than the other two, possibly even zero within experimental error. As magnetization is closely tied to Fermi surface shape and size in an itinerant ferromagnet, this is consistent with the change inγbeing due to changes in Fermi surface. The fact thatγsaturates could be indicative of an ETT, especially as the saturation field is close to the moment rotation transition and possible ETT described in4.5.2. But it could also be due to the changing surfaces ceasing to contribute through other means, such as filling level changing the effective mass.

There are then two possible opportunities to match up the observed frequencies to the specific heat. First at zero field along b, and secondly the changes between there and high field along b. At zero field along b, we have the pockets measured with B_kc, both of which seem to be field independent, so can be assumed to be the same size at zero field. The larger contributes 12 mJmol−1_K−2 _{per pocket in the zone, the smaller might add another 10 mJmol}−1_K−2 _{if it is}

the same mass. Both could be larger or smaller if the pockets are not spherical. Allowing then 8 copies of each pocket in the zone, these alone can make up the entire γ. Alternatively, and perhaps more likely, they could fall far short, and there are other bands not observed due to their mass or simply because they are open.

When considering the changes with field, there are two relevant observations, those in sections

4.5.2 and 4.5.3. These could be the same orbit, if the low field one does not disappear at an

ETT, or could be different ones. One small surface cannot exist in isolation, as the changing population of the bands associated with the changing magnetization must have another band or bands to transfer to. This does not necessarily imply a second rapidly changing band though, as the population can move to a band with a large density of states at the Fermi level without major effect. To avoid concluding that other bands exist would require that the population is transferring from one of these to the other, and as one grows and the other shrinks, they account for the change inγ. The larger of these bands is estimated to contribute about 2 mJmol−1_K−2

at 10 T, though with the unknown linear term, possible non-spherical nature, and multiple copies per zone, could be more. It seems unlikely that it could account for the observed reduction inγ of 30 mJmol−1_K−2_{. So we reach the unsurprising conclusion that there are other bands present}

with changing occupation levels, even if they themselves are not strongly field dependent. Another observation is that all the bands where a mass has been obtained are heavy, ranging from 8 to 75 me. Generally speaking, if light orbits were present, one would expect them to be

observed. Various measurements have been taken at higher temperatures where larger currents are possible and signal to noise is improved. Whilst it is possible that the curvature factor on these bands is responsible for their non-appearance, it is also possible that they are not observed as they are open sheets, in keeping with the conclusions from previous sections.

Overall it must be concluded that with the presently available sample quality, SdH is not a good probe of Fermi surfaces. It remains however one of the best available to us. Attempts to measure de Haas-van Alphen via torque are complicated by the large ferromagnetic moment and have thus far proven unsuccessful[88], even in samples where SdH can be observed. Susceptibility measurements have not yet been attempted, and could prove more successful. The other main direct probe of a Fermi surface is ARPES, but the results from an ARPES measurement are (in the section4.4 are also rather inconclusive.