High-Field de Haas-van Alphen Effect in non-centrosymmetric CeCoGe3 and LaCoGe3
Ilya Sheikin, Pierre Rodiere, Rikio Settai, Yoshichika Onuki
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J. Phys. Soc. Jpn. (2011) SACeCoGe3˙dHvA˙Tokyo˙revisedc (cid:13) High-Field de Haas-van Alphen Effect in non-centrosymmetric CeCoGe and LaCoGe Ilya Sheikin ∗ , Pierre Rodiere , Rikio Settai , and Yoshichika ¯Onuki Grenoble High Magnetic Field Laboratory, CNRS, BP 166, 25 Av. des Martyrs, 38042 Grenoble, France Institute N´eel, CNRS-UJF, 25 Av. des Martyrs, 38042 Grenoble, France Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
We report on de Haas-van Alphen effect measurements in the non-centrosymmetric systems CeCoGe and LaCoGe in magnetic field up to 28 Tesla. In both compounds, two new high frequencies were ob-served in high fields. The frequencies were not detected in previous lower field measurements. The fre-quencies do not originate from magnetic breakdown, and, therefore, are likely to be intrinsic features ofthe compounds. In CeCoGe , the corresponding effective masses are strongly enhanced, being of the orderof 30 bare electron masses. KEYWORDS: CeCoGe , LaCoGe , non-centrosymmetric, de Haas-van Alphen effect Following the discovery of superconductivity in the non-centrosymmetric heavy-fermion compound CePt Si, mate-rials without inversion symmetry in their crystal structurehave attracted a lot of experimental and theoretical inter-est. The interest is mainly due to a fascinating theoreti-cal prediction
2, 3) that superconductive pairing in such sys-tems requires an admixture of a spin-singlet with a spin-triplet state. Subsequent observation of superconductivity inother non-centrosymmetric compounds CeRhSi , CeIrSi , CeCoGe ,
6, 7) and CeIrGe has further stimulated the re-search efforts. Very unusual superconducting properties wereindeed observed in some systems, such as enormously highupper critical field in CeIrSi and CeRhSi . The absence of inversion symmetry in the crystal latticeof a metal brings about a strong spin-orbit coupling, whichin turn leads to the splitting of the electronic energy bands.The Fermi-surface of such a metal is, therefore, also split intotwo surfaces characterized by different chirality. This natu-rally results in the appearance of two distinct frequencies inthe spectra of de Haas-van Alphen (dHvA) oscillations. It wasdemonstrated theoretically, that the analysis of the oscilla-tory spectra in such materials provides a direct measure of thestrength of the spin-orbit coupling. It is thus very important toobtain detailed and precise dHvA frequencies and their angu-lar dependence in materials without inversion center. In mostnon-centrosymmetric compounds this coupling is extremelystrong being of the order of 1000 K.CeCoGe and its non-4 f analog LaCoGe crystallize inthe tetragonal BaNiSn -type crystal structure. CeCoGe is amoderate heavy-fermion system with a Sommerfeld coeffi-cient of the specific heat γ = 0 . J/molK . It undergoesan untiferromagnetic transition at T N = 21 K, followed bytwo more transitions at T N = 12 K and T N = 8 K. Three consecutive metamagnetic transitions were observedfor magnetic field applied along the easy magnetic c -axis.The high pressure phase diagram of CeCoGe is quite com-plicated demonstrating six different phases. Magnetic ordervanishes around 55 kbar, and superconductivity is observed inthe range of 54-75 kbar. ∗ E-mail address: [email protected]
The dHvA effect in CeCoGe and LaCoGe was previ-ously investigated in magnet fields up to 17 Tesla. In bothcompounds, four fundamental frequencies were identified, allof them split due to spin-orbit interaction. The frequenciesthemselves and their angular dependencies are similar in bothcompounds and are in a rather good agreement with the re-sults of theoretical band structure calculations performed forLaCoGe . As compared to other non-centrosymmetric com-pounds, the splitting of dHvA frequencies in CeCoGe andLaCoGe is relatively small, implying a moderate spin-orbitcoupling of about 100 K. In LaCoGe , all the dHvA frequen-cies were doubled implying either a slightly unperfect qual-ity of the sample or a field dependence of the frequencies.The highest effective mass observed in CeCoGe is 12 bareelectron masses corresponding to the β -branch. Finally, onlyone frequency originating from the α -branch representing thebiggest Fermi surface was initially observed in CeCoGe . We present here the results of the dHvA effect measure-ments in non-centrosymmetric CeCoGe and LaCoGe inmagnetic fields up to 28 Tesla produced by a resistive mag-net in GHMFL. The measurements were performed on sin-gle crystals similar to those studied by Thamizhavel et al . The details of crystals preparation and characterization aregiven elsewhere.
The measurements were performed us-ing a torque cantilever magnetometer. The magnetometer wasmounted in a top-loading dilution refrigerator equipped witha low-temperature rotation stage.Figure 1 shows the oscillatory torque and the correspondingFourier transform in LaCoGe in field from 20 to 28 Tesla. Allthe previous dHvA frequencies can be clearly identified,and their values are very close. The most remarkable differ-ence with lower field measurements is the observation of twonew fundamental frequencies denoted as A and B in figure 1.The new frequencies, F A = 14 . kT and F B = 21 kT, areconsiderably higher than the highest frequency, F α = 9 . kT, reported for lower fields.The dHvA oscillations observed in CeCoGe between 20and 28 T are shown in the upper panel of figure 2. Likein LaCoGe , all the fundamental frequencies previously ob-served in CeCoGe are still present at high field (lower panelof figure 2). In addition, both components of the α -branch are SACeCoGe3˙dHvA˙Tokyo˙revised-1 . Phys. Soc. Jpn. (2011) SACeCoGe3˙dHvA˙Tokyo˙revised SACeCoGe3˙dHvA˙Tokyo˙revised-2
15 20 25
20 22 24 26 28-4-3-2-10123 -+---+-- A m p lit ud e ( a r b . un it s ) dHvA frequency (kT) - + + + A - + A m p lit ud e F (kT) B T o r qu e ( a r b . un it s ) H (Tesla)LaCoGe = 2 o T = 60 mK
Fig. 1. High field (20–28 T) dHvA oscillations (upper panel) and itsFourier spectrum (lower panel) in LaCoGe for magnetic field applied at2 ◦ from the c -axis at 60 mK. The frequencies that were observed in theprevious lower-field measurements are denoted by Greek letters, while thenew frequencies observed at high field only are denoted A and B . now clearly resolved. With magnetic field applied at 9 ◦ fromthe crystallographic c -axis, the two frequencies are close toeach other, F α + = 10 . kT and F α − = 10 . kT. Themost significant result, however, is the presence of the newfrequencies, A and B , in the Fourier spectrum of CeCoGe .The frequencies are somewhat lower than in LaCoGe being F A = 12 . kT and F B = 19 . kT. Like in LaCoGe , bothnew frequencies are fundamental.Figure 3 shows the temperature dependence of the dHvAamplitudes of the new frequencies A and B as well as α and β -branches in CeCoGe for magnetic field applied at 9 ◦ fromthe crystallographic c -axis, the same orientation as in figure 2.These data allow one to determine effective masses by fittingthe experimental points to the temperature-dependent part ofthe Lifshits-Kosevich formula. The best fits to the formulaalong with the extracted effective masses are also shown infigure 3. It was previously reported that α and β -branchespossess the highest effective masses of 8 and 12 bare electronmasses respectively. These values are very close to the currentresults if only the α − frequency is considered and taking intoaccount that only a single frequency from the α -branch wasinitially observed in previous measurements. Interestingly, theaffective masses of the two frequencies originating from the α -branch differ by a factor of more than two, being 14.9 and7.3 bare electron masses for α + and α − frequencies respec-
15 20 25 - + A m p lit ud e F (kT) B -+ - -+ -+ - --+ A m p lit ud e ( a r b . un it s ) dHvA frequency (kT) A = 9 o T = 60 mK T o r qu e ( a r b . un it s ) H (Tesla)CeCoGe Fig. 2. dHvA oscillatory signal (upper panel) and its Fourier spectrum(lower panel) observed in CeCoGe with magnetic field (20–28 T) appliedat 9 ◦ from [100] to [110] at T = 60 mK. The frequencies denoted θ , ǫ , β and α were observed in the previous lower field measurements (with theexception of α + -branch). The frequencies denoted A and B are observedonly at high field and were not detected in the previous measurements. tively. This is in contrast with all the other branches where theeffective masses of the two components are quite close to eachother. The most surprising result, however, is that the effectivemasses of the new frequencies are strongly enhanced being 27and 31 bare electron masses for A and B respectively. Thesevalues by far exceed the masses of the other previously ob-served frequencies.Figure 4 shows the angular dependence of the dHvA fre-quencies in CeCoGe for the magnetic field rotation from[001] towards [100] direction. The frequencies were deter-mined from the Fourier transform over the field range from20 to 28 Tesla. The angular dependence of the frequenciesobserved at lower fields is very similar to the previously re-ported one. The highest of the new frequencies, B , existsonly over a small angular range at about 10 ◦ from the c -axis.The other new frequency, A , however, is observed over an an-gular range of about 15 ◦ and is centered around the c -axis.It is not perfectly clear whether the new dHvA frequencies A and B observed both in LaCoGe and CeCoGe emergeonly at high field above 17 T or exist at lower fields as well,but can not be detected due to experimental limitations. Verysmall amplitudes of the corresponding oscillations as well asstrongly enhanced effective masses found in CeCoGe makethe latter scenario quite possible. In LaCoGe , however, while . Phys. Soc. Jpn. (2011) SACeCoGe3˙dHvA˙Tokyo˙revised SACeCoGe3˙dHvA˙Tokyo˙revised-3 + m - m + m - m A m B m d H v A a m p lit ud e ( a r b . un it s ) Temperature (K)CeCoGe = 9 o Fig. 3. (Color online) Temperature dependence of the dHvA amplitude isshown for α and β -branches as well as the new frequencies A and B ofCeCoGe with magnetic field applied at 9 ◦ from c to a -axis. Lines arethe fits to the temperature dependent part of the Lifshits-Kosevich formula A ( T ) ∝ αm ∗ T/B sinh( αm ∗ T/B ) , where α ≈ . T/K. The effective masses, m ∗ , obtained from the fits are also shown. m is the bare electron mass. d H v A fr e qu e n c y ( k T ) Field angle (deg.)A[001] [100]CeCoGe Fig. 4. Angular dependence of the dHvA frequencies in CeCoGe isshown for the magnetic field rotated from [001] towards [100] direction.Only fundamental frequencies are shown. The new frequencies A and B are shown as closed symbols. the amplitudes of A and B oscillations are still relativelysmall, the effective masses must be small too. The new fre-quencies, if present, should therefore be possible to observeat lower field. An appealing possibility is a decrease of theDingle temperature at high field. Since the oscillatory am-plitude depends exponentially on the Dingle temperature, theoscillations might be too small to detect at low field, but be-come ”visible” at higher field where the Dingle temperature islower. Such scenario is indeed realized in CeCoIn , wheresome of the dHvA frequencies are detected only at high fieldabove an abrupt change of the Dingle temperature. Nonethe-less, if the new frequencies exist, even if experimentally un-detectable, already at low field, it would be difficult to ex-plain their absence in theoretical band structure calculationsat least for LaCoGe , where neither magnetic order nor 4 f -electrons complicate the picture. Moreover, the Fermi-surface cross-sections corresponding to both frequencies do not ex-ceed the area of the Brillouin zone perpendicular to the ap-plied magnetic field. On the other hand, if the emergence ofthe new frequencies is intrinsically related to high magneticfields, this would easily account for their absence in the bandstructure calculations performed for zero magnetic field. Ifthis indeed is the case, the new frequencies certainly do notoriginate from a magnetic breakdown as there are no two fun-damental frequencies that would sum up to yield any of them.Furthermore, the high effective masses observed in CeCoGe also rule out such a possibility. Thus, the new frequencies arelikely to be an intrinsic property of the compounds and seemto originate from a field-induced modification of the Fermi-surface.In conclusion, two new high dHvA frequencies have beenobserved both in LaCoGe and CeCoGe in high magneticfield up to 28 T. The frequencies are similar in both com-pounds. Neither of the new frequencies was detected in theprevious lower-field measurements or revealed by theoreti-cal band structure calculations. In CeCoGe , the frequenciescorrespond to strongly enhanced effective masses implyingthat they represent thermodynamically important parts of theFermi-surface. While it is not certain if the frequencies ap-pear in high magnetic field only or simply experimentally un-detectable at lower field, they certainly do not originate frommagnetic breakdown. They are therefore likely to be intrinsicfor both compounds and are possibly due to a field-inducedmodification of the Fermi-surface.Part of this work has been supported by the EuroMagNETII under the EU contract number 228043.
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