Unconventional metals at low temperatures and high magnetic fields

Unconventional metals at low temperatures and high magnetic fields

Physica B 246—247 (1998) 97—103 Unconventional metals at low temperatures and high magnetic fields Alex H. Lacerda!,*, C.H. Mielke!, N. Harrison!, W...

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Physica B 246—247 (1998) 97—103

Unconventional metals at low temperatures and high magnetic fields Alex H. Lacerda!,*, C.H. Mielke!, N. Harrison!, W.P. Beyermann", A. Yatskar", P.C. Canfield#, S.L. Bud’ko#, G.M. Schmiedeshoff$, M.S. Torikachvili%, R.M. Vestal&, L.K. Montgomery& ! National High Magnetic Field Laboratory, Pulse Facility, Los Alamos National Laboratory — MST 10, Los Alamos, NM 87545, USA " Department of Physics, University of California, Riverside, CA 92521, USA # Ames Laboratory, Iowa State University, Ames, IA 50011, USA $ Department of Physics, Occidental College, Los Angeles, CA 90041, USA % Department of Physics, San Diego State University, San Diego, CA 92182, USA & Department of Physics, Indiana University, Bloomington, IN 47405, USA

Abstract This paper focuses on recent magnetotransport and magnetization measurements on unconventional metals and molecular conductors down to 350 mK and in magnetic fields up to 60 T. Measurements were performed at the National High Magnetic Field Laboratory — Los Alamos Facility. Three variants of unconventional materials will be presented. First, the magnetic field effects on the thermodynamic and magnetotransport properties of the Fermi liquid regime of the heavy Fermion compound YbNi B C. Second, we present recent investigations of the Fermiology of the pnictide 2 2 compound SmSb by means of Shubnikov—de Haas and de Haas—van Alphen quantum oscillations. Finally, we present 2 recent Fermi surface measurements of j-(ET) Cu[N(CN) ]Br, the layered organic superconductor with the highest ¹ at 2 2 # ambient pressure. ( 1998 Elsevier Science B.V. All rights reserved.

1. Introduction Investigations of strongly correlated electron systems at the extreme conditions of high magnetic field and very low temperatures are still of

* Corresponding author. Tel.: #1 505 665 6504; fax: #1 505 665 4311; e-mail: [email protected]

paramount importance to understand the unique underlying physics and fundamental issues of condensed matter physics. This paper reports on magnetotransport and magnetization experiments down to 350 mK in magnetic fields to 60 T in two variations of strongly correlated materials: YbNi B C and SmSb and the recent observation 2 2 2 of quantum oscillations at ambient pressure in the molecular conductor j-(ET) Cu[N(CN) ]Br. 2 2

0921-4526/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII S 0 9 2 1 - 4 5 2 6 ( 9 7 ) 0 0 0 3 3 - 7

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2. Experimental procedures The correlated metal single-crystal samples of YbNi B C and SmSb , used in this investigation, 2 2 2 were grown using the Ames Labs flux growth technique. Single crystals as large as a couple of square millimeters could be obtained by this method. Xray diffraction spectra found tetragonal and orthorhombic structures for YbNi B C and SmSb , 2 2 2 respectively. Molecular conductor samples were grown using the standard electrocrystallization technique [1]. Magnetotransport and magnetization measurements were performed using a 20 T superconducting magnet and a 60 T pulsed field (rise time of 8 ms) at the National High Magnetic Field Laboratory-Los Alamos Facility. For both magnets, standard AC-lockin techniques have been used. Electrical contacts were made using 25.4 lm platinum wires, and the current was applied along the ab-plane for YbNi B C and SmSb and along 2 2 2 b*-axis for the molecular conductor j-(ET) 2 Cu[N(CN) ]Br. A combination of, flow cryostats, 2 dilution refrigerators and 3He refrigerator were used to reach the desired temperature range.

3. Correlated metals at extreme conditions

lowest temperature investigated (50 mK), a clear crossover to a Fermi liquid regime is observed below 2 K. In an applied magnetic field of 18 T, the Fermi liquid regime is extended to 4 K, and the coefficient of the quadratic term (o"o #A¹2) decreases by 0 33% as the magnetic field increases to 18 T. Such a decrease of the A term by application of a magnetic field has also been observed in the prototype HF compound CeCu [4]. Due to the difficulties 6 of incorporating in the scattering mechanisms the effect of an external magnetic field, only very few theoretical models treat the magnetotransport of HF compounds [5,6]. However, since the A term is proportional to the density of quasiparticules states evaluated at the Fermi level [5,6], it is reasonable to expect a monotonic decrease of the latter term as a function of increasing magnetic field. To better understand the magnetotransport properties of this compound in the Fermi liquid, regime we have measured transverse magnetoresistance (BoI) for fields applied along and perpendicular to the c-axis. Fig. 1 shows the transverse magnetoresistance for the case where B is perpendicular to the c-axis. Below 4 K, a shallow local maximum is observed. This maximum in the magnetoresistance moves to lower field as the temperature is decreased. As the temperature is increased above 10 K only a negative magnetoresistance is observed, consistent with

3.1. YbNi B C 2 2 Many years have elapsed since HF compounds were first identified by the extraordinary large electronic specific heat coefficient (C/¹"c) at low temperatures (see Ref. [2] and references therein). It is remarkable that the understanding of the competition between local and intersite fluctuation in HF compounds is still an open question. Experimentally, it has been shown that the application of an external magnetic field is an excellent tool for investigating the ground-state properties of HF compounds. The first system to be presented in this paper will be a prototype heavy fermion (HF) compound YbNi B C. Many unique features are re2 2 lated to this Yb-based HF system. Among them its large c ("530 mJ/mol K2) and the relatively low Kondo temperature (¹ ) of 10 K [3]. Even though K there is no long-range order observed down to the

Fig. 1. Transverse magnetoresistance of YbNi B C for B per2 2 pendicular to the c-axis.

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more localized interactions, expected at high temperatures [7]. At magnetic fields above 30 T and temperatures below 2 K a slight up-turn to a positive magnetoresistance is observed. This may be due to the intense magnetic field breaking down the strong correlations of the quasiparticles responsible for the HF state. It is again remarkable that the magnetotransport properties of this Yb-based HF compound are also similar to CeCu . 6 From the theoretical point of view, only very few models deal with magnetotransport properties of HF compounds even in the Fermi liquid regime. In the simplest case of the one-impurity Kondo limit [8], a negative magnetoresistance is predicted. However, for the case of the Kondo lattice [9], the magnetoresistance is positive for ¹'¹ and negaK tive for ¹(¹ . Experimentally, it is interesting to K note that a positive magnetoresistance is found in only a few HF compounds in the Fermi liquid regime. Early [3] magnetic susceptibility measurements in this compound showed a negative Weiss temperature, suggesting the presence of antiferromagnetic correlations. To further investigate this possibility, we have measured the magnetization of this compound over a wide range of temperatures. Fig. 2a shows isothermal magnetization curves at 1.7 K for B parallel and perpendicular to the c-axis. Even though a magnetic anisotropy is observed, the magnetization appears to follow a distinct Brillouintype saturation characteristic of a pure paramagnetic system. This result in itself is remarkable, since in almost all the HF compounds known to date, with a Kondo temperature of this order (e.g. CeRu Si [10]) a magnetic-field-induced transition 2 2 is observed. To explore the possibility of a magnetic-field-induced transition at higher fields, Fig. 2b shows the magnetization at 400 mK to 50 T and no indication of transition is observed. We have also measured magnetization to 18 T down to 20 mK, and the same magnetization curve was observed. It is striking that, even though a very anisotopic magnetotransport behavior is observed in this compound, a featureless magnetoresistance persists to 50 T and down to 20 mK. This might be linked to the fact that the system is very closed to a magnetic instability.

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Fig. 2. Magnetization of YbNi B C (a) at 1.7 K to 18 T, and (b) 2 2 at 400 mK to 50 T for B parallel to the c-axis.

3.2. SmSb 2 We have recently measured the magnetization and magnetotransport of the RESb (RE"Ce, La, 2 Nd, Sm) series [11,12]. These light rare-earth diantimonides crystallize in an orthorhombic structure [13] and present highly anisotropic magnetic properties [9]. One of the Sb sites forms 2D sheets, while the other Sb site and RE sites form slabs of triangular prisms which separate the Sb sheets. A diversity of ground-state properties is found among the series, from superconductivity at low temperatures

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to antiferromagnetism and metamagnetic transitions [14,11]. Even though this series has been known for many years, only now have highquality single crystals been obtained by means of the Ames flux grown technique. The high-quality single crystals form in layered sheets with typical residual resistance ratios (RRR) of 500. This section presents a detailed study of the Fermi surface of SmSb compound. Fig. 3c shows 2 the zero-field resistivity; a sharp antiferromagnetic transition is observed at 12.5 K. The sharp decrease of resistivity at the transition is probably due to the suppression of the spin disorder scattering above the antiferromagnetic transition (¹ ). The large N value of RRR of this compound and the extremely sharp transition observed at ¹ indicates the high N quality of this material, making it a good candidate for quantum oscillations at low temperatures. In Fig. 3a we plot the high-field transverse magnetoresistance results. Clear Shubnikov—de Hass (SdH)

oscillations are observed above 20 T. It is interesting to notice that the range of measurable frequencies for this compound extends only up to &1000 T (Fig. 3b). This is very unusual for a good metal, and may indicate a fragmented Fermi surface, possibly due to the low-temperature antiferromagnetic ordering. By fitting the temperature dependence of the quantum oscillations observed in Fig. 2b with the Lifshitz—Kosevich formalism, an effective mass corresponding to the a-frequency of 0.65m is determined [12]. % In Fig. 4 we show pulsed magnetization measurements (the figure shows data only from 4.5 to 15 T), where de Haas—van Alphen oscillations can be observed in magnetic fields as low as 4 T. The cross-over to higher-frequency oscillations at &6.5 T is suggestive of magnetic breakdown effects. Evidence for Stark quantum interference is also present in the magnetoresistance spectra which further suggest the notion of magnetic breakdown.

Fig. 3. (a) Magnetoresistance of SmSb at various temperatures to 60 T. (b) The spectral analysis of the SdH quantum oscillations 2 between 15 and 60 T. (c) The temperature dependence of the resistance showing ¹ at 12.6 K. N

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Fig. 4. de Haas—van Alphen oscillations are shown for fields between 4.5 and 15 T.

4. Molecular conductors Recent 13C-NMR [15] and low-temperature specific-heat measurements, [16] have aroused considerable interest in the possibility that j(ET) Cu[N(CN) ]Br possess an unconventional 2 2 Fermi-liquid ground state [17]. An investigation of the magnetotransport at high fields and low temperatures has been undertaken to address this point. An example of high-field magnetotransport data is shown in Fig. 5a. The data clearly indicates the crossover transition (H ) from the supercon#2 ducting to the normal metal state at &10 T. However, not until fields of &38 T do quantum oscillations appear. Fourier transformation reveals that the SdH frequency of 3798$5 T (Fig. 5b) is very near to the area of the BZ (3795 T) determined by means of low-temperature (20 K) X-ray crystallography [18]. While band-structure calculations [19] for j-(ET) Cu[N(CN) ]Br yield a Fermi surface 2 2 composed of a closed hole pocket (a orbit) bounded by Q1D sheets, a frequency equal to the BZ is

generally observed at high fields in the j-phase salts [20] due to magnetic breakdown [21] effects. The absence of other frequencies, corresponding to a pocket, implies that j-(ET) Cu[N(CN) ]Br is in 2 2 the complete magnetic breakdown regime at the high magnetic fields at which the quantum oscillations are observed. A similar result was found for the BEDT-TSF (or BETS) analogue salt, and implies that the probability of the quasiparticles tunneling across the gap at the BZ boundary is close to unity. This contrasts with the situation in j-(ET) Cu(NCS) (¹ "10.6 K), in which a fre2 2 # quency still persists at high magnetic fields [22]. Evidently, the gap in j-(ET) Cu[N(CN) ]Br is 2 2 much smaller than in the latter compound as suggested by band structure calculations [19]. A fit of the temperature dependence of the SdH oscillations to the function R "X/sinh(X) [23] T (where X"14.69m*¹/B) is shown in Fig. 5c. Fitting to the Lifshitz—Kosevich (LK) temperature reduction factor in a Q2D metal is warranted in the case where the amplitude of the oscillations is small

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Fig. 5. (a) Magnetoresistance of j-(ET) Cu[N(CN) ]Br at various temperatures to 60 T. (b) The spectral analysis of the SdH quantum 2 2 oscillations between 15 and 60 T. (c) The effective mass of j-(ET) Cu[N(CN) ]Br determined by fits of the amplitude of the SdH 2 2 oscillations.

compared to the background magnetoresistance [22]. It should be noted that the fit to the LK temperature reduction factor is consistent with conventional Fermi liquid behavior. In contrast to the low effective mass obtained by Kartsovnik et al. [24] the effective mass we obtain in j-(ET) 2 Cu[N(CN) ]Br (m*"5.4$0.1 m for the b fre" % 2 quency) is found to be comparable with other ET j-phase salts [20—22]. The effective mass of 5.4 m % is nevertheless lighter than m* in j-(ET) Cu(NCS) " 2 2 [22]. However, recent calculations [25] predict m* for j-(ET) Cu[N(CN) ]Br to be lighter than in " 2 2 the latter salt, although our results indicate a difference of only &23%. Finally, we note that our results indicate that the mean free path in j-(ET) Cu[N(CN) ]Br, as 2 2 determined from our effective mass and Dingle temperature analysis, is significantly shorter than in many other organic conductors and superconduc-

tors that give rise to quantum oscillations. A more detailed description of this analysis is given elsewhere [26].

Acknowledgements Work performed at the National High Magnetic Field Laboratory was supported under the auspices of the National Science Foundation and the US Department of Energy. Researchers at the Univ. of California Riverside (WPB and AY) were supported by the National Science Foundation (DMR-9624778). Work at Ames Laboratory was supported by the Director for Energy Research, Office of Basic Energy Science. Research at Indiana University was supported by the Division of Materials Research of the National Science Foundation (NSF DMR-9023347) and the Air Force Office

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of Scientific Research, Directorate of Chemistry and Materials Science (F49620-92-J-0534). One of us (SLB) was partially supported by IITAP — Iowa State University and CNPq (Brazil). AHL is thankful to Mr. J. Detwiler for helping with experiments.

[14]

References

[16] [17] [18]

[1] L.K. Montgomery, in: J.-P. Farges (Ed.), Organic Conductors, Fundamentals and Applications, Ch. 4, Marcel Dekker, New York, 1994. [2] G.R. Stewart, Rev. Mod. Phys. 56 (1984) 755. [3] A. Yatskar et al., Phys. Rev. B 54 (1996) R3772. [4] A. Amato et al., J. Low Temp. Phys. 68 (1987) 317. [5] C. Chen et al., J. Phys.: Condens. Matter 5 (1993) 95. [6] A.J. Millis, P.A. Lee, Phys. Rev. B 35 (1987) 3395. [7] W.P. Beyermann et al., unpublished. [8] P. Schlottman, Phys. Rep. 181 (1989) 1. [9] F.J. Ohkawa, Solid State Commun. 71 (1989) 907. [10] P. Haen et al., J. Low Temp. Phys. 67 (1987) 391; A. Lacerda et al., Phys. Rev. B40 (1989) R11429. [11] S.L. Bud’ko et al., to be published. [12] C.H. Mielke et al., to be published. [13] R. Wang, H. Steinfink, Inorg. Chem. 6 (1967) 1685; F. Hullinger, in: K.A. Gshneider, L. Eyring (Eds.), Handbook

[15]

[19] [20] [21] [22]

[23] [24] [25]

[26]

103

of Physics and Chemistry of Rare Earth, vol. 4, NorthHolland, Amsterdam, 1979, p. 153. F. Hullinger, H.R. Ott, J. Less-Common. Met. 55 (1977) 103. K. Kawamoto et al., Phys. Rev. Lett. 74 (1995) 3455; P. Mayaffre et al., Phys. Rev. Lett. 75 (1995) 4122; C.P.M. De Soto et al., Phys. Rev. B 54 (1996) 16101. K. Nakazawa, K. Kanoda, Phys. Rev. B 55 (1997) R8670. R. McKenzie, APS March Meetings, 1997. T. Burgin et al., J. Mater. Chem. 5 (1995) 1659; U. Geiser et al., Acta Crystallogr. C 47 (1991) 190. M. Kini et al., Inorg. Chem. 29 (1990) 2555. E. Bathers et al., Z. Phys. B 79 (1996) 163; F.A. Meyer et al., Eur. Phys. Lett. 32 (1995) 681. D. Shoenberg, in Magnetic Oscillations in Metals, Chs. 2 and 4, Cambridge University Press, Cambridge, 1984. C.C. Agosta et al., in: Physical Phenomenon at High Magnetic Fields, World Scientific, Singapore, 1996, p. 297; N. Harrison et al., J. Phys: Condens Matter 8 (1996) 5415. I.M. Lifsitz, A.M. Kosevich, Zh. Eksp. Theor. Fiz. 29 (1955) 730 [JETP 2 (1956) 636]. M.V. Kartsovnik et al., Phys. Rev. B 52 (1995) R15715. First-principles band calculation yields a somewhat more complex Fermi surface, but the area of the hole surface is similar. See, W.Y. Ching et al., Phys. Rev. B 55 (1997) 2780. C.H. Mielke et al., Phys. Rev. B 56 (1997) R 4309.