Journal of Superconductivity: Incorporating Novel Magnetism, Vol. 13, No. 3, 2000
Magnetic Susceptibility Investigations on the Layered Superconductors Y2C2Br2:RE (RE ⴝ Gd, Dy, Er) R. W. Henn,1 R. K. Kremer, and A. Simon Received 1 October 1999
We investigated the magnetic properties of pure and lanthanoid (RE ⫽ Gd, Dy, or Er) doped samples of Y2C2Br2 (Tc ⫽ 5.04 K) by means of SQUID magnetization measurements. The analysis of the high-field susceptibility of the undoped material allows the determination of the Pauli susceptibility, the electronic density of states, and the Stoner enhancement. Tc decreases with increasing spin momenta S and doping concentrations x (0 ⱕ x ⱕ 1.2 at.%/ Y) of the paramagnetic lanthanoid dopants. We estimate the exchange integral 兩Iex兩 of the lanthanoid spin and the conduction electron spin as well as the critical concentrations xc, relying on the Ginzburg–Landau–Abrikosov–Gor’kov (GLAG) theory of impurity pair breaking for dilute alloys (x 씮 0). KEY WORDS: Pair breaking; magnetic susceptibility; carbide superconductors.
1. INTRODUCTION
the Fermi level. Such local maxima in the DOS take effect on the electronic and superconducting properties. When two flat bands with opposite curvature cross to form a hyperbolic saddle point at the Fermi surface, the DOS is expected to diverge logarithmically [6–9]. Second, because of the low density of charge carriers in these compounds, electronic screening is reduced, and electronic correlations become pronounced [10,11]. For the layered rare-earth carbide halides RE2C2X2, with RE being Y or La and X being Cl, Br, or I, we had reported superconductivity up to 11.6 K [12–14]. Before giving details of our susceptibility measurements, we briefly summarize results of earlier investigations on the yttrium carbide halide superconductors: The crystal structure of Y2C2Br2 consists of close-packed Y metal atom bilayers that are sandwiched between sheets of Br atom layers (Fig. 1). Quasimolecular C2 dumbbells occupy octahedral voids within the metal atom bilayers. Such Br-Y-C2-Y-Br layer units stack in a three-layer monoclinic unit cell (3s-type) [13]. We note, that the structure of the recently discovered Hf and Zr nitride halide phases with Tc 앒 25 K [15–17] bears some similarity to that of the rare-earth carbide halides. The electronic structures of the RE2C2X2 compounds were first investigated by Extended–Hueckel calculations [18]. According to these calculations, the
The discovery of high-Tc superconductivity in the oxocuprates [1] has focused attention onto unconventional superconductors with layered crystal structures because of the variety of unusual electronic effects observed in these compounds. Prominent examples are the organic BEDT–TTF superconductors, which exhibit a charge transfer from spacer interlayers to the conducting layers [2,3]. The Ta and Nb dichalcogenides and their intercalated derivatives were investigated intensively in the 1970s. There, the anisotropy of the order parameter in the superconducting state could be tuned quite favorably by varying the interlayer distances and concomitantly the interlayer coupling [4,5]. It appears to be accepted that two effects predominantly govern the electronic and superconducting phenomena in these materials. First, because of the structural and electronic anisotropy, there are electronic bands of low dispersion, flat bands, which give rise to local maxima in the electronic density of states (DOS) that become important particularly at 1
Max-Planck-Institut fu¨r Festko¨rperforschung, Heisenbergstraße 1, D-70569 Stuttgart, Germany. E-mail:
[email protected]; phone: 0049 711 689 1364; fax: 0049 711 689 1010.
471 0896-1107/00/0600-0471$18.00/0 2000 Plenum Publishing Corporation
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Fig. 1. Perspective view of the crystal structure of (3s-form) Y2C2Br2 along [010]. Halogen atoms are represented by large circles, rareearth metal atoms by smaller circles. The octahedral voids of the yttrium atom bilayers are occupied by dimeric carbon interstitials (small filled circles). The dashed lines indicate the monoclinic unit cell. The cell parameters are listed in section 3.1.
Henn, Kremer, and Simon of electron correlations in terms of the Stoner enhancement factor S. The chemical preparation of Y2C2Br2 comprises several steps (see below) in which impurities can unintentionally be incorporated into the product phases. Impurities that carry a magnetic moment (e.g. magnetic RE atoms), due to pair-breaking, may reduce Tc. We studied the influence of magnetic RE impurities on Tc with a series of RE-doped samples Y2C2Br2 (RE ⫽ Gd, Dy, Er; 0 ⱕ x ⱕ 1.2 at.% /Y) relying on GLAG theory of impurity pair breaking for dilute alloys [22]. The exchange interaction 兩Iex兩 of the RE moments and the conduction electron spin density have been estimated from an analysis of the dependence of the depression of Tc on dopant concentration x. Moreover, knowledge of these effects is crucial for a precise interpretation of the carbon isotope effect on Tc, which was reported to be negligible [13].
2. EXPERIMENTAL metallic behavior of the phases RE2C2X2 can be explained by an overlap of Y-d states and antibonding C-앟* states. An improved band structure calculation on Y2C2Br2 using TB-LMTO methods supports the former statements. Moreover, these calculations reveal flat electronic bands close to the Fermi energy, which result in a peak in the DOS [13]. Fat-band representations of the band structure show that these flat bands consist mainly of Y-d and C-앟* states [19]. The upper critical magnetic field of Y2C2Br2 amounts to Bc2 ⫽ 3 ⫾ 0.2T at T ⫽ 0K in a polycrystalline average [19,20]. The Ginzburg–Landau (GL) co˚ exceeds the lattice herence length GL(0) ⫽ 110 A constants by more than one order of magnitude. For the isostructural Y2C2I2 compound, the anisotropy ratio ⌫ ⫽ B储c2 /B⬜c2 앒 5.1 of the upper critical magnetic field parallel (储) and perpendicular (⬜) to the ab planes was measured by an ac-susceptibility experiment on a single crystal specimen [19]. According to these results, the order parameter in the superconducting state of Y2C2X2 is anisotropic, but still overlaps across the layer units. The Y2C2Br2 phase is an extreme type-II superconductor exhibiting a large GL-parameter GL ⫽ 50 ⫾ 3 [20]. In this contribution, we present new results on high- and low-field magnetic susceptibility measurements on the layered superconductor Y2C2Br2 with a transition temperature of Tc ⫽ 5.04 K. At first, we determine the Pauli-susceptibility of the undoped material. By comparing our results with specific heat data [14,19,21], we gain information on the strength
2.1. Sample Preparation Single-phase samples of pure and RE-doped Y2C2Br2 were synthesized by mixing yttrium metal chips (99.999% Johnson-Matthey), repeatedly distilled salts REX3, and graphite powder (Aldrich) in stoichiometric ratios. The starting materials were sealed in tantalum crucibles and reacted at 1050⬚C for several days, followed by quenching the samples to room temperature [23]. Owing to the educts and the products sensitivity to moisture, all handling was performed in an argon or helium gas atmosphere.
2.2. Susceptibility Measurements Measurements of the high- and low-field dc magnetic susceptibilities were performed with a SQUID magnetometer (MPMS, Quantum Design). The samples were sealed in quartz glass ampules that were designed to give a small background signal. The ampules were filled with dried helium gas to provide sufficient thermal contact to the environment. Diamagnetic shielding [zero field cooled (ZFC) susceptibility] and Meissner fraction [field-cooled (FC) susceptibility] were recorded in an external magnetic field of 1 mT between 2 K and 10 K. Tc was determined as the onset temperature of the diamagnetic shielding. The width of the transition from normal to superconducting state, ⌬Tc, was evaluated from
Magnetic Susceptibility Investigations on the Layered Superconductors the temperature difference of 10% and 90% of the diamagnetic shielding fraction reached at 2 K. The high temperature susceptibilities were measured in external fields between 0.1 T ⱕ Bext ⱕ 5 T, and a correction for ferromagnetic impurities was done according to the Honda–Owen method [24]. The magnetic moment of the ferromagnetic impurities corresponds to less than 2 ppm of the saturation magnetic moment of Gd, for example. Pair-breaking effects of these impurities may be neglected in the interpretation of the susceptibility data. The diamagnetic signal from the quartz glass ampules was determined in separate runs and substracted from the raw (T, B) data.
3. RESULTS AND DISCUSSION 3.1. Sample Characterization Phase purity of all samples under investigation was established by x-ray diffraction (XRD) with the modified Guinier technique [25]. The lattice parameters of all our undoped Y2C2Br2 samples are the same within the experimental error (a ⫽ 695.5 ⫾ 0.3 pm, b ⫽ 376.4 ⫾ 0.2 pm, c ⫽ 993.0 ⫾ 0.2 pm, and 웁 ⫽ 99.97 ⫾ 0.02⬚) and agree well with the literature data [26]. Table I compiles the superconducting properties of our samples. The superconducting transition onset temperatures are reproducible within a very narrow range of 20 mK. Because the rare-earth carbide halides are chemically very reactive and decompose at T 앒 1500 K before the grains sinter, all measurements
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were performed on powder samples. Below the onset temperature of diamagnetic shielding, the susceptibility curves are broadened due to flux pinning as well as inter- and intragrain shielding. Ninety percent of maximum shielding is reached in a temperature range between 0.8 K and 2 K, depending on the sample. However, the onset of diamagnetic shielding appears at well-defined temperatures, as is displayed in Fig. 2. Zero field heat capacity measurements, which were performed on the identical, undoped Y2C2Br2 samples [14,19], show a very narrow, reproducible transition to superconductivity of only 1% of Tc. According to the heat capacity analysis, we rule out chemical inhomogeneities in our samples. The onset transition temperatures were determined from the intercept of the normal state baseline and a linear regression to the data in a range of ⫺0.001 emu/g ⬍ g ⬍ 0 emu/g below the onset temperature of diamagnetic shielding (see Fig. 2). The diamagnetic shielding is complete for all samples, whereas the Meissner fractions typically reach 30% of the maximum shielding. Doping of small amounts of paramagnetic RE ions (x ⱕ 1.2 at.%/Y) leads to an almost linear reduction of Tc due to the pair-breaking effects of the magnetic moments. Figure 2 displays the Tc reduction
Table I. Transition Temperatures Tc , Transition Widths ⌬Tc , Meissner Fraction , and Doping Concentrations x of Y2C2Br2:RE (RE Being Gd, Dy, or Er)a Sample no.
Dopant
x (at.%/Y)
1 2 3 4 5 6 7 8 9 10 11 12
Undoped Undoped Undoped Gd Gd Gd Gd Gd Dy Dy Er Er
0.5 0.6 0.3 0.292 0.197 0.763 0.887 1.816 0.312 1.050 0.314 0.840
a
Tc (K) 5.05 ⫾ 5.03 ⫾ 5.04 ⫾ 4.45 ⫾ 4.70 ⫾ 3.48 ⫾ 2.77 ⫾ ⬍0.3 4.87 ⫾ 4.52 ⫾ 4.96 ⫾ 4.91 ⫾
0.02 0.01 0.01 0.05 0.1 0.01 0.01 0.04 0.03 0.02 0.05
⌬Tc (K)
(%)
1.7 1.8 1.6 1.2 1.4 0.8 — — 0.8 0.8 2.0 1.5
23 44 21 19 14 32 — — 41 57 28 29
For the undoped samples, x corresponds to at.%/Y-atom of impurity S ⫽ 1/2 entities.
Fig. 2. Dependence of the superconducting transition onset temperatures on the doping concentration of dilute Y2C2Br2:RE samples, RE being Er (squares), Dy (circles), and Gd (diamonds). The full lines indicate linear regressions to the data of Dy- and Er-doped samples. For the Gd-doped samples, Eq. (5) is used to calculate the Tc dependence vs the doping concentration x (dashed line). The insert displays the onset of diamagnetic shielding for two samples (nos. 2 and 5). Tc was determined from a linear regression to the data below the diamagnetic onset.
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as a function of increasing concentration x of the paramagnetic dopants. The pair breaking effect of Gd (8S7/2 ground state) is strongest, followed by Dy (6H15/2 ground state) and Er (4I15/2 ground state). An analysis and discussion of the impurity pair breaking follows below. In order to determine the exact concentration of the RE dopants, the temperature dependence of the high-field susceptibilities (Bext ⫽ 1 T, T ⬎ 100 K) of the Y2C2Br2:RE samples were measured and analyzed with a modified Curie-law (Eq. (1); see Table I). The concentrations of magnetic impurities were derived from a series of high-field high-temperature (1 T ⬍ Bext ⬍ 5 T, T ⬎ 100 K) measurements and subsequent Honda–Owen analyses [24]. Paramagnetic impurities in the undoped samples typically amount to 0.5 at.%/Y or less of spin S ⫽ 1/2 entities. This value corresponds to a level of 0.02% of Gd (S ⫽ 7/2) impurities. From the slope dTc(x)/dx observed for Gd (see Fig. 2), we estimate the Tc reduction due to pair-breaking effects of such unintentional paramagnetic impurities to be less than 5 mK. It is significantly smaller than the temperature reduction induced by paramagnetic pair breaking of the REdoped samples.
3.2. Pauli Susceptibility
Fig. 3. Magnetic susceptibility of Y2C2Br2 (sample no. 3) recorded between room temperature and 80 K. A fit of a modified Curie law [Eq. (1)] is indicated by the full line.
The Curie term C/T describes contributions from paramagnetic impurities that are most likely imported by the handling and contaminations of the starting materials (see section 3.1). Deviations that could indicate a further T-dependence of the Pauli susceptibility [e.g., a quadratic term in mol(T)] were not detected. The temperature independent part, 0 , is a sum of the contributions from electrons in the closed shells, dia, the Landau diamagnetism, Landau, and the Pauli paramagnetism, Pauli.
0 ⫽ dia ⫹ Landau ⫹ SPauli
From an analysis of the high-field susceptibility measured on a series of undoped Y2C2Br2 samples (no. 1, 2, 3; see Table I), the different parts contributing to the molar susceptibility mol(T) were separated. Figure 3 displays the moler susceptibility mol(T) of sample no. 3. Each data point was obtained from an extrapolation B 씮 앝, of a set of magnetization measurements at constant temperature (Honda– Owen method). The temperature dependence of the magnetic susceptibilities of all investigated samples fitted very well to a modified Curie law (Fig. 3).
mol(T) ⫽ C/T ⫹ 0
(1)
dia was calculated from the diamagnetic increments of the particular ion per formula unit: [27] Y3⫹ ⫽ ⫺12 · 10⫺6 emu mol⫺1, Br⫺ ⫽ ⫺36 ⭈ 10⫺6 emu mol⫺1, ⫺6 and C4⫺ emu mol⫺1. The diamagnetic 2 ⫽ ⫺12 ⭈ 10 increment of the carbon atoms was assumed to originate from a C2 unit with a double bond [28]. The Landau diamagnetism was included in an isotropic free electron limit, Landau ⫽ ⫺애2BN(F)/3(1 ⫹ )2. The last term in Eq. (2), S Pauli , represents the enhanced Pauli paramagnetism. The enhancement is considered by the Stoner factor S ⫽ 1/[1 ⫺ I N(F)], where I represents the intra-atomic exchange integral. The Stoner factor S⫽
Table II. Contributions to the Temperature Independent Magnetic Susceptibility 0 of Y2C2Br2 Sample no.
0
1 2 3
⫺60 ⫾ 2 ⫺54 ⫾ 1 ⫺55 ⫾ 1
(10⫺6
dia emu mol⫺1) ⫺101 ⫺101 ⫺101
SPauli 41 47 46
(2)
0 ⫺ dia 1 ⫹ 2 애BN(F) 3(1 ⫹ )2
(3)
can be estimated from the magnetic susceptibility data relying on the density of states N(F) ⫽ 0.44 eV⫺1 per formula unit and mass enhancement factor ⫽ [m*/m ⫺ 1] ⫽ 0.75 gained from an analysis of the specific heat [14,21]. The enhancement of S ⫽ 1.5 corresponds to an intra-atomic exchange of I 앒
Magnetic Susceptibility Investigations on the Layered Superconductors 0.7eV per formula unit. These values evidence a markedly enhanced Pauli paramagnetism as compared to YC2, which exhibits more isotropic electronic properties [29,30]. Table II summarizes the contributions to the susceptibility of the undoped Y2C2Br2 samples (nos. 1, 2, and 3). The enhancement of the Pauli susceptibility in Y2C2Br2 may be caused by the pronounced peak in the DOS in the vicinity of the Fermi energy F, which has been revealed by TB–LMTO calculations [13]. If F lies close to a singularity in the DOS, electron correlations become essential according to the theory of van Hove singularities [7–9]. Such a scenario was experimentally supported by a nonlinear temperature dependence in the spin lattice relaxation rate of the 13C-NMR in Y213C2Br2 . The deviation from a linear Korringa relaxation was explained by a strong positive curvature of the DOS at F [31]. Second, a cusp in the Tc(y) dependence in the series of halogen mixed compounds Y2C2Br2⫺yIy [13,32] for y ⫽ 1.5 (Tc(y ⫽ 1.5) ⫽ 11.6 K) was explained by a peak in the DOS. In the Y2C2Br2⫺yIy series Tc(y) rises from 5.04 K for the bromide to the peak at y ⫽ 1.5, and decreases monotonically to 9.97 K for Y2C2I2. Within a rigid band model, it has been argued that a lattice-expansion due to increasing iodine content y causes a lowering of the Fermi energy with respect to the peak in the DOS. Hence, with increasing iodine content, F is shifted across the peak in the DOS, giving rise to the variation of N(F, y) and the observed Tc(y) dependence. First investigations of the Tc(y) dependence on hydrostatic pressure support this statement [33]: for Y2C2I2, the pressure coefficient dTc(y ⫽ 2, p)/dp is positive (앒0.1K/kbar); for Y2C2Br1I1, with a composition at the opposite side with respect to the Tc(y) cusp (y ⱕ 1.5), dTc(y ⫽ 1, p)/dp is negative (앒 ⫺0.11 K/kbar) and of the same order of magnitude as for y ⫽ 2. Applying pressure obviously counteracts the volume expansion due to iodine replacement.
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change energy is best approached by the Hamiltonian [22] H ⫽ ⫺2Iex(gJ ⫺ 1)J · s
(4)
wherein Iex represents the exchange integral of the spin of RE dopant and s the spin density of the conduction electrons. The term (gJ ⫺ 1)J arises from the projection of the spin momenta of the RE ions onto the total angular momentum J of the ground state given by Hund’s rules. Abrikosov and Gor’kov evaluated the reduction of Tc with respect to the transition temperature of the undoped material Tc0 by a pairbreaking potential 움 ln
冉 冊 冉冊 冉
冊
Tc 1 1 움 ⫽ ⫺ ⫹ . Tc0 2 2 2앟kB Tc
(5)
where (x) represents the digamma function. The pair breaking energy 움 ⫽ 2 앟 x I2exN (F) DGF scales with the de Gennes factor (DGF ⫽ (gJ ⫺ 1)2 J (J ⫹ 1)) and the impurity concentration x. For small arguments 움/Tc Ⰶ 1 or small concentrations x 씮 0 of the pair-breaking impurity, expression (5) can be linearized [22]
冉 冊 dTc(x) dx
x씮0
⫽
앟2 2 I exN(F)DGF 2kB
(6)
Figure 4 displays the reduction of the transition temperature related to the de Gennes factor ⌬Tc (x)/ DGF. Linear behavior is observed at low concentra-
3.3. Pair Breaking by RE Impurities The pair-breaking effect on Tc has been investigated on series of Y2C2Br2 samples doped with Gd, Dy, and Er in low concentrations (x ⱕ 1.2 at.%/Y). Pair breaking and the reduction of Tc by magnetic impurities is due to the exchange interaction of the spins of the magnetic impurities and the conduction electrons. In case of magnetic RE impurities the ex-
Fig. 4. The change in the transition temperatures ⌬Tc related to the de Gennes factor is plotted vs the doping concentrations. The symbols refer to the same samples as in Fig. 2. The Er- and Dydoping series coincide, which is indicated by the straight full line, whereas, the Gd-doped samples clearly show a stronger ⌬Tc(x)/ DGF reduction, as shown by the dashed line according to Eq. (5).
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tions with the reduction by Gd about twice as strong as for Er and Dy (see Table III). The Abrikosov–Gor’kov theory of magnetic impurity pair breaking was derived within the Born approximation for magnetic scattering on s-wave orbitals, which is only a reasonable assumption for Gd (orbital angular momentum L ⫽ 0). For Er and Dy, the magnetic ground state L ⬆ 0 is split due to crystal field effects, and deviations from Eq. (6) may occur due to partial depopulation of the excited crystal field states [34,35]. At present, the precise crystal field groundstates of the RE ions in Y2C2Br2:RE are not available. Using the inital slope of (dTc /dx)x씮0, the solid line in Fig. 2 has been calculated from Eq. (5) and a critical concentration xc of 1.8 at.% Gd has been extrapolated.
4. SUMMARY AND CONCLUSION We obtained single-phase samples of Y2C2Br2 doped with the RE ions Gd, Dy, and Er in low concentrations, as well as undoped samples. Pair-breaking effects caused by unintentional magnetic impurities were shown to be negligible in the undoped material. In an analysis of the high-field susceptibility, the different magnetic contributions were analyzed. We found an enhanced Pauli paramagnetism in Y2C2Br2, as compared to the binary carbide YC2, the latter can be considered a 3D counterpart of the Y2C2Br2. The enhancement due to electron correlations is attributed to a peak in the DOS near the Fermi energy. In the RE-doped samples, the superconducting transition temperatures are reduced gradually below 2K due to impurity pair breaking. For the Gd-doped samples, the pair-breaking effect is in fair agreement within GLAG theory. However, deviations from
Table III. Paramagnetic Ground State Parameters, Lande´ Factor gJ , and de Gennes factor [DGF ⫽ (gJ ⫺ 1)2 J(J ⫹ 1)] of the Inserted RE Impuritiesa Dopant Ground state gJ DGF (dTc/dx)/DGF Iex/kB xc a
Gd 8
(K/at.%/Y) (K) (at.%/Y)
S7/2 2 15.75 ⫺0.121 270 1.8
Dy
Er
6
4 H15/2 I15/2 4/3 6/5 7.08 2.55 ⫺0.066 190 — —
The initial slope of Tc depression (dTc(x)/dx)x씮0/DGF, the strength of the spin exchange integral Iex, and the critical concentration xc were calculated as explained in the text.
GLAG theory are observed for Er and Dy L ⬆ 0 ions, which experience crystal field splitting.
ACKNOWLEDGMENTS We thank E. Bru¨cher for technical support and experimental assistance during the SQUID magnetization measurements, as well as R. Eger and T. Gulden for valuable advice for the sample preparation. We are also grateful to A. Bussmann-Holder for carefully reading the manuscript.
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