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Breakdown of de Gennes scaling in HoxLu1−xNi2B2C
Journal of Magnetism and Magnetic Materials 187 (1998) 309 —317
Breakdown of de Gennes scaling in Ho Lu Ni B C x 1~x 2 2 J. Freudenberger!,*, G. Fuchs!, K. Nenkov!,1, A. Handstein!, M. Wolf !, A. Kreyssig", K.-H. Mu¨ller!, M. Loewenhaupt", L. Schultz! ! Institut fu( r Festko( rper- und Werkstofforschung Dresden, Postfach 270016, D-01171 Dresden, Germany " Institut fu( r Angewandte Physik, Technische Universita( t Dresden, D-01062 Dresden, Germany Received 6 January 1998; received in revised form 3 March 1998
Abstract The temperature dependence of magnetic ordering and the superconducting transition have been studied for polycrystalline Ho Lu Ni B C compounds by susceptibility and resistivity measurements as well as neutron diffracx 1~x 2 2 tion. For Ho concentrations in the range 0)x)0.7, the superconducting transition temperature, ¹ , decreases from # 16.5 K at x"0 linearly with increasing x and, consequently, with increasing effective de Gennes factor. This is in accordance with a generalized Abrikosov—Gor’kov theory. At x"0.7, ¹ reaches 8.5 K i.e. the value of HoNi B C. Pair # 2 2 breaking by the Ho magnetic moments is stronger in Ho Lu Ni B C compared to Ho Y Ni B C. This is attributed x 1~x 2 2 x 1~x 2 2 to the difference between the lattice constants of the Ho—Y and the Ho—Lu systems resulting in different electronic structure parameters. A complete breakdown of the scaling behaviour of ¹ occurs for x'0.7, where ¹ becomes # # independent of the effective de Gennes factor. In this range of x re-entrant behaviour and the presence of an incommensurate a-axis, modulated antiferromagnetic structures have been observed below a characteristic temperature ¹ . Commensurate and incommensurate c-axis modulated antiferromagnetic structures that are observed both in the . Ho—Y and the Ho—Lu systems coexist with superconductivity. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 74.70.!b; 74.70.Ad Keywords: Borocarbides; Superconductivity; Antiferromagnetism; De Gennes scaling
1. Introduction The discovery of the superconducting rare-earth nickel borocarbides [1—3] RNi B C, with R"Sc, 2 2
* Corresponding author. Tel.: #49 351 4659 553; fax: #49 351 4659 537; e-mail: [email protected]. 1 On leave from: International Laboratory of High Magnetic Fields and Low Temperatures, Wroclaw, Poland.
Y, Dy, Ho, Er, Tm, Lu, has reanimated the research on the interplay of superconductivity and magnetic ordering in intermetallic compounds, which has been a topic of interest for many years [4]. The decrease, *¹ , of the superconducting transition # temperature ¹ within the RNi B C series from # 2 2 R"Lu or Y (¹ +17 or 16 K) to Tb (¹ "0) was # # shown to roughly scale with the de Gennes factor DG"(g!1)2J(J#1), where g is the Lande´ factor and J the total angular momentum of the
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R3` Hund’s-rule ground state [5,6]. De Gennes scaling of *¹ had been predicted by the Ab# rikosov—Gor’kov theory [7] for the limit of low concentration n of R ions in a superconducting material *¹ &nN(E )I2(g!1)2J(J#1), # F
(1)
where N(E ) is the conduction electron density of F states at the Fermi level E and I is the conducF tion-electron R-ion exchange coupling parameter. Furthermore, it is well known from ternary compounds that the de Gennes scaling of *¹ also # works for high R concentrations if (i) the 4f states are only weakly hybridized with the conduction electron states and (ii) N(E )I2 remains constant F across the considered series of isostructural rareearth compounds [4]. It should be noted that YbNi B C is not superconducting and cannot be 2 2 described by the same *¹ versus DG curve de# scribing the de Gennes scaling of *¹ of the pure # quaternary compounds containing other heavy 4f elements [8,9]. This observation is attributed to a strong 4f-electron conduction—electron hybridization resulting in a breakdown of the de Gennes scaling [9]. For DyNi B C the transition to super2 2 conductivity is found at ¹ "6 K where the Dy # moments are antiferromagnetically ordered, i.e. ¹ is below the Ne´el temperature ¹ "11 K [6]. # N This leads to the question whether, below ¹ , the # magnetically ordered state persists coexisting with the superconducting state. Coexistence of antiferromagnetism and superconductivity was theoretically confirmed to be possible [10] and has been found for many materials [4]. However, no universal rules exist concerning the interplay of these two collective phenomena [11]. In the case of DyNi B C, below ¹ , the Dy moments are aligned 2 2 N ferromagnetically within layers perpendicular to the tetragonal c-axis with the moments of consecutive layers aligned in opposite directions [12] and little interaction appears to be present between the superconducting state and the antiferromagnetic structure [13]. A rather good linear scaling with the de Gennes factor is also observed for the magnetic transition temperature ¹ across the RNi B C N 2 2 series with heavy R elements including Gd [6]. This common DG scaling for both, *¹ and ¹ , is # N
known for various isostructural series of R compounds, which is due to the fact that both, superconductivity and antiferromagnetism, are influenced by the same type of conduction-electron 4f-electron exchange interaction [4]. According to this overall de Gennes scaling of *¹ and ¹ , # N magnetic ordering in TmNi B C, ErNi B C and 2 2 2 2 HoNi B C occurs below ¹ and, for sufficiently 2 2 # low temperatures, coexistence of antiferromagnetic order and superconductivity is observed [6]. In these compounds, however, the interplay of superconductivity and magnetism is more complicated than in the case of DyNi B C. For example, in 2 2 HoNi B C three different types of antiferromag2 2 netic structures have been observed by neutron scattering, (i) a commensurate structure [14] which is equivalent to that known for DyNi B C, 2 2 (ii) an incommensurate spiral along the c-axis [14] and (iii) a further incommensurate magnetic component that develops along the tetragonal a-axis [15]. These three magnetic structures exist in temperature ranges which are not identical but show some overlap. HoNi B C becomes supercon2 2 ducting at ¹ +8 K, then re-enters the normal # state at about 5 K, to become superconducting again with further reduction of temperature [5]. Below about 4.5 K only the commensurate antiferromagnetic structure remains and, obviously, coexists with the superconducting state. The spiral structure along c-axis [16] as well as the component along the a-axis [17] have been considered to be responsible for the observed reentrant behaviour of HoNi B C. To clarify this open problem, poly2 2 crystalline samples of the pseudoquaternary compounds Ho Y Ni B C (0)x)1) have x 1~x 2 2 been investigated by resistivity and susceptibility measurements as well as neutron diffraction [18—20]. To study the scaling behaviour of pseudoquaternary compounds R R3 Ni B C, an x 1~x 2 2 effective de Gennes factor, i.e. the weighted average of the contributions of the two ions, DG[R] and DG[R3 ], was used DG"xDG[R]#(1!x)DG[R3 ].
(2)
It was found that *¹ and ¹ of Ho Y Ni B C # N x 1~x 2 2 roughly scale with DG on the same straight lines as those describing the behaviour of the pure
J. Freudenberger et al. / Journal of Magnetism and Magnetic Materials 187 (1998) 309 —317
quaternary compounds with R"Lu/Y, Tm, Er, Ho, Dy and Tb [18]. The three different types of antiferromagnetic order in HoNi B C, mentioned 2 2 above, have also been detected for xO1. However, the temperature ranges where they exist are sensitive to the Ho concentration and this x-dependence is different for the different types of magnetic order. Therefore, in a detailed analysis of the interplay of superconductivity and magnetism in these materials, it is not sufficient to describe magnetic ordering by only one characteristic temperature ¹ . It N has been shown that not only the commensurate antiferromagnetic state but also the incommensurate c-axis spiral can coexist with superconductivity, whereas the incommensurate a-axis component seems to be responsible for pair-breaking in the Ho—Y system [19,20]. Magnetic and superconducting properties have also been studied for polycrystalline Gd Y Ni B C samples x 1~x 2 2 [21] and Ho Y Ni B C, Gd Lu Ni B C, x 1~x 2 2 x 1~x 2 2 Dy Lu Ni B C and Dy Ho Ni B C single x 1~x 2 2 x 1~x 2 2 crystals [22]. For not too large Gd concentrations, the *¹ versus DG curves of the Gd—Y and the # Gd—Lu systems are straight lines, however, they are considerably steeper than the corresponding curve for the series of pure quaternary compounds. In Ref. [22], the more effective pair-breaking of Gd in Gd Lu Ni B C has been referred to the mechax 1~x 2 2 nism described by the original Abrikosov—Gor’kov theory [7], whereas the reduction in pair-breaking by the Tm, Er, Ho, Dy, and Tb moments, observed in the pure quaternary and the paramagnetic pseudoquaternary compounds has been attributed to crystalline electric field (CEF) effects, similarly as in the modified Abrikosov—Gor’kov theory of Keller and Fulde [23]. For those RNi B C 2 2 systems investigated in Ref. [22] whose ¹ is # above ¹ , specific types of de Gennes scaling of N *¹ could be identified. On the other hand, a # complete breakdown of the de Gennes scaling of *¹ was found for pseudoquaternary systems # with ¹ '¹ . This breakdown is inferred to N # arise from pair breaking by collective magnetic excitations [22]. In the present paper, the scaling behaviour of *¹ and of characteristic temperatures that de# scribe magnetic ordering have been investigated for the Ho Lu Ni B C family. x 1~x 2 2
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2. Experimental details Polycrystalline samples of Ho Lu Ni B C x 1~x 2 2 were prepared by a standard arc melting technique. Powders of the elements were weighed in the stoichiometric compositions with a surplus of 10 wt% boron to compensate the high losses of boron caused by the arc melting. The powder was pressed to pellets that were melted under argon gas on a water-cooled copper plate in an arc furnace. To get homogeneous samples, they were turned over and melted again four times. After the melting procedure the solidified samples were homogenized at 1100°C for ten days. The actual sample composition is uncertain due to evaporation losses while melting. Owing to this the nominal composition, in particular the nominal Ho content x, is given in this paper. A powder X-ray diffractometer in Bragg— Brentano geometry was used to investigate the phase purity of the samples and to determine lattice parameters. For this purpose, Co Ka radiation was utilized and scans were taken from 2h"20—140° in steps of 0.015°. From the measured X-ray data, lattice parameters were determined by means of the DBWS Rietveld program. The AC susceptibility s was measured at zero DC field with a field amplitude of 0.01 mT at a frequency of 133 Hz. The values of the superconducting transition temperature ¹ were # determined from susceptibility versus temperature curves s(¹) using the condition s(¹ )"0.9s , # N where s is the susceptibility value in the normal N state. The electrical resistance of the samples, R, was measured by the standard four-probe technique, as a function of magnetic field and temperature in the range from 1.7 K up into the normal conducting state. The upper critical field H at a given temperature was determined from #2 the midpoint of the resistive transition curves, i.e. at 50% of the fictive normal state resistivity obtained by an extrapolation from the R versus ¹ curves measured above ¹ . Furthermore, the magnetic # structure was investigated by means of neutron diffraction experiments described elsewhere [24]. Characteristic temperatures that describe the various types of magnetic ordering were determined from s(¹) as well as R(¹, H) and neutron diffraction data.
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3. Results and discussion The lattice constants a and c of our Ho Lu Ni B C samples are presented in Fig. 1. x 1~x 2 2 The values obtained for x"0 and 1 agree well with those reported for the pure quaternary compounds [25]. The standard deviations of the lattice parameters obtained from the Rietveld analysis result in error bars that are of the order of symbol size in Fig. 1, i.e. 4]10~4 nm. Thus the deviations of the lattice parameters from the linear dependence on x (Vegard’s law) are obviously correlated with intrinsic properties of the samples, may be with uncertainties in their actual chemical composition. The straight lines in Fig. 1 indicate that, in spite of the evaporation losses that cannot be avoided during preparation, the samples show a systematic dependence of the lattice constants on the nominal degree of the substitution of Lu by Ho. In Fig. 2, the temperature dependence of the AC susceptibility s is shown for some of the investigated samples. A shift of the superconducting transition curves from ¹ "16.6 K, for x"0, to # about 8.5 K, for x*0.7, is observed. In the range between x"0.7 and 1, the superconducting transition practically does not depend on x. The ¹ values obtained from susceptibility measure# ments do not significantly differ from those obtained from the midpoint of the resistive transition
Fig. 1. Lattice parameters, a and c, obtained by a Rietveld analysis of X-ray data, as a function of the Ho concentration x.
Fig. 2. Temperature dependence of the AC susceptibility of Ho Lu Ni B C for various values of the Ho concentration x. x 1~x 2 2
curve. In the concentration range where ¹ is con# stant, the transition curves have a very small width of d¹ +0.2 K. The quantity d¹ was determined # # as d¹ "¹(0.9s )!¹(0.1s ). Relatively broad # N N transition curves with d¹ +1.2 K are observed in # the concentration range x(0.7. The width d¹ # reflects the phase purity and, in the range x(0.7, where ¹ changes with x, the homogeneity of # stoichiometry. As seen from X-ray and neutron diffraction experiments, no significant fraction of phase impurities could be determined in the powder samples; the stoichiometry is considered to be responsible for the relatively large value of d¹ . # A fluctuation of the Ho concentration x of about $0.03 has been estimated from d¹ "1.2 K and # from the ¹ (x) dependence in the range of Ho # concentrations x(0.7 (see below: Fig. 6). Fig. 3 shows the temperature dependence of the inverse susceptibility, 1/s(¹), in the normal state for several Ho concentrations. In the investigated temperature interval these curves can well be described by the Curie—Weiss law, s"C/(¹!h), where C& xk2 is the Curie constant and k is the paramag1 1 netic moment of the magnetic ion. The fitted value k "(10.2$0.2) l is very close to the theoretical 1 B value, 10.61 l , for the Hund’s rule ground state of B
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Fig. 3. The temperature dependence of the inverse AC susceptibility of Ho Lu Ni B C samples, measured for various values x 1~x 2 2 of x, fairly obeys the Curie—Weiss law. (The susceptibilitiy is measured in SI units, i.e. it is dimensionless.)
a free Ho3` ion. The paramagnetic Curie temperature h was found to be negative, of the order of a few Kelvin, for all concentrations of x, which indicates a negative mean exchange interaction between the magnetic moments. However, unlike the lattice constants (Fig. 1) and the slope of the 1/s versus x curves (Fig. 3), h does not show a systematic dependence on x. The temperature dependence of the resistance R, measured on a Ho Lu Ni B C sample for 0.95 0.05 2 2 several applied magnetic fields is shown in Fig. 4. A non-monotonic temperature dependence of R appears between 0.15 and 0.35 T. Such a re-entrant behaviour is observed only for samples with Ho concentrations x'0.8, suggesting a certain type of magnetic ordering in this concentration range. For a given concentration, the position of the local minimum of the resistance versus temperature curves, for increasing magnetic field, remains unchanged whereas the re-entrance maximum shifts slightly to higher temperatures. The position of the minima and the maxima of the R versus ¹ curves for different x (not completely shown here) can be used to determine relevant temperatures ¹ and .
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Fig. 4. Electrical resistance of a Ho Lu Ni B C sample 0.95 0.05 2 2 versus temperature, measured for various magnetic fields H. Re-entrant behaviour, characterized by the temperatures ¹ and ¹ , is evident for fields 0.15 T)k H(0.35 T. The . 1 0 arrows mark ¹ and ¹ for the arbitrarily chosen field . 1 k H"0.2 T. 0
¹ , respectively, that characterize the pair-breaking 1 effect of magnetic ordering. These characteristic temperatures can also be determined by analyzing the temperature dependence of the upper critical field H which is very sensitive to pair-breaking #2 effects caused by magnetic ordering [19]. This is shown in Fig. 5, where the results of neutron diffraction experiments and the temperature dependence of H are compared. The curves in Fig. 5b #2 show an increasing depression of H with increas#2 ing Ho concentration, providing evidence for magnetic pair breaking. For x)0.8, the H (¹) curves #2 remain monotonic. As can be seen in the inset of Fig. 5b, for small Ho concentrations, the H ver#2 sus ¹ curves show an upward curvature near ¹ . # This is consistent with similar findings for LuNi B C single crystals [26]. For x'0.8, with 2 2 decreasing temperature, H increases from zero at #2 ¹ up to a local maximum, then it decreases in # a small temperature range and it increases again at lower temperatures. As for the compounds HoNi B C [14] and Ho Y Ni B C [19,20], 2 2 x 1~x 2 2
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three types of magnetically ordered structures have been determined for Ho Lu Ni B C by neutron x 1~x 2 2 diffraction [24]. Besides the commensurate antiferromagnetic structure, two incommensurate antiferromagnetic structures with a- and c-axis modulated wave vectors have been detected. In Fig. 5a the temperature dependence of the neutron diffraction peak intensities of only the a-axis modulated structure is shown. For decreasing temperature, the peak intensities of this magnetic structure start growing at ¹"¹ , where H (¹), in Fig. 5b, has . #2 its maximum and they reach their maximum at the temperatures ¹ where the H (¹) curves show 1 #2 their local minimum. These definitions of ¹ and 1 ¹ are consistent with those made earlier using the . maximum and the minimum, respectively, of the resistance versus temperature curve. Thus the incommensurate antiferromagnetic structure with a-axis modulation which is present in the same narrow temperature range as the anomalies of the H (¹) curves is considered to be responsible for #2 pair breaking in Ho Lu Ni B C. Neither the x 1~x 2 2 commensurate nor the incommensurate c-axis modulated structures, also found in these samples, show any effect on the superconducting behaviour [24]. It should be noted that this result cannot be simply generalized to other RNi B C compounds. 2 2 For instance, a certain re-entrant behaviour [27] as well as some a-axis modulated structure [13] have been observed in ErNi B C. But contrary to the 2 2 case of HoNi B C, the a-axis modulated structure 2 2 of ErNi B C fully exists down to 2 K, whereas the 2 2 re-entrant behaviour and a corresponding H (¹) #2 anomaly is found only in the temperature range between 5 and 6 K. Thus, the reason why H (¹) of #2 ErNi B C behaves anomalously remains unclear. 2 2 In Fig. 6, the superconducting transition temperatures ¹ and specific temperatures that character# ize details of the magnetic ordering are plotted against the Ho concentration x. ¹ decreases lin# early with increasing x, reaches the ¹ value of # HoNi B C at x"0.7 and remains unchanged for 2 2 concentrations x*0.7. A linear depression of ¹ # with increasing Ho concentration is expected under the assumption that x has no influence on N(E )I2 in Eq. (1) but only controls n. A complete F breakdown of the scaling behaviour occurs for x'0.7, where ¹ becomes independent of the Ho #
Fig. 5. (a) Temperature dependence of the neutron diffraction peak intensities for various values of the Ho concentration x, normalized to the calculated value for fully magnetically ordered phases with 10 l for Ho3` (free ion), of the incommensurate B antiferromagnetic a-axis modulated structure; (b) upper critical field H versus temperature of Ho Lu Ni B C samples for #2 x 1~x 2 2 various Ho concentrations x. ¹ and ¹ , both marked for the . 1 case x"0.95, characterize the onset and the maximum, respectively, of the intensity peak in (a) and the position of the maximum and the minimum of H , respectively, in (b). #2
concentration and, thus, of the effective de Gennes factor. The initial magnetic ordering that develops upon cooling is the incommensurate spiral structure along the c-axis, characterized by its onset
J. Freudenberger et al. / Journal of Magnetism and Magnetic Materials 187 (1998) 309 —317
Fig. 6. Superconducting transition temperature ¹ and specific # temperatures characterizing magnetic ordering, ¹ *, ¹ , ¹ and # N . ¹ , of Ho Lu Ni B C versus the holmium concentration x. 1 x 1~x 2 2 ¹ *, ¹ and ¹ are the onset temperatures for the incommensur# N . ate spiral with c-axis modulation, the commensurate antiferromagnetic structure and the a-axis modulated incommensurate component, respectively. (¹ : see Fig. 5). The solid and dashed 1 lines are guides to the eye.
temperature ¹ * [24]. For the pure quaternary # compound with x"1, magnetic ordering and superconductivity arise at nearly the same temperature, ¹ *+¹ +8.5 K. The onset temperatures # # for the commensurate antiferromagnetic structure and the incommensurate a-axis modulated structure, ¹ and ¹ , have nearly the same value [24]. N . For higher concentrations x, the onset temperatures ¹ *, ¹ and ¹ , as well as the temperature # N . where the neutron-diffraction intensity peak of the a-axis modulated structure has its maximum, ¹ , 1 show a linear dependence on x, indicating some de Gennes-type scaling. Extrapolating ¹ (x) to lower 1 concentrations, ¹ would vanish at the same value 1 of the Ho concentration, x+0.7, where the de Gennes scaling of ¹ breaks down. It is interesting # to note that for x(0.75, the peaks of the commensurate c-axis structure of Ho Lu Ni B C and x 1~x 2 2 those of the a-axis modulated structure are below the detection limit. For x)0.65, only the incom-
315
Fig. 7. Comparison of ¹ versus DG curves for of # Gd Lu Ni B C (j, taken from Ref. [22]), Gd Y Ni B C x 1~x 2 2 x 1~x 2 2 (h, taken from Ref. [21]), Ho Y Ni B C (n, taken from Ref. x 1~x 2 2 [18]) and Ho Lu Ni B C (v, this work), where ¹ is the x 1~x 2 2 # superconducting transition temperature and DG is the effective de Gennes factor of the pseudoquaternary compounds, as defined by Eq. (2), and ¹ "¹ (x"0). #,0 #
mensurate c-axis structure was found at low temperatures. De Gennes scaling of characteristic temperatures describing magnetic ordering in magnetically diluted systems is expected not to work below a certain critical concentration x resulting 1 from percolation effects. The actual value of x is 1 sensitive to the range of the exchange interaction between the magnetic ions as well as a possible short range order of these ions. The lowest Ho concentration down to which magnetic ordering exists in the Lu—Ho system is still under investigation. In Fig. 7, the dependence of the superconducting transition temperature on the effective de Gennes factor DG, as defined by Eq. (2), of our Ho Lu Ni B C compounds is compared with x 1~x 2 2 results reported in literature for three other pseudoquaternary systems. In the concentration range where ¹ decreases linearly with DG, the # Gd—Lu and the Gd—Y systems show a considerably steeper decrease than the Ho—Lu and the Ho—Y systems, respectively. These differences could be mainly caused by CEF effects as mentioned in
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Chapter 1 [22]. However, considerable differences in the slopes of the linear ¹ versus DG curves are # also observed for systems with the same effective de Gennes factor, caused by the same magnetic ion. Thus the Ho—Lu and the Gd—Lu systems show a stronger depression of ¹ than the Ho—Y and the # Gd—Y systems, respectively. Analyzing these findings it should be taken into account that the substitution of Y by Lu causes an increase of the lattice parameter c and a reduction of the lattice parameter a of the RNi B C structure [25]. This may 2 2 result in a change of the electronic property N(E )I2 that governs the exchange interaction beF tween the magnetic ions and, according to Eq. (1), controls the depression of ¹ . The unusual # behaviour of the ¹ versus DG curve of # Ho Lu Ni B C at DG+3.2 (i.e. x"0.7) is not x 1~x 2 2 yet understood. A similar ¹ versus DG curve was # reported for Ho Dy Ni B C [22]. In that case, 1~x x 2 2 ¹ scales with DG only in the range of composi# tions where ¹ '¹ , i.e. up to Dy concentrations # N of x+0.3. For x*0.3, i.e. the range where ¹ '¹ , ¹ does not depend on DG. This breakN # # down of de Gennes scaling was assumed to be caused by antiferromagnetic magnons [22]. However, for the Ho Lu Ni B C family investigated x 1~x 2 2 in this study, a non-varying ¹ is observed in the # paramagnetic state. For Ho concentrations in the range x"0.7 to 0.8, ¹ is much higher than the # characteristic temperatures ¹ *, ¹ and ¹ de# . N scribing the onset of various types of long-range magnetic ordering (cf. Fig. 6). Therefore, an explanation by magnons, even those related to shortrange order, is not convincing.
influence on the superconducting behaviour, could be found in this concentration range, for temperatures above 2 K. For x'0.7, ¹ remains con# stant, whereas the temperature characterizing the onset of the incommensurate a-axis modulated structure, ¹ , increases nearly linearly with in. creasing x up the value of HoNi B C, ¹ "6.5 K. 2 2 . The relatively strong depression of ¹ with increas# ing Ho concentration x for x)0.7, compared with the case of Ho Y Ni B C, was referred to differx 1~x 2 2 ences in the lattice parameters of the Ho—Y and the Ho—Lu systems resulting in different electronic structures. Anomalies in the temperature dependence of the upper critical field H (¹) were observed #2 for x'0.8. They symbolize the re-entrant behaviour appearing for these Ho concentrations in the same temperature range where the incommensurate antiferromagnetic structure with a-axis modulation is present and the de Gennes scaling of ¹ # breaks down. For higher Ho concentrations the characteristic temperatures describing the different types of magnetic ordering, ¹ *, ¹ , ¹ and ¹ , # N . 1 scale with the de Gennes factor. Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft within the project Sonderforschungsbereich 463 ‘Seltenerd U®bergangsmetallverbindungen: Struktur, Magnetismus und Transport’. Furthermore, we would like to thank S.L. Drechsler for helpful discussions. References
4. Summary The superconducting transition temperature ¹ and the specific temperatures characterizing # magnetic ordering in Ho Lu Ni B C polycrysx 1~x 2 2 talline samples were investigated by susceptibility and resistivity measurements as well as neutron diffraction. Two composition ranges with different behaviour could be distinguished: for x)0.7, ¹ decreases linearly with increasing Ho concentra# tion. Only the magnetic structure with incommensurate c-axis modulation, which seems to have no
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[17] C.V. Tomy, L.J. Chang, D.Mck. Paul, N.H. Andersen, M. Yethiraj, Physica B 213&214 (1995) 139. [18] K. Eversmann, A. Handstein, G. Fuchs, L. Cao, K.-H. Mu¨ller, Physica C 266 (1996) 27. [19] K.-H. Mu¨ller, A. Kreyssig, A. Handstein, G. Fuchs, C. Ritter, M. Loewenhaupt, J. Appl. Phys. 81 (1997) 4240. [20] A. Kreyssig, M. Loewenhaupt, K.-H. Mu¨ller, G. Fuchs, A. Handstein, C. Ritter, Physica B 234—236 (1997) 737. [21] M. El Massalami, S.L. Bud’ko, B. Giordanengo, M.B. Fontes, J.C. Mondragon, E.M. Baggio-Saitovich, Physica B 235—240 (1994) 2563. [22] B.K. Cho, P.C. Canfield, D.C. Johnston, Phys. Rev. Lett. 77 (1996) 163. [23] J. Keller, P. Fulde, J. Low Temp. Phys. 4 (1971) 289. [24] A. Kreyssig, C. Sierks, M. Loewenhaupt, J. Freudenberger, G. Fuchs, K.-H. Mu¨ller, C. Ritter, Physica B 241—243 (1998) 826. [25] T. Siegrist, R.J. Cava, J.J. Krajewski, W.F. Peck Jr., J. Alloys Comp. 216 (1994) 135. [26] V. Metlushko, U. Welp, A. Koshelev, I. Aranson, G.W. Crabtree, P.C. Canfield, Phys. Rev. Lett. 79 (1997) 1738. [27] B.K. Cho, P.C. Canfield, L.L. Miller, D.C. Johnston, W.P. Beyermann, A. Yatskar, Phys. Rev. B 52 (1995) 3684.
Breakdown of de Gennes scaling in Ho Lu Ni B C x 1~x 2 2 J. Freudenberger!,*, G. Fuchs!, K. Nenkov!,1, A. Handstein!, M. Wolf !, A. Kreyssig", K.-H. Mu¨ller!, M. Loewenhaupt", L. Schultz! ! Institut fu( r Festko( rper- und Werkstofforschung Dresden, Postfach 270016, D-01171 Dresden, Germany " Institut fu( r Angewandte Physik, Technische Universita( t Dresden, D-01062 Dresden, Germany Received 6 January 1998; received in revised form 3 March 1998
Abstract The temperature dependence of magnetic ordering and the superconducting transition have been studied for polycrystalline Ho Lu Ni B C compounds by susceptibility and resistivity measurements as well as neutron diffracx 1~x 2 2 tion. For Ho concentrations in the range 0)x)0.7, the superconducting transition temperature, ¹ , decreases from # 16.5 K at x"0 linearly with increasing x and, consequently, with increasing effective de Gennes factor. This is in accordance with a generalized Abrikosov—Gor’kov theory. At x"0.7, ¹ reaches 8.5 K i.e. the value of HoNi B C. Pair # 2 2 breaking by the Ho magnetic moments is stronger in Ho Lu Ni B C compared to Ho Y Ni B C. This is attributed x 1~x 2 2 x 1~x 2 2 to the difference between the lattice constants of the Ho—Y and the Ho—Lu systems resulting in different electronic structure parameters. A complete breakdown of the scaling behaviour of ¹ occurs for x'0.7, where ¹ becomes # # independent of the effective de Gennes factor. In this range of x re-entrant behaviour and the presence of an incommensurate a-axis, modulated antiferromagnetic structures have been observed below a characteristic temperature ¹ . Commensurate and incommensurate c-axis modulated antiferromagnetic structures that are observed both in the . Ho—Y and the Ho—Lu systems coexist with superconductivity. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 74.70.!b; 74.70.Ad Keywords: Borocarbides; Superconductivity; Antiferromagnetism; De Gennes scaling
1. Introduction The discovery of the superconducting rare-earth nickel borocarbides [1—3] RNi B C, with R"Sc, 2 2
* Corresponding author. Tel.: #49 351 4659 553; fax: #49 351 4659 537; e-mail: [email protected]. 1 On leave from: International Laboratory of High Magnetic Fields and Low Temperatures, Wroclaw, Poland.
Y, Dy, Ho, Er, Tm, Lu, has reanimated the research on the interplay of superconductivity and magnetic ordering in intermetallic compounds, which has been a topic of interest for many years [4]. The decrease, *¹ , of the superconducting transition # temperature ¹ within the RNi B C series from # 2 2 R"Lu or Y (¹ +17 or 16 K) to Tb (¹ "0) was # # shown to roughly scale with the de Gennes factor DG"(g!1)2J(J#1), where g is the Lande´ factor and J the total angular momentum of the
0304-8853/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 1 3 0 - 9
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R3` Hund’s-rule ground state [5,6]. De Gennes scaling of *¹ had been predicted by the Ab# rikosov—Gor’kov theory [7] for the limit of low concentration n of R ions in a superconducting material *¹ &nN(E )I2(g!1)2J(J#1), # F
(1)
where N(E ) is the conduction electron density of F states at the Fermi level E and I is the conducF tion-electron R-ion exchange coupling parameter. Furthermore, it is well known from ternary compounds that the de Gennes scaling of *¹ also # works for high R concentrations if (i) the 4f states are only weakly hybridized with the conduction electron states and (ii) N(E )I2 remains constant F across the considered series of isostructural rareearth compounds [4]. It should be noted that YbNi B C is not superconducting and cannot be 2 2 described by the same *¹ versus DG curve de# scribing the de Gennes scaling of *¹ of the pure # quaternary compounds containing other heavy 4f elements [8,9]. This observation is attributed to a strong 4f-electron conduction—electron hybridization resulting in a breakdown of the de Gennes scaling [9]. For DyNi B C the transition to super2 2 conductivity is found at ¹ "6 K where the Dy # moments are antiferromagnetically ordered, i.e. ¹ is below the Ne´el temperature ¹ "11 K [6]. # N This leads to the question whether, below ¹ , the # magnetically ordered state persists coexisting with the superconducting state. Coexistence of antiferromagnetism and superconductivity was theoretically confirmed to be possible [10] and has been found for many materials [4]. However, no universal rules exist concerning the interplay of these two collective phenomena [11]. In the case of DyNi B C, below ¹ , the Dy moments are aligned 2 2 N ferromagnetically within layers perpendicular to the tetragonal c-axis with the moments of consecutive layers aligned in opposite directions [12] and little interaction appears to be present between the superconducting state and the antiferromagnetic structure [13]. A rather good linear scaling with the de Gennes factor is also observed for the magnetic transition temperature ¹ across the RNi B C N 2 2 series with heavy R elements including Gd [6]. This common DG scaling for both, *¹ and ¹ , is # N
known for various isostructural series of R compounds, which is due to the fact that both, superconductivity and antiferromagnetism, are influenced by the same type of conduction-electron 4f-electron exchange interaction [4]. According to this overall de Gennes scaling of *¹ and ¹ , # N magnetic ordering in TmNi B C, ErNi B C and 2 2 2 2 HoNi B C occurs below ¹ and, for sufficiently 2 2 # low temperatures, coexistence of antiferromagnetic order and superconductivity is observed [6]. In these compounds, however, the interplay of superconductivity and magnetism is more complicated than in the case of DyNi B C. For example, in 2 2 HoNi B C three different types of antiferromag2 2 netic structures have been observed by neutron scattering, (i) a commensurate structure [14] which is equivalent to that known for DyNi B C, 2 2 (ii) an incommensurate spiral along the c-axis [14] and (iii) a further incommensurate magnetic component that develops along the tetragonal a-axis [15]. These three magnetic structures exist in temperature ranges which are not identical but show some overlap. HoNi B C becomes supercon2 2 ducting at ¹ +8 K, then re-enters the normal # state at about 5 K, to become superconducting again with further reduction of temperature [5]. Below about 4.5 K only the commensurate antiferromagnetic structure remains and, obviously, coexists with the superconducting state. The spiral structure along c-axis [16] as well as the component along the a-axis [17] have been considered to be responsible for the observed reentrant behaviour of HoNi B C. To clarify this open problem, poly2 2 crystalline samples of the pseudoquaternary compounds Ho Y Ni B C (0)x)1) have x 1~x 2 2 been investigated by resistivity and susceptibility measurements as well as neutron diffraction [18—20]. To study the scaling behaviour of pseudoquaternary compounds R R3 Ni B C, an x 1~x 2 2 effective de Gennes factor, i.e. the weighted average of the contributions of the two ions, DG[R] and DG[R3 ], was used DG"xDG[R]#(1!x)DG[R3 ].
(2)
It was found that *¹ and ¹ of Ho Y Ni B C # N x 1~x 2 2 roughly scale with DG on the same straight lines as those describing the behaviour of the pure
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quaternary compounds with R"Lu/Y, Tm, Er, Ho, Dy and Tb [18]. The three different types of antiferromagnetic order in HoNi B C, mentioned 2 2 above, have also been detected for xO1. However, the temperature ranges where they exist are sensitive to the Ho concentration and this x-dependence is different for the different types of magnetic order. Therefore, in a detailed analysis of the interplay of superconductivity and magnetism in these materials, it is not sufficient to describe magnetic ordering by only one characteristic temperature ¹ . It N has been shown that not only the commensurate antiferromagnetic state but also the incommensurate c-axis spiral can coexist with superconductivity, whereas the incommensurate a-axis component seems to be responsible for pair-breaking in the Ho—Y system [19,20]. Magnetic and superconducting properties have also been studied for polycrystalline Gd Y Ni B C samples x 1~x 2 2 [21] and Ho Y Ni B C, Gd Lu Ni B C, x 1~x 2 2 x 1~x 2 2 Dy Lu Ni B C and Dy Ho Ni B C single x 1~x 2 2 x 1~x 2 2 crystals [22]. For not too large Gd concentrations, the *¹ versus DG curves of the Gd—Y and the # Gd—Lu systems are straight lines, however, they are considerably steeper than the corresponding curve for the series of pure quaternary compounds. In Ref. [22], the more effective pair-breaking of Gd in Gd Lu Ni B C has been referred to the mechax 1~x 2 2 nism described by the original Abrikosov—Gor’kov theory [7], whereas the reduction in pair-breaking by the Tm, Er, Ho, Dy, and Tb moments, observed in the pure quaternary and the paramagnetic pseudoquaternary compounds has been attributed to crystalline electric field (CEF) effects, similarly as in the modified Abrikosov—Gor’kov theory of Keller and Fulde [23]. For those RNi B C 2 2 systems investigated in Ref. [22] whose ¹ is # above ¹ , specific types of de Gennes scaling of N *¹ could be identified. On the other hand, a # complete breakdown of the de Gennes scaling of *¹ was found for pseudoquaternary systems # with ¹ '¹ . This breakdown is inferred to N # arise from pair breaking by collective magnetic excitations [22]. In the present paper, the scaling behaviour of *¹ and of characteristic temperatures that de# scribe magnetic ordering have been investigated for the Ho Lu Ni B C family. x 1~x 2 2
311
2. Experimental details Polycrystalline samples of Ho Lu Ni B C x 1~x 2 2 were prepared by a standard arc melting technique. Powders of the elements were weighed in the stoichiometric compositions with a surplus of 10 wt% boron to compensate the high losses of boron caused by the arc melting. The powder was pressed to pellets that were melted under argon gas on a water-cooled copper plate in an arc furnace. To get homogeneous samples, they were turned over and melted again four times. After the melting procedure the solidified samples were homogenized at 1100°C for ten days. The actual sample composition is uncertain due to evaporation losses while melting. Owing to this the nominal composition, in particular the nominal Ho content x, is given in this paper. A powder X-ray diffractometer in Bragg— Brentano geometry was used to investigate the phase purity of the samples and to determine lattice parameters. For this purpose, Co Ka radiation was utilized and scans were taken from 2h"20—140° in steps of 0.015°. From the measured X-ray data, lattice parameters were determined by means of the DBWS Rietveld program. The AC susceptibility s was measured at zero DC field with a field amplitude of 0.01 mT at a frequency of 133 Hz. The values of the superconducting transition temperature ¹ were # determined from susceptibility versus temperature curves s(¹) using the condition s(¹ )"0.9s , # N where s is the susceptibility value in the normal N state. The electrical resistance of the samples, R, was measured by the standard four-probe technique, as a function of magnetic field and temperature in the range from 1.7 K up into the normal conducting state. The upper critical field H at a given temperature was determined from #2 the midpoint of the resistive transition curves, i.e. at 50% of the fictive normal state resistivity obtained by an extrapolation from the R versus ¹ curves measured above ¹ . Furthermore, the magnetic # structure was investigated by means of neutron diffraction experiments described elsewhere [24]. Characteristic temperatures that describe the various types of magnetic ordering were determined from s(¹) as well as R(¹, H) and neutron diffraction data.
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3. Results and discussion The lattice constants a and c of our Ho Lu Ni B C samples are presented in Fig. 1. x 1~x 2 2 The values obtained for x"0 and 1 agree well with those reported for the pure quaternary compounds [25]. The standard deviations of the lattice parameters obtained from the Rietveld analysis result in error bars that are of the order of symbol size in Fig. 1, i.e. 4]10~4 nm. Thus the deviations of the lattice parameters from the linear dependence on x (Vegard’s law) are obviously correlated with intrinsic properties of the samples, may be with uncertainties in their actual chemical composition. The straight lines in Fig. 1 indicate that, in spite of the evaporation losses that cannot be avoided during preparation, the samples show a systematic dependence of the lattice constants on the nominal degree of the substitution of Lu by Ho. In Fig. 2, the temperature dependence of the AC susceptibility s is shown for some of the investigated samples. A shift of the superconducting transition curves from ¹ "16.6 K, for x"0, to # about 8.5 K, for x*0.7, is observed. In the range between x"0.7 and 1, the superconducting transition practically does not depend on x. The ¹ values obtained from susceptibility measure# ments do not significantly differ from those obtained from the midpoint of the resistive transition
Fig. 1. Lattice parameters, a and c, obtained by a Rietveld analysis of X-ray data, as a function of the Ho concentration x.
Fig. 2. Temperature dependence of the AC susceptibility of Ho Lu Ni B C for various values of the Ho concentration x. x 1~x 2 2
curve. In the concentration range where ¹ is con# stant, the transition curves have a very small width of d¹ +0.2 K. The quantity d¹ was determined # # as d¹ "¹(0.9s )!¹(0.1s ). Relatively broad # N N transition curves with d¹ +1.2 K are observed in # the concentration range x(0.7. The width d¹ # reflects the phase purity and, in the range x(0.7, where ¹ changes with x, the homogeneity of # stoichiometry. As seen from X-ray and neutron diffraction experiments, no significant fraction of phase impurities could be determined in the powder samples; the stoichiometry is considered to be responsible for the relatively large value of d¹ . # A fluctuation of the Ho concentration x of about $0.03 has been estimated from d¹ "1.2 K and # from the ¹ (x) dependence in the range of Ho # concentrations x(0.7 (see below: Fig. 6). Fig. 3 shows the temperature dependence of the inverse susceptibility, 1/s(¹), in the normal state for several Ho concentrations. In the investigated temperature interval these curves can well be described by the Curie—Weiss law, s"C/(¹!h), where C& xk2 is the Curie constant and k is the paramag1 1 netic moment of the magnetic ion. The fitted value k "(10.2$0.2) l is very close to the theoretical 1 B value, 10.61 l , for the Hund’s rule ground state of B
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Fig. 3. The temperature dependence of the inverse AC susceptibility of Ho Lu Ni B C samples, measured for various values x 1~x 2 2 of x, fairly obeys the Curie—Weiss law. (The susceptibilitiy is measured in SI units, i.e. it is dimensionless.)
a free Ho3` ion. The paramagnetic Curie temperature h was found to be negative, of the order of a few Kelvin, for all concentrations of x, which indicates a negative mean exchange interaction between the magnetic moments. However, unlike the lattice constants (Fig. 1) and the slope of the 1/s versus x curves (Fig. 3), h does not show a systematic dependence on x. The temperature dependence of the resistance R, measured on a Ho Lu Ni B C sample for 0.95 0.05 2 2 several applied magnetic fields is shown in Fig. 4. A non-monotonic temperature dependence of R appears between 0.15 and 0.35 T. Such a re-entrant behaviour is observed only for samples with Ho concentrations x'0.8, suggesting a certain type of magnetic ordering in this concentration range. For a given concentration, the position of the local minimum of the resistance versus temperature curves, for increasing magnetic field, remains unchanged whereas the re-entrance maximum shifts slightly to higher temperatures. The position of the minima and the maxima of the R versus ¹ curves for different x (not completely shown here) can be used to determine relevant temperatures ¹ and .
313
Fig. 4. Electrical resistance of a Ho Lu Ni B C sample 0.95 0.05 2 2 versus temperature, measured for various magnetic fields H. Re-entrant behaviour, characterized by the temperatures ¹ and ¹ , is evident for fields 0.15 T)k H(0.35 T. The . 1 0 arrows mark ¹ and ¹ for the arbitrarily chosen field . 1 k H"0.2 T. 0
¹ , respectively, that characterize the pair-breaking 1 effect of magnetic ordering. These characteristic temperatures can also be determined by analyzing the temperature dependence of the upper critical field H which is very sensitive to pair-breaking #2 effects caused by magnetic ordering [19]. This is shown in Fig. 5, where the results of neutron diffraction experiments and the temperature dependence of H are compared. The curves in Fig. 5b #2 show an increasing depression of H with increas#2 ing Ho concentration, providing evidence for magnetic pair breaking. For x)0.8, the H (¹) curves #2 remain monotonic. As can be seen in the inset of Fig. 5b, for small Ho concentrations, the H ver#2 sus ¹ curves show an upward curvature near ¹ . # This is consistent with similar findings for LuNi B C single crystals [26]. For x'0.8, with 2 2 decreasing temperature, H increases from zero at #2 ¹ up to a local maximum, then it decreases in # a small temperature range and it increases again at lower temperatures. As for the compounds HoNi B C [14] and Ho Y Ni B C [19,20], 2 2 x 1~x 2 2
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three types of magnetically ordered structures have been determined for Ho Lu Ni B C by neutron x 1~x 2 2 diffraction [24]. Besides the commensurate antiferromagnetic structure, two incommensurate antiferromagnetic structures with a- and c-axis modulated wave vectors have been detected. In Fig. 5a the temperature dependence of the neutron diffraction peak intensities of only the a-axis modulated structure is shown. For decreasing temperature, the peak intensities of this magnetic structure start growing at ¹"¹ , where H (¹), in Fig. 5b, has . #2 its maximum and they reach their maximum at the temperatures ¹ where the H (¹) curves show 1 #2 their local minimum. These definitions of ¹ and 1 ¹ are consistent with those made earlier using the . maximum and the minimum, respectively, of the resistance versus temperature curve. Thus the incommensurate antiferromagnetic structure with a-axis modulation which is present in the same narrow temperature range as the anomalies of the H (¹) curves is considered to be responsible for #2 pair breaking in Ho Lu Ni B C. Neither the x 1~x 2 2 commensurate nor the incommensurate c-axis modulated structures, also found in these samples, show any effect on the superconducting behaviour [24]. It should be noted that this result cannot be simply generalized to other RNi B C compounds. 2 2 For instance, a certain re-entrant behaviour [27] as well as some a-axis modulated structure [13] have been observed in ErNi B C. But contrary to the 2 2 case of HoNi B C, the a-axis modulated structure 2 2 of ErNi B C fully exists down to 2 K, whereas the 2 2 re-entrant behaviour and a corresponding H (¹) #2 anomaly is found only in the temperature range between 5 and 6 K. Thus, the reason why H (¹) of #2 ErNi B C behaves anomalously remains unclear. 2 2 In Fig. 6, the superconducting transition temperatures ¹ and specific temperatures that character# ize details of the magnetic ordering are plotted against the Ho concentration x. ¹ decreases lin# early with increasing x, reaches the ¹ value of # HoNi B C at x"0.7 and remains unchanged for 2 2 concentrations x*0.7. A linear depression of ¹ # with increasing Ho concentration is expected under the assumption that x has no influence on N(E )I2 in Eq. (1) but only controls n. A complete F breakdown of the scaling behaviour occurs for x'0.7, where ¹ becomes independent of the Ho #
Fig. 5. (a) Temperature dependence of the neutron diffraction peak intensities for various values of the Ho concentration x, normalized to the calculated value for fully magnetically ordered phases with 10 l for Ho3` (free ion), of the incommensurate B antiferromagnetic a-axis modulated structure; (b) upper critical field H versus temperature of Ho Lu Ni B C samples for #2 x 1~x 2 2 various Ho concentrations x. ¹ and ¹ , both marked for the . 1 case x"0.95, characterize the onset and the maximum, respectively, of the intensity peak in (a) and the position of the maximum and the minimum of H , respectively, in (b). #2
concentration and, thus, of the effective de Gennes factor. The initial magnetic ordering that develops upon cooling is the incommensurate spiral structure along the c-axis, characterized by its onset
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Fig. 6. Superconducting transition temperature ¹ and specific # temperatures characterizing magnetic ordering, ¹ *, ¹ , ¹ and # N . ¹ , of Ho Lu Ni B C versus the holmium concentration x. 1 x 1~x 2 2 ¹ *, ¹ and ¹ are the onset temperatures for the incommensur# N . ate spiral with c-axis modulation, the commensurate antiferromagnetic structure and the a-axis modulated incommensurate component, respectively. (¹ : see Fig. 5). The solid and dashed 1 lines are guides to the eye.
temperature ¹ * [24]. For the pure quaternary # compound with x"1, magnetic ordering and superconductivity arise at nearly the same temperature, ¹ *+¹ +8.5 K. The onset temperatures # # for the commensurate antiferromagnetic structure and the incommensurate a-axis modulated structure, ¹ and ¹ , have nearly the same value [24]. N . For higher concentrations x, the onset temperatures ¹ *, ¹ and ¹ , as well as the temperature # N . where the neutron-diffraction intensity peak of the a-axis modulated structure has its maximum, ¹ , 1 show a linear dependence on x, indicating some de Gennes-type scaling. Extrapolating ¹ (x) to lower 1 concentrations, ¹ would vanish at the same value 1 of the Ho concentration, x+0.7, where the de Gennes scaling of ¹ breaks down. It is interesting # to note that for x(0.75, the peaks of the commensurate c-axis structure of Ho Lu Ni B C and x 1~x 2 2 those of the a-axis modulated structure are below the detection limit. For x)0.65, only the incom-
315
Fig. 7. Comparison of ¹ versus DG curves for of # Gd Lu Ni B C (j, taken from Ref. [22]), Gd Y Ni B C x 1~x 2 2 x 1~x 2 2 (h, taken from Ref. [21]), Ho Y Ni B C (n, taken from Ref. x 1~x 2 2 [18]) and Ho Lu Ni B C (v, this work), where ¹ is the x 1~x 2 2 # superconducting transition temperature and DG is the effective de Gennes factor of the pseudoquaternary compounds, as defined by Eq. (2), and ¹ "¹ (x"0). #,0 #
mensurate c-axis structure was found at low temperatures. De Gennes scaling of characteristic temperatures describing magnetic ordering in magnetically diluted systems is expected not to work below a certain critical concentration x resulting 1 from percolation effects. The actual value of x is 1 sensitive to the range of the exchange interaction between the magnetic ions as well as a possible short range order of these ions. The lowest Ho concentration down to which magnetic ordering exists in the Lu—Ho system is still under investigation. In Fig. 7, the dependence of the superconducting transition temperature on the effective de Gennes factor DG, as defined by Eq. (2), of our Ho Lu Ni B C compounds is compared with x 1~x 2 2 results reported in literature for three other pseudoquaternary systems. In the concentration range where ¹ decreases linearly with DG, the # Gd—Lu and the Gd—Y systems show a considerably steeper decrease than the Ho—Lu and the Ho—Y systems, respectively. These differences could be mainly caused by CEF effects as mentioned in
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Chapter 1 [22]. However, considerable differences in the slopes of the linear ¹ versus DG curves are # also observed for systems with the same effective de Gennes factor, caused by the same magnetic ion. Thus the Ho—Lu and the Gd—Lu systems show a stronger depression of ¹ than the Ho—Y and the # Gd—Y systems, respectively. Analyzing these findings it should be taken into account that the substitution of Y by Lu causes an increase of the lattice parameter c and a reduction of the lattice parameter a of the RNi B C structure [25]. This may 2 2 result in a change of the electronic property N(E )I2 that governs the exchange interaction beF tween the magnetic ions and, according to Eq. (1), controls the depression of ¹ . The unusual # behaviour of the ¹ versus DG curve of # Ho Lu Ni B C at DG+3.2 (i.e. x"0.7) is not x 1~x 2 2 yet understood. A similar ¹ versus DG curve was # reported for Ho Dy Ni B C [22]. In that case, 1~x x 2 2 ¹ scales with DG only in the range of composi# tions where ¹ '¹ , i.e. up to Dy concentrations # N of x+0.3. For x*0.3, i.e. the range where ¹ '¹ , ¹ does not depend on DG. This breakN # # down of de Gennes scaling was assumed to be caused by antiferromagnetic magnons [22]. However, for the Ho Lu Ni B C family investigated x 1~x 2 2 in this study, a non-varying ¹ is observed in the # paramagnetic state. For Ho concentrations in the range x"0.7 to 0.8, ¹ is much higher than the # characteristic temperatures ¹ *, ¹ and ¹ de# . N scribing the onset of various types of long-range magnetic ordering (cf. Fig. 6). Therefore, an explanation by magnons, even those related to shortrange order, is not convincing.
influence on the superconducting behaviour, could be found in this concentration range, for temperatures above 2 K. For x'0.7, ¹ remains con# stant, whereas the temperature characterizing the onset of the incommensurate a-axis modulated structure, ¹ , increases nearly linearly with in. creasing x up the value of HoNi B C, ¹ "6.5 K. 2 2 . The relatively strong depression of ¹ with increas# ing Ho concentration x for x)0.7, compared with the case of Ho Y Ni B C, was referred to differx 1~x 2 2 ences in the lattice parameters of the Ho—Y and the Ho—Lu systems resulting in different electronic structures. Anomalies in the temperature dependence of the upper critical field H (¹) were observed #2 for x'0.8. They symbolize the re-entrant behaviour appearing for these Ho concentrations in the same temperature range where the incommensurate antiferromagnetic structure with a-axis modulation is present and the de Gennes scaling of ¹ # breaks down. For higher Ho concentrations the characteristic temperatures describing the different types of magnetic ordering, ¹ *, ¹ , ¹ and ¹ , # N . 1 scale with the de Gennes factor. Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft within the project Sonderforschungsbereich 463 ‘Seltenerd U®bergangsmetallverbindungen: Struktur, Magnetismus und Transport’. Furthermore, we would like to thank S.L. Drechsler for helpful discussions. References
4. Summary The superconducting transition temperature ¹ and the specific temperatures characterizing # magnetic ordering in Ho Lu Ni B C polycrysx 1~x 2 2 talline samples were investigated by susceptibility and resistivity measurements as well as neutron diffraction. Two composition ranges with different behaviour could be distinguished: for x)0.7, ¹ decreases linearly with increasing Ho concentra# tion. Only the magnetic structure with incommensurate c-axis modulation, which seems to have no
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