Superconductivity in rare earth and actinide compounds1

Superconductivity in rare earth and actinide compounds1

Journal of Alloys and Compounds 250 (1997) 585–595 L Superconductivity in rare earth and actinide compounds M. Brian Maple*, Marcio C. de Andrade, J...

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Journal of Alloys and Compounds 250 (1997) 585–595

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Superconductivity in rare earth and actinide compounds M. Brian Maple*, Marcio C. de Andrade, Jan Herrmann, Robert P. Dickey, Neil R. Dilley, Seungho Han Department of Physics and Institute for Pure and Applied Physical Sciences, University of California, San Diego, La Jolla, CA-92093, USA

Abstract Rare earth and actinide compounds and the extraordinary superconducting and magnetic phenomena they exhibit are surveyed. The rare earth and actinide compounds described belong to three classes of novel superconducting materials: high temperature, high field superconductors (intermetallics and layered cuprates); superconductors containing localized magnetic moments; heavy fermion superconductors. Recent experiments on the resistive upper critical field of high T c cuprate superconductors and the peak effect in the critical current density of the f-electron superconductor CeRu 2 are discussed. Keywords: Superconductivity; Actinide; Rare earth

1. Introduction Rare earth and actinide elements are essential components of compounds that belong to three classes of novel superconducting materials: high temperature, high field superconductors (including intermetallics and layered cuprates); superconductors containing localized magnetic moments; and heavy fermion superconductors. Whereas the outermost electrons (s, p, and d electrons) of the rare earth and actinide ions are involved in the superconductivity of the high temperature, high field superconductors, it is the localized 4f and 5f electrons that are primarily responsible for the remarkable superconducting and magnetic phenomena found in superconductors containing localized magnetic moments and heavy fermion superconductors. In the first part of this article, we briefly survey the rare earth and actinide compounds that belong to these three classes of novel superconducting materials as well as the extraordinary superconducting and magnetic phenomena they exhibit. In the second part of the article, we discuss experiments on two subjects of recent interest: the resistive upper critical field of high T c cuprate superconductors and

*Corresponding author. Physics Department 0319, University of California, San Diego, 9500 Gilman Drive, La Jolla CA 92093-0319. Fax: (11-619) 534-1241; e-mail: [email protected]

0925-8388 / 97 / $17.00  1997 Elsevier Science S.A. All rights reserved PII S0925-8388( 96 )02832-0

the peak effect in the critical current density of the felectron superconductor CeRu 2 .

2. High temperature, high field superconductors

2.1. Intermetallics Rare earth and actinide intermetallic compounds are promising candidates for applications of superconductivity. A number of these compounds have superconducting critical temperatures T c and upper critical fields Hc2 that rival the values of T c and Hc2 of the A15 compound Nb 3 Ge, which held the record for the highest T c from 1973 until the discovery of the high T c cuprate superconductors in 1986. The values of T c and Hc2 (0) for the compound Nb 3 Ge are T c ¯23 K [1] and Hc2 (0)¯38 T [2]. Recently, rare earth and actinide borocarbide materials have been discovered [3,4] with values of T c comparable to that of Nb 3 Ge, YPd 5 B 3 C 0.3 with T c ¯23 K [4], rapidly-quenched YPd 2 B 2 C with T c ¯21 K [5], and ThPd 3 B 3 C with T c ¯ 21 K [6]. Rapidly-quenched YPd 2 B 2 C and the material ThPd 3 B 3 C have values of Hc2 (0) of |10 T [5] and |17 T [6], respectively. Excluding the high T c cuprate superconductors, the highest values of Hc2 (0) are found among the Chevrel phase compounds: for LaMo 6 Se 8 (T c ¯11 K [7]), Hc2 (0)¯

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45 T [8], while for PbMo 6 S 8 (T c ¯15 K [9]), Hc2 (0)¯60 T [10,11]. It is interesting to note that among the elements, La metal has the highest value of T c (|11 K at a pressure of |16 GPa [12]).

2.2. Layered cuprates The first high T c cuprate superconductors discovered, which are also some of the more important materials both with respect to scientific interest as well as technological potential, are based on rare earth and actinide elements [13]. The first superconducting oxide system found with T c values exceeding the 23 K record value held by Nb 3 Ge was La 22x Ba x CuO 4 which has a maximum value T c ¯30 K for x¯0.15 [14,15]. Shortly thereafter, La 22x M x CuO 4 systems with M5Sr, Ca, and Na were synthesized which exhibited superconductivity with maximum values of T c of |40 K for M5Sr [16], |20 K for M5Ca [17], and |20 K for M5Na [18,19]. The first superconductors with values of T c exceeding the boiling point of liquid nitrogen (77 K) belong to the RBa 2 Cu 3 O 72d family. Superconductivity occurs for R5Y [20] and all of the lanthanides [21] except Ce and Tb (which do not form the phase) and Pr (which does form the phase, but is insulating and thereby not superconducting) with T c values that range from |92 K for R5Y to |95 for R5Nd. RBa 2 Cu 3 O 72d compounds have enormous values of Hc2 (T ). Extrapolation of the Hc2 (T ) curves measured resistively between 0 and |10 T to T5 0 K, using the WHHM theory without paramagnetic limiting, yields values of Hc2 (0)¯160 T [22]. The La 22x M x CuO 4 and RBa 2 Cu 3 O 72d compounds are hole-doped superconductors, as are most of the high T c cuprates. The first system of electron-doped cuprate superconductors discovered was Ln 22x M x CuO 42y (Ln5Pr, Nd, Sm, Eu; M5Ce, Th; x¯0.120.18; y¯0.02) [23–26]. The highest values of T c found among the electron-doped superconductors are |25 K. All of the cuprate superconductors have layered perovskite-like crystal structures which contain conducting CuO 2 planes within which the superconducting charge carriers are believed to primarily reside. The Ln 22x M x CuO 42y electron-doped materials have a tetragonal crystal structure that is similar to that of the La 22x M x CuO 4 hole-doped materials, but without the apical oxygen atoms. The unit cell of these two classes of materials contains a single CuO 2 layer, in contrast to unit cell of the RBa 2 Cu 3 O 72d compounds which contains two CuO 2 layers. There has been considerable interest in systems of the type R 12x Pr x Ba 2 Cu 3 O 72d , especially for R5Y [27]. This interest was initially driven by the puzzling observation that PrBa 2 Cu 3 O 72d is insulating and nonsuperconducting, whereas the other RBa 2 u 3 O 72d compounds that can be formed are metallic and superconducting with T c s¯92–

95 K. The Y 12x Pr x Ba 2 Cu 3 O 72d system is replete with interesting physical phenomena including a metal-insulator transition at x cr ¯0.55, a monotonic depression of T c with x that vanishes near x cr in the metallic phase, a striking crossover in the pressure dependence of T c from positive to negative with increasing x, a large g T contribution to the low temperature specific heat that is reminiscent of heavy fermions, and Cu 21 and Pr n1 antiferromagnetic ordering in the insulating phase with T N (Cu 21 ).T N (Pr n1 ), where T N ´ temperature. It has been suggested that these is the Neel and other peculiar properties of this system are related to hybridization between the Pr localized 4f states and the valence band states associated with the conducting CuO 2 planes [27]. Similar phenomena are found in the related Y 12x Pr x Ba 2 Cu 4 O 8 system which has also been extensively investigated [28]. In addition to these rare earth and actinide based cuprates, many other high T c cuprates have been discovered, some of which also contain rare earth elements. The material with highest T c presently known is HgBa 2 Ca 2 Cu 3 O 81d , which has a T c of |133 K at atmospheric pressure [29,30] that can be increased to |160 K at high pressure [31,32]. Achieving an understanding of the normal and superconducting state properties of the high T c cuprate superconductors has proven to be an enormous challenge. Some researchers believe that the normal state properties of the cuprates are unconventional and violate the Landau–Fermi liquid paradigm [33,34]. Insofar as the normal state properties are a reflection of an electronic structure that underlies the high T c superconductivity, it may first be necessary to attain an understanding of the normal state before it will be possible to elucidate the origin and nature of the superconductivity. The anomalous normal state properties include an electrical resistivity in the ab-plane of the form rab (T )5rab (0)1cT for T .T c with rab (0)¯0 [35], a c-axis resistivity that diverges as T →0 while rab remains metallic over an appreciable range of carrier concentration [36], a Hall angle uH described by cotuH ; rxx /rxy 5a1bT 2 [37,38], and the presence of a pseudo gap (often referred to as a spin gap) that develops above T c in underdoped cuprates [39]. There is mounting evidence for an anisotropic singletspin superconducting state in YBa 2 Cu 3 O 72d with d x 2 2y 2 symmetry in which the energy gap has nodes on the Fermi surface [33,40]. The evidence is based on a variety of measurements including the temperature dependence of the microwave penetration depth [41], Josephson tunneling interferometry [42], and tri-crystal ring magnetometry [43]. However, Josephson tunneling along the c-axis in YBa 2 Cu 3 O 72d -oxide–Pb tunnel junctions suggests that there is an s-wave component to the superconducting order parameter of YBa 2 Cu 3 O 72d [44]. On the other hand, microwave penetration depth [45] and Raman spectroscopy measurements [46] on the electron-doped superconductor

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Nd 1.85 Ce 0.15 CuO 42y indicate that the superconducting order parameter has s-wave symmetry. Because of their high T c s, short coherence lengths, long penetration depths, and large anisotropy, the cuprate superconductors exhibit a wealth of striking vortex phases and phenomena that are currently being vigorously investigated [47,48].

3. Superconductors containing localized magnetic moments Superconductors containing localized magnetic moments display many remarkable phenomena due to the interplay between superconductivity and magnetism. One of these phenomena is reentrant superconductivity in which superconductivity that occurs in a material at a critical temperature T c1 is destroyed at a lower critical temperature T c2 , T c1 , below which the material reenters the normal state. Reentrant superconductivity is found in certain superconductors containing small concentrations of Ce impurities which exhibit a Kondo effect in which the Kondo temperature T K is much smaller than T c . Examples include the superconducting-Kondo systems La 12x Ce x Al 2 and (La 12y Th y ) 12x Ce x [49]. Here, the destruction of superconductivity at T c2 is related to the competition between superconducting electron singlet spin pairing with characteristic energy k B T c and the formation of a many body singlet state between the conduction electrons and each Ce impurity ion with characteristic energy k B T K . Reentrant superconductivity is also encountered in certain ternary rare earth compounds [50] such as ErRh 4 B 4 [51] and HoMo 6 S 8 [52] in which the destruction of superconductivity at T c2 is induced by the occurrence of ferromagnetic ordering of the rare earth magnetic moments. These systems are especially interesting since the screening of the electromagnetic interaction at long wavelengths by the supercurrent results in the formation of an ˚ that oscillatory magnetic state with a wavelength¯100 A coexists with superconductivity in a narrow temperature interval above T c2 [53]. Many of the RRh 4 B 4 [54], RMo 6 S 8 [55] and RMo 6 Se 8 [56] compounds exhibit the coexistence of superconductivity and antiferromagnetic ordering of the R magnetic moments [50]. The ternary rare earth compounds such as the RRh 4 B 4 and RMo 6 X 8 (X5S, Se) are well suited to investigations of the interplay between superconductivity and magnetic order since they contain an ordered sublattice of magnetic R ions, but nevertheless are superconducting. The occurrence of superconductivity, even in the presence of relatively large concentrations of R ions, can be attributed to the crystal structures of these materials which are built up from R ions and transition metal clusters. The superconductivity appears to be associated primarily with the transition metal 4d electrons which interact only weakly with the R ions.

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Recently, the coexistence of superconductivity and antiferromagnetic order was observed in several RNi 2 B 2 C compounds [57]. Another class of materials in which the coexistence of superconductivity and antiferromagnetism occurs are high T c cuprates containing R ions such as the RBa 2 Cu 3 O 72d and Ln 22x M x CuO 42y compounds discussed above [13]. One of the most dramatic manifestations of the interplay between superconductivity and magnetism is the phenomenon of magnetic field induced superconductivity (MFIS) [50,58], also known as the Jaccarino–Peter effect [59]. MFIS occurs in type II superconductors containing ions which carry magnetic moments in which Hc2 (T ) is paramagnetically limited and the exchange field associated with the magnetic ions is negative (opposite to the applied field). Because of the compensation of the exchange field Hex by the external field H (both Hex and H act upon the spins of the conduction electrons and break superconducting electron pairs), a sequence of transitions from superconducting to normal to superconducting and back to normal occurs upon increasing the magnetic field at low temperatures. One of the best examples of MFIS is found in the compound Eu 0.75 Sn 0.25 Mo 6 S 7.2 Se 0.8 which exhibits two domains of superconductivity in the H–T plane, one at low fields and the other at high fields [60].

4. Heavy fermion superconductors A small class of heavy fermion superconductors includes one Ce compound, CeCu 2 Si 2 [61], and five U compounds, UBe 13 [62], UPt 3 [63], URu 2 Si 2 [64], UNi 2 Al 3 [65], and UPd 2 Al 3 [66]. The heavy fermion compounds are characterized by enormous values of the linear coefficient of the electronic specific heat (Ce 5g T ) which can be as high as |1 J mol 21 K 22 , and a correspondingly large electron effective mass m * |10 2 –10 3 m e , where m e is the free electron mass [67–69]. The origin of the heavy fermion state is believed by many researchers to be associated with the Kondo effect. In several of these compounds, weak antiferromagnetism and superconductivity coexist over different parts of the Fermi surface with T N .T c (UPt 3 , URu 2 Si 2 , UNi 2 Al 3 , UPd 2 Al 3 ) [67]. The heavy fermion superconductors appear to exhibit an unconventional type of anisotropic superconductivity in which the superconducting energy gap D(k) vanishes at points or lines on the Fermi surface and the electron pairing is mediated by antiferromagnetic spin fluctuations. Evidence for the anisotropic superconductivity includes power law temperature dependences in the superconducting state in various physical properties such as ultrasonic attenuation, spin lattice relaxation rate, thermal conductivity, and magnetic field penetration depth. The occurrence of the two superconducting transitions in some heavy fermion compounds such as UPt 3 has been attributed to

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coupling between a multicomponent superconducting order parameter and the antiferromagnetic order parameter. Another common behavior that is emerging for superconducting heavy fermion uranium compounds is the tendency of chemical substitutions to suppress both superconductivity and weak antiferromagnetism (AFM) and induce local moment AFM or ferromagnetism (FM) with moments of the order of a mB [67]. In UPt 3 , local moment AFM is produced by substituting Th for U and Pd or Au for Pt, while in URu 2 Si 2 , local moment AFM appears upon substitution of Rh for Ru and local moment FM occurs when Re or Tc is substituted for Ru, the first example of a ferromagnetic instability in a heavy electron system. Within the past several years, there has been a great deal of interest in a new class of f-electron systems which exhibit non Fermi-liquid (NFL) behavior at low temperatures [70]. These materials are Ce and U intermetallics which, with a few possible exceptions, have been doped with a nonmagnetic element. Many of the f-electron systems exhibit the following NFL temperature dependences of the electrical resistivity r, specific heat C, and magnetic susceptibility x for T ,T o where T o is a characteristic temperature [70]: r (T )|12a(T /T o ), where a,0 or .0, C(T ) /T|(21 /T o )ln (T / bT o ), and x (T )|12c(T / T o )1 / 2 . In several of the f-electron systems, the characteristic temperature T o can be identified with the Kondo temperature T K . Some of the interest in non Fermi-liquid behavior in strongly correlated electron systems, particularly copper oxides and f-electron materials, is associated with the unconventional superconductivity found in these two classes of materials. In spite of the disparity in the values of T c , which are as high as |133 K for the copper oxide superconductors but #2 K for the f-electron heavy fermion materials, the superconducting states of both of these materials share some striking similarities – the superconducting state appears to be anisotropic, with an energy gap that may vanish at points or lines on the Fermi surface, and the superconducting electron pairing may be mediated by antiferromagnetic spin fluctuations. An understanding of the source of the NFL behavior in these systems may provide important information about the electronic structure and excitations in these systems, as well as the origin of the unconventional superconductivity.

ductors has strong positive curvature over a wide temperature range and appears to diverge as T →0. This unusual behavior of Hc2 (T ) has been reported for many different cuprate superconductors including the electron-doped materials Ln 1.85 Ce 0.15 CuO 42y (Ln5Pr, Nd, Sm) [71–73], the underdoped compounds R 12x Pr x Ba 2 Cu 3 O 72d (R5Y,Gd) [27,74], and YBa 2 Cu 32x Zn x O 72d [75], and the overdoped compounds Tl 2 Ba 2 CuO 6 [76] and Bi 2 Sr 2 CuO 6 [77]. It was previously suggested that positive curvature of the resistively determined Hc2 (T ) curve may be a general property of high T c cuprate superconductors. However, the T-dependence of the resistively determined Hc2 (T ) curve was interpreted as a measure of the T-dependence of the irreversibility line [78]. Interestingly, an Hc2 (T ) curve with positive curvature has also been observed for an organic superconductor [79]. In the hole-doped cuprates, T c can be reduced to values near 20 K in underdoped or overdoped material obtained through appropriate substitutions of other elements. The decrease in T c is accompanied by a corresponding decrease in the value of Hc2 , making the low temperature–high field regime of the H–T phase diagram more accessible to magnetic fields available in the laboratory. An example where it has been possible to access a large portion of the Hc2 (T ) curve is shown in Fig. 1 for the underdoped compound Y 0.47 Pr 0.53 Ba 2 Cu 3 O 72d [27]. The Hc2 (T ) data were extracted from electrical resistivity measurements performed on single crystals with applied magnetic fields parallel (Hic) and perpendicular (H'c) to the c-axis. The superconducting critical temperature T c (H ) was defined as the temperature at which the resistivity ( rab ) drops to 50% of its extrapolated normal state value. We observe that for both Hic and H'c, Hc2 (T ) exhibits positive curvature. In the electron-doped high T c cuprate superconductors, lower T c s (|25 K) naturally occur in the optimally doped regime, making these layered superconductors excellent candidates for studying the temperature dependence of Hc2 . The resistively determined Hc2 (T ) curves for three elec-

5. Resistive upper critical field of high T c cuprate superconductors One of the most striking features of the high T c cuprate superconductors is the unusual temperature dependence of the resistively determined upper critical field Hc2 . Whereas the Hc2 (T ) curve of conventional superconductors has negative curvature and saturates to a constant value as T →0, the Hc2 (T ) curve of the high T c cuprate supercon-

Fig. 1. Resistively determined upper critical field vs. temperature curves with Hic and H'c for Y 0.47 Pr 0.53 Ba 2 Cu 3 O 72d (after Ref. [27]).

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tive curvature of Hc2 (T ) of high T c cuprate superconductors include some type of dimensional crossover [81], mixing of superconducting order parameter components [82], and the presence of magnetic impurities [83]. The behavior of Hc2 (T ) of the Nd 1.85 Ce 0.15 CuO 42y single crystal at lower temperature is different than that of the other two Ln 1.85 Ce 0.15 CuO 42y (Ln5Pr, Sm) crystals as shown in Fig. 2. We observe that the Hc2 (T ) curve for the Nd 1.85 Ce 0.15 CuO 42y sample in Fig. 2(b) exhibits a tendency towards saturation as T →0 as predicted for conventional superconductors [84]. On the other hand, for the other two samples, Pr 1.85 Ce 0.15 CuO 42y and Sm 1.85 Ce 0.15 CuO 42y in Fig. 2(a) and Fig. 2(c), respectively, Hc2 (T ) is still increasing rapidly as T →0, greatly exceeding the value of Hc2 (0) that would be expected for a conventional superconductor. The effect of reduced T c on the Hc2 (T ) curve by under or over oxygenating or changing the Ce concentration of crystals in the Nd 22x Ce x CuO 42y system is also rather extraordinary and substantially different from that in the Pr 22x Ce x CuO 42y and Sm 22x Ce x CuO 42y systems. It has been shown [80] that the systematic reduction of T c changes the behavior of Hc2 (T ) in Nd 1.85 Ce 0.15 CuO 42y crystals rather profoundly, while for the other two Pr and Sm based compounds the change in behavior induced by reducing T c is less

Fig. 2. Resistively determined upper critical field vs. temperature curves with Hic and H'c for single crystal specimens of (a) Pr 1.85 Ce 0.15 CuO 42y ; (b) Nd 1.85 Ce 0.15 CuO 42y (after Ref. [80]); (c) Sm 1.85 Ce 0.15 CuO 42y (after Ref. [72]).

tron-doped compounds, Ln 1.85 Ce 0.15 CuO 42y (Ln5Pr, Nd, Sm), are displayed in Fig. 2. The superconducting critical temperature T c (H ) was defined in the manner described above. The data for Ln5Nd and Sm in Fig. 2(b) and Fig. 2(c) were obtained from refs. [80] and [72], respectively. We observe that for H'c, Hc2 (T ) exhibits a slight upward curvature near T c . For Hic, Hc2 (T ) has positive curvature throughout the entire temperature range. It is important to point out that the positive curvature in Hc2 (T ) that has been reported for some high T c cuprates could be accounted for in terms of flux-creep dissipation or fluctuation effects. However, these effects are generally accompanied by appreciable broadening of the resistive transition curves which does not occur for the electron-doped compounds considered here. Other possible explanations for the posi-

Fig. 3. Electrical resistivity rab as a function of temperature for Nd 1.85 Ce 0.15 CuO 42y in applied magnetic fields Hic as noted in the figure. (a) Single crystal with T c ¯7 K (after Ref. [80]); (b) over-oxygenated thin film with T c ¯15 K (after Ref. [88]).

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dramatic. Shown in Fig. 3 are resistive transition curves in magnetic fields Hic for a Nd 1.85 Ce 0.15 CuO 42y single crystal [Fig. 3(a)] and thin film [Fig. 3(b)]. The samples have reduced T c s in both cases. The application of a magnetic field initially (low fields) results in the expected parallel shift of the superconducting transition curve, a typical behavior of the electron-doped compounds. However, as the applied magnetic field is increased, a gradual change of shape of the resistive transition curve away from the parallel shift behavior is noticeable for temperatures below 4 K. For the sample in Fig. 3(a), an unusual dependence on applied field becomes evident around 1 kOe. For fields between 1 kOe and 2 kOe, rab (T ) initially decreases with temperature, then increases below 2 K, and finally goes through a maximum around 1.1 K, before it undergoes a second transition that is much narrower than the initial one. This second transition becomes narrower with increasing magnetic field. The same qualitative behavior is observed for the sample in Fig. 3(b), an overoxygenated thin film. The T c of the film is slightly higher than that of the crystal in Fig. 3(a), and the effect is less dramatic. However, in both cases, the temperature interval in which the anomaly in rab (T ) starts to develop is very close to the temperature where the Nd 31 ions order antiferromagnetically in Nd 1.85 Ce 0.15 CuO 42y [85]. This observation suggests the possibility of reentrant superconductive behavior induced by magnetic order [50]. The fact that the anomaly is not observed for the optimally doped samples, but becomes more pronounced for samples with lower T c s, suggests a systematic development of the anomaly with decreasing T c . The coexistence of superconductivity and antiferromagnetism in the electron-doped compounds (Ln5Nd and Sm) has previously stimulated the search for the interaction of superconductivity and magnetic ordering of the rare earth ions in these materials. In a Sm 1.85 Ce 0.15 CuO 42y single crystal with a reduced T c ¯11.5 K, a change in the curvature of the Hc2 (T ) curve was interpreted as indirect evidence for the interaction between superconductivity and antiferromagnetic ordering of the Sm 31 ions [71]. However, the measurements upon which the Hc2 (T ) curves in Fig. 2 are based do not show any anomalous behavior in the resistive transitions for the Sm 1.85 Ce 0.15 CuO 42y crystal nor for the nonmagnetic Pr 1.85 Ce 0.15 CuO 42y crystal with lower T c s. The observation of the striking anomalies in the resistive superconducting transition curves of Nd 1.85 Ce 0.15 CuO 42y single crystals and thin films with reduced T c s in magnetic fields seems, however, to provide more direct evidence of the existence of this interaction in high temperature cuprate superconductors. Another peculiarity of the resistive transitions in Nd 1.85 Ce 0.15 CuO 42y is revealed for large applied magnetic fields. High magnetic fields can completely suppress superconductivity and reveal a negative magnetoresistance with a logarithmic temperature dependence rab (T )|ln (1 / T ). This behavior was interpreted as an indication of 2D

weak localization [86,87]. In Fig. 3(b), the rab (H,T ) data indicate a tendency towards a magnetic field induced superconductor–insulator transition at low temperature and high fields where rab appears to saturate. It is possible that the saturation of rab could correspond to an intermediate metallic state between superconducting and insulating behavior, respectively [88]. Additional low-temperature experiments in higher magnetic fields are underway to further explore this transition.

6. Peak effect in the critical current density of CeRu 2 The binary compound CeRu 2 , which crystallizes in the cubic MgCu 2 (C15) structure, was found to exhibit superconductivity nearly 40 years ago [89]. Its T c of 6.1 K is the highest among the known intermetallic compounds of Ce. The interplay between superconductivity and magnetic order has been studied extensively in pseudobinary compounds of the form Ce 12x R x Ru 2 where Ce is partially replaced by a rare earth element R which carries a localized magnetic moment due to a partially filled 4f electron shell [89,90]. Substitution of Ru by Co in CeRu 22x Co x results in a rapid suppression of superconductivity with x, even though CeCo 2 is a superconductor with T c ¯0.9 K [91]. In resonant photoemission and bremsstrahlung isochromat spectroscopy studies of CeRu 2 , a large amount of Ce 4f spectral weight was observed in the vicinity of the Fermi level [92,93]. The recent observation of an irreversible peak feature in magnetization M vs. magnetic field H isotherms [94,95] in the field region close to the upper critical field Hc2 for temperatures T #5.0–5.5 K has revived interest in the superconducting properties of CeRu 2 . This anomaly closely resembles the irreversible M(H ) curves observed in superconducting samples exhibiting a peak effect in the critical current density [96] which involves an increase and subsequent decrease of the pinning force density acting on the flux lines as the superconducting transition is approached from within the mixed state. Such a peak effect has been observed in both low [97,98] and high T c [99,100] superconductors. One scenario that was put forth to explain the peak anomaly in CeRu 2 [101,102] is the formation of a spatially non-uniform Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state [103,104] at high fields near Hc2 . In the FFLO state, the superconducting order parameter is modulated along the direction of the magnetic field which could lead to a segmentation of vortices and, in analogy to the situation in the anisotropic, layered cuprate superconductors, to increased pinning when the vortex segments adapt more easily to random pinning sites. The transition into the FFLO state is predicted to be of first order. Arguments in favor of this explanation include the observation of hysteresis in magnetization and magnetostriction and pronounced magnetocaloric anomalies [101,102,105] as well as the

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similarities to results obtained for the heavy fermion superconductors UPd 2 Al 3 and UPt 3 [106–108]. Although it has been claimed [109,110] that the anomaly should not be observed close to T c since the FFLO state is predicted to exist only for T #0.55T c [111], recent theoretical work indicates that singlet–triplet mixing of the superconducting order parameter may induce the FFLO state at higher reduced temperature [112]. Alternative explanations of the peak effect in CeRu 2 include a softening of the shear modulus of the flux line lattice (FLL) that proceeds more rapidly than the depletion of the pinning interaction as H →Hc2 , such that the FLL can adjust better to the pinning centers [113], and a collective pinning approach in which the rapid softening of the FLL is accompanied by a decrease in the longitudinal and transverse correlation lengths which may result in an increase of the pinning force density when the transverse correlation length matches the lattice spacing of the FLL [114]. We have studied the magnetization M(H,T ) and electrical resistance R(H,T,J) of a polycrystalline CeRu 2 sample as a function of magnetic field H, temperature T and

Fig. 4. (a) Examples of magnetization curves M(H ) measured on CeRu 2 at different temperatures using a SQUID magnetometer. Both the irreversible anomaly and the hysteretic behavior near the onset field Hi (T ) are clearly visible. The characteristic fields are indicated for the curve measured at T52.00 K. (b) H–T phase diagram constructed from measurements similar to those shown in (a). T i (H ) and T c (H ) were extracted from M(T ) measurements at fixed H.

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transport current density J. Fig. 4(a) presents typical examples of the irreversible peak feature observed in M( H,T ) in the field interval between an onset field Hi (T ) and the upper critical field Hc2 (T ). Hc2 (T ) is defined as the field where M(H ) attains its linear paramagnetic normal state slope that extrapolates to M(H50)50. The temperature dependence of these characteristic fields is summarized in the H–T phase diagram of Fig. 4(b). With decreasing temperature, the width of the irreversible anomaly increases, and considerable hysteresis in Hi (T ) is observed for increasing and decreasing field. For temperatures above |5.0 K, the anomaly disappears (Hi →Hc2 ), an observation that has stimulated speculation about the existence of a critical point in this temperature region and has been interpreted as an indication for the formation of the FFLO state. However, we do not observe any appreciable change in the slope of Hc2 (T ) in this temperature region. We note that the M( H,T ) anomaly is very robust against substitution of Nd for Ce, which introduces local moments and increases T c , against substitutions of Co for Ru, which decreases T c , and against changes in the Ru concentration. Another interesting feature of the M( H,T ) measurements is the small yet finite irreversibility that is seen at fields below the anomaly. The observation of this residual irreversibility depends on the experimental details: if the sample experiences slight field inhomogeneities during the measurement (as is the case in typical measurements in SQUID magnetometers where the sample is moved distances of the order of cm), the M(H ) curves below the anomaly are reversible. On the other hand, measurements in which the sample remains stationary, as in a Faraday magnetometer, clearly reveal the irreversibility, which can be traced in minor hysteresis loops. More experimental details can be found in Ref. [115]. Typical experimental results for R(H,T ) measured with a fixed transport current density J513.2 A cm 22 are presented in Fig. 5. We observe a distinct resistive anomaly in the mixed state well below the superconducting transition at Hc2 (T ). For R(H ) and increasing field, this anomaly first appears at the onset field H1 (T ). At another characteristic field H2↑ (T ), R(H ) drops below the sensitivity level (zero) and remains there up to the field H0 (T ) corresponding to the onset of the main superconducting transition (in subscripts, ↑ and ↓ represent increasing and decreasing field or temperature, respectively). With increasing temperature, the maximum resistance attained in the anomaly, R max (T ), increases and the drop of R(H ) near H2↑ (T ) becomes increasingly sharp. At the same time, the width of the field interval H0 (T )2H2↑ (T ), where R(H ) drops to zero, decreases and eventually vanishes for T $5.4 K, so that only a local minimum in R(H ) remains visible which can be traced up to T55.9 K. While in the temperature interval T $5.4 K, the R(H ) curves are completely reversible for increasing and decreasing H, the transition into the resistive state at H2 (T ) becomes hysteretic for T ,5.4 K with the width of this hysteresis increasing for decreasing

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Fig. 6. H–T phase diagram obtained from isothermal R(H ) measurements with J513.2 A cm 22 (open symbols) and magnetization curves M(H ) (solid symbols) showing a large resistive region in the mixed state (shaded). H90% (T ) corresponds to the field where R(H ) drops to 90% of its normal state value. Hc2 (T ) was determined from magnetization curves (Fig. 4). For a definition of the other characteristic fields, see text.

Fig. 5. Examples of R(H,T ) data measured using a fixed excitation current density of 13.2 A cm 22 . Note the onset of hysteresis at the transition into the resistive state as R(H,T ) drops to zero below the main superconducting transition. (a) R(H ) measured at different temperatures for increasing fields (solid symbols) and decreasing fields (open symbols). (b) R(T ) measured at different fields upon warming (solid symbols) after zero-field cooling (ZFC) and cooling (open symbols). The R(T ) curves measured upon warming and cooling in a field are identical. Note the lowtemperature instabilities observed upon warming for the highest field.

R(H ) drops to zero in the field interval H0 (T )...H2↑ (T ), the width of which increases with decreasing current. (Here, the sensitivity level defining zero is determined by our voltage resolution of |2 nV.) At the same time, hysteresis appears at H2↑ (T ); and for yet lower J, the resistive anomaly becomes undetectable, in complete analogy to the R(H,T ) and R(T,H ) measurements. Depending on temperature, the value of J max (T ) determines whether R(H ) drops c to zero for the lowest currents used in the measurements, and thus whether hysteresis is observed at H2↑ (T ). For our sensitivity level, the crossover, characterized by J max (T * )→0, occurs at T * 55.4 K. We want to emphasize, c however, that we observe a local minimum in R(H,T ) to temperatures as high as T55.9 K. From isothermal field sweeps similar to those presented in Fig. 5(a) performed

temperature. The anomalous behavior of the mixed-state resistance is quantitatively reproduced in the R(T ) measurements, with the characteristic fields Hn (T ) (n50,1,2) being replaced by the respective characteristic temperatures T n (H ). In addition, we observed severe thermal instabilities and frequent jumps of R(T ) in the temperature interval right above T 1 (H ) upon warming for fields m0 H $ 0.7 T. Fig. 6 summarizes the temperature dependences of the different characteristic fields obtained from R(H,T ) measurements with J513.2 A cm 22 . The resistive features strongly depend on the transport current density J. We investigated the influence of varying J on the R(H,J) curves measured at fixed temperature and observed that its effect is very similar to the changes caused by varying the temperature: For J . J max , where c J cmax is the maximum critical current density Jc in the peak of Jc (H,T ) (see Fig. 7 below), R(H ) remains finite throughout the entire field interval and the R(H ) curves are completely reversible. With J decreasing below J max (T ), c

Fig. 7. Field dependence of the critical current density Jc (H ) corresponding to a 5 nV voltage criterion at T54.51, 5.00, and 5.30 K. Solid (open) symbols indicate Jc values obtained for increasing (decreasing) H, and all lines are guides to the eye. The maximum current density in our experiment is J max ¯26 A cm 22 . The high field boundary of the peak in Jc (H ) corresponds to the (reversible) onset of the main superconducting transition.

M.B. Maple et al. / Journal of Alloys and Compounds 250 (1997) 585 – 595

for different transport current densities J, and employing a voltage criterion of 5 nV, we deduced the field dependences of the critical current density Jc (H ) by identifying Jc with the (fixed) J at the field H where the voltage reached the criterion threshold value. The results obtained at different temperatures are summarized in Fig. 7. Only for T5 5.30 K, were we able to achieve J . J max ¯6.5 A cm 22 , c max since our maximum J was limited to J ¯26 A cm 22 . (For higher temperatures, the voltage never dropped below the criterion value.) Note that we always observe hysteresis at the onset of the peak in Jc (H ) close to H2↑ (T ), and that for the lowest temperature there is also a slight hysteresis near the onset of the resistive anomaly at H1 . We also want to emphasize that the residual irreversibility DM observed in the magnetization curves in fields below the anomaly for T ,5.0–5.5 K is corroborated by the finite Jc values observed throughout the mixed state in the R( H,T, J) measurements. Thus, from our transport studies of the mixed state of polycrystalline CeRu 2 , we can confirm that the irreversible feature in M(H ) observed in the mixed state is indeed due to a peak effect in Jc (H ), which seems to change in character above T * 55.4 K. From our data however, we cannot decide whether the crossover temperature T * , where the peak critical current density J max vanishes c depends on the sensitivity level of the transport measurement and thus, whether a correlation with the temperature at which a possible critical point may be situated, is coincidental. On the other hand, the hysteretic behavior observed in both M(H ) and R(H,T ) for T ,T * is similar to the hysteretic features reported from M(H ) and magnetostriction measurements [102] as well as from the diamagnetic anomaly in the ac magnetic susceptibility x 9 [116]. This may be an indication that the transition that the FLL undergoes is of first order, which has been cited as evidence for the formation of the FFLO state. The results of our transport study on CeRu 2 are qualitatively very similar to those obtained for the layered superconductor 2H-NbSe 2 , which also exhibits a peak effect [117]. For the latter system, it has been proposed that the FLL undergoes a dynamic crossover (instead of a thermodynamic transition) from defective, plastic flow at low drives near Jc , to a coherent motion as the FLL heals at drives well above Jc [118]. While this seems consistent with our observations, the question whether the hysteretic transition seen in the present study is indeed of first order has to be answered by measurements of thermodynamic quantities.

Acknowledgments This research was supported by the U.S. Department of Energy under Grant No. DE FG03-86ER-45230 and the National Science Foundation under Grant No. NSF DMR94-08835.

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