Paramagnetism and Superconductivity in Eu0.7Sm0.3Ba2Cu3O7??

C 2004) Journal of Superconductivity: Incorporating Novel Magnetism, Vol. 17, No. 6, December 2004 (
DOI: 10.1007/s10948-004-0830-8

Paramagnetism and Superconductivity in Eu0.7Sm0.3Ba2Cu3O7−δ V. Sandu,1 S. Popa,1 D. Di Gioacchino,2 and P. Tripodi2,3 Received 1 July 2004; accepted 17 August 2004

Magnetic properties of sintered Eu0.7 Sm0.3 Ba2 Cu3 O7−δ were investigated both in dc and ac magnetic fields. The dc response reflects the interplay between the rare earth ion paramagnetic and the superconducting charge carrier subsystems, respectively. The harmonic susceptibilities exhibit special features: the second harmonic is anomalously high and the third harmonic in zero dc-field has reversed temperature dependence with respect to the theoretical models. The magnetic relaxation at low fields is monotonous and occurs as a two-stage relaxation, each stage obeying logarithmical time dependence with different rates. At high fields, the relaxation is nonmonotonous with a peak at intermediate time suggesting a temporary re-entrance of irreversibility when the flux-line density increases in the center of the sample because of the redistribution of the vortices toward that region. KEY WORDS: Eu0.7 Sm0.3 Ba2 Cu3 O7−δ ; magnetic susceptibility; magnetic relaxation; multiharmonic susceptibility.

1. INTRODUCTION

magnetic order set in only below 2 K [2,3]. At high temperature in an applied magnetic field, the R subsystem shows a paramagnetic response with a natural tendency of the R spins to align along the field. In contrast with the low temperature superconductors, there is no pair breaking in high-Tc cuprates produced by the exchange interaction between the conduction electrons and the localized f -shell spins of the R ions. This fact is the result of the large separation between the conducting CuO2 layers and the R ion relative to the small coherence length ξ of Cooper pairs in superconducting cuprates and very low f -shell radius of the R ions. Therefore, the R ions do not affect the superconductivity and their magnetic state is controlled barely by the crystalline electric field. In an applied magnetic field the copper and rare-earth ions behaves very differently. Due to its particular interaction with the mobile holes from CuO2 layers [4], the Cu ion subsystem, at optimally doping, is practically insensitive to moderately applied fields and only the R3+ subsystem is responsible for paramagnetism. Although at the scale ξ the effect of the R ions is less effective, at longer scale, of order

The compounds with more than one rare-earth element in the R site of RBa2 Cu3 O7−δ are still the subject of an active interest due to the possibility of the interplay between the paramagnetic moments corresponding to different oxidation states and Cooper pair system. The conduction band of RBa2 Cu3 O7−δ is primarily composed of Cu3d and O2p orbitals [1], with a negligible small contribution of the R-ions to the Fermi level. Therefore, the magnetic ordering of the Cu ions is sensitive to the charge carrier density, whereas the R ions remain rather unaffected. Moreover, due to the large distance between R sites their coupling is small, hence, save the long range 1 National

Institute of Materials Physics, Bucharest-Magurele, POB-MG-7, R-76900 Romania. 2 INFN-LNF, National Laboratory of Frascati, Via E. Fermi 40, 00044 Frascati, Italy. 3 H.E.R.A., Hydrogen Energy Research Agency, Corso della Republica 448, 00049 Velletri, Italy. 4 Present address: Department of Physics, Kent State University, Kent, OH 44242.

701 C 2004 Springer Science+Business Media, Inc. 0896-1107/04/1200-0701/0


702 of magnetic penetration length λL it become important. Therefore, the interest in the investigation of the mixed state in systems with paramagnetism and superconductivity coexist [5–9]. A complete picture of the behavior of these systems in magnetic field must involve both dc and ac measurements. Concernig the latter, a special attention was paid in the last decade to the high harmonics of the magnetic susceptibility, considered as a valuable source of information. However, by our knowledge, there is no report concerning the multiharmonic response of a superconducting RBa2 Cu3 O7−δ with R different of yttrium. Due to the sensitivity of the high harmonics to the field, we expect to find the fingerprint in their dependence on temperature and applied field. In our investigation, we have chosen a combination between two R ions, europium (Eu) and samarium (Sm) for the following reasons: (i) Eu3+ and Sm3+ have the closest ionic radii r among all rare ˚ therefore, earth elements with rSm − rEu = 0.013 A, no lattice distortions are expected when substituting each other; (ii) the multiplet structure of the electronic levels is comparable with thermal energy for both elements; (iii) both elements can substitute barium and, subsequently, create the same type of disorder, and; (iv) the increasing magnetic moment of Sm3+ at low temperature [10] compensates the saturation of the Eu3+ [11]. The response of this system was investigated both in dc and ac magnetic field. First, we analyze the dc behavior, which is better understood, and use the same as a reference for the multiharmonic ac data.

2. EXPERIMENTAL Eu0.7 Sm0.3 Ba2 Cu3 O7−δ polycrystalline samples were fabricated from reagent grade Eu2 O3 , Sm2 O3 , CuO, and BaCO3 by solid-state reaction at 950◦ C for 24 h in flowing oxygen. The reacted samples were powdered and sifted. The powder was pressed into rectangular bar-like pellets, which were sintered, in flowing oxygen at 936◦ C for 16 h. Finally, the samples were slowly cooled for several hours down to the room temperature. The critical temperature is 90 K, as obtained from dc and ac susceptibility (see Figs. 3a and 6a below), and resistivity measurements (data not shown). The structure, composition, and morphology of the samples were checked by scanning electron microscopy and exhibit good compactness with small pores and average grain sizes between 10

Sandu, Popa, Gioacchino, and Tripodi and 20 µm. The global electron dispersive spectroscopy (EDS) showed that all samples were essentially single phase with an average stoichiometry Eu0.82 Sm0.23 Ba1.95 Cu3 O7−δ . The slight excess of rare earth element and the deficit in barium could be the result of substitution of a small amount of Ba by R2+ ions. The substitution should be possible because the ionic radius of both Sm2+ and Eu2+ , 1.31 ˚ respectively, are slightly lower than Ba2+ and 1.27 A, ˚ radius (1.49 A). All the measurements reported later were made using standard techniques. The magnetic measurements, magnetization and dc-susceptibility, were measured using a Quantum Design SQUID magnetometer sweeping both temperature and magnetic field. The magnetization was measured from 2 to 86 K. The dc-susceptibility was measured both in zero-field-cooling (ZFC) regime, and field cooling (FC) regime, as the average on three successive measurements. The temperature was swept between 10 and 180 K at a constant magnetic field. The ac-susceptibilities including the higher harmonics were measured with a homemade susceptometer [12] based on pick-up double coils surrounded by a driven coil. The sample was mounted on a sapphire holder inserted in one of the pick-up coils. The temperature was measured with a platinum thermometer (PT100) in a good thermal contact with the samples. The whole assembly was cooled in ZFC, in a thermally controlled He gas flow cryostat provided with an 8 T superconducting magnet. The measurements have been done on sweeping the temperature with a rate of 0.3 K/min up to a temperature greater than the zero field critical temperature of the samples (i.e. between 65 and 110 K). The ac driving magnetic field had an amplitude of 6 × 104 T at a frequency of f = 1070 Hz. The dc magnetic field was in the range from 0 to 1 T. The induced signal has been measured with a multi-harmonic EG&G lock-in amplifier. Both ac and dc fields were applied parallel to longest size of the sample. Magnetic relaxation was measured in a dc-mode. A magnetic field higher than the full penetration field was applied at a constant temperature, and the time evolution of the magnetization was registered. After each set of data, the sample was warmed up above Tc and then cooled down to the new temperature. The initial time t = 0 was defined as the time of the first data acquisition after the field was stabilized. Therefore, a certain time delay of about 50 s was necessary to set up before starting the measurement.

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Fig. 1. Magnetization curve at 65 K. The dotted line is the equilibrium magnetization Meq . On the graph are marked the field value where relaxation measurements were performed (see Fig. 5). Inset: magnetization vs. applied field at 80 K (lower curve), and at 86 K (upper curve).

3. RESULTS AND DISCUSSION Figure 1 shows the dependence of the volume magnetization M versus applied dc field He at 65 K. The inset presents M–He curves at temperatures close to Tc . The hysteresis loop exhibits a counterclockwise rotation as compared with the YBa2 Cu3 O7 samples, which is typical when a paramagnetic R ion substitutes yttrium [7]. Consequently, at 65 K, the magnetization is positive for an applied field µ0 He > 2.09 T for the ascending magnetization M and recovers the negative values for µ0 He < 1.05 T on the descending branch M+ . The low field dip is sharp and the sharpness increases at higher T indicating a good homogeneity of the sample but with low bulk pinning. The reversible magnetization, + − , is linear at high field with an Meq (He ) ≡ M +M 2 increasing slope when T decreases; from 0.104 emu/ T cm3 at 86 K to 1.51 emu/T cm3 at 2 K (data not shown). This effect should be expected because of the increasing paramagnetic susceptibility at low temperature (see below). The intercept of the linear extrapolation of the high-field part of Meq is rather large (+8.57 emu/cm3 at 2 K), positive, and decreases with increasing T far from Tc . However, at higher temperatures it switches to negative values. Because of the asymmetry of the hysteresis loop, we checked the M versus He dependence for the existence of surface barriers. It is important to clarify this aspect

Fig. 2. The field dependence of the entry magnetization at low temperature. Inset: data for high temperature; the intermediate temperature T = 65 K is also presented. Solid lines connecting data are the linear fit in the appropriate coordinates.

because the even harmonics are dependent on this asymmetry. Following Burlachkov [13], the entry magnetization Men , for negligible bulk pinning, H2

should comply with the law Men ≈ Hpe , for He just above the first penetration field Hp . Figure 2 (and inset) shows that in our case the dependence is much slower and can be cast in a simple analytic form only for the limits of the measuring temperature range; 2 (T) for T  Tc (linear in namely, Men ≈ M0 (T) log HH e a semilog plot in Fig. 2), and Men ≈

3/2

H1

1/2

He

for T, 0.8Tc

(linear in a log-log plot, inset to Fig. 2). H1 , H2 , and M0 , are temperature-dependent constants. The fit at the lowest temperature extends practically up to 9 T. Besides, in that temperature range, the entire descending branch follows a law similar to the theoretical dependence of Meq . Subsequently, the surface barriers are less effective relative to bulk pinning in that temperature range. At high temperature, the strong asymmetry might be ascribed to the surface barrier but with appropriate modifications of the field dependence of the entry magnetization. An analytical description of the processes evolving in such a complex state is a rather difficult problem. Therefore, we will proceed to a qualitative

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picture based on the critical state model. In the presence of the pinning forces the average magnetization M is obtained from the relationship connecting the spatial average of the local induction B(r, H) and the applied field He as M = µ−1 0 B− He . The induction B can be derived as the solution of the Maxwell and material equations connecting the critical current density JC (B, T), paramagnetic susceptibility χp (He , T), and lower critical field Hc1 (T), with the appropriate border conditions. For a long cylinder of radius R with the axis parallel to the applied field, we have [7,14]: B(r) = µµ0 [He − m(H)Hc1 (T)] ± µ0 J c (r − R), (1a) J c (B, T) ≈ J c (B, 0)f (T) ≈ J c (0, 0)f (B) 
df T n , n ≥ 1; × 1− < 0 (1b) Tirr dB 
T (1c) Hc1 = Hc1 (0) 1 − Tc µ(H, T) = 1 + χp (H, T)

(1d)

The + (−) sign stand for the flux moving in (out) the sample; m(H), f (B), and χP (H, T) are slowly H dependent functions. The field dependence of the average magnetization, hence of the dc-susceptibility, is given by: M = χp (He , T)[He − m(He )Hcl (T)] − [m(He )Hcl (T) ± J c (He , 0)g(T)],

(2)

where g(T) collects all the factors resulting from the integration of Eqs. (1) preserving the same T-dependence as J c . The first term is always positive, m(H)Hcl  He , and accounts for the paramagnetic contribution whereas the last term is just the superconducting response of the system without paramagnetic impurities. The magnetization is negative as long as the second term prevails over the first one. At T lower than the irreversibility temperature, Tirr , g(T) > 0 and, increasing the applied field, the first term of Eq. (2) becomes dominant due to the weak H dependence of the other terms. There should be one point H+ (H− ) on each branch of the M versus He curve so that M+ (H+ ) = M− (H− ) = 0 (Fig. 1). However, H− (on the ascending branch) could be negative if the critical current is high enough (or the temperature too low). As expected, for T > Tirr , there is only one solution where M(H) = 0 and the magnetization is negative as long as He < Hirr

(see the inset to Fig. 1). For He Hcl , Eq. (2) reads: Meq ≈ χp (He , T)He − m(He )Hcl (T),

(3)

1 ln HHc 2 [15] is positive at low The term m(He ) ≈ 2k temperature (Hc2 He ) so that the positive intercept found at T  Tc might be explained only by the presence of some remnant magnetic moments (Fig. 2). The dc susceptibilities are shown in the Figs. 3a and 3b, for ZFC and FC regime, respectively. The critical temperature, as obtained from the derivative of χZFC , decreases from Tc = 90 K at µ0 H = 10−3 T to 81.85 K at 1.5 T. We used the derivative due to its higher capability to single out the setting in of the diamagnetic response within an increasing paramagnetic signal at high-applied field. Below Tc , we discerned three temperature ranges with distinct behavior of zero-field-susceptibility χZFC . Starting from low temperature, the susceptibility increases slowly on a large temperature range (approximately 30 K), follows a fast raise at higher temperatures, and slows down close to Tc . At moderate fields, the first range is strongly shrunk while the latter extends on a much larger temperature range starting from the knee at Tk . This crossover temperature Tk shifts with increasing He from Tk = 39 K at 0.1 T to 19 K at 1.5 T. At µ0 He = 2 T, the ZFC susceptibility changes the dependence. It is positive in the whole range of explored temperature but non-monotonous with a kink at the critical temperature Tc = 88 K and a minimum at Td = 60 K (see the inset of the Fig. 3a). FC susceptibility χFC , is also nonmonotonous below Tc (Fig. 3b). Specifically, it shows a very conspicuous beginning of the flux expulsion at Tc , reaches a deep at Td , and turns up to lower temperature. If the field is high enough, the positive value of χFC is recovered. At µ0 He = 2 T, the susceptibility remains positive in the whole range of temperature, even if displays the same functional dependence. Td shifts to higher value when the applied field increases. It is noteworthy that χZFC > χFC at low temperature. The dc susceptibility for T > Tc , χ(T > Tc ) ≡ χp , is reversible and exhibits a temperature dependence that agrees with Van Vleck theory of paramagnetism. In this temperature range, the contribution of the thermal population of the excited states, 7 Fj >0 of Eu3+ and 6 Hj >5/2 of Sm3+ , is important due to the small energetic gap, of order kB T, between these states and the ground state. We have obtained good fit of χp (insert to Fig. 3b) using a combination of the

Paramagnetism and Superconductivity in Eu0.7 Sm0.3 Ba2 Cu3 O7−δ

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Fig. 3. Temperature dependence of the dc-susceptibility at different applied fields. The arrows mark the crossover from the linear dependence, at high temperature, to the typical Meissner response: (a) zero-field cooled susceptibility. Inset: zoom of the encircled region; the line is guide for the eye; (b) field-cooled dc-susceptibility. Inset: the normal state susceptibility; the solid line is the fit with the Van Vleck model (Eq. 4).

free ion susceptibility of Eu3+ and Sm3 : χp = a1 [a2 χEu + (1 − a2 )χSm ]

(4)

with χEu,sm given by Eq. (23), Ref. [16]. The fitting parameters, as obtained with first three Van

Vleck and Curie terms, were a1 = 2.55 and a2 = 2.13. The fit provides an anomalous high weight of Sm, which is primarily due to the neglect of the contribution arising from the effect of the crystalline field [17,18].

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The behavior of magnetization, M versus H, and susceptibility, χdc versus T, reflect the presence of two contributions with opposite, hence competing, magnetic properties. One originates in the superconducting-pair subsystem and has a diamagnetic response with a negative susceptibility χs < 0 depending on the cooling regime (ZFC or FC), whereas the other one has a paramagnetic origin, hence positive susceptibility χp > 0. The examination of the susceptibility as a function of temperature is complex because the effects of the sample morphology are noticeable, mainly at low field. Equation (2) suggests that χ ≈ χp (He , T) + χ± s (He , T). The sample is built as a collection of superconducting grains that are supposed to be phase locked at very low fields and temperatures in ZFC regime. Hence, up to a certain temperature, a low field cannot penetrate the sample due to the screening currents flowing on the outer surface of the sample. In this temperature range the paramagnetic contribution should be zero because B = 0. Above that relatively high temperature (T > 0.87 Tc ), the grains are gradually disconnected and the field penetrates in-between them. Even in this state, the paramagnetic term is too low to be effective because only a negligible number of paramagnetic ions is located at the grain border. With the field already at their border and due to the fast decrease of Hc2 , the grains can be easily penetrated by the field for a further increase of T. Close to Tc , χZFC will slow down its increase due to the flattening of the flux profile, once the center of the grains is reached [14]. At small He , the magnetization is dominated by superconductivity and χ ≈ χ± s (H, T) < 0 because χp  1. Increasing the applied field, the disconnection of the grains occurs at low temperature and the conspicuous kink at Tp corresponds to the intragranular full penetration field. The temperature dependence of χ is governed by the interplay of χp , Hc1 and J c and should reach a minimum provided dχ that dT |Td = 0. Practically, this condition reads:         dχp   = 1 m(H)Hcl (0) ±  dJ c     dT  H Tc dT  e

(5)

The right hand member of Eq. (3) should have a negative slope decreasing with increasing He in the ZFC regime (∝ −He−α , α > 1) while in the FC regime the slope is always positive (∝ +He−α ). Thus, in the case of ZFC regime, Eq. (5) has solution only if  field is high enough to flatten the slope of  dJthe  c  versus T curve and hence to intersect the left dT

Fig. 4. Magnetic relaxation curves at 65 K at µ0 He = 0.3, 1.5, and 2.0 T. The letter corresponding to each field is also marked on Fig. 1. Vertical arrows point to the crossover between bulk and surface dominated relaxation. The data for µ0 He = 2 T are connected by spline function.

dχ

hand function | dTp | whose slope is always negative. In the case of FC regime, there should be always an intercept between the left hand and the right hand functions of the relationship (5) due to the positive slope of latter. This is indeed the situation as reflected in the experimental data, Figs. 3a and 3b. In the followings, we address the issue of time dependence of the irreversible magnetization Mirr = |M − Meq |. Figure 4 exhibits the relaxation curves for different magnetic field. In order to compare with the magnetization M(H) curve at 65 K (Fig. 1), where the effect of the magnetic ions is more conspicuous, we measured the Mirr (t) at the following fields marked also on Fig. 1: (a) µ0 He = 0.3 T, where both M− and M+ are negative and the second peak was not reached yet; (b) µ0 He = 1.5 T, where M− < 0, Meq < 0 but He beyond the second peak; (c) and µ0 He = 2 T, where Meq > 0. In a semilog plot, Mirr (t) consists two linear segments each corresponding to a specific pinning processes. Conventionally, the irreversible magnetization can be divided into two contributions in the presence of surface barriers [13]. One part mirrors the surface effects resulting from the vortex-image interaction at the sample edge while the other is related to the bulk irreversibility. Therefore, the relaxation is a two-step process, each contribution dominating in a certain period and both obeying a logarithmic

Paramagnetism and Superconductivity in Eu0.7 Sm0.3 Ba2 Cu3 O7−δ time dependence, Mirr ∝ M0i log(t0 τ/t). First relaxes in the contribution with the lowest pinning energy and when that is over, the second part starts to relax. For the first two fields (0.3 and 1.5 T), both relaxMirr ) increase with increasing field ation rates (− d log d log t due to the reduction of the activation energy, yet these fields are located on different positions relative to the peak field. The duration length of the first period shrinks with increasing field for the same reason. The most striking effect is the relaxation of Mirr (t) at µ0 He = 2 T which is nonmonotonous. In the very early stages, it decreases faster than previous ones following the general trend but after t = 200 s starts to increase, reaches a maximum at t = 850 s, and finally recovers the initial decreasing trend. A tentative explanation is as follows: in the first stage relax in the surface magnetization is observed, whereas the bulk irreversible magnetization starts relaxing after the former is exhausted. This means that the gradient of density of the flux lines is practically constant and high (∝ µ0 j c ) in the first stage, and the paramagnetic moments falling in the vortex area, hence susceptible to be aligned along the field, are almost those ones located to the sample edge. As the flux gradient decreases, the concentration of flux lines increases toward the center of the sample/grains and more and more spins are incorporated within vortices. Therefore, the rate of spin flip increases inducing an extra current within sample and increasing temporarily the irreversibility. However, these currents decay and for long enough time Mirr restores the natural tendency of decrease toward Meq . A further insight in the behavior of the system regards the vortex dynamic. The most valuable information is provided by ac-susceptibility, fundamental and higher harmonics. In this kind of investigation, the vortices are submitted to a driving force exerted by the currents induced by the timedependent magnetic field. The processes are investigated at a time scale of order t0 = ν−1 , where ν is the frequency of the ac field. The real part of the fundamental harmonic χ1 , relates to the screening of the ac-magnetic field impinging into the sample whereas the imaginary part χ1 is proportional to the dissipation related to the vortex motion. The higher harmonics are extremely sensitive to the magnetic structure (χ2 ) and those flux-diffusion regimes where the E–j relationship turns out to be nonlinear (χ3 ). Actually, even harmonics are completely absent when the excitation ac field is perfectly sinusoidal and the critical current density is field independent [19,20].

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Fig. 5. Temperature dependence of the real part of the first three harmonics of ac-susceptibility: (a) zero-applied magnetic field; (b) the evolution of the third harmonic χ3 with increasing dc-field µ0 H0 = 0; 0.002; 0.01; 0.1, and 1 T.

In Figs. 5a and 5b, are shown the temperature dependences of the real parts χn of the first three harmonics (n = 1, 2, 3) of the ac-susceptibilities versus temperature. In zero applied magnetic field, all χn (Fig. 5a) show an onset temperature of 90 K in agreement with the dc results. The fundamental harmonic is typical for HTS pollycrystals but the higher harmonics exhibits some special features. First, the second harmonics is slightly higher than χ3 ; second, both have a small anomaly at Tg = 89.5 K (a dip for χ2 and a step for χ3 ) and a large dip at a lower temperature (Td2 (0) = 84.5 K and Td3 (0) = 85.6 K). Increasing the dc-field (see Fig. 5b for χ3 ), the amplitude of all harmonics decreases, the small dip of χ2 becomes a step, the step of χ3 splits into two sub-steps, and all the characteristic temperatures shifts to lower values. The imaginary parts χn are shown in Fig. 6 (a to e). At zero field (Fig. 6a), χ1 has a distinct peak at

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Fig. 6. Temperature dependence of the imaginary part of the first three harmonics of ac-susceptibility: (a) zero dc-field; (b) µ0 He = 0.01 T; (c) µ0 He = 0.1 T; (d) µ0 He = 1 T.

Tpi = 83.5 K, usually related to the sample granularity, and a small shoulder at 89.5 K of intragranular origin. The higher harmonics exhibit a series of dips and peaks that we use to separate different regimes of loss, hence of pinning. Figures 6b–6e, exhibits the evolutions of the pinning regimes with increasing the dc-field up to µ0 He =1 T. Both peaks and dips rapidly shifts to lower temperatures and broadens with increasing field. The intragranular response in χ1 is visible just as a small shoulder close to Tc . Increasing the field, it shifts slowly to lower temperatures (from 89.5 K at zero field to 87.8 K at 0.01 T. At µ0 He =1 T, two peaks at Tg1 = 81.3 and Tg2 = 83.5 K reflecting intragrain inhomogeneities are well separated. The coincidence of the small dip in χ2 and χ3 at 89.5 K with the shoulder of χ1 suggests their connection with the intragranular processes.

In the critical state model, it is considered that the peak in χ1 occurs when the flux reaches the center of the sample. In the presence of the paramagnetic ions, the position of the peaks, as obtained from Eq. (2a), is shifted to a lower temperature than in the absence of R ions, 6/16/04Tpi (He ) ≈ Tirr (He )[1 − (1+χp )(He +ho ) 1 ] n . Here, D Ri , (T, H) R is the size of the Ri (He )J c (0,0)f (B) largest subsystem still showing superconducting coherence for a given T. At low temperature, R is right to the sample radius whereas close to Tc it is the average grain size. Due to the factor 1 + χp , Tpi decreases slightly faster with increasing He when paramagnetic f (B) irr < 0 and ddH < 0). ions are present ( dT dHe e The high amplitude of the dips of χ2 implies either the presence of an important internal field or the existence of surface barriers. It is to note that critical state model predicts a similar negative dip in χ3

Paramagnetism and Superconductivity in Eu0.7 Sm0.3 Ba2 Cu3 O7−δ when He 0 [21]. Significant even harmonics are expected for strong dependence of J c versus B, asymmetric hysteresis loop, and when the amplitude of the ac field is of the same order the applied dc field. Due to the presence of the paramagnetic moments, even small internal fields can be enhanced up to values comparative with the ac field (6 G). The existence of an internal field is suggested by the analysis of the field dependence of Meq . Because it is not plausible a spontaneous ordering of the paramagnetic ions, the remnant field may result during the cooling process in the earth field enhanced by the paramagnetic factor (1 + χp ). Other cause, as the paramagnetic orbits [20], is possible but we could not discriminate yet. The fast reduction of χ2 with the dc field hints at the strong dependence of the critical current density on the magnetic field, as already have been suggested by the analysis of the dc susceptibility. Indeed, for Hdc Hac , J c (Hac + Hdc ) ≈ J c (Hdc ). Hence, J c is practically constant during a sub-loop sweeping by Hac , and Bean model, which predict χ2n = 0, is applicative. Nevertheless, the extreme asymmetry of the M versus He curves hints at the presence of surface barriers (insert to Fig. 1) at least at high temperature where the bulk pinning is negligible. The third harmonic shows very interesting features which are in a strong contradiction with the critical state models [19] that predict positive values for χ3 except the case when a small external field He is applied. When dynamical phenomena are considered, negative values are present [23–25]. In our case χ3 is negative in the whole range of investigated temperatures and fields. The imaginary part also disagrees with the critical models. Indeed, it must be negative at high temperatures and positive at lower temperatures. Figure 5 shows that the process is reversed except the intragrain signal at zero field. The contribution of the dynamic processes can be identified by comparison with the simulations of different models [24]. At low temperatures, T < Tp , the creep process must be dominant while above the peak temperature the fingerprint of the flux flow and thermally-activated-flux flow (TAFF) could be recognized mainly in χ3 . Increasing the field, an enhancement of the intragranular response is observed together with the repositioning to lower temperatures of all structure. This is a consequence of the reB0 duction of the pinning energy (Up ∝ |B|+B ) in field 0 that enhances both the creep and TAFF processes and extends the temperature range where Up (B) ≤ kBT. It is noteworthy the absence of any double peaked structure in χ3 at µ0 H = 1 T which suggests

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that the peak at 81.3 K in χ1 is due to a normal or magnetic phase loss. In conclusion, the magnetic response of sintered Eu0.7 Sm0.3 Ba2 Cu3 O7−δ in both static and variable magnetic field is the result of the superposition of the properties of two coexisting subsystems, which reacts differently to the magnetic field: the rare-earth ions that line up along the field and provide a paramagnetic response, and the subsystem of charge carriers that, below a critical temperature, displays superconductivity. Therefore, the general response is paramagnetic above the critical temperature, but reflecting the properties of the rare earths through the Van Vleck paramagnetism, and diamagnetic below Tc with a field and temperature dependent paramagnetic contribution. At low fields, the diamagnetic effect is dominant and the dc susceptibility is negative. χdc starts to increase below Td < Tc if the system is cooled down in magnetic field. At high fields, the paramagnetism dominates even if just below Tc the diamagnetism of the superconducting subsystem generates a decrease of the χdc . Beside these effects, some features point out the existence of a mixture of remnant magnetic moments and surface barriers. Therefore, ac susceptibilities and particularly the high harmonics exhibit anomalous responses. The presence of the paramagnetic ions affects the relaxation at high fields (high vortex concentration) when the current density increases temporarily most likely due to the turning over the spins along the field. ACKNOWLEDGMENT The research was performed in the framework of the TARI contract HPRI-CT-1999-00088 at the INFN-LNF Frascati and CERES 78 of the Romanian MEC. We would like to thank to Dr. Paolo Laurelli and Dr. Sergio Bertolucci for the special support. REFERENCES 1. S. Masida, J. Yu, A. J. Freeman, and D. D. Koelling, Phys. Lett. 122, 198 (1987). 2. T. Chattopadhyay, Phys. Rev. B 38, 838 (1988). 3. J. W. Lynn (ed), High Temperature Superconductors, Chapter 8 (Springer, New York, 1990). 4. H. Zhou, C. L. Seaman, Y. Dalicaouch, B. W. Lee, K. N. Yang, R. R. Hake, and M. B. Maple, Physica C 152, 321–328 (1988). 5. H. B. Tang, Y. Ren, Y. L. Liu, Q. W. Yan, and X. Y. Shao, Appl. Phys. Lett. 53, 1007 (1988). 6. J. D. Livingstone, H. R. Hart Jr., and W. P. Wolf, J. Appl. Phys. 64, 5806 (1988).

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