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Dimensional crossover and peak effect in a superconducting Pr1.85Ce0.15CuO4-y single crystal
PHYSICA ELSEVIER
Physica C 273 (1997) 268-274
Dimensional crossover and peak effect in a superconducting Prl.85Ce0.15CuO4_y single crystal M.C. de Andrade a, G. Triscone a, M.B. Maple a, S. Spagna b, j. Diederichs b, R.E. Sager u a Department of Physics and lnstitute Jbr Pure arm Applied Physical Sciences, University of California, San Diego, La Jolla, CA 92093-0319, USA b Quantum Design Inc., San Diego, CA 92121, USA
Received 1 October 1996; revised manuscript received 1 November 1996
Abstract
Magnetic measurements were performed on a Prl.85Ceo.15CuO4_y single crystal with Tc = 22.5 K in magnetic fields H applied parallel to the tetragonal c-axis (H]lc). An anomaly in the magnetic hysteresis loop that is reminiscent of a peak effect is observed. The anomaly occurs at a nearly temperature independent crossover field Hcr= 230 Oe in the reduced temperature t = T I T c region 0.75 < t < 0.9 and completely disappears for t < 0.75. The irreversibility line follows a power law of the form Hirr(T)ot (1 - t ) 2 in the regime 0.1 < t < 0.9. The lower critical magnetic field Hcl,c(T) was estimated from the first penetration of flux at the border between the Meissner state and the mixed state. A quantitative low temperature magnetic phase diagram based upon these measurements is presented. Keywords: Peak effect; Magnetization; Single crystals; Electron-doped superconductors
1. I n t r o d u c t i o n A large body of experimental and theoretical research has revealed the presence of a number of different states of the vortex ensemble in the mixed state of high temperature superconductors. Although the main features of the vortex phase diagram now seem to be well established, the microscopic origins of the vortex phases and phenomena constitute one of the most challenging problems in this field. An important feature of the magnetic phase diagram is the irreversibility line Hirr(T) [1-6] which lies below the mean field second order phase transition at the upper critical field Hc2(T) and separates regions of strong vortex pinning (Jc 4: 0" lower temperatures and fields) and one with vanishing pinning (Jc = 0:
higher temperatures and fields). In addition, thermal fluctuations can cause the flux line lattice (FLL) to melt [7-1 l] in the high temperature region. The FLL that forms in clean samples of the highly anisotropic cuprates consists of quasi two-dimensional (2D) " p a n c a k e " vortices which reside in the CuO 2 planes and are Josephson-coupled to vortices in neighboring CuO 2 planes. With increasing magnetic field, the FLL is predicted to undergo a dimensional crossover from three-dimensional (3D) behavior with strong interplanar coupling between the pancake vortices to a 2D regime where the 2D FLL of pancake vortices within each layer is independent of those in the adjacent sheets. The pancake vortices can also experience a complete loss of correlation when they are decoupled [12-14]. It has also been proposed that
0921-4534/96/$17.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0921-4534(96)00634-X
M.C. de Andrade et al./Physica C 273 (1997) 268-274
vortex lines in a bulk superconductor with point disorder should go through a second order phase transition and freeze into a vortex glass phase at low temperatures [15-17]. Consistent results seem to provide convincing evidence for the existence of the vortex glass transition [18-24]. Magnetization measurements on certain high temperature cuprate superconductors have uncovered a striking peak in the irreversible part of the magnetic hysteresis loop. Materials in which this peak has been observed include the highly anisotropic Bi2Sr2CaCu2Ox (Bi-2212) superconductors [3,2527] as well as the less anisotropic YBa2Cu30 7 superconductors [28]. As far as we know, no systematic study of magnetic hysteresis loops of electron-doped superconductors of the type Ln2_xMxCuO4_y (Ln = Pr, Nd, Sm, Eu; M = Ce, Th) has heretofore been undertaken. The much lower values of the superconducting critical temperature Tc and, hence, lower values of the upper critical field H~2(T= 0) of the Ln 2- xM xCuO4_ r electron-doped cuprate superconductors, allow easier access to the low temperaturehigh field regime of the magnetic phase diagram making these materials good candidates for investigating vortex phases and phenomena. In this paper, we report measurements of isothermal magnetic hysteresis loops on a single crystal of the electron-doped superconductor PrL85Ce0.15CuO4_y. We have observed a peak in the hysteretic magnetization curve that is qualitatively similar to the peak observed in the magnetization curve of Bi-2212 samples, suggesting that the anomalies in both materials arise from a common origin. The measurements also yielded the irreversibility line Hirr(T), which can be described by a single power law throughout the entire temperature range of the measurements 0.1 < T / T c < 0.9, an estimate of the lower critical field Hcj(T), and a quantitative low temperature magnetic phase diagram.
2. Experimental details Single crystals of Prl.85Ce0.15CuO4_y were grown using a self-flux method as described elsewhere [29]. The crystals were annealed in an ultra-high purity
269
argon atmosphere at 1000°C for 48 hours in order to reduce the oxygen concentration to its near optimum value. A 0.291 mg sample in the shape of a parallelepiped of dimensions 1 × 1.3 X 0.05 mm 3 was selected for the magnetic investigation. The high quality of the sample was inferred from the high superconducting transition temperature Tc ~ 22.5 K and narrow width (AT~ = 0.9 K) observed in ac magnetic susceptibility measurements. The shielding zero-field-cooling (ZFC) susceptibility was corrected with a demagnetization factor D a = 0.88 in order to obtain consistency with perfect screening at low temperature; XvM/(1 --4"n'Da XvM) = - 1 / 4 ~ (CGS units) where )(vM is the measured volume magnetic susceptibility. The difference between D a and the demagnetization factor D m -- 0.93 estimated from the sample dimensions is very small indicating the bulk superconducting nature of the single crystal. The magnetization measurements were performed with the applied magnetic field H parallel to the c-axis of the crystal ( H l[c) using commercial SQUID magnetometers (Quantum Design MPMS-l, MPMS5 and MPMS-7) in magnetic fields up to 7 T. In order to improve the signal to noise ratio, for some of the measurements, we used a recently developed Reciprocating Sample Option (RSO) technique [30] which minimizes spurious induction effects when moving the sample in an inhomogeneous magnetic field. A comparison with magnetization measurements made with a conventional small dc scan length (3 cm) revealed that the data obtained using the RSO technique have a much better signal/noise ratio. Because our investigation of the magnetic phase diagram does not require absolute values of the magnetization, we did not take into account corrections arising from the sample holder susceptibility. The hysteresis loops M ( H ) were obtained after cooling the sample in zero field to the desired temperature. The measurements were performed in the temperature range 2 <_ T < 23 K. The magnetization loops were then traced in the RSO mode while increasing/decreasing the magnetic field in small steps (_< 10 Oe). The low field M ( H ) data used for the Hcl.c(T) determination were obtained using the low field MPMS-1 magnetometer. The measurements were started after ZFC and the scan length was set at 3 cm.
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M.C. de Andrade et al./Physica C 273 (1997) 268-274
3. Results and discussion Shown in Fig. 1 are plots of the irreversible part of the isothermal magnetization. The M(H) curves exhibit a peak which can be characterized by three main features: the peak (a) has a weak temperature dependence, (b) occurs for low values of the applied field, and (c) disappears for temperatures lower than T = 17.5 K. It is interesting to note that these three characteristics are also present in other high temperature superconductors with comparableanisotropy such as Bi-2212. In these strongly anisotropic cuprate superconductors, the anomalous peak observed in the magnetization curves [3,25-27] is also nearly inde0.4
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pendent of temperature, occurs at low fields, and disappears for lower temperatures. In addition, the peak anomaly in the magnetization loops of PrL85Ce0.~sCUQ_y is quite different from that observed in similar measurements on the less anisotropic superconductor YBa2Cu30 7_ ~ [28]. For the latter material, the anomaly in the irreversible magnetization curves, often referred to as "fish tail" effect, consists of an anomalous increase in the irreversible magnetization on increasing magnetic field. In this case, a strong temperature dependence is observed, and the peak occurs in much higher applied magnetic fields and does not disappear at lower temperatures. In addition, this "fish tail" can be reversibly removed using an appropriate annealing treatment [31]. Therefore, it seems reasonable to conclude that the origin of the peak in the electrondoped cuprate is the same as the bismuth based cuprates. One explanation for the rapid decrease of the irreversible magnetization with increasing temperature in the highly anisotropic Josephson-coupled Bi2212 superconductors is the decoupling of a 3D vortex lattice into a 2D array of pancake vortices. This hypothesis is supported by results of recent IxSR [32-34] and neutron diffraction [35] experiments which reveal a 3D vortex lattice that disappears above the temperature independent field Her. The qualitative similarity of our results with those in the Bi-2212 materials suggests that the peak in M ( H ) may be due to a dimensional crossover of the vortex lattice. According to Glazman and Koshelev [ 14], the crossover field should occur at
1
700
H (Oe) Fig. I. Magnetic hysteresis curves at selected temperatures for a Prl.ssCeo ]sCuO4_y single crystal. The data were divided (16 K, 17.5 K) or multiplied (19 K, 20 K) by factors of 2.5, 1.5 or 1.5 respectively, so that they fit in the same plot. The shaded region defines the crossover field Her above which a drop in the magnetization is observed in the temperature range 16 < T < 20 K.
where S is the interlayer distance, 3, is the anisotropy parameter, and ~bo is the flux quantum. Using S = 12 ,~ for Prl.85Ce0.15CuOa_y obtained from Xray diffraction [36,37], one obtains "y--450. This value is comparable to Y--400 estimated for electron-doped Nd2_aCexCuO4_y single crystals from analysis of the dc magnetic susceptibility [38]. However, this value is markedly larger than y--- 4 previously derived from magnetization measurements on grain-aligned specimens of Sm 1.85Ce0.15CuO4_y [39]
M.C. de Andrade et al./Physica C 273 (1997)268-274 using the Hao-Clem model [40]. We do not presently understand the reason for this discrepancy. From the above analysis, we speculate that large anisotropy and, in turn, a dimensional crossover, is responsible for the peak in the magnetization loop of the electron-doped superconductors as well as the bismuth based superconductors. The absence of a peak for temperatures below 16 K could be an indication of a more continuous character of the dimensional crossover in this temperature range. More recently, a theory providing a quantitative description of the elastic vortex lattice in the presence of point disorder was developed [41]. The main prediction of this theory is the existence of a low field/weak disorder "Bragg glass phase" which, upon raising the field, should undergo a transition into another phase which could be a pinned liquid or another type of glass (e.g., vortex glass). In this picture, as the magnetic field increases, the effective disorder also increases, driving the Bragg glass through this transition to a different phase. The Bragg glass is destroyed due to the increase of the effective disorder. The observed peak in M ( H ) in our experiments could be interpreted from this viewpoint: upon increasing the field (disorder), the system shifts from a weak disorder regime to a highly disordered one. In this case, the peak marks the transition from the Bragg glass to another vortex phase. A detailed investigation of this possibility is now currently underway. We have also extracted the temperature dependence of the irreversibility line Hirr(T) from the magnetic hysteresis loops. We define the irreversibility field Hir~ as the field where the difference between the values of the magnetization for increasing and decreasing fields begins to deviate from zero within the accuracy of the experiment ( _ 1 0 - 6 emu). We find that the temperature dependence of the irreversibility line H~r(T) can be described by the power law,
Hirr(T)
=
H o 1 - ~c
'
(2)
271
crystals of Prl.85Ce0.15CuO4_y [42]. However, investigations [4,27] of Bi-2212 superconductors show a change of the irreversibility line from a power law in the 3D vortex regime close to T~ to an exponential form Hitrot exp(Eo/kBT) in the 2D vortex regime at lower temperatures. The absence of exponential behavior at low temperature in the case of Pr~.85Ce0.15CuO4_y could be due to the inherent disorder of the electron-doped system associated with both oxygen vacancies and substitutional Ce [43,44]. An understanding of sample inhomogeneities is important for the interpretation of the physical properties of superconductors in the mixed state. It has been shown that the irreversibility line can be sample dependent in the electron-doped Lnz_xMxCuO4_y superconductors, possibly due to changes in oxygen vacancy a n d / o r Ce concentrations [29]. Inhomogeneities could place the electron-doped system in the dirty limit where a power law behavior of H~r~(T) at low temperatures and high fields has previously been observed [5,39]. It has also been reported that close to Tc, the irreversibility line seems to coincide with the melting of the FLL and can be related to the presence of barriers at the sample surfaces [45]. In this situation, the field distribution due to demagnetization effects [46] and the presence of defects within the sample would cause the melting of the FLL to have a more continuous character, making it difficult to track the onset of the melting phase transition. Furthermore, sufficiently close to Tc, the diamagnetic response of the sample is within the noise level of the magnetometers, so it is very difficult to extract the irreversibility field. Therefore, we are unable to determine both the behavior of the irreversibility line as well as the possible melting transition of the 3D vortex lattice in the temperature and field range close to T~ for the PrL85Ce0.lsCuO4_y single crystal. The lower critical field for Hllc, ncl.c, was estimated from the first penetration of flux at the border between the Meissner state and the mixed state at a field Hin(T) ,
/-/ex,(r)
Hc'(T)--nin(r)--- (1-Oa)' with H o = 3 7 kOe in the range 0 . 1 < T / T c<_0.9. The temperature dependence of the irreversibility line is in agreement with that inferred from recent magnetoresistance measurements on other single
(3)
where D a = 0.88 and He, t is the applied magnetic field. The penetration of flux appears as a deviation from linearity in the M ( H ) curves at low field.
272
M.C. de Andrade et al./Physica C 273 (1997) 268-274
10 s
Naturally, this determination depends on the accuracy of the demagnetization factor. Shown in Fig. 2 a are M versus H data at selected temperatures, and in Fig. 2b, the deviation A M from perfect diamagnetism versus H data, based on the data in Fig. 2a, for PrL85Ce0.jsCuO4_ y.
•
Ha ~(T)
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IrreversibleRegion
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17.5K 16.25K -20
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200
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400
600
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800
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.
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1000
Hin(Oe)
101 0
, 5
~ 10
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~ m~ l mx~
~ 15
J 20
25
T(K) Fig. 3. Magnetic field H - temperature T phase diagram for a Prl.s~Ceo.15CuOa_y single crystal with Tc = 22.5 K. The solid lines represent fits of the data to theoretical expressions as described in the text.
4
The magnetic phase diagram in Fig. 3 summarizes all of the results of this investigation. The line representing Hirr(T) in Fig. 3 is a fit of Eq. (2) to the data. The line depicting Hcl,c(T) was obtained using the expression H¢l.c(T) 0 0
200
400
600
800
1000
H,.(Oe) Fig. 2. (a) Magnetization as a function of the internal magnetic field, Hin, for selected temperatures. The plot shows the deviation from linear behavior (perfect screening, dashed line) for each temperature. (b) Difference between the measured magnetization and the linear magnetization (perfect screening), A M, for selected temperatures as a function of the applied magnetic field. The value for the lower critical magnetic field Hc~.c was estimated as the field where A M starts to deviate from zero.
~o ln(h~h(T ) 4"n"[ Aab(T)] 2
/~dpo/2ZrHc2,c(Y ) ),
(4)
The upper critical field Hc2.c(0)= 100 kOe was estimated from magnetoresistance measurements on a Prl.ssCe0.nsCuOa_y single crystal [42]. Assuming the WHH approximation [47] for Hcz(T) and a parabolic temperature dependence for the thermodynamic critical field He(T) [48], we obtain for the penetration depth in the ab plane, hob(0) -- 1500 A.
M.C. de Andrade et al./Physica C 273 (1997) 268-274
4. Summary Isothermal magnetization loop measurements on a Prl.85Ce0.15CuO4_y single crystal reveal the existence of a peak effect which, to our knowledge, has not heretofore been observed in electron-doped superconductors. The peak anomaly in Prl.85Ce0AsCuOa_y is qualitatively similar to that previously observed in Bi-2212 samples. This suggests that the peak effect in electron-doped superconductors and Bi-2212 superconductors have a common origin, namely, high anisotropy. The peak could be a manifestation of a dimensional crossover. Analysis of the data in terms of a transition from a 3D vortex lattice to quasi 2D pancake vortices yielded an estimate for the anisotropy ratio, y = 450. However, the microscopic origin of this peak and its relation to the FLL or Josephson vortex lattice remains unclear at this point. Our results for the irreversibility line show that the irreversibility line follows a single power law, in the low temperature regime. Whether there is a change in the character of the FLL in the low temperature- high field regime remains to be established by further investigations.
Acknowledgements Research at UCSD was supported by the US Department of Energy under Grant No. DE-FG0386ER-45230. G.T. acknowledged support from the Swiss National Science Foundation. We thank S. Moehlecke and B. Revaz for fruitful discussions.
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[34] M. Inui and D.R. Harshman, Phys. Rev. B 47 (1993) ! 2205. [35] R. Cubitt, E.M. Forgan, G. Yang, S.L. Lee, D. McK. Paul, H.A. Mook, M. Yethiraj, P.H. Kes, T.W. Li, A.A. Menovsky, Z. Tamawski and K. Mortensen, Nature 365 (1993) 407. [36] T.C. Huang, E. Moran, A.I. Nazzal and J.B. Torrance, Physica C 158 (1989) 148. [37] Y. Dalichaouch, M.C. de Andrade and M.B. Maple, Physica C 218 (1993) 309. [38] F. Zuo, S. Khizroev, X. Jiang, J.L. Peng and R.L. Greene, Phys. Rev. Lett. 72 (1994) 1746. [39] C.C. Almasan, S.H. Han, E.A. Early, B.W. Lee, C.L. Seaman and M.B. Maple, Phys. Rev. B 45 (1992) 1056. [40] Z. Hao, J.R. Clem, M.W. McEIfresh, L. Civale, A.P. Malozemoff and F. Holtzberg, Phys. Rev. B 43 (1991) 2844. [41] T. Giamarehi and P. Le Doussal, Phys. Rev. B 52 (1995) 1242.
[42] M.C. de Andrade, J. Herrmann, R.P. Dickey, G. Triscone and M.B. Maple, to be published. [43] A.R. Drews, M.S. Osofsky, H.A. Hoff, J.L. Peng, Z.Y. Li, R.L. Greene and T.A. Vanderah, Physica C 200 (1992) 122. [44] P. Lightfoot, D.R. Richards, B. Dabrowski, D.G. Hinks, S. Pei, D.T. Marx, A.W. Mitchell, Y. Zheng and J.D. Jorgensen Physica C 168 (1990) 627. [45] E. Zeldov, D. Majer, M. Konczykowski, V.B. Geshkenbein, V.M. Vinokur and H. Shtrikman, Nature 375 (1995) 373. [46] D. Majer, E. Zeldov and H. Shtrikman, to be published. [47] N.R. Werthamer, E. Helfand and P.C. Hohenberg, Phys. Rev. B 147 (1966) 295. [48] T.P. Orlando and K.A. Delin, Foundations of Applied Superconductivity (Addison-Wesley, Reading, 1991) p. 289.
Physica C 273 (1997) 268-274
Dimensional crossover and peak effect in a superconducting Prl.85Ce0.15CuO4_y single crystal M.C. de Andrade a, G. Triscone a, M.B. Maple a, S. Spagna b, j. Diederichs b, R.E. Sager u a Department of Physics and lnstitute Jbr Pure arm Applied Physical Sciences, University of California, San Diego, La Jolla, CA 92093-0319, USA b Quantum Design Inc., San Diego, CA 92121, USA
Received 1 October 1996; revised manuscript received 1 November 1996
Abstract
Magnetic measurements were performed on a Prl.85Ceo.15CuO4_y single crystal with Tc = 22.5 K in magnetic fields H applied parallel to the tetragonal c-axis (H]lc). An anomaly in the magnetic hysteresis loop that is reminiscent of a peak effect is observed. The anomaly occurs at a nearly temperature independent crossover field Hcr= 230 Oe in the reduced temperature t = T I T c region 0.75 < t < 0.9 and completely disappears for t < 0.75. The irreversibility line follows a power law of the form Hirr(T)ot (1 - t ) 2 in the regime 0.1 < t < 0.9. The lower critical magnetic field Hcl,c(T) was estimated from the first penetration of flux at the border between the Meissner state and the mixed state. A quantitative low temperature magnetic phase diagram based upon these measurements is presented. Keywords: Peak effect; Magnetization; Single crystals; Electron-doped superconductors
1. I n t r o d u c t i o n A large body of experimental and theoretical research has revealed the presence of a number of different states of the vortex ensemble in the mixed state of high temperature superconductors. Although the main features of the vortex phase diagram now seem to be well established, the microscopic origins of the vortex phases and phenomena constitute one of the most challenging problems in this field. An important feature of the magnetic phase diagram is the irreversibility line Hirr(T) [1-6] which lies below the mean field second order phase transition at the upper critical field Hc2(T) and separates regions of strong vortex pinning (Jc 4: 0" lower temperatures and fields) and one with vanishing pinning (Jc = 0:
higher temperatures and fields). In addition, thermal fluctuations can cause the flux line lattice (FLL) to melt [7-1 l] in the high temperature region. The FLL that forms in clean samples of the highly anisotropic cuprates consists of quasi two-dimensional (2D) " p a n c a k e " vortices which reside in the CuO 2 planes and are Josephson-coupled to vortices in neighboring CuO 2 planes. With increasing magnetic field, the FLL is predicted to undergo a dimensional crossover from three-dimensional (3D) behavior with strong interplanar coupling between the pancake vortices to a 2D regime where the 2D FLL of pancake vortices within each layer is independent of those in the adjacent sheets. The pancake vortices can also experience a complete loss of correlation when they are decoupled [12-14]. It has also been proposed that
0921-4534/96/$17.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0921-4534(96)00634-X
M.C. de Andrade et al./Physica C 273 (1997) 268-274
vortex lines in a bulk superconductor with point disorder should go through a second order phase transition and freeze into a vortex glass phase at low temperatures [15-17]. Consistent results seem to provide convincing evidence for the existence of the vortex glass transition [18-24]. Magnetization measurements on certain high temperature cuprate superconductors have uncovered a striking peak in the irreversible part of the magnetic hysteresis loop. Materials in which this peak has been observed include the highly anisotropic Bi2Sr2CaCu2Ox (Bi-2212) superconductors [3,2527] as well as the less anisotropic YBa2Cu30 7 superconductors [28]. As far as we know, no systematic study of magnetic hysteresis loops of electron-doped superconductors of the type Ln2_xMxCuO4_y (Ln = Pr, Nd, Sm, Eu; M = Ce, Th) has heretofore been undertaken. The much lower values of the superconducting critical temperature Tc and, hence, lower values of the upper critical field H~2(T= 0) of the Ln 2- xM xCuO4_ r electron-doped cuprate superconductors, allow easier access to the low temperaturehigh field regime of the magnetic phase diagram making these materials good candidates for investigating vortex phases and phenomena. In this paper, we report measurements of isothermal magnetic hysteresis loops on a single crystal of the electron-doped superconductor PrL85Ce0.15CuO4_y. We have observed a peak in the hysteretic magnetization curve that is qualitatively similar to the peak observed in the magnetization curve of Bi-2212 samples, suggesting that the anomalies in both materials arise from a common origin. The measurements also yielded the irreversibility line Hirr(T), which can be described by a single power law throughout the entire temperature range of the measurements 0.1 < T / T c < 0.9, an estimate of the lower critical field Hcj(T), and a quantitative low temperature magnetic phase diagram.
2. Experimental details Single crystals of Prl.85Ce0.15CuO4_y were grown using a self-flux method as described elsewhere [29]. The crystals were annealed in an ultra-high purity
269
argon atmosphere at 1000°C for 48 hours in order to reduce the oxygen concentration to its near optimum value. A 0.291 mg sample in the shape of a parallelepiped of dimensions 1 × 1.3 X 0.05 mm 3 was selected for the magnetic investigation. The high quality of the sample was inferred from the high superconducting transition temperature Tc ~ 22.5 K and narrow width (AT~ = 0.9 K) observed in ac magnetic susceptibility measurements. The shielding zero-field-cooling (ZFC) susceptibility was corrected with a demagnetization factor D a = 0.88 in order to obtain consistency with perfect screening at low temperature; XvM/(1 --4"n'Da XvM) = - 1 / 4 ~ (CGS units) where )(vM is the measured volume magnetic susceptibility. The difference between D a and the demagnetization factor D m -- 0.93 estimated from the sample dimensions is very small indicating the bulk superconducting nature of the single crystal. The magnetization measurements were performed with the applied magnetic field H parallel to the c-axis of the crystal ( H l[c) using commercial SQUID magnetometers (Quantum Design MPMS-l, MPMS5 and MPMS-7) in magnetic fields up to 7 T. In order to improve the signal to noise ratio, for some of the measurements, we used a recently developed Reciprocating Sample Option (RSO) technique [30] which minimizes spurious induction effects when moving the sample in an inhomogeneous magnetic field. A comparison with magnetization measurements made with a conventional small dc scan length (3 cm) revealed that the data obtained using the RSO technique have a much better signal/noise ratio. Because our investigation of the magnetic phase diagram does not require absolute values of the magnetization, we did not take into account corrections arising from the sample holder susceptibility. The hysteresis loops M ( H ) were obtained after cooling the sample in zero field to the desired temperature. The measurements were performed in the temperature range 2 <_ T < 23 K. The magnetization loops were then traced in the RSO mode while increasing/decreasing the magnetic field in small steps (_< 10 Oe). The low field M ( H ) data used for the Hcl.c(T) determination were obtained using the low field MPMS-1 magnetometer. The measurements were started after ZFC and the scan length was set at 3 cm.
270
M.C. de Andrade et al./Physica C 273 (1997) 268-274
3. Results and discussion Shown in Fig. 1 are plots of the irreversible part of the isothermal magnetization. The M(H) curves exhibit a peak which can be characterized by three main features: the peak (a) has a weak temperature dependence, (b) occurs for low values of the applied field, and (c) disappears for temperatures lower than T = 17.5 K. It is interesting to note that these three characteristics are also present in other high temperature superconductors with comparableanisotropy such as Bi-2212. In these strongly anisotropic cuprate superconductors, the anomalous peak observed in the magnetization curves [3,25-27] is also nearly inde0.4
•
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z A A ZX
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•
17.5K 19K 20K
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400
500
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600
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pendent of temperature, occurs at low fields, and disappears for lower temperatures. In addition, the peak anomaly in the magnetization loops of PrL85Ce0.~sCUQ_y is quite different from that observed in similar measurements on the less anisotropic superconductor YBa2Cu30 7_ ~ [28]. For the latter material, the anomaly in the irreversible magnetization curves, often referred to as "fish tail" effect, consists of an anomalous increase in the irreversible magnetization on increasing magnetic field. In this case, a strong temperature dependence is observed, and the peak occurs in much higher applied magnetic fields and does not disappear at lower temperatures. In addition, this "fish tail" can be reversibly removed using an appropriate annealing treatment [31]. Therefore, it seems reasonable to conclude that the origin of the peak in the electrondoped cuprate is the same as the bismuth based cuprates. One explanation for the rapid decrease of the irreversible magnetization with increasing temperature in the highly anisotropic Josephson-coupled Bi2212 superconductors is the decoupling of a 3D vortex lattice into a 2D array of pancake vortices. This hypothesis is supported by results of recent IxSR [32-34] and neutron diffraction [35] experiments which reveal a 3D vortex lattice that disappears above the temperature independent field Her. The qualitative similarity of our results with those in the Bi-2212 materials suggests that the peak in M ( H ) may be due to a dimensional crossover of the vortex lattice. According to Glazman and Koshelev [ 14], the crossover field should occur at
1
700
H (Oe) Fig. I. Magnetic hysteresis curves at selected temperatures for a Prl.ssCeo ]sCuO4_y single crystal. The data were divided (16 K, 17.5 K) or multiplied (19 K, 20 K) by factors of 2.5, 1.5 or 1.5 respectively, so that they fit in the same plot. The shaded region defines the crossover field Her above which a drop in the magnetization is observed in the temperature range 16 < T < 20 K.
where S is the interlayer distance, 3, is the anisotropy parameter, and ~bo is the flux quantum. Using S = 12 ,~ for Prl.85Ce0.15CuOa_y obtained from Xray diffraction [36,37], one obtains "y--450. This value is comparable to Y--400 estimated for electron-doped Nd2_aCexCuO4_y single crystals from analysis of the dc magnetic susceptibility [38]. However, this value is markedly larger than y--- 4 previously derived from magnetization measurements on grain-aligned specimens of Sm 1.85Ce0.15CuO4_y [39]
M.C. de Andrade et al./Physica C 273 (1997)268-274 using the Hao-Clem model [40]. We do not presently understand the reason for this discrepancy. From the above analysis, we speculate that large anisotropy and, in turn, a dimensional crossover, is responsible for the peak in the magnetization loop of the electron-doped superconductors as well as the bismuth based superconductors. The absence of a peak for temperatures below 16 K could be an indication of a more continuous character of the dimensional crossover in this temperature range. More recently, a theory providing a quantitative description of the elastic vortex lattice in the presence of point disorder was developed [41]. The main prediction of this theory is the existence of a low field/weak disorder "Bragg glass phase" which, upon raising the field, should undergo a transition into another phase which could be a pinned liquid or another type of glass (e.g., vortex glass). In this picture, as the magnetic field increases, the effective disorder also increases, driving the Bragg glass through this transition to a different phase. The Bragg glass is destroyed due to the increase of the effective disorder. The observed peak in M ( H ) in our experiments could be interpreted from this viewpoint: upon increasing the field (disorder), the system shifts from a weak disorder regime to a highly disordered one. In this case, the peak marks the transition from the Bragg glass to another vortex phase. A detailed investigation of this possibility is now currently underway. We have also extracted the temperature dependence of the irreversibility line Hirr(T) from the magnetic hysteresis loops. We define the irreversibility field Hir~ as the field where the difference between the values of the magnetization for increasing and decreasing fields begins to deviate from zero within the accuracy of the experiment ( _ 1 0 - 6 emu). We find that the temperature dependence of the irreversibility line H~r(T) can be described by the power law,
Hirr(T)
=
H o 1 - ~c
'
(2)
271
crystals of Prl.85Ce0.15CuO4_y [42]. However, investigations [4,27] of Bi-2212 superconductors show a change of the irreversibility line from a power law in the 3D vortex regime close to T~ to an exponential form Hitrot exp(Eo/kBT) in the 2D vortex regime at lower temperatures. The absence of exponential behavior at low temperature in the case of Pr~.85Ce0.15CuO4_y could be due to the inherent disorder of the electron-doped system associated with both oxygen vacancies and substitutional Ce [43,44]. An understanding of sample inhomogeneities is important for the interpretation of the physical properties of superconductors in the mixed state. It has been shown that the irreversibility line can be sample dependent in the electron-doped Lnz_xMxCuO4_y superconductors, possibly due to changes in oxygen vacancy a n d / o r Ce concentrations [29]. Inhomogeneities could place the electron-doped system in the dirty limit where a power law behavior of H~r~(T) at low temperatures and high fields has previously been observed [5,39]. It has also been reported that close to Tc, the irreversibility line seems to coincide with the melting of the FLL and can be related to the presence of barriers at the sample surfaces [45]. In this situation, the field distribution due to demagnetization effects [46] and the presence of defects within the sample would cause the melting of the FLL to have a more continuous character, making it difficult to track the onset of the melting phase transition. Furthermore, sufficiently close to Tc, the diamagnetic response of the sample is within the noise level of the magnetometers, so it is very difficult to extract the irreversibility field. Therefore, we are unable to determine both the behavior of the irreversibility line as well as the possible melting transition of the 3D vortex lattice in the temperature and field range close to T~ for the PrL85Ce0.lsCuO4_y single crystal. The lower critical field for Hllc, ncl.c, was estimated from the first penetration of flux at the border between the Meissner state and the mixed state at a field Hin(T) ,
/-/ex,(r)
Hc'(T)--nin(r)--- (1-Oa)' with H o = 3 7 kOe in the range 0 . 1 < T / T c<_0.9. The temperature dependence of the irreversibility line is in agreement with that inferred from recent magnetoresistance measurements on other single
(3)
where D a = 0.88 and He, t is the applied magnetic field. The penetration of flux appears as a deviation from linearity in the M ( H ) curves at low field.
272
M.C. de Andrade et al./Physica C 273 (1997) 268-274
10 s
Naturally, this determination depends on the accuracy of the demagnetization factor. Shown in Fig. 2 a are M versus H data at selected temperatures, and in Fig. 2b, the deviation A M from perfect diamagnetism versus H data, based on the data in Fig. 2a, for PrL85Ce0.jsCuO4_ y.
•
Ha ~(T)
NN~- (T) 03
IrreversibleRegion
o~
17.5K 16.25K -20
1
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--- 13.75K
A @3
E "~ E
0v -i-
15K
~D
~12.5K
0
-40 10 2
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-60 (a) -80
200
I
I
400
600
I
800
~.
.
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o~
1000
Hin(Oe)
101 0
, 5
~ 10
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~ m~ l mx~
~ 15
J 20
25
T(K) Fig. 3. Magnetic field H - temperature T phase diagram for a Prl.s~Ceo.15CuOa_y single crystal with Tc = 22.5 K. The solid lines represent fits of the data to theoretical expressions as described in the text.
4
The magnetic phase diagram in Fig. 3 summarizes all of the results of this investigation. The line representing Hirr(T) in Fig. 3 is a fit of Eq. (2) to the data. The line depicting Hcl,c(T) was obtained using the expression H¢l.c(T) 0 0
200
400
600
800
1000
H,.(Oe) Fig. 2. (a) Magnetization as a function of the internal magnetic field, Hin, for selected temperatures. The plot shows the deviation from linear behavior (perfect screening, dashed line) for each temperature. (b) Difference between the measured magnetization and the linear magnetization (perfect screening), A M, for selected temperatures as a function of the applied magnetic field. The value for the lower critical magnetic field Hc~.c was estimated as the field where A M starts to deviate from zero.
~o ln(h~h(T ) 4"n"[ Aab(T)] 2
/~dpo/2ZrHc2,c(Y ) ),
(4)
The upper critical field Hc2.c(0)= 100 kOe was estimated from magnetoresistance measurements on a Prl.ssCe0.nsCuOa_y single crystal [42]. Assuming the WHH approximation [47] for Hcz(T) and a parabolic temperature dependence for the thermodynamic critical field He(T) [48], we obtain for the penetration depth in the ab plane, hob(0) -- 1500 A.
M.C. de Andrade et al./Physica C 273 (1997) 268-274
4. Summary Isothermal magnetization loop measurements on a Prl.85Ce0.15CuO4_y single crystal reveal the existence of a peak effect which, to our knowledge, has not heretofore been observed in electron-doped superconductors. The peak anomaly in Prl.85Ce0AsCuOa_y is qualitatively similar to that previously observed in Bi-2212 samples. This suggests that the peak effect in electron-doped superconductors and Bi-2212 superconductors have a common origin, namely, high anisotropy. The peak could be a manifestation of a dimensional crossover. Analysis of the data in terms of a transition from a 3D vortex lattice to quasi 2D pancake vortices yielded an estimate for the anisotropy ratio, y = 450. However, the microscopic origin of this peak and its relation to the FLL or Josephson vortex lattice remains unclear at this point. Our results for the irreversibility line show that the irreversibility line follows a single power law, in the low temperature regime. Whether there is a change in the character of the FLL in the low temperature- high field regime remains to be established by further investigations.
Acknowledgements Research at UCSD was supported by the US Department of Energy under Grant No. DE-FG0386ER-45230. G.T. acknowledged support from the Swiss National Science Foundation. We thank S. Moehlecke and B. Revaz for fruitful discussions.
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