The superconducting flux dynamic of the transition metal carbide Sc3CoC4 which exhibits a quasi-one-dimensional structure is studied. Besides zero-field-cooling (zfc), field-cooling (fc) and magnetization measurements, especially flux creep relaxation experiments are performed. The relaxation rates S = dM/dlnt are determined at selected temperatures below the transition temperature Tc in two magnetic fields of 50 Oe and 100 Oe just above Hc1. The resulting supercurrent dependence on the mean activation energy is analyzed according to the collective pinning theory which predicts U ∼ ((j/jc)-μ –1). The calculated μ-values differ in the high and low temperature region. The μ-values below about 2.5 K are ≈ 0.5 - 0.68 depending slightly on the applied magnetic field whereas at higher temperatures the μ-values are ≈ 0.22 - 0.34. These results might indicate a transition between different types of vortex pinning around 2.5 K changing from single vortex creep at higher temperatures to collective creep of vortex bundles at lower temperatures

Baenitz, M.

Lüders, K.

Scheidt, Ernst-Wilhelm

Scherer, Wolfgang

English

The superconducting flux dynamic of the transition metal carbide Sc3CoC4 which
exhibits a quasi-one-dimensional structure is studied. Besides zero-field-
cooling (zfc), field-cooling (fc) and magnetization measurements, especially
flux creep relaxation experiments are performed. The relaxation rates S =
dM/dlnt are determined at selected temperatures below the transition
temperature Tc in two magnetic fields of 50 Oe and 100 Oe just above Hc1. The
resulting supercurrent dependence on the mean activation energy is analyzed
according to the collective pinning theory which predicts U ∼ ((j/jc)-μ –1).
The calculated μ-values differ in the high and low temperature region. The
μ-values below about 2.5 K are ≈ 0.5 - 0.68 depending slightly on the applied
magnetic field whereas at higher temperatures the μ-values are ≈ 0.22 - 0.34.
These results might indicate a transition between different types of vortex
pinning around 2.5 K changing from single vortex creep at higher temperatures
to collective creep of vortex bundles at lower temperatures

Scheidt, E.-W.

Lüders, Klaus

Scherer, W.

Institutional Repository of the Freie Universität Berlin

                                                                                                               Flux Creep in the Quasi-1D Superconducting Carbide Sc3CoC4           M Baenitz1, E-W Scheidt2, K Lüders1,3, W Scherer2                   1Max-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187 Dresden, Germany                  2Institut für Physik, Universität Augsburg, 86135 Augsburg, Germany                  3Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany              E-Mail: lueders@physik.fu-berlin.de  Abstract. The superconducting flux dynamic of the transition metal carbide Sc3CoC4 which exhibits a quasi-one-dimensional structure is studied. Besides zero-field-cooling (zfc), field-cooling (fc) and magnetization measurements, especially flux creep relaxation experiments are performed. The relaxation rates S = dM/dlnt are determined at selected temperatures below the transition temperature Tc in two magnetic fields of 50 Oe and 100 Oe just above Hc1. The resulting supercurrent dependence on the mean activation energy is analyzed according to the collective pinning theory which predicts U ~ ((j/jc)-μ –1). The calculated μ-values differ in the high and low temperature region. The μ-values below about 2.5 K are ≈ 0.5-0.68 depending slightly on the applied magnetic field whereas at higher temperatures the μ-values are ≈ 0.22-0.34. These results might indicate a transition between different types of vortex pinning around 2.5 K changing from single vortex creep at higher temperatures to collective creep of vortex bundles at lower temperatures.       1. Introduction Recently, superconductivity in the transition metal carbide Sc3CoC4 was reported [1]. In spite of the close structural relationship of the isotypic Sc3TC4 carbides (T = Fe, Co, Ni) consisting of quasi one-dimensional [TC4] chains embedded in a scandium matrix only the Co system shows superconductivity. It can be regarded as a model system to study the rare phenomenon of quasi one-dimensional superconductivity. Scheidt et al. [2] already determined detailed superconducting properties like critical quantities, magnetization and specific heat behavior in connection with structural features indicating some characteristics of low dimensional superconductivity. In order to obtain further information about superconducting properties detailed measurements of the flux creep relaxation are performed. The results are discussed within the scope of a thermally activated flux creep model based on the Anderson-Kim theory [3] which is frequently applied to conventional  type-II [4] as well as to high-Tc superconductors [5, 6].      2. Experimental Powder samples of Sc3CoC4 are prepared following the procedure described in Ref. [7]. Using a sample with a mass of 120.4 mg zero field cooled (zfc), field cooled (fc), magnetization, and flux creep relaxation measurements are performed by means of a commercially available magnetometer (MPMS, Quantum Design Inc.).   3. Results and discussion Fig. 1 shows the zfc-fc transition curves for a magnetic field of 100 Oe. The paramagnetic contribution due to this field obtained from the behavior above Tc, is subtracted. The onset transition temperature in this field is Tc = 4.4 K.       An example of a magnetization loop is shown in Fig. 2. The first minimum at T = 1.8 K occurs at about H = 40 Oe, the values at higher temperatures are slightly smaller. Accordingly the relaxation measurements are started after applying higher field values, in our case H = 50 Oe and H = 100 Oe, respectively.                                                                                     Figure 1. Zero field cooled (zfc, open symbols) and field cooled (fc, closed symbols) curves for a magnetic field of H = 100 Oe. The paramagnetic contribution due to this field is subtracted.                                                                             Figure 2. Central part of the magnetization loop at T = 1.8 K. The paramagnetic contribution is subtracted. Relaxation measurements are performed at fields of  H = 50 Oe and H = 100 Oe.        The results of the relaxation measurements are summarized in Figs. 3 - 6. Two examples of relaxation curves obtained at T = 2 K and T = 3.5 K after application of a magnetic field of H = 100 Oe are shown in Fig. 3. At both temperatures, according to the Anderson-Kim theory [3], a logarithmic decay is observed. In comparison to the 2 K curve, the slope of the relaxation curve at higher temperature is considerably reduced. Such a behavior is also found in further measurements, performed at selected temperatures T = 1.8 K, 2.5 K, and 3.0 K. The resulting temperature dependence of the relaxation rates S = dM/dlnt for the applied magnetic field values H = 50 Oe and H = 100 Oe are plotted in Fig. 4. The curves increase continuously from the transition temperature Tc = 4.4 K down to T = 1.8 K. The reduced relaxation rate at 1.8 K and 50 Oe might be due to the small magnetic field value just above HC1. However, it is obvious that the relaxation behavior differs in the high and low temperature region. For 100 Oe the two low temperature rates are rather high compared to those at higher temperatures. The rate at 2.5 K corresponds more to those at 3 K and 3.5 K. For 50 Oe, however, the rate at 2.5 K corresponds more to the low temperature values. This might be a first hint                Figure 3. Relaxation curves of the magnetic moment recorded at T = 2 K and T = 3.5 K after applying a magnetic field of H = 100 Oe. The curves follow logarithmic time dependence (solid lines). Figure 4. Temperature dependence of the relaxation rate S = dM/dlnt after application of a magnetic field of H = 50 Oe (open symbols) and 100 Oe (closed symbols)      for a transition between different types of vortex pinning around 2.5 K in the field region between 50 and 100 Oe.             Such a transition in the pinning behavior is supported by further analysis of the relaxation measurements according to the collective pinning theory [8]. Following a method proposed by Maley et al. [9], the relaxation at different temperatures leads to a consistent plot of the activation energy U (Figs. 5 and 6). It is based on the rate equation dM/dt  ~ exp(–U/kBT), leading to U = kBT(c – ln(dM/dt)). Here, c is used as fit parameter, yielding a smooth dependence of U vs. M. Since M  is proportional to the superconducting current density,  j, at least the functional form of U(j) can be determined. In our case, this leads to a power law according to the collective pinning theory, which generally predicts U ~ ((j/jc)-μ –1) (solid lines in Figs. 5 and 6); jc is the critical current density and μ is a critical exponent that depends on dimensionality and effective bundle size of the vortex assembly.       As can be seen in Fig. 5, two µ-values result for a starting field of 100 Oe: µ = 0.68 for lower temperatures and µ = 0.34 for higher temperatures. Similar µ-values result for a starting field of 50 Oe (Fig. 6): µ = 0.5 for lower temperatures and µ = 0.22 for higher temperatures. The difference is that the behavior at 2.5 K for the starting field of 100 Oe again corresponds to the higher temperature region and can be described by the same µ-value belonging to 3 K and 3.5 K whereas for 50 Oe it changes to the low temperature µ-value belonging to 2 K and 1.8 K. This means that in the H-T-diagram a borderline between different pinning mechanisms just runs between 2 K and 3 K and between 50 Oe and 100 Oe. At higher fields and temperatures the lower µ-values are close to theoretical values for single vortex creep, µ = 0.18 - 0.25 whereas in the low field and temperature region they correspond to those for creep of vortex bundles or Bragg glass behavior, µ = 0.5 - 0.78 [10].                       Figure 5. Mean activation energy as a function of supercurrent density normalized to the critical current density for a magnetic field of H = 100 Oe applied after zero field cooling  Figure 6. The same plot as in Figure 5 for a magnetic field of H = 50 Oe applied after zero field cooling     4. Conclusions The analysis of flux relaxation measurements below the irreversibility line of the quasi one-dimensional (1D) superconductor Sc3CoC4 shows a different behavior at higher and lower temperatures. The pinning mechanism changes at about 2.5 K, dominated by single vortex flux creep above this temperature and vortex bundle flux creep below 2.5 K. The origin of this behavior might be connected with a transition in the type of superconductivity, changing for instance from surface to volume superconductivity with decreasing temperature. This might correspond with specific heat measurements which exhibit a peak just at 2.5 K [2] obviously indicating the formation of full volume superconductivity.       Acknowledgments The authors would like to thank H. Rave for her help in experiments. One of us (KL) would like to thank F. Steglich for his kind hospitality and the possibility of doing research at the MPI-CPfS. This work was supported by the Deutsche Forschungsgemeinschaft (SPP1178).   References [1]    Scherer W, Hauf Ch, Presnitz M, Scheidt E-W, Eickerling G, Eyert V, Hoffmann R-D,              Rodewald U, Hammerschmidt A, Vogt Ch and Pöttgen C 2010 Angew. Chem. Int. Ed. 49 1578 [2]    Scheidt E-W, Hauf C, Reiner F, Eickerling G and Scherer W 2011 J Phys.: Conf. Ser. 273             012083 [3]    Anderson P W and Kim Y B 1964 Rev. Mod. Phys. 36 39 [4]    Beasley M R, Labusch R and Webb W W 1969 Phys. Rev. 181 682 [5]    Campbell I A, Fruchter L and Cabanel R 1990 Phys. Rev. Lett. 64 1561 [6]    Baenitz M, Lüders K, Barišić N, Cho Y, Li Y, Yu G, Zhao X and Greven M 2010 J. Phys.: Conf.                Ser. 234 012024 [7]    Rohrmoser B, Eickerling G, Presnitz M, Scherer W, Eyert V, Hoffmann R-D, Rodewald U C,               Vogt C and Pöttgen R 2007 J. Am. Chem. Soc. 129 9356  [8]    Blatter G, Feigel’man M V, Geshkenbein V B, Larkin A I and Vinokur V M 1994 Rev. Mod.                   Phys.  66 1125 [9]    Maley M P, Willis J O, Lessure H and McHenry M E 1990 Phys. Rev. B 42 2639 [10]  Blatter G and Geshkenbein V B in: Bennemann K H and Ketterson J B (Eds.)               Superconductivity, Vol. I, Springer Berlin Heidelberg 2008, p. 495  

Flux Creep in the Quasi-1D Superconducting Carbide Sc3CoC4

AbstractThe superconducting flux dynamic of the transition metal carbide Sc3CoC4 which exhibits a quasi-one-dimensional structure is studied. Besides zero-field-cooling (zfc), field-cooling (fc) and magnetization measurements, especially flux creep relaxation experiments are performed. The relaxation rates S = dM/dlnt are determined at selected temperatures below the transition temperature Tc in two magnetic fields of 50Oe and 100Oe just above Hc1. The resulting supercurrent dependence on the mean activation energy is analyzed according to the collective pinning theory which predicts U ∼ ((j/jc)-μ –1). The calculated μ-values differ in the high and low temperature region. The μ-values below about 2.5K are ≈ 0.5 - 0.68 depending slightly on the applied magnetic field whereas at higher temperatures the μ-values are ≈ 0.22 - 0.34. These results might indicate a transition between different types of vortex pinning around 2.5K changing from single vortex creep at higher temperatures to collective creep of vortex bundles at lower temperatures

Elsevier - Publisher Connector 

 Physics Procedia  36 ( 2012 )  698 – 703 
1875-3892  © 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Guest Editors. 
doi: 10.1016/j.phpro.2012.06.270 
 
__________ 
* Corresponding author. 
E-mail address: lueders@physik.fu-berlin.de 
Superconductivity Centennial Conference 
Flux Creep in the Quasi-1D Superconducting Carbide 
Sc3CoC4 
M. Baenitza, E.-W. Scheidtb, K. Lüdersa,c,*, W. Schererb 
aMax-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187 Dresden, Germany 
bInstitut für Physik, Universität Augsburg, 86135 Augsburg, Germany 
cFachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany      
 
Abstract 
The superconducting flux dynamic of the transition metal carbide Sc3CoC4 which exhibits a quasi-one-dimensional 
structure is studied. Besides zero-field-cooling (zfc), field-cooling (fc) and magnetization measurements, especially 
flux creep relaxation experiments are performed. The relaxation rates S = dM/dlnt are determined at selected 
temperatures below the transition temperature Tc in two magnetic fields of 50 Oe and 100 Oe just above Hc1. The 
resulting supercurrent dependence on the mean activation energy is analyzed according to the collective pinning 
theory which predicts  U ~ ((j/jc)-μ –1). The calculated  μ-values differ in the high and low temperature region. The μ-
values below about 2.5 K are ≈ 0.5 - 0.68 depending slightly on the applied magnetic field whereas at higher 
temperatures the μ-values are ≈ 0.22 - 0.34. These results might indicate a transition between different types of vortex 
pinning around 2.5 K changing from single vortex creep at higher temperatures to collective creep of vortex bundles 
at lower temperatures. 
 
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Horst Rogalla and 
Peter Kes. 
Keywords: Low dimensional superconductivity; flux creep relaxation; collective pinning 
1. Introduction 
Recently, superconductivity in the transition metal carbide Sc3CoC4 was reported [1]. In spite of the close 
structural relationship of the isotypic Sc3TC4 carbides (T = Fe, Co, Ni) consisting of quasi one-
dimensional [TC4] chains embedded in a scandium matrix only the Co system shows superconductivity. It 
can be regarded as a model system to study the rare phenomenon of quasi one-dimensional 
superconductivity. Scheidt et al. [2] already determined detailed superconducting properties like critical 
quantities, magnetization and specific heat behavior in connection with structural features indicating some 
characteristics of low dimensional superconductivity. In order to obtain further information about 
superconducting properties detailed measurements of the flux creep relaxation are performed. The results 
Available online at www.sciencedirect.com
© 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Guest Editors.
Open access under CC BY-NC-ND license.
Open access under CC BY-NC-ND license.
 M. Baenitz et al. /  Physics Procedia  36 ( 2012 )  698 – 703 699
are discussed within the scope of a thermally activated flux creep model based on the Anderson-Kim 
theory [3] which is frequently applied to conventional type-II [4] as well as to high-Tc superconductors  
[5, 6]. 
 
 
2. Experimental 
 
Powder samples of Sc3CoC4 are prepared following the procedure described in Ref. [7]. Using a sample 
with a mass of 120.4 mg zero field cooled (zfc), field cooled (fc), magnetization, and flux creep relaxation 
measurements are performed by means of a commercially available magnetometer (MPMS, Quantum 
Design Inc.). 
 
 
3. Results and discussion 
 
Fig. 1 shows the zfc-fc transition curves for a magnetic field of 100 Oe. The paramagnetic contribution 
due to this field obtained from the behavior above Tc, is subtracted. The onset transition temperature in 
this field is Tc = 4.4 K. 
 
                                             
 
Figure 1.  Zero field cooled (zfc, open symbols) and field cooled (fc, closed symbols) curves for a magnetic field of 
H = 100 Oe. The paramagnetic contribution due to this field is subtracted. 
 
 
     An example of a magnetization loop is shown in Fig. 2. The first minimum at T = 1.8 K occurs at 
about H = 40 Oe, the values at higher temperatures are slightly smaller. Accordingly the relaxation 
measurements are started after applying higher field values, in our case H = 50 Oe and H = 100 Oe, 
respectively. 
     The results of the relaxation measurements are summarized in Figs. 3 - 6. Two examples of relaxation 
curves obtained at T = 2 K and T = 3.5 K after application of a magnetic field of H = 100 Oe are shown in 
Fig. 3. At both temperatures, according to the Anderson-Kim theory [3], a logarithmic decay is observed. 
In comparison to the 2 K curve, the slope of the relaxation curve at higher temperature is considerably 
reduced. Such a behavior is also found in further measurements, performed at selected temperatures T = 
1.8 K, 2.5 K, and 3.0 K. The resulting temperature dependence of the relaxation rates  S = dM/dlnt  for the  
700   M. Baenitz et al. /  Physics Procedia  36 ( 2012 )  698 – 703 
                                         
 
Figure 2. Central part of the magnetization loop at T = 1.8 K. The paramagnetic contribution is subtracted. 
Relaxation measurements are performed at fields of H = 50 Oe and H = 100 Oe. 
 
 
applied magnetic field values H = 50 Oe and H = 100 Oe are plotted in Fig. 4. The curves increase 
continuously from the transition temperature Tc = 4.4 K down to T = 1.8 K. The reduced relaxation rate at 
1.8 K and 50 Oe might be due to the small magnetic field value just above Hc1. However, it is obvious 
that the relaxation behavior differs in the high and low temperature region. For 100 Oe the two low 
temperature rates are rather high compared to those at higher temperatures. The rate at 2.5 K corresponds 
more to those at 3 K and 3.5 K. For 50 Oe, however, the rate at 2.5 K corresponds more to the low 
temperature values. This might be a first hint for a transition between different types of vortex pinning 
around 2.5 K in the field region between 50 and 100 Oe. 
 
                                        
 
Figure 3. Relaxation curves of the magnetic moment recorded at T = 2 K and T = 3.5 K after applying a magnetic 
field of H = 100 Oe. The curves follow logarithmic time dependence (solid lines). 
                                                                            
      
 M. Baenitz et al. /  Physics Procedia  36 ( 2012 )  698 – 703 701
                                      
 
Figure 4. Temperature dependence of the relaxation rate S = dM/dlnt after application of a magnetic field of 50 Oe 
(open symbols) and 100 Oe (closed symbols) 
 
 
     Such a transition in the pinning behavior is supported by further analysis of the relaxation 
measurements according to the collective pinning theory [8]. Following a method proposed by Maley et 
al. [9], the relaxation at different temperatures leads to a consistent plot of the activation energy U (Figs. 5 
and 6). It is based on the rate equation dM/dt ~ exp(–U/kBT), leading to U = kBT (c – ln(dM/dt)). Here, c is 
used as fit parameter, yielding a smooth dependence of U vs. M. Since M is proportional to the 
superconducting current density j, at least the functional form of U(j) can be determined. In our case, this 
leads to a power law according to the collective pinning theory, which generally predicts for the 
activation energy U ~ ((j/jc)-μ –1) (solid lines in Figs. 5 and 6); jc is the critical current density and μ is a 
critical exponent that depends on dimensionality and effective bundle size of the vortex assembly. 
 
                                      
 
Figure 5. Mean activation energy as a function of supercurrent density normalized to the critical current density for a 
magnetic field of H = 100 Oe applied after zero field cooling 
 
 
702   M. Baenitz et al. /  Physics Procedia  36 ( 2012 )  698 – 703 
      
                                       
 
Figure 6. The same plot as in Figure 5 for a magnetic field of H = 50 Oe applied after zero field cooling 
 
 
     As can be seen in Fig. 5, two μ-values result for a starting field of 100 Oe: μ = 0.68 for lower 
temperatures and μ = 0.34 for higher temperatures. Similar μ-values result for a starting field of 50 Oe 
(Fig. 6): μ = 0.5 for lower temperatures and μ = 0.22 for higher temperatures. The difference is that the 
behavior at 2.5 K for the starting field of 100 Oe again corresponds to the higher temperature region and 
can be described by the same μ-value belonging to 3 K and 3.5 K whereas for 50 Oe it changes to the low 
temperature μ-value belonging to 2 K and 1.8 K. This means that in the H-T-diagram a borderline 
between different pinning mechanisms just runs between 2 K and 3 K and between 50 Oe and 100 Oe. At 
higher fields and temperatures the lower  μ-values are close to theoretical values for single vortex creep, 
μ = 0.18 - 0.25 whereas in the low field and temperature region they correspond to those for creep of 
vortex bundles or Bragg glass behavior,  μ = 0.5 - 0.78 [10]. 
 
 
4. Conclusions 
 
     The analysis of flux relaxation measurements below the irreversibility line of the quasi one-
dimensional (1D) superconductor Sc3CoC4 shows a different behavior at higher and lower temperatures. 
The pinning mechanism changes at about 2.5 K, dominated by single vortex flux creep above this 
temperature and vortex bundle flux creep below 2.5 K. The origin of this behavior might be connected 
with a transition in the type of superconductivity, changing for instance from surface to volume 
superconductivity with decreasing temperature. This might correspond with specific heat measurements 
which exhibit a peak just at 2.5 K [2] obviously indicating the formation of full volume 
superconductivity. 
 
 
Acknowledgements 
 
     The authors would like to thank H. Rave for her help in experiments. One of us (KL) would like to 
thank F. Steglich for his kind hospitality and the possibility of doing research at the MPI-CPfS. This work 
was supported by the Deutsche Forschungsgemeinschaft  (SPP1178). 
 
 M. Baenitz et al. /  Physics Procedia  36 ( 2012 )  698 – 703 703
 
References 
[1]    Scherer W, Hauf Ch, Presnitz M, Scheidt E-W, Eickerling G, Eyert V, Hoffmann R-D,  
            Rodewald U, Hammerschmidt A, Vogt Ch and Pöttgen C 2010 Angew. Chem. Int. Ed. 49 1578 
[2]    Scheidt E-W, Hauf C, Reiner F, Eickerling G and Scherer W 2011 J Phys.: Conf. Ser. 273 
            012083 
[3]    Anderson P W and Kim Y B 1964 Rev. Mod. Phys. 36 39 
[4]    Beasley M R, Labusch R and Webb W W 1969 Phys. Rev. 181 682 
[5]    Campbell I A, Fruchter L and Cabanel R 1990 Phys. Rev. Lett. 64 1561 
[6]    Baenitz M, Lüders K, Barišić N, Cho Y, Li Y, Yu G, Zhao X and Greven M 2010 J. Phys.: Conf.   
             Ser. 234 012024 
[7]    Rohrmoser B, Eickerling G, Presnitz M, Scherer W, Eyert V, Hoffmann R-D, Rodewald U C,  
             Vogt C and Pöttgen R 2007 J. Am. Chem. Soc. 129 9356  
[8]    Blatter G, Feigel’man M V, Geshkenbein V B, Larkin A I and Vinokur V M 1994 Rev. Mod.      
             Phys.  66 1125 
[9]    Maley M P, Willis J O, Lessure H and McHenry M E 1990 Phys. Rev. B 42 2639 
[10]  Blatter G and Geshkenbein V B in: Bennemann K H and Ketterson J B (Eds.)  
             Superconductivity, Vol. I, Springer Berlin Heidelberg 2008, p. 495 
 
 
 
 
 
 


Flux Creep in the Quasi-1D Superconducting Carbide Sc3CoC4 

Scheidt, E.

MPG.PuRe

Flux Creep in the Quasi-1D Superconducting Carbide Sc<sub>3</sub>CoC<sub>4</sub>

Online-Publikationserver Augsburg

Flux creep in the quasi-1D superconducting carbide Sc3CoC4

Max Planck Society eDoc Server

OPUS Augsburg

 Physics Procedia  36 ( 2012 )  698 – 703 1875-3892  © 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Guest Editors. doi: 10.1016/j.phpro.2012.06.270  __________ * Corresponding author. E-mail address: lueders@physik.fu-berlin.de Superconductivity Centennial Conference Flux Creep in the Quasi-1D Superconducting Carbide Sc3CoC4 M. Baenitza, E.-W. Scheidtb, K. Lüdersa,c,*, W. Schererb aMax-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187 Dresden, Germany bInstitut für Physik, Universität Augsburg, 86135 Augsburg, Germany cFachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany       Abstract The superconducting flux dynamic of the transition metal carbide Sc3CoC4 which exhibits a quasi-one-dimensional structure is studied. Besides zero-field-cooling (zfc), field-cooling (fc) and magnetization measurements, especially flux creep relaxation experiments are performed. The relaxation rates S = dM/dlnt are determined at selected temperatures below the transition temperature Tc in two magnetic fields of 50 Oe and 100 Oe just above Hc1. The resulting supercurrent dependence on the mean activation energy is analyzed according to the collective pinning theory which predicts  U ~ ((j/jc)-μ –1). The calculated  μ-values differ in the high and low temperature region. The μ-values below about 2.5 K are ≈ 0.5 - 0.68 depending slightly on the applied magnetic field whereas at higher temperatures the μ-values are ≈ 0.22 - 0.34. These results might indicate a transition between different types of vortex pinning around 2.5 K changing from single vortex creep at higher temperatures to collective creep of vortex bundles at lower temperatures.  © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Horst Rogalla and Peter Kes. Keywords: Low dimensional superconductivity; flux creep relaxation; collective pinning 1. Introduction Recently, superconductivity in the transition metal carbide Sc3CoC4 was reported [1]. In spite of the close structural relationship of the isotypic Sc3TC4 carbides (T = Fe, Co, Ni) consisting of quasi one-dimensional [TC4] chains embedded in a scandium matrix only the Co system shows superconductivity. It can be regarded as a model system to study the rare phenomenon of quasi one-dimensional superconductivity. Scheidt et al. [2] already determined detailed superconducting properties like critical quantities, magnetization and specific heat behavior in connection with structural features indicating some characteristics of low dimensional superconductivity. In order to obtain further information about superconducting properties detailed measurements of the flux creep relaxation are performed. The results Available online at www.sciencedirect.com© 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Guest Editors.Open access under CC BY-NC-ND license.Open access under CC BY-NC-ND license. M. Baenitz et al. /  Physics Procedia  36 ( 2012 )  698 – 703 699are discussed within the scope of a thermally activated flux creep model based on the Anderson-Kim theory [3] which is frequently applied to conventional type-II [4] as well as to high-Tc superconductors  [5, 6].   2. Experimental  Powder samples of Sc3CoC4 are prepared following the procedure described in Ref. [7]. Using a sample with a mass of 120.4 mg zero field cooled (zfc), field cooled (fc), magnetization, and flux creep relaxation measurements are performed by means of a commercially available magnetometer (MPMS, Quantum Design Inc.).   3. Results and discussion  Fig. 1 shows the zfc-fc transition curves for a magnetic field of 100 Oe. The paramagnetic contribution due to this field obtained from the behavior above Tc, is subtracted. The onset transition temperature in this field is Tc = 4.4 K.                                                Figure 1.  Zero field cooled (zfc, open symbols) and field cooled (fc, closed symbols) curves for a magnetic field of H = 100 Oe. The paramagnetic contribution due to this field is subtracted.        An example of a magnetization loop is shown in Fig. 2. The first minimum at T = 1.8 K occurs at about H = 40 Oe, the values at higher temperatures are slightly smaller. Accordingly the relaxation measurements are started after applying higher field values, in our case H = 50 Oe and H = 100 Oe, respectively.      The results of the relaxation measurements are summarized in Figs. 3 - 6. Two examples of relaxation curves obtained at T = 2 K and T = 3.5 K after application of a magnetic field of H = 100 Oe are shown in Fig. 3. At both temperatures, according to the Anderson-Kim theory [3], a logarithmic decay is observed. In comparison to the 2 K curve, the slope of the relaxation curve at higher temperature is considerably reduced. Such a behavior is also found in further measurements, performed at selected temperatures T = 1.8 K, 2.5 K, and 3.0 K. The resulting temperature dependence of the relaxation rates  S = dM/dlnt  for the  700   M. Baenitz et al. /  Physics Procedia  36 ( 2012 )  698 – 703                                           Figure 2. Central part of the magnetization loop at T = 1.8 K. The paramagnetic contribution is subtracted. Relaxation measurements are performed at fields of H = 50 Oe and H = 100 Oe.   applied magnetic field values H = 50 Oe and H = 100 Oe are plotted in Fig. 4. The curves increase continuously from the transition temperature Tc = 4.4 K down to T = 1.8 K. The reduced relaxation rate at 1.8 K and 50 Oe might be due to the small magnetic field value just above Hc1. However, it is obvious that the relaxation behavior differs in the high and low temperature region. For 100 Oe the two low temperature rates are rather high compared to those at higher temperatures. The rate at 2.5 K corresponds more to those at 3 K and 3.5 K. For 50 Oe, however, the rate at 2.5 K corresponds more to the low temperature values. This might be a first hint for a transition between different types of vortex pinning around 2.5 K in the field region between 50 and 100 Oe.                                           Figure 3. Relaxation curves of the magnetic moment recorded at T = 2 K and T = 3.5 K after applying a magnetic field of H = 100 Oe. The curves follow logarithmic time dependence (solid lines).                                                                                    M. Baenitz et al. /  Physics Procedia  36 ( 2012 )  698 – 703 701                                       Figure 4. Temperature dependence of the relaxation rate S = dM/dlnt after application of a magnetic field of 50 Oe (open symbols) and 100 Oe (closed symbols)        Such a transition in the pinning behavior is supported by further analysis of the relaxation measurements according to the collective pinning theory [8]. Following a method proposed by Maley et al. [9], the relaxation at different temperatures leads to a consistent plot of the activation energy U (Figs. 5 and 6). It is based on the rate equation dM/dt ~ exp(–U/kBT), leading to U = kBT (c – ln(dM/dt)). Here, c is used as fit parameter, yielding a smooth dependence of U vs. M. Since M is proportional to the superconducting current density j, at least the functional form of U(j) can be determined. In our case, this leads to a power law according to the collective pinning theory, which generally predicts for the activation energy U ~ ((j/jc)-μ –1) (solid lines in Figs. 5 and 6); jc is the critical current density and μ is a critical exponent that depends on dimensionality and effective bundle size of the vortex assembly.                                         Figure 5. Mean activation energy as a function of supercurrent density normalized to the critical current density for a magnetic field of H = 100 Oe applied after zero field cooling   702   M. Baenitz et al. /  Physics Procedia  36 ( 2012 )  698 – 703                                               Figure 6. The same plot as in Figure 5 for a magnetic field of H = 50 Oe applied after zero field cooling        As can be seen in Fig. 5, two μ-values result for a starting field of 100 Oe: μ = 0.68 for lower temperatures and μ = 0.34 for higher temperatures. Similar μ-values result for a starting field of 50 Oe (Fig. 6): μ = 0.5 for lower temperatures and μ = 0.22 for higher temperatures. The difference is that the behavior at 2.5 K for the starting field of 100 Oe again corresponds to the higher temperature region and can be described by the same μ-value belonging to 3 K and 3.5 K whereas for 50 Oe it changes to the low temperature μ-value belonging to 2 K and 1.8 K. This means that in the H-T-diagram a borderline between different pinning mechanisms just runs between 2 K and 3 K and between 50 Oe and 100 Oe. At higher fields and temperatures the lower  μ-values are close to theoretical values for single vortex creep, μ = 0.18 - 0.25 whereas in the low field and temperature region they correspond to those for creep of vortex bundles or Bragg glass behavior,  μ = 0.5 - 0.78 [10].   4. Conclusions       The analysis of flux relaxation measurements below the irreversibility line of the quasi one-dimensional (1D) superconductor Sc3CoC4 shows a different behavior at higher and lower temperatures. The pinning mechanism changes at about 2.5 K, dominated by single vortex flux creep above this temperature and vortex bundle flux creep below 2.5 K. The origin of this behavior might be connected with a transition in the type of superconductivity, changing for instance from surface to volume superconductivity with decreasing temperature. This might correspond with specific heat measurements which exhibit a peak just at 2.5 K [2] obviously indicating the formation of full volume superconductivity.   Acknowledgements       The authors would like to thank H. Rave for her help in experiments. One of us (KL) would like to thank F. Steglich for his kind hospitality and the possibility of doing research at the MPI-CPfS. This work was supported by the Deutsche Forschungsgemeinschaft  (SPP1178).   M. Baenitz et al. /  Physics Procedia  36 ( 2012 )  698 – 703 703 References [1]    Scherer W, Hauf Ch, Presnitz M, Scheidt E-W, Eickerling G, Eyert V, Hoffmann R-D,              Rodewald U, Hammerschmidt A, Vogt Ch and Pöttgen C 2010 Angew. Chem. Int. Ed. 49 1578 [2]    Scheidt E-W, Hauf C, Reiner F, Eickerling G and Scherer W 2011 J Phys.: Conf. Ser. 273             012083 [3]    Anderson P W and Kim Y B 1964 Rev. Mod. Phys. 36 39 [4]    Beasley M R, Labusch R and Webb W W 1969 Phys. Rev. 181 682 [5]    Campbell I A, Fruchter L and Cabanel R 1990 Phys. Rev. Lett. 64 1561 [6]    Baenitz M, Lüders K, Barišić N, Cho Y, Li Y, Yu G, Zhao X and Greven M 2010 J. Phys.: Conf.                Ser. 234 012024 [7]    Rohrmoser B, Eickerling G, Presnitz M, Scherer W, Eyert V, Hoffmann R-D, Rodewald U C,               Vogt C and Pöttgen R 2007 J. Am. Chem. Soc. 129 9356  [8]    Blatter G, Feigel’man M V, Geshkenbein V B, Larkin A I and Vinokur V M 1994 Rev. Mod.                   Phys.  66 1125 [9]    Maley M P, Willis J O, Lessure H and McHenry M E 1990 Phys. Rev. B 42 2639 [10]  Blatter G and Geshkenbein V B in: Bennemann K H and Ketterson J B (Eds.)               Superconductivity, Vol. I, Springer Berlin Heidelberg 2008, p. 495       

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Flux creep in the quasi-1D superconducting carbide Sc3CoC4

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