Layered Pnictides are proven to be a great reservoir for superconductors in
the past and ternary zirconium pnictide chalcogenides of ZrXY-type (X = P, As;
Y = S, Se) might be a platform for new superconductors. The superconducting
properties of carefully grown (chemical transport reaction) single crystals of
ZrP1.54S0.46 with a transition temperature of Tc = 3.5 K are investigated.
This compound (PbFCl structure type) contains square planar nets: One of the
nets is completely occupied (no vacancies) by P, the other one characterized
by a random distribution of P and S (full occupation: no vacancies). Besides
zero-field-cooling (zfc), field-cooling (fc), and remanent moment (rem)
measurements, especially magnetization and ac susceptibility measurements are
performed. A nearly ideal type-II behavior with a Ginzburg-Landau parameter κ
= 24 is found. The magnetization curves between Bc1 and Bc2 for increasing
field are in excellent agreement with theoretical calculations performed by E.
H. Brandt based on the Ginzburg-Landau theory. The decreasing branches of the
magnetization curves are asymmetric about the field axis indicating weak
pinning and also large diamagnetic behavior

Baenitz, M.

Kniep, R.

Lüders, Klaus

Schmidt, M.

Steglich, F.

Abstract Layered Pnictides are proven to be a great reservoir for superconductors in the past and ternary zirconium pnictide chalcogenides of ZrXY-type (X = P, As; Y = S, Se) might be a platform for new superconductors. The superconducting properties of carefully grown (chemical transport reaction) single crystals of ZrP1.54S0.46 with a transition temperature of Tc = 3.5 K are investigated. This compound (PbFCl structure type) contains square planar nets: One of the nets is completely occupied (no vacancies) by P, the other one characterized by a random distribution of P and S (full occupation: no vacancies). Besides zero-field-cooling (zfc), field-cooling (fc), and remanent moment (rem) measurements, especially magnetization and ac susceptibility measurements are performed. A nearly ideal type-II behavior with a Ginzburg-Landau parameter κ = 24 is found. The magnetization curves between Bc1 and Bc2 for increasing field are in excellent agreement with theoretical calculations performed by E. H. Brandt based on the Ginzburg-Landau theory. The decreasing branches of the magnetization curves are asymmetric about the field axis indicating weak pinning and also large diamagnetic behavior

Lüders, K.

MPG.PuRe

Type-II Superconductivity in Ternary Zirconium Pnictide Chalcogenide Single Crystals

AbstractLayered Pnictides are proven to be a great reservoir for superconductors in the past and ternary zirconium pnictide chalcogenides of ZrXY-type (X = P, As; Y = S, Se) might be a platform for new superconductors. The superconducting properties of carefully grown (chemical transport reaction) single crystals of ZrP1.54S0.46 with a transition temperature of Tc = 3.5K are investigated. This compound (PbFCl structure type) contains square planar nets: One of the nets is completely occupied (no vacancies) by P, the other one characterized by a random distribution of P and S (full occupation: no vacancies). Besides zero-field-cooling (zfc), field-cooling (fc), and remanent moment (rem) measurements, especially magnetization and ac susceptibility measurements are performed. A nearly ideal type-II behavior with a Ginzburg-Landau parameter κ = 24 is found. The magnetization curves between Bc1 and Bc2 for increasing field are in excellent agreement with theoretical calculations performed by E. H. Brandt based on the Ginzburg-Landau theory. The decreasing branches of the magnetization curves are asymmetric about the field axis indicating weak pinning and also large diamagnetic behavior

Elsevier - Publisher Connector 

 Physics Procedia  81 ( 2016 )  65 – 68 
Available online at www.sciencedirect.com
1875-3892 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the ISS 2015 Program Committee
doi: 10.1016/j.phpro.2016.04.026 
ScienceDirect
28th International Symposium on Superconductivity, ISS 2015, November 16-18, 2015, Tokyo, 
Japan
Type-II Superconductivity in Ternary Zirconium Pnictide 
Chalcogenide Single Crystals
M Baenitza*, K Lüdersa,b, R Kniepa, F Steglicha, M Schmidta
aMax-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187 Dresden, Germany 
bFachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
Abstract
Layered Pnictides are proven to be a great reservoir for superconductors in the past and ternary zirconium pnictide chalcogenides 
of ZrXY-type (X = P, As; Y = S, Se) might be a platform for new superconductors. The superconducting properties of carefully 
grown (chemical transport reaction) single crystals of ZrP1.54S0.46 with a transition temperature of Tc = 3.5 K are investigated. 
This compound (PbFCl structure type) contains square planar nets: One of the nets is completely occupied (no vacancies) by P,
the other one characterized by a random distribution of P and S (full occupation: no vacancies). Besides zero-field-cooling (zfc),
field-cooling (fc), and remanent moment (rem) measurements, especially magnetization and ac susceptibility measurements are 
performed. A nearly ideal type-II behavior with a Ginzburg-Landau parameter ț = 24 is found. The magnetization curves 
between Bc1 and Bc2 for increasing field are in excellent agreement with theoretical calculations performed by E. H. Brandt based 
on the Ginzburg-Landau theory. The decreasing branches of the magnetization curves are asymmetric about the field axis 
indicating weak pinning and also large diamagnetic behavior.
© 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the ISS 2015 Program Committee.
Keywords: Layered Pnictides; Type-II superconductivity
1. Introduction
     Recently, superconductivity in single crystals of ternary Zr pnictide chalcogenides was reported [1,2]. Depending 
on the chemical composition the highest superconducting transition temperature of Tc = 3.5 K was found for the 
* Corresponding author. Tel.: +49 351 4646 3217; fax: +49 351 4646 3232
E-mail address: Michael.Baenitz@cpfs.mpg.de
© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the ISS 2015 Program Committee
66   M. Baenitz et al. /  Physics Procedia  81 ( 2016 )  65 – 68 
system ZrP1.54S0.46 which was established by zfc and fc magnetization data as well as by specific heat measurements, 
providing evidence for bulk superconductivity in this system. These findings are remarkable in comparison with the 
behavior of the closely related system ZrAs1.58Se0.39 showing superconductivity only at Tc = 0.14 K [1,2]. Both 
systems crystallize in the tetragonal PbFCl structure type [3]. ZrAs1.58Se0.39 has about 3 at.% vacancies within the 
monoatomic As layer, whereas  ZrP1.54S0.46 contains the P layers without detectable indications for any kind of 
vacancies. The absence of vacancies in ZrP1.54S0.46 might promote the superconductivity in this system.
     On the other hand early investigations of the sub-systems Zr-P and Zr-S exhibit superconducting transition 
temperatures comparable to that of ZrP1.54S0.46)RUĮ-ZrP transition temperatures from 4.3 to 4.9 K were reported 
for NaCl-type ZrP1.0-0.9. For the system Zr0.83-0.85S, also with NaCl-type structure, transition temperatures from 3.70 
to 3.87 K were found [4]. However, the samples used in these investigations, were no single crystals but powdered 
materials. Although the crystal structures of these binary compounds are different from those of the ternary phases, 
the atomic distances between Zr and P or S, respectively, are comparable. In the binary compounds the distances are 
263 pm for Zr-P and 258 pm for Zr-S [4], whereas in the ternary compound the distance between the Zr- and the P-
layers is 260 pm and between the Zr- and P/S-layers is 287 pm. In view of this background it is desirable to get more 
detailed information on the superconducting properties of ZrP1.54S0.46 which are presented in this contribution.
2. Experimental
     Single crystals of ZrP1.54S0.46 are prepared by chemical transport reaction as already described in Ref. [1]. Using a 
sample with a mass of 10.2 mg zero field cooled (zfc), field cooled (fc), remanent moment (rem), magnetization, 
and ac susceptibility measurements are performed by means of commercially available magnetometers (MPMS and 
PPMS, Quantum Design Inc.).
3. Results and discussions
3.1 Phase diagram
                                          
Fig. 1. (a) Field-temperature phase diagram for ZrP1.54S0.46, temperature dependence of the critical magnetic fields Bc1 and Bc2; (b) phase diagram 
including the irreversibility field Birr (markers for Birr: triangles: ac measurements, others: magnetization measurements)
     Fig. 1(a) shows the temperature dependence of the lower and upper critical field Bc1(T) and Bc2(T) determined 
from magnetization curves. Within the error bars they follow a quadratic function crossing the temperature axis at 
the transition temperature Tc = 3.2 K. The onset transition occurs at 3.5 K. Following the expressions connecting the 
Ginzburg-Landau parameter ț with the ratio of the two critical fields given in Ref. [5], leads to a value of ț = 24. An 
analysis of the slopes of the magnetization curves at Tc results in similar values. This ț-value means that there exists 
a relatively large area in the phase diagram where magnetic flux penetrates into the sample. However, for a rather 
large part of this area the pinning forces are negligible as can be seen in fig. 1(b), showing in addition to the critical 
field curves the irreversibility line Birr(T). Its values are only larger by a factor of about 5 compared to Bc1(0) but 
smaller by a factor of nearly 60 compared with Bc2(0). This means that the system shows nearly ideal type-II 
superconducting behavior. The temperature dependence of the irreversibility line follows also a quadratic function 
but with a small correction described by an exponent m, (1 – (T/Tc)
2)m with m = 1.3. This leads to a smooth negative 
bending near Tc similar to the behavior of high-Tc superconductors [6] which, according to the theory of Matsushita 
(a) (b)
 M. Baenitz et al. /  Physics Procedia  81 ( 2016 )  65 – 68 67
[7], is based on a depinning mechanism caused by thermally activated flux creep. The deviation of the values 
determined from magnetization measurements might be due to another pinning mechanism perhaps depending on 
the grain size which is comparable to the magnetic penetration depth Ȝ in this region. 
3.2 Magnetization
     Fig. 2(a) shows examples of magnetization loops for three different temperatures. The peaks where magnetic flux 
starts to penetrate into the sample are rather sharp also indicating type-II behavior with very weak pinning. For 
further analyzing of the magnetization curves the parts between Bc1 and Bc2 are  considered.  As  example  the  curve 
for the temperature  1.8 K is shown in fig. 2(b). The magnetic moment –M is normalized to its maximum value Bc1
occurring at b = B/(Bc2 – Bc1) on the horizontal axis, where b
0.5 is plotted in order to stretch the low field region. 
Such plots can be compared with theoretical expressions calculated by E.H. Brandt [5] from the Ginzburg-Landau 
theory for the entire range of fields between Bc1 and Bc2 and a set of Ginzburg-Landau parameters between ț = 0.85 
and ț = 200. In the figure the prediction for ț = 24 is plotted which leads to a very good agreement with our 
experimental data. This means, that the field inside the sample corresponds to an ideal triangular vortex lattice.
                                          
Fig. 2. (a) Central parts of magnetization loops for three different temperatures; (b) magnetization data for 1.8 K between Bc1 and Bc2 in 
comparison with the prediction calculated from the Ginzburg-Landau theory [5]
3.3 Ac susceptibility
     In order to get more information about the vortex dynamics ac susceptibility measurements are performed. The 
temperature dependence of the real and imaginary parts of the ac susceptibility, ȤƍDQGȤƍƍZDVUHFRUGHGLQPDJQHWLF
fields up to 3 mT. Frequency and ac field amplitude were fixed to 1 kHz and 0.1 mT, respectively. Fig. 3(a) shows 
some results. Comparing the applied magnetic fields with the phase diagram in fig. 1(b) shows that the curves for 2 
and 3 mT do not enter the Meissner phase below Bc1. For further analysis the ac results are used which are obtained 
for the fields where the zero field state is reached at the temperature of 1.8 K (0.27, 0.7, and 1.0 mT in fig. 3(a)). The 
imaginary parts of the ac susceptibility are plotted against their real parts (fig. 3(b)). The peak heights of Ȥƍƍ DUH
about 0.24 if the minimum values of ȤƍDUHQRUPDOL]HGWR௅6RWKLVSORWVKRZVWKHEHKDYLRURIWKHWUDQVLWLRQUHJLRQ
from the field to the zero field state. This kind of plot can be compared with theoretical predictions [8] based either
on Bean’s critical state model or another model based on diffusive motion of the flux lines, both indicated in the 
figure. Only at temperatures very near to the onset temperature to superconductivity the experimental values seem to 
correspond to the model of diffusive motion. Mainly, however, their behavior agrees well with the prediction of the 
critical state model.
3.4 Zfc, fc, and rem measurements
     Zero field cooled (zfc), field cooled (fc), and remanent moment (rem) measurements are performed in different 
applied magnetic fields (0.12, 0.335, 0.5, 1.0, and 5.0 mT). These field values are similar to the variety of fields
applied in the ac measurements in order to allow comparisons of the results of both methods. In agreement with the 
ac results the zfc curves show that for applied fields below Bc1 (at 1.8 K below 1.0 mT) complete flux expulsion is 
reached. With increasing temperature flux penetration occurs earlier in higher applied magnetic fields. However, the
(a) (b)
68   M. Baenitz et al. /  Physics Procedia  81 ( 2016 )  65 – 68 
                                                 
Fig. 3. (a) Real parts ȤƍFORVHGV\PEROVDQGLPDJLQDU\SDUWVȤƍƍRIWKHDFVXVFHSWLELOLW\IRUGLIIHUHQWDSSOLHGPDJQHWLFILHOGV; (b) ȤƍƍSORWWHG
against ȤƍIRUWKUHHILHOGVLQWKHORZILHOGUHJLRQFRPSDUHGZLWKWKHRUHWLFDOSUHGLFWLRQVWULDQJOHV0.27, circles: 0.7, squares: 1.0 mT)
magnetic moments at 1.8 K (measured at the three magnetic fields 0.12, 0.335, and 0.5 mT) are not proportional to 
these field values. An extrapolation to zero shows that their zero line occurs at about – HPXJ§ 4 % of the 
magnetic moment at 0.12 mT). This indicates an additional diamagnetic contribution which obviously is due to 
shielding currents localized in the surface region of the sample. This effect of diamagnetism cannot be neglected in 
superconductors in which the pinning force is weak [9] which is reasonable in our case. Also the fc and rem 
behavior supports such diamagnetism conspicuously. For both groups of curves the extrapolated zero line differs 
from the real zero line: for the fc curves at their merging points and for the rem curves at the point where the sign of 
the slope is changing. At temperatures above these points only this diamagnetic contribution is responsible for the 
measured magnetic moments, whereas below these points in addition the flux line caused diamagnetism (fc) or 
paramagnetism (rem), respectively, is present.
4. Conclusions
Single crystals of the layered zirconium pnictide chalcogenide ZrP1.54S0.46 exhibit superconductivity below 3.5 K. 
According to magnetization, ac susceptibility, zfc/fc, and rem measurements the material can be classified as a 
nearly ideal type-II superconductor. In the mixed state the magnetization follows the prediction of the Ginzburg-
Landau theory with a ț-value of 24. The corresponding area in the phase diagram is relatively large with only weak 
pinning forces. Furthermore the ac susceptibility behavior agrees well with the prediction of Bean’s critical state 
model. The presence of weak pinning is also supported by an additional diamagnetic contribution observed in the 
zfc/fc and rem measurements. In comparison with other Zr pnictide chalcogenides it is obvious that the absence of 
vacancies in ZrP1.54S0.46 is essential for its superconducting properties.
Acknowledgements
We would like to thank H. Rave for experimental help and T. Cichorek for fruitful discussions. One of us (KL) 
would like to thank F. Steglich and A.P. Mackenzie for their kind hospitality and the possibility of doing research at 
the MPI-CPfS.
References
[1]  T. Cichorek, L. Bochenek, A. Czulucki, M. Schmidt, R. Niewa, G. Auffermann, Y. Prots, R. Wawryk, M. Baenitz, F. Steglich, R. Kniep,
Scientific Report MPG/CPfS (2011) 103 (www.cpfs.mpg.de/2081022/B_2009-2010.pdf). 
[2]  T. Cichorek, to be published. 
[3]  A. Schlechte, R. Niewa, M. Schmidt, G. Auffermann, Y. Prots, W. Schnelle, D. Gnida, T. Cichorek, F. Steglich, R. Kniep, Sci. Techn. Adv. 
Mater. 8 (2007) 341.
[4]  A.R. Moodenbaugh, D.C. Johnston, R. Viswanathan, R.N. Shelton, L.E. DeLong, W.A. Fertig, J. Low Temp. Phys. 33 (1978) 175.
[5]  E.H. Brandt, Phys. Rev. B 68 (2003) 054506.
[6]  P. Schilbe, K. Lüders, M. Baenitz, D.A. Pavlov, A. Abakumov, E.V. Antipov, Physica C 388-389 (2003) 247.
[7]  T. Matsushita, Physica B 164 (1990) 150.
[8]  X. Ling, J.I. Budnick, in R.A. Hein, T.L. Francavilla, D.H. Liebenberg (Eds.), Magnetic Susceptibility of Superconductors and other Spin
Systems, Plenum Press, New York and London, 1991, p. 377.
[9] T. Matsushita, Flux pinning in superconductors, second ed., Springer, Berlin Heidelberg, 2014, Sec. 2.6.
(a) (b)


Type-II Superconductivity in Ternary Zirconium Pnictide Chalcogenide Single Crystals 

Institutional Repository of the Freie Universität Berlin

 Physics Procedia  81 ( 2016 )  65 – 68 Available online at www.sciencedirect.com1875-3892 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the ISS 2015 Program Committeedoi: 10.1016/j.phpro.2016.04.026 ScienceDirect28th International Symposium on Superconductivity, ISS 2015, November 16-18, 2015, Tokyo, JapanType-II Superconductivity in Ternary Zirconium Pnictide Chalcogenide Single CrystalsM Baenitza*, K Lüdersa,b, R Kniepa, F Steglicha, M SchmidtaaMax-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187 Dresden, Germany bFachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, GermanyAbstractLayered Pnictides are proven to be a great reservoir for superconductors in the past and ternary zirconium pnictide chalcogenides of ZrXY-type (X = P, As; Y = S, Se) might be a platform for new superconductors. The superconducting properties of carefully grown (chemical transport reaction) single crystals of ZrP1.54S0.46 with a transition temperature of Tc = 3.5 K are investigated. This compound (PbFCl structure type) contains square planar nets: One of the nets is completely occupied (no vacancies) by P,the other one characterized by a random distribution of P and S (full occupation: no vacancies). Besides zero-field-cooling (zfc),field-cooling (fc), and remanent moment (rem) measurements, especially magnetization and ac susceptibility measurements are performed. A nearly ideal type-II behavior with a Ginzburg-Landau parameter ț = 24 is found. The magnetization curves between Bc1 and Bc2 for increasing field are in excellent agreement with theoretical calculations performed by E. H. Brandt based on the Ginzburg-Landau theory. The decreasing branches of the magnetization curves are asymmetric about the field axis indicating weak pinning and also large diamagnetic behavior.© 2016 The Authors. Published by Elsevier B.V.Peer-review under responsibility of the ISS 2015 Program Committee.Keywords: Layered Pnictides; Type-II superconductivity1. Introduction     Recently, superconductivity in single crystals of ternary Zr pnictide chalcogenides was reported [1,2]. Depending on the chemical composition the highest superconducting transition temperature of Tc = 3.5 K was found for the * Corresponding author. Tel.: +49 351 4646 3217; fax: +49 351 4646 3232E-mail address: Michael.Baenitz@cpfs.mpg.de© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the ISS 2015 Program Committee66   M. Baenitz et al. /  Physics Procedia  81 ( 2016 )  65 – 68 system ZrP1.54S0.46 which was established by zfc and fc magnetization data as well as by specific heat measurements, providing evidence for bulk superconductivity in this system. These findings are remarkable in comparison with the behavior of the closely related system ZrAs1.58Se0.39 showing superconductivity only at Tc = 0.14 K [1,2]. Both systems crystallize in the tetragonal PbFCl structure type [3]. ZrAs1.58Se0.39 has about 3 at.% vacancies within the monoatomic As layer, whereas  ZrP1.54S0.46 contains the P layers without detectable indications for any kind of vacancies. The absence of vacancies in ZrP1.54S0.46 might promote the superconductivity in this system.     On the other hand early investigations of the sub-systems Zr-P and Zr-S exhibit superconducting transition temperatures comparable to that of ZrP1.54S0.46)RUĮ-ZrP transition temperatures from 4.3 to 4.9 K were reported for NaCl-type ZrP1.0-0.9. For the system Zr0.83-0.85S, also with NaCl-type structure, transition temperatures from 3.70 to 3.87 K were found [4]. However, the samples used in these investigations, were no single crystals but powdered materials. Although the crystal structures of these binary compounds are different from those of the ternary phases, the atomic distances between Zr and P or S, respectively, are comparable. In the binary compounds the distances are 263 pm for Zr-P and 258 pm for Zr-S [4], whereas in the ternary compound the distance between the Zr- and the P-layers is 260 pm and between the Zr- and P/S-layers is 287 pm. In view of this background it is desirable to get more detailed information on the superconducting properties of ZrP1.54S0.46 which are presented in this contribution.2. Experimental     Single crystals of ZrP1.54S0.46 are prepared by chemical transport reaction as already described in Ref. [1]. Using a sample with a mass of 10.2 mg zero field cooled (zfc), field cooled (fc), remanent moment (rem), magnetization, and ac susceptibility measurements are performed by means of commercially available magnetometers (MPMS and PPMS, Quantum Design Inc.).3. Results and discussions3.1 Phase diagram                                          Fig. 1. (a) Field-temperature phase diagram for ZrP1.54S0.46, temperature dependence of the critical magnetic fields Bc1 and Bc2; (b) phase diagram including the irreversibility field Birr (markers for Birr: triangles: ac measurements, others: magnetization measurements)     Fig. 1(a) shows the temperature dependence of the lower and upper critical field Bc1(T) and Bc2(T) determined from magnetization curves. Within the error bars they follow a quadratic function crossing the temperature axis at the transition temperature Tc = 3.2 K. The onset transition occurs at 3.5 K. Following the expressions connecting the Ginzburg-Landau parameter ț with the ratio of the two critical fields given in Ref. [5], leads to a value of ț = 24. An analysis of the slopes of the magnetization curves at Tc results in similar values. This ț-value means that there exists a relatively large area in the phase diagram where magnetic flux penetrates into the sample. However, for a rather large part of this area the pinning forces are negligible as can be seen in fig. 1(b), showing in addition to the critical field curves the irreversibility line Birr(T). Its values are only larger by a factor of about 5 compared to Bc1(0) but smaller by a factor of nearly 60 compared with Bc2(0). This means that the system shows nearly ideal type-II superconducting behavior. The temperature dependence of the irreversibility line follows also a quadratic function but with a small correction described by an exponent m, (1 – (T/Tc)2)m with m = 1.3. This leads to a smooth negative bending near Tc similar to the behavior of high-Tc superconductors [6] which, according to the theory of Matsushita (a) (b) M. Baenitz et al. /  Physics Procedia  81 ( 2016 )  65 – 68 67[7], is based on a depinning mechanism caused by thermally activated flux creep. The deviation of the values determined from magnetization measurements might be due to another pinning mechanism perhaps depending on the grain size which is comparable to the magnetic penetration depth Ȝ in this region. 3.2 Magnetization     Fig. 2(a) shows examples of magnetization loops for three different temperatures. The peaks where magnetic flux starts to penetrate into the sample are rather sharp also indicating type-II behavior with very weak pinning. For further analyzing of the magnetization curves the parts between Bc1 and Bc2 are  considered.  As  example  the  curve for the temperature  1.8 K is shown in fig. 2(b). The magnetic moment –M is normalized to its maximum value Bc1occurring at b = B/(Bc2 – Bc1) on the horizontal axis, where b0.5 is plotted in order to stretch the low field region. Such plots can be compared with theoretical expressions calculated by E.H. Brandt [5] from the Ginzburg-Landau theory for the entire range of fields between Bc1 and Bc2 and a set of Ginzburg-Landau parameters between ț = 0.85 and ț = 200. In the figure the prediction for ț = 24 is plotted which leads to a very good agreement with our experimental data. This means, that the field inside the sample corresponds to an ideal triangular vortex lattice.                                          Fig. 2. (a) Central parts of magnetization loops for three different temperatures; (b) magnetization data for 1.8 K between Bc1 and Bc2 in comparison with the prediction calculated from the Ginzburg-Landau theory [5]3.3 Ac susceptibility     In order to get more information about the vortex dynamics ac susceptibility measurements are performed. The temperature dependence of the real and imaginary parts of the ac susceptibility, ȤƍDQGȤƍƍZDVUHFRUGHGLQPDJQHWLFfields up to 3 mT. Frequency and ac field amplitude were fixed to 1 kHz and 0.1 mT, respectively. Fig. 3(a) shows some results. Comparing the applied magnetic fields with the phase diagram in fig. 1(b) shows that the curves for 2 and 3 mT do not enter the Meissner phase below Bc1. For further analysis the ac results are used which are obtained for the fields where the zero field state is reached at the temperature of 1.8 K (0.27, 0.7, and 1.0 mT in fig. 3(a)). The imaginary parts of the ac susceptibility are plotted against their real parts (fig. 3(b)). The peak heights of Ȥƍƍ DUHabout 0.24 if the minimum values of ȤƍDUHQRUPDOL]HGWR௅6RWKLVSORWVKRZVWKHEHKDYLRURIWKHWUDQVLWLRQUHJLRQfrom the field to the zero field state. This kind of plot can be compared with theoretical predictions [8] based eitheron Bean’s critical state model or another model based on diffusive motion of the flux lines, both indicated in the figure. Only at temperatures very near to the onset temperature to superconductivity the experimental values seem to correspond to the model of diffusive motion. Mainly, however, their behavior agrees well with the prediction of the critical state model.3.4 Zfc, fc, and rem measurements     Zero field cooled (zfc), field cooled (fc), and remanent moment (rem) measurements are performed in different applied magnetic fields (0.12, 0.335, 0.5, 1.0, and 5.0 mT). These field values are similar to the variety of fieldsapplied in the ac measurements in order to allow comparisons of the results of both methods. In agreement with the ac results the zfc curves show that for applied fields below Bc1 (at 1.8 K below 1.0 mT) complete flux expulsion is reached. With increasing temperature flux penetration occurs earlier in higher applied magnetic fields. However, the(a) (b)68   M. Baenitz et al. /  Physics Procedia  81 ( 2016 )  65 – 68                                                  Fig. 3. (a) Real parts ȤƍFORVHGV\PEROVDQGLPDJLQDU\SDUWVȤƍƍRIWKHDFVXVFHSWLELOLW\IRUGLIIHUHQWDSSOLHGPDJQHWLFILHOGV; (b) ȤƍƍSORWWHGagainst ȤƍIRUWKUHHILHOGVLQWKHORZILHOGUHJLRQFRPSDUHGZLWKWKHRUHWLFDOSUHGLFWLRQVWULDQJOHV0.27, circles: 0.7, squares: 1.0 mT)magnetic moments at 1.8 K (measured at the three magnetic fields 0.12, 0.335, and 0.5 mT) are not proportional to these field values. An extrapolation to zero shows that their zero line occurs at about – HPXJ§ 4 % of the magnetic moment at 0.12 mT). This indicates an additional diamagnetic contribution which obviously is due to shielding currents localized in the surface region of the sample. This effect of diamagnetism cannot be neglected in superconductors in which the pinning force is weak [9] which is reasonable in our case. Also the fc and rem behavior supports such diamagnetism conspicuously. For both groups of curves the extrapolated zero line differs from the real zero line: for the fc curves at their merging points and for the rem curves at the point where the sign of the slope is changing. At temperatures above these points only this diamagnetic contribution is responsible for the measured magnetic moments, whereas below these points in addition the flux line caused diamagnetism (fc) or paramagnetism (rem), respectively, is present.4. ConclusionsSingle crystals of the layered zirconium pnictide chalcogenide ZrP1.54S0.46 exhibit superconductivity below 3.5 K. According to magnetization, ac susceptibility, zfc/fc, and rem measurements the material can be classified as a nearly ideal type-II superconductor. In the mixed state the magnetization follows the prediction of the Ginzburg-Landau theory with a ț-value of 24. The corresponding area in the phase diagram is relatively large with only weak pinning forces. Furthermore the ac susceptibility behavior agrees well with the prediction of Bean’s critical state model. The presence of weak pinning is also supported by an additional diamagnetic contribution observed in the zfc/fc and rem measurements. In comparison with other Zr pnictide chalcogenides it is obvious that the absence of vacancies in ZrP1.54S0.46 is essential for its superconducting properties.AcknowledgementsWe would like to thank H. Rave for experimental help and T. Cichorek for fruitful discussions. One of us (KL) would like to thank F. Steglich and A.P. Mackenzie for their kind hospitality and the possibility of doing research at the MPI-CPfS.References[1]  T. Cichorek, L. Bochenek, A. Czulucki, M. Schmidt, R. Niewa, G. Auffermann, Y. Prots, R. Wawryk, M. Baenitz, F. Steglich, R. Kniep,Scientific Report MPG/CPfS (2011) 103 (www.cpfs.mpg.de/2081022/B_2009-2010.pdf). [2]  T. Cichorek, to be published. [3]  A. Schlechte, R. Niewa, M. Schmidt, G. Auffermann, Y. Prots, W. Schnelle, D. Gnida, T. Cichorek, F. Steglich, R. Kniep, Sci. Techn. Adv. Mater. 8 (2007) 341.[4]  A.R. Moodenbaugh, D.C. Johnston, R. Viswanathan, R.N. Shelton, L.E. DeLong, W.A. Fertig, J. Low Temp. Phys. 33 (1978) 175.[5]  E.H. Brandt, Phys. Rev. B 68 (2003) 054506.[6]  P. Schilbe, K. Lüders, M. Baenitz, D.A. Pavlov, A. Abakumov, E.V. Antipov, Physica C 388-389 (2003) 247.[7]  T. Matsushita, Physica B 164 (1990) 150.[8]  X. Ling, J.I. Budnick, in R.A. Hein, T.L. Francavilla, D.H. Liebenberg (Eds.), Magnetic Susceptibility of Superconductors and other SpinSystems, Plenum Press, New York and London, 1991, p. 377.[9] T. Matsushita, Flux pinning in superconductors, second ed., Springer, Berlin Heidelberg, 2014, Sec. 2.6.(a) (b)

Type-II Superconductivity in Ternary Zirconium Pnictide Chalcogenide Single
Crystals

M. Baenitz

K. Lüders

R. Kniep

F. Steglich

M. Schmidt

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Physics Procedia

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Type-II Superconductivity in Ternary Zirconium Pnictide Chalcogenide Single Crystals

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