By

Koustav Chandra

Dept. of Physics& Astronomy

National Institute of Technology, Rourkela

Under the guidance of

Dr. C.S. Yadav

School of Basic Science

IIT Mandi

Magneto-transport study of

superconducting materials

Internship Report:

2

Abstract:

Magneto-transport study were performed on FeTe0.6Se0.4 sample for determining

its low temperature electrical and magnetic properties. A transition in its

properties were observed at 12.75 K, thus marking its superconducting phase

transition. The upper critical field of Hc2 (0) =42.010 K was found from its

electrical properties. The magnetic susceptibility of the material shows the

material to be a bulk superconductor with the superconducting volume fraction

of 83.4 %. The polycrystalline samples of another superconductor PdTe2 were also

prepared in the light of further investigation. Also a brief theoretical study of the

related subject matter is provided for a complete understanding.

3

Acknowledgment

Dated: 21st Feb, 2015

“It is not possible to prepare a project report without the assistance & encouragement of

other people. This one is certainly no exception.”

On the very outset of this report, I would like to extend my sincere & heartfelt obligation

towards all the personages who have helped me in this endeavor. Without their active

guidance, help, cooperation & encouragement, I would not have made headway in the

project.

I am ineffably indebted to Surender Lal Sharma for conscientious guidance and

encouragement to accomplish this assignment.

I am extremely thankful and pay my gratitude to my guide and instructor Dr. C.S.

Yadav for his valuable guidance and support on completion of this project in it’s

presently.

I extend my gratitude to IIT Mandi for giving me this opportunity.

I also acknowledge with a deep sense of reverence, my gratitude towards my parents

and member of my family, who has always supported me morally as well as

economically.

At last but not least gratitude goes to all the members of the Low Temperature

Physics Lab who directly or indirectly helped me to complete this project report.

Any omission in this brief acknowledgment does not mean lack of gratitude.

Gracias

Koustav Chandra

Dept. Of Physics & Astronomy

NIT Rourkela

4

Sec A: Introduction

When in the year 1911, Kammerlingh Onnes found the perfect conductivity in mercury

(Hg) at 4.18 K, a new wing of Condensed Matter Physics cropped up known as the

Superconductivity. Over the years a lot of developments has taken place in the subject. For

the benefit of the readers a brief account of the necessary stuff related to the subject matter

is provided to suffice the theoretical understanding required to appreciate the results of the

experiments discussed in the report.

The name superconductor was awarded to those few compounds, alloys and elements

because of the vanishing resistance when cooled below a specific temperature thus marking

a phase transition from normal state to “super”-conducting state. The temperature

corresponding to it is named as the critical temperature (Tc).

Fig A-1: Picturing the difference in between normal materials and superconductors (source: cyberphysics.co.uk)

Further a superconductor has an amazing property of mocking a “perfect diamagnet”;

meaning it repels all the applied magnetic flux lines. When resistance falls to zero, a current

can circulate inside the material without any dissipation of energy. Secondly, provided they

are sufficiently weak, external magnetic fields will not penetrate the superconductor, but

remain at its surface. The phenomenon named as “Meisnner Effect” after the first observer,

German physicist Walther Meissner. A sketch marking the difference in perfect

conductivity and superconductivity is shown in fig. A-2.

At any given temperature, T < Tc, there is a certain minimum field Bc (T), called the

critical field, which will kill superconductivity. It is found (experimentally and theoretically)

that Bc is related to T by the equation: Bc = B0 [1− (T/Tc) 2], where B0 is the asymptotic value of the critical field as T →0 K.

5

Fig A-2: Explaining Meisnner Effect, in superconductor where the magnetic flux is completely

expelled out of the bulk material when cooled below Tc unlike the perfect

conductor.(Source:physics.ox.ac.uk)

The superconducting state can be destroyed by a rise in temperature or in the applied

magnetic field, which then penetrates the material and suppresses the Meisnner effect.

From this perspective, a distinction is made between two types of superconductors. Type-I

materials remain in the superconducting state only for relatively weak applied magnetic

fields. Above a given threshold, the field abruptly penetrates into the material, shattering

the superconducting state. Conversely, Type-II superconductors tolerate local penetration

of the magnetic field, which enables them to preserve their superconducting properties in

the presence of intense applied magnetic fields. This behavior is explained by the existence

of a mixed state where superconducting and non-superconducting areas coexist within the

material. For the type-II superconductors there are 2 associated values of critical magnetic

fields as shown in fig. A-5. The Hc2 is called upper critical field and lower one Hc1 as lower

critical field.

Fig A-3: Critical field plotted against temperature for various type-I superconductors (source: web.mit.edu/8.13)

6

To account for an explanation for these effects, the London brothers marked that

superconductivity was due to a macroscopic quantum phenomenon in which there was long

range order of the momentum vector. This implies condensation in momentum space. Fritz

London also realized that it is the rigidity of the superconducting wave function ψ which is

responsible for perfect diamagnetism. The London equation,

J = -nq2A/m

was developed from Maxwell’s equations. This leads to an equation for the magnetic

field B (= ∇ × A) of the form

∇2B = B/λ 2

where λ is the London penetration depth. The λ demarcates the extent to which

the external field can penetrate within the superconductor (fig.A-4).

Fig A-4: Explaining the fall in Magnetic flux lines inside the superconductor (B=Boexp (-x/))

Unsatisfied by this explanation, Ginzburg proposed an extended version of Landau

theory arguing over the fact that the superconductivity of the sample is due to a phase

transition from normal to a superconducting state. From the free energy equation:

Fs = Fn + d3r [a (T)|ψ(r)|2 + b2|ψ(r)|4 + 1/2m | − iℏ ∇ψ(r) + 2eAψ(r)|2+ (B(r)−B0)2/2µ0]

where ψ(r) = ψ0e iθ(r) is the complex order parameter and B0 is the applied field, he arrived

at

∇ 2ψ = ψ/ξ 2

where ξ=√ℏ 2/2m|a(T )| using the fact that near Tc we can neglect the bψ2 term because ψ

→ 0.The coherence length, ξ gives the measure of the distance within which the

superconducting current carrier concentration cannot change drastically in a spatially-

varying magnetic field. The real significance of the 2 length parameters are realized when

one takes the ratio κ = λ/ξ. If κ < 1/ √2, we have a type I superconductor. If κ > 1/ √2, we

have a type II superconductor.

7

(A) (B)

Fig A-5 :( A) For type-I superconductor, (B) For type-II superconductor

However none of these theory are rivaled when compared to the celebrated BCS theory.

The trio American physicist, put forward the fact that interaction between electron and

phonons(quantized lattice vibrations) causes a reduction in Coulombic repulsion between

electrons below Tc ,to provide a net long range attraction to form Bose-particles with

opposite momentum and spin known as Cooper pairs. Since they are bosons they have the

privilege of occupying the same quantum state. At T<Tc these cooper pairs condense into a

single quantum state accounting for zero resistance.

The quenching of superconductivity occurs when due to the added energy above Tc,

the Cooper pairs can no longer withstand the increasing repulsion thus breaking up into

constituent electrons.

(A) (B) (C)

Fig A-5: Discussing the formation of Cooper pairs. (A),(B) & (C)Shows how an approaching electron

distorts the ions in its neighborhood thus providing a region where the incoming electrons get entrapped followed by another electron when it nears into the decreased positively charged

region(Source: physics.ox.ac.uk )

However the BCS theory failed when high temperature superconductivity came into

the scenario for BCS theory roughly predicted that one can’t obtain superconductors

beyond a certain temperature. To fill in many theories are still being proposed but in vain.

8

Experimental Setup

Sec B: PPMS-Dynacool (Physical Property Measurement System)

The quantum design PPMS system is a cryogen-free instrument that helps in measurement

in physical property of the sample under investigation. Using this highly sophisticated

device measurement of resistivity against temperature was figured out. Since the sample

had undergone some form of corrosion, errors in the measurement was expected.

Resistivity Option

Since only resistivity was measured using this apparatus so a brief overview of the

Resistivity option for the device is provided. The Resistivity option can report resistance

as well as resistivity, conductance, and conductivity. Resistivity sample pucks (Fig B-2)

have four contacts ⎯ one positive and one negative contact for current and voltage for

each user bridge board channel to which a sample may be conventionally wired. Up to

three samples may be mounted on a Resistivity puck, so the Resistivity option may

measure up to three samples at one time.

Fig B-1: PPMS-Dynacool system

9

Sample Mounting

The sample with dimension of just 2.83 mm and area of cross section of 0.36 mm2 was

quite an uphill battle when it came to mounting for a greenhorn like me. So under the witty

advice of my guide the sample was stuck to a thin piece of mica sheet using GE varnish

along with 4 copper wires stripped at their ends only before mounting on Resistivity Puck

(Fig. B-2).

One of the end of the wires were then stuck to the sample using silver paste to ensure

perfect contact. The other ends of the wires were then soldered to the puck, and then scaled

on the Sample Wiring Test Station.

(A) (B)

Fig B-2 :( A) Resistivity Puck with the 3 channels shown (B) A sketch of its bird’s eye view.

After some measurement on the puck, to ensure near perfect contacts using multimeter the

sample was mounted into the PPMS system. The PPMS DynaCool uses an innovative style

of sample mounting by providing at the bottom of the sample chamber a 12-pin connector

pre-wired to the system electronics. This connector allowed to plug in a removable sample

insert (or “puck”) for convenient access to electrical leads and sample mounting.

Why 4-probe measurement used?

Using four wires to attach a sample to a sample puck greatly reduces the contribution of

the leads and joints to the resistance measurement. In a four-wire resistance measurement,

current is passed through a sample via two current leads, and two separate voltage leads

measure the potential difference across the sample (Fig B-9(B)). The voltmeter has a very

high impedance, so the voltage leads draw very little current. In theory, a perfect voltmeter

10

draws no current whatsoever. Therefore, by using the four-wire method, it is possible to

know, to a high degree of certainty, both the current and the voltage drop across the sample

and thus calculate the resistance with Ohm’s law.

11

Sec C: MPMS-3(Magnetic Property Measurement System)

The MPMS-3 system is a Squid (Superconducting Quantum Interference Device)

magnetometry device that provides three possible measurement modes: DC Scan Mode,

VSM Mode and AC Susceptibility Mode. In the report an outlook of the DC mode is

given for it was the one used in the measurement procedure.

Sample Packing

The cleaned sample was then stuck to brass half-tube sample holder (fig. B-1) using GE

low temperature varnish after proper cleaning of the sample holder using ethanol and cotton

buds. It was then centered using sample mounting station to ensure it lies in about 66mm.

Fig C-1:- Brass Half-tube Sample Holder

The sample is mounted in a sample holder that is attached to the end of a rigid sample

rod. The sample rod was then introduced into the sample space through a special type of

double seal (called the lip seal) designed to allow the rod to be actuated by a drive

mechanism located outside of the chamber. Since I was using the DC Mode of measurement,

I had to do the process of centering in the DC mode. This is done to ensure the sample is

present in the surrounding of the super-conducting magnetic coil where it is the strongest.

12

Fig C-2:- Graph showing about the centering of the sample.

Fig C-3: DC Centering Measurement and Measured SQUID Voltage Response

Measurements

Magnetic Properties measurement using MPMS-3(Magnetic Property

Measurement System)

As cited earlier the measurements taken was in the DC Mode using which measurements

13

of magnetic moment of sample against an applied field of 10 Oe at various temperature and

variation of magnetic moment against magnetic field at 2K temperature was measured. To

do so a sequence suggesting the former was run in the MPMS Multi-Vu software. MPMS

Multi-Vu integrates all system operations into one versatile and easy-to-use Windows 7

interface. The sequence was programmed in a fashion after the proper set of measurement

algorithm was known (Appendix-B).

Fig B-3:-The MPMS-3 system

14

Sec D: Experimental Analysis

For Resistivity vs. Temperature

Fig D-1: Temperature dependence of the resistivity of FeTe0.60Se0.40 single crystals, measured in the

magnetic fields (from right to left) H = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 & 10T

From the experimental data it was confirmed that the sample shows a superconductive

phase transition at 12.5K unlike the expected value of 14.5K. Further as observed from the

graph B-10 it can be seen that the sample shows a gradual conversion into superconductive

phase transition rather than the sharp transition expected as usual. The error can be

accounted to the failure on my part to make perfect silver point contacts in the sample.

In the Fig. B-11, a H-T phase diagram was plotted for the crystals, corresponding to

the temperatures where the resistivity drops to 90% of the normal state resistivity ρn, (where

ρn is taken at temperature T = 16 K) and 50% of ρn, where the two are labeled as T onset and

T mid respectively. Using these data, the value of Hc (0), critical magnetic field at 0K using

the formula:

Hc=Hc (0)[1-(T/Tc)2]

which was found to be at 20.95T for T onset and 11.06T for T mid using the value of

temperatures at field of 8T (arbitrary). To get a better result of the values the Werthamer–

Helfand–Hohenberg (WHH) formula:

Hc2 (0)=-0.693(dHc2/dT)Tc

was used. Using this formula a value of 28.152T for T mid and 42.010T for T onset.

0 2 4 6 8 10 12 14 16 18

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

(

cm

)

T(K)

FeTe0.6Se0.4

1-10T

15

Fig D-2: The upper critical field versus temperature phase diagram is shown for the points where

electrical resistivity drops to 90% &50% of n, shown by T onset and T mid.

For Magnetic Moment vs Temperature measurement

The temperature dependence of magnetic moment obtained from the MPMS3 was used in

getting an idea about temperature dependence of susceptibility which was graphed against

temperature using OriginLab Origin 9.01b.

The Magnetic moment dependence on temperature plot as shown in fig. (B-4) exhibits a

transition of the sample from its normal state to its superconducting state at a temperature

of about 12.75 K. The error exhibited while measurement could have been due to oxidation

of the sample.

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8 9 10 11 12

T(K)

H(T

) (T

)

T onset

T mid

FeTe0.6Se0.4

16

Fig D-3: Magnetic moment dependence on temperature at 10Oe field

To investigate upon the fact a plot of 4 vs. T using the data obtained and the

electrodynamics relations:

M=H

B=H (1+4)

From the plot in fig. (B-5) we figure out the fact that there is a gradual drop and not an

abrupt fall as expected from the theoretical data and previous experimental measurements

as performed by other individuals.

Fig D-4: 4 vs. T at 10Oe field

Further as clearly visible from the plot the transition does not stop at 1.8 K, the point beyond

0 5 10 15 20 25-0.00030

-0.00025

-0.00020

-0.00015

-0.00010

-0.00005

0.00000

0.00005

M(e

mu

)

T(K)

FeTe0.6Se0.4

0 5 10 15 20 25

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

-4(e

mu/g

m-O

e)

T(K)

FeTe0.6Se0.4

17

which the MPMS-3 used can’t cool. So we can surmise that the sample which had been

boxed up for so long had been oxidized to a certain extent that has led to it unveiling its

ferromagnetic property even at that low temperature instead of undergoing a phase

transition into diamagnetic state as expected from Meissner effect on superconductor.

Fig B-6: M-H plot at 2K

For Magnetization vs. Magnetic Moment

To determine the dependence of the duo the M-H algorithm was run in the MPMS-3 system

and using the obtained data points a trace was made. As shown in the fig. (B-6) the line

scatter diagram shows a hysteresis curve of a ferromagnetic sample rather than an expected

a mirror-anthill illustration. So a further confirmation about the sample rusting away with

time can be uttered.

To extract a further evidence an M-T measurement at higher applied magnetic field is

done and from its field cooling plot as manifested in the fig. (B-7) a conclusion can be

drawn that the specimen under investigation has been oxidized thus affecting its property.

-60000 -30000 0 30000 60000

-0.04

-0.02

0.00

0.02

0.04

M(e

mu

)

H(Oe)

DC Moment Fixed Ctr (emu)

FeTe0.6Se0.4

18

Fig B-7: M-T plot at 100Oe field

Conclusion

So, the data obtained and the plots displays a lot of erroneous results caused primarily due to

corrosion of FeTe0.6Se0.4, the sample under investigation. Yet a lot of experience gained at the

end of the day on the subject concerned. An experimental outlook on how the magnetic

properties of the sample undergoes a turmoil when cooled beyond its transition temperature is

learned in first hand, an experience to ponder upon.

0 50 100 150 200 250 300-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

M(e

mu)

T(K)

FeTe0.6Se0.4

19

Synthesis of bulk PdTe2,

Poly-crystalline bulk PdTe2 compound was synthesized via solid state route. For the

preparation of 1gm of sample 0.2942 gm. of Pd(99.9%-3N) and 0.7057gm of Te(99.99%-

4N) from Sigma Aldrich was mixed and grounded to ensure a molar ratio of 1:2 using

mortar and pestle for a period of over 1 hour to ensure they form a finely mixed powder.

The well mixed sample was then made into a pellet using a clean pellet press by applying

a pressure of 75kg/cc. The pressed pellets were then sealed off inside an evacuated quartz

tube(<10-3 torr) and put into a tube furnace immediately for heating at 850oC at the rate of

100oC/h for 24h before cooling it off at 500oC to which it was dropped at the rate of 50oC/h

until it was finally stopped.

Fig E-1: Mortar with pestle

The shiny black sample was taken out from inside the quartz tube, grounded into fine

powder, pelletized and kept back vacuumed and sealed inside the tube furnace following

the same sequence as earlier for sintering. The dense, shiny gray one-piece was taken out,

wrapped in a butter paper for further experiments to be performed upon.

Sec E: Preparation of bulk superconducting compounds

20

Fig E-2: Lindberg Blue M TF55035A-1 Tube Furnace

Synthesis of bulk Pd1Se1

Poly-crystalline bulk PdSe compound was prepared via solid state reaction. A mixture of

the ingredients Pd (99.9%-3N) and Se (99.99%-4N) from Sigma Aldrich in 1:1

ratio(Amount of Pd=0.5741gm & amount of Se=0.4259gm for 1 gm. of sample) was

pelletized by 65gm/cc pressure and were then sealed in an evacuated quartz tube(which

was vacuumed to 10-6 torr using diffusion pump). The sealed tube along with its contents

were then kept in a tube furnace at a temperature of 750oC with a heating rate of 100oC/h

for a period of over 24h and then cooled to 500oC @ 50oC/h until the furnace was switched

off. The obtained sample was then ground, pelletized and sintered at the same temperature

to give the final product which was then made available for further experiments to be

performed upon.

21

Appendix-A

The resistivity of the sample was carried out based on the following algorithm.

For R-T Measurement

1. Set Temperature at 2 K @ 1 K/min uniformly without overshoot and resistivity was

measured at every point.

2. The temperature is increased 20 K @ 0.2 K/min uniformly without any overshoot and

resistivity is measured at every point.

3. A field of 1 T was set and the temperature was dropped to 2 K.

4. The temperature is increased 20 K @ 0.2 K/min uniformly without any overshoot and

resistivity is measured at every point.

5. The above 2 steps are iterated for magnetic fields of 2,3,4,5,6,10 T

Appendix-B

The measurements of magnetic-properties were carried out based on these set of

algorithms.

Measurement Algorithm

For measurement of M-T at 10Oe.

6. Set Temperature at 300K @ 12K/min in Fast Settle mode and wait for 10 s.

7. Set Magnetic Field at 1T at 100 Oe/s in Linear Stable mode and delay for 30s.

8. Next set Field to 0Oe @ 100 Oe/s in Oscillatory mode and wait for 30s.

9. Set temperature to 10K @ 12K/min in fast settle mode and pause for 30s before further

action

10. Next set to 2K @ 1K/min in fast settle mode and wait for 60s.

11. Set Field to 10Oe @ 10 Oe/s in Linear Stable mode and hold for 10s.

12. DC Moment was measured against temperature from 2 K-25 K in sweep continuous

mode.

13. Set temperature to 2K @ 1K/min in fast settle mode and pause for 60s.(Field Cooling)

14. DC moment was next measured against temperature from 2 K to 25 K in sweep

continuous mode.

15. The field is next set to 0Oe @ 10Oe/s in Linear Stable mode followed by setting

temperature to 300K to complete the measurement sequence.

For measurement of M-H at 2K.

1. Set Temperature at 300K @ 12K/min in Fast Settle mode and wait for 10s.

2. Set Magnetic Field at 1T at 100 Oe/s in Linear Stable mode and delay for 30s.

3. Next set Field to 0Oe @ 100 Oe/s in Oscillatory mode and wait for 30s.

4. Set temperature to 10K @ 12K/min in fast settle mode and pause for 30s before further

22

action.

5. Next set to 2K @ 1K/min in fast settle mode and wait for 60s.

6. MPMS3 Moment (DC) vs Field 1 Quadrant 0 to 10000 Oe Step Linear Auto-tracking

was done.

7. MPMS3 Moment (DC) vs Field 1 Quadrant 10500 Oe to 50000Oe Step Linear Auto-

tracking was run next to it.

8. MPMS3 Moment (DC) vs Field 1 Quadrant 50000 Oe to -50000Oe Step Linear Auto-

tracking was run next to it.

9. Before taking out the sample the field was set to 0 Oe @ 10oe/s and re-setting

temperature to 300K @ 12K/min thus completing the sequence algorithm.

23

Bibliography

1. Prof. G. Rangarajan, Lectures on Condensed matter Physics, nptel.ac.in/courses/115106061

2. Charles Kittel, Introduction to Solid State Physics(8th edition) ,chapter-10

superconductivity

3. Upper critical field, lower critical field and critical current density of FeTe0. 60Se0.

40 single crystals(CS Yadav, PL Paulose)New Journal of Physics 11 (10), 103046

4. PdTe: a 4.5 K type-II BCS superconductor(B Tiwari, R Goyal, R Jha, A Dixit, VPS

Awana)Superconductor Science and Technology 28 (5), 055008

24