magnetic properties

IIT Mandi Low Temperature Physics Laboratory

1

Magneto-transport study of

superconducting materials

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

Internship Report

Summer 2015


Internship Report: Koustav Chandra 2

Abstract

Magneto-transport study was 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 83.0%. The polycrystalline samples of another

superconductor PdTe2 were also prepared in the light for further investigation. Also, a

brief theoretical study of the related subject matter is provided for a complete

understanding.



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. Special thanks to Juhi Pandey for editing

the report and suggesting requisite changes.

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 its 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



Section 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 diamagnetic

material”; 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 “Meissner

Effect” after the first observer, German physicist Walther Meissner. A sketch marking the

difference in perfect conductivity and superconductivity is shown in fig. A-1.

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.

https://en.wikipedia.org/wiki/Walther_Meissner



Fig A-2: Explaining Meissner 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 Meissner 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 two 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)



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=Bo exp(-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 b2|ψ(r)|4 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 two length parameters is

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.



(A) (B)

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

However, none of these theory is 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.



Section B: Experimental Setup

B.1 PPMS-DynaCool (Physical Property Measurement System)

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

measurement of 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.

B.1.1 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



B.1.2 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 four 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 three channels shown (B) A sketch of its bird’s eye view.

After some measurements 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-2(B)). The voltmeter has a very

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



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

possible to know, with a high degree of certainty, both the current and the voltage drop

across the sample and thus calculate the resistance with Ohm’s law.

B.2 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.

B.2.1 Sample Mounting

The cleaned sample was then stuck to brass half-tube sample holder (fig. B-3) 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

66 mm.

Fig B-3: 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 DC mode of measurement was used,

the process of centering was done in DC mode. This is done to ensure the sample is

present in the surrounding of the super-conducting magnetic coil where the magnetic field

is the strongest.



Fig B-4: Graph showing about the centering of the sample.

Fig B-5: DC Centering Measurement and Measured SQUID Voltage Response

B.2.2 Magnetic Properties measurement using MPMS-3(Magnetic

Property Measurement System)

The measurements were carried out in DC Mode with the magnetic moment dependence

on temperature being measured at different temperatures while the magnetization



dependence on magnetic field accomplished at 2 K temperature. To do so a sequence

suggesting the former was run in the MPMS MultiVu software. MPMS MultiVu

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 C-4: The MPMS-3 system



Section C: Experimental Results & Analysis

C.1 The dependence of resistance with temperature

4 8 12 16

0.000

0.004

0.008

0.012

(

cm)

T(K)

FeTe0.6

Se0.4

1-10T

Fig C-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 12.5 K unlike the expected value of 14.5 K. Further as observed from

the graph C-1 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. C-2, 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 20.95 T for Tonset and 11.06 T for Tmid using the value of

temperatures at field of 8 T (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 28.152 T for T mid and 42.010 T for T onset.



0

3

6

9

12

15

6 9 12

T(K)

H(T

)

FeTe0.6

Se0.4

Tmid

Tonset

Fig C-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.

C.2 Magnetization Dependence with Temperature

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 Origin Lab Origin 9.01b.

The Magnetic moment dependence on temperature plot as shown in fig.C-3 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 5 10 15 20 25-0.020

-0.015

-0.010

-0.005

0.000

0.005

M(e

mu/g

m)

Temperature (K)

ZFC

FC

FeTe0.6

Se0.4

Fig C-3: Magnetic moment dependence on temperature at 10 Oe 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.(C-4) 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.

0 5 10 15 20 25

-0.8

-0.6

-0.4

-0.2

0.0

0.2

-4(e

mu/g

m-O

e)

Temperature (K)

ZFC

FC

FeTe0.6

Se0.4

Fig C-4: 4 vs T at 10 Oe field

FeTe0.6Se0.4



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

beyond 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.

-60000 -30000 0 30000 60000

-0.04

-0.02

0.00

0.02

0.04

M

(em

u)

H(Oe)

FeTe0.6

Se0.4

Fig C-5: M-H plot at 2 K

C.3 Change in Magnetization with Applied Magnetic Field

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.(C-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.(C-7) a conclusion can be

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



0 50 100 150 200 250 300-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

M(e

mu/g

m)

Temperature(K)

ZFC

FC

FeTe0.6

Se0.4

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

Conclusion

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

low temperature electrical and magnetic properties showed a transition in its properties 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 which was quite low as

compared to the expected one. This was because of the poor contact points that was

formed while creating the contacts. Assumption of oxidation of the sample can be

guessed to form ferromagnetic compound. The magnetic susceptibility of the material

shows the material to be a bulk superconductor with the superconducting volume fraction

of 83.0%.



Sec D: Preparation of bulk superconducting compounds

D.1 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 0.7057 gm 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 75 kg/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 D-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.



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

D.2 Synthesis of bulk PdSe

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 65 gm/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.



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

https://scholar.google.co.in/citations?view_op=view_citation&hl=en&user=tYdcF-UAAAAJ&citation_for_view=tYdcF-UAAAAJ:u5HHmVD_uO8C

https://scholar.google.co.in/citations?view_op=view_citation&hl=en&user=tYdcF-UAAAAJ&citation_for_view=tYdcF-UAAAAJ:u5HHmVD_uO8C

https://scholar.google.co.in/citations?view_op=view_citation&hl=en&user=yxnG9WQAAAAJ&citation_for_view=yxnG9WQAAAAJ:lSLTfruPkqcC



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.

For measurement of M-T at 10Oe.

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

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

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

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

further action

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

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

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

mode.

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

Cooling)

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

continuous mode.

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

temperature to 300 K to complete the measurement sequence.

For measurement of M-H at 2 K.

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

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

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

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

further action.

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



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 50000 Oe Step Linear

Auto-tracking was run next to it.

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

Auto-tracking was run next to it.

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

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

magnetic properties

Documents

project report

koustav chandra

low temperature electrical

guidance of

lack of gratitude

brief theoretical study

related subject matter

valuable guidance