Magnetic properties and Superconductivity

SREEPRIYA SUKU
SRUTHI M K
VANDANA
VIGHNESH K

Atoms are composed of protons, neutrons and electrons. Electrons carry a negative
electrical charge and produce a magnetic field as they move through space. A magnetic field is
produced whenever an electrical charge is in motion.
Magnetism is a phenomenon by which materials exert an attractive or repulsive force on
other materials. There are two types of magnetic poles, conventionally called north and
south.
Unlike electric charges, magnetic poles always occur in North-South pairs; there are no
magnetic monopoles.
MAGNETISM
In most atoms, electrons occur in pairs. Each electron in a pair spins in the opposite
direction. So when electrons are paired together, their opposite spins cause there magnetic
fields to cancel each other. Therefore, no net magnetic field exists. Alternately, materials with
some unpaired electrons will have a net magnetic field and will react more to an external field.
Most materials can be classified as diamagnetic, paramagnetic, or ferromagnetic.

DIRECTION OF MAGNETIC FIELD
 When a current flows through a
conductor, a magnetic field surrounds
the conductor. As current flow
increases, so does the number of lines
of force in the magnetic field.
THE RIGHT HAND RULE

Permeability (μ)
This is the characteristic property of a medium.
It indicates the ease with which the material allows the
magnetic lines of force to pass through it.
OR
It is the measure of the ability of a material to support the
formation of a magnetic field within itself.
OR
In other words, it is the degree of magnetization that a material
obtains in response to an applied magnetic field.
0 r
μr- relative permeability of the medium
μ0 – permeability of free space or perme 4π×10−7 H.m-1
SI UNITS: Henry per meter(H.m-1), Newton per Ampere square (N.A-2)

Magnetic field intensity (H)
Magnetic field intensity at any point in the magnetic field is
the force experienced by an unit north pole placed at that point.
Magnetic susceptibility ( ):
Magnetic susceptibility is the degree of magnetization of a
material in response to an applied magnetic field.
HM
HM



The proportionality constant is called susceptibility. Its value may be
zero, positive or negative.
Where
M is magnetization,
H is magnetic field intensity

The magnetic induction and magnetic field intensity are related by
In vacuum HB 0
HB )1(0  
HB 
0 r
In a medium
)(0 MHB  
, Since M=0
)1(  r
Since,
HM )(0 MHB  
where Relative permeability

Quantity Symbol
SI Units
(Sommerfeld)
SI Units
(Kennelly)
CGS Units
(Gaussian)
Field H A/m A/m Oersteds
Flux Density
(Magnetic
Induction)
B Tesla Tesla Gauss
Flux f Weber Weber Maxwell
Magnetization M A/m - erg/Oe-cm3
Conversion between CGS and SI magnetic units.

EFFECTS OF TEMPERATURE:CURIE AND CURIE-
WEISS LAWS
Curie’s law states that the magnetic susceptibility is inversely proportional
to temperature.
χ=C/T C-Curie constant
Many paramagnetic substances obey Curie law, especially at high
temperatures.
Curie-Weiss law better fit to the experimental data
χ=C/T+θ
Ferromagnetic materials show a very large susceptibility at low
temperature.
Above a certain temperature(ferromagnetic Curie temperature Tc),
ferromagnetic materials reverts to paramagnetic, where Curie-Weiss law is
usually observed.

CLASSIFICATION OF MAGNETIC MATERIALS
 DIAMAGNETISM
 PARAMAGNETISM
 FERROMAGNETISM
 FERRIMAGNETISM
 ANTIFERROMAGNETISM

DIAMAGNETISM
 Diamagnetism characterizes the substances that have only non-
magnetic atoms (lack of permanent diople moment).
 Origin:
• An electron moving around the nucleus results in magnetic
moment.
• Due to different orientations of various orbits of an atom, the
net magnetic moment is zero in diamagnetic materials.
• When an external field is applied the motion of electrons in
their orbits changes resulting in induced magnetic moment in a
direction opposite to the direction of applied field.

 The magnetization induced by the applied magnetic field is very weak
and the magnetic lines of force are repelled.
 This magnetism is also exist in substances with magnetic atoms, but very
weak and completely masked by the contribution of magnetic atoms.
 Relative permeability is slightly less than unity.
 The magnetic susceptibility is independent of applied magnetic field
strength.
Magnitude of
susceptibility
Temperature dependence Examples
Small & negative Independent Organic materials,
light elements
Intermediate &
negative
Below 20K varies with field and
temperature
Alkali earths,
Bismuth
Large & Negative Exists only below critical
temperature (Meissner effect)
Superconducting
materials

PARAMAGNETISM
 The paramagnetic substances consists of magnetic atom that
posses permanent dipole moment
 Origin
 Each electron in an orbit has an orbital magnetic moment and a
spin magnetic moment.
 When the shells are unfilled there is net magnetic moment.
 In the absence of the external field the net moments of the
atoms are arranged in random directions because of thermal
fluctuations. Hence there is no magnetization.
 When external magnetic field is applied, there is tendency for the
dipoles to align with the field giving rise to an induced positive
dipole moment.
 The induced magnetism is the source for paramagnetic behaviour.

 Paramagnetic susceptibility is small and positive and is
independent of applied field strength.
 Spin alignment is random.
Magnitude of
susceptibility
Small & positive Independent Alkali metals,
transition
metals, rare
earths
Large & positive Curie law
Curie-Weiss law
T
C





T
C

FERROMAGNETISM
 Even in the absence of external applied field, some substances
exhibits strong magnetization.
 This is due to a special form of interaction called exchange coupling
between adjacent atoms that results in spontaneous magnetization
of the substance.
 When placed inside a magnetic field, it attracts the magnetic lines
of force very strongly.
 Each ferromagnetic material has a characteristic temperature
called the ferromagnetic Curie temperature θf. Below this
temperature the spontaneous magnetization exists.

Magnitude of
susceptibility
Very large &
positive
For T>θf paramagnetic behavior
For T<θf ferromagnetic behavior
Fe, Co, Ni, Gd




T
C
 Spin alignment is parallel.
 Ferromagnetic materials exhibit Hysteresis.
 They Consists of a number of small regions which are called domains.

Magnetic properties and Superconductivity

ANTI-FERROMAGNETISM
 Antiferromagnetism macroscopically similar to paramagnetism, is a weak
form of magnetism.
 In certain materials when the distance between the interacting atoms is
small the exchange forces produce a tendency for antiparallel alignment of
electron spins of neighboring atoms.
 The magnetic susceptibility increase with the increase of temperature and
reaches maximum at a certain temperature. This temperature is known as
Neel temperature (TN). Above this temperature the susceptibility again
decreases.

Spins are aligned antiparallel
Magnitude of
susceptibility
small & positive when T>TN
when T<TN
Salts of
transition
metals




T
C
T

FERRIMAGNETISM
 This is a special case of antiferromagnetism.
 The net magnetization of magnetic sublattices is not zero, since
antiparallel moments are of different magnitudes.
 Hence ferrimagnetic materials possesses a net magnetic moment.
 This moment disappears above a Curie temperature analogous to the
Neel temperature.
 Above TC, thermal energy randomizes the individual magnetic
moments and the material becomes paramagnetic.

 Ferrimagnetic domains become magnetic bubbles to act as memory
elements.
 Spin alignment is antiparallel of different magnitudes.
Magnitude of
susceptibility
Very large &
positive
when T>TN
when T<TN behaves as paramagnetic
material
Ferrites




T
C

HYSTERESIS
Hysteresis of ferromagnetic materials refers to the lag of magnetization
behind the magnetizing field.
 A hysteresis loop is a curve showing the change in
magnetic induction of a ferromagnetic material
with an external field.
 When the external magnetic field is increased the
magnetic induction increases.

 Once magnetic saturation has been achieved, a decrease in the
applied field back to zero results in a macroscopically permanent
or residual magnetization, known as remanance, Mr. The
corresponding induction, Br, is called retentivity or remanent
induction of the magnetic material. This effect of retardation by
material is called hysteresis.
 The magnetic field strength needed to bring the induced
magnetization to zero is termed as coercivity, Hc. This must be
applied anti-parallel to the original field.
 A further increase in the field in the opposite direction results in
a maximum induction in the opposite direction. The field can once
again be reversed, and the field-magnetization loop can be closed,
this loop is known as hysteresis loop or B-H plot or M- H plot.

DISCOVERY OF SUPERCONDUCTIVITY
 Kamerlingh Onnes passed a current through a
very pure mercury wire and measured its
resistance as he steadily lowered the
temperature. Much to his surprise there was no
resistance at 4.2K.
1913

SUPERCONDUCTIVITY
Superconductivity is a quantum state of matter and it is the phenomenon of
exactly zero electrical resistance and expulsion of magnetic fields occurring in
certain materials when cooled below a characteristic critical temperature.
ZERO ELECTRICAL
RESISTANCE
EXPULSION OF
MAGNETIC FIELD
No collisions!!
No energy loss!!
 IDEAL DIAMAGNETISM

The superconducting state is defined by three very important factors:
critical temperature (Tc), critical field (Hc), and critical current density
(Jc). Each of these parameters is very dependent on the other two
properties present
•Critical temperature (Tc) The highest temperature at which
superconductivity occurs in a material. Below this transition
temperature T the resistivity of the material is equal to zero.
•critical magnetic field (Hc ) Above this value of an externally applied
magnetic field a superconductor becomes nonsuperconducting.
•critical current density (Jc) The maximum value of electrical current
per unit of cross-sectional area that a superconductor can carry
without resistance.

CHARACTERISTICS PROPERTIES OF A SUPERCONDUCTOR :
FACTOR AFFECTING
Temperature : If a ring made of superconducting material is cooled in a magnetic field from ordinary
temperature to a value below its critical temperature and then the magnetic field is removed, an induced
current is set up in the ring. The resistance in the superconducting state being practically zero, the decay of
this induced current will take infinitely long time.
Magnetic field : Application of magnetic field to a superconducting specimen brings a stage when for
H=Hc, the critical field, the superconductor behaves like a normal material i.e., the superconductivity
disappears.
Current : If the magnetic field around the superconductor is increased beyond the critical field the
superconductivity is destroyed and the sample behaves as a normal material. Therefore the supercurrent will
flow only up to its critical value .Once the field exceeds Hc(T) the current becomes just the ordinary current.

Stress : Application of stress increases the transition temperature. As Hc(T) is temperature
dependent, increased stress is found to result in a slight change of Hc(T).
Size : Size of specimen exhibiting superconductivity is an important parameter for its behaviour.
Impurity : The presence of impurities changes almost all properties of a superconductor
especially its magnetic behaviour.
Isotopic Constitution of the Specimen : The critical temperature of a
specimen depends on the isotopic mass. The presence of various isotopes in a given specimen
decided what its average isotope mass will be. The dependence of Tc on such a mass is also called
Isotope Effect.
MaTc = constant or Tc  M-1/2

The Meissner and Ochsenfeld Effect
T > Tc T < Tc

BCS THEORY OF SUPERCONDUCTIVITY
John Bardeen Leon Cooper Bob Schrieffer
“ B. C. S.”
 The BCS theory successfully shows that electrons can be attracted to
one another through interactions with the crystalline lattice. This
occurs despite the fact that electrons have the same charge.
 When the atoms of the lattice oscillate as positive and negative
regions, the electron pair is alternatively pulled together and pushed
apart without a collision.
 The electron pairing is favorable because it has the effect of putting
the material into a lower energy state.
 When electrons are linked together in pairs, they move through the
superconductor in an orderly fashion.
1972

Cooper Pair:
• Two electrons that appear to "team up" in accordance with theory - BCS
or other - despite the fact that they both have a negative charge and
normally repel each other. Below the superconducting transition
temperature, paired electrons form a condensate - a macroscopically
occupied single quantum state - which flows without resistance
Leon Cooper

HIGH TEMPERATURE SUPERCONDUCTIVITY
 High-temperature superconductors (abbreviated high-Tc or HTS) are materials that behave
as superconductors at unusually high temperatures..The first high-Tc superconductor was discovered in
1986 by IBM researchers Georg Bednorz and K. Alex Müller, who were awarded the 1987 Nobel Prize in
Physics "for their important break-through in the discovery of superconductivity in ceramic materials".
 Type-II superconductors are usually made of metal alloys or complex oxide ceramics. All high
temperature superconductors are type-II superconductors. While most elemental superconductors are
type-I, niobium, vanadium and technetium are elemental type-II superconductors. Boron-
doped diamond and silicon are also type-II superconductors. Metal alloy superconductors also exhibit
type-II behavior (e.g.niobium-titanium and niobium-tin).
 Other type-II examples are the cuprate-perovskite ceramic materials which have achieved the highest
superconducting critical temperatures. These include La1.85Ba0.15CuO4, BSCCO, and YBCO (Yttrium-
Barium-Copper-Oxide), which is famous as the first material to achieve superconductivity above the
boiling point of liquid nitrogen (77 K). Due to strong vortex pinning, the cuprates are close to ideally
hard superconductors.

DISCOVERY OF HIGH TEMPERATURE SUPERCONDUCTIVITY
 In 1986, 75 years after the discovery of
superconductivity, George Bednorz and Karl Müller
at IBM, Zurich demonstrated superconductivity in a
perovskite structured lanthanum based cuprate
oxide which showed a Tc of 35 K for which the
inventors also won Physics Noble prize in 1987.
1987
PRESS RELEASE

HIGH TEMPERATURE SUPERCONDUCTORS

CUPRATES
HIGH TEMPERATURE SUPERCONDUCTORS
PEROVSKITE

 High-transition-temperature (Tc) superconductivity in copper oxides (cuprates) is one of the most
intriguing emergent phenomena in strongly correlated electron systems.
 It has attracted great attention since its discovery because Tc can exceed the boiling temperature of
liquid nitrogen, which is much higher than the putative limit of Tc ~ 40 K derived from the BCS theory for
conventional superconductivity.
 The cuprate superconductors have a layered crystal structure consisting of CuO2 planes separated by
charge reservoir layers, which may dope electrons or holes into the CuO2 planes.
 On doping holes, the antiferromagnetic Mott insulating phase of the parent compounds disappears and
superconductivity emerges. Tc follows a dome-like shape as a function of doping, with a
maximum Tc around 16% doped per CuO2 plaquette.
 A similar phase diagram is seen on doping electrons, albeit with a more robust antiferromagnetic phase
and a lower Tc. On the hole-doped side, there exists an enigmatic state above Tc called the pseudogap,
where the electron density of states within certain momentum region is suppressed.

IRON BASED HIGH TEMPERATURE
SUPERCONDUCTORS

APPLICATIONS OF SUPERCONDUCTORS
 MAGLEV TRAINS
MRI

 TELECOMMUNICATIONS
• Superconductors are used as efficient filters in
cellular telephone towers (now 700 worldwide)
• Separate signals of individual phone calls.
• Because of electrical resistance, conventional
interference filters eat away part of the signal.
 TRANSMISSION LINES
• 15% of generated electricity is dissipated in transmission
lines
• Potential 100-fold increase in capacity
• BNL Prototype: 1000 MW transported in a diameter of
40 cm
 TELECOMMUNICATIONS

Magnetic properties and Superconductivity

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