Unit Unit Unit Unit – – – 3 3 3 Magnetic Magnetic Magnetic Magnetic Materials Materials Materials Materials 1
Engineering Physics 2 Unit-3
Nov 02, 2014
Engineering Physics 2 Unit-3
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Uni
t U
nit
Uni
t U
nit
– –––3 333
Uni
t U
nit
Uni
t U
nit
– –––3 333
Mag
neti
c
Mag
neti
c
Mag
neti
c
Mag
neti
c M
ater
ials
Mat
eria
lsM
ater
ials
Mat
eria
ls
1
Mag
netic
mat
eria
lsar
esu
bsta
nce
whi
chup
on
bein
gin
trod
uced
into
anex
tern
alm
agne
tfie
ld,
they
them
selv
esbe
com
esou
rce
ofan
addi
tiona
lmag
netic
field
.
Mag
neti
c M
ater
ials
Mag
neti
c M
ater
ials
Mag
neti
c M
ater
ials
Mag
neti
c M
ater
ials
Mat
eria
ls w
itho
utw
itho
utw
itho
utw
itho
ut
perm
anen
t m
agm
omen
ts
Mat
eria
ls w
ith
wit
hw
ith
wit
hpe
rman
ent
mag
mom
ents
2
perm
anen
t m
agm
omen
ts
mag
mom
ents
Dia
Dia
Dia
Dia
Par
aP
ara
Par
aP
ara
Fer
roF
erro
Fer
roF
erro
Wea
kS
tron
g
Sp
ace
aro
und
the
mag
net
or
curr
en
tca
rryi
ng
con
du
ctor
whe
reth
em
ag
ne
tice
ffe
ctis
felt.(A
mp/
m).
Mag
netic
Fie
ld
Mag
netic
Lin
es o
f For
ce
Ma
gn
etic
file
dis
ass
um
ed
toco
nsi
sts
ofl
ine
so
fma
gn
etic
forc
es.
Th
ese
lines
off
orc
es
see
ms
totrav
ele
xte
rna
llyfr
om
Nor
thto
Sou
thp
ole
sof
the
Ma
gn
et.
Th
islin
es
off
orc
es
are
calle
da
sth
em
agne
ticlin
esof
forc
es.
Mag
netic
Flu
x (Φ
)
“To
tal n
umbe
r of m
ag
ne
tic li
ne
s o
f fo
rce
pa
ssin
g th
rou
gh
a s
urf
ace
”.
(Web
er).
BA
φ=
3
Mag
netic
indu
ctio
n or
Mag
netic
flux
den
sity
(B
)
“Th
e n
um
be
r o
f ma
gn
etic
lin
es
of fo
rce
pa
ssin
g
perp
endi
cula
rlyth
rou
gh
a u
nit
are
a”.
(Wb/
m2
or T
esla
).
[1 W
eb
er
= 1
08m
ag
ne
tic li
ne
s].
BAφ
=
For
ceex
perie
nced
by
au
nit
nort
hp
ole
pla
ced
at
tha
tp
oin
tin
am
ag
ne
ticfie
ld.(A
mp/
m).
Ra
tiob
etw
ee
nth
em
ag
ne
ticin
du
ctio
n(B
)a
nd
the
pe
rme
ab
ility
oft
he
me
diu
min
wh
ich
ma
gn
etic
field
exi
sts.
Mag
netic
Fie
ld In
tens
ity (
H)
BH
µ=
Two
eq
ua
lan
du
nlik
ep
ole
sse
pa
rate
db
ya
dis
tan
ce.
Mag
netic
Dip
oles
Dip
ole
Mom
ent (
µ m)
4
“Th
e p
rod
uct
of m
agne
ticpo
lest
reng
th(m
) a
nd
leng
tho
f th
e m
ag
ne
t (l)”.
(Am
p/m
2 ).
mm
lµ
=m
IA
µ=
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
“Th
em
ea
sure
oft
he
ma
gn
etiz
atio
nin
an
ym
ag
ne
ticm
ate
ria
l”.
“T
hem
agne
tic“m
omen
tper
unit
volu
me”.
(Wb/
m2 )
.
Inte
nsity
of M
agne
tizat
ion
(I)
Mag
netic
Sus
cept
ibili
ty (χ
m)
mI
Vµ=
“Ra
tioo
fth
ein
ten
sity
ofm
ag
ne
tiza
tion
(I)
pro
du
ced
toth
ea
pp
lied
ma
gn
etic
field
inte
nsi
ty(H
)”.
χ mof
am
ater
iali
sa
mea
sure
ofth
eea
sew
ithw
hich
the
mat
eria
lcan
be
mag
netis
ed.
Mag
netic
Sus
cept
ibili
ty (χ
m)
Boh
r M
agne
ton
(µB)
Th
e o
rbita
l ma
gn
etic
mo
me
nt a
nd
th
e s
pin
ma
gn
etic
mo
me
nt o
f an
ele
ctro
n
m
I Hχ
=
5
Th
e o
rbita
l ma
gn
etic
mo
me
nt a
nd
th
e s
pin
ma
gn
etic
mo
me
nt o
f an
ele
ctro
n
in a
n a
tom
is e
xpre
sse
d in
te
rms
of
atom
ic u
nit c
alle
d B
ohr
mag
neto
n.
Ele
ctro
nch
arge
xP
lanc
ksco
nsta
nt
2x
elec
tron
char
ge2
Be
e mµ
==ℏ
24
29
.27
10
Bx
Am
µ−
=
The
ratio
be
twe
en
them
agne
ticflu
xde
nsity
(B)
and
the
appl
ied
mag
netic
field
inte
nsity
(H).
The
me
asu
reo
fd
eg
ree
at
wh
ich
the
lines
of
forc
eca
np
ene
trate
thro
ug
hth
em
ate
ria
l.Mag
netic
Per
mea
bilit
y (µ
)
Bµ
µµ
==
or
B Hµ
µµ
==
Mag
netic
indu
ctio
n (B
) du
e to
mag
netic
fiel
d in
tens
ity (
H)
are
dire
ctly
pr
opor
tiona
l to
each
oth
er.
oB
Hµ=B
Hα
whe
re µ 0
-pe
rmea
bilit
y of
free
sp
ace
(vac
uum
) 4πx
10–7
H/m
.
If th
e fie
ld is
app
lied
in a
ny m
ediu
m o
f per
mea
bilit
y (µ
) th
en
6
If th
e fie
ld is
app
lied
in a
ny m
ediu
m o
f per
mea
bilit
y (µ
) th
en
BHµ=B H
µ=
“Th
era
tiob
etw
een
the
pe
rme
abili
tyo
fth
emed
ium
toth
ep
erm
ea
bili
tyo
ffree
spac
e”.
Rel
ativ
e P
erm
eabi
lity
(µr)
roµ
µµ
=
Rel
atio
n be
twee
n µ r
and χ m
0(
)to
tal
flux
den
sity
BH
Mµ
∴=
+
We
know
,B
µ=
Rel
atio
n be
twee
n µ r
and χ m
Whe
n a
mag
netic
mat
eria
l is
plac
ed in
a m
agne
tic fi
eld
(H),
then
tw
o ty
pes
of li
nes
of in
duct
ion
pass
es th
roug
h th
e m
ater
ial.
viz.
,
(i)D
ue to
mag
netiz
ing
field
(H)
(ii)D
ue to
mat
eria
l its
elf b
eing
mag
netiz
ed b
y in
duct
ion
(M)
7
We
know
,
BHµ=
B Hµ
=
Equ
atin
g eq
uatio
ns (
1) a
nd (
2), w
e ge
t
0(
)H
HM
µµ
=+
Sin
ce
00(
)rH
HM
µµ
µ=
+
0r
µµ
µ=
00
()
r
MH
HH
µµ
µ=
+H
m
M Hχ
=S
ince
00
(1)
rm
HH
µµ
µχ
=+
(1)
rm
µχ
=+
8
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
Whe
nan
exte
rnal
field
isap
plie
dto
the
spec
imen
itism
agne
tised
and
whe
nth
efie
ldisr
emov
edit
isde
mag
netis
ed.
But
som
em
ate
rialsd
ono
tco
mpl
etel
yde
mag
netis
ew
hen
field
isre
mov
ed.
Ret
entiv
ity
rem
oved
.T
here
isso
me
mag
netis
mleft
outi
nth
esp
ecim
en.
“Th
ere
sidu
alm
agne
tism
wh
ich
isle
fto
ut
eve
nafte
rthe
rem
oval
oft
he
ext
ern
alm
ag
ne
ticfie
ld”
-Ret
entiv
ityor
Rem
anen
ce.
Coe
rciv
ity
The
res
idua
l mag
netis
m c
an b
e re
mov
ed c
ompl
etel
y fr
om t
he
9
The
res
idua
l mag
netis
m c
an b
e re
mov
ed c
ompl
etel
y fr
om t
he
mat
eria
l by
appl
ying
a r
ever
se m
agne
tic fi
eld.
“T
he
rev
erse
mag
netic
fiel
d wh
ich
is u
sed
to co
mpl
etel
y re
mov
e th
e r
esi
du
al m
ag
ne
tism
” -C
oerc
ivity
.
Mac
rosc
opic
mag
netic
prop
ertie
sof
asu
bsta
nce
are
aco
nseq
uenc
eof
mag
netic
mom
entsa
ssoc
iate
dwith
indi
vidu
alel
ectr
ons.
Eac
hel
ectr
onin
anat
omha
sm
agne
ticm
om
ents
that
orig
inat
efr
omthe
follo
win
gtw
oso
urce
s.
Orig
in o
f Mag
netic
Mom
ents
follo
win
gtw
oso
urce
s.i.
Orb
ital
mag
netic
mom
ento
fele
ctro
ns.
ii.S
pin
mag
netic
mom
ento
fele
ctro
ns.
10
Thr
ee c
ontr
ibut
ions
for
the
mag
netic
dip
ole
mom
ent o
f an
atom
.
i.O
rbita
l mag
netic
mom
ent:
Orb
ital m
otio
n of
ele
ctro
ns (
i.e.,
the
mot
ion
of e
lect
rons
in th
e cl
osed
orb
its a
roun
d th
e nu
cleu
s). It
s m
agni
tude
is a
lway
s sm
all.
ii.S
pin
mag
netic
mom
ent:
ii.S
pin
mag
netic
mom
ent:
Spi
n m
otio
n of
the
elec
tron
s (i.
e., d
ue to
el
ectr
on s
pin a
ngul
ar in
m
omen
tum
).iii
.N
ucle
ar m
agne
tic m
omen
t:C
ontr
ibut
ion
from
the
nuc
lear
spi
n (i.
e., d
ue to
nu
clea
r sp
in an
gula
r m
omen
tum
). I
t is
near
ly 10
3tim
es sm
alle
rtha
n th
at o
f ele
ctro
n sp
in, i
t is
not t
aken
into
con
side
ratio
n.
For
allp
ract
ical
purp
oses
-m
agne
ticm
omen
tar
ises
due
toth
eel
ectr
onsp
inig
norin
gth
eor
bita
land
the
nucl
earm
agne
ticm
omen
tsas
thei
rm
agni
tude
sar
esm
all.
11
e–-
revo
lvin
gn
ucl
eus-
circ
ular
orb
it.
Cu
rren
tcar
ryin
gci
rcu
larc
oil
pro
du
cem
agn
etic
field┴
rto
itsp
lan
e.
i)O
rbita
lan
gula
rmom
entu
mof
the
e–s
Th
us
thee
lect
roni
cor
bits
are
asso
ciat
edw
itha
mag
netic
mom
ent.
Ele
ctro
nch
arg
ex
Pla
nck
sco
nst
an
t
2x
ele
ctro
na
ssB
mµ
==
Orb
italm
agne
ticm
omen
tofan
e–in
anat
omca
nb
eex
pre
ssed
inte
rms
of
atom
icun
itof
mag
netic
mom
entca
lled
Boh
rMag
netr
on.
ii)E
lect
ron
spin
mag
netic
mom
ent2
e
e mℏ
Intr
od
uce
d in
ord
er to
exp
lain
the de
tails
of a
tom
ic s
pect
ra-re
fer s
pin
of th
e e– .
Acc
ord
ing
to qu
antu
m th
eory
, th
e sp
in a
ng
ula
r m
om
entu
m a
lon
g a
giv
en d
ir is
ei
ther
()
44
hh
or
ππ
+−
4
eh
mπ+
4
eh
mπ
−=
+1
Boh
r m
agne
tron
=
-1
Boh
r mag
netr
on.
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
12
An
gu
lar
mo
men
tum
asso
ciat
edw
ithn
ucl
ear
spin
isal
som
easu
red
inu
nits
ofh/
2π.
Mas
so
fth
enu
clea
ris
larg
erth
anth
ato
fan
e–b
ya
fact
or
of
the
ord
ero
f103 .
Hen
cen
ucl
ear
spin
mag
net
icm
om
enti
so
fth
eo
rder
of
10–3
Boh
rmag
netr
ons.
iii)
Nuc
lear
mag
netic
mom
entu
m
Mag
neti
c M
ater
ials
Mag
neti
c M
ater
ials
Mag
neti
c M
ater
ials
Mag
neti
c M
ater
ials
Mat
eria
ls w
itho
utw
itho
utw
itho
utw
itho
ut
perm
anen
t m
agm
omen
ts
Mat
eria
ls w
ith
wit
hw
ith
wit
hpe
rman
ent
mag
mom
ents
Wea
kS
tron
g
perm
anen
t m
agm
omen
ts
mag
mom
ents
Dia
Dia
Dia
Dia
Par
aP
ara
Par
aP
ara
Fer
roF
erro
Fer
roF
erro
13
Whe
n a
mat
eria
l is pl
aced
with
in a
mag
netic
fiel
d, t
he m
agne
tic fo
rces
of
the
mat
eria
l's e
lect
rons
will
be
affe
cted
. Thi
s ef
fect
is k
now
n as
Far
aday
's
Law
of M
agne
tic In
duct
ion.
Far
aday
's L
aw o
f Mag
netic
Indu
ctio
n.
How
ever
, mat
eria
ls c
an r
eact
qui
te d
iffer
ently
to
the
pres
ence
of
an e
xter
nal
mag
netic
fie
ld.
Thi
s re
actio
n is
dep
ende
nt o
n a
num
ber
of f
acto
rs,
such
as
the
atom
ican
d m
olec
ular
str
uctu
reof
the
mat
eria
l, an
d th
e net m
agne
tic fi
eld
asso
ciat
ed
with
the
atom
s. M
agne
tic m
om
ents
ass
ocia
ted
with
ato
ms
have
th
ree
orig
ins.
In m
ost
ato
ms,
elec
tron
socc
ur
in pa
irs. E
lect
ron
s in
a p
air
spin
in
oppo
site
di
rect
ions
. So
, wh
en e
lect
ron
s ar
e p
aire
d t
og
eth
er, t
hei
r o
pp
osi
te s
pin
s ca
use
th
eir
dire
ctio
ns. S
o, w
hen
ele
ctro
ns
are
pai
red
to
get
her
, th
eir
op
po
site
sp
ins
cau
se t
hei
r
mag
net
ic f
ield
s to
canc
el e
ach
othe
r. Th
eref
ore
, no
net
mag
net
ic f
ield
exi
sts.
Alte
rnat
ely,
mat
eria
ls w
ith s
om
e unpa
ired
elec
tron
s will
hav
e a n
etm
agn
etic
fie
ld a
nd
will
rea
ct m
ore
to
an
ext
ern
al f
ield
.
14
Par
amet
erD
iam
agne
tic
Par
amag
netic
Fer
rom
agne
tic
Def
initi
on
It is
a m
ater
ial i
n
wh
ich
ther
e is
no
perm
anen
t dip
ole
mo
men
t.
It is
a m
ater
ial i
n w
hic
h
ther
e is
perm
anen
t di
pole
mo
men
t in
eac
h
ato
m.
It is
a m
ater
ial i
n w
hic
h
ther
e is
enor
mou
s pe
rman
ent d
ipol
e m
om
ent.
mo
men
t. at
om
. m
om
ent.
Beh
avio
ur
of
mat
eria
l in
th
e pr
esen
ce
of e
xter
nal
mag
netic
fie
ld.
e- s w
ill a
lign
op
posi
teto
the
field
d
irect
ion
, hen
ce it
re
duce
sth
e m
agn
etic
in
du
ctio
n.
Wea
km
agne
ts.
e- s w
ill a
lign
pa
ralle
lto
the
field
d
irect
ion
, hen
ce t
he
mat
eria
l is
mag
netiz
ed.
Str
ong
mag
nets
.
e- s w
hic
h a
re alre
ady
alig
ned
para
llelw
ill
reor
ient
itsel
f alo
ngth
e fie
ld d
irect
ion
, will
be
very
eas
ily m
agne
tized
. Ve
ry s
tron
g m
agne
ts.
Dip
ole
orie
ntat
ion
with
& w
/o
field
15
Mo
vem
ent
of
mag
netic
flu
x lin
es
repe
lled
away
fr
om
th
e m
ater
ial
and
hen
ce Bou
t>
Bi
attr
acte
d to
war
ds
the
cen
tre
of m
ater
ial a
nd
h
ence
Bin
>B
out.
high
ly a
ttrac
ted
tow
ard
s th
e ce
ntr
e o
f m
ater
ial a
nd
hen
ce
Bin
>>
Bou
t.
Tem
pera
ture
dep
end
ence
In
depe
nden
tof
tem
per
atu
re.
It is
inve
rsel
y pr
opor
tiona
l ab
solu
te
tem
per
atu
re.
It de
pend
on
te
mp
erat
ure
in a
co
mp
lex
man
ner
dep
end
ence
te
mp
erat
ure
.te
mp
erat
ure
.co
mp
lex
man
ner
Spi
nal
ign
men
t (o
r) M
agne
ticm
om
ent
alig
nm
ent.
No
spin
(o
r)
Mag
net
ic
Mo
men
t.
All
spin
s o
rt m
agn
etic
m
om
ents
are
rand
omly
or
ient
ed.
All
spin
s o
r m
agn
etic
m
om
ent
are o
rder
ly
orie
nted
.
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
16
Larm
or P
rece
ssio
n (e
lect
rom
agn
etis
m)
Aco
mm
onro
tatio
nsu
perp
osed
upon
the
mot
ion
ofa
syst
emof
char
ged
part
icle
s,al
lhav
ing
the
sam
era
tion
ofch
arge
tom
ass,
bya
mag
netic
field
.
Inph
ysic
s,La
rmor
prec
essi
on(n
amed
afte
rJos
eph
Larm
or)is
the
prec
essi
onof
the
mag
netic
mo
men
tsof
elec
tron
s,at
omic
nucl
ei,an
dat
oms
abou
tan
exte
rnalm
agne
ticfie
ld.
The
mag
netic
field
exer
tsato
rque
onth
em
agne
ticm
om
ent,
whe
reis
the
torq
ue,i
sth
em
agne
ticdi
pole
mom
ent,
isth
ean
gula
rm
om
entu
mvec
tor,
isth
eex
tern
alm
agne
ticfie
ld,
isth
e cro
sspr
oduc
t,an
dis
the
gyro
mag
netic
ratio
whi
chgi
ves
the
prop
ortio
nalit
yco
nsta
ntbe
twee
nthe
mag
netic
mom
ent
ratio
whi
chgi
ves
the
prop
ortio
nalit
yco
nsta
ntbe
twee
nthe
mag
netic
mom
ent
and
the
angu
lar
mom
entu
m.
The
angu
lar
mo
men
tumv
ecto
rpr
eces
ses
abou
tth
eex
tern
alfie
ldax
isw
ithan
angu
lar
freq
uenc
yknow
nas
theL
arm
orfr
eque
ncy.
17
Orig
in
Aris
es f
rom
th
e la
rmo
rp
rece
ssio
n
of e
lect
roni
c or
bits
in th
e p
rese
nce
of
appl
ied
mag
Aris
es f
rom
th
e m
agm
om
ents
orig
inat
ion
alon
g th
e ex
tern
al m
agfie
ld
dire
ctio
n a
nd
mag
mo
men
ts
orie
nta
tion
is la
rgel
y d
eter
min
ed b
y tem
pera
ture
A r
ises
fro
m t
he
spon
tane
ous
mag
netiz
atio
nd
ue
tolo
cal m
olec
ular
m
agne
tic fi
eld
wh
ich
aris
es
fro
m e
xch
ang
e inte
ract
ion
bet
wee
n un
pa
ired
ele
ctro
ns
appl
ied
mag
field
.d
eter
min
ed b
y tem
pera
ture
and
mag
field
.
bet
wee
n un
pa
ired
ele
ctro
ns
& a
dja
cen
t ato
ms in
the
crys
tal l
attic
e.
Mag
net
ic
phas
e tr
ansi
tion
Wh
en th
e tem
pera
ture
is le
ssth
an th
e critic
al
tem
pera
ture,
the
dia
mag
net
ism
su
dd
enly
d
isap
pea
rs a
nd
bec
om
es
Wh
en th
e tem
pera
ture
grea
tert
han
its c
urie
tem
pera
ture,
it is
co
nve
rted
in to
a
diam
agne
tic
Wh
en th
e tem
pera
ture
is g
reat
erth
an it
s cu
rie
tem
pera
ture
it is
co
nve
rted
into
pa
ram
agne
tic.
dis
app
ears
an
d b
eco
mes
a
norm
al m
ater
ial.
diam
agne
tic
sub
stan
ce.
para
mag
netic
.
Per
mea
bilit
yVe
ry le
ss (µ
r<1
) (S
ince
mag
. lin
es
div
erg
eaw
ay
fro
m it
)
Hig
h(µ
r>1
) (S
ince
m
ag.
lines
pa
ssth
rou
gh
it)
Very
hig
h (µ
r>
>1
) (S
ince
mag
. lin
es pa
ssth
rou
gh
it)
18
Sus
cept
ibili
tyN
egat
ive.
Po
sitiv
e &
sm
all.
Po
sitiv
e &
larg
e.
�T
his
imp
lies
that
the s
usce
ptib
ility
decr
ease
swith
incr
ease
in te
mpe
ratu
re. I
t is
o
bse
rved
that
the
susc
eptib
ility
var
ies
inve
rsel
yw
ith te
mp
erat
ure
.i.e
.,1 T
χα
C Tχ
=
Exa
mp
leA
u, G
e, A
g, P
b,
Cu
,Mg
, Mo
, Li,
tan
talu
m,
Cu
So 4
, Pt,
Cr,
Mn
So 4,
N
iSo 4
,N
i, C
o, F
e,
�T
his
is k
no
wn
as
the C
urie
Law
of P
aram
agne
tism
and
‘C’ i
s a
con
stan
t cal
led
C
urie
con
stan
t.
19
Wei
ssT
heor
yof
Fer
rom
agne
tism
1907
-P.
Wei
ss-
Mol
ecul
ar fi
eld
theo
ry -
expl
ain
-sa
lient
fea
ture
s of
F.
M
Inte
rnal
mol
ecul
ar
field
sets
ups
pont
aneo
us m
agne
tisat
ion.
Ent
ire f
erro
ma
gnet
ic v
olum
e split
sin
to a
larg
e nu
mbe
r of s
mal
l reg
ions
calle
d E
ntire
fer
rom
agn
etic
vol
ume sp
lits
into
a la
rge
num
ber o
f sm
all r
egio
ns ca
lled
Dom
ains
.
Siz
e of
a d
omai
n va
ries
from
10
–6m
to th
e ent
ire s
ize o
f th
e cr
ysta
l.
A d
om
ain
act
s as
a s
ing
le m
agn
etic
dip
ole
.
With
indo
mai
n, a
ll th
e spi
n m
ag m
omen
ts ar
e or
ient
ed in
on
e sp
ecifi
c di
r.
Bec
ause
of
the ra
ndom
orie
ntat
ion
of th
e do
mai
ns,
the ne
t-mag
netis
atio
nB
ecau
se o
f th
e rand
om o
rient
atio
n of
the
dom
ains
, th
e net-m
agne
tisat
ion
of th
e fe
rro
mag
netic
mat
eria
l in
the ab
senc
eof
the
field
is ze
ro.
With
inea
chd
om
ain
,th
em
ag
net
icm
om
ents
(sp
in)
are
ori
ente
dpa
ralle
lto
the
ano
ther
ande
nerg
yo
fe
ach
do
mai
nis
char
acte
rised
by
adefin
iteva
lue
and
dire
ctio
no
fth
em
agn
etic
field
.
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
20
All
do
mai
ns
are
sep
arat
edfr
om
the
do
mai
ns
by
the
Dom
ain
wal
l(o
r)B
lock
wal
l.
Mat
eria
lis
sub
ject
edto
anext
erna
lmag
netic
field
,th
edo
mai
nsro
tate
and
atte
mp
ttoa
lign
thei
rm
agn
etic
mo
men
tsw
ithth
efie
lddi
rect
ion
.fie
lddi
rect
ion
.
Spo
ntan
eous
mag
netiz
atio
nof
eac
hd
om
ain
isd
ue
toth
epres
ence
ofa
nex
chan
gefie
ldB E
wh
ich
ten
ds
top
rodu
ceapa
ralle
lalig
nmen
to
fth
eat
om
icd
ipo
les.
Acc
ordi
ng to
Wei
ss T
hoer
y“th
e fi
eld
BE
is a
ssu
me
d to
be
pro
po
rtio
na
l
to th
e m
ag
ne
tiza
tion M o
f ea
ch d
om
ain
”, i.
e.,
BM
λ=
wh
ereλ
isa
con
stan
tca
lled
Wei
ss-f
ield
EB
Mλ
=w
her
eλ
isa
con
stan
tca
lled
Wei
ss-f
ield
cons
tant
and
isin
depe
nden
toft
emp.
21
Dom
ain
The
ory
of F
erro
mag
netis
m
Wh
enex
tern
alm
agn
etic
field
isap
plie
d,
ther
ear
etw
op
oss
ib
lew
ays
of
alig
nm
ent
of
ara
nd
om
do
mai
n.
(i)B
yth
em
ovem
ento
fdom
ain
wal
ls-
wea
km
agn
etic
field
-d
om
ain
sgrow
s.
(ii)
By
rota
tion
ofdo
mai
ns-
stro
ngm
agn
etic
field
-fu
llyg
row
nd
om
ain
ste
nd
toro
tate
.
22
Dom
ain
Ene
rgie
s an
d E
xpla
natio
n fo
r O
rigin
of D
omai
ns
Tota
lin
tern
alen
erg
yo
fth
ed
om
ain
stru
ctu
rein
afe
rro
mag
net
icm
ater
iali
sm
ade
up
i.E
xcha
ngee
ner
gy
(or)M
agne
ticfie
lden
erg
y
ii.C
ryst
allin
een
erg
y(o
r)Ani
sotr
opy
ener
gy.
iii.
Dom
ain
wal
len
erg
y(o
r)Blo
chw
alle
ner
gy.
iv.
Mag
neto
stric
tion
ener
gy.
i.E
xcha
nge
ener
gy(o
r)M
agne
ticfie
lden
ergy
“Th
e in
tera
ctio
n e
ner
gy
wh
ich
mak
es t
he
adja
cent
dip
oles
alig
n th
emse
lves”
is
the
calle
d ex
chan
ge e
nerg
y (o
r) m
agne
tic fi
eld
ener
gy.
�It
aris
esfr
om
inte
ract
ion
ofe
lect
ron
spin
s.It
depe
ndsu
po
nth
eint
er-a
tom
icdi
stan
ce.
�T
his
exch
ang
een
erg
yal
soca
lled
mag
netic
field
ener
gy,th
een
erg
yre
qu
ired
inass
embl
ingt
he
ato
mic
mag
net
sin
toa
sing
ledo
mai
n.
23
Infe
rro
mag
net
icmat
eria
lsth
erea
retw
oty
pes
ofd
irect
ion
sofm
agn
etis
atio
nnam
ely,
ii.A
niso
trop
y(o
r)C
ryst
allin
eE
nerg
y
Exc
ess
ener
gyre
qu
ired
tom
agn
etiz
ea
spec
imen
inpart
icul
ardi
rect
ion
ove
rth
at
req
uire
dto
mag
net
ize
italo
ngth
eea
sydi
rect
ion
isca
lled
the
crys
talli
nean
isot
ropy
ener
gy.
Infe
rro
mag
net
icmat
eria
lsth
erea
retw
oty
pes
ofd
irect
ion
sofm
agn
etis
atio
nnam
ely,
easy
dire
ctio
no
fm
agn
etis
atio
n,w
eak
field
can
be
app
lied
and
inhar
ddi
rect
ion
of
mag
net
isat
ion
,stro
ng
field
sho
uld
be
app
lied
.
Fo
rexa
mp
le,i
nB
CC
iron
theea
sydi
rect
ioni
s[1
00],
the
med
ium
dire
ctio
nis
[11
0],
an
dth
ehard
dire
ctio
nis
[111
].T
he
ener
gy
diff
eren
ceb
etw
een
har
dan
dea
syd
irect
ion
tom
agn
etis
ethe
mat
eria
lisab
ou
t1.4
x104
Jm-3
.ea
syd
irect
ion
tom
agn
etis
ethe
mat
eria
lisab
ou
t1.4
x104
Jm-3
.
Th
isen
erg
yis
very
imp
ort
anti
ndete
rmin
ing
the
char
acte
ristic
do
mai
nb
ou
nd
arie
s.
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
24
Th
esi
zeo
fth
eb
loch
wal
lsar
eabou
t200
to30
0la
ttice
con
stan
tth
ickn
ess.
Go
ing
fro
mon
ed
om
aint
oan
othe
rdo
mai
n,t
hee
lect
ron
spin
chan
ges
grad
ually.
En
erg
yo
fdo
mai
nw
alli
sd
ue
tob
oth
exch
ang
een
erg
yan
dan
iso
tro
pic
ener
gy.
iii.
Dom
ain
wal
lene
rgy
orB
loch
wal
lene
rgy
Bas
edo
nth
esp
inal
ign
men
ts,
(i)T
hick
Wal
l:W
hen
the
spin
sat
the
bo
und
ary
are
mis
alig
ned
and
ifth
ed
irec
tion
oft
he
spin
chan
ges
grad
ually,
itle
ad
sto
ath
ick
blo
chw
all.
(ii)
Thi
nW
all
:W
hen
the
spin
sat
the
bo
un
dar
ieschan
ges
abru
ptly,
then
the
an
iso
tro
pic
en
erg
yb
eco
mes
very
less
.
25
Wh
ena
mat
eria
lism
agne
tized
,iti
sfo
un
dth
atit
suffe
rsac
hang
ein
dim
ensi
ons.
Th
isp
hen
om
eno
nis
kno
wn
asMag
neto
stric
tion.
Th
isd
efo
rmat
ioni
sd
iffer
enta
lon
gdi
ffere
ntcr
ysta
ldire
ctio
ns.
iv.
Mag
neto
stric
tion
ener
gy
Th
isd
efo
rmat
ioni
sd
iffer
enta
lon
gdi
ffere
ntcr
ysta
ldire
ctio
ns.
So
ifth
ed
om
ain
sar
em
agn
etiz
edin
diff
eren
tdire
ctio
ns,
the
yw
illei
ther
expa
ndor
shrin
k.
Th
ism
ean
sth
atwo
rkm
ust
bed
one
agai
nstth
eel
astic
rest
orin
gfo
rces.
Th
ew
ork
done
by
the
mag
netic
field
agai
nstt
hes
eela
stic
rest
orin
gfo
rces
isca
lled
them
agne
to-e
last
icen
ergy
orm
agne
tost
rictiv
een
ergy.
26
Hys
tere
sis
Hys
tere
sis
Hys
tere
sis
Hys
tere
sis
The
wor
dhy
ster
esisl
itera
llym
eans
lagg
ing
behi
nd.
“Wh
en
afe
rro
ma
gn
etic
ma
teria
lis
take
nth
roug
hacycl
eof
mag
ntis
atio
n,th
eva
riatio
nof
B(m
ag
ne
ticin
du
ctio
n)
with
resp
ect
toH(a
pplie
dfie
ld)ca
nb
ere
pre
sente
db
ya
close
dlo
op
(or)
curv
e(h
yste
resi
slo
op
or
curv
e)”
isca
lled
hyst
eres
is.
The
wor
dhy
ster
esisl
itera
llym
eans
lagg
ing
behi
nd.
27
1.
Bin
crea
ses
alo
ng
the
curv
eO
Aw
ithth
eH.
Bey
on
dth
ep
oin
tA,ev
enif
the
His
incr
eas
ed
,Bdo
esno
tin
crea
sea
nd
itre
mai
nsco
nsta
nt-
spe
cim
en
issa
tura
tedw
ithm
ag
netis
atio
n.
2.W
hen
His
decr
ease
d,B
does
notd
ecre
asea
tth
e2.
Wh
enH
isde
crea
sed,B
does
notd
ecre
asea
tth
e
rate
atw
hic
hit
isin
crea
sed
.W
henH
=0,
B≠0
,th
em
ag
net
icin
du
ctio
nh
asa
def
inite
valu
ere
pre
sen
ted
by
OB
and
itis
kno
wn
asR
eten
tivity
.
3.T
he
app
lied H
isre
vers
edan
din
crea
sedg
rad
ual
ly
tillt
he
po
intC
isre
ach
ed.B
=0
atp
oin
tCan
d
neg
ativ
eHst
ren
gth
app
liedt
ore
mo
vere
sid
ual
neg
ativ
eHst
ren
gth
app
liedt
ore
mo
vere
sid
ual
mag
entis
mis
den
ote
db
yOC
and
itis
kno
wn
asC
oerc
ivity
.
4.F
urt
her
incr
ease
ofH
,Bin
crea
ses
alo
ng
CD
inth
ere
vers
ed
irect
ion
.
Ifth
em
agn
etic
field
isva
rie
db
ackw
ard
s,th
em
agn
etic
ind
uct
ion
follo
ws
acu
rve
DE
FA.
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
28
Fro
mth
eab
ove
fact
,it
iscl
ear
that
themag
netic
indu
ctio
nB
will
not
beco
me
zero
,w
hen
the
mag
netic
field
stre
ngth
His
zero
.It
sho
ws
that
the
mag
net
icin
du
ctio
nla
gs
beh
ind
the
app
lied
mag
net
icfie
ldst
ren
gth
.
“Hys
tere
sis
Loop
”
Th
isla
gg
ing
of
ma
gn
etic
ind
uct
ion
beh
ind
the
ap
plie
dfie
ldst
ren
gth
isca
lled
“th
e a
mo
un
t of m
agne
tic in
duct
ion
reta
ined
in th
e m
ate
ria
l aft
er
rem
ovi
ng
th
e m
ag
netis
ing
field
”.
Th
isla
gg
ing
of
ma
gn
etic
ind
uct
ion
beh
ind
the
ap
plie
dfie
ldst
ren
gth
isca
lled
Mag
netic
Hys
tere
sis. R
eten
tivity
or
Res
idua
l mag
netis
m
Coe
rciv
ity o
r C
oerc
ive
forc
e
“th
e a
mo
un
t of m
ag
netis
ing
field
ap
plie
d in
th
e
reve
rse
dire
ctio
n to
rem
ove
the r
esi
du
al m
ag
netis
m c
om
ple
tely
fro
m th
e m
ate
ria
l”.
Coe
rciv
ity o
r C
oerc
ive
forc
e
29
Wh
en
th
e s
peci
men
is t
ake
n th
rou
gh
a c
ycle
of m
ag
ne
tiza
tion
, th
ere
is a
loss
of
ener
gy in
th
e fo
rm o
f hea
t. T
his
loss
of en
erg
y is
kn
ow
n a
sH
yste
resi
s Lo
ss.
Are
ao
f th
e lo
op
rep
rese
nts
en
ergy
loss
per
cyc
le pe
r u
nit
volu
me
of t
he
spec
imen
.
Hys
tere
sis
loss
Wh
ena
ferr
om
agn
etic
mat
eria
lis
sub
ject
edto
anexte
rnal
field
,th
ere
isa
nin
crea
sein
the
valu
eo
fth
ere
sulta
ntm
agn
etic
mo
men
toft
he
spec
imen
.Th
isis
du
eto
1.
Mov
emen
tofd
om
ain
wal
ls(lo
wfie
ld)
2.
Rot
atio
no
fdo
mai
n(la
rge
field
).
Exp
lana
tion
ofH
yste
resi
son
the
basi
sof
Dom
ain
theo
ry
Wh
enas
mal
lext
erna
lfie
ldis
app
lied
,th
ed
om
ain
wal
lsar
edi
spla
ced
slig
htly
inth
eea
sydi
rect
ion
of
wal
lsar
edi
spla
ced
slig
htly
inth
eea
sydi
rect
ion
of
ma
gn
etis
atio
n.
Th
isg
ives
rise
tosm
all
mag
net
isat
ion
corr
esp
on
din
gto
the
initi
alp
ort
ion
of
the
hys
tere
sis
curv
e(O
A).
Wh
enth
eap
plie
dfie
ldisre
mov
edth
enth
ed
om
ain
sre
turn
toits
orig
inal
stat
ean
dis
kno
wn
asreve
rsib
ledo
mai
ns.
30
Iffie
ldis
incr
ease
d,la
rge
nu
mb
ero
fd
om
ain
sco
ntr
ibu
teto
the
mag
net
isat
ion
.N
ow
,eve
nw
hen
the
field
isrem
oved
,bec
ause
oft
he
dis
pla
cem
ento
fdo
mai
nw
all
toa
very
larg
ed
ista
nce
the
do
mai
nb
ou
nda
riesdo
not
com
eba
ckto
thei
ro
rigin
alp
osi
tion
.Th
isp
roce
ssis
ind
icat
edasAB
and
are
calle
dirre
vers
ible
dom
ains
.
Wh
enth
efie
ldisfu
rthe
rin
crea
sed,
the
dom
ains
star
tro
tatin
gal
on
gth
efie
ldd
irect
ion
and
the
anis
otr
op
icen
erg
yis
sto
red
inth
eha
rddi
rect
ion
rep
rese
nte
db
yBC
.S
pec
ime
nis
said
toh
ave
atta
ined
the
max
imu
mm
ag
net
isat
ion
.A
tth
isp
osi
tion
,ev
enaf
ter
the
rem
ova
lo
fe
xter
nal
field
the
ma
teri
alp
oss
es
max
imu
mm
agn
etis
atio
nca
lled
resi
dual
mag
netis
m(o
r)
rete
ntiv
ityre
pre
sen
ted
byO
D
On
the
rem
ova
l of t
he
exte
rnal
fie
ld, t
he
spec
i`men
will
try
to
On
the
rem
ova
l of t
he
exte
rnal
fie
ld, t
he
spec
i`men
will
try
to
atta
in th
e o
rigin
al c
on
figu
ratio
n .
Bu
t th
is m
ove
me
nt
is s
top
ped
d
ue
to th
e pre
senc
e of
impu
ritie
s, la
ttice
impe
rfec
tions
etc
. T
her
efo
re to
ove
rco
me
this
, a la
rge
amo
un
t o
f re
vers
e m
agne
tic
field
is a
pp
lied
to th
e sp
ecim
en t
o r
edu
ce t
he
mag
net
isat
ion
to
zero
is c
alle
d co
erci
vity
rep
rese
nte
d b
y OE
31
Cla
ssifi
catio
nof
Mag
netic
mat
eria
lsB
ased
on
thea
rea
ofth
ehy
ster
esis
loop
,
1S
oftM
agne
ticm
ater
ials
Th
ese
are
ma
teria
lsw
hic
ha
reeas
ilym
ag
netis
ed
an
dd
em
ag
netis
ed
.T
he
yar
eal
soca
lled
as tem
pero
rym
agne
ts.M
agn
etic
ma
teri
als
wh
ich
do
no
tre
tain
the
alig
nm
ento
fm
ag
net
icd
om
ain
saft
erth
ere
mo
valo
fth
eex
tern
alm
agn
etic
field
are
alig
nm
ento
fm
ag
net
icd
om
ain
saft
erth
ere
mo
valo
fth
eex
tern
alm
agn
etic
field
are
kno
wn
asso
ftm
agn
etic
mat
eria
ls.
Exa
mp
les:
Pu
reiro
n,
Cas
tir
on
,C
arb
on
stee
l,S
ilico
nst
eel
,m
ang
anes
ea
nd
nic
kel
stee
l,so
ftfe
rrite
s.
2H
ard
Mag
netic
mat
eria
lsT
hese
are
ma
teria
lsw
hic
ha
reeas
ilym
ag
netis
ed
bu
ta
redi
fficu
ltto
dem
ag
netis
e.Th
eyar
eca
lled
asper
man
entm
agne
ts.M
ater
ials
wh
ich
reta
inp
erm
an
ently
the
alig
nm
ento
fth
em
agn
etic
do
mai
ns
Mat
eria
lsw
hic
hre
tain
per
ma
nen
tlyth
eal
ign
men
toft
he
mag
net
icd
om
ain
sev
enaf
ter
the
rem
ova
lo
fth
eex
tern
alm
agn
etic
field
are
kno
wn
ash
ard
mag
net
icm
ater
ials
.
Exa
mp
les:
Tu
ng
sten
stee
l,C
ob
alt
stee
l,H
yper
nic
(co
nta
ins
50
%n
icke
lan
d5
0%
iron
).
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
32
S.N
oS
oft M
agne
tic m
ater
ials
(Tem
pora
ry m
agne
t)H
ard
Mag
netic
mat
eria
ls(P
erm
anen
t mag
net)
1E
asily
mag
net
ised
& d
emag
net
ised
.E
asily
mag
net
ised
& diffi
cult
to
dem
agn
etis
e.
2Lo
wp
erm
eab
ility
an
d s
usc
eptib
ility
.H
igh
per
mea
bili
tyan
d s
usc
eptib
ility
.
3M
agn
etic
en
erg
y st
ore
d is
no
t hig
h.M
agn
etic
en
erg
y st
ore
d
is h
igh.
4Lo
w h
yste
resi
s lo
sses
due
to s
mal
l h
yste
resi
s lo
op
are
a.La
rge
hyst
eres
is lo
sses
d
ue
to la
rge
hys
tere
sis
loo
p a
rea.
5H
yste
resi
s lo
op
is v
ery na
rrow
.H
yste
resi
s lo
op
is v
ery br
oad.
6C
oer
civi
ty a
nd
Ret
entiv
ity a
re
smal
l.C
oer
civi
ty a
nd
Ret
entiv
ity a
re
larg
e.
7T
he
edd
y cu
rren
t lo
ss is
sm
all
du
e to
its
hig
her
res
istiv
ity.
Th
e ed
dy
curr
ent
loss
is
mor
ed
ue
to
its s
mal
ler
resi
stiv
ity.
du
e to
its
hig
her
res
istiv
ity.
its s
mal
ler
resi
stiv
ity.
33
S.N
oS
oft M
agne
tic m
ater
ials
(Tem
pora
ry m
agne
t)H
ard
Mag
netic
mat
eria
ls(P
erm
anen
t mag
net)
8M
ove
men
t o
f do
mai
n w
all –e
asy.
and
hen
ce e
ven
for
a sm
all a
pp
lied
fie
ld la
rge
mag
net
izat
ion
occ
urs
.
Mo
vem
ent
of d
om
ain
wal
l - not
eas
y. d
ue
to th
e p
rese
nce
of i
mp
urit
ies
and
h
ence
larg
e fie
ld is
req
uire
d.
Mat
eria
ls a
re free
from
irre
gu
larit
ies
Mat
eria
ls h
ave la
rge
amou
nt o
f 9
Mat
eria
ls a
re free
from
irre
gu
larit
ies
like
stra
in o
r im
pu
ritie
s.M
ater
ials
hav
e larg
e am
ount
of
imp
urit
ies
and
latti
ce d
efec
ts.
10
Th
ey a
re p
rod
uce
d b
y h
eatin
g th
em
into
su
ffici
ent
tem
per
atu
re &
th
en
allo
wed
to co
ol s
low
ly co
nn
ectin
g
pro
cess
.
Th
ese
are
pro
du
ced
by
hea
ting
them
in
to s
uffi
cien
t te
mp
erat
ure
& t
hen
pl
ungi
ng it
sud
denl
y in
to c
old
oil.
11E
xam
ples
: Iro
n s
ilico
n a
lloy,
Nic
kel,
Ir
on
allo
y, S
ilico
n s
teel
s, F
errit
es.
Exa
mpl
es: T
un
gst
en
ste
el,
Co
ba
lt,
Ste
el, A
lini,
Aln
ico
, Cu
nife
.Ir
on
allo
y, S
ilico
n s
teel
s, F
errit
es.
Ste
el, A
lini,
Aln
ico
, Cu
nife
.
12
App
licat
ions
Ele
ctric
mo
tor,
gen
erat
ors
, tr
ansf
orm
ers
, re
lays
, te
lep
ho
ne
rece
iver
s, R
AD
AR
an
d
SO
NA
R e
qu
ipm
ents
.
App
licat
ions
Th
ey a
re u
sed
in lo
ud
sp
eake
rs a
nd
el
ectr
ical
mea
surin
g in
stru
men
ts.
34
Cur
ies
Law
Su
scep
tibili
ty o
f par
amag
net
ic m
ater
ials
var
ies
inve
rsel
yw
ith te
mp
. 1 T C
χ χ
∞ ∞w
her
e
C i
s
Cu
rie c
on
stan
t.
ho
lds
go
od
on
ly fo
r p
aram
agn
etic
mat
eria
ls a
t hi
gh te
mp.
C Tχ
∞
Cur
ies
-Wie
sLa
w
C
Tχ
θ=
−w
her
e θ
is
Cu
rie te
mp
erat
ure
.
ho
lds
go
od
on
ly fo
r p
aram
agn
etic
mat
eria
ls a
t lo
w te
mp.
35
Cla
ssifi
catio
n of
Fer
rom
agne
tic m
ater
ials
Bas
edo
np
erm
anen
tmag
net
icd
ipo
les,
mat
eria
lsar
efu
rth
ercl
assi
fied
into
a)A
ntife
rrom
agne
ticm
ater
ials
b)F
errim
agne
ticm
ater
ials
.
a)A
ntife
rrom
agne
tism
Inth
isth
esp
ins
are
alig
ned
inan
tipar
alle
lm
anne
rd
ue
toun
favo
urab
leIn
this
the
spin
sar
eal
ign
edin
antip
aral
lel
man
ner
du
eto
unfa
vour
able
exch
ange
inte
ract
ion
amon
gth
em,re
sulti
ng
inze
rom
agn
etic
mo
men
t.
Th
esu
scep
tibili
tyin
crea
ses
with
incr
easi
ng
tem
per
atu
rean
dre
ach
esa
max
imu
mat
ace
rtai
nte
mp
erat
ure
calle
dN
eelt
empe
ratu
re,T
N.
With
furt
her
incr
ease
inte
mp
erat
ure
,th
em
ater
ialg
oes
int
opa
ram
agne
ticst
ate.
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
36
In th
e p
aram
agn
etic
sta
te,
the
varia
tion
of i
nve
rse
su
scep
tibili
ty (
1/χ)
with
te
mp
erat
ure
is li
nea
r fig
(b
).T
he
extr
apo
latio
n o
f th
e p
aram
agn
etic
lin
e in
Fig
. (b
) to
1/χ
= 0
yie
lds
a ne
gativ
e θ. T
he
varia
tion
of s
usc
eptib
ility
with
tem
per
atu
re
ob
eys C
urie
-Wei
ss L
aw.
Th
eref
ore
Cur
ie -
Wei
ss L
aw is
mod
ified
as.
CC
Wh
ere θ
is c
alle
d P
aram
agn
etic
Cu
rie t
emp
erat
ure
an
d C
is
Cu
rie c
on
stan
t.
()
af
CC
TT
χθ
θ=
=−
−+
whe
n T
> T
N
Pro
pert
ies
of a
nti-f
erro
mag
netic
mat
eria
ls
i.E
lect
ron
sp
in -
alig
ned
an
ti-p
aral
lel -ne
t mag
netis
atio
nis
zer
o.ii.
Su
scep
tibili
ty de
pend
s gr
eatly
on te
mp
erat
ure
.ii.
Su
scep
tibili
ty de
pend
s gr
eatly
on te
mp
erat
ure
.iii
. S
usc
eptib
ility
of m
ater
ial i
s smal
l an
dpo
sitiv
e. It
is g
iven
by
Wh
en T
> T N
iv.
In
itial
ly s
usce
ptib
ility
incr
ease
sslig
htly
with
tem
per
atu
re a
nd
bey
on
d
Nee
l te
mpe
ratu
reth
e su
scep
tibili
ty de
crea
sesw
ith th
e te
mp
erat
ure
.
C
Tχ
θ=
+
37
Fer
rimag
netic
Mat
eria
ls (
or)
Fer
rites
·F
erri
tes
orF
erri
mag
netic
mat
eria
lsar
eth
em
odifi
edst
ruct
ure
ofiro
nw
ithou
tca
rbon
.of
iron
with
out
carb
on.
InF
errit
esth
esp
ins
ofad
jace
ntio
nsin
the
pres
ence
ofa
mag
netic
field
are
inopp
osite
dire
ctio
nsw
ithdi
ffere
ntm
agni
tude
s.
+=
38
Fer
rimag
netic
Mat
eria
ls (
or)
Fer
rites
Th
ere
are
sub
stan
ces
in w
hic
h th
e m
agn
etic
mo
men
ts
of t
he
two
su
b la
ttice
s ar
e o
pp
osi
te in
dire
ctio
n b
ut n
ot e
xact
ly
equa
l in m
ag
nitu
de (
beca
use
of th
e t
wo
typ
es
of i
on
s in
th
e
latt
ices)
. S
uch
cry
sta
ls p
oss
ess
asp
onta
neou
s m
agne
tizat
ion an
d e
xhib
it m
ost
of th
e
pro
pert
ies
of f
err
om
ag
nets
. T
his
un
com
pen
sate
d a
nti
ferr
o-m
ag
netis
m is
kn
ow
n a
s
+=
pro
pert
ies
of f
err
om
ag
nets
. T
his
un
com
pen
sate
d a
nti
ferr
o-m
ag
netis
m is
kn
ow
n a
s F
errim
agne
tism
.M
ater
ials
wh
ich
exh
ibit
ferr
imag
net
ism
are
cal
led
fe
rrim
agne
tic
mat
eria
ls o
rfer
rites
.
Str
uctu
re o
f fer
rites
Fer
rites
are
th
e m
agn
etic
co
mp
ou
nd
s co
nsi
stin
g o
f tw
oo
r mor
edi
ffere
nt
X2+
Fe
3+O
X2+
kin
ds
of a
tom
s. G
ener
ally
fer
rites
are
exp
ress
ed a
s X
2+F
e 23+
O4
wh
ere X
2+st
and
s fo
r di
vale
ntm
etal
s io
ns
such
as Mg
2+, Z
n2+
, Fe2+
, Mn
2+,
Ni2+
etc.
No
rmal
ly,
ther
e ar
e tw
o t
ypes
of s
tru
ctu
res
pre
sen
t in
the
ferr
ites
i.R
egul
arsp
inal
Mg
2+F
e3+
ii.In
vers
esp
inal
39
In th
e re
gula
r sp
inal
, ea
ch triv
alen
t met
al io
n oc
cupi
es a
n oct
ahed
rals
ite [O
HS
] an
d ea
ch di
vale
nt io
n oc
cupi
es a
tetr
ahed
rals
ite [T
HS]
of F
CC
oxy
gen
latti
ce.
Reg
ular
Spi
nal
X2+
Fe 2
3+O
4
latti
ce.
FC
C–
oxyg
en
3+–
OH
S2+
–
TH
SE
x :
Fer
rous
ferr
ite (
Fe2+
Fe 2
3+O
4)
Inth
eab
ove
stru
ctur
e,th
ediva
lent
met
alio
nis
tetr
ahed
rally
surr
ound
edby
four
oxyg
enio
nsan
dit
isca
lled
asTet
rahe
dral
Site
[Site
A]
and
the
triv
alen
tm
etal
ion
isoc
tahe
dral
lyby
six
oxyg
enio
nsan
dit
isca
lled
Oct
ahed
ralS
ite[S
iteB]
.
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
40
In th
e re
gu
lar
spin
al ty
pe,
eac
h
met
al a
tom
(div
alen
t) is
su
rro
un
ded
by
four
O2–
ion
s in
a te
trag
onal
fash
ion
.
Fo
r ex
amp
le in
Mg
2+F
e3+,
the
stru
ctu
re o
f Mg
2+is
giv
en in
the
Fig
. an
d
it is
cal
led
‘A’ s
ite. T
ota
lly in
an
un
it ce
ll, t
her
e w
ill b
e 8 te
trah
edra
l (8A
)site
s.
Reg
ular
Spi
nal
Eac
h F
e3+(t
rival
ent)
is s
urr
ou
nd
ed b
y ‘6’ O
2–io
ns
and
fo
rms
an octa
hedr
al
16 o
ctah
edra
lfa
shio
n a
s sh
ow
n in
Fig
. To
tally
th
ere
will
be 16
oct
ahed
rals
ites
in th
e u
nit
cell.
Th
is is
ind
icat
ed b
y ‘B’ s
ite.
Th
us
in a
regu
lar
spin
el,
each
diva
lent
met
al io
n (M
g2+)
exis
ts in
a
tetr
ahed
ral f
orm
(A
site
) an
d e
ach
triv
alen
t met
al io
n (F
e3+)
exis
ts in
a oc
tahe
dral
fo
rm (
B s
ite).
Hen
ce,
the
site
s A
an
d B
co
mbi
ne to
geth
er to
form
a r
egu
lar
spin
elfe
rrite
str
uct
ure
41
Inth
isty
pe,
we
con
sid
erth
ear
ran
ge
me
nt
of
dip
ole
so
fa
sing
lefe
rrou
sfe
rrite
mol
ecul
eF
e3+
[Fe2
+F
e3+],
Fe3
+io
ns
(triv
alen
t)o
ccu
pie
s
allA
site
s(t
etra
hedr
al)a
ndha
lfo
fth
eB
site
s(o
ctah
edra
l)als
o.
left
out
Inve
rse
Spi
nal
Th
us
thele
ftou
tB
site
swill
be
occ
up
ied
by
thed
ival
ent(
Fe2+
).T
he
inve
rse
spin
alst
ruct
ure
.
42
i.P
oss
es ne
t mag
netic
mo
men
t.ii.
Abo
ve C
urie
tem
pera
ture
, it
bec
om
es pa
ram
agne
ticw
hile
it b
ehav
es a
s fe
rrim
agn
etic
mat
eria
l bel
ow
Cu
rie t
emp
erat
ure
.iii
.S
usc
eptib
ility
is ve
ry la
rge
and
pos
itive
. It
is t
emp
erat
ure
dep
end
ent a
nd
is
giv
en b
y Pro
pert
ies
of fe
rri-m
agne
tic m
ater
ials
giv
en b
y
iv.
Bey
on
d N
eel t
emp
erat
ure
, χde
crea
ses
v.S
pin
alig
nm
ent
is a
ntip
aral
lel o
f diff
eren
t m
agn
itu
des
.vi
.M
ech
anic
ally
, it
has
pure
ion
char
acte
r.vi
i.H
igh
per
mea
bili
ty a
nd
hig
h r
esis
tivity
.vi
ii.Lo
wed
dy
curr
ent
loss
es a
nd
low
hys
tere
sis.
af
C
Tχ
θ=
±fo
r T
> T
N
43
Mag
netic
rec
ordi
ng a
nd r
eado
ut m
echa
nism
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
44
Mag
net
ic T
apes
Mag
net
ic T
ape
Rec
ord
Blo
ck
Rec
ord
ing
an
d R
epro
du
cin
g in
Mag
net
ic T
ape
45
Har
d D
isk
Flo
pp
y d
isk
46
Sup
erco
nduc
tivity
-Kam
mer
lingh
Onn
es-
1911
.
Firs
tth
eore
tical
expl
anat
ion
for
this
phen
omen
onw
asgi
ven
by
Sup
erco
nduc
tivity
Firs
tth
eore
tical
expl
anat
ion
for
this
phen
omen
onw
asgi
ven
byB
arde
en,
Coo
per
and
Shr
ieffe
rin19
57an
dca
me
tobe
know
nas
the
BC
Sth
eory
.
Su
perc
ond
uct
ivity
isth
eph
enom
enon
ofex
hibi
tingze
roel
ectr
ical
resi
stan
ceby
cert
ain
mat
eria
lwhe
nit
iscoo
led
belo
wace
rtai
nte
mpe
ratu
re(c
ritic
alte
mpe
ratu
reT
c).
47
Tem
pera
ture
dep
ende
nce
of R
esis
tanc
e
Su
perc
ond
uct
ivity
isth
ep
he
no
me
non
of
exh
ibiti
ng
zero
elec
tric
alre
sist
ance
Sup
erco
nduc
tors
zero
elec
tric
alre
sist
ance
by
cert
ain
ma
teri
alw
he
nit
isco
oled
belo
wa
cert
ain
tem
pera
ture
(cri
tica
lte
mp
era
ture
T c).
Sup
erco
nduc
tors
The
mat
eria
ls w
hich
exh
ibit
the pr
oper
ty o
f sup
erco
nduc
tivity
at
very
low
tem
pera
ture
s ar
e ca
lled
Sup
erco
nduc
tors
.
Exa
mp
le: M
erc
ury
(H
g),
Tin
(S
n),
Zin
c (Z
n),
Va
na
diu
m (
V)
etc
.,
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
48
Crit
ical
Tem
pera
ture
(or
) Tr
ansi
tion
Tem
pera
ture
Th
ete
mp
era
ture
atw
hic
hth
etran
sitio
nfr
om
norm
alst
ate
tosu
per
cond
uctin
gst
ate
take
spl
ace
onco
olin
gin
the
abse
nce
ofm
agne
ticfie
ld.
field
.
(i) If
the
tran
sitio
n te
mpe
ratu
re is
low
, th
en th
e su
per
co
nd
uct
ors
are
kn
ow
n a
s Low
Tem
pera
ture
Sup
er C
ondu
ctor
s.
(ii)
If th
e tr
ansi
tion
tem
pera
ture
is h
igh
(eve
n 3
0 K
elvi
n)
then
it is
kn
ow
n a
s Hig
h Te
mpe
ratu
re S
uper
Con
duct
ors.
Ele
men
t / C
ompo
und
Tc(K
)
Ti
0.3
9
Y B
a 2C
u 3O
79
0
49
(1)
Mei
ssne
r E
ffect
–D
iam
agne
tic P
rope
rty
Whe
na
wea
km
agne
ticfie
ldis
appl
ied
toa
supe
rcon
duct
ing
Whe
na
wea
km
agne
ticfie
ldis
appl
ied
toa
supe
rcon
duct
ing
spec
imen
atat
empe
ratu
rebe
low
tran
sitio
nte
mpe
ratu
re(T
c),t
hem
agne
ticflu
xlin
esar
eex
pelle
d.T
hesp
ecim
enac
tsas
anid
eald
iam
agne
t.T
his
effe
ctis
calle
d“M
eiss
ner
effe
ct”.
T <
Tc
T
> T
c
T <
Tc
H
< H
cT
> T
c
H >
Hc
(a) N
orm
al s
tate
(b) S
uper
cond
uctin
g st
ate
50
Inth
esu
per
con
duct
ing
stat
e,a
mat
eria
lp
oss
esse
sze
roel
ectr
ical
resi
stan
cean
db
ehav
esas
ad
iam
agn
etic
mat
eria
l.B
elo
wT c
ifsu
ffici
ently
stro
ngm
agne
ticfie
ldis
app
lied
,th
esu
per
cond
uct
ingp
rop
erty
of
the
mat
eria
lis
dest
roye
dan
dth
e
(2)
Effe
ct o
f Mag
netic
Fie
ld
sup
erco
ndu
ctin
gpro
per
tyo
fth
em
ate
rialis
dest
roye
dan
dth
em
ater
ialr
ever
tsb
ack
toits
no
rmal
stat
e.
Th
e m
inim
um fi
eld
requ
ired
to
dest
roy
the
supe
rcon
duct
ing
pro
per
ty is
kn
ow
n a
s th
e criti
cal
mag
netic
fiel
d (H
c). H
T Tc
0
2
1−F HGI KJ
L NM MO QP P
Hc
=
51
(3)
Silb
ee r
ule
(or)
Effe
ct o
f cur
rent
�W
hen
acur
ren
tpas
ses
thro
ug
ha
sup
erco
nd
uct
or
wh
ich
isin
the
form
ofa
wire
,am
agne
ticfie
ldis
setu
par
ound
the
wire
.
�If
the
curr
enti
sla
rge
enou
ghso
that
them
agne
ticfie
ldpr
oduc
edis
equa
lto
the
criti
cal
mag
netic
field
,th
enth
esu
perc
ondu
ctin
gis
equa
lto
the
criti
cal
mag
netic
field
,th
enth
esu
perc
ondu
ctin
gpr
oper
tyis
dest
roye
d.
Th
us
acur
rent
pass
ing
thro
ug
hth
esu
per
con
du
ctin
gw
irecan
dest
roy
itso
wn
sup
erco
nd
uct
ing
pro
per
ty.
The
min
imu
mcu
rren
tre
quire
dfo
rth
iscr
itica
l
I c=
2 π
r H
c
happ
enis
know
nas
thecr
itica
lcu
rren
t,gi
ven
by,
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
52
(4)
Effe
ct o
f Pre
ssur
e
Wh
enpr
essu
reis
appl
ied
toa
sup
erco
ndu
ctin
gm
ater
ial,
tran
sitio
nte
mpe
ratu
rein
crea
ses.
Th
us
itis
qu
itep
ossi
ble
that
theT c
of
am
ate
ria
lca
nb
em
ad
eto
app
roa
chro
omte
mp
era
ture
by
the
ap
plic
atio
no
fhig
hp
ress
ure
s.a
pp
lica
tion
ofh
igh
pre
ssu
res.
Tcof
cesi
umis
1.5
K,
but
byth
eap
plyi
ngla
rge
pres
sure
cesi
umbe
com
esa
supe
rcon
duct
oreven
ata
tem
pera
ture
ashi
ghas
110
K.
(5)
Isot
ope
Effe
ct
In s
up
erco
nd
uct
ing
mat
eria
ls,
“th
e Tc
varie
sw
ith th
e av
erag
e is
otop
ic
In s
up
erco
nd
uct
ing
mat
eria
ls,
“th
e Tc
varie
sw
ith th
e av
erag
e is
otop
ic
mas
s of t
hei
r co
nst
ituen
ts”.
T c∞
M–a
Ma T c
=C
onst
ant
M -
ato
mic
ma
ss
a-
iso
top
ic e
ffect
co
eff
icie
nt.
53
Du
ring
the
tran
sitio
nfr
omn
orm
alst
ate
tosu
per
con
du
ctin
gst
ate,
spec
ific
heat
decr
ease
sex
pone
ntia
lly.
(6)
H
eat C
apac
ity
Fo
rn
orm
alco
nd
uct
ing
mat
eria
l,th
esp
ecifi
ch
eatv
arie
ssm
oo
thly
atlo
wte
mp
erat
ure
s.C
V=
ex
p −b
T TC
(7)
Jos
ephs
on E
ffect
Jose
phso
nfo
und
thatC
oope
rpa
irof
elec
tron
sco
uld
tunn
elth
roug
han
insu
latin
gla
yer
of
1m
mth
ickn
ess,
wh
ichs
epar
ates
two
supe
rco
nduc
tors
.
54
Th
e ap
plie
d m
agn
etic
fie
ld
(H)
doe
s no
t van
ishe
s su
dden
ly a
t the
su
rfac
e o
f su
per
co
nd
uct
ing
mat
eria
l bu
t del
ays
acco
rdin
g t
o th
e re
latio
n.(8
)
Lond
on p
enet
ratio
n de
pth
rela
tion
.
H (
0)
is th
e fie
ld a
pp
lied
at t
he
surf
ace
at x
= 0
an
d ‘x
’ is
the
dis
tan
ce
fro
m t
he
surf
ace
and
the
len
gthλis
cal
led
the
Lond
on p
enet
ratio
n de
pth.
ex
− λH
(x)
= H
(0
)
Itm
ayb
ed
efin
edas
the
effe
ctiv
ede
pth
tow
hic
ha
mag
netic
field
Itm
ayb
ed
efin
edas
the
effe
ctiv
ede
pth
tow
hic
ha
mag
netic
field
pene
trat
esth
rou
gh
asu
per
con
du
cto
r.
λ(T
) =
λ(o)
14
−F HGI KJ
F HG GI KJ J
T Tc
55
Type
s of
Sup
erco
nduc
tors
Div
ided
into
two
cate
gorie
sd
epen
din
go
nth
ew
ayin
whi
chth
etr
ansi
tion
fro
msu
perc
ondu
ctin
gto
norm
alst
ate
pro
ceed
sw
hen
the
inte
rnal
lyap
plie
dm
agne
ticfie
ldex
ceed
s(H C
).
Type
I S
.C (S
oftS
uper
cond
ucto
rs)
Type
II S
.C (H
ard
Sup
erco
nduc
tors
)
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
56
S.C
SVo
rtex
S
tate
No
rmal
S
tate
HC
HC
2H
C1
MM
HH
C
S.C
. Sta
teN
orm
al
Sta
te
Type
I S
.CTy
pe II
S.C
Sof
tS.C
Har
dS
.C
Has
onl
y one
crit
ical
fiel
d.H
as tw
o cr
itica
l fie
lds.
i.e
., lo
wer
crit
ical
fiel
d (H
C1)
an
d up
per
criti
cal f
ield
(H C2
)
No
mix
ed s
tate
Vert
ex(o
r) M
ixed
sta
te is
pre
sent
.
Str
ictly
follo
w t
he M
eiss
ner
effe
ct.
do n
ot s
tric
tly fo
llow
the
Mei
ssne
r ef
fect
.
Low
Mag
Fie
ld S
tren
gth
(0.1
Tesl
a)H
igh
Mag
Fie
ld S
tren
gth
(10 T
esla)
57
S.C
SVo
rtex
S
tate
No
rmal
S
tate
HC
HC
2H
C1
MM
HH
C
S.C
. Sta
teN
orm
al
Sta
te
Type
I S
.CTy
pe II
S.C
Pha
se c
hang
e oc
curs
ab
rupt
ly.
Pha
se c
hang
e oc
curs
gr
adua
lly.
Lead
, Alu
min
ium
,Mer
cury
, Tin
, et
cN
iobi
um, V
anad
ium
, Cer
tain
C
uO, e
tc
58
John
Bar
deen
, Leo
n Coo
per,
and
Joh
n Schr
ieffe
r -B
CS
The
ory
-19
57.
BC
S T
heor
y
BC
Sth
eory
dea
lsw
ithth
ebe
havi
our
ofel
ectr
ons
insu
per
cond
uct
ing
BC
Sth
eory
dea
lsw
ithth
ebe
havi
our
ofel
ectr
ons
insu
per
cond
uct
ing
mat
eria
lsat
very
low
tem
pera
ture
s.Lo
wte
mp
erat
ure
smin
imiz
eth
evi
brat
iona
len
ergy
of
ind
ivid
ual
ato
ms
inth
ecr
ysta
llat
tice.
59
1)
Ele
ctro
nsf
orm
pairs
calle
dC
oope
rpa
irs,
atlo
wte
mp
era
ture
Two
Prin
cipl
e F
eatu
res
of B
CS
The
ory
1)
Ele
ctro
nsf
orm
pairs
calle
dC
oope
rpa
irs,
atlo
wte
mp
era
ture
by
over
com
ing
repu
lsiv
efo
rce.
Th
eyp
ropa
gat
eth
roug
hou
tth
ela
ttic
e.
2)
Su
chp
rop
agat
ion
isw
ithou
tsc
atte
ring
(with
out
any
resi
stan
ce),b
ecau
seel
ectr
on
sm
ove
inreso
nanc
ew
ithph
onon
s.N
ow
the
mat
eria
lbec
om
esa
sup
erco
nd
uct
or
.
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
60
1)Tw
oel
ectr
onsp
rop
agat
eal
on
gasi
ngle
latti
cero
w.
2)
Imag
ine
amet
alas
ala
ttice
ofpo
sitiv
eio
ns,w
hich
can
mov
eas
ifat
tach
edb
yst
iffsp
ring
s.
3)
Eac
hel
ectr
on
exp
erie
nce
sanat
trac
tion
tow
ard
sits
nea
rest+
veio
n.io
n.
4)
Wh
enel
ectr
onge
tclo
seto
each
oth
erin
there
gion
betw
een
ions
,th
eyre
pele
ach
oth
erd
ue
toCou
lom
bfo
rce.
5)
Inan
equi
libriu
mco
nditi
on,
aba
lanc
eb
etw
een
attr
actio
nan
dre
pu
lsio
nis
esta
blis
hed
and
thetw
oel
ectr
ons
com
bine
tofo
rmC
oo
per
pai
r.
6)
At
norm
alte
mpe
ratu
re,at
trac
tive
forc
eis
too
smal
l,pa
iring
ofe-
sdo
esno
ttak
epl
ace.
7)
At
low
tem
pera
ture,
attr
activ
efo
rce
isst
rong
,pa
iring
ofe-
sta
kepl
ace
ener
gitic
ally.
61
The
regi
onof
incr
ease
dpo
sitiv
ech
arge
dens
itypr
opag
ates
thro
ugh
the
crys
tal
asa
quan
tized
soun
dw
avec
alle
dap
hono
n.T
hepa
ssin
gele
ctro
nsem
ita
phon
on.
Coo
perP
airs
The
pass
inge
lect
rons
emit
aph
onon
.
The
pair
ofel
ectr
ons
form
eddu
eto
elec
tron
-la
ttice
(pho
nos)
-el
ectr
onin
tera
ctio
n(fo
rces
ofat
trac
tion)
byov
erco
min
gth
e
elec
tron
-ele
ctro
nin
tera
ctio
n(forc
esof
repu
lsio
n )w
itheq
ual
and
oppo
site
mo
men
tum
and
spin
s(i.
e.,)
with
wav
eve
ctor
and
are
calle
dC
oope
rPai
rs.
Thi
sis
also
calle
das
elec
tron
–ph
onon
–ele
ctro
nin
tera
ctio
n.
62
7)
Th
usd
ense
clou
dof
coop
erpa
irsfo
rma
colle
ctiv
est
ate
and
the
mot
ion
ofa
llth
eco
op
erp
airs
iscor
rela
ted.
8)
Su
chco
op
erp
airsd
riftc
o-op
erat
ivel
yth
rou
gh
the
mat
eria
l.
9)
Sin
cede
nsity
ofco
oper
pair
isve
ryhi
gh,
elec
tro
ns
mo
vew
ithlo
wve
loci
ty.
10
)S
mal
lvel
oci
tyo
ford
ered
coop
erp
airsm
inim
ize
colli
sion
proc
ess
andle
ads
toze
rore
sist
ivity
.
11
)W
hen
the
tem
per
atu
re(T
)isle
ssth
ancr
itica
ltem
pera
ture
(Tc)
,th
ere
sist
ivity
du
eto
latt
ice
vib
ratio
nsw
illb
ele
ss.
there
sist
ivity
du
eto
latt
ice
vib
ratio
nsw
illb
ele
ss.
63
�E
lect
ron
s o
f Co
op
er p
air
hav
e a low
er e
nerg
y th
an tw
o u
np
aire
d e- s
.
�T
his
theo
ry p
red
icte
d th
e ex
iste
nce
of a
n
ener
gy g
ap be
twee
n th
e g
rou
nd
sta
te (
S.C
. Sta
te)
and
firs
t exc
ited
sta
te.
�T
he
en
erg
y g
ap
rep
rese
nts
the en
ergy
req
uire
d to
bre
ak u
p a
co
op
er p
air.
�La
rger
ener
gy
gap
co
rres
po
nd
s to
m
ore
stab
le S
.Con
duct
ors.
�A
cco
rdin
g to
BC
S th
eory
, ener
gy g
ap at
0 K
is g
iven
by
()0
23.
5g
cE
kT
=∆
≅
�E
ner
gy
gap
is g
ener
ally
of o
rder
10
-3eV
.
�E
lect
rons
ina
coop
erpa
irpo
sses
san
ti-pa
ralle
lspi
n,r
esul
ting
ina
tota
lspi
nof
zero
for
the
pair.
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
64
1)
Itis
app
licab
lefo
rhig
hte
mpe
ratu
resu
per
con
du
cto
rs.
2)
Itis
bas
edon
the
idea
ofe
xist
ence
ofsh
ortr
ange
repu
lsiv
efo
rce
R V
BT
heor
y (R
eson
ance
Val
ence
Bon
dT
heor
y)
2)
Itis
bas
edon
the
idea
ofe
xist
ence
ofsh
ortr
ange
repu
lsiv
efo
rce
bet
wee
nth
eel
ectr
on
sin
an
arro
wban
d.
3)
Su
per
cond
uct
ivity
occ
urs
wh
enth
em
ate
rial
isdope
dto
crea
teho
lesi
nit.
4)
Th
ese
ho
les
then
formp
airs
and
un
der
goB
ose
cond
ensa
tion.
65
Hig
h Te
mpe
ratu
re S
uper
cond
ucto
rs (
HT
S)
Any
sup
erco
nduc
tor
with
a
tran
sitio
n te
mpe
ratu
re a
bove
100
K is
Year
Mat
eria
lT
c / K
1974
LiT
i 2O4
1319
75B
a(P
bBi)O
313
Any
sup
erco
nduc
tor
with
a
tran
sitio
n te
mpe
ratu
re a
bove
100
K is
in
gen
eral
cal
led H
igh
T csu
perc
ondu
ctor
.
1975
Ba(
PbB
i)O3
1319
86La
2–x
Sr x
Cu
O4
38
1987
YB
a 2C
u 3O
792
1988
Tl 2
Ca 2
Ba 2
Cu 3
O1
012
5
66
Hig
h T c
supe
rcon
duct
ors
deve
lope
d so
far
belo
ng to
five
chem
ical
sy
stem
havi
ng th
e fo
llow
ing
gene
ral f
orm
ulae
.1.
B
aP
b 1–x
Bi x
O3
2.
La 2
–xM
xC
u O
4–x
(M =
Ba,
Sr)
3.
Ba 2
MC
u 3 O
7–x
(M =
Yor
rare
ear
th m
etal
s su
ch a
s Gd,
Eu,
etc
.,)
4.
Ba
La
Cu
O4.
B
a 2–x
La 1
+xC
u 3 O
8
5.
Bi 2
Ca
Sr 2 C
u 2 O
8
Ith
asb
een
real
ized
thatth
ero
leof
oxyg
enis
esse
ntia
lfor
hig
hT c
oxi
de
sup
erco
nd
uct
ors.
Uni
tcel
lofh
igh
T csu
per
con
du
cto
rsh
aveco
mpl
icat
edst
ruct
ure.
Ifth
ece
llco
nta
inso
neat
omo
frar
eea
rth
met
al,t
wo
bariu
mIf
the
cell
con
tain
sone
atom
ofr
are
eart
hm
etal
,tw
oba
rium
ato
ms,
thre
eco
pper
ato
ms
ands
even
oxyg
enat
om
s,th
ensu
chco
mp
ou
nd
s=
1-2-
3su
perc
ondu
ctor
s.
Mo
sto
fth
eco
mp
ou
nd
sar
elaye
red
copp
erox
ide
mat
eria
ls.
67
1.
Th
ey a
re ox
ides
of c
oppe
r in c
ombi
natio
nw
ith o
ther
ele
men
ts.
2.
Th
ey h
ave p
erov
skite
(i.e.
, la
yere
d)
crys
tal s
tru
ctu
re.
Pro
pert
ies
of H
TS
2.
Th
ey h
ave p
erov
skite
(i.e.
, la
yere
d)
crys
tal s
tru
ctu
re.
3.
Th
ey a
re dire
ctio
n de
pend
ent.
4.
T
hey
are
cera
mic
s (b
rittle
) th
ey c
ann
ot b
e ea
sily
form
ed.
5.
T
hey
hav
e hig
h T c
.
6.
T
hey
are
ref
erre
d a
s 1 -
2 -
3 sy
stem
(a)
Co
mp
ou
nd
.
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
68
Cry
stal
Str
uctu
re o
f Y
Ba 2
Cu 3
O7
Itis
prep
ared
byhe
atin
gY2O
3,B
aCO
3an
dC
uOin
the
corr
ect
prop
ortio
nat
ave
ryhi
ghte
mpe
ratu
resa
y110
0ºC.
At
this
tem
pera
ture
,BaC
O3
deco
mpo
sesin
toB
aOan
dC
O2,
whi
chgi
ves
rise
tope
rovs
kite
crys
tals
truc
ture
.ris
eto
pero
vski
tecr
ysta
lstr
uctu
re.
The
X-r
ayan
dne
utro
npo
wde
rdi
ffrac
tion
tech
niqu
esre
veal
edth
atY
Ba 2
Cu 3
O7
iste
trag
onal
pero
vski
test
ruct
ure
with
trip
led
cell.
Latti
ceco
nsta
nts
a=
3.82
Å,b
=3.
86Å
and
c=
11.6
81Å
.
Un
itce
llco
nta
inso
neat
omo
fra
reea
rth
Un
itce
llco
nta
inso
neat
omo
fra
reea
rth
met
al(i.
e.,
yitt
rium
),tw
oba
rium
ato
ms,
thre
eco
pper
ato
ms
ands
even
oxyg
enat
om
s
=1-
2-3
supe
rcon
duct
ors.
69
One
Yttr
ium
atom
in on
e un
it ce
ll.
Dis
trib
utio
n of
the
atom
s in
the
unit
cell
Yttr
ium
ato
ms
Y B
a 2C
u 3O
7
One
Yttr
ium
atom
in on
e un
it ce
ll.
1/1t
h of
the
atom
s is
sha
red
by th
at u
nit c
ell.
No
of y
ttriu
m a
tom
s pe
r un
it ce
ll ° °°
° °°
11
1x
x
=
1.
.1
xT
ota
lno
of
Ytt
riu
ma
tom
sx
No
of
ce
lls
=
(Yttr
ium
ato
m)
= 1
ato
m/u
nit c
ell
11
11
xx
=
70
One
Bar
ium
atom
in on
e un
it ce
ll.
Dis
trib
utio
n of
the
atom
s in
the
unit
cell
Bar
ium
ato
ms
Y B
a 2C
u 3O
7
One
Bar
ium
atom
in on
e un
it ce
ll.
1\1t
h o
f the
ato
m is
sha
red
by th
at
part
icul
ar u
nit c
ell.
No
of B
ariu
m a
tom
s pe
r un
it ce
ll
° °° ° °°
1
=
1.
.1
xT
ota
lno
of
Ba
riu
ma
tom
sx
No
of
ce
lls
=
1
12
1x
x
=
(Bar
ium
ato
m)
= 2
ato
ms/
unit
cell
71
8 C
oppe
r ato
ms
in on
e un
it ce
ll.
Dis
trib
utio
n of
the
atom
s in
the
unit
cell
Cop
per
atom
s
Y B
a 2C
u 3O
7
8 C
oppe
r ato
ms
in on
e un
it ce
ll.[S
ince
cop
per
is t
he c
orne
r at
om
].
1/8t
hof
the
ato
m is
sha
red
by o
ne u
nit
cell.
Num
ber
of C
oppe
r at
om
s pe
r un
it ce
ll
° °°
° °°
1.
.8
xT
ota
lno
of
Co
pp
er
ato
ms
xN
oo
fc
ell
s
=
1
1
83
8x
x
=
(Cop
per
atom
s)
= 3
ato
ms/
unit
cell
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
72
4 O
xyge
n ato
m in
one
unit
cell.
Dis
trib
utio
n of
the
atom
s in
the
unit
cell
Oxy
gen
atom
s
Y B
a 2C
u 3O
7
4 O
xyge
n ato
m in
one
unit
cell.
[Sin
ce o
xyge
n at
oms
are
situ
ated
at m
idpo
ints
be
twee
n tw
o co
rner
ato
ms]
.
1/4t
hof
the
atom
is s
hare
d by
one
uni
t cel
l.
Num
ber
of O
2at
oms
per
unit
cell
° °°
° °°
1.
.x
To
taln
oo
fO
xy
ge
na
tom
sx
No
of
ce
lls
=
.
.4
xT
ota
lno
of
Ox
yg
en
ato
ms
xN
oo
fc
ells
=
11
23
4x
x
=
(Oxy
gen
atom
s)
= 9
ato
ms/
unit
cell
73
Itis
foun
dth
ata
ctua
lfo
rmu
lash
ould
beY
1B
a 2C
u 3O
9.B
utth
e
O
Oxy
gen
defe
ct m
odifi
catio
n
9cr
ysta
lfor
med
isY 1
Ba 2
Cu 3
O7.
Hen
ceth
ecr
ysta
lst
ruct
ure
ofth
ese
ma
teri
als
are
oxyg
ende
fect
mo
difi
catio
nof
the
Per
ovsk
itest
ruct
ure,
with
abou
ton
e-t
hrid
ofth
eox
ygen
posi
tions
vaca
nt.
The
refo
rew
eca
nsa
y,th
enu
mbe
rof
oxyg
enat
om
spe
run
itce
ll=
7.
74
The
pos
itive
and
neg
ativ
e io
n va
canc
ies
are
base
d on
Y
+3
Ba+
2C
u+2
O–2
Pos
itive
ion
vaca
ncy
= V
acan
cy x
Num
ber
of a
tom
s / u
nit c
ell
(i.e.
,) fo
rY+
3B
a+2
Cu+
2(i.
e.,)
forY
+3
Ba+
2C
u+2
we
have
+ 3
x 1
+ 2
x 2
+ 2
x 3
po
sitiv
e io
n va
canc
y =
+ 1
3 va
canc
ies
.
Neg
ativ
e io
n va
canc
y =
vac
ancy
x n
umbe
r of
ato
ms/
unit
cell
i.e.,
for
O–2w
e ha
ve –
2 x
7 ne
gativ
e io
n va
canc
y =
-14
vac
anci
es.
The
oxy
gen
cont
ent
per
cell
can
be c
hang
ed r
ever
sibl
y fr
om 7
to 6
ato
ms,
si
mp
ly b
y pu
mpi
ng
oxyg
en in
and
out
of t
he p
aral
lel c
hain
s of
CuO
.
75
App
licat
ion
of s
uper
cond
ucto
rs
Cry
otro
n (o
r) F
asie
lect
rical
sw
itchi
ng
Jose
phso
n de
vice
s
Sup
erco
nduc
ting
Qua
ntum
Inte
rfer
ence
Dev
ice
(SQ
UID
)
Mag
netic
levi
tatio
n
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
76
Prin
cipl
e:
Su
perc
on
du
ctin
g p
rop
ert
y disa
ppea
rsw
hen
th
e m
ag
netic
fie
ld is
gr
eate
r th
an c
ritic
al
field
(H
c).
(A)
HC
A<
HC
B
Cry
otro
n (
or)
Fas
iEle
ctric
al S
witc
hing
(B)
Cur
ren
t flo
w in
‘B
’-in
duce
s mag
netic
field
in
‘A.’
Cu
rren
tin
B-
mag
net
icfie
ldp
rod
uce
disgr
eate
rth
anH
CA
of
A-
supe
rcon
duct
ing
stat
eo
fAis
dest
roye
d-
does
nota
llow
acu
rren
tto
pas
s.
Cu
rren
tin
B-
mag
net
icfie
ldp
rodu
ced
isless
than
HC
Ao
fA
-A
isin
the
supe
rcon
duct
ing
stat
e-
allo
wcu
rren
tto
flow
.
Th
us
acur
rent
flow
ing
inB
cont
rols
the
curr
enti
nA.
Sw
itch
-eq
uiv
alen
tto
asw
itch
inth
eO
Nst
ate
-eq
uiv
alen
tto
asw
itch
inth
eO
FF
stat
e.
Tant
alum
(T
c=
4.5
K) i
s th
e gat
e an
dni
obiu
m (
Tc=
9.5
K) i
s th
e con
trol
.
77
Jose
phso
n D
evic
es
Prin
cipl
e:P
ersi
sten
tcu
rren
tin
d.c.
volta
geis
the
prin
cipl
eus
edin
Jose
phso
nde
vice
s.
Sup
erco
nduc
tor-
insu
lato
r-
supe
rcon
duct
orla
yer.
Sup
erco
nduc
tor-
insu
lato
r-
supe
rcon
duct
orla
yer.
Insu
lato
rac
tsas
abar
rier
toth
eflo
wof
cond
uctio
nel
ectr
onsf
rom
on
esu
per
con
du
cto
rto
the
oth
er.
Ifa
volta
ge‘V
’is
app
lied
acro
ssth
esu
per
con
du
cto
rs,
then
curr
ent
star
tsflo
win
gb
etw
een
the
sup
erco
nd
uct
ors
by
tunn
elin
gef
fect
.
i.
D.C
. Com
pone
nt:
i.
D.C
. Com
pone
nt:
Th
is c
urr
ent
com
po
nen
t pers
ists
eve
n afte
r th
e ex
tern
al vo
ltage
is c
utof
f.
ii.
A.C
. Com
pone
nt:
Th
is c
urr
ent
com
po
nen
t pers
ists
onl
y up
to w
hic
h t
he
exte
rnal
vo
ltage
is a
pplie
d.
78
Asu
perc
on
duct
ing
mate
rialb
eh
ave
sas
adi
amag
netic
mat
eria
l.H
ence
whe
na
supe
rcon
duct
orispl
aced
over
am
agne
ticfie
ld,th
em
ater
ialf
loat
s.T
his
effe
ctis
know
nasm
agne
ticle
vita
tion.
Mag
netic
levi
tatio
n
Prin
cipl
e Ele
ctro
-mag
netic
indu
ctio
nis
used
asth
epr
inci
ple
(i.e.
,)w
hen
ther
eis
arel
ativ
em
otio
nof
aco
nduc
tor
acro
ssth
emag
netic
field
,cur
rent
isin
duce
din
the
cond
ucto
ran
dvi
ceve
rsa.
79
Tra
inco
nsi
sts
ofsu
perc
ondu
ctin
gm
agne
tspla
ced
onea
chsi
de.
Initi
ally
wh
enth
etr
ain
star
ts,t
heys
lide
onth
era
ils.
Wh
enth
etr
ain
mo
ves
fast
er,
thesupe
rcon
duct
ing
mag
netso
nea
chsi
de
oft
he
trai
nw
illin
duce
curr
ent.
Indu
ced
curr
ent
gen
erat
esa
ma
gn
etic
forc
ein
the
coils
insu
cha
wa
yth
att
he
low
erIn
duce
dcu
rren
tg
ener
ates
am
ag
net
icfo
rce
inth
eco
ilsin
such
aw
ay
tha
tth
elo
wer
hal
fco
ilh
asth
esa
me
mag
net
icp
ole
as
that
of
the
sup
erco
nd
uct
ing
ma
gn
etin
the
trai
n,w
hile
the
up
per
hal
fhas
the
op
po
site
mag
net
icp
ole
.
Th
eref
ore
the
tota
lup
war
dm
agn
etic
forc
ea
cts
on
the
trai
na
nd
henc
eth
etr
ain
isle
vita
ted
(or)
rised
abo
veth
ew
hee
ls(i.
e.,)
the
trai
nn
ow
float
sab
ov
eth
eai
r.
No
w,
by
alte
rnat
ivel
ych
angi
ngth
epo
leso
fth
esu
per
con
du
ctin
gm
ag
net
inth
etr
ain
alte
rnat
ing
curr
ent
can
be
ind
uce
d.
Th
us,
alte
rnat
ing
serie
so
fno
rth
and
sou
thm
ag
net
icp
ole
sa
rep
rod
uce
din
the
coils
,w
hic
hp
ulls
and
pu
shes
the
sup
er
ma
gn
etic
po
les
are
pro
du
ced
inth
eco
ils,
wh
ich
pu
llsan
dp
ush
esth
esu
pe
rco
nd
uct
ing
mag
net
sin
the
trai
nan
dh
ence
the
trai
nis
furt
herm
oved
.
Tra
vela
spee
do
f500
km/h
our,
wh
ich
isd
ou
ble
the
spee
do
fexi
stin
gfa
stes
ttra
in.
Dr
Sel
vaku
mar
, Dep
t o
f P
hys
ics,
R.M
.D E
ng
inee
rin
g C
olle
ge
80
AS
QU
IDis
ado
uble
junc
tion
qu
antu
min
terf
ero
met
erfo
rmed
fro
mtw
oJo
seph
son
junc
tionm
ou
nte
do
na
supe
rcon
duct
ing
ring.
Sup
erco
nduc
ting
Qua
ntum
Inte
rfer
ence
Dev
ice
(SQ
UID
)
Mag
netic
field
isap
plie
dnor
mal
toth
ep
lan
eo
fth
erin
gan
dre
sults
inth
eindu
cem
ento
fcu
rren
t,at
the
two
jun
ctio
ns.
Det
ect
ion
coils
,co
nn
ectin
gw
ires
and
the
SQ
UID
inp
ut
coilsform
acl
ose
dsu
per
con
du
ctin
grin
g,s
oany
chan
gepr
oduc
edis
det
ect
ed,a
nd
ispro
port
iona
lto
the
chan
gein
mag
netic
flux.
Th
eref
ore
SQ
UID
Sar
eu
sed
tod
etec
tth
eva
riatio
nin
very
min
ute
mag
netic
Th
eref
ore
SQ
UID
Sar
eu
sed
tod
etec
tth
eva
riatio
nin
very
min
ute
mag
netic
sign
alsi
nte
rmo
fqu
antu
mflu
x.
Th
eyar
eal
sou
sed
inth
estud
yof
eart
hqu
akes
,re
mov
ing
para
mag
netic
impu
ritie
s,d
etec
tion
ofm
agne
ticsi
gnal
sfr
omth
ebr
ain
,hea
rtet
c.
81
82
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