Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe₂ single crystals in a peak-effect regime
Magnetostriction mea sure ments in the mixed state of superconducting 2H-NbSe₂ single crystals under in-plane magnetic fields 0-12 T have revealed a peak on the magnetostriction versus magnetic field dependences in the vicinity of the upper critical field Hc₂. The peak value of the longitudinal magn...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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nasplib_isofts_kiev_ua-123456789-1291592025-02-09T14:08:43Z Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe₂ single crystals in a peak-effect regime Eremenko, V.V. Sirenko, V.A. Shabakayeva, Yu.A. Gammel, P.L. Свеpхпpоводимость, в том числе высокотемпеpатуpная Magnetostriction mea sure ments in the mixed state of superconducting 2H-NbSe₂ single crystals under in-plane magnetic fields 0-12 T have revealed a peak on the magnetostriction versus magnetic field dependences in the vicinity of the upper critical field Hc₂. The peak value of the longitudinal magnetostriction is higher by more than an order of magnitude in comparison with that of the trans verse magnetostriction when measured along the hexagonal axis. Analysis of the measured field dependences of the magnetostriction and magnetization of 2H-NbSe₂ allows one to relate the observed peculiarities of magnetostriction with the loss of order in the lat tice of Abrikosov vortices, which occurs by a first-order phase transition. Remove selected 2002 Article Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe₂ single crystals in a peak-effect regime / V.V. Eremenko, V.A. Sirenko, Yu. A. Shabakayeva, R.Schleser, P.L. Gammel // Физика низких температур. — 2002. — Т. 28, № 1. — С. 10-15. — Бібліогр.: 25 назв. — англ. 0132-6414 PACS: 75.80.+q, 74.25.Hq, 74.70.Ad https://nasplib.isofts.kiev.ua/handle/123456789/129159 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная |
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Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная Eremenko, V.V. Sirenko, V.A. Shabakayeva, Yu.A. Gammel, P.L. Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe₂ single crystals in a peak-effect regime Физика низких температур |
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Magnetostriction mea sure ments in the mixed state of superconducting 2H-NbSe₂ single crystals under in-plane magnetic fields 0-12 T have revealed a peak on the magnetostriction versus magnetic field dependences in the vicinity of the upper critical field Hc₂. The peak value of the longitudinal magnetostriction is higher by more than an order of magnitude in comparison with that of the trans verse magnetostriction when measured along the hexagonal axis. Analysis of the measured field dependences of the magnetostriction and magnetization of 2H-NbSe₂ allows one to relate the observed peculiarities of magnetostriction with the loss of order in the lat tice of Abrikosov vortices, which occurs by a first-order phase transition.
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Eremenko, V.V. Sirenko, V.A. Shabakayeva, Yu.A. Gammel, P.L. |
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Eremenko, V.V. Sirenko, V.A. Shabakayeva, Yu.A. Gammel, P.L. |
| author_sort |
Eremenko, V.V. |
| title |
Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe₂ single crystals in a peak-effect regime |
| title_short |
Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe₂ single crystals in a peak-effect regime |
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Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe₂ single crystals in a peak-effect regime |
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Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe₂ single crystals in a peak-effect regime |
| title_full_unstemmed |
Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe₂ single crystals in a peak-effect regime |
| title_sort |
irreversible magnetostriction and magnetization of the superconduting 2h-nbse₂ single crystals in a peak-effect regime |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2002 |
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Свеpхпpоводимость, в том числе высокотемпеpатуpная |
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https://nasplib.isofts.kiev.ua/handle/123456789/129159 |
| citation_txt |
Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe₂ single crystals in a peak-effect regime / V.V. Eremenko, V.A. Sirenko, Yu. A. Shabakayeva, R.Schleser, P.L. Gammel // Физика низких температур. — 2002. — Т. 28, № 1. — С. 10-15. — Бібліогр.: 25 назв. — англ. |
| series |
Физика низких температур |
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2025-11-26T15:23:08Z |
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| fulltext |
Fizika Nizkikh Temperatur, 2002, v. 28, No. 1, p. 10–15
Irreversible magnetostriction and magnetization of the
superconduting 2H-NbSe2 single crystals
in a peak-effect regime
V. V. Eremenko, V. A. Sirenko, and Yu. A. Shabakayeva
B. Verkin Institute for Low Temperature Physics and Engineering
of the National Academy of Sciences of Ukraine, 47 Lenin Ave., 61103 Kharkov, Ukraine
E-mail: sirenko@ilt.kharkov.ua
R. Schleser
Grenoble High Magnetic Field Laboratory,
MPI-FKF and CNRS BP-166, F-38042, Grenoble Cedex 09, France
P. L. Gammel
Bell Laboratories, Lucent Technologies Murray Hill, New Jersey 07974, USA
Received August 31, 2001
Magnetostriction mea sure ments in the mixed state of super con duct ing 2H-NbSe2 sin gle
crys tals un der in-plane mag netic fields 0–12 T have re vealed a peak on the magnetostriction
ver sus mag netic field dependences in the vi cin ity of the up per crit i cal field Hc2 . The peak
value of the lon gi tu di nal magnetostriction is higher by more than an or der of mag ni tude in
com par i son with that of the trans verse magnetostriction when mea sured along the hex ag o nal
axis. Anal y sis of the mea sured field dependences of the magnetostriction and mag ne ti za tion of
2H-NbSe2 al lows one to re late the ob served pe cu liar i ties of magnetostriction with the loss of
or der in the lat tice of Abrikosov vor ti ces, which oc curs by a first-order phase tran si tion.
PACS: 75.80.+q, 74.25.Hq, 74.70.Ad
1. Introduction
The ob ser va tion of gi ant magnetostriction in
high-temperature su per con duc tors [1–3], along
with es tab lish ing its re la tion to the in ter ac tions be -
tween the crys tal lat tice inhomogeneities and the
ar range ment of Abrikosov vor ti ces [4], en ables one
to use magnetostriction mea sure ments as the tool
for ex am i na tion of a va ri ety of phe nom ena in the
vor tex as sem bly, which re sults from mag netic flux
pin ning. An im por tant di rec tion in this field of in -
ves ti ga tion is elu ci da tion of the or i gin of the peak
ef fect, which is the peak on the field dependences
of the crit i cal cur rent near the up per crit i cal field
Hc2 , man i fested as the max i mum on the field
dependences of the ir re vers ible mag ne ti za tion [5],
and of its con nec tion with the phase tran si tions in a
flux-line lat tice [6]. It should be men tioned that an
ad van tage of mag netic stud ies of the peak ef fect is
that they pro vide di rect data on the ther mo dy namic
pa ram e ters of the tran si tion.
Many years of re search on the field dependences
of the crit i cal cur rents and mag ne ti za tion of type-II
su per con duc tors have shown that in gen eral the
peak ef fect is ob served in dif fer ent ranges of mag -
netic fields be tween the lower Hc1 and up per Hc2
crit i cal fields, and the shape of the peak is de -
scribed by an ex pres sion ( ) ( )H f bc
n
2 , with f b( ) si -
milar at all tem per a tures be low TSN , where b is
the re duced mag netic in duc tion in the sam ple, and
n = 1–3, de pend ing on the type of pin ning cen ter
and the pin ning mech a nism in volved [5]. The peaks
on the field dependences of the magnetostriction
were ob served in [2,7,8] on sin gle crys tals of
high-temperature su per con duc tors (HTSCs) of the
1-2-3 type with rare-earth sub sti tu tions, poly crys -
© V. V. Eremenko, V. A. Sirenko, Yu. A. Shabakayeva, R. Schleser, and P. L. Gammel, 2002
tals of Nb–Ti al loys, and sin gle crys tals of the laye -
red com pound 2H-NbSe2 , re spec tively. For HTSCs
it was shown [2] that the peaks in the in ter me di ate
field range cor re spond to the tra di tional mech a -
nisms of pin ning (n = 2.5). For ex pla na tion of the
ob served value n = 4.5 for the magnetostriction
peak in Nb–Ti the field de pend ence of the Young’s
moduli of the crys tal lat tice was taken into ac -
count. The value n = 6.5 ± 0.2 for the mag neto -
striction in 2H-NbSe2 will be an a lyzed in the pre -
sent work.
2. Experimental results
The mea sure ments were per formed on high- qua -
lity sin gle crys tals of the super con duct ing com -
pound 2H-NbSe2 with the super con duct ing tran si -
tion tem per a ture TSN = 7.2 K.
2.1. Magnetostriction measurements
The magnetostriction mea sure ments were per -
formed in a cryo genic ca pac i tance dilatometer [8].
The lon gi tu di nal λ( , )a a and trans verse λ( , )c a mag -
netostriction val ues were mea sured in a field ap -
plied in the basal plane of the sam ple along the a
axis. The mea sure ments of λ( , )c a and λ( , )a a in in -
creased field at tem per a ture T = 1.5 K are pre sented
in Fig. 1. It is clearly seen that at fields near Hc2 a
pro nounced peak is ob served, and the ab so lute val -
ues of λ( , )c a are much lower than those for λ( , )a a .
2.2. Magnetization measurements
The mag ne ti za tion mea sure ments were per -
formed along the crys tal lo graphic c di rec tion by
means of a mag netic ca pac i tance torque meter tech -
nique [9]. The ab so lute val ues of the mag ne ti za tion
were ob tained us ing a cal i bra tion coil [10].
The mea sure ments at tem per a ture T = 1.5 K are
shown in Fig. 2. Fig ure 3 pres ents ir re vers ible com -
po nent of mag ne ti za tion for dif fer ent tem per a tures.
Fig ure 4 dem on strates ir re vers ible magnetostriction
and mag ne ti za tion in re duced co or di nates. For the
magnetostriction and mag ne ti za tion mea sure ments
the scal ing law with n = 6.5 ± 0.2 is ful filled.
3. Discussion
The unit cell of this com pound com prises two
sand wiches. Each of them is a hex ag on ally packed
plane of Nb be tween two hex ag on ally packed
planes of Se. The planes are shifted with re spect to
each other, and at oms of Se form a trigonal en vi -
ron ment of the Nb at oms. The Nb planes are re spon -
Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe
2
single crystals
Fizika Nizkikh Temperatur, 2002, v. 28, No. 1 11
Fig. 1. Magnetostriction λ versus magnetic field mea -
sure ments.
Fig. 2. Absolute magnetization measurements along the
c di rection for an in-plane direction of the magnetic
field. The in set shows the enlarged region of the peak
effect.
Fig. 3. Field dependence of the irreversible mag ne ti -
zation.
si ble for the su per con duc tiv ity of this com pound.
The dis tance be tween the near est Nb planes is
d c= =/ .2 6 27 Å where c is the lat tice spac ing
along the hex ag o nal axis. The in-plane lat tice pa -
ram e ters are a b= = 3 45. Å. The ra tio of the lat tice
pa ram e ters at tests to pro nounced crys tal lo graphic
ani so tropy. At the same time 2H-NbSe 2 should not
be con sid ered as quasi-two-dimensional su per con -
duc tor, as its super con duct ing co her ence length
along the hex ag o nal axis is twice the interplane
spac ing ξ c d> (ξc( )0 23= Å). This is a typ i cal
highly anisotropic su per con duc tor (ξab( )0 78= Å),
which is char ac ter ized by an ani so tropy pa ram e ter
γ ξ ξ= = ≈( / ) //M m ab c
1 2 3, or in al ter na tive
def i ni tions ε2 0 09= ≈m M/ . (m m m= =1 2 and
M m= 3 are the ef fec tive elec tron masses along and
nor mal to the crys tal lo graphic planes). Such high
val ues of the ani so tropy pa ram e ters of 2H-NbSe 2
pro vide an ad e quate de scrip tion of its super con -
duct ing prop er ties by the Ginzburg–Lan dau equ -
ations [11] with the anisotropic mass ten sor ([12]
and ref er ences therein). For our case m1 = <m m2 3 ;
m m H c H cc c1 3 2 2
2/ [ ( | | )/ ( )]= ⊥ . We take into
con sid er ation the fol low ing ex pres sion
Hc ab2 0
2 2 2 1 2 22( ) /[ (sin cos ) ]/θ π θ ε θ ξ= +Φ (1)
(Φ0 is the quan tum of mag netic flux, and θ is the
an gle be tween the di rec tion of the ap plied mag netic
field and the c axis), which de fines the co her ence
length val ues.
Va lid ity of this ap proach sig nif i cantly sim pli fies
anal y sis of the an gu lar dependences of the mea -
sured prop er ties, which in part will be con sid ered
in this pa per.
3.1. Anisotropy of magnetostriction at
H H Hc1 c2< <<
The ob served dif fer ences of λ( , )c a and λ( , )a a in
the fields be low the peak val ues may be ex plained
in the fol low ing way. In fields ap plied along the
ex tended sur face of the sam ple in the a axis di rec -
tion, mag netic flux pen e trates the sam ple along the
b axis. Un der this con di tion the pen e tra tion is post -
poned by a sur face bar rier un til the mag netic field
H is in creased to the value H Hc≈ 2 7. [5], where
Hc is the crit i cal field, which is de ter mined by the
dif fer ence of free en ergy val ues in the nor mal and
super con duct ing states, and which is much higher
than Hc1. The low-temperature limit of Hc for the
com pound un der in ves ti ga tion is Hc ≈ 0 14. T [13].
In this range of mag netic fields the magneto stric -
tion is de ter mined by the pres sure of the mag netic
field and by the ra tio of elas tic con stants in diffe -
rent crys tal lo graphic di rec tions. From the the ory of
elas tic ity the re la tion be tween λ( , )c a and λ( , )a a
may be de rived:
λ λ( , )/ ( , ) ( )/( ).c a a a C C C C C C= − − −13 11 12 11 33 13
2
The right side of this re la tion in cludes the
components of the elas tic-modulus ten sor of
the crys tal lat tice. In tro ducing their val ues
from [13], one ob tains the ra tio λ λ( , )/ ( , )a a c a =
= − = −0 76 0 12 6 3. / . . , which is in good agree ment
with the mea sure ments in fields well be low Hc2 .
When the mag netic flux pen e trates the sam ple
along the b axis, the val ues of λ( , )c a are de ter -
mined by the ra tios of the vol umes of the nor mal
and super con duct ing parts of the sam ple [8] and
are pro por tional to the size dif fer ences δT c(| | ) in
the nor mal and super con duct ing states along the
dis tin guished crys tal lo graphic di rec tion in the ab -
sen ce of mag netic field. This quan tity is de ter mi ned
by re la tion δT c cc H H P c(| | ) ~ [ / (| | )]∂ ∂ , or accor -
ding to [13] δT c(| | ) ~ H T T P cc SN SN
2 / [ / (| | )]∂ ∂ .
Sub sti tu tion of the val ues ∂ ∂T P cSN / (| | ) ≈
≈ ⋅18 1010. from [14] gives a sa tisfactory agree ment
with the mea sure ments [8] δT c(| | ) ≈ ⋅ −2 10 7. It is
known [14] that the in-plane pres sure de pend ence
of TSN dif fers sig nif i cantly from that in the c
direction. Pres sure along the c axis weakly in -
creases the tran si tion tem per a ture, while in-plane
pres sure in creases it sig nif i cantly. In first ap prox i -
ma tion it should be as sumed that the be low peak
val ues, λ( , )a a is also de fined by the vol u met ric ra -
tio of the nor mal part of the sam ple due to weak
pin ning (the ra tio of the crit i cal cur rents of de -
pinning and depairing j jc / 0
610≈ − [15] is sur -
pris ingly small). There fore, the ra tio of λ( , )c a to
λ( , )a a in the field be low peak is de fined by the
relation [ / (| | )]/[ / ( )] .∂ ∂ ∂ ∂ ⊥ ≈T P c T P cSN SN 0 45
[15], which sat is fies the ex per i men tal data for the
re vers ible com po nent of the magnetostriction [8].
It ap pears that for ex pla na tion of the ir re vers ible
magnetostriction we can not ne glect the pin ning in
the basal plane par al lel to ap plied mag netic field.
3.2. Magnetostriction in the fields near Hc2
In [16,17] the peak ef fect in the field de pen -
dences of the crit i cal cur rents near Hc2 was attri -
buted to the change of the elas tic moduli of the
flux-line lat tice when the field ap proaches Hc2 .
In [16] it was the de crease of the shear modu lus
C66 , which oc curs faster than the de crease of the
pin ning force. As a re sult, the vor texes re dis trib ute
in ac cor dance with the spa tial dis tri bu tion of pin -
ning cen ters or the pin ning po ten tial re lief. This
sit u a tion cor re sponds to a loss of spa tial or der in
12 Fizika Nizkikh Temperatur, 2002, v. 28, No. 1
V. V. Eremenko, V. A. Sirenko, Yu. A. Shabakayeva, R. Schleser, and P. L. Gammel
the flux-line lat tice and, in prin ci ple, re sem bles
melt ing pro cesses. It was de scribed in [18] in terms
of the cor re la tion vol ume Vc of the flux-line lat tice
re gions which can move in de pend ently of each
other. The re sults of this work have been used suc -
cess fully for ex am i na tion of trans for ma tions in the
vor tex ar rays of anisotropic su per con duc tors. The
pos si bil ity of trans for ma tions de vel op ing via a
first- order phase tran si tion was an a lyzed in [19]. It
was sug gested that the tran si tion is re al ized in the
fluc tu a tion re gime when the Lindemann cri te -
rion [20] is ful filled, i.e. when the mean-square am -
pli tude of the vor tex fluc tu a tion dis place ments
amounts to about 0.2a0 , where a0 is the vor tex lat -
tice pa ram e ter. It is a re sult of the loss of or der in
the vor tex lat tice or the de crease of Vc when the
mag netic field ap proaches Hc2 . A com par a tive ana -
l y sis of the magnetostriction and mag ne ti za tion
mea sure ments al lows us to check if this sit u a tion is
char ac ter is tic for our case. It should be noted that a
fluc tu a tion con tri bu tion to the be hav ior of su per -
conducting 2H-NbSe 2 is prob a ble, as the Ginz burg
num ber [21], which char ac ter izes im por tance of the
fluc tu a tion con tri bu tion, is rather high: Gi =
= ≈ −k T HB SN c/ 2 3 410εξ . For HTSCs it is of the
or der of 10 2− , and for other con ven tional su per con -
duc tors it is of the or der 10 8− [15]. This is, in part,
the rea son for the no tice able dif fer ence be tween
the fields Hc2 and H*, where H* is the field
above which all ir re vers ible char ac ter is tics van ish
(H Hc
* ≈ 2). The ad van tage of 2H-NbSe2 for ana -
lysis of the tran si tion pro cesses is that, in con trast
to HTSCs, there is no flux creep in it, not with -
stand ing the high level of ther mal fluc tu a tions. In
ad di tion, the in set in Fig. 2 dem on strates that
in the peak re gime the mag ne ti za tion run (the
low-field arm of the peak) is ir re vers ible. It may
be a proof of the first-order phase tran si tion, on the
one hand, and a man i fes ta tion of vor tex lat tice dis -
or der ing and the con se quent spread over pin ning
cen ters, on the other. So, the ex per i men tal data do
not con tra dict the pro posed de scrip tion.
In com par ing the data on the magnetostriction
and mag ne ti za tion we should keep in mind that in
the lat ter case the torque was reg is tered in a tilted
field, which is a nec es sary con di tion for ap pli ca tion
of such a mea sur ing tech nique. The cho sen value
θ = °77 cor re sponds to the max i mum sig nal [22].
Anal y sis of the an gu lar dependences and com par i -
son of the data ob tained at dif fer ent θ is pos si ble
due to ap pli ca bil ity of Ginzburg–Lan dau the ory
with an anisotropic mass ten sor to the com pound
un der study (the re la tions are pre sented in [6]).
3.3. Phase transition
In or der to an a lyze the pos si bil ity that a first-
or der phase tran si tion in the vor tex ar ray is ma -
nifestated in the peak ef fect, the re la tion de rived
for the flux-line lat tice from the Lindemann cri te -
rion [19,20] will be used:
H T c H T Tm m L c SN( ) ( / ) ( )( / )= ×β Gi 2
20
× − −[ ( / ) / ( )]1 02
2T T H HSN m c , (2)
where β m ≈ 5 6. , cL = 0.23–0.15 is the Lindemann
cri te rion in sys tems with vari able pin ning, and Hm
is the melt ing field of the flux-line lat tice. The lo -
ca tion of the mea sured high-field mag ne tostriction
and mag ne ti za tion peak-effect curves, namely H*,
suits well the value of H Tm( ) if the superconduc -
ting pa ram e ters of 2H-NbSe2 are sub sti tuted into
Eq. (2). The ex per i men tally ob served jump in the
equi lib rium mag ne ti za tion near H* at T = 1.5 K is
∆M ≈ 5 G, and the cor re spond ing elon ga tion is
∆L ≈ ⋅ −2 10 8 mm. There fore, the pres sure de riv a -
tive of the tran si tion field may be es ti mated us ing
the Clapeyron–Clausius re la tion: ∆ ∆L c M(| | )/ =
= ∂ ∂H P c* / (| | ). Sub sti tu tion of the mag ni tudes
ob tained gives a rea son able [14] es ti mate
∂ ∂ ≈H P c* / (| | ) 0.6–0.8 G/bar.
3.4. Scaling law for isothermal field dependences
of magnetostriction
The anal y sis of the magnetostriction mea -
surements in the peak re gime ac cord ing to the
scheme [2,7] have shown that the field depen -
dences of the ir re vers ible com po nent of the mag -
netostriction λ irr ( , )c a mea sured at dif fer ent tem -
per a tures fol low the scal ing laws M H n
irr ~ ( )* and
λirr ~ ( )*H n with the same power n = 6.5 ± 0.2.
Con se quently, for anal y sis of the ob served de pen -
dences the con cepts de vel oped for the triv ial peak
ef fect may be used, and the field dependences of
the elas tic moduli of the crys tal lat tice may in our
case be ex cluded from con sid er ation of the mag -
netostriction peak. In view of the soft en ing of the
flux-line lat tice in a peak ef fect re gime and the in -
de pend ent dis place ments of its parts with the cor -
re la tion vol ume Vc , the re la tion for col lec tive pin -
ning in the peak re gion [18] may be used for
de scrip tion of the ir re vers ible mag ne ti za tion:
M n f Vp p cirr ∼ ( / ) /2 1 2 , (3)
where np is the den sity of pin ning cen ters, fp is the
elementary pin ning force, and n fp p
1 2/ is the vol ume
den sity of the pin ning force. Usually, the lat ter is
char ac ter ized by a power-law de pend ence on Hc2
Fizika Nizkikh Temperatur, 2002, v. 28, No. 1 13
Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe
2
single crystals
with a power of 1–3 for dif fer ent types of pin ning
cen ters [5]. Its con tri bu tion to n may be also es ti -
mated from anal y sis of the broad max i mum of the
mag ne ti za tion in fields of about H = 2.4 T. The
nearly same po si tion of the max ima at dif fer ent
tem per a tures sug gests a match ing be tween the
flux-line lat tice spac ing and the dis tance be tween
the pin ning cen ters in volved [5]. The flux-line lat -
tice spac ing may be es ti mated from the well known
re la tion a B0 0
1 2 178≈ =( / ) /Φ Å, which can eas ily
cor re spond to the dis tance be tween the stack ing
faults in Nb planes aris ing be low the
charge-density-wave tran si tion (TCDW = 34 K),
with the ap pear ance of an in com men su rate struc -
ture of ni o bium at oms, char ac ter ized by a lat tice
spac ing of about 3 0a [23]. Es ti ma tion of the cor re -
spond ing pin ning force from [24] gives the power
n1 ≈ 2.5.
Now the con tri bu tion of the cor re la tion vol ume
Vc will be es ti mated. It goes as the in verse square
of the tilt and shear moduli of the vor tex lat tice, or
( )Hc2
4− , which means that ex pres sion (3) com -
prises a multi pli ca tive fac tor with the power n2 2= .
And, fi nally, the thermofluctuational char ac ter
of the tran si tion near H* means that ex pres sion (3)
should be sup ple mented by a tem per a ture-de pend -
ent fac tor [25]. It is de ter mined by tem per a ture de -
pend ence of the depinning en ergy for ther mal fluc -
tu a tions, which to a first ap prox i ma tion is lin ear in
the tem per a ture [5]. Using the tem per a ture de -
pend ence of the crit i cal fields, a fac tor with n3 2=
is ob tained.
In this way a to tal power n = 6.5 is ob tained,
which agrees with that de rived from magne to -
striction and mag ne ti za tion mea sure ments in the
peak-effect re gime.
Conclusions
It was found that the max i mum on the field
dependences of ir re vers ible magnetostriction in su -
per con duct ing 2H-NbSe 2 cor re sponds to the field
range of struc tural trans for ma tions in the vor tex ar -
ray, which is re al ized af ter a first-order phase tran -
si tion sce nario. The mea sured field de pend ence in
the peak re gion is de scribed by a scal ing law
λ irr ~ ( )* . .H 6 5 0 2± , sim i lar to that for the irrever sible
mag ne ti za tion M Hirr ~ ( )* . .65 02± . It is shown that
the power n = 6.5 ± 0.2 is de ter mined by the field
dependences of the el e men tary pin ning force and
cor re la tion vol ume and by ther mal fluc tu a tions
near the up per crit i cal field. It should noted that
the anal y sis pre sented is the first one of this kind,
but the sim i lar dependences may be ex pected for
the ir re vers ible magnetostriction in HTSCs in the
high-field peak-effect re gimes. Ac cord ing to the ar -
gu ments pro posed, in con ven tional su per con duc tors
with a low prob a bil ity of ther mal fluc tu a tions the
power of Hc2 in the high-field-peak sca ling law
should be a few times lower.
14 Fizika Nizkikh Temperatur, 2002, v. 28, No. 1
V. V. Eremenko, V. A. Sirenko, Yu. A. Shabakayeva, R. Schleser, and P. L. Gammel
Fig. 4. Reduced field dependence of the irreversible
mag neto striction [8] and magnetization, normalized to
their values at the peak.
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Fizika Nizkikh Temperatur, 2002, v. 28, No. 1 15
Irreversible magnetostriction and magnetization of the superconduting 2H-NbSe
2
single crystals
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