Manifestation of history dependent critical currents via dc and ac magnetisation measurements in single crystals of CeRu2 and 2H-NbSe2

8 Pages·0.18 MB·English

by  G. Ravikumar

Manifestation of history dependent critical currents via dc and ac magnetisation
measurements in single crystals of CeRu and 2H −NbSe
2 2
G. Ravikumar, V.C. Sahni, P.K. Mishra and T.V. Chandrasekhar Rao
Technical Physics and Prototype Engineering Division, Bhabha Atomic Research Centre, Mumbai
8 400 085, INDIA
9 S.S. Banerjee, A.K. Grover, S. Ramakrishnan and S. Bhattacharya∗
9
1 Department of Condensed Matter Physics and Material Science, Tata Institute of Fundamental
n Research, Mumbai -400 005, INDIA
a M.J. Higgins
J
NEC Research Institute,4 Independence way, Princeton, NJ 08540
3
2 E. Yamamoto 1, Y. Haga1, M. Hedo 2, Y. Inada2 and Y.Onuki1,2
1Faculty of Science, Osaka University, Toyonaka 560, JAPAN

n] 2Advanced Science Research centre, Japan Atomic Energy Research Institute, Tokai, Ibaraki
o 319-11, JAPAN
c
-
pr A study of path dependent effects in single crystals of CeRu2 and 2H−NbSe2 show that critical current density Jc of the
vortexstatedependson itsthermomagnetichistory overaverylarge partof(H,T)parameterspace. Thepathdependencein
u
s Jc is absent abovethe peak position (i.e., H >Hp) of thepeak effect region, which we believe identifies thecomplete loss of
. order in the vortex structure. The highly disordered FC state can be healed into a relatively ordered vortex lattice by
t
a subjecting it toa large enough changein dc field (few tensof Oe) or byshaking theFCstate with sufficient ac field (few Oe).
m
-
d Ms number: PACS Numbers: 64.70 Pf, 74.60 Ge, 74.25 Ha, 74.70 Ad, 74.60 Jg
n
o
c
Investigatingstructureofvortexlatticeorfluxlinelat- experimentsinthe twosuperconductorsarepresentedso
[
tice (FLL) in the mixed state of type II superconductors as to elucidate history effects well before, just prior to,

1 continues to be of intense interest. Recent theoretical during and after the occurence of peak of the PE phe-
v
studieshavepostulatedvariousglassystatesinFLLaris- nomenon. Ourresultsinter alia addanewerfacetto the
7
ing from quenched disorder and thermal fluctuations [1]. wellknownCriticalState Model (CSM) [9] whichpostu-
4
2 Experimentalefforts havebeenfocusedondetection and lates a unique critical current density Jc for the vortex
1 characterisation of such states. The appearance of the state for a given field (H) and temperature (T).
0 Peak Effect (PE) in some systems involving an anoma- Werecallthathysteresisinmagnetisationisrelatedto
8 lous enhancement of critical current density J in close J (H) [10]. In isothermal magnetisation measurements,
c c
9 proximity of the softening/melting in their FLL [2–4] - this single valued J translates into a generic magneti-
c
/
t has been explained in terms of a loss of spatial order in sation hystersis loop (see Fig.1) such that the forward
a
FLL [5]. But the precise nature of this loss of order and and reverse branches of the magnetisation curve define
m
its relationship to the glassy state of FLL are topics of an envelope [10], within which lie all the magnetisation
-
current debate. values that can be measured at the given temperature
d
n Indisorderedmagneticsystemssuchasspinglasses[6], along various paths with different thermomagnetic his-
o one encounters the appearance of thermomagnetic his- tories [11]. For instance, Fig.1 schematically illustrates
c toryeffects. Thetemperaturebelowwhichmagnetisation that the FC magnetisation curve generated by decreas-
:
v valuesunderzerofieldcooled(ZFC)andfieldcooled(FC) ingthefieldaftercoolingthe sampleinadcfieldeventu-
i conditions differ is usually identified as the spin glass ally merges into the reverse magnetisation branch. The
X
transition temperature T [6]. We find analogous man- new result of our experiments is that the magnetisation
g
r ifestations in the magnetic behaviour in weakly pinned curve,originating fromagivenFCstate,neednotalways
a
superconducting systems, viz., 2H − NbSe2(Tc=6.1K) be confined within the generic hysteresis loop. We argue
[7] andCeRu2(Tc=6.3K)[8], as reflected in their Jc val- thattheobservednewbehaviourelucidatestheexistence
ues. This difference in the FC and ZFC response, we of multivalued nature of J (H,T), i.e., the critical cur-
c
believe, reflects the different extents of FLL correlations rentdensity ofvortexstate ata given(H,T)depends on
in these states, and is seen to persist upto the peak po- its thermomagnetic history. Our inference by an equi-
sition of PE. In this sense the locus of PE in H-T plane librium dc magnetisation technique strengthens an ear-
may be regarded as the counterpart of spin glass transi- lierconclusionfromnon-equilibriumtransportstudieson
tiontemperature. Theresultsofdcandacmagnetisation 2H −NbSe2 by Henderson et al [7], who measured that
1
the transportJ in ZFC state is considerablylower than response given by Eqn.1. On the other hand the half-
c
that in the FC state for fields below the peak field H . scan response measured between z = −2 cm and z = 0
p
AC susceptibility measurements in superimposed dc gives an excellent fit to Eqn.1. The SQUID response of
fields were performed on a home built ac susceptome- 2H −NbSe2 single crystal, shown in Fig.2 is measured
ter [12]. The dc magnetisation measurements have been at 4.5K in a field of 8 kOe, i.e., very close to peak field
performed using Quantum Design (QD) Inc. (Model H . Similarly, to obtain the magnetic moment on the
p
MPMS) SQUID magnetometer. The single crystals of reverse magnetisation curve, the sample is initially posi-
cubic CeRu2 and hexagonal 2H−NbSe2 were mounted tioned at z = 0 (i.e., where the field is maximum along
on the sample holder such that the field is parallel to the axis of the solenoid). The SQUID response shown in
cube edge and c-axis, respectively. Usually, the mea- Fig.2b is recorded by moving the sample between z = 0
surement of magnetic moment m in the MPMS SQUID and z =l. Magnetic moment is then obtained by fitting
magnetometer involves sample motion along the pickup this response to Eqn.1. The SQUID responses shown in
coil array in the second derivative configuration, over a Fig.2(a) and (b) have been compensated for the offset a
scan length 2l. The magnetic moment m is obtained by and the drift bz (cf. Eqn. 1).
fitting the sample response measured over −l < z <l to Figs. 3 and 4 summarize the central results of mag-
the form, netisationhysteresisandacsusceptibilityexperimentsin
crystals of 2H −NbSe2 (2×2×0.4 mm3) and CeRu2
(3×1.5×0.8 mm3). (It may be stated here that the
V =a+bz+mcφ(z−z0), (1) 2H−NbSe2 crystal is from the same batch as was used
byHendersonetal[7]andCeRu2 crystalisthe oneused
where,
forde-HaasvanAlphenstudiesearlier[15]. Asmentioned
φ(z)=(µ0R2/2) [−[R2+(z+Z)2]−3/2 earlier, both these superconducting systems are weakly
pinned and the crystal pieces chosen for present mea-
surements have comparable levels of quenched disorder
in them [16]). Figs. 3a and 4adisplay the magnetisation
+2[R2+z2]−3/2−[R2+(z−Z)2]−3/2] (2) hysteresis loops in the PE regime of 2H −NbSe2 and
CeRu2respectively. Thepronouncedincreaseinthehys-
Here,a,bandz0accountforconstantoffset,lineardrift teresisinthe PEregionofboth 2H−NbSe2 andCeRu2
and possible off-centering of the sample respectively. R signifytheanomalousincreaseinthecriticalcurrentden-
(=0.97cm)istheradiusand2Z (=3.038cm)isthedis- sity at the onset of PE. Figs. 3a and 4a, also, show
tance between the two outerturns ofthe pick-upcoil ar- themagnetisationcurvesmeasuredinreducingfields,af-
ray. zisthesampledistancefromthecentreofthepickup ter having cooled the samples in the pre-selected mag-
coilarrayandcisthecalibrationfactor. Thisanalysisim- neticfieldstoagiventemperature. Thepre-selectedfield
plicitly assumesthatm isconstantalongthe scanlength cooledmagnetisationstatescanbeidentifiedbyfilleddi-
andthereforeindependentofz. But,asdescribedinRef. amondslyingonthedashedlineinFigs. 3aand4a. Mag-
[13],whenasuperconductingsample,whichexhibitsPE, netisationofthe FC sample in reducing magnetic fieldis
ismovedinaninhomogeneousexternalfield,itsmagnetic measured in the same way as the reverse magnetisation
momentcanbecomestronglypositiondependent,leading curve is generated. In ac susceptibility measurements,
to spurious experimental artefacts in the data. Thus, an the PE manifests via an enhanced (shielding) diamag-
appropriate method needs to be devised to obtain mag- neticresponse. Fig.3(b)showstheplotofin-phaseacsus-
netisation values which are free from such artefacts. We ceptibility(χ′)vsHinZFCandFCstatesin2H−NbSe2
have done this, by analysing the raw data using a new crystal at 5.1 K and Fig. 4(b) shows similar results for
procedurethatcanbe termedashalf-scan technique and CeRu2 crystalat 4.5 K. The χ′ data points in FC states
its salient features are detailed below. were measured after cooling down the sample in a given
In 5.5 Tesla QD MPMS model, on either side of the H to the respective temperatures from the normal state.
centre of the magnet [14] the field due to the supercon- It can be seen in Figs.3(a) and 4(a) that the magneti-
ducting solenoidmonotonicallydecreasesalongthe axial sationcurvemeasuredonfieldcoolinginH >H readily
p
direction. The central idea of the half scan technique is mergeswiththe usualreversemagnetisationcurve. This
torecordthesampleresponsebymovingitoverthatpart can be well understood within the framework of conven-
of the axis so that the sample does not experience field tionalCriticalStateModel[9,10],whichassumesthatJ
c
excursions. On the forward magnetisation curve, this is is single valued function of (H,T) (see Fig. 1). However,
accomplished by recording the sample response only be- when field cooled in H < H , the magnetisation values
p
tween z = −l and z = 0. As the magnetisation of the obtained by reducing the external field initially over-
sample stays nearly constant for −l < z < 0, we can fit shoot the reverse magnetisation curve (see Fig. 3a and
this data to Eqn. 1 and obtain magnetic moment m on Fig. 4a). On further reducing the field, the magneti-
theforwardmagnetisationcurve. AsillustratedinFig.2a, sation values fall sharply and FC magnetisation curve
the SQUID response in the conventional measurement merges into the usual reverse magnetisation hysteresis
(spanning −l to l) fits very poorly to the ideal dipolar branch. Thefirstobservationthatthemagnetisationval-
2
ues initially go beyond the conventional hysteresis loop state of superconductors, the PE phenomena in weakly
is a clear indication of J at a given H in the FC state pinned samples [2,7,8] of these two systems has been in
c
(JFC) being larger than that for the vortex state at the current focus (apparently) due to different reasons. PE
c
sameH valueontheusualreversemagnetisationbranch. in CeRu2 has (often) been considered to relate to re-
The later observation that the FC magnetisation curve alization of Generalized Fulde-Ferrel Larkin Ovchinikov
eventually merges into the reverse magnetisationbranch (GFFLO) state [8], whereas in very clean samples of
implies that the FC vortex state transforms to a more 2H −NbSe2, PE is ascribed to FLL softening [2]. Since
ordered ZFC like state as the vortex state adjusts to a normal state paramagnetism of 2H −NbSe2 is small, it
large enough change ( 102 Oe for CeRu2 and 10 Oe for couldnotbeaseriouscandidatefortheoccurenceofGF-
2H-NbSe2) in the externaldc field. A neutronstudy [17] FLO state. The present findings, that the experimental
on a crystal of CeRu2 had shown that the FC state far featuresofthemixedstatepriortoandacrossthePEre-
belowthePEregioncomprisedmuchmorefinelydivided gion of these two systems follow identical course, would
blocks than that in the ZFC state. Keeping this in view, support the view that their behaviour in the PE regime
on the basis of present results, it may be stated that the presumably reflects same generic physical phenomenon
finely divided FC vortex state heals to the more ordered that occurs in the mixed state in a weakly pinned flux
ZFCstateinresponsetochangesinducedbylargeexter- line lattice while approaching Hc2.
nal field variation. Toconclude,wehavedemonstratedthroughdcandac
The ac susceptibility data in Figs. 3(b) and 4(b) cor- magnetisation measurements with a new half-scan tech-
roborate the above stated conclusions. As per a CSM nique, in the mixed state of CeRu2 and 2H −NbSe2,
result [9], χ′ = −1+αh /J , where α is a shape and that there are sizable thermomagnetic history effects in
ac c
size dependent parameter and h is the ac field ampli- their critical currents below H , where the peak of the
ac p
tude, the higherdiamagneticresponseinthe FC stateas PE occurs. We have shown that these effects imply a
compared to that for the ZFC state, reflects larger J in more finely divided disordered vortex arrangement for
c
′
the former state. The history dependence in χ response the FC state, as compared to that for the ZFC state. It
ceasesabovethepeakpositionofthePEregion. Also,at should be noted that the critical current, remains finite
very low fields (H < 1kOe), the difference between FC above H . This suggets that the glassy state above H
p p
′
and ZFC χ response is seen to decrease,consistent with is weakly pinned and a change to completely unpinned
transport J measurements of Henderson et al [7]. statedoesnotappearuntilthehigherfieldH . Theim-
c irr
IntheLarkin-Ovchinikov[18]descriptionofpinningin plicationoftheseresultswithrespecttotheoccurenceof
superconductors,J ∝V−1/2,whereV isthevolumeofa PEbehaviour,fishtail(secondpeak),etc.,intheCuprate
c c c
Larkindomainwithinwhichfluxlinesremaincorrelated. superconductors, such as, YBCO and BSCCO, remains
SmallerJ intheZFCstate[7,19],therefore,corresponds an interesting topic for further investigations.
c ∗
to a more orderedFLL than in the case ofFC state. For Present and permanent address: NEC Research In-
H >H , flux lines form a quasi-pinned state, which ap- stitute,4IndependenceWay,Princeton,NJ08540,USA.
p
pearstobeindependentofhowthestateisapproachedin
(H,T) space. For H <H , the larger JFC can therefore
p c
be attributed to the formation of a more finely divided
disordered state, with concomitant more pinning. While
subjectingtheFCstatetoadecreaseintheexternalfield,
this state eventually goes over into a relatively more or-
[1] T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 72,
dered ZFC state with a larger V , as manifested by a
c 1530 (1994); Phys. Rev. B 52, 1242 (1995); M. Gingras
steepfallinthe magnetisationvalues(after overshooting
andD.A.Huse,Phys.Rev.B53,15193 (1996); G.Blat-
the reverse magnetisationbranch). A changefrom a dis-
teretal,Rev.Mod.Phys.66,1125(1994)andreferences
ordered state to more ordered vortex state can also be
therein.
brought about by other kinds of perturbations as well.
[2] S. Bhattacharya and M.J. Higgins, Phys. Rev. Lett. 70,
For example, in our ac measurements, we observed that 2617(1993);Phys.Rev.B52,64(1995);PhysicaC257,
the large (shielding) diamagnetism of FC state suddenly
232 (1996) and references therein.
collapses to that of the ZFC state on increasing the ac [3] W.K. Kwok et al, Phys. Rev.Lett. 73, 2614 (1994)
fieldamplitudemomentarilytoabout5Oe. Althoughby
[4] A.I. Larkin et al, Phys.Rev.Lett. 75, 2992 (1995); K.
no means obvious this way of annealing away the disor- Ghosh et al, ibid, 76, 4600 (1996).
der of the FLL in the FC case is akin to annealing by a [5] T.V.C. Rao et al, Physica C (in press); S.S. Banerjee et
passage of large transport current [7]. al (unpublished).
CeRu2 and 2H−NbSe2 arevery dissimilar supercon- [6] J.A. Mydosh, Spin glass: An experimental introduction,
ductingsystemsasregardstheirmicroscopicphysics;the Taylor and Francis, London (1993)
former is a mixed valent system whereas the latter is a [7] W. Henderson et al, Phys.Rev.Lett. 77 2077 (1996).
layered chalcogenide which exhibits charge density wave [8] R.Modleretal,Phys.Rev.Lett.76,1292(1996); Czech
behaviour in its normal state. In the context of vortex J. Phys.46, Suppl.S6, 3123 (1996); A.Yamashita et al,
3
Phys.Rev.Lett. 79, 3771 (1997).
[9] C.P. Bean, Rev.Mod. Phys. 36, 31 (1964).
[10] P. Chaddah, K.V. Bhagwat and G. Ravikumar, Physica
C 159, 570 (1989) and references therein.
[11] A.K. Grover et al, Physica C 162-164, 337 (1989);
Pramana-J Phys 33, 297 (1989); B.V.B. Sarkissian et
al, ibid 38, 641 (1989).
[12] S.Ramakrishnan et al, J. Phys. E 18, 650 (1985).
[13] G. Ravikumaret al, Physica C 276, 9 (1997).
[14] QunatumDesign Technical Advisory MPMS No.1
[15] M. Hedoet al, J. Phys. Soc. of Japan 64, 4535 (1995).
[16] TransportJc valuesin CeRu2 and2H−NbSe2 areesti-
mated to be ∼ 102 A/cm2 and ∼ 103 A/cm2, respec-
tively.
[17] A.D.Huxley et al, Physica B 223-224, 169 (1996).
[18] A.I. Larkin and Yu.N. Ovchinikov, J.Low Temp. Phys.
34, 409 (1979).
[19] N.R.Dilley et al, Phys. Rev.B 56, 2379 (1997).
FIG. 1. A schematic showing magnetisation hysteresis
curvesinanirreversibletypeIIsuperconductor. Forwardand
reverse magnetisation branches corresponding to increasing
and decreasing field cycles. A magnetisation curve measured
duringreducingfieldcycleaftercooling inafieldisindicated
as field cooled (FC) curve. MFC denotes the FC magnetisa-
tion value.
FIG.2. (a)(◦) SQUID response of the sample in the PE
region, on the forward magnetisation curve using a conven-
tional full symmetric scan of 4cm length. The corresponding
fittoEqn.1isshownbyadottedline. Thehalf-scanresponse
for −2cm < z < 0 (•) and its fit to Eqn.1 (continuous line)
is also shown. (b) The SQUID response from 0 to 2 cm for
the reverse case is shown along with the corresponding fit to
Eqn.1 after compensating for the offset a and linear drift bz.
FIG. 3. (a) A portion of the magnetisation hysteresis
curve (encompassing the PE region) recorded at 5.1K for
H k c using the half-scan technique in a 2H −NbSe2 crys-
tal. Also shown are the magnetisation values recorded while
decreasing thefield after cooling thesample in (pre-selected)
different external fields. The initial MFC values are identi-
fied by filled diamonds lying on the dashed curve. Each FC
magnetisationcurveinitiatesfromadifferentMFC value. (b)
ACsusceptibilitymeasuredwithhac =0.5Oeatf =211Hz,
for H k c at 5.1K (i) after cooling the sample in zero field
(ZFC) and (ii) after cooling the sample different fields each
′ ′
time (FC). χ(H) values are normalized to χ(0)
FIG. 4. (a) A portion of the magnetisation hysteresis
curve of CeRu2 recorded at 4.5K for H k [100] using the
half-scantechnique. TheFCmagnetisationcurvesoriginating
from different MFC values are also shown. (b) AC suscepti-
bility for H k [100] in both ZFC and FC modes as described
in thecaption of Fig.3b.
4
M
Reverse
F C
H

M
FC
Forward

figure 1
G. Ravikumar et al
10 20
2H-NbSe (b)
(a)
2

5 15
)
s
t 2H-NbSe
i
n 2
10
u
0
.
b
r
a
5
( -5
)
z
(
0
V
-10
-5
-15 forward reverse
-10
-2 -1 0 1 2 0 1 2

z (cm) z(cm)

figure 2
G. Ravikumar et al
8.0 (a)
reverse
6.0
)
G
4.0 M forward
( H FC
M
p
2.0
CeRu
2 PE region
T = 4.5K
0.0
17 18 19 20 21 22

0.0 (b)
) -0.2
0
=
H -0.4
(

/ -0.6
c/

/
-0.8
PE
c ZFC
FC
-1.0
0.0 5.0 10.0 15.0 20.0
H (kOe)
Figure 3
G. Ravikumar et al
3
(a)
2 reverse
1
)
G
( 0
M
M
FC
-1
H forward
p
-2 2H-NbSe
2 PE region
5.1K
-3

0.0 (b)
)
0 -0.2
=
H
-0.4
(

/
c/ -0.6

/
ZFC
c
-0.8
FC
-1.0
1 2 3 4 5 6 7
H (kOe)