Weak pinning and vortex bundles in anisotropic Ca$_{10}$(Pt$_4$As$_8$)[(Fe$_{1-x}$Pt$_x$)$_2$As$_2$]$_5$ single crystals

0.43 MB·English

by  O. E. Ayala-Valenzuela

Weak pinning and vortex bundles in anisotropic Ca10(Pt4As8)[(Fe1−xPtx)2As2]5 single
crystals
O. E. Ayala-Valenzuela,1 N. Haberkorn,2 A. B. Karki,3 Jisun Kim,3 R. Jin,3 and Jeehoon Kim1,4,
∗
1Center for Artificial Low Dimensional Electronic Systems,
Institute for Basic Science (IBS), 77 Cheongam-Ro, Pohang 790-784, Korea
2Centro At´omico Bariloche, Comisio´n Nacional de Energ´ıa At´omica. Av., Bariloche, Argentina†
3Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
5 4Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Korea
1 (Dated: February 2, 2015)
0
2 We report the magnetic field – temperature (H − T) phase diagram of
n Ca10(Pt4As8)[(Fe1−xPtx)2As2]5 (x ≈ 0.05) single crystals, which consists of normal, vortex
liquid, plastic creep and elastic creep phases. The upper critical field anisotropy is determined
a
by a radio frequency technique via the measurements of magnetic penetration depth, λ. Both,
J
irreversibility line, Hirr(T), and flux creep line, HSPM(T), are obtained by measuring the
0
magnetization. WefindthatHirr(T)iswelldescribedbytheLindemanncriterion withparameters
3 similar to those for cuprates, while small HSPM(T) results in a wide plastic creep regime. The

flux creep rates in the elastic creep regime are in qualitative agreement with the collective creep
]
n theory for random point defects. A gradual crossover from a single vortex to a bundles regime
o is observed. Moreover, we obtain λ(4 K) = 260(26) nm through the direct measurement of the
c London penetration depth bymagnetic force microscopy.
-
r PACS numbers: 74.25.Dw, 74.25.Ha, 74.25.Wx, 74.25.Op
p
u
s I. INTRODUCTION ThevortexdynamicsofFeSC hasbeenextensivelyex-
.
t plored.17–19 For example, giant flux creep and glassy re-
a
m laxation have been reported.17 The critical current den-
Since the discovery of high-temperature superconduc- sity (J ) can be enhanced by introducing pinning cen-
- c
d tivity in LaFeAsO1 xFx,1 many new iron-based super- ters.18 Depending on the applied magnetic field (H), Jc
n conductors (FeSC)−have been found and classified into is governedby strong defects at low magnetic fields, and
o families such as “122” (e.g. BaFe2As2),2 “11” (e.g. by a mixed pinning landscape between strong and weak
c FeSe),3 and “111” (e.g. LiFeAs).4 These materials are pinning(randompointdefects)atintermediatemagnetic
[
built from layers of edge-sharing tetrahedra, in which fields.19 At high fields a crossover from elastic to plastic

1 each Fe atom is surrounded by four As or Se atoms. creephasbeenreportedinFeSC.17TheJ valuesinsingle
c
v Recently, the family of Ca10(PtnAs8)(Fe2As2)5 [with crystals of the 10-3-8 and 10-4-8 compounds are smaller
7 n = 3 (10-3-8) and n = 4 (10-4-8)] has been re- than those with similar T but smaller anisotropy.20,21
67 ported.5–7 They consist of intermediate layers of PtnAs8 This can be attributed to lcow pinning energies and high
7 stacked in a Ca–PtnAs8–Ca–Fe2As2 sequence. Super- thermal fluctuations due to high γ values.9 The irre-
0 conductivity in this system occurs under applied pres- versibility line or irreversible field (Hirr) appears in lay-
. sure8 or with chemical doping.9–11 The two different ered superconductors and divides the H T phase dia-
1 types of intermediate layers (n = 3 and n = 4) af- graminto regionswith frozenflux (zero re−sistance)state
0
5 fect significantly the physical properties of these highly and regions with moving flux (finite resistance) in re-
1 anisotropic compounds.5,12 For example, the optimally sponse to an applied current.15
: doped Ca (Pt As )[(Fe Pt ) As ] has a supercon-
v ducting tr1a0nsit3ion8temp1e−raxturxe 2(T )2 5around 10 K and The upper critical field values were obtained in mag-
i c
X an upper critical field of Hc (0) 20 T.13 The up- netic fields up to 60 T. The γ value changes from 5
ar pfreormcr1i0ticcallosfieeltdoaTnisototro1p.5y ac(2tγ lo=w∼Htecam2b/pHercca2)tudreesc.reaFsoers fiartowunitdhTtchetoL≈ind3eamta2n0nKcr.iTtehreiairbryevceornsisbidileitryinlgince ca=n≈0b.2e
c L
Ca (Pt As )[(Fe Pt ) As ] , T can reach38 K with anda Ginzburg number Gi 0.016. We find a crossover
10 4 8 1 x x 2 2 5 c
x 0.36.6 An upp−er critical field of Hc (0) 92 T and field at low magnetic fields w≈here the flux creep rate de-
≃ c2 ∼
a change in γ from 6-7 close to T to 1 at low tem- creases when the magnetic field increases. This can be
c
≈
peratures has been reported for a sample with T 26 understood by considering the weak collective pinning
c
K and x 0.26.14 The high H and γ values in t∼hese scenario (random point defects) where a change in the
c2
≃
compounds allow us to study vortex matter with intrin- vortexdynamicsisexpectedinthecrossoverbetweenthe
sic high thermal fluctuations.5,15,16 In this context, the singlevortexandvortexbundleregimes. Whenthemag-
importantissueofpinningsuppressionbythermalfluctu- netic field is increased, the vortex dynamics presents a
ationsinmaterialswithrandompointdefects andmixed crossover from elastic to plastic at a field much smaller
pinning landscapes stimulates a wide description of the than the upper critical field and below the irreversibil-
phenomena outside of the cuprate scenario.15 ity line. In addition, the absolute value of the magnetic
2
penetration depth λ(4 K) = 260(26) nm is determined λ (T) = λ (T)+δλ(T), where δλ is the magni-
10 4 8 Nb
by magnetic force microscopy (MFM). tud−e o−f the shift δz. The difference δλ between Nb and
10-4-8 is 150 nm, resulting in λ (4 K) = 260(30)
10 4 8
nm. Our experimental error is ar−ou−nd 10 %, resulting
II. EXPERIMENTAL DETAILS
from the overlay process of the two Meissner curves of
the different λ values. The uncertainty of the λ extrap-
High quality Ca (Pt As )((Fe Pt ) As ) (x olation from 4 K to 0 K is as small as few percent, and
10 4 8 1 x x 2 2 5
0.05) single crystals were grown by−the flux method.2≈2 thus negligible compared to the main source of the un-
Formeasuringthepenetrationdepth(λ),MFMmeasure- certainty.11
ments were carried out: two Meissner response curves, The 10-4-8phase Ca (Pt As )[(Fe Pt ) As ]
10 4 δ 8 0.97 0.03 2 2 5
one from the 10-4-8 single crystal and one from a Nb with δ 0.246 and T = 26.5−K shows H (0) values of
c c2
reference film, are directly compared in a single cool- around≈90 T for H//c and 92 T for H//ab.14 The upper
down.23 The magnetic field dependence of radio fre- critical field anisotropy thus changes from 7 close to
quency (rf) contactless penetration depth, known as T to 1 at low temperatures. By using t≈hese values,
c
proximitydetectionoscillator(PDO),24wasmeasuredby we obt≈ain the coherence length ξ (0) = 1.90 0.02 nm
ab
applyingmagneticfieldsupto60Tbothparallel(H//ab) and ξ (0) = 1.85 0.01 nm from Hc = Φ /±[2πξ2 (0)]
and perpendicular (H//c) to the ab plane of the sample and Hcab =Φ /[2π±ξ (0)ξ (0)] (with Φc2 the s0ingle qabuan-
c2 0 ab c 0
in a pulsed magnet system. The rf technique is a sen- tum flux), respectively. As discussed below, the H (T)
c2
sitive and accurate method for determining the Hc2 of in our sample presents similar dependences to those re-
superconductors, especially in pulsed magnetic fields.25 ported in Ref.[14]. Small changes in ξ (0) and ξ (0) in
ab c
The details of the Hc2 determination are described in our sample compared to Ref.[14] are expected consid-
Ref.[14]. Magnetizationmeasurementswereperformedin ering the difference in superconducting transition tem-
a commercial superconducting quantum interference de- perature (i.e. H at 15 K is 10 % higher than
c2
vice (SQUID) magnetometer. The critical current den- that in Ref.[14]). By using ξ (≈0) = 1.9(1) nm and
ab
sity was estimated by applying the Bean critical-state λ (0) = 260(26) nm, we obtain the thermodynamic
ab
model26 to the magnetization data, obtained in hystere- critical field H (T = 0 K) = Φ0 = 4700 (400) Oe.
sis loops, which lead to J = 20∆m , where ∆m is c 2√2πλξ
c dw2(l w/3) These values are related to a theoretical depairing cur-
the difference in magnetization bet−ween the upper and rent J (T = 0 K) = cHc = 77 (7) MAcm 2 (with c
lower branches of the hysteresis loop, and d = 0.2 mm, c 3√6πλ −
the light speed). The strength of the order parameter
w =1.5mm,andl=2mmarethethickness,width,and
thermal fluctuations, estimated by the Ginzburg num-
lengthofthesample(l >w),respectively. Thefluxcreep
ber Gi = 1[ γTc ]2 0.016, is of the same order
rate,S = d(lnJc),wasrecordedoverperiodsofonehour 2 Hc2(0)ξ3(0) ≈
− d(lnt) of magnitude as that for YBa2Cu3O7 (YBCO).15 The
(with t being the time). The initial time was adjusted
Ginzburg number Gi is related to the width of the crit-
considering the best correlation factor in the log-log fit-
ical regime, ∆T > Gi T , and the melting line (B )
c c m
ting of the Jc(t) dependence. The initial critical state B = 5.6c4LH (0)(1 T·/T )2 (here c =0.2 is the Lin-
foreachcreepmeasurementwasgeneratedbyapplyinga m Gi c2 − c L
field variation of H 4H , where H is the field for the demann number).15
∗ ∗
full-flux penetration≈.27 Deviations from the logarithmic In order to study the vortex dynamics, we performed
decay in relaxation measured over a long period of time magnetization experiments. Fig. 1(a) shows the criti-
were adjusted by considering the interpolation equation cal current density (J ) as a function of the magnetic
c
(see description below).15 field (H) at different temperatures. Line I marks the
self-field regime (SF, H = J d). Here, the magneti-
∗ c
· ?
zation is affected by geometricalbarriers. Line II iden-
III. EXPERIMENTAL RESULTS AND
tifies the fishtail or second peak in the magnetization
DISCUSSION (SPM).Thiscrossoverline(HSPM)hasbeenextensively
discussed and was associated with a change in the vor-
We will first focus on the determination of the mag- texdynamicsfromelastictoplasticcreep.17,31 Notethat
netic penetration depth λ and the coherence length ξ, below 17 K, J (H) increases with increasing H between
c
before moving on to vortex dynamics. In superconduct- the lines I and II. This can be attributed to a change
ing single crystals and films whose thickness exceeds λ, in the pinning landscape by the magnetic field due to
theMeissnerresponseforceactinguponamagneticforce the suppression of superconductivity around point de-
microscopy tip obeys a universal power-law dependence fects.32 In this context, the SPM is strongly reduced by
F(z) (z +λ) 2 in the monopole approximation.28,29 removing inhomogeneities in the samples.33,34 However,
−
∼
The frequency shift of the tip resonance is proportional similarfeaturesinthe J (H)dependence ofcleanYBCO
c
to the gradient of the force, i.e., δf dF(z)/dz. There- single crystals have been discussed in the context of a
∼
fore, by shifting the Meissner data of the 10-4-8 sam- crossoverbetweensingle vortexand vortexbundle relax-
ple with respect to that of Nb along the z axis (in or- ation.35 The absence of a fishtail at T > 17 K could be
der to overlay one another), one can obtain λ of 10-4-8: relatedtostrongreductioninthe pinning(pointdefects)
3
J curvesandthefluxcreeprate(S)betweentheSFand
c
the SPM are well described by considering single vortex
2 K I
-1 4.5 K II pinning (see discussion below) and relaxation by vortex
2 ) 10 7 K bundles.38 Inthiscontext,theincreaseofJc valuesatin-
m
9.5 K termediate fields can be related to strong changes in the
c
A/ -2 vortexdynamicsandareductioninthevortexrelaxation.
M 10 12 K
In order to verify the pinning mechanism at differ-
(
J c 22 K ent temperatures we analyze the pinning force (Fp =
15 K J H). In conventional superconductors, F (H,T) scales
-3 25 K c p
10 as F /F =Ahm(1 h)l , where F is the max-
17 K p p,max p,max
27 K −
imum F (H) at each temperature, A is a constant, m
p
20 K and l are exponents that depend on the pinning mech-
-4 (a)
10 anism, and h = H/H (T).39 This relationship cannot
0.01 0.1 1 10 c2
0H (T) be directly applied here because it is only valid for h
1.0 defined by H (T) rather than H (T) (see discussion
(b) 7 K c2 irr
below). However, our analysis allows a comparison of
9.5 K
ax 0.8 12 K pinningforcesatdifferenttemperatures. Fig. 1(b)shows
m
p 15 K the F /F vs. h (defined as h = H/H ) at differ-
F p p,max irr
F / p 0.6 1270 KK eirnrtevteermsipbeleramtuargense.tiTzahteionHi(rTr >lin2e0wKas) adnedterbmyinuesidngfrtohme
22 K
Lindemann criterion (T < 20 K, see discussion below).
25 K
0.4 The different curves at T > 7.5 K show the maximum
pinning force at h 0.25. This value is similar to the
≈
0.2 one obtained in Na doped CaFe As single crystals with
2 2
random point defects introduced by proton irradiation
(√2ξ(T)> defect radius).40
0.0
0.00 0.25 0.50 0.75 1.00 To further understand the collective pinning scenario,
H / Hirr weperformedcreeprelaxationmeasurementsatdifferent
temperatures and magnetic fields.38 Fig. 2(a) shows the
FIG. 1. (Color online) (a) Magnetic field dependence of the
temperature dependence of the flux relaxation rate S at
critical current density (Jc) for the 10-4-8 single crystal at
µ H = 1 T. The S values at low temperatures suggest
different temperatures. Lines I and II indicate the regions 0
the presence of quantum creep (see fit line Fig. 2 (a)).41
affected by self-field andthemaximum Jc at thefish tail, re-
spectively. (b)Normalized pinningforce(Fp)versusnormal- The theoretical value for the quantum creep can be esti-
izedmagneticfield(h=H/Hirr(T))attemperaturesbetween mated by SQ = e2ρn Jc (where ρ is the resistivity in
7.5 K and 25 K. ∼ h¯ ξ qJ0 n
the normal state). The theoretical prediction SQ 0.02
≈
isingoodagreementwiththe extrapolationto zerotem-
perature from the experiment (see Fig. 2 (a)). For the
by thermalsmearing(depinning temperature). In highly estimation we use ρ = 0.25 mΩcm and ξ (0) = 1.9
n ab
anisotropicmaterials,thethermalsofteningofthevortex nm.14,22 Onthe other hand,the S value presentsamod-
core pinning will occur when fluctuations become com- ulation in temperature and a crossover to fast (plastic)
parable to ξ, and thus the pinning landscape is smeared creep at T > 15 K. The modulation in S(T) can be un-
out on the same length scale.13 In addition, the anoma- derstood as a modulation in pinning energy or a change
lous Hc2(T) dependence produces a strong change in ξ. in the vortex dynamics by considering single vortex and
Forexample,consideringHcc2 (17K)≈23Tweobtainξc vortexbundle relaxation. Fig. 2 (b) shows a comparison
(17K)=3.8(1)nm,whichreducestheindividualpinning between the J (H) and S(H) at 2 K, 4.5 K, and 7.5 K,
c
forceofarandompointdefectinthecollectivepinningin respectively. The self-field region was excluded from the
a similarwayto that incupratesdue to the increaseinξ analysis.42 Note that between the SF and the SPM the
andthethermallyactivateddepinning.35Similarfeatures S values are remarkably large at low H, and their min-
in Jc(H) related to the absence of SPM have been ob- imum at intermediate fields shifts systematically. The
served in Co doped BaFe2As2 above 20 K.17,36 We have collective pinning theory predicts15
not observed a power law behavior, J vs. H α, which
c −
is usually associated with pinning dominated by strong T
S = (1)
pinningcenters(√2ξ(T)<defectradius).37Ontheother −U +µTln(t/t )
0 0
hand, the absolute J (H = 0) values have strong tem-
c
perature dependence with 0.25 MAcm 2 at 2 K and whereU isthecollectivebarrierintheabsenceofadriv-
− 0
0.12 MAcm 2 at 4.5 K≈. The J (H = 0) at 2 K is ing force, µ is the glassy exponent and t is an effective
− c 0
≈
0.3 % of J , which is consistent with the weak collec- hopping attempt time. The nature of the vortex struc-
0
t≈ivepinning(weakdisorderpotentialwithJ J ).15The ture and the vortex pinning mechanisms can be inferred
c 0
≪
4
length, Lc = γ 1ξ J /J ). Above γL a the vor-
0.09 (a) ticesbeginc toin−terapcta0sthcerelaxationslcow≈sd0own. This
S
p regime is associated with relaxation by vortex bundles,
e0.06 and a new crossover from µ = 3/2(sb) to µ = 7/9(lb) is
e
Cr expected. The U (H//c) in the SVR can be estimated
c
0.03 by UcSVR ≈ γHξc23 Jcc/J0 ≈ TcqJcc(1J−0GT/iTc).15 Consider-
1 T ingJ (T =0) p0.25MAcm 2andJ =77MAcm 2,we
0.000 5 10 15 20 obtaicnUSVR(0≈) 15K.The−crossov0erbetweenSV−Rand
Temperature (K) c ≈
vortex bundles (in an anisotropic superconductor with
H//c) is expected at B = β JcH , with β 5.15
Single (b) 0.06 BasedonourexperimentsablresusltbsJ,0thec2SVRshousbld≈beex-
vortex Vortex
0.2 Self field tended to µ H 1 T at 0 K. The B (T) dependence is
effects bundles 0 ≈ sb
0.04 givenbyβ H 1+ T exp 2c(α+ T )3 ,where
sb c
≈ (cid:20) TS (cid:21) (cid:20)− TS (cid:21)
dp dp
0.1 2 K 0.02 candα(≈1)areconstanftsand TdSpisthedefpinningtem-
2 J (MA/cm) c00..1105 Svoinr tgelex bVuonrdtelexs 00..0046Creep S aβpOcotlenbrrrBa=tethlsubpe2(ro0,eon)γt(dhS≈s≈eVrtR1ohβal−bBniHsd2c,s2[uar(peJcfpSJ.r1r1Vo0.e4R5ss]ss)oa[elvndne1d(r.bγ8κfyκrToJ=tmS.JhV0λeTRsrahbm)be](t2a0o/lp)3/rl,flbeξudawicbsich(t0uetiicx)aohptn≈ieowccn1toise3tr)hd0-.
lb
≈ −
0.05 4.5 K 0.02 responds to a narrow sb regime still at 0 K.15 By using
ln(t/t ) 29,38 and considering negligible U , plateaus
0 0
Vortex 0.06 [S = 1/µ≈ln(t/t )] with S 0.022(sb) and S 0.042(lb)
Single bundles 0 ≈ ≈
vortex are expected. These values are smaller than the exper-
0.06
0.04 imental observations above the self-field regions (i. e.
S 0.05 (2 K, 0.5 T), S 0.06 (4.5 K, 0.2 T), S 0.06
≈ ≈ ≈
(7 K, 0.1 T) and S 0.06 (15 K, 0.03 T)), and indicate
7.5 K
0.03 0.02 that relaxation by v≈ortex bundles cannot be applied at
0.1 1
0H (T) small fields (above the SF effect). One important differ-
ence between our data and the expectation for the SVR
FIG.2. (Coloronline)(a)Temperaturedependenceoftheflux
is that J (H) is not a constant (magnetic field indepen-
creep rate (S) at µ0H =1 T. (b) Magnetic field dependence c
dent) in the range where huge S values are observed.
of Jc (black boxes) and S (blue spheres) at 2 K, 4.5 K, and
7.5 K. The dotted lines are guides for the eye to show the However, a similar field dependence of Jc has been ob-
crossover from the single vortex to bundle regime and from servedinYBCOsinglecrystalswithSVRduetorandom
vortex bundleto plastic creep. point defects,38 and attributed to the fast relaxationbe-
low the crossover to vortex bundles.35 In our case, the
experimental S values corresponding to the SVR (above
from µ, which scales the effective energy barrier and the thetheoreticalpredictionforbundles)canbeobtainedby
persistent current density (J) as consideringU (2K) 30Kandµ=1/7.15However,
SVR
≈
J µ gradual changes in µ by increasing the magnetic field
U(J) U c (2) have been observed in YBCO films with random point
0
≈ (cid:18)J (cid:19) defects.43 In YBCO, µ=1/7 is only observed above the
SF at magnetic fields where the vortex-vortex interac-
and depends on the creep regime. The glassy exponent
tion is negligible. At higher fields, µ in the SVR evolves
µ depends on the dimension and length scales for the
gradually to small vortex bundles.38
vortex lattice in the collective-pinning model. For ran-
dom point defects in the three-dimensional case µ is 1/7 In order to determine the exponent µ, we investigate
(single vortex, SVR), 3/2 or 5/2 (small vortex bundles, the nonlogarithmic current decay over a very long pe-
sb), and 7/9 (large vortex bundles, lb).15 The critical riod of time ( 16 hours) at 7 K and 15 K (we assume
current-density ratio (J/J ) is the fundamental quantity T < TS and≈H > SF). Fig. 3(a) shows the time de-
0 dp
characterizingthestrengthofthedisorderpotential. The pendence of persistent currentdensity plotted in a semi-
SVR corresponds to weak fields where the distance be- logarithmic scale. The curves were adjusted by using
tween the vortex lines is large and their interaction is the interpolation equation J = J [µTln t ] 1/µ.15 The
c Uc t0 −
small compared to the interaction between the vortices µ values obtained from the fit in both cases were 0.50
and the quenched randompotential. The SVR occurs at (5). These values are larger than the prediction for the
low fields during the initial stage of the relaxation when SVR with µ = 1/7 but in the same range as those for
J < J . Single-vortex collective pinning is expected as YBCO single crystals.38 Fig. 3(b) shows the J (H) and
c c
longasγL <inter-vortexdistance(a )(L istheLarkin S(H)at15K.The insetpresentsµ(H) obtainedby con-
c 0 c
5
Normal
0.040 60 Vortex
(a) regime
liquid
2 m)0.035
c T = 7 K Hc2 // c Hc2 // ab
MA/0.030 T = 15 K 0H = 0.2 T
J (0.025 0 =H 0=. 500.0 (25 )T = 0.50 (5) H (T)0 40
Hirr LC
0.010 Plastic
100 1000 10000 20 creep
t (s)
0.10
2 A/cm) 0.1 (b) 01..50 0.08Cre 0 Elastic creep HSPM
M 0.1 1 e 0 5 10 15 20 25 30
J (c 0H (T) 0.06p S Temperature (K)
0.01
0.04 FIG. 4. (Color online) The H −T phase diagram for su-
15 K
H // c-axis perconductingCa10(Pt4As8)[(Fe0.95Pt0.05)2As2]5 single crys-
0.02 tal in the mixed state. Magnetization (open white circles),
0.1 1 electrical transport (solid black diamonds), LC: Lindemann
0H (T) criterion, and SPM: second peak in themagnetization.
FIG. 3. (Color online) (a) Persistent current density J vs.
ln(t) at 7 K (µ0H = 0.2 T) and 15 K (µ0H = 0.02 T). The below the matching field B : the density of vorticesand
Φ
red and green lines are fits using the interpolation equation. defects are the same. The double kink mechanism was
(b)MagneticfielddependenceofJc andS at15K.Theinset ascribedtothepresenceofdifferentcreepregimes: ahalf
shows µ(H) estimation at 15 K.
vortex loop with µ 1 at low temperatures, superkinks
≈
with µ 1/3 in the low-temperature side of the peak
≈
up to the maximum in S(T), and a collective regime
sidering negligible U values (see Eq. 1) and bundles (bundles) above the peak. The pinning in samples with
0
S =1/µln(t/t ). We selectthis temperature asit is high columnardefectsdependsonthedensityandangulardis-
0
enough to avoid self-field problems and low enough to tribution of the tracks, the intensity and orientation of
be well within the regime where the second peak in the the applied field, temperature, and current density. In
magnetization exists, so that only a small errorin S can order to verify the absence of correlated pinning we per-
be expected. Similarly,the modulationinJ (H)at15K formed S measurements (not shown) with the magnetic
c
canbeunderstoodbyconsideringfastcreeprelaxationin field rotated10◦ awayfrom the c-axis. In this configura-
SVR, and a crossover to vortex bundles. Detailed mea- tion high creep rates are expected from the expansionof
surements of S(H) indicate that µ is smaller ( 1.15) doublekinks. However,nolargechanges(noincrements)
≈
than the theoretical value µ = 3/2 (see inset Fig 3(b)). in the S values were observed,which rules out the possi-
Beyond the maximum in µ, a crossover from sb to lb bility of a double kink mechanism in the sample.45 This
with a gradualreduction to µ 7/9 is observed. Finally fact is also consistent with the low J/J ratio estimated
c
≈
the creep changes to a plastic regime above the SPM as aboveandwiththeglassyrelaxationobservedatdifferent
was described in ref.[17]. Nevertheless, our data can be temperatures during the long time measurements.44
qualitativelydescribedbythecollectivevortextheoryfor Fig. 4 shows a summary of the H T vortex phase
randompointdefects,whilethereisdifferenceinµ. Sim- diagram for the 10-4-8 single crystal.−The H (T) ob-
c2
ilar discrepancies, including no discrete µ values, have tained from PDO for µ H up 60 T shows a similar tem-
0
been observedin cuprates.38 It is worth to mention that perature dependence to that observed in ref.[14]. The
the theory considers negligible vortex-vortex interaction shapes of the H (T) curves for H//ab and H//c close
c2
in comparison with the quenched random potential. In to T exhibit the conventional linear field dependence
c
reality, due to the changes in λ(T), some interaction be- with clearly different slopes for the two field orienta-
tween the vortices cannot be completely discarded even tions. The γ value changes from 5 close T to 3
c
at small magnetic fields.11 at 20 K. A gradual change in γ ≈1 is expected by≈re-
→
Another scenario to understand the huge S values ducingthetemperatureandincreasingthemagneticfield
(higherthanthepredictionforlargevortexbundles)isto above 60 T.14 At low temperatures, H (T) with H//ab
c2
consider a non-glassy relaxation by a double kink mech- presents a tendency to saturate, whereas the curve for
anism.44 This mechanismappearsinYBCO withcolum- H with H//c shows a steep increase likely associated
c2
nar defects and is manifested as a peak in the relaxation with two band contribution. Using the same tempera-
6
ture dependence of H (T) as in ref.[14], H (0) values IV. CONCLUSION
c2 c2
close to 100 T are expected in our sample (see green
dotted line H //ab in Fig. 4). The irreversibility line
c2 We have found that the sample presents a wide vor-
(H ) was estimated by considering the irreversibility
irr tex liquid phase similar to that predicted in cuprates
magnetization and electrical transport (zero resistance).
by considering the Lindemann criteria (c = 0.2 and
The H and H curves spread apart monotonically as L
c2 irr Gi 0.016). The pinning landscape can be associ-
H increases. Similar features are observed in high-Tc ated≈with random point defects in the whole tempera-
superconductors where a vortex liquid phase appears.15
ture range (√2ξ(T) < defect radius). The creep S(H)
The H line is well described by the Lindemann crite-
irr is in agreement with small pinning energies and a grad-
rion described above. The fit in Fig. 4 (black dashed
ual crossover from single vortex to relaxation by vortex
line)correspondstoc =0.2andGi 0.016,whichisin
L ≈ bundles. Our results are in qualitative agreement with
goodagreementwiththeexperimentaldataandsuggests
the theory developed for the influence of random point
awidevortexliquidphaseevenatlowtemperatures. The
centers on the resulting vortex dynamics of cuprates. In
crossoverfromelastictoplastic(fast)creepwasobtained
addition, the absolute value of the magnetic penetration
from the SPM as shown in Fig. 1(a). This line sepa-
depth λ(4 K) was directly determined in order to under-
rates elastic motion with a positive µ to plastic motion
standtheroleoftheintrinsicsuperconductingproperties
with a negative critical exponent.17 A wide region with
such as thermal fluctuations in the resulting vortex dy-
plastic motion of vortices (fast creep) is identified in the
namics.
H T phase diagram. The temperature dependence of
−
the elastic to plastic crossover was adjusted by consid-
ering HSPM(T) = HSPM(0)(1 T )nexp. The data fits
− Tc
well by considering HSPM(0) = 10 T and n = 3.5.
exp ACKNOWLEDGMENTS
This n value is larger than those found for Co-doped
exp
BaFe As , indicating a sharpertemperature dependence
2 2
oftheSPM.46 Finally,theelasticregimeiswelldescribed ThisworkwassupportedbytheInstituteforBasicSci-
bythecollectivepinningtheorydevelopedforcuprates.15 ence (IBS) throughthe Center for ArtificialLow Dimen-
At small fields the vortex dynamics can be described by sional Electronic Systems by Project Code (IBS-R015-
considering the SVR with a gradual crossover to vortex D1). N. H. is member of CONICET (Argentina). RJ
bundles. It should be noted that the as-grownsupercon- was supported by US NSF DMR-1002622. We thank
ductorwithaweakpinningpotentialisagoodcandidate Jun Sung Kim for a magnetization measurement. We
to investigate the resulting H T phase diagramby the acknowledgethesupportoftheNationalHighFieldLab-
inclusion of strong pinning cen−ters.45 oratory at Los Alamos.
∗ Corresponding author: [email protected] 26, 2346 (2014).
† Corresponding author: [email protected] 9 N. Ni, W. E. Straszheim, D. J. Williams, M. A. Tanatar,
1 Y.Kamihara,T.Watanabe,M.Hirano,andH.Hosono,J. R. Prozorov, E. D. Bauer, F. Ronning, J. D. Thompson,
Am. Chem. Soc. 130, 3296 (2008). and R. J. Cava, Phys.Rev.B 87, 060507 (2013).
2 M.Rotter,M.Tegel,D.Johrendt,I.Schellenberg,W.Her- 10 S. Thirupathaiah, T. Sturzer, V. B. Zabolotnyy, D.
mes, and R.Po¨ttgen, Phys.Rev. B 78, 020503 (2008). Johrendt, B. Buchner, and S. V. Borisenko, Phys. Rev.
3 X.C.Wang,Q.Q.Liu,Y.X.Lv,W.B.Gao,L.X.Yang,R.C. B 88, 140505 (2013).
Yu,F.Y.Li,andC.Q.Jin, Solid StateCommun.148,538 11 K. Cho, M. A. Tanatar, N. Ni, and R. Prozorov, Super-
(2008). cond. Sci. Technol. 27, 104006 (2014).
4 F.C. Hsu, J.Y. Luo, K.W. Yeh, T.K. Chen, T.W. Huang, 12 X. P. Shen, S. D. Chen, Q. Q. Ge, Z. R. Ye, F. Chen, H.
P.M.Wu,Y.C.Lee,Y.L.Huang,Y.Y.Chu,D.C.Yan,and C. Xu,S.Y.Tan,X.H.Niu,Q.Fan, B.P.Xie,and D.L.
M.K.Wu,Proc.Natl.Acad.Sci.U.S.A.105,14262(2008). Feng, Phys.Rev. B 88, 115124 (2013).
5 N. Ni, J. M. Allred, B. C. Chan, and R. J. Cava, Proc. 13 M.D.Watson,A.McCollam, S.F.Blake,D.Vignolles, L.
Natl. Acad. Sci. (USA)108, E1019 (2011). Drigo,I.I.Mazin,D.Guterding,H.O.Jeschke,R.Valenti,
6 Satomi Kakiya, Kazutaka Kudo, Yoshihiro Nishikubo, N.Ni,R.Cava,andA.I.Coldea,Phys.Rev.B89,205136
Kenta Oku, Eiji Nishibori, Hiroshi Sawa, Takahisa Ya- (2014).
mamoto,ToshioNozaka,andMinoruNohara,J.Phys.Soc. 14 Eundeok Mun, Ni Ni, Jared M. Allred, Robert J. Cava,
Jap. 80, 093704 (2011). OscarAyala,RossD.McDonald,NeilHarrison,andVivien
7 C. L¨ohnert, T. Stu¨rzer, M. Tegel, R. Frankovsky, G. S. Zapf, Phys. Rev.B 85, 100502 (2012).
Friederichs, and D. Johrendt, Angew. Chem. Int. Ed. 50, 15 G. Blatter, M. V. Feigelman, V. B. Geshkenbein, A. I.
9195 (2011). Larkin, and V. M. Vinokur, Rev. Mod. Phys. 66, 1125
8 Peiwen Gao, Liling Sun, Ni Ni, Jing Guo, Qi Wu, Chao (1994).
Zhang, Dachun Gu, Ke Yang, Aiguo Li, Sheng Jiang, 16 J. Kim, F.Ronning, N.Haberkorn,L. Civale, E. Nazaret-
Robert Joseph Cava, and Zhongxian Zhao, Adv. Mater. ski, Ni Ni, R. J. Cava, J. D. Thompson, and R.
7
Movshovich, Phys. Rev.B 85, 180504 (2012). 30 M. Daumling and D. C. Larbalestier, Phys. Rev. B 40,
17 R.Prozorov,N.Ni,M.A.Tanatar,V.G.Kogan,R.T.Gor- 9350 (1989); L. W. Conner and A. P. Malozemoff, ibid.
don,C.Martin,E.C.Blomberg,P.Prommapan,J.Q.Yan, 43, 402 (1991).
S.L. Bud’ko, and P.C. Canfield, Phys. Rev. B 78, 224506 31 Y. Abulafia, A. Shaulov, Y. Wolfus, R. Prozorov, L.
(2008). Burlachkov, Y. Yeshurun, D. Majer, E. Zeldov, H. Wu¨hl,
18 Tsuyoshi Tamegai, Toshihiro Taen, Hidenori Yagyuda, V.B. Geshkenbein, and V.M. Vinokur, Phys. Rev. Lett.
Yuji Tsuchiya, Shyam Mohan, Tomotaka Taniguchi, Ya- 77, 1596 (1996).
suyukiNakajima,SatoruOkayasu,MasatoSasase,Hisashi 32 T.Das,J.X.Zhu,andM.J.Graf,Phys.Rev.B84,134510
Kitamura, TakeshiMurakami, Tadashi Kambara, and Ya- (2011).
suyukiKanai,Supercond.Sci.Technol.25,084008(2012). 33 A.Oka,S.Koyama,T.Izumi,Y.Shiohara,J.Shibata,and
19 C.J.vanderBeek,G.Rizza,M.Konczykowski,P.Fertey,I. T. Hirayama, Japan J. Appl.Phys. 39, 5822 (2000).
Monnet, Thierry Klein, R.Okazaki,M. Ishikado, H.Kito, 34 N. Haberkorn et al., (unpublished).
A.Iyo,H.Eisaki, S.Shamoto,M.E.Tillman, S.L.Bud’ko, 35 L. Krusin-Elbaum, L. Civale, V. M. Vinokur, and F.
P.C. Canfield, T. Shibauchi, and Y. Matsuda, Phys. Rev. Holtzberg, Phys.Rev.Lett. 69, 2280 (1992).
B 81, 174517 (2010). 36 Jeehoon Kim, N. Haberkorn, K. Gofryk, M.J. Graf, F.
20 Qing-Ping Ding, Yuji Tsuchiya, Shyam Mohan, Toshihiro Ronning,A.S. Sefat, R.Movshovich, and L.Civale, Solid
Taen, Yasuyuki Nakajima, and Tsuyoshi Tamegai, Phys. State Commun. 201, 20 (2015).
Rev.B 85, 104512 (2012). 37 C. J. van der Beek, M. Konczykowski, A. Abal’oshev, I.
21 T. Tamegai, Q.P. Ding, T. Taen, F. Ohtake, H. Inoue, Y. Abal’osheva, P. Gierlowski, S.J. Lewandowski, M.V. In-
Tsuchiya, S. Mohan, Y. Sun, Y. Nakajima, S. Pyon, and denbom, and S. Barbanera, Phys. Rev. B 66, 024523
H. Kitamura, Physica C 494, 65 (2013). (2002).
22 A. B. Karky et al., (unpublished). 38 L. Civale, L. Krusin-Elbaum, J. R. Thompson, and F.
23 Jeehoon Kim, L. Civale, E. Nazaretski, N. Haberkorn, Holtzberg, Phys.Rev.B 50, 7188 (1994).
F. Ronning, A.S. Sefat, T. Tajima, B.H. Moeckly, J.D. 39 D. Dew-Hughes,Philos. Mag. 30, 293 (1974).
Thompson, and R. Movshovich, Supercond. Sci. Technol. 40 N. Haberkorn, J. Kim, B. Maiorov, I. Usov, G. F. Chen,
25, 112001 (2012). W. Yu,and L. Civale, Supercond.Sci. Technol. 27, 95004
24 M. M. Altarawneh, C. H. Mielke, and J. S. Brooks, Rev. (2014).
Sci. Instrum.80, 066104 (2009). 41 T. Klein, H. Grasland, H. Cercellier, P. Toulemonde, and
25 C. Mielke, J. Singleton, M.S. Nam, N. Harrison, C. C. C. Marcenat, Phys. Rev.B 89, 014514 (2014).
Agosta, B. Fravel, and L. K. Montgomery, J. Phys.: Con- 42 N.Haberkorn,M.Miura,B.Maiorov,G.F.Chen,W.Yu,
dens. Matter 13, 8325 (2001). and L. Civale, Phys. Rev.B 84, 094522 (2011).
26 C. P. Bean, Phys. Rev. Lett. 8, 250 (1962); C. P. Bean, 43 J.R.Thompson,YangRenSun,D.K.Christen,L.Civale,
Rev.Mod. Phys.36, 31 (1964). A.D.Marwick, andF.Holtzberg,Phys.Rev.B49,13287
27 Y.Yeshurun,A.P.Malozemoff,andA.Shaulov,Rev.Mod. (1994).
Phys. 68, 911(1996). 44 D.Niebieskikwiat,L.Civale,C.A.Balseiro,andG.Nieva,
28 J. H. Xu, J. H. Miller, and C. S. Ting, Phys. Rev. B 51, Phys. Rev.B 61, 7135 (2000).
424 (1995). 45 L. Civale, Supercond.Sci. Technol. 10, 11 (1997).
29 M. W.Coffey, Phys. Rev.B 52, R9851 (1995). 46 BingShen,PengCheng,ZhaoshengWang,LeiFang,Cong
Ren,LeiShan,andHai-HuWen,Phys.Rev.B81,014503
(2010).