Table Of ContentVortex images on Ba K Fe As observed directly by the magnetic force microscopy
1−x x 2 2
Huan Yang,1,∗ Bing Shen,2 Zhenyu Wang,2 Lei Shan,2 Cong Ren,2 and Hai-Hu Wen1,†
1Center for Superconducting Physics and Materials,
National Laboratory of Solid State Microstructures and Department
of Physics, Nanjing University, Nanjing 210093, China and
2Institute of Physics and Beijing National Laboratory for Condensed Matter Physics,
Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China
2 ThevortexstatesonoptimallydopedBa0.6K0.4Fe2As2 andunderdopedBa0.77K0.23Fe2As2 single
1 crystals are imaged by magnetic force microscopy at various magnetic fields below 100 Oe. Local
0 triangular vortex clusters are observed in optimally doped samples. The vortices are more ordered
2 thanthoseinBa(Fe1−xCox)2As2,andthecalculatedpinningforceperunitlengthisabout1orderof
magnitudeweakerthan thatinoptimally Co-doped 122at thesame magneticfield,indicating that
n
theCodopingattheFesitesinducesstrongerpinning. Theproportionofsix-neighboredvorticesto
a
the total amount increases quickly with increasing magnetic field, and the estimated value reaches
J
100%atseveraltesla. Vortexchainsarealsofoundinsomelocalregions,whichenhancethepinning
1
force as well as the critical current density. Lines of vortex chains are observed in underdoped
3
samples, and they may have originated from the strong pinning near the twin boundaries arising
from thestructural transition.
]
n
o PACSnumbers: 74.70.Xa,74.25.Uv,74.25.Wx
c
-
pr I. INTRODUCTION all the measurements were taken on Ba(Fe1−xCox)2As2
u orBa(Fe1−xNix)2As2 samples. Differentdetectingmeth-
s ods give similar results, i.e., the vortex structure seems
t. Sincethediscoveryoftheiron-basedsuperconductors,1 to be verydisorderedbecauseofthe strongpinning.13–17
a the mechanism of their superconductivity and vortex Recently, the scanning tunneling microscopy measure-
m
dynamics has attracted considerable interest. Multiple ment on Ba K Fe As shows the ordered vortices as
0.6 0.4 2 2
- electron and hole Fermi pockets, as well as multiple su- well as the Andreev bound states,18 which seems to be
d
perconducting gaps, have greatly enriched the physics verydifferentfromCo-doped122inwhichneithertheor-
n
o of superconductivity in this new system.2,3 Theoreti- dered vortex lattice or the in-core Andreev bound states
c cally it was suggested that the unique sign-reversal s- wereobserved.16ThisisquitenaturalsincetheCodoping
[ wave pairing, namely, s±, could be the main pairing takes place right at the Fe-As planes, while the K dop-
2 symmetry of the iron pnictide superconductors, and the ing at the Ba sites induces most probably the off-plane
v nesting between hole and electron pockets is important disorders. Therefore it is very interesting to investigate
8 for achieving superconductivity.4 This extended s-wave the vortices at low fields on K-doped 122 samples and
7 model results in nodeless superconducting gaps and a compare them with those in the Co-doped samples. In
5 sign change of the order parameter between the nested this paper we present the direct imaging of vortices on
2 pockets, which seems to be supported by scanning tun- high-quality Ba K Fe As single crystals detected by
2. neling microscopy measurement in Fe(Se,Te) samples.5 magnetic force m1−icxroxscop2y b2elow 100Oe. The difference
1 Recent angle-resolved specific heat measurements show in vortex structure in both K-doped and Co-doped sam-
1 a fourfold oscillation of the specific heat as a function of ples is analyzed and discussed in detail.
1
thein-planemagneticfielddirection,whichsuggeststhat
:
v thegapisanisotropic.6Asatype-IIsuperconductorwith
i such a multiband and fascinating pairing symmetry, the
X II. EXPERIMENTS
vortex dynamics of pnictides is also attractive. The 122
r
a family of iron pnictides provides a good opportunity to
explore the vortex dynamics because of the availability The Ba K Fe As single crystals were grown by
1−x x 2 2
of its high-quality single crystals. The parent compound the self-flux method using FeAs as flux, and the de-
BaFe As has both hole and electron pockets with al- tailed procedures of synthesizing are similar to previous
2 2
mostbalancedchargecarriers. Superconductivitycanbe reports.18–20 The measurements of x-ray diffraction in-
achieved via chemical doping, for example via K substi- dicate a highly c-axis orientation and crystalline quality
tution at Ba sites7 and Co substitution at Fe sites.8 The of our samples. The bulk diamagnetic characterizations
multiband property plays an important role in electric of single crystals were measured by a magnetic property
transport for both hole- and electron-doped samples.9,10 measurement system (MPMS, Quantum Design). Mag-
Themagnetizationmeasurements11,12showthatthehole netic force microscopy (MFM) used in this work is the
orelectronoptimallydopedsamplesbothhavethesecond atto-MFMsystem(attocube)basedonthephysicalprop-
magnetizationpeakeffectandaverysimilarvortexphase ertiesmeasurementsystem(PPMS-9,QuantumDesign).
diagram. For the vortex imaging measurement, almost Hard magnetic coating point probes from NanoWorld
2
were used for all the measurements. The vortex figures
aremadebyWSxMsoftware.21ForeveryMFMmeasure-
ment, the Ba K Fe As single crystal was mounted
1−x x 2 2
on the sample holder of MFM immediately after it was
0
cleaved along the ab plane in air at room temperature.
Thefreshtopsurfaceisalwaysflatandmirror-likeforthe 3 m) -4
MFM measurements, and usually the measured rough- c
ness on the cleaved surface is less than 1 nm, which ap- mu/ -8 OP
proaches the measuring precision of the system. Then M (e H=20 Oe
the sample wascooledina low-pressureheliumgasenvi-
-12 OP ZFC
ronment. ThemagneticpropertyandtheMFMmeasure- OP FC
ments were carried out with the magnetic field perpen- UD UD ZFC
dicular to the top surface (ab plane). The magnetic field -16 UD FC a
0.02
was applied at the temperature above critical tempera-
turetoobtainthefield-coolingprocessforMFMmeasure- 0.00 OP
ments. The attocube scanners in the atto-MFM system
werecalibratedbyastandardsampletoobtaintheexact -0.02
scanningparametersatdifferenttemperatures. Themag- χ
nets of the MPMS and PPMS systems were degaussed -0.04
before the measurements to minimize the residual mag-
OP FC
netic field. The first step in the measurement is to find -0.06 UD UD FC
a rather flat place by a tip tapping mode. Then we keep
b
a constant distance between the tip and the sample sur- -0.08
face (e.g., 10 nm) and detect the resonance frequency 10 20 30 40
change in the presence of the field distribution around T (K)
the vortices. Since the density of vortices changes with
the magnetic field, we use more scanning pixels to get a FIG.1: (Coloronline)(a)Temperaturedependenceofvolume
clearer image at higher fields. magnetization of the optimally doped Ba0.6K0.4Fe2As2 and
underdoped Ba0.77K0.23Fe2As2 samples after zero-field cool-
ing (ZFC) and field cooling (FC) at 20 Oe. The difference
intheZFCmagnetization ofthetwosamplescomesfromthe
III. RESULTS different demagnetizing effect. (b) Field cooled susceptibili-
ties versus temperature. Since the susceptibilities are rather
small, it seems that very few vortices are excluded from the
A. Sample characterization sample in theFC process.
Figure 1(a) shows the temperature dependence of the
B. Vortex image in OP samples
volumemagnetization(M) afterzero-field-cooling(ZFC)
and field cooling (FC) processes. Both the optimally
doped(OP)sampleandunderdoped(UD)sampleusedin In Fig. 2 we show the vortex image on the OP sample
our MFM measurementsshows verygoodsuperconduct- atdifferentmagneticfieldsat2KbyanFCprocess. The
ing transitions. The critical transition temperature of maximum field reaches 100Oe which is almost the limit
theOPsampleis38.8K(10%M )withatransition todistinguishthenearestvorticesinMFMmeasurement.
T=10K
width of 0.6 K, while the value for the UD sample it is The calculated number of vortices in this certain range
24.7Kwith atransitionwidth of1.5K.Ba K Fe As was almost the same as the calculated magnetic flux at
1−x x 2 2
single crystals are usually very thin, so the demagnetiz- each field, which is consistent with the FC susceptibility
ing factor approaches 1.0. That is the reason the ZFC mentionedabove. The distance between the neighboring
magnetization values of these two samples are different. vortices seems to be very uniform, which is similar to
The error in the measurement of dimensions, especially the Bitter decoration result on some Ba(Fe Co ) As
1−x x 2 2
the thickness, could give error in the calculation of the samples,14 but moreorderedthan otherreports.13,15 Lo-
ZFC susceptibility. Figure 1(b) shows the temperature cal vortex chains observed in the vortex image are dis-
dependence of the FC volume susceptibility (χ ), from cussed in Sec. IIIC.
FC
whichwecanestimatetheratioofvorticesexcludedfrom To make the figure more clear, we took the coordi-
the sample. The χ values of the OP and UD samples nates of all the vortex centers and used the Delaunay
FC
are only 1% and 6%, which means that a large number triangulation to figure out the vortex distribution. The
of vortices are pinned in the samples after field cooling. result at 100 Oe is shown as an example in Fig. 3. One
In our MFM measurementswe also find that the density can find that almost half of the vortices are six-nearest-
of vortices is close to that calculated from the magnetic neighbored, and more importantly there are distorted
field. triangle lattice fragments in some local areas. The self-
3
form a squarelike structure in the local area. With in-
creasing the magnetic field (or the density of vortices),
the nearestpatternloopintheself-correlationfigurewill
changeintoacircularshape,whichsuggeststhatpairsof
neighbored vortices have contiguous distances but ran-
dom orientations. They are not ordered enough to form
thevortexlattice. Statisticsofthedistancesbetweentwo
nearest vortices by the Delaunay triangulation method
H=10 Oe H=20 Oe H=50 Oe are shown in Fig. 4(f). The Gaussian function fits the
statistic data very well in semilogarithmic scale, and the
maximum points from the fits are between the values
calculated from a normal square and a hexagonal vor-
tex lattice at the same fields. The half-width decreases
quicklywithincreasingmagneticfield,whichmeansthat
the strongerforceathigherfields makesthe distance be-
tweennearestvorticesmoreuniform. Itisverydifficultto
get the square pattern in Delaunay triangulation plots,
so we do the statistic of angles of the Delaunay trian-
gles as shown in Fig. 5(a). According to the fitting to
a Gaussian distribution, the square (with characteristic
H=75 Oe H=100 Oe
angles of 45◦ and 90◦) and hexagonal structure (with
a characteristic angle of 60◦) vortices coexist at 100Oe.
FIG. 2: (Color online) Vortex image of an OP
Figure5(b)showsthefielddependenceofthenumberra-
Ba0.6K0.4Fe2As2 singlecrystalmeasuredbyMFMat2Kand
tio of six neighbored vortices, which behaves linearly in
different magnetic fields from 10 to 100 Oe. The scanning
range for each image is 19µm×19µm. a semilog plot. The ratio increases with magnetic field,
as the vortexsystemfavorsa six-neighboredsituationat
high magnetic field. If we do the linear extrapolationon
thecurvetohigherfields,theratiomayreach100%ata
fieldmagnitudeofseveraltesla,whichmeansthatalmost
allofthevorticeshavesixnearestneighborsatsuchhigh
fields. So it is not strange that the vortices become the
ordered hexagonal phase in several vortex spacings at a
magnetic field of 9T.18
ThevorticesintheK-dopedsampleseemtodistribute
more orderly than in the Co-doped sample, which re-
quires some data to prove. The pinning force per unit
length and the pinning energy are the parameters char-
acterizing the vortex pinning. The vortex structure will
be more disordered if the pinning energy or the pinning
force is bigger. As a sum of the scalar quantities, the
pinning energy has a more close relationship with the
magnitude of the magnetic field than the pinning force,
so we calculate the pinning force per unit length of the
FIG.3: (Color online) Delaunaytriangulation of thevortices vorticestodofurtheranalysis. Thepinningforceperunit
on the OP sample at 100 Oe and 2 K. The red solid circles
length on the ith vortex, which is related to the shield-
denote 6-neighbored vortices, while the pink empty ones de-
ingcurrentatitslocationfromtheothervortices,canbe
note the other number of neighbored vortices. To avoid the
expressed as
error from thevortices nearthescanning edge, only theones
with the distance more than 1 µm from the edges are taken
φ2 r |r |
into account. The light green blocks show area of distorted f = 0 ij K ij . (1)
triangle lattice. i 2πµ λ3|r | 1(cid:18) λ (cid:19)
Xj6=i 0 ij
Here φ is the magnetic flux quantum, µ is the perme-
0 0
correlationfigures for eachvorteximage atvariousfields abilityofthevacuum,r isthespacevectorbetweenthe
ij
are shown in Figs. 4(a)–(e). At 10Oe the irregular loop jthandithvortex,andK (r j/λ)isthefirst-ordermodi-
1 i
aroundthe center indicatesthatthe nearestdistancebe- fiedBesselfunction. Figure6presentstheabsolutevalue
tweenvorticeshasabroaddistribution,anditmeansthat of pinning force per unit length (f ) distributions for ev-
i
the force among the vortices is very small. The approx- ery vortex at 10 and 50 Oe. The statistic result shows
imative four fold loop at 20 Oe shows that the vortices thatmostofthe valuesoff arearound2×10−7 N/mat
i
4
200
H=100 Oe
Exp. data
µ µ µ µ µ
aaH=10 O41emf b H=20 O1emc H=50 O12em d H=75 1O hdem c(ehnetexeragHo=n1a0l01 Ome unts (a.u.)110500 Occceeevnnnetttreeearrrl===l469500ooo
u.) 3 HH== 1200 OOee dcenter m)1 s ( slaqtutiacree) Co 50
(a. HH== 5705 OOee µd ( lattice)
ex H=100 Oe h s
Nvort 2 0 µ50 100 0 20 40 60 80 100 120
nt/ 0H (Oe) Angle (d egree)
u 60
Co 1 %)
n ( 55
o
0 orti
0.1 µ1 p 50
o
d ( m) pr
or 45
b
h
g
FIG. 4: (Color online) (a)-(e) Self-correlations of vortex im- ei 40
n
ages at different fields. (f) Statistics of distance between 6-
the nearest vortices (d) in Delaunay triangulation at various 35
10 100
fields. Thesolidlinein(f)istheGaussianfitinsemilogarith-
H (Oe)
micscale. Theinsetof(f)showsthecomparisonbetweenthe
peak-value (dcenter) and the distances expected for a normal
square (s) and a hexagonal (h) vortex lattices. The errors of FIG. 5: (Color online) (a) Statistics on the angle values of
dcenter are full width at 90% maximum. Delaunaytriangles. ThesolidlineshowstheGaussianfittings
at 45, 90, and 60 degrees which are the typical angle of a
square, or a hexagonal vortex lattice. (b) The proportion of
10Oe,whichis1orderofmagnitudeweakerthanthatin the6-nearestneighboredvorticesatdifferentfieldsinsemi-log
the Co-doped 122 system at the same magnetic field.13 plot. It is obvious that the vortices favor 6-neighbored more
atahigherfields. Theproportionmay reach100% atseveral
The penetration depth used here is 0.25µm at 2K from
tesla if we do linear extrapolation in semi-log plot.
values of the tunnel diode resonator technology22 and
µSR.23 It should be noted that if we use the larger pen-
etration depth, i.e., 1.2 µm, as used for the Co-doped
sample in Ref.13, the calculated value of f would be- Asthepenetrationdepthhere(0.25µm)ismuchsmaller
i
come even 1 order of magnitude smaller. So the big dif- than the average distance (1.4 µm) between the neigh-
ferenceinpinningforceintheelectron-orhole-doped122 boringvortices,therarevorticeshaveverysmallinterac-
systemisnotfromthedifferentchosenvaluesofpenetra- tions,whichmaybethereasonforthesmalljc. Thepeak
tion depth. Small-size normal cores are the pinning cen- value of jc increases slightly with the magnetic field, as
ters in Ba0.6K0.4Fe2As2, which may originate from the showninFig.6(e). At100Oejc atthemostfrequentpo-
local doping-induced disorders or some local magnetic sition is about 1.4×105 A/cm2 and the maximum value
moments.11 Although the phase diagrams10,24 of super- reaches1.9×106A/cm2,whichis of the same amplitude
conductivity are similar for both doping sides, the elec- as the value taken on the magnetization curve.11
trondopinginducesimpuritybysubstitutingtheFesites The newly cleaved fresh surface is very flat, except
with Co, which may be the source of the extra pinning that some surface steps are formed by the cleaving. In
centers.9 Fig.7weshowthecaseoftwostepswithabout10nmin
The estimated critical current density j is propor- height, and the vortices were pinned by these steps. At
c
tionalto the piningforceper unitlength,i.e., j =f/φ . first glance the pinning of vortices by these steps is sup-
c 0
Weak pinning in Ba K Fe As means a very small posed to be induced by the Bean-Livingston pinning.25
0.6 0.4 2 2
criticalcurrentdensity,butitisnotconsistentwithother When a vortex is close to the parallel mirror surface, an
experiment results. One reliable explanation is that the attractive interaction is formed between the vortex and
K-doped sample has higher T , and the pair-breaking its image(with opposite sign).13 Inthis casethe vortices
c
scattering in the Co-doped sample suppresses the super- should stay at the higher side of the stage. This kind of
fluid density. In this way the intrinsic critical current pinning can only happen when the step is high enough
densitiesareverydifferentinK-dopedorCo-dopedsam- leading to a large mirror area parallel to the vortices.
ples. Itshouldbe notedthatthe comparedpinningforce This can readily explain why the vortices along the up-
mentionedaboveistheaverageone. Forexample,thecal- persteplocateonthe highstageandkeepsomedistance
culated average j = 104 A/cm2 is very small at 10 Oe. awayfromthestep,notontopoftheclear-cutline. How-
c
5
10-6 N/m
18
15 a H=10 Oe 1 u.) b H =10 Oe
µm)12 0.7 s (a. 20
y (9 0.4 unt
6 o
C
3 0.1 00.0 0.5 1.0 1.5
3 6 9µ 12 15 18 -6
x ( m) 10-6 N/m fi (10 N/m) a b
18
c H=50 Oe 7 80
15 6 u.) d H=50 Oe
m)12 5 a.
µy ( 69 234 Counts (40 FimIGag.e7(:b)(Cinoltohreopnrleisneen)cVeoorfttewxoimstaepgeso(na)thaendsuirtfsacdeiffaetr1e0ntOiael
3 1 0
0 2 4 6 8 and4.2K.Theinsertin(a)showstheheightlandscapealong
3 6 9µ 12 15 18 -6
x ( m) fi (10 N/m) the white line. It is clear that the heights of the two steps
6 are about 10nm, and the image dimension is 19µm×19µm.
40 2.0x10
e Thevorticesnearthestepswerepinnedalongtheedgeofthe
f (N/m)i123000 e H=10 Oe H=20 Oe H=50 Oe H=75 Oe H=100 O 511...005xxx111000566 φ2 jf=/ (A/cm)c0i steps.
0 0.0
Counts (a.u.)
FIG. 6: (Color online) Two-dimensional color mapped pin-
ning force per unit length of every vortex at 10 Oe (a) and
50 Oe (c), while the distributions of the pinning force per
unit length are shown in the histograms of (b) and (d), re-
a b
spectively. The highest frequency value of the pinning force
perunitlengthat10Oeisabout2×10−7 N/m,whichis1or-
derofmagnitudesmallerthanthevalueintheCo-doped122 FIG. 8: (Color online) Vortex image (a) and its self-
system at the same field.13 (e) Pinning force per unit length correlation map (b) of an underdoped Ba0.77K0.23Fe2As2
and the related critical current density distributions at each sample at 10 Oe and 2 K with a scanning range up to
magnetic field. 22 µm×22 µm. The white line shows the main distance of
thechains, which is about 3.2µm in each small division.
ever,thevorticesalongthebottomstepseemtolocatein
bothsidesoftheline. Thismaysuggestthattwinbound- inBi-2212,weneed asignificantmisalignment,i.e. more
aries are induced near the step, which may have weaker than45◦,betweenthedirectionofthemagneticfieldand
superconductivity and thus construct a strong pinning thec-axisofthesample,whileinourexperimentthemis-
well. This is similar to the recent report of the vortex alignment is smaller than 5◦. Additionally, no evidence
state near the twin boundaries.26 foreither pancakevorticesorthe Josephsonvorticeswas
observed in the K-doped 122.
To investigate the vortex chains, we did the further
C. Vortex image in UD sample experiment on the underdoped samples. Fig. 8 shows
the vortex image of the underdoped Ba K Fe As .
0.77 0.23 2 2
As mentioned in Part IIIB, there are some vortex Clearly, there are vortex chains along the same direc-
chains in optimally doped sample as shown in Fig. 2, tion, and the distances between the chains are sev-
while the pinning force per unit length is also large on eral micrometers. The vortex chains in underdoped
thesevortices,asshowninFigs.6(a),(c). Therearesome sample are very similar to the ones found in twinned
reports on the vortex chain state in the presence of a YBa Cu O 30,31 or ErNi B C29. The iron pnictides
2 3 7−δ 2 2
tilted magnetic field from the c-axis in cuprates27,28. It have the spin-density-wave and the structural transition
was shown later that these vortex chains are formed by in underdoped samples24,32. This structural transition
thevortexpancakeswhicharedraggedbytheunderneath from orthorhombic to tetragonalcauses the twin bound-
Josephsonvortex. Thereforetoobservethevortexchains aries which are parallel each other and have several mi-
6
crometers in distance33. The self-correlation result of a similar distance at higher magnetic field (higher than
these vortex images shows that the averaged space be- 20 Oe). Some vortex chains are observed together with
tween the two vortex chains is about 3.2 µm, which is a roughly random distribution (with short-range hexag-
consistent with the space between the domain walls. No onal order) of vortices between them. The calculated
doubt, these twin boundaries enhance the critical cur- pinning force per unit length seems much smaller than
rent density as counted from the gradient of the vortex that in the Co-doped 122 system at the same field, indi-
density.15,34 If we come back to the case in optimally catingthatthepinningatFesitesyieldsstrongerpinning
doped sample, some strong pinning centers also show up and vortex disorders. The vortex system becomes more
near the vortex chains, as shown in Fig. 6. Therefore, ordered and favors a six-neighbored structure at higher
even in the optimally doped sample, we also have the magneticfield. Wefindsomesurfacestepsasthepinning
twinboundariesasthestrongpinningcenters. Itisthese centersbuttheymaynotactastheBean-Livingstonmir-
strong and large scale pinning centers that enhance the ror pinning. A vortex chain state is also observed in the
critical current density greatly in the weak field region, underdopedsampleandisascribedtothepinningbythe
leading to a sharp magnetization peak near zero field. twinboundariesgeneratedbythestructuraldistortionof
When the magnetic field is increased to a high value, the orthorhombic state. We observed a cooperative pin-
more vorticesfill into the area between the “network”of ning induced by the large-scale twin boundaries and the
thesetwinboundaries. Thereforeitisquitenaturaltoob- weaklocaldisorders,whichmaybe a commonpicture to
servesomecomplexstructureofmagnetizationhysteresis describe the vortex dynamics in iron pnictide supercon-
loopswhichexhibitmultiplemagnetizationpeaks.35 Our ductors.
MFMdatahere givea directvisualizationofthis kindof
picture for vortex pinning in the iron pnictide supercon-
ductors. Acknowledgments
We appreciate useful discussions with Ted Forganand
IV. CONCLUSIONS C. van der Beek. This work is supported by the NSF
of China, the Ministry of Science and Technology of
We present the vortex images on optimally doped China (973 Projects: No. 2011CBA00102 and No.
Ba K Fe As andunderdopedBa K Fe As sin- 2010CB923002),PAPD,andtheChineseAcademyofSci-
0.6 0.4 2 2 0.77 0.23 2 2
gle crystals with magnetic fields below 100 Oe. The ences.
vortices are very diluted and widespread when the mag- ∗ [email protected]
netic field is several oersteds, but they get crowded with † [email protected]
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