Collective vortex pinning and crossover between second order to first order transition in optimally doped Ba1-xKxBiO3 single crystals

1.7 MB·

by  Yanjing Jiao

Collective vortex pinning and crossover between second order to first order transition
in optimally doped Ba K BiO single crystals
1−x x 3
Yanjing Jiao, Wang Cheng, Qiang Deng, Huan Yang and Hai-Hu Wen*
National Laboratory of Solid State Microstructures and Department of Physics,
Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
Measurements on magnetization and relaxation have been carried out on an optimally doped
Ba0.59K0.47BiO3+δ single crystal with Tc = 31.3 K. Detailed analysis is undertaken on the data.
7 Both thedynamicalrelaxation andconventionalrelaxation havebeen measured leadingtotheself-
1 consistent determination of the magnetization relaxation rate. It is found that the data are well
0 described by thecollective pinning model leading to the glassy exponent of about µ≈ 1.64 to 1.68
2 with the magnetic fields of 1 and 3 T. The analysis based on Maley’s method combining with the

n conventionalrelaxationdataallowsustodeterminethecurrentdependentactivationenergyU which
a yieldsaµvalueofabout1.23to1.29forthemagneticfieldsof1and3T.Thesecondmagnetization
J peaks appear in wide temperature region from 2 K to 24 K. The separation between the second

5 peak field and the irreversibility field becomes narrow when temperature is increased. When the
two fields are close to each other, we find that the second peak evolves into a step like transition

] ofmagnetization, suggesting a crossoverfrom thesecond ordertofirstordertransition. Finally, we
n presentavortexphasediagramanddemonstratethatthevortexdynamicsinBa1−xKxBiO3 canbe
o
used as a model system for studyingthecollective vortex pining.
c
-
r PACSnumbers: 74.25.Ha,74.25.Wx,74.25.Uv,74.70.-b
p
u
s I. INTRODUCTION conductors, the most conspicuous feature of BKBO is
.
t the lack of two-dimensionalCuO planes. So the uncon-
a 2
m Vortex related properties are very interesting and im- ventional, most likely the magnetic origin driven mecha-
nism proposed for cuprate superconductors may not be
d- portant for type-II superconductors, especially for the suitable for BKBO19. Some other anomalous features
high power applications. Numerous detailed studies on
n also have been discovered from the experiments, includ-
the vortex dynamics of cuprate and iron based super-
o ingalargeoxygenisotopeeffect20,21 andthesofteningof
conductors have been performed1–4. Some interesting
c phononsinthe BKBOsystem22,23. The secondmagneti-
[ phenomena like magnetic flux jump5,6, collective vor-
tex creep7, and second peak effect have been discovered zation peak effect has been observed in the underdoped
1 Ba K BiO withT =27K24. Inthatpaperthey
throughthe experiments. Although the collective vortex 0.66 0.32 3+δ c
v observed second magnetization peak in the intermedi-
creep theory has successfully interpreted some features
6 ate temperature region and its general behavior looks
4 or vortex dynamics8–12 in cuprate and iron based super-
like that in YBa Cu O (YBCO). But vortex dynamics
3 conducting materials,the crystalstructuresinthosesys- 2 3 7
on optimally doped BKBO single crystal with a higher
1 tems are generally complicated, which will bring in the
0 complex in the behavior of vortex physics. For exam- Tc K has not been studied before. In present work, we
. make a detailed study on the vortex dynamics of opti-
1 ple, a quite sophisticatedvortexphase diagramhas been
mally doped BKBO single crystal with measurements of
0 reported for some cuprate superconductors, such as the
magnetizationandrelaxation,includingtheconventional
7 Bi Sr CaCu O (Bi2212)13. So the research of vortex
1 2 2 2 8 and dynamical relaxations.
physics in crystals with simpler structure may give us
:
v a better way to understand vortex motion and pinning
i mechanism, especially for checking the collective vortex
X
II. EXPERIMENT
pinning. For this reason, the Ba1−xKxBiO3 (BKBO)
r
a superconductor has attracted much attention after the
discovery14,15. It has relatively simple basic cubic per- Near optimally doped single crystals of Ba1−xKxBiO3
ovskite crystal structure for 0.375 < x < 0.5 and it is are grown by the molten-salt-electrochemical method
close to a three dimensional system16. Moreover,the co- which is similar to that reported previously25,26. Molten
herencelengthinBKBOisabout3-6nm17,18. Thisvalue KOH with slight deionized water were used as the
is higher than that of cuprate superconductors, which growth environment. We adjust the mass ratio between
may suggest that the weak link effect between grains Ba(OH) ·8H O and Bi O to about 2:5 to growthe op-
2 2 2 3
is not very crucial and the simple powder-in-tube tech- timally doped sample, and the growth time is about 3
nique for making the superconducting wires can be ap- days. With this method, we successfully get single crys-
plied. Thislongcoherencelengthisalsohelpfulformak- tals with volume in the range of 2-5 mm3. To check the
ing the superconducting quantum coherence device. In quality of these single crystals, X-ray diffraction (XRD)
addition, in the BKBO superconductor, the conducting measurementsareperformedonthesamplesbyaBruker
layer is BiO layer. Compared with the cuprate super- D8 Advanced diffractometer with the Cu-K radiation.
2

1.0
(a)
(a)
0.8 T = 2 K
m) 120 T = 4 K
Ω m 0.6 0H = 0 T 0H = 5 T T = 6 K
(m 0.4 0H = 1 T 0H = 7 T 3 m)60
0H = 3 T 0H = 9 T c
0.2 u/
m
e 0
0.00 20 40 60 80 M (
T (K)
2.0 (b) (c) 0.0 -60
(Ω mmm) 11..05 0H = 0 T 0H =F C20 Oe --10..68 3 M (emu/cm) -120 TTT === 111058 KKK
0.5 -2.4 -6 -4 -2 0 2 4 6
ZFC
0.0 -3.2 0H (T)
0 100T (K)200 300 0 10 T 2( 0K) 30 40 20 (b) T = 20 K
T = 22 K
T = 24 K
FIG. 1: (Color online) (a) Temperature dependence of re-
sistivity of Ba0.59K0.47BiO3+δ measured at various magnetic 3 m)10
c
fields. (b) Temperature dependent resistivity at zero field u/
with the temperature range from 2 K to room temperature. m
e 0
(c) Magnetization measured in theZFC and FC processes at M (
a magnetic field of 20 Oe.
-10
T = 25 K
T = 26 K
The XRD pattern of the sample matches very well with
-20 T = 28 K
the previous reported results in the slightly underdoped
samples24. The chemical composition of the sample was
-4 -2 0 2 4
characterizedbyusingthe Energy-dispersiveX-rayspec- 0H (T)
troscopy(EDX/EDS)attachedtoascanningelectronmi-
croscope (Hitachi Co., Ltd.), and the resultant chemical
FIG. 2: (Color online) Magnetization hysteresis loops of the
compositionisclosetoBa K BiO ,whichisclose
0.59 0.47 3+δ BKBOsinglecrystalatvarioustemperaturesrangingfrom(a)
to the reported optimal doping value x ≈ 0.4 to 0.5. All
2 K to 18 K, (b) 20 K to 28 K underdifferent field sweeping
themagnetizationmeasurementswerecarriedoutwitha
rates of 200 Oe/s (solid lines) and 50 Oe/s (dashed lines),
SQUIDmagnetometer(SQUID-VSM-7T,QuantumDe- respectively.
sign). During the measurements, the magnetic field H
was always parallel to c axis of the sample. Resistiv-
ity was measured by the standard four-lead method in a
magnetic field with a wide temperature range from 2
QuantumDesigninstrument,thephysicalpropertymea-
K to room temperature. The residual resistance ratio
surement system (PPMS).
RRR = R(T = 300 K)/R(T = 32 K) = 2.28, which
is rather small and indicates the strong scattering of
the charge carriers in the sample. Temperature depen-
III. RESULTS AND DISCUSSIONS dence of magnetization measured with zero-field-cooling
(ZFC) and field-cooling (FC) process at 20 Oe is shown
A. Superconducting transition and second peak in Fig. 1(c). The irreversibility temperature of the ZFC-
effect FCmagnetizationcurvesat20Oeisabout31.1Kwhich
is comparable to T from the resistance measurements.
c0
Figure 1(a) shows the temperature dependent resis- The magnetization measured in the ZFC process in the
tivity ρ at different magnetic fields ranging from 0 to 9 temperature region from 2 to 20 K shows a flat temper-
T. The critical temperature T taken from zero resis- ature dependence, which indicates again a full magnetic
c0
tance at zero field is about 30 K, and the onset crit- shielding effect. The large difference between the ZFC
ical temperature Tonset with a criterion of 90%ρ is and FC magnetizationcurves indicates a strong hystere-
c n
31.3 K, here ρ is the normal state resistivity. The sis of magnetization and thus strong vortex pinning.
n
narrow transition width shows the high quality of the Figure 2 shows the magnetization hysteresis loops
sample. Figure 1(b) is the ρ-T curve measured at zero (MHLs)atdifferenttemperaturesfrom2Kto28Kwith
3
temperature and magnetic field. Thus a generaldescrip-
tion of the activation energy was suggested as28,29

5
10
2K U j
U(j )= c[( c)µ−1], (2)
4 6K s µ j
10 10K s
2 m) 12K whereUc istheintrinsicpinningenergy,jc istheunre-
A/c103 laxedcriticalcurrentdensity which is alwayslargerthan
j (s 15K transientcurrentdensityjs,µistheglassyexponentthat
involves the most attempting size of the vortex motion
2
10 and the wandering factor of an elastic object in a three
dimensional manifold1,30. In a three-dimensionalsystem
18K
µ> 0 can be used to describe a elastic flux creep while
1
10 28K 27K 26K 24K 22K 20K µ< 0 for plastic motion31,32. In particular, µ = −1 cor-
responds to the classical Kim-Anderson model33.
0 1 2 3 4 5 6 7 Combining above two equations, we can derive
0H (T)
µk T v B
FIG. 3: (Color online) Magnetic field dependence of js cal- js =jc[1+ B ln( 0 )]−1/µ. (3)
culated from the Bean critical state model at different tem- Uc E
peratures in semi-log plot. The solid lines stand for the js
We canalsofurther understandthe secondpeak effect
with field sweeping rate of 200 Oe/s, while the dashed lines
from field dependent transient superconducting current
represent thosewith 50 Oe/s.
density j -µ H curve. The j can be obtained based on
s c s
the extended Bean critical state model34,
different magnetic field sweeping rates. The symmetric
∆M
MHLs indicate that the bulk vortex pinning rather than j =20 . (4)
s
a(1−a/3b)
the surface shielding current dominates the magnetiza-
tion in the sample. We have measured the MHLs with
Herethefielddependentirreversiblemagnetizationwidth
twodifferentfieldsweepingrates: 50Oe/sand200Oe/s.
∆M,whichiscorrespondingtothetransientcriticalcur-
One can see clear difference between the MHLs shown
rent density in a superconductor, and can be calculated
by solid (dH/dt = 200 Oe/s) and dashed (dH/dt = 50
by ∆M =M −M . Here M (M ) is the magneti-
Oe/s) line. This difference will allow us to extract the in de in de
zation associated with increasing (decreasing) magnetic
dynamicalrelaxationrate. FromFig. 2, one canfind ob-
fieldswiththeunitofemu/cm3 . Thelengthscalesaand
vious second peak effect over a wide temperature range
b in unit of cm are the width and length of the sample
beginningfromthelowesttemperature2K.Theso-called
(a < b). In Fig. 3, we show field dependent j with two
second peak of magnetization is relative to the first one s
different field sweeping rates of 200 Oe/s and 50 Oe/s.
near the zero magnetic field. It should be noted that
It is obvious that j are different from each other with
flux jump effect shows up as the large scale anomalous s
different field sweeping rates, a faster sweeping rate cor-
jumps of the magnetization below 4 K in the low field
responds to a higher current density. The calculated j
range, which is similar to the result in the underdoped s
at 2 K and 0 T can reach a value of 105 A/cm2. More-
sample24.
over, the second peak effect is very clear in Fig. 3, i.e.,
at certain temperature, curve j decreases first, then in-
s
creases,and finally keeps decreasing with the increase of
B. Theoretical models for treating the data
magnetic field. The general shape of magnetization hys-
teresis loops and related features are similar to that in
The vortex dynamics is mainly described with the cuprate superconductor YBCO35. In addition, the peak
model of thermally activated flux motion (TAFM)27.
positionH moves closerto the irreversibilityfield H
sp irr
Based on this model, the electric field E induced by the
with increasing of temperature resulting in a continuous
vortex motion is written as
increasing ratio of H /H . The origin of this second
sp irr
peakeffect hasseveralpossiblescenarios. Onpicture ex-
−U(j ) plainsthiseffectasthecrossoverbetweendifferentvortex
s
E =v0B×exp[ ]. (1) pinningregimes. Thedominatedsingle-vortexpinningat
k T
B
low magnetic field may be replaced by pinning of vortex
In above equation, v is the largest vortex moving bundlesorentangledvorticesinhighfieldregion,andthe
0
speed, B is the averaged magnetic induction, U(j ) is transient superconducting current keeps increasing with
s
the flux activation energy which is defined as a function the magnetic field as the flux creep is lowered. How-
of current density j . Generally, it is also a function of ever, in high magnetic region, some dislocations will be
s
4
Here M is the instantaneously measured magnetiza-
tion, and M is the equilibrium magnetization which
eq
= is taken from the average of magnetization of increas-
(a) 0 1.0 T ing and decreasing field of the full MHL taken at a cer-
2K tain magnetic field and corresponding temperature. For
4.2
3K
datameasuredathightemperatures,itisveryimportant
4K
to removethis equilibrium magnetizationawaysince the
M)eq 4.0 5K MHL becomes asymmetric. The time t is taken from
M- 6K the moment when the critical state is prepared. A long
3.8
n -( 7K waitingtime isnecessaryfordeterminingthe meaningful
l 8K relaxation rate.
3.6
9K In contrast, the so called dynamic magnetization-
10K relaxation measurements are carried out by measuring
3.4
11K the MHLs with different field sweeping rates dH/dt
=
(b) as described above. The corresponding magnetization-
0 3.0 T
2K relaxation rate Q can be obtained from
4.2
3K
4K
M)eq 4.0 5K Q= dlnjs . (6)
M- 6K dln(dB/dt)
ln -( 3.8 78KK The very small difference between the two js-µcH
3.6 9K curves measured with four times difference of sweep-
ing rate corresponds to a very small magnitude of Q.
FromEq.3, one caneasily havethe message that S ≈Q.
3.4 11K
Here, in deriving the conventional magnetization relax-
2 3 4 5 6 7 8 9
ation rate, we assume that E ∝ dj /dt; in deriving the
ln t s
dynamical relaxation rate, we assume E ∝dB/dt.
Thetimedependenceofmagnetizationatvarioustem-
FIG. 4: (Color online) Time dependence of the nonequilib- peraturesareshowninFig.4atmagneticfieldsof1Tand
riummagnetization onalog-logplotatvarioustemperatures
3T.Herealmostlinearrelationshipbetween−(M−M )
atfieldsof(a)1T(b)3T.Herethemagneticfieldisapplied eq
andtimeinlog-logplotisobservedinthelongtimelimit,
parallel to c-axis of thesample.
being consistent with the model of thermally activated
flux motion. According to the definition of the conven-
tional relaxation rate as Eq. 5, the absolute value of the
formed in the vortex system leading to the plastic vor-
slope of the log-log plot in Fig. 4 gives the conventional
tex motion, the transient critical current density j will
s relaxation rate, we thus determine S through a linear
decrease. At higher temperatures, the second peak ef-
fit to the double logarithmic plot from the data in the
fectbecomesweakerandH becomesmoreclosertothe
sp long time limit with the time window of lnt = 4 to 8.18.
H . From our data, we can see that the second peak
irr The dynamic relaxation rates Q calculated from Eq. 6
effectbecomesastepliketransitionwhentemperatureis
and Fig. 3 as well as the conventional relaxation rates
28 K.
S calculated from Eq. 5 and Fig. 4 versus temperature
are shown in Fig. 5(a). One can find that relaxation
rates calculated from the two methods at the same field
C. Magnetization relaxation rate and glassy are consistent with each other. To get more information
exponent about the vortex dynamics, we can calculate the activa-
tion energy and the glassy exponent which is strongly
It has been proven that magnetization relaxation is a related to the relaxation rate. If combining Eq. 1 and
very effective way to investigate the vortex dynamics36. Eq. 3 and the definition of the dynamic relaxation men-
Themagnetizationrelaxationcanbecategorizedintothe tioned above, the following equation can be obtained37,
conventional relaxation and dynamical relaxation. In a
typical conventional magnetic relaxation measurement,
T U (T)
time dependent decay of magnetization is measured af- = c +µCT, (7)
ter applying a field following the ZFC process. The cor- Q(T) kB
responding magnetization-relaxationrate S is defined as
where C = ln(v B/E) is a parameter that almost in-
0
dependent of temperature. According to this equation,
dln[−(M −M )] the relaxation rate Q is determined by the balance be-
eq
S =− . (5) tween the two temperature dependent parts U (T) and
dlnt c
5

0.30
(a)
-0.04 0H=1.0 T Fit line
0.24 Q (H =1.0 T) 0H=3.0 T Fit line
Q (H =3.0 T)
S 0.18 Q (H =5.0 T)
Q or 0.12 QSS (((HHH ===136...000 TTT))) nj/dTS-0.06
dl
-0.08
0.06
0.00
0 5 10 15 20 25 -0.10
T (K ) 0.0016 0.0020 0.0024 0.0028 0.0032
-1
Q/T (K )
(b)
T/Q (H =1.0 T) T/Q (H =3.0 T)
1000
T/Q (H =5.0 T) T/Q (H =6.0 T) FIG. 6: (Color online) Correlation between dlnjs(T)/dT vs.
Q, T/S (K) 680000 TT//SS ((HH ==13..00 TT)) KQ3of,(TlTtn.h)jI/esnnTvogasre.tdtelTotrhw,teaotncecodmarlrpQceues(rplTaaott)neu/dTrteihnsvegsfo.vdraaTlttuhaebe,aemtwtwetaehgeiennnetseta2irmcpKoefileaatletndmedsptoahefber1oadutauatntrd8ae
T/ from both correlations and plot them here. The slope gives
400 thevalueof C.
200
0
0 3 6 9 12 15
T (K)
µ. We plot temperature dependence of T/Q and T/S at
FIG. 5: (Color online) (a) Temperature dependence of the differentmagneticfieldsinFig.5(b). Herewedoalinear
dynamic relaxation rate Q ranging from 1 T to 6 T, and fit of the data T/Q vs. T between 2 and 8 K to get the
the conventional relaxation rate S at 1 T and 3 T. (b) Tem- intercept at T = 0 K and the slope. From the intercept
perature dependence of the ratio T/Q and T/S at various
value at T = 0 K, we get the the values of U (0)/k =
c B
magnetic fields.
194 K and 233 K at 1 T and 3 T, respectively. These
values are larger than that of Ba(Fe1−xCox)2As2 single
crystals38. Basedonthemethodthatwediscussedabove,
µCT, and shows a complex temperature-dependent be-
the values of µC ≈ 45.38 and 48.18 at 1 T and 3T can
havior. However if the second part is too small and can
be determined. Meanwhile, taking the values of C that
be ignored at very low temperature, then Q will show
determined above, we can get the glassy exponent µ ≈
a linear dependence on T, the ratio T/Q should give a
1.64 at 1 T and 1.68 at 3 T.
constant which is just the intrinsic pinning energy. By
extrapolating the curve T/Q down to zero temperature,
one can obtain the value of U (0). The value of µC can
c The relaxation rates show a monotonic temperature
be determined from the slope of T/Q vs. T. Meanwhile,
dependence for different fields, as shown in Fig. 5(a).
from Eq.3 one can derive that
While it exhibits clearly a plateau in the intermedi-
ate temperature region, which was also observed in
Q(T) YBa2Cu3O7−δ39. The temperature window of the
−dlnj /dT =C× . (8)
s plateau in Q-T curve shrinks when magnetic field is in-
T
creased and almost disappears at µ H = 6.0 T. This
0
Therefore the parameter C can be calculated2 by the plateaucanbeexplainedbythevortexcollectivepinning
slop of −dlnj /dT vs. Q/T. In Fig.6, we show the data model as Eq. 7. When the second term µCT is much
s
of-lnj (T)vs. Q(T)/T atlowtemperaturesforthemag- larger than U at high temperatures, the first term can
s c
netic field of 1 and 3 T. One can see that the curves are be ignoredandalmosttemperatureindependent valueof
roughly straight, so we can get the C values of 27.6 and Q can be obtained. This plateau of S or Q in the inter-
28.7 for 1 and 3 T, respectively. With the values of µC mediate temperature region strongly suggests the appli-
determinedabove,wecandeterminetheglassyexponent cability of the collective vortex pinning model.
6
aturedependenceofU (T)isweak. The glassyexponent
c
can be obtained by fitting the scaled curves with Eq. 2

360 by TAFM model. The fitting gives an independent eval-
K) (a) T =2.5 K T =3.0 K uation of Uc/kB = 199 K, µ = 1.23 at 1 T, and Uc/kB
A] ( 300 T =3.5 K T =4.0 K = 269 K, µ = 1.29 at 3 T, which are close to the results
dt)- TT ==54..55 KK TT ==65..50 KK ftrhoemµavnaalluyessisdberaisveeddoinn tEhqe.t7w.oTmheethdoidffseriesncinedbuectewdebeny
dM/ 240 T =7.5 K the distinct andcrude assumptionsadoptedin analyzing
= -T [ln( 180 = TT ==88..05 KK mthaeydlaotcaa.teTinhetrheeforreegwioencoafn1.c2ontoclu1d.7e.tAhastwtehediµscuvsasluede
kB 0 1.0 T above, in the model of collective creep, the glassy ex-
U/ 120 Fit line ponent µ influences on the vortex dynamics. Actually,
theoreticalprediction30 for the µ values is that: µ = 1/7
for single vortex; µ = 3/2 for small bundles of vortices;
60
µ = 7/9 for large bundles of vortices. The value µ =
360 (b) T =2.0 K T =2.5 K 3/2 locates just between the two calculated values that
K) T =3.0 K T =3.5 K obtained by different methods. So our results here may
A] ( 300 T =4.0 K T =5.0 K suggest that the collective vortex motion is in the small
dt)- T = 6 . 0 K TT ==76..55 KK bundlesvortexregime. Nevertheless,theµvaluesderived
M/ 240 T =8.5 K in different methods suggest that the collective pinning
n(d T =9.0 K model is applicable in this kind of superconductors.
= -T [lB 180 0 = 3.0 T
k
U/ 120 Fit line E. Crossover from the second to first order
transition at high temperatures
60
40 50 60 70 Recalling the MHLs with the second peak effect, we
3 see that there is a large gap between the second peak
-(M - Meq) (emu/cm)
field H and the irreversible field H when the tem-
sp irr
perature is not high. In this case, the merging of the
FIG. 7: (Color online) Nonequilibrium magnetization depen- magnetizationcurvesinthe fieldascendinganddescend-
dence of the scaled activation energy U obtained by the Ma-
ingprocessesisgradual,showingalongtailofthecritical
leys method with parameter A = 28. A fitting result with
currentdensityj versusH,asshowninFig. 3forT =18
Eq.2ispresentedasthereddotlinewiththeparameterµ= s
K to 24 K. However, when the temperature is increased
1.23 with a magnetic field of 1 T. (b) The same as (a) while
further, this gap becomes narrow and narrow, showing
withadifferentmagneticfieldof3T,theparametersA=28,
a step like behavior in both the MHL near the H or
theglassy exponent µ = 1.29. irr
the curve of j versus H. We present the MHLs at high
s
temperatures (22 to 28 K) in Fig. 8. It is clear that the
D. To derive the U(js) dependence and µ MHLsneartheirreversibilitylineisindeedchangingfrom
parameter from Maley’s method a long tail behavior to a step like. We argue this change
ofthebehaviorfromasmoothtoastepliketransitionas
thecrossoverfromthesecondordertransitionofvortices
In order to verify the calculatedactivation energy and
glassy exponent, we also use the Maley’s method40 to to the first order transition. The second order transition
nearH atalowtemperatureandhighmagneticfieldis
analyzethedataoftimedependentnonequilibriummag- irr
understood as the transition from a plastic motion dom-
netization. From Eq. 1. and the basic assumption of
inated vortex dynamics to the vortex liquid. While the
E ∝|dM/dt|, we have
stepliketransitioncorrespondstoamoreorderedvortex
U(j ) system (now the vortex density is quite low) to the vor-
s
=−T[ln(dM/dt)−A], (9)
tex liquid transition. Our observation here is quite close
k
B tothetheoreticallypredictedphasediagram1 inthehigh
where A is a time-independent constant related to the temperature and low field region, where the first order
average hoping velocity. By adjusting A we can scale transition occurs and the phase line connects to the sec-
the curves measured at low but different temperatures ondordertransitionathighmagneticfields. Thisfirstor-
onto one curve. This is shown in Fig. 7. From the fig- der transitionmay be similar to that observedin YBCO
ure, we can see that all the curves can be well scaled single crystals41,42, but the magnetic field is much lower
together at temperatures below 6.5 K, while the scaling in present BKBO sample. Since our sample is a bulk,
fails athigher temperatures. The temperatureregionfor the global measurement for the step like transition gives
the good scaling may be in the range where the temper- stillacertainwidthofthe transition. Itishighly desired
7

22 K
dH/dt = 200 Oe/s
4 24 K 5 Hirr Hc2
25 K 1.42
3 cm) 2 2267 KK 4 (1 - T/Tc)1.51 (1 - T/Tc)
mu/ 28 K HSP
(eM 0 H (T) 3 2ndOT
0
-2 2 Hmin
st
1 OT
-4
1

-4 -2 0 2 4
0H (T) 0 5 10 15 20 25 30 35

T (K)
FIG. 8: (Color online) Enlarged view of theMHLs measured
attemperatures22K24K25K26K27Kand28Kfromoutside
FIG. 9: (Color online) The vortex phase diagram of the op-
to inside. With increasing temperature, the MHL near the
timally doped sample BKBO. The filled symbols are taken
irreversibilitypointHirr changesfromasmoothlongtaillike from the magnetization measurements while the open ones
transition to a step like transition.
are taken from the resistive measurements. The upper criti-
calfieldHc2 isdeterminedwiththecriterion of90%ρn,while
the irreversibility field Hc2 is determined with 10%ρn. The
to use the smallHall probe orlocalmeasurementsto de- red solid (Hc2) and blue dashed (Hirr) lines are the fitting
tect this first order transition as that done in cuprate curveswith theformula H(T)=H(0)(1−T/Tc)n.
superconductor Bi221213,43,44.
fitted by the expressions H (T)=H (0)(1−T/T )1.42
c2 c2 c
F. Vortex phase diagram and general discussion and Hirr(T)= Hirr(0)(1−T/Tc)1.51. The two lines are
veryclosetoeachother,whichsuggeststhattheflux liq-
uid region in this material is rather narrow. This is be-
With above results, finally, we depict a vortex phase
cause the material itself is more three dimensional like,
diagramfor the optimally doped Ba K BiO sin-
0.59 0.47 3+δ
not that much two dimensional as in the cuprates.
gle crystal in Fig. 9. Here H is the irreversibility field
irr
thatisdeterminedfromj -µ H curveswiththecriterion
s 0
of j = 10 A/cm2 (blue open circles). The field position
s
H is the point with minimum j between the first IV. CONCLUDING REMARKS
min s
and the second magnetization peak position H . The
SP
upper critical field H and the irreversible field H In conclusion, we have investigated the vortex dy-
c2 irr
shown as open squares are obtained from the resistive namics through the dynamical and conventional mag-
measurementwithcriterionsof90%ρ andof10%ρ ,re- netization relaxation methods on optimally doped
n n
spectively. Below the second peak effect field, the vor- Ba K BiO single crystal with T = 31.3 K. A
0.59 0.47 3+δ c
tex motion can be well interpreted with the collective second peak effect is obvious on the magnetization hys-
vortex motion with the glassy exponent µ ≈ 1.2 to 1.7, teresis loops over a very wide temperature range from 2
this suggestsanelastic flux creep. While with increasing to24K.Basedonthe BeancriticalstatemodelandMa-
magnetic field, the flux creep becomes faster and system ley’s method, we calculate the transient critical current
enters into the plastic creep regime. This crossover may density and obtained the characteristic pinning energy.
correspond to the second peak field, or slightly higher We also get the glassy exponent of µ ≈ 1.2 to 1.7 for
than that field. Finally, the motion of vortices changes the magnetic field of 1 T and 3 T in low temperature
into vortex liquid state above the irreversibility field or regime. It indicates that the vortex collective pinning
temperature. However, a quite large area between the model can describe the vortex dynamics in this mate-
H −T andH −T curvesintheintermediatetemper- rial very well. The second peak position become very
irr SP
ature region suggests that the vortex dissipation is still closetotheirreversibilityfieldatthetemperaturesabove
through a plastic motion in this region, via for example 0.9T , which may suggest that the vortex phase transi-
c
theproliferationofthevortexkinkyloops1. Atveryhigh tionchangesfromthe secondordertothe firstorder. Fi-
temperatures and magnetic fields, we see the vortex liq- nally,thevortexphasediagramisobtainedbycombining
uidbehaviorwiththeveryfastvortexmotion. Wefitthe theresistivityandmagnetizationmeasurements. Ourre-
H (T) and H (T) curves and find that they are well sults show that the optimally doped BKBO is a model
c2 irr
8
platform to investigate the vortex collective pinning and ples. This work was supported by the National
related physics. Key Research and Development Program of China
(2016YFA0300401,2016YFA0401700), and the National
Natural Science Foundation of China (NSFC) with the
Acknowledgments projects: A0402/11534005,A0402/11374144.
The authors acknowledge the help of Jian Tao
for sharing the experience in growing the sam-
1 G. Blatter, M. V. Feigelman, V. B. Geshkenbein, A. I. A. W.Mitchell, Nature 335, 419 (1988).
Larkin, and V. M. Vinokur, Rev. Mod. Phys. 66, 1125 21 C. K. Loong, D. G. Hinks, P. Vashishta, W. Jin, R. K.
(1994). Kalia, M. H. Degani, D. L. Price, J. D. Jorgensen, B.
2 H.H.Wen,H.G.Schnack,R.Griessen,B.Dam,J.Rector, Dabrowski, A. W. Mitchell, D. R. Richards, Y. Zheng,
Physica C 241, 353(1995). Phys. Rev.Lett. 66, 3217 (1991).
3 L. Krusin-Elbaum, L. Civale, V. M. Vinokur, and F. 22 M. Braden,W.Reichardt,W.Schmidbauer,A.S.Ivanov,
Holtzberg, Phys.Rev. Lett.69, 2280 (1992). A. Yu.Rumiantsev, J. Superconductivity.8, 595 (1995).
4 L. Klein, E. R. Yacoby, Y. Yeshrun, A. Erb, G. Miiller- 23 H. J. Kang, Y. S. Lee, J. W. Lynn, S. V. Shiryaev, S. N.
Vogt,V.BreitandH.Wiihl,Phys.Rev.B49,4403(1994). Barilo, Physica C 471, 303 (2011).
5 D. V. Shantsev, A. V. Bobyl, Y. M. Galperin, T. H. Jo- 24 J.Tao, Q.Deng,H.Yang,Z.H.Wang,X.Y.Zhu,andH.
hansen, and S. I. Lee,Phys. Rev. B72, 024541 (2005). H. Wen,Phys.Rev.B 91, 214516 (2015).
6 D. V. Denisov, A. L. Rakhmanov, D. V. Shantsev, Y. M. 25 M. L. Norton, Mat. Res. Bull. 24, 1391 (1989).
Galperin, and T. H. Johansen Phys. Rev. B 73, 014512 26 T.Nishio,H.Minami,H.Uwe,PhysicaC357,376(2001).
(2006). 27 P. W. Anderson,Phys. Rev.Lett. 9, 309 (1962).
7 J. P.Rodriguez. Phys.Rev.B 70, 224507 (2004). 28 M. V. Feigel’man and V. M. Vinokur, Phys. Rev. B 41,
8 J. R.Thompson, Y.R.Sun,D.K.Christen, L. Civale, A. 8986 (1990).
D. Marwick, and F. Holtzberg, Phys. Rev. B 49, 13287 29 A.P.MalozemoffandM.P.A.Fisher,Phys.Rev.B42,6784
(1994). (1990).
9 L.Miu,T.Noji,Y.Koike,E.Cimpoiasu, T.Stein,andC. 30 M. V.Feigel’man, V.B. Geshkenbein,A.I. Larkin,V.M.
C. Almasan, Phys. Rev.B 62, 15172 (2000). Vinokur,Phys. Rev.Lett. 63, 2303 (1989).
10 H. Yang, C. Ren, L. Shan, H. H. Wen, Phys. Rev. B 78, 31 H.H.Wen,A.F.Th.Hoekstra,R.Griessen, S.L.Yan,L.
092504 (2008). Fang, and M. S.Si, Phys. Rev.Lett. 79, 1559 (1997).
11 N.Haberkorn,M.Miura,B.Maiorov,G.F.Chen,W.Yu, 32 Hai-Hu Wen, Paul Ziemann, Henri A. Radovan and
and L.Civale, Phys. Rev.B 84, 094522 (2011). Thomas Herzog, Physica C 305,185 (1998).
12 T. Taen, Y. Nakajima, T. Tamegai, and H. Kitamura, 33 P. W. Anderson, Y. B. Kim, Rev. Mod. Phys. 36, 39
Phys. Rev.B 86, 094527 (2012). (1964).
13 H.Beidenkopf,N.Avraham,Y.Myasoedov,H.Shtrikman, 34 C. P. Bean, Rev.Mod. Phys. 36, 31 (1964).
E. Zeldov, B. Rosenstein, E. H. Brandt, and T. Tamegai, 35 S.Kokkaliaris,A.A.Zhukov,P.A.J.deGroot,R.Gagnon,
Phys. Rev.Lett. 95, 257004 (2005). L. Taillefer, and T. Wolf, Phys.Rev.B 61, 3655 (2000)
14 L.F.Mattheiss, E.M.Gyorgy,andD.W.Johnson,Phys. 36 E. H. Brandt, Rep.Prog. Phys. 58, 1465 (1995).
Rev.B 37, 3745 (1988). 37 H.H. Wen,R.Griessen, D.G. de Groot, B. Dam, J. Rec-
15 R.J. Cava, B. Batlogg, J. J. Krajewski, R.Farrow, L. W. tor, J. Alloys Compd. 195, 427 (1993).
RuppJr,A.E.White,K.Short,W.F.Peck,T.Kometani, 38 B.Shen,P.Cheng, Z.S.Wang,L.Fang,C.Ren,L.Shan,
Nature (London) 332, 814 (1988). and H. H.Wen, Phys.Rev.B 81, 014503 (2010).
16 S.Y.Pei, J. D.Jorgensen, B. Dabrowski, D.G.Hinks,D. 39 Y.Yeshurun,A.P.Malozemoff,andA.Shaulov,Rev.Mod.
R. Richards, A. W. Mitchell, J. M. Newsam, S. K. Sinha, Phys. 68, 911 (1996).
D. Vaknin, and A. J. Jacobson, Phys. Rev. B 41, 4126 40 M. P. Maley, and J. O. Willis, Phys. Rev. B 42, 2639
(1990). (1990).
17 M. Affronte, J. Marcus, C. Escribe-Filippini, A. Sulpice, 41 U. Welp, J. A. Fendrich, W. K. Kwok, G. W. Crabtree,
H.Rakoto,J.M.Broto,J.C.Ousset,S.Askenazy,andA. and B. W. Veal, Phys.Rev.Lett. 76, 4809 (1996).
G. M. Jansen, Phys. Rev.B 49, 3502 (1994) 42 A.M.Petrean,L.M.Paulius,W.K.Kwok,J.A.Fendrich,
18 W.K.Kwok,U.Welp,G.Crabtree,K.G.Vandervoort,R. and G.W. Crabtree, Phys. Rev.Lett. 84, 5852 (2000).
Hulsher, Y. Zheng, B. Dabrowski, and L. G. Hinks, Phys. 43 B. Khaykovich,E. Zeldov, D.Majer, T. W. Li, P.H. Kes,
Rev.B 40, 9400 (1989). and M. Konczykowski,Phys. Rev.Lett. 76, 2555 (1996).
19 H.J.Kaufmann,OlegV.Dolgov,andE.K.H.Salje.Phys. 44 B.Kalisky,Y.Myasoedov,A.Shaulov,T.Tamegai,E.Zel-
Rev.B 58, 9479 (1998). dov,andY.Yeshurun,Phys.Rev.Lett.98,107001(2007).
20 D. G. Hinks, D. R. Richards, B. Dabrowski, D. T. Marx,