Magnetic-field effects on the in-plane electrical resistivity in the single-crystal La$_{2-x}$Ba$_x$CuO$_4$ and La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ around $x=1/8$: Relating to the field-induced stripe order

0.33 MB·English

by  T. Adachi

Magnetic-field effects on the in-plane electrical resistivity in the single-crystal
La2−xBaxCuO4 and La1.6−xNd0.4SrxCuO4 around x = 1/8:
Relating to the field-induced stripe order
5
0
0 T. Adachi, N. Kitajima, T. Manabe, Y. Koike
2
Department of Applied Physics, Graduate School of Engineering, Tohoku University,

n Aoba-yama 6-6-05, Aoba-ku, Sendai 980-8579, Japan
a
J
K. Kudo, T. Sasaki, N. Kobayashi

0 Institute for Materials Research, Tohoku University,
2 Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan
(Dated: February 2, 2008)
]
n Temperature dependence of the in-plane electrical resistivity, ρab, in various magnetic fields
o has been measured in the single-crystal La2−xBaxCuO4 with x = 0.08, 0.10, 0.11 and
c
La1.6−xNd0.4SrxCuO4 with x=0.12. It has been found that the superconducting transition curve
-
r shows a so-called fan-shape broadening in magnetic fields for x = 0.08, while it shifts toward the
p low-temperature side in parallel with increasing field for x = 0.11 and 0.12 where the charge-spin
u stripeorderisformedatlowtemperatures. Asforx=0.10,thebroadeningisobservedinlowfields
s
. anditchangestotheparallelshiftinhighfieldsabove9T.Moreover,thenormal-statevalueofρab
t at low temperatures markedly increases with increasing field up to 15 T. It is possible that these
a
m pronounced features of x = 0.10 are understood in terms of the magnetic-field-induced stabiliza-
tion of the stripe order suggested from the neutron-scattering measurements in theLa-214 system.
d- The ρab in the normal state at low temperatures has been found to be proportional to ln(1/T) for
n x=0.10, 0.11 and 0.12. The ln(1/T) dependenceof ρab is robust even in thestripe-ordered state.
o
c
[ I. INTRODUCTION (BSLCO) below p (the hole concentration per Cu) ∼

0.12,[5] suggestingthat the ln(1/T)dependence may be
2
v Magnetic fields can tune the electronic state of a common feature of ρab in the normal state of the un-
8 strongly-correlated electron systems. It is well-known derdoped high-Tc cuprates at low temperatures.
8 that magnetic fields strongly affect the superconducting Recently, magnetic-field effects on the charge-spin
0 properties as well as the normal-state ones. For conven- stripe order [6, 7] have also attracted great interest.
5
tional superconductors, the superconducting transition Elastic neutron scattering measurements in magnetic
0
curve in magnetic fields shifts to the low-temperature fields for LSCO with x = 0.10 (Ref. [8]) under the
4
side in parallel with increasing field, which is attributed orthorhombic mid-temperature (OMT) structure (space
0
/ tothesmallsuperconductingfluctuationoriginatingfrom group: Bmab) have revealedthat the intensity of the in-
t
a the large superconducting coherence length. (This is commensuratemagneticpeaksaround(π,π)intherecip-
m called a parallel shift.) For the high-Tc cuprates, on rocallattice space increases with increasing field parallel
the other hand, the superconducting transition curve to the c-axis, suggesting the stabilization of the mag-
-
d shows a so-called fan-shape broadening in the under- netic order. For LSCO with x = 0.12, on the other
n doped regime, [1, 2] which is attributed to the large hand,the enhancementofthe incommensuratemagnetic
o
superconducting fluctuation originating from the small peaks is observable but small. [9] The magnetic order
c
superconducting coherence length and the quasi-two- is considered to be almost stabilized even in zero field
:
v dimensional superconductivity. for x ∼ 1/8, [10, 11] so that the development of the
i
X As for magnetic-fieldeffects on the normal-stateprop- magnetic order by the application of magnetic field is
erties, some interesting behaviors of the normal-state slight. The enhancement of the incommensurate mag-
r
a electricalresistivityatlowtemperaturesbelowthesuper- netic peaks has also been observedfor the excess-oxygen
conducting transition temperature Tc have been found doped La2CuO4+δ (LCO) with the stage-4 and state-6
through the destruction of the superconductivity by structures. [12, 13] For La1.6−xNd0.4SrxCuO4 (LNSCO)
the application of magnetic field. In the underdoped withx=0.15wherethecharge-spinstripeorderisstabi-
La2−xSrxCuO4 (LSCO), for example, the in-plane re- lizedunder the tetragonallow-temperature(TLT) struc-
sistivity, ρab, in the normal state exhibits an insulating ture (space group: P42/ncm), on the contrary, field ef-
behavioratlowtemperatures,diverginginproportionto fectsonneitherthechargenormagneticpeaksassociated
ln(1/T),thoughtheoriginoftheln(1/T)dependencehas with the charge-spin stripe order have been observed up
notbeenclarified.[3,4]Theln(1/T)dependencehasalso to 7 T. [14] These results suggest that a sort of spin
been observed in the underdoped Bi2Sr2−xLaxCuO6+δ stripe order in the OMT phase of LSCO and in LCO is
2
100 KSuozikuke ie et ta al.l. La2-xBaxCuO4 Cetr aalw.ford La1.6-xNd0.4SrxCuO4 II. EXPERIMENTS
Present
80 work Present OMT Single crystals of LBCO with x=0.08, 0.10, 0.11 and
work T
d2 LNSCO with x = 0.12 were grown by the traveling-
T [K] 60 OMT Td2 s4olbveanr.t floTahteingd-eztoanieledmeptrhoocdeduunredserarfleowdiensgcrOib2edgaeslsoe-f
40 Pccn
TLT TLT where. [20] Ba and Sr contents of each crystal were ana-
lyzed by the inductively-coupled-plasma (ICP) measure-
20
T
Tc c ments. The ρab was measured by the standard dc four-
0 probe method on field cooling in magnetic fields parallel
0.04 0.06 0.08 00..110 0.12 0.14 0.16 0.06 0.08 00..110 0.12 0.14 0.16
to the c-axis up to 15 T.
x (Ba) x (Sr)
FIG. 1: (left) Phase diagram of La2−xBaxCuO4. Open cir- III. RESULTS
clesrepresentTc,definedasthemid-pointtemperatureinthe
resistive superconducting transition. [15] Open squares rep-
Figure 2 displays the temperature dependence of ρab
resent the structural phase transition temperature between
in various magnetic fields for LBCO with x=0.08,0.10,
theOMTandTLTphases,Td2.[16](right)Phasediagramof
0.11 and LNSCO with x = 0.12. For x = 0.10, 0.11 and
La1.6−xNd0.4SrxCuO4. [17] Open circles represent Tc. Open
squaresrepresentthestructuralphasetransitiontemperature 0.12, a jump in ρab is observed at Td2 ∼ 41 K, ∼ 51 K
betweentheOMTandTLT/Pccnphases,Td2. Opentriangles and ∼ 67 K with decreasing temperature, respectively.
representthetemperaturebetweenthePccnandTLTphases. For x = 0.08, no jump is observed, suggesting that no
Closedcirclesandsquaresinthebothdiagramsrepresentthe structural transition to the TLT phase occurs and that
present Tc and Td2 estimated from the ρab measurements, theOMTphaseremainsatleastdowntothelowestmea-
respectively. sured temperature of 1.5 K. [18]
Focusing the attention on the superconducting tran-
sition curve, the broadening is observed with increasing
field for x=0.08,asusually observedin the underdoped
stabilized by the application of magnetic field, while the high-Tc cuprates. For x = 0.11, on the other hand, it
is found that the superconducting transition curve shifts
charge-spin stripe order in the TLT phase of LNSCO is
to the low-temperature side in parallel with increasing
almost never affected.
field. [21] To be more visible, contour maps of ρab in
In this paper, with the aim to clarify the relation be- the H vs T plane are shown in Fig. 3 for LBCO with
tween the superconducting and normal-state properties x=0.08, 0.10 and 0.11. In each x, the region where the
andtheformationofthestripeorder,wehaveperformed color starts to change from that at high temperatures of
ρab measurements in magnetic fields up to 15 T for the ∼60Kwithdecreasingtemperatureroughlycorresponds
single-crystal La2−xBaxCuO4 (LBCO) with x = 0.08, totheonsetregionofthesuperconductingtransition. For
0.10, 0.11 and LNSCO with x = 0.12. As shown in x = 0.08, it is found that the relatively sharp transition
Fig. 1, it is noted that both LNSCO with x = 0.12 of ρab around Tc in zero field is broadened with increas-
and LBCO with x = 0.11 are located in the regime ing field. For x = 0.11, on the contrary, the transition
where the superconductivity is suppressed in the neigh- of ρab around Tc remains sharp even in magnetic fields.
borhood of p = x = 1/8, while LBCO with x = 0.08 The parallel shift of ρab is also observed for x = 0.12 in
is located outside this regime. LBCO with x = 0.10 LNSCO as shown in Fig. 2. These suggest an intimate
is just at the boundary between the inside and outside relationbetweenthe parallelshift andthe suppressionof
of this regime. In the elastic neutron scattering mea- superconductivity around p = 1/8 or the formation of
surements of LBCO [18] and LNSCO [6, 7], the incom- the charge-spinstripe order.
mensurate elastic charge and magnetic peaks associated A remarkable feature is for x = 0.10 that the super-
with the stripe order have been observed for x = 0.10 conducting transition curveshows the broadening in low
and 0.12 below the structural phase transition temper- fields, while it changes to the parallel shift in high fields
ature between the OMT and TLT/Pccn phases, Td2, in above 9 T. In Fig. 3, it is found that the broad transi-
zero field, but not for x = 0.08. These mean that the tionofρab aroundTc below9Tchangestothesharpone
static charge-spinstripe order is formed at low tempera- above 9 T for x = 0.10. This dramatic change indicates
tures below Td2 for x = 0.10, 0.11 and 0.12 even in zero that the application of magnetic field causes a crossover
field. Moreover, it has been found that the intensity of from the usual state of the underdoped high-Tc cuprates
the elastic charge peaks is weaker in x = 0.10 than in to the peculiar state around p=1/8.
x∼1/8 of LBCO, [18, 19] suggestive of a less-stabilized Another remarkable feature observed for x = 0.10
static charge order in x = 0.10. For x = 0.08, on the is that the normal-state-like behavior of ρab, character-
other hand, the stripe order is not stabilized even at low ized by the almost linear T-dependence, is observed be-
temperatures. tween Td2 and the onset temperature of superconductiv-
3
FIG. 2: (color online) Temperature dependence of the in-plane electrical resistivity, ρab, in various magnetic fields parallel to
the c-axis for La2−xBaxCuO4 with x = 0.08, 0.10, 0.11 and La1.6−xNd0.4SrxCuO4 with x = 0.12. The temperature where
a jump of ρab occurs is in correspondence to the structural phase transition temperature between the OMT and TLT/Pccn
phases, Td2.
ity, Tconset, of ∼ 15 K at 9 T and that ρab between Td2 the superconducting transition curve in magnetic fields.
and Tonset increases with increasing field above 9 T and Both LBCO with x = 0.11 and LNSCO with x = 0.12
c
finally exhibits an insulating behavior forH ≥13 T. For arepeculiarsamplesaroundp=1/8characterizedbythe
x=0.11and0.12,onthe otherhand, the increaseofρab parallel shift of the superconducting transition curve in
between Td2 and Tconset with increasing field is negligi- magnetic fields. LBCO with x =0.10 is a rather unique
bly small up to 15 T, compared with that for x = 0.10. sample that shows the broadening in low fields and the
To be summarized, LBCO with x = 0.08 is a typical parallel shift in high fields above 9 T and whose ρab in
underdoped sample characterized by the broadening of the normal state below Td2 markedly increases with in-
4
La Ba CuO teristic of the underdoped high-Tc cuprates with large
2-x x 4 superconducting fluctuation. [1, 2] On the other hand,
x = 0.08 m] the parallelshift of the superconducting transitioncurve
c is observed for x = 0.11 and 0.12 and for x = 0.10
(cid:1)(cid:1)(cid:1)(cid:1)
m above 9 T. The parallel shift has also been observed
[ in LNSCO with x = 0.15 (Ref. [14]) and LSCO with
b
a x = 0.12 (Ref. [22]) where the static stripe order of
(cid:0)(cid:0)(cid:0)(cid:0)
charges and/or spins is formed at low temperatures.
Thesesuggestthatboththesuperconductivitywithsmall
superconducting fluctuation and the static stripe order
are realized in one sample. Here, it is an important is-
sue whether the superconducting region and the static
stripe-ordered one coexist microscopically or are sepa-
ratedmacroscopically. Fromtheneutronscatteringmea-
x = 0.10 surements in La1.875Ba0.125−xSrxCuO4, the static stripe
order has been suggested to compete with the supercon-
]
m ductivity. [23] Moreover, from the muon-spin-relaxation
c
(cid:1)(cid:1)(cid:1)(cid:1) measurementsinLa2−xSrxCu1−yZnyO4 aroundx=1/8,
m it has been suggested that the superconductivity is de-
] [
T b stroyed in a region where frequencies of the dynamical
H [ (cid:0)(cid:0)(cid:0)(cid:0)a stripe fluctuations are lower than ∼1011 Hz. [24] There-
fore, the superconducting region and the static stripe-
ordered one are probably separated macroscopically.
The reason why the superconductivity with small su-
perconductingfluctuationisrealizedinasamplewiththe
static stripe-ordered region is still an open question. A
possible origin is that the out-of-plane superconducting
coherence length, ξc, might be relatively large under the
x = 0.11 influenceofthecorrelationofthestaticstripeorderalong
] thec-axis,[7,25]leadingtothethree-dimensionalsuper-
m
c conductivity with small superconducting fluctuation.
(cid:1)(cid:1)(cid:1)(cid:1)
m Next, we discuss the relation between the change of
[b the normal-state behavior of ρab in magnetic fields and
a
(cid:0)(cid:0)(cid:0)(cid:0) the field-induced stripe order. Considering the results of
theelasticneutronscatteringmeasurements[6,7,18,19]
mentioned in Sec. I, the negligibly small increase of ρab
below Td2 with increasing field for x = 0.11 and 0.12
seemstoindicatethatthestripeorderisnearlyperfectly
stabilized in zero field and is insensitive to the applied
field. [14] As for x = 0.10, the marked increase of ρab
below Td2 with increasing field reminds us some possible
origins. The first is the normal-state magnetoresistance.
T [K]
However,thisisnotapplicable,becausethenormal-state
magnetoresistance is usually as small as an order of 1 %
at 15 T, as in the case of x = 0.11 and 0.12. The sec-
FIG. 3: (color online) Contour maps of ρab in the H vs T
ondisthesuppressionofthesuperconductingfluctuation
plane for La2−xBaxCuO4 with x=0.08, 0.10 and 0.11.
by the applied field. The positive magnetoresistance ap-
pearsevenattemperaturesjustbelowTd2farfromTconset
in high fields. On the other hand, reports on the Nernst
creasing field up to 15 T.
effect in LSCO have suggested that the vortex state sur-
vives evenat higher temperatures far aboveTc, meaning
that the superconducting fluctuation exists even at high
IV. DISCUSSION
temperatures.[26,27]Therefore,thispossibleorigincan-
notbeexcludedandfurthermeasurementsareneededto
First, we discuss the intimate relationbetween the su- conclude. Nevertheless,itappears thatthis is not a can-
perconducting transition curve and the stripe order. It didate, because the large positive magnetoresistance is
is well-known that the broadening of the superconduct- observedonlyforx=0.10andnotforx=0.11nor0.12.
ing transition curve observed for x = 0.08 is charac- The third is enhancement of the localization of holes in-
5
for H ≥ 11 T, as seen in Fig. 2. The slope of the
ln(1/T) dependence is found to increase with increas-
ing x, indicating that the localization of holes becomes
strong with increasing x toward x = 1/8 at 15 T. The
ln(1/T) dependence is known to be characteristic of the
weaklocalizationandtheelectron-electroninteractionin
the two-dimensional Anderson-localized state where the
in-plane electrical conductivity σab actually changes in
proportion to ln(1/T) even in magnetic fields. [28] For
x=0.10, 0.11 and 0.12, however, σab does not show the
ln(1/T) dependence below Td2, as in the case of the un-
derdoped LSCO. [3, 4] Although the true origin of the
ln(1/T) dependence of ρab is not clear, the localization
of holes with the ln(1/T)dependence observedwidely in
the underdoped high-Tc cuprates is robust even in the
stripe-ordered state of LBCO and LNSCO. [29]
V. SUMMARY
FIG.4: PlotofρabvslnT at15TforLa2−xBaxCuO4(LBCO) It has been found that the superconducting transition
withx=0.10,0.11andLa1.6−xNd0.4SrxCuO4(LNSCO)with
curve shows the parallel shift by the application of mag-
x=0.12.
netic field in LBCO with x = 0.11 and LNSCO with
x = 0.12 where the charge-spin stripe order is formed
duced by the applied field. The localization behavior of at low temperatures. These suggest that both the su-
ρab becomesmarkedwithincreasingfieldandappearsto perconductivity with small superconducting fluctuation
approach the behavior of LNSCO with x = 0.12 where and the static stripe order are realized in one sample for
the stripe order is perfectly stabilized. In the long run, x=0.11 and 0.12. For LBCO with x=0.10, the broad-
the most probable origin is that the charge-spin stripe ening in low fields changes to the parallel shift in high
order is stabilized by the applied field in x = 0.10. This fields above 9 T. Moreover, ρab in the normal state be-
maybethefirstexperimentalevidence,toourknowledge, low Td2 increases with increasing field up to 15 T. It is
ofthechargestripeorderstabilizedinmagneticfields. To possible that these pronounced features of x = 0.10 are
bemoreconclusive,theneutronscatteringmeasurements understood in terms of the field-induced stabilization of
in magnetic fields are under way. the charge stripe order. The ρab in the normal state at
Finally, we discuss the temperature dependence of ρab low temperatures has been found to be proportional to
belowTd2. Sofar,ithasbeenclarifiedintheunderdoped ln(1/T) for x = 0.10, 0.11 and 0.12, suggesting the lo-
LSCO and BSLCO [3, 4, 5] that ρab in the normal state calization of holes with the ln(1/T) dependence of ρab
shows the ln(1/T) dependence at low temperatures in whichisrobusteveninthestripe-orderedstateofLBCO
magnetic fields, suggesting that the ln(1/T) dependence and LNSCO.
isacommonfeatureoftheunderdopedhigh-Tc cuprates.
To check this suggestion, ρab’s of LBCO with x = 0.10,
0.11 and LNSCO with x=0.12 at 15 T are plotted ver- Acknowledgments
sus lnT, as shown in Fig. 4. Below ∼ 20 K, it is found
thatρab inthenormalstateisproportionaltoln(1/T)in The high magnetic field experiments were partly sup-
each x, though ρab deviates downward from ln(1/T) at ported by the High Field Laboratory for Superconduct-
lowtemperatures becauseofthe superconductingtransi- ingMaterials(HFLSM),InstituteforMaterialsResearch,
tion for x= 0.10 and 0.11. The small deviation below 3 TohokuUniversity. ThisworkwassupportedbyaGrant-
K for x=0.12 is irrelevantto the superconducting tran- in-Aid for Scientific Research from the Ministry of Edu-
sition, because ρab is independent of the field strength cation, Science, Sports, Culture and Technology, Japan.
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