Hall coefficient in the ground state of stripe-ordered La_2-x_Ba_x_CuO_4_ single crystals

0.4 MB·English

by  T. Adachi

Hall coefficient in the ground state of the charge stripe-ordered La Ba CuO single
2−x x 4
crystals
T. Adachi, N. Kitajima, and Y. Koike
Department of Applied Physics, Graduate School of Engineering, Tohoku University,
0 6-6-05 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan
1 (Dated: September16, 2010)
0
2 Temperature dependence of the Hall coefficient, RH, has been investigated in charge-spin
stripe-ordered La-214 high-Tc superconductors. Using the simplest stripe-ordered system of
p La2−xBaxCuO4, it has been clarified for the first time, to our knowledge, that both the behav-
e ior of RH and its sign exhibit significant dependences on the hole concentration. That is, RH is
S
zero in the ground state of the charge-spin stripe order at x=1/8, while it is negative in the less-
5 stabilized state of thecharge stripe for x<1/8. These are interpreted as being due to thedelicate
1 balance of the contributions of the hole-like Fermi surface and the possible electron pocket arising
from theformation of thecharge-spin stripe order.

]
n
o The Hall coefficient, RH, in the high-Tc superconduct- possible formation of the charge stripe order. In YBCO,
c
ing (SC) cuprates has attracted considerable attention however, effects of the possible charge stripe order on
-
r due to its peculiar behavior since the early stage of the variousphysicalproperties are relatively weakcompared
p
high-Tc research. The RH inthe normalstate is strongly with those in the La-214 cuprates, preventing one from
u
dependent on temperature, which is unusual in conven- understanding explicitly the relation between the elec-
s
. tional metallic superconductors. The temperature de- tron pocket and the charge stripe order.
t
a pendenceofRH athightemperatureshasbeenexplained In this Letter, RH in the charge stripe-ordered state
m
based upon the Fermi-liquid model [1] or the two-carrier is investigated in La-214 cuprates with various values of
- model [2] taking into accountspin fluctuations or charge p. It has been found for the first time, to our knowl-
d fluctuations, respectively, but the behavior at low tem- edge, in LBCO with x = 0.08−0.12 and LNSCO with
n
o peratures has not yet been understood. x = 0.12 that the behavior of RH including the sign at
c TheexperimentalresultsofRH atlowtemperaturesin low temperaturesexhibits a significantdependence onp.
[ theLa-214cupratessuchasLa2−xBaxCuO4 (LBCO)[3– That is, RH for x = 0.10−0.12 undergoing the phase

2 5] and La1.6−xNd0.4SrxCuO4 (LNSCO) [6] around transitiontothe TLTphasemarkedlydecreaseswithde-
v x = 1/8 have revealed that RH markedly decreases creasingtemperaturebelowTd2. Moreover,asignchange
2 withdecreasingtemperaturebelow the structural-phase- of RH is observed at low temperatures for x = 0.10 and
5 transition temperature between the tetragonal low- the absolute value of the negative RH decreases with in-
4 temperature (TLT) phase (space group: P42/ncm) creasing x, followed by almost zero for x = 0.12 where
3 and the orthorhombic mid-temperature (OMT) phase thechargestripeorderiscompletelystabilized. Thesere-
9. (Bmab), Td2. This has been explained as being due sults indicate that RH is zero in the ground state of the
0 to the disappearance of the Hall voltage in the one- charge-spinstripeorderatx∼1/8andthatRH becomes
9 dimensional (1D) charge stripe-ordered state [7] stabi- negative in the less-stabilized state of the charge stripe.
0 lized through the structural phase transition [6] or due It appears that there exists a close correlation between
:
v to the cancellation of the Hall voltage by equal numbers the stability of the charge stripe order, the sign of RH
i ofholesandelectronsinthechargedomaininthestripe- and the topology of the Fermi surface discussed later.
X
orderedstate,[8]althoughitisstillcontroversial. Agrad- SinglecrystalsofLBCOwithx=0.08,0.10,0.11,0.12
r
a ual decrease in RH in the normal state with decreasing and LNSCO with x=0.12 were grown by the traveling-
temperature at low temperatures has been observed in solvent floating-zone method. The detailed procedures
YBa2Cu3O7−δ (YBCO) with δ = 0.15−0.40 (Ref. [9]) are described elsewhere. [4, 12] The composition of each
and slightly Zn-substituted La2−xSrxCu1−yZnyO4 with crystal was analyzed by the inductively-coupled-plasma
x = 0.115 and 0.15, [10] which has been discussed in analysis. For LBCO and LNSCO with x = 0.10−0.12,
relation to the formation of the charge stripe order. the charge stripe order is formed at low temperatures
Recently, measurements of RH in high magnetic fields below Td2, [7, 13, 14] while it is not for LBCO with x=
for underdoped YBCO with the hole concentration per 0.08.[14]BothRH andthe ab-planeelectricalresistivity,
Cu in the CuO2 plane, p, = 0.10−0.14 by LeBoeuf et ρab,weremeasuredbythestandardacsix-probemethod
al.[11]haverevealedasignchangeofRH atlowtemper- inmagneticfieldsparalleltothec-axisupto9T,usinga
atures. They have proposed that the negative RH origi- commercial apparatus (Quantum Design, PPMS). Both
nates from the formation of an electron pocket through temperature and magnetic-field dependences of the Hall
the reconstruction of the Fermi surface caused by the voltage were measured, resulting in good agreement of
2
2.0 0.3
La2-xBaxCuO4 9T 0 T x= 6 La2-xBaxCuO4 x = 0.10
0.08
0.10 I // ab-plane
1.5 0.11 H // c-axis 0.2
4
0K Td2 3m/C) cm)
8 / ρρρρρρρρababab 1.0 -3R (10 c (10H 2 RHT d ρρρρ2ab H9 T 0.1 (mΩΩρρΩΩρρabab
6
0.5 9T 0 T x= 0 4 0
0.12-A 2
0.12-B 1
LNSCO 0
(0.12) -2
0 0 10 20 30 40 50 60
0 20 40 60 80 T (K)
T (K)
FIG. 2: (color online) Temperature dependences of the Hall
FIG. 1: (color online) Temperature dependence of the ab- coefficient, RH, (left axis) and the ab-plane electrical resis-
plane electrical resistivity, ρab, in zero field and a magnetic tivity, ρab, (right axis) in various magnetic fields parallel to
field of 9 T parallel to the c-axis normalized by its value at the c-axis up to 9 T for La2−xBaxCuO4 with x=0.10. The
80 K, ρ8a0bK, for La2−xBaxCuO4 with x = 0.08 −0.12 and arrow indicates the structural-phase-transition temperature
La1.6−xNd0.4SrxCuO4 (LNSCO) with x = 0.12. Note for between the TLT and OMT phases, Td2.
La2−xBaxCuO4 with x = 0.12 that the descriptions ’A’ and
’B’ correspond to different batches of the crystal. Arrows
indicatethestructural-phase-transition temperaturebetween
theTLT and OMT phases, Td2. because their reported ρab in zero field is metallic even
below Td2, suddenly drops around 40 K and decreases
gradually toward zero with decreasing temperature.
values of RH each other. Temperature dependences of RH and ρab in various
Figure 1 shows the temperature dependence of ρab in magnetic fields up to 9 T are displayed in Fig. 2 for
zerofieldandamagneticfieldof9Tparalleltothec-axis LBCO with x = 0.10. It is noted that similar tempera-
normalized by its value at 80 K for LBCO and LNSCO ture dependences of RH and ρab are observed for LBCO
with x = 0.08−0.12. A jump in ρab due to the struc- with x = 0.11 (Ref. [5]). With increasing field, the SC
tural phase transition to the TLT phase is observed for transitioncurveinρab vs. T exhibits broadeningcharac-
x = 0.10−0.12, as shown by arrows. For LBCO, Td2 teristic ofthe underdopedhigh-Tc cuprates.[12]The RH
systematicallyincreaseswithanincreaseinx, the values isalmostindependentoftemperatureaboveTd2,whereas
ofwhicharealmostinagreementwiththoseformerlyre- itsuddenlydecreasesbelowTd2. Moreover,asignchange
ported.[15]Inzerofield, ρab exhibitsametallicbehavior of RH is observed below about 26 K and eventually RH
belowTd2 forx=0.10and0.11,whereasitisless metal- goes to zero at low temperatures. Since temperatures at
lic or semiconducting for x = 0.12. The behavior of ρab which RH and ρab become zero are in good agreement
for x=0.12 is typical of the sample with p∼1/8 where with each other, the behavior of RH going to zero at low
the charge stripe order is stabilized. For x = 0.12 in temperaturesisduetotheSCtransition. Accordingly,it
LBCO, ρab gradually decreases with decreasing temper- is concluded that the sign of RH in the ground state of
atureroughlybelow30Kandgoestozero,whichmaybe LBCO with x=0.10 is negative.
duetotiny inclusionofregionsofx<0.12havinghigher Figure 3 shows the p-dependent behavior of RH in 9
SCtransitiontemperatures,Tc’s,inthesample. Itisalso T parallel to the c-axis. For LBCO with x = 0.11, data
probable that the different behavior of ρab between the of RH obtained from the measurements of the magnetic-
sample ’A’ and ’B’ of x = 0.12 is due to the different fielddependence ofthe Hallvoltageat70K(aboveTd2),
amountoftiny inclusionofx<0.12. Fromthe magnetic 45K(alittlebelowTd2)and30K(atatemperaturewith
susceptibility measurements, in fact, Tc, defined as the negative RH) are also plotted, exhibiting a good agree-
cross point between the extrapolated line of the steepest ment with data of RH obtained from the measurements
part of the shielding diamagnetism and zero susceptibil- of the temperature dependence of the Hall voltage in 9
ity, is estimated to be as low as 4.2 K, indicating that T.Athightemperaturesaround80K,RH isfoundto be
most regions in the sample are made of x = 0.12. It is positive anddecrease with increasing x, as in the case of
noted that the present behavior of ρab for x = 0.12 in La2−xSrxCuO4 (LSCO) single crystals. [2] For x=0.08,
LBCO is different from that reported by Li et al., [16] RH above the onset temperature of the SC transition,
3
(0, ππππ) First, the marked decrease in RH below Td2 is dis-
cussed. The sudden decrease in RH accompanied by the
formation of the charge stripe order has formerly been
10 La Ba CuO
2-x x 4 observed in LBCO [3–5] and LNSCO. [6] These former
x= 0.10 results of RH are compatible with the present ones. A
8
0.12 possible origin of the decrease in RH together with the
((((0, 0) ((((ππππ, 0) formationofthechargestripeorderhasbeenproposedby
) 6 Noda et al. [6] to be the disappearance of the Hall volt-
C
3/ age due to the formation of a 1D charge domain in the
m
c 4 stripe-ordered state. From direct numerical calculations
3 including a stripe potential within the t-J model, on the
-00
11 TT otherhand,Prelovˇseket al.[8]havesuggestedthatequal
( (H 22 d2 numbersofholesandelectronsduetothehalfoccupancy
R
x= 0.08 ofholes in the chargedomainleads to the disappearance
0 0.10 of the Hall voltage. For x = 0.10 and 0.11 where the
0.11
0.12-A half occupancy in the 1D charge domain is guessed to
-2 Tconset I // ab-plane LNS0C.1O2-B be maintained, [14] however, RH exhibits negative finite
H = 9 T (// c-axis) (x= 0.12) values at low temperatures, as shown in Fig. 3. There-
-4 fore,thesetwowaysofthinkingarenotenoughtoexplain
0 20 40 60 80 thelow-temperaturebehaviorofRH inthestripe-ordered
T (K) state.
The sign change of RH is often observed in the SC
fluctuation regime, which is understood to be due to the
FIG.3: (coloronline)TemperaturedependenceoftheHallco- vortex motion. In this case, it has been suggested that
efficient,RH,in9Tparallel tothec-axisforLa2−xBaxCuO4 the application of magnetic field tends to suppress the
(LBCO) with x = 0.08 − 0.12 and La1.6−xNd0.4SrxCuO4 sign change. [17] As shown in Fig. 2, however, the sign
(LNSCO) with x=0.12. Note for LBCO with x=0.12 that change is not suppressed but enhanced by the applica-
the descriptions ’A’ and ’B’ correspond to different batches
tionofmagneticfield,andmoreover,RH isnegativeeven
of the crystal. Solid arrows indicate the structural-phase- in the normal state above Tonset for x = 0.10 and 0.11.
transition temperature between the TLT and OMT phases, c
Therefore,the vortexmotionisnotthe originofthe sign
Td2. Open arrows indicate the onset temperature of the SC
transition,Tconset,in9Testimatedfromρab showninFig. 1. change of RH in LBCO with x = 0.10 and 0.11. Sim-
OpendiamondsshowdataofRH obtainedfromthemeasure- ply thinking, the sign of RH is sensitive to the subtle
ments of the magnetic-field dependence of the Hall voltage curvature of the Fermi surface. As mentioned before,
for LBCO with x = 0.11. The inset is a schematic drawing recently, LeBoeuf et al. [11] have found a pronounced
of one possible reconstruction of the Fermi surface through sign change of RH at low temperatures in strong mag-
the formation of a commensurate antiferromagnetic order or netic fields in underdoped YBCO with p = 0.10−0.14.
ad-density-waveorder[21]forLBCOwithx=0.10and0.12. SincequantumoscillationshavebeenobservedinYBCO
with p = 0.10, [18] they have suggested that the neg-
ative RH is a product of the formation of an electron
Tconset, estimated from ρab in 9 T shown in Fig. 1, is pocket through the Fermi-surface reconstruction caused
by the possible formation of the charge stripe order. A
almostindependentoftemperature,whereasitgradually
decreases with decreasing temperature below Tonset due similar behavior of RH has formerly been found in 2H-
c
to the SC transition. For x = 0.11 and 0.12, on the TaSe2 where both a strong decrease and a sign change
other hand, RH markedly decreases below Td2 as well as ofRH areobservedaccompaniedby the transitionto the
for x = 0.10 shown in Fig. 2. Since Tonset is far below charge-density-wave (CDW) state. [19] These have the-
c
oretically been explained in terms of the Fermi-surface
Td2, the marked decrease in RH is irrespective of the SC
reconstruction due to the opening of the CDW gap. [20]
transition. Comparing the data of x = 0.10 with those
of x = 0.11, the extrapolation of the data above Tonset Accordingly, the sign change of RH at low temperatures
c
in LBCO with x = 0.10 and 0.11 is possibly explained
to zero temperature suggests that the sign change of RH
as being due to the creation of an electron pocket on
is more marked for x = 0.10 than for 0.11, as shown
the Fermi surface caused by the formation of the charge
by broken lines in Fig. 3. For LBCO and LNSCO with
stripe order.
x=0.12,on the other hand, RH becomes almostzero at
low temperatures. These results are summarized as fol- Then, why does the behavior of RH at low tem-
lows. For the samples in the TLT phase andtherefore in peratures depend on p significantly? Supposed that
the charge stripe-ordered state, RH markedly decreases the Fermi surface in the underdoped cuprates is recon-
with decreasing temperature below Td2. Moreover, the structed through the formation of a commensurate anti-
sign change of RH at low temperatures exhibits a signif- ferromagnetic(AF)orderorad-density-wave(dDW)or-
icant dependence on p. der,[21]bothholepocketsandanelectronpocketarecre-
4
atedonthe Fermisurface,locatedaround(±π/2, ±π/2) of the charge stripe order for x<1/8.
and (±π, 0), (0, ±π) in the reciprocal lattice space,
Finally,we commentonthe value ofRH in the ground
respectively, which is schematically shown in the inset
state of LBCO. For x = 0.10, the extrapolated value
of Fig. 3. Actually, recent angle-resolved photoemis-
of RH to zero temperature is estimated from Fig. 3
sion experiments have revealed a pocket around (π/2, to be −0.00375 cm3/C. Thus, based on the simple one-
π/2).[22,23]Consideringthe p-dependentchangeofthe
carrier model, the carrier density nHall is calculated to
Fareormuni-dsu(r±faπc,e0t)o,p(o0lo,g±y,π[)24t]enthdesptoosssihbrlienkelewctitrhoninpcorcekaest- be nHall = −Vcell/eRH/2 = 0.0795 per Cu in the CuO2
plane,whereVcell isthevolumeoftheunitcellintheno-
ing p, as shown in the inset of Fig. 3. This is naturally
tationofthetetragonalathightemperature(I4/mmm).
suggestive of the weakening of the electron aspect and
For YBCO with p =0.10, [11] on the other hand, it has
the development of the hole aspect on RH with increas- been reported that nHall = 0.0145 per Cu in the CuO2
ing p. This picture is consistent with the present results
plane. This value is comparable to the deduced value
thatthe signchangeofRH graduallyweakensandRH at of 0.019 per Cu in the CuO2 plane from the quantum-
low temperatures becomes zero with increasing x from
oscillationexperiments.[18]Assumingthenegativevalue
x = 0.10 to 0.12. It is noted that RH is positive at of RH is originated from a possible pocket on the Fermi
low temperatures for LNSCO with x = 0.15, [6] which
surface, a simple comparison of nHall between LBCO
is also consistent with this picture. Accordingly, the p-
and YBCO results in a larger pocket in LBCO than in
dependentchangeofRH inthegroundstateisabletobe YBCO. This appears to be inconsistent with that ex-
understood by the delicate balance of the contributions
pected from the experimentally observed Fermi-surface
of hole and electron pockets.
topology,[24,28]becausethereconstructedFermisurface
Millis et al. [25] and Lin et al. [26] have theoretically
due to the commensurate AF order or the dDW order
investigated the Fermi-surface reconstruction within the
is expected to produce a larger electron pocket around
tight-binding model including the charge andspin stripe (±π,0), (0,±π) in YBCO than in LBCO. Accordingly,
potential. Accordingtotheircalculations,rathercompli-
it is hard to make quantitative discussion on the neg-
cated arrangement of electron pockets and hole pockets
ative value of RH in the ground state using the simple
is reconstructed and the development of the spin stripe
one-carrier model.
correlationmakesRH negative,whilethedevelopmentof
the charge stripe correlation makes RH positive. That In conclusion, RH in the stripe-ordered LBCO and
LNSCOinthe TLTphasemarkedlydecreasesdue tothe
is,inthe charge-spinstripe-orderedstate,the signofRH
formation of the charge-spin stripe order. In the ground
depends on the delicate balance of the developments of
the charge and spin stripe order. Based upon their cal- state, on the other hand, RH is zero in the completely
ordered charge-spin stripe state at x = 1/8, while it is
culations, it follows that RH becomes zero due to com-
negative in the less-stabilized state of the charge stripe
plete developments of both charge and spin stripe order
at x = 1/8 and that RH becomes negative due to the for x < 1/8. The p-dependent behavior of RH including
itssignisinterpretedasbeingduetothedelicatebalance
incomplete development of the charge stripe order for
ofthecontributionsofthehole-likeFermisurfaceandthe
x < 1/8. [14] Actually, the sign change of RH has been
observed in YBCO with p = 0.10−0.14 (Ref. [11]) and possibleelectronpocketarisingfromtheformationofthe
charge-spinstripe order.
LSCOwithx=0.12(Ref.[27])wherethespinstripecor-
relation is developed but the charge stripe order is not. FruitfuldiscussionswithT.Tohyamaaregratefullyac-
Accordingly, it may be the case that RH becomes zero knowledged. ThisworkwassupportedbyaGrant-in-Aid
due tothe stabilizationofthe charge-spinstripeorderat for Scientific Research from the Ministry of Education,
x=1/8,while it becomes negative due to the instability Science, Sports, Culture and Technology, Japan.
[1] H.Kontani et al., Phys. Rev.B 59, 14723 (1999). [14] M. Fujita et al., Physica C 426-431, 257 (2005).
[2] S.Ono et al., Phys.Rev. B 75, 024515 (2007). [15] T. Suzuki, and T. Fujita, J. Phys. Soc. Jpn. 58, 1883
[3] M. Sera et al., Solid State Commun. 69, 851 (1989). (1989).
[4] T. Adachiet al., Phys.Rev.B 64, 144524 (2001). [16] Q. Li et al., Phys. Rev.Lett. 99, 067001 (2007).
[5] T. Adachiet al., J. Phys. Chem. Solids 63, 1097 (2002). [17] Y. Matsuda et al., Phys.Rev.Lett. 69, 3228 (1992).
[6] T. Noda et al., Science 286, 265 (1999). [18] N. Doiron-Leyraud et al., Nature (London) 447, 565
[7] J.M.Tranquadaetal.,Nature(London)375,561(1995). (2007).
[8] P.Prelovˇsek et al., Phys.Rev. B 64, 052512 (2001). [19] H. N.S. Lee et al., J. Solid StateChem. 1, 190 (1970).
[9] K. Segawa, and Y. Ando, Phys. Rev. B 69, 104521 [20] D. V. Evtushinsky et al., Phys. Rev. Lett. 100, 236402
(2004). (2008).
[10] T. Adachiet al., J. Low Temp. Phys. 117, 1151 (1999). [21] S. Chakravarty, and H.-Y. Kee, Proc. Natl. Acad. Sci.
[11] D.LeBoeuf et al., Nature (London) 450, 533 (2007). U.S.A. 105, 8835 (2008).
[12] T. Adachiet al., Phys.Rev.B 71, 104516 (2005). [22] J. Chang et al., New J. Phys. 10, 103016 (2008).
[13] M. Fujita et al., Phys. Rev.B 70, 104517 (2004). [23] J. Meng et al., Nature (London) 462, 335 (2009).
5
[24] A.Ino et al., Phys.Rev. B 65, 094504 (2002). [27] T. Suzukiet al., Phys.Rev.B 66, 104528 (2002).
[25] A. J. Millis, and M. R. Norman, Phys. Rev. B 76, [28] K. Nakayamaet al., Phys.Rev.B 75, 014513 (2007).
220503(R) (2007).
[26] J.Lin,andA.J.Millis, Phys.Rev.B78,115108 (2008).