Magnetic-field-induced spin excitations and renormalized spin gap of the underdoped superconductor La$_{1.895}$Sr$_{0.105}$CuO$_{4}$

0.15 MB·English

by  J. Chang

Magnetic-field-induced spin excitations and renormalized spin gap of the underdoped
superconductor La Sr CuO
1.895 0.105 4
J. Chang,1 A.P. Schnyder,2 R. Gilardi,1 H.M. Rønnow,1 S. Pailhes,1 N.B. Christensen,1,3
Ch. Niedermayer,1 D.F. McMorrow,4,5 A. Hiess,6 A. Stunault,6 M. Enderle,6 B.
7 Lake,7 O. Sobolev,7 N. Momono,8 M. Oda,8 M. Ido,8 C. Mudry,2 and J. Mesot1,∗
0
1 Laboratory for Neutron Scattering, ETH Zurich and PSI Villigen, CH-5232 Villigen PSI, Switzerland
0
2 Condensed Matter Theory Group, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
2
3 Risø National Laboratory, DK-4000 Roskilde, Denmark

n 4 London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London, UK
a 5ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, UK
J 6 Institut Laue-Langevin, BP 156, F-38042 Grenoble, France

7 7 BENSC Hahn-Meitner-Institut, 14109 Berlin Wannsee, Germany
1 8 Department of Physics, Hokkaido University - Sapporo 060-0810, Japan
(Dated: February 4, 2008)
]
n High-resolutionneutroninelasticscatteringexperimentsinappliedmagneticfieldshavebeenper-
o
formedonLa1.895Sr0.105CuO4 (LSCO).Inzerofield,thetemperaturedependenceofthelow-energy
-c peakintensityattheincommensuratemomentum-transferQIC =(0.5,0.5±δ,0),(0.5±δ,0.5,0)ex-
r hibitsananomaly at thesuperconductingTc which broadensandshifts tolower temperatureupon
p the application of a magnetic field along the c-axis. A field-induced enhancement of the spectral
u
weight is observed, but only at finite energy transfers and in an intermediate temperature range.
s
These observations establish the opening of a strongly downward renormalized spin gap in the un-
.
t derdoped regime of LSCO. This behavior contrasts with the observed doping dependence of most
a
m electronic energy features.
-
d
In studies of high-temperature superconductors functionofenergy~ω,magneticfieldH andtemperature
n
o (HTSC), one central challenge is to explain the evolu- T, we identify similarities and differences between the
c tion from anantiferromagnetic (AF) Mott insulator to a magneticresponseinthe underdopedandoptimaldoped
[ metallic superconductor upon doping. For example, the regimes of LSCO. Our main result is the observation of

1 intimate interplaybetweenmagnetismandsuperconduc- a dramatic field induced enhancementof the responseat
v tivity has been revealed in momentum resolved inelastic low energies and the identification, below T , of a SG in
c
4 neutronscattering (INS) experiments on La2−xSrxCuO4 the underdopedregime(x=0.105),whosecharacteristic
0
(LSCO) [1, 2, 3, 4, 5] and YBa Cu O (YBCO) [6, 7] energyisstronglyrenormalizedrelativetothatmeasured
4 2 3 6+x
that showed the opening of a spin gap (SG) ∆ at the atoptimaldoping. Wealsoshowthatthisbehaviorisnot
1 sg
0 superconducting (SC) critical temperature (Tc). In con- specific to LSCO but corresponds to what is observed
7 trastto the single-particleSCgapprobedby,e.g.,angle- in YBCO. Unlike at optimal doping, the opening of the
0 resolvedphotoemissionspectroscopy(ARPES)[8,9],the x=0.105SGisincompleteallthewaydowntothelowest
/
at SG scales with Tc in the overdoped to slightly under- achievable temperature.
dopedregime. Thesituationismorecomplicatedinmore
m Ourexperimentshavebeenperformedonalargecylin-
- underdoped samples. For instance, in YBCO the ratio drical single crystal of La2−xSrxCuO4 (m ∼ 3.86g,
d ∆sg/(kBTc) decreases with strong underdoping [10, 11], x = 0.105) grown by the traveling solvent floating
n while for underdoped LSCO (x <0.12) the changes are
zone (TSFZ) method [18]. The SC volume fraction
o even more dramatic, since no direct neutron scattering
was estimated from measurements of the specific heat
c
evidence for a SG has been reported so far [12]. This
: C. At T = 30K, we observed a jump of ∆C/T =
v latter fact would seem to indicate that the underdoped 2c c
3mJ/(K mol). Below T the electronic contribution
Xi regime of LSCO cannot be described in terms of a ho- was estimated to be Cs/cT = γs = 0.5mJ/(K2mol)
mogeneous electronic liquid and more exotic scenarios el el
r while in the normal state we found Cn/T = γn =
a have been suggested, such as the formation of dynami- el el
2
5.5mJ/(K mol). ThisindicatesthattheSCvolumefrac-
cal stripes [13] or presence of a d-density wave (DDW)
tion1−γs/γn islargerthan90%. Togetherwithasharp
order [14]. Further insight into the interplay between el el
SC transition(∆T =1.5K),this demonstratesthe high
magnetism and superconductivity in LSCO has been re- c
quality of the crystal. The structural transition from
vealed in a number of studies of the effects of an ap-
the high-temperature tetragonal to the low-temperature
plied magnetic field, which at optimal doping enhances
orthorhombic phase occurs at 290K, which confirms
thelow-energymagneticfluctuationsandatunderdoping
x = 0.105±0.005. The magnetic response is peaked in
induces static antiferromagnetism [15, 16, 17].
the reciprocal space at the incommensurate wave vector
In this paper, based on high-resolution INS data as a Q =(0.5±δ,0.5,0),(0.5,0.5±δ,0)(intetragonalunits
IC
2
14 a) 3 −hω=0 meV
VORTEX NORMAL T=2 K
d [T] 1102 LIQUID STATE H)/I(0) 2 .25
c fiel 8 I( 1 .15 a)
eti 6 Hc2(T)
n
Mag 4 2.5 −h−hωω==01. m3meVeV b)
2 VORTEX −hω=2 meV
LATTICE
0 0) 2 T=22.3 K
HH==100 TT b) H)/I( 1.5
−hω=1 meV I(
Q=Q
IC 1
n.
mi
30 120 0.5
er 0 2 4 6 8 10 12 14 16
s p Magnetic field [Tesla]
nt
u
o
C FIG. 2: Magnetic field dependence of the response at QIC
T
c for LSCO (x = 0.105). (a) Elastic response with T = 2 K.
80
The solid line is a theoretical prediction [15]. (b) Inelastic
response with T =22.3 K, solid lines are guides to theeye.
0 5 10 15 20 25 30 35 40 45 50
Temperature [K]
removed higher-order contamination from the scattered
FIG.1: (a)PhasediagramofunderdopedLSCO(x=0.105) beam. The sample was cut into two pieces which were
as a function of a magnetic field H and temperature T [20].
coaligned within less than a degree and mounted in a
Fullcirclesarethemeasuredvaluesforthemeltinglineofthe
15T verticalcryomagnetsuchthat momentumtransfers
vortex lattice [20]. The straight line is the position of T as
c Q=(Q ,Q ,0) were accessible. All measurements were
a function of H. The dashed arrows indicate the T and H h k
scans that are described in this paper. (b) Two T scans at performedafterfieldcoolingfromaboveTc. Withasim-
QIC and~ω=1meVtransfer. Opentriangles(filledsquares) ilar setup the field dependence of the elastic signal at
denote the measured intensity at H = 10T (H = 0T), solid the incommensurate wave vectors was measured on the
lines are guides to theeye. FLEX spectrometer at Hahn-Meitner Institute.
In Fig. 1b, we show the effect of H on the T depen-
dence of the intensity at Q with an energy transfer of
IC
of 2π/a = 1.65 ˚A−1 used throughout this paper). The ~ω =1 meV. These data demonstrate that the intensity
value δ =0.097±0.005is in line with a Sr concentration is enhanced by application of H =10T in an intermedi-
of x = 0.105±0.005 [19]. The sample has been charac- ated temperature range 10K < T < T , corresponding
c
terized by magnetization and ac-susceptibility measure- roughlytothe liquidregionofthe vortexphasediagram,
ments in magnetic fields H up to 8T along the crys- see Fig. 1a. A similar behavior was previously reported
tallographic c axis [20], as well as small-angle neutron for LSCO samples close to optimal doping [4, 16]. This
scattering (SANS) and µSR [21]. All measurements in- wasinterpretedintermsofinducedexcitationsinsidethe
dicate that in the underdoped regime of LSCO, the vor- vortex core [16]. In effect, H shifts and broadens the
tex liquid phase dominates the magnetic phase diagram, cusp-likeanomalyatT toalowerT (H). The shiftcor-
c c
while a quasi-long-range ordered vortex lattice can only respondsqualitativelytotheshiftinT asseeninFig.1a.
c
be observed at low fields/temperatures [21]. This con- We note that the lower limit on the field effect might be
trastswiththewell-orderedvortexlatticeobservedatall relatedto the onset atT =10KofCu moment freezing
f
fields in the low-temperature regime of optimally doped observed by µSR on the same sample [23].
LSCO[22]. Themeltinglineofthevortexlatticeisshown
Next, we plot in Fig. 2 the H dependence of the nor-
in Fig. 1a. malized intensity at Q . The elastic magnetic signal at
IC
INS measurements of the spin excitations were per- T =2Kexhibitsalargeenhancementinagreementwith
formed on the cold neutron spectrometer IN14 at the previous reports on samples of similar doping levels [17],
Institut Laue Langevin, Grenoble, France. We used a andiswellfittedbytheequationI ∼(H/H )ln(H /H)
c2 c2
vertically curved graphite monochromator and a hori- predicted by Demler et al. [15]. Remarkably, the inelas-
zontally curved graphite analyzer with fixed final energy tic response at T=23 K exhibits a field dependence at
E in the range 3.5−5 meV that gave an energy reso- low energy transfers similar to the elastic signal. The
f
lution of about 60−150 µeV. A cooled Beryllium-filter dependence on ~ω and Q of the intensity, taken at dif-
3
1.2
Counts per 18 min. 112 5050 00000 TT==323 K.5 K HQ==0Q TIC a) −hHω=TT0=== 0T23.5 3K .m5 eKV b) ∆∆/(Opt)sgsg 0000 ....12468 YYLLBBSSCCCCOOOO x=0.17x=0.1xx6==00..11045 Intensity A.U. 1122305050 HQ−hωΓΓ==///0Q∆∆∆ T000IC===000...285
5
n. 100 c) HH==01 0T T d) 0 0
12 mi T−h=ω2=20..33 KmeV 0 0.2 T0.c4/Tc( 0O.6pt) 0.8 1 0 0.2 0.4 T 0./6Tc 0.8 1 1.2
er 50
p FIG. 4: (a) Normalized ∆ versus normalized T for LSCO
s sg c
nt (opensymbols)andYBCO(filledcircles[10]andfilledsquares
Cou 0 H=0 T Q=QIC [11]). The open circles are taken from previously published
H=10 T T=22.3 K data, x = 0.14 [25], x = 0.16 [5] and x = 0.17 [4] while
open squares are from this work (x = 0.105) and Ref. [23]
0 1 2 3 0.55 0.6 0.65
−hω [meV] Qh [r.l.u.] (x = 0.14). (b) Intensity at QIC, at the energy transfer
~ω = 0.5∆0, and at H = 0 T versus T calculated within
FIG. 3: Energy and Q dependence of magnetic scattering a phenomenological Fermi-liquid (PFL) approach. The solid
from LSCO (x=0.105). Energy scans are taken at QIC: (a) (dashed)lineusestheinverselifetimeΓ=0.2∆0(Γ=0.8∆0).
Comparison of theresponse intheSCphasewith thatof the
normal state in zero field. (c) Effect of a 10T field at T =
22.3K. QscansthroughQIC: (b)Comparisonoftheresponse malstate[26]. InourunderdopedLSCOsample,weinfer
in theSC phase with that of thenormal state using ~ω=0.5
from Figs. 1b and 3 similar spin gap features as in op-
meV. (d) The effect of a 10T field at 22.3 K, ~ω =0.3 meV,
timally doped LSCO. (i) An applied magnetic field acts
E =3.5 meV. In this configuration the resolution (HWHM)
f
to redistribute the spectral weight for 10K < T < T
was 0.03 meV. The data have been background subtracted c
and lines are guide to theeye. at ~ω < 1.5 meV (Fig. 1b and 3c). (ii) There is the
cusp-like anomaly at T scanning the temperature for
c
fixed energybelow 1.5 meV. (iii) Energyscans revealan
ferent temperatures and fields, is shown in Fig. 3. In anomaly at ~ω = 1.5 meV which disappears in the nor-
Fig. 3a the intensity at Q , and at H = 0 T shows a mal state. The field effect (i) alone provides compelling
IC
smooth dependence on ~ω above T . At T = 2 K, an evidence for a spin gap at 1.5 meV. This is further sup-
c
anomaly is exhibited at ~ω = 1.5 meV below which in- ported by the cusp at T (ii), and consistent with the
c
tensity is reduced relative to that in the normal state. energy dependence (iii). We also find that the intensity
Figure 3b shows the effect of cooling through T in the at Q displays the same functional dependence as that
c IC
QscanthroughQIC atH =0Tandwith~ω =0.5meV. reportednearoptimaldoping[27]asafunctionofT >Tc
Cooling from 33.5 K to 2 K results in a two-fold reduc- or ~ω >1.5 meV.
tion of the intensity at Q . Figures 3c and 3d show the We plot in Fig. 4a the dependence of the SG on T
IC c
changeinthedependenceon~ωandQoftheintensityat for LSCO and YBCO samples. Vertical and horizon-
fixed T = 22.3 K upon applying H = 10T, respectively. tal axes have been normalized by the values of the SG
The effect of the applied field, Fig. 3c, is to remove the and SC critical temperature at optimal doping, respec-
zero-field anomaly at ~ω = 1.5 meV, and is similar to tively. Theratio∆ /(k T )exhibitsastrongdownward
sg B c
the effect of raising the temperature above T , Fig. 3a. multiplicativerenormalizationintheunderdopedregime.
c
Note that here the magnetic-field-induced redistribution This strong renormalizationwas also observedin YBCO
of spectral weight is limited to frequencies smaller than [10, 11], in which context it was attributed to inhomo-
1.5 meV. geneities induced by oxygendoping [11]. We must, how-
Tobetterappreciatethefeaturesoftheexcitationspec- ever, rule out this explanation for our x = 0.105 LSCO
trum described above, a comparison with the SG sig- sample in view of the sharpness of the SC transition
natures observed in optimally doped LSCO is relevant. (∆T = 1.5 K). Instead, we believe that the proper
c
(i) Although the details vary from experiment to exper- interpretation of Fig. 4 is that of a universal doping de-
iment [4, 16, 24], magnetic field-induced excitations for pendence of∆ /∆ (Opt) with a linear regime thatde-
sg sg
~ω <∆ andT <T remainacommonobservation. (ii) finestheapproachtooptimaldopingandanunderdoped
sg c
For ~ω <∆ , beside the suppression of intensity at low regime whose defining property is a doping dependent
sg
temperatures,ananomalywasreportedatT thatmarks ∆ /(k T ).
c sg B c
the closingofthe spingapas the temperaturecrossesT It is remarkable that ∆ /(k T ) decreases in the un-
c sg B c
[25]. (iii) A strong suppression of the intensity below derdoped regime, since this is opposite to the doping
~ω ≈∆ is observedinthe SC state but notin the nor- dependence of most energy features (maximum SC gap
sg
4
or pseudogap) which are found, from ARPES measure- gap. The cuspuponheatingthroughT implies thatthe
c
ments, to increase with underdoping [8, 9]. In a phe- gapremainswell-definedasitclosesinenergy,whichalso
nomenological Fermi-liquid (PFL) picture, which is rel- indicates thatthe SGis directly coupledtothe SC-order
atively successful at optimal doping, the SG is directly parameter.
related to the SC gap. Although its maximum increases This work was supported by the Swiss National Sci-
with underdoping, the slope of the SC d-wave gap has ence Foundation (through NCCR, MaNEP, and grant
been measured to soften at the nodes with underdoping Nr 200020-105151) and the Ministry of Education and
[28]. Thismeansthattheratio∆ /(k T )willdecrease Science of Japan. Work in London was supported by a
sg B c
with underdoping [29]. In this picture, the anomaly at Wolfson Royal Society Research Merit Award.
T inthetemperaturedependencedisplayedinFig.1bis
c
causedbytheclosingoftheSGuponenteringthenormal
state. In Fig. 4b we show the calculated dependence on
temperatureofthezerofieldneutronintensityatQ and
IC ∗
energy transfer ~ω = 0.5∆ using the PFL parameters Electronic address: [email protected]
0 [1] S. Wakimoto et al., Phys.Rev.Lett. 92, 217004 (2004).
chosen to reproduce the T dependence at optimal dop-
[2] T. E. Mason et al.,Phys. Rev.Lett. 68, 1414 (1992).
ing[30]. Acusp-likeanomalyatT separatesthenormal
c [3] K. Yamada et al.,Phys. Rev.Lett. 75, 1626 (1995).
regimefroma d-waveSC regimewithadecreasingresid- [4] R. Gilardi et al.,Europhysics Letters 66, 840 (2004).
ual intensity due to a phenomenologicalinverse life-time [5] B. Lakeet al.,Nature400, 43 (1999).
of Γ = 0.2∆ . In this spirit, to reproduce the measured [6] P. Bourges, Neutron Scattering in Novel Materials
0
residual spectral weight at low T in x = 0.105 LSCO (World Scientific, 2000).
would require Γ ≈ ∆ resulting in strong broadening [7] P. Dai et al., Science 84, 1344 (1999).
sg [8] J. C. Campuzano et al., Physics of Superconductors
of the peak at T as shown in Fig. 4b. Thus, the naive
c (Springer, Berlin, 2004).
PFL approachis unable to reconcile a sharp anomaly at
[9] A. Damascelli et al.,Rev.Mod. Phys.75, 473 (2003).
Tc (∆sg) for small enough ~ω (T) and the large, com- [10] P. Bourges et al., Physica B 215, 30 (1995).
pared to optimal doping, residual intensity in the low-T [11] P. Dai et al., Phys.Rev.B 63, 054525 (2001).
(low-~ω) tail of Fig. 1b (Fig. 3a). [12] C.-H Lee et al.,J. Phys.Soc. Jpn.69, 1170 (2000).
[13] S. A. Kivelson et al.,Rev.Mod. Phys.75, 1201 (2003).
One way to explain the large residual intensity at low
[14] S. Chakravarty et al.,Phys. Rev.B 63, 094503 (2001).
temperaturesandenergiesinstronglyunderdopedHTSC
[15] E. Demler et al.,Phys. Rev.Lett. 87, 067202 (2001).
could be in terms of a two-component model. The first
[16] B. Lakeet al.,Science 291, 1759 (2001).
component would correspond to the gapped response [17] B. Lakeet al.,Nature415, 299 (2002).
seen around optimal doping. The second (quasi-elastic) [18] T. Nakanoet al., J. Phys. Soc. Jpn. 67, 2622 (1998).
component could be related to the slowing down of the [19] K. Yamada et al.,Phys. Rev.B 57, 6165 (1998).
magnetic signal observed by µSR [31], and the central [20] R. Gilardi et al.,Eur. Phys. J. B 47, 231 (2005).
[21] U.K.Divakaretal.,Phys.Rev.Lett.92,237004(2004).
mode recently reported in YBCO (T =18 K) [32]. The
c [22] R. Gilardi et al.,Phys. Rev.Lett. 88, 217003 (2002).
fact that both components developwell-definedpeaks at
[23] J. Chang et al.,Unpublished.
Q suggests an inter-twinning of the two components
IC [24] J.M.Tranquadaet al.,Phys.Rev.B69,174507 (2004).
on a nanometer length scale. This could possibly be ex- [25] T.E.Masonet al.,Phys.Rev.Lett.77,1604(1996)and
plainedwithin apicture ofstatic andfluctuating stripes, T. E. Mason et al.,Physica B 199, 284 (1994).
although it remains a challenge to quantify this picture [26] N. B. Christensen et al., Phys. Rev. Lett. 93, 147002
to describe the detailed field and temperature effects of (2004).
[27] G. Aeppliet al.,Science 278, 1432 (1997).
the magnetic response reported here.
[28] J.Mesotet al.,Phys.Rev.Lett.83,840(1999) andS.V.
Insummary,wehavereportedadramaticfield-induced
Borisenko et al., Phys.Rev.B 66, 140509(R) (2002).
enhancementoftheINSresponseforlowenergytransfers [29] A. Schnyderet al.,Phys. Rev.B 70, 214511 (2004).
in a restricted temperature range. The field dependence [30] The imaginary part of the magnetic susceptibility of a
suggests that the approachdeveloped [15] to explain the weakly interacting gas of SC quasiparticles is calculated
previously observed field-induced static magnetic order withintherandomphaseapproximation.Thefermiology
[16] (see also Ref. 17) may also be applicable to the dy- parametersarechosentoreproducetheT dependenceof
the INS response at optimal doping in LSCO (see Ref.
namics. The field-induced excitation may be more diffi-
culttocaptureinaPFLapproach. Furthermore,wehave [28]), with the Ansatz ∆(Q,T) = ∆0(Q)p1−(T/Tc)4
and ∆0(0,π) = 10 meV for the T dependence of the d-
identified a SG, ∆ = 1.5 meV in underdoped LSCO
sg wave SC gap.
x =0.105. The strong renormalization of the SG as a [31] Ch.Niedermayeretal.,Phys.Rev.Lett.80,3843(1998).
function of underdoping appears to be a generic feature [32] C. Stock et al., Phys.Rev.B 73, 100504(R) (2006).
of HTSC and might signal a profound modification of
the underlying electronic excitations as the system ap-
proachesits Mott insulating phase. In particular,we are
not dealing with a simple damping or smearing of the