Spin correlations in the electron-doped high-transition-temperature superconductor Nd{2-x}Ce{x}CuO{4+/-delta}

0.28 MB·English

by  E. M. Motoyama

Spin correlations in the electron-doped high-transition-temperature
superconductor Nd Ce CuO
2−x x 4±δ
E.M. Motoyama,1 G. Yu,1 I.M. Vishik,1 O.P. Vajk,2 P.K. Mang,3 and M. Greven3,4,∗
1Department of Physics, Stanford University, Stanford, California 94305, USA
7 2NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
0 3Department of Applied Physics, Stanford University, Stanford, California 94305, USA
0 4Stanford Synchrotron Radiation Laboratory, Stanford, California 94309, USA
2

n
a High-transition-temperature (high-T ) super- and three-dimensional couplings, NCCO exhibits three-
c
J
conductivity develops near antiferromagnetic dimensionalAForderatanon-zeroN´eeltemperature,as
1
phases, and it is possible that magnetic exci- observedintheelasticscatteringchannel[2,6]. Thespin
1
tations contribute to the superconducting pair- stiffness ρ (x) decreases monotonically with increasing
s
] ing mechanism. To assess the role of antifer- electron concentration, with ρs(0.18)/ρs(0) ≈ 25% [6],
n
romagnetism, it is essential to understand the andthedopingdependenceofρ (x)andoftheamplitude
s
o
doping and temperature dependence of the two- A(x)isremarkablyclosetothatfortherandomly-diluted
c
- dimensional antiferromagnetic spin correlations. spin-one-half square-lattice Heisenberg antiferromagnet
r
p The phase diagram is asymmetric with respect La2Cu1−z(Zn,Mg)zO4 [14].
u to electron and hole doping, and for the com- Magnetic inelastic neutron-scattering experiments in
s paratively less-studied electron-doped materials, the SC phase have become possible only in recent years
.
t the antiferromagnetic phase extends much fur- [15, 16]. We have carried out two-axis measurements of
a
m ther with doping [1, 2] and appears to overlap thespincorrelationsineightoxygen-reducedNCCOcrys-
with the superconducting phase. The archetyp- talsinthe ceriumconcentrationrange0.038≤x≤0.154
-
d ical electron-doped compound Nd2−xCexCuO4±δ (Fig. 1). The data are fit to a 2D lorentzian, S(q2D) =
n (NCCO) shows bulk superconductivity above x S(0)/(1+q2 ξ2), convoluted with the calculated instru-
o ≈ 0.13[3, 4], whileevidence forantiferromagnetic mental reso2luDtion, where q is the distance in momen-
[c orderhasbeenfounduptox ≈0.17[2,5,6]. Here tum space from the 2D A2FDzone center (Fig. 2). The
we report inelastic magnetic neutron-scattering non-SC samples (x ≤ 0.129) follow equation (1), con-
2
measurements that point to the distinct possibil- sistent with bulk AF order in the ground state (Fig. 3).
v
6 ity that genuine long-range antiferromagnetism Althoughthisbehaviourisqualitativelythesameasthat
8 and superconductivity do not coexist. The data foras-grownNCCO[6],thespinstiffnessdecreasesmuch
3 reveal a magnetic quantum critical point where more rapidly with doping. The data for the SC sample
9 superconductivity first appears, consistent with withx=0.134arefittoequation(1)withasmallvalueof
0
an exotic quantum phase transition between the thespinstiffnessρ ,butareequallywelldescribedbythe
6 s
two phases [7]. We also demonstrate that the simple power law ξ ∝1/TνT with exponent ν =1.0(5).
0 T
/ pseudogap phenomenon in the electron-doped The power-lawbehaviour,indicatedbythe dashedcurve
t
a materials, which is associated with pronounced in Fig. 3, would imply that ρs is already zero and that
m chargeanomalies[8,9,10,11],arisesfromabuild- the system is quantum critical at this cerium concentra-
- up of spin correlations, in agreement with recent tion. Fig. 4a demonstrates that ρs approaches zero at
d theoretical proposals [12, 13]. x = 0.134(4) in an approximately linear fashion. In a
n AF
In their as-grown state, the electron-doped materials fundamentaldeparturefromtheabovebehaviour,wefind
o
c exhibit antiferromagnetic(AF) order throughoutthe ac- that in the SC samples with x ≥ 0.145, ξ remains finite
: cessibledopingrange,andanoxygenreductiontreatment down to the lowest temperatures. The low-temperature
v
i is required to induce superconductivity [3]. Previous in- correlation length ξ0 for these samples increases as xAF
X elasticneutronscatteringexperimentsonas-grown,non- is approached from above (Fig. 4a).
r superconducting (non-SC) NCCO demonstrated [6] that Previous elastic neutron measurements [2, 4, 6] indi-
a
the two-dimensional (2D) spin correlation length ξ ob- cated that oxygen-reduced NCCO exhibits AF order up
served above the N´eel temperature is exponentially de- to x ≈ 0.17. Such measurements in our crystals indeed
pendent on inverse temperature: reveal N´eel order. However, our inelastic results demon-
strate that, contrary to previous belief [4, 11, 17], the
ξ(x,T)=A(x)exp(2πρ (x)/T) (1)
s
groundstateofSCsamplesexhibitsonlyshort-rangespin
for cerium concentrations ranging from zero up to the correlations. Moreover,priorinelasticneutron-scattering
solubility limit of x≈0.18. This behaviour indicates the experiments clearly revealeda SC magnetic gap, despite
existence of an underlying ground state with long-range the presence of AF Bragg peaks in the elastic response
2D AF order. Owing to weak spin-space anisotropies [15, 16]. We conclude that the AF phase boundary in
2
fact terminates at x = 0.134(4), and that magnetic field [18] due to the paramagnetic decomposition prod-
AF
Bragg peaks observed at higher cerium concentrations uct (Nd,Ce) O .
2 3
originatefromregionsofthesampleswhichwerenotfully Foras-grownNCCO [6]andforLa2Cu1−z(Zn,Mg)zO4
oxygen-annealed. While a relatively small volume frac- [14]itwasfoundthat,toaverygoodapproximation,the
tion of such macroscopic remnants of the AF as-grown
statecangiveriseto significantBraggscattering,ourin-
elastic measurements are fortunately insensitive to their 4500 a x=0.038 d x=0.145 1100
presence. This conclusion is consistent with the obser- T=250K T=35K
4000 ξ/a=260 ξ/a=46
vation that the N´eel transition is very broad in SC sam- 1000
3500
ples(Fig.4b),andalsowithmuonspin-resonanceresults
3000
[4], which show a significant decrease of the AF volume 900
2500
ftricacstiigonnanlefarormx =the0.1re4m. nWaentnoAtFe trheagtiotnhsesshpouurlidounsoetlabse- 10 min)22680000 b xT==04.0003K8 e xT==02.0104K5 380010 min)
confused with the spurious elastic signal in a magnetic s/ ξ/a=14 ξ/a=16 s/
ount2400 3600ount
C C
sity (2200 3400sity (
500 en en
Int6200 c x=0.106 f x=0.154 4300Int
T=300K T=1.8K
2 6000 ξ/a=10 ξ/a=10 4200
400
5800
5 4100
5600
K) 10 5400 4000
ure (300 20 0.45 H 0(r..5l.0u.) 0.55 0.45 H 0(r.5.l.0u.) 0.55
erat ξ/a
mp 50 FIG.2: Representativetwo-axisscansusedtomeasure
Te200 the spin correlation length. The scans are along (h,h)
100 about the 2D AF zone centre (1/2,1/2) and are fitted (solid
blue curves) to a 2D Lorentzian convoluted with the calcu-
200
100 latedinstrumentalresolution(dashedredcurves). Shownare
400 data at a, T = 250K ≈ TN and b, T = 400K for x = 0.038;
c, T = 300K for x = 0.106; d, T = 35K and e, T = 200K
for x = 0.145; and f, T = 1.8K for x = 0.154. Wavevectors
0
0 0.05 0.1 0.15 0.2 are represented as (h,k,l) in reciprocal lattice units (r.l.u.),
x where Q = (2πh/a,2πk/a,2πl/c) is the momentum trans-
fer, and a and c are the lattice constants of the tetragonal
FIG. 1: The temperature-doping phase diagram for system (space group I4/mmm; for x = 0.038, for exam-
oxygen-reduced NCCO. The red and blue hashed areas ple, the room-temperature lattice constants are a = 3.93˚A
indicate long-range AF order and superconductivity, respec- and c = 12.09˚A). Vertical error bars represent uncertain-
tively. The black circle at zero temperature indicates the ties(1σ)assumingPoissonstatistics. Themeasurementswere
approximate location of a magnetic quantum phase transi- performed in two-axis mode on the BT2 and BT9 triple-axis
tion. Theinstantaneous2Dspin-correlation lengthξ(x,T)in spectrometersattheNISTCenterforNeutronResearch. The
the CuO2 sheets was measured at the doping levels and over incident neutron energy was Ei = 14.7meV. In previous ex-
the temperature ranges indicated by the vertical bars. The perimentsonLa2Cu1−z(Zn,Mg)zO4[14]andas-grownNCCO
colour scale shows ξ, in units of the planar lattice constant [6], this energy proved to be sufficiently large in the temper-
a, interpolated and extrapolated from the measured values. ature region TN < T < 2TN to reliably extract the instanta-
TheN´eeltemperatureTN isshownasthedottedcurve,while neousstructurefactorS(Q). Thecollimationswere: a,b,40′-
the dashed curve is the extrapolated contour of ξ/a = 400. 23′-sample-20′; c, 60′-40′-sample-40′; d, 40′-47′-sample-10′;
The measurement of TN is contaminated by remnants of the e, 40′-47′-sample-20′; and f, 40′-47′-sample-40′. The NCCO
as-grown state of NCCO, so that the true AF phase extends crystals were grown in 4atm of oxygen using the travelling-
only to xAF ≈ 0.13, close to where superconductivity first solvent floating-zone technique, and subsequently annealed
appears. This is established from the fact that ξ diverges for 10 h at 970◦C in argon, followed by 20 h at 500◦C in
exponentially upon cooling for non-superconducting compo- oxygen. The sample masses range from 1 to 5g. The oxy-
sitionsatlowerelectronconcentrations,whileitremainsfinite gen reduction treatment, required for superconductivity to
insuperconductingsamples. Thesmallremainingoverlapin- appear, isa non-equilibriumprocess resulting in unavoidable
dicated in the figure may be caused by cerium and oxygen oxygeninhomogeneities. Ceriumconcentrationsxweredeter-
inhomogeneities. The grey and white circles indicate optical mined from inductively coupled plasma (ICP) spectroscopy,
conductivity measurements of of the pseudogap temperature with typical variation of ∆x≈0.005 along the growth direc-
T∗ on NCCO crystals [9] and Pr2−xCexCuO4±δ thin films tion. Superconductivity is observed from magnetic suscepti-
[11],respectively. Thedot-dashedcurveisaguidetotheeye. bility measurements for x≥0.134.
3
N´eeltemperature T (x) is a contour of constant2D cor- nario: a second-orderquantum phase transitionbetween
N
relationlengthwithξ/a=200-400and100,respectively. the AF and SC phases. This quantum phase transition
Following the observations for as-grown NCCO, we plot would be described by a dynamic critical exponent of
the extrapolatedcontour of ξ/a=400 as a dashedcurve z = 1/ν ≈ 1.0(5), which differs from the value z = 2
T
inFig.1. ThisestimateoftheunderlyingbulkN´eeltem- predicted for a transition from the antiferromagnet to
perature coincides with the measured T at x = 0.038,
N
but it lies systematically lower at higher cerium concen-
trations, approaching T =0 at x ≈0.134.
N AF
22 50
The decrease to zero of the spin stiffness at x ≈ a
AF
40
0.134 and the finite values of ξ for x > x indicates 11..55
0 AF
agrofuunnddasmtaetnet.aTl hcehacnognetriibnuttihoenonfattuhreeAoFfrtehmenamnatgsnmetaiyc πρ2/Js 11 2300ξ/a0
lead to a slight over-estimate of the spin correlations, 00..55
10
and consequently of ρ and ξ , but we emphasize that
s 0 00 0
the qualitative change in behaviour is a robust result. 300
b
The NCCO phase diagram resembles those of other un-
conventionalsuperconductors,suchastheheavy-fermion TN200
compound CeRhIn5, in which the AF and SC phases arent
are believed to be separated by a first-order boundary pp100
A
[19]. Although we cannot rule out a genuine under-
lying coexistence between AF and SC order, such co- 0
existence would be confined to a rather narrow doping 40 c
range. However,the behaviour of ρ (x), which decreases 30
s
continuously by more than an order of magnitude with ξ*/a20
doping, together with the crossover to power-law be-
10
haviour of ξ(x,T) near x = 0.134, suggests another sce-
0
0 0.05 0.1 0.15 0.2
x
500
x=0.038 FIG. 4: Spin stiffness, spin correlations at low-
x=0.075 temperature, apparent N´eel temperature, and spin
x=0.106 correlations along T∗. a, Doping dependence of the spin
200
x=0.129 stiffness ρs (plotted as 2πρs/J, where J = 125meV is the
a
ξ/ x=0.134 AFsuperexchangefortheundopedMott insulator Nd2CuO4
gth 100 x=0.145 [2, 6]) and of the low-temperature spin correlation length ξ0.
n len x=0.150 zVoenrttaiclaelrerrorrorbabrasrsinhaelrlepraenperlessernetpruensecnetrttahinetimeseaosfu1reσd. rHanorgie-
o 50 x=0.154
ati of cerium concentration in each crystal. Dashed curves are
orrel guidestotheeye. Thespin stiffnessdecreases smoothly with
c doping and reaches zero in an approximately linear fashion
pin 20 around xAF ≈ 0.134. The ground state for x < xAF has
S
long-range AF order, whereas long-range order is absent for
10 x > xAF, as seen from the finite values of ξ0. The doping
dependence of ξ0 indicates a divergence as the critical point
is approached from the right. b, Apparent N´eel temperature
5
0 100 200 300 400 TN, as determined from elastic scattering, as a function of
Temperature (K) doping. The temperature dependence of the measured order
parameter (not shown) was modelled using agaussian distri-
FIG. 3: The temperature dependence of the spin bution of TN, and the vertical bars indicate the full-width at
correlation length at various cerium concentrations. half-maximum (FWHM) of this distribution. Measurements
Vertical bars represent uncertainties of 1σ. The data for were not performed on all samples; previous data [6] are in-
x ≤ 0.134 are fit to equation (1). The spin stiffness may dicated by open symbols. The dotted and dashed curves are
alreadybezeroforx=0.134, becauseafittoasimplepower thesame as in Fig. 1. c,The spin correlation length ξ∗ mea-
law ξ ∝ 1/T describes the data equally well (dashed curve); sured at or extrapolated to the pseudogap temperature T∗.
power-law behaviourisexpectedat aquantumcritical point. Vertical bars represent uncertainties of 1σ. Below optimal
For x=0.145 and higher, ξ does not diverge, but instead re- doping (x < 0.15), ξ∗ is given by the single-particle thermal
mains finite at low temperatures, demonstrating the absence deBrogliewavelengthandincreasesasξ∗ ∝1/(x∗−x)(fitted
of genuine long-range AF order. The curves drawn for these curve). However, this relationship breaks down near optimal
latter data are guides to the eye. Superconductivity is ob- doping, where ξ∗ is found not to exceed the SC coherence
served for x≥0.134. length.
4
a non-SC paramagnet [12]. If hyperscaling holds, the the contributions from the remnant AF regions to our
spin stiffness for a 2D system is expected to decrease as measured ξ(x,T) are negligible.
ρ ∝ (x −x)ν0z, where ν is the exponent describing Equation(2)wouldsuggestthatξ∗divergesatx ≈x∗.
s AF 0 c
the divergence of ξ as x is approached from above. However,as seen from Fig. 4c, this relationbreaks down
0 AF
Fromtheapproximatelylinearbehaviourofthespinstiff- nearoptimaldoping,presumablyowingtotheemergence
ness,wethereforehaveν ≈1. Wecannotindependently ofa new length scalethat limits the developmentofspin
0
determine ν , since we do not have sufficient informa- correlations. Interestingly,atoptimal doping (x=0.15),
0
tion for ξ (x). It is also possible that the system lies ξ∗ ≈ ξ is comparable to the SC coherence length [20]
0 0
above the upper critical dimension, in which case mean- ξ = 58˚A ≈ 15a. The spin correlations near optimal
SC
fieldbehaviourwithρ ∝(x −x)2βmean field isexpected. doping are still relatively large, consistent with sugges-
s AF
β = 1/2, so this is consistent with the observed tions basedon Ramanscattering [21] and photoemission
mean field
behaviour. [22]thatthedx2−y2 SCorderparameterisnon-monotonic
Our results for ξ(x,T) also have important conse- due to AF fluctuations.
quences for the relationship between AF correlations The new experimental results for the magnetic phase
and the pseudogap physics in the electron-doped cop- diagram and pseudogap physics contain important im-
per oxides, which appears to be different from that of plications for theories of high-T superconductivity. By
c
the hole-doped materials [9, 12, 13]. The pseudogap avoiding spurious scattering that significantly contami-
(charge anomalies associated with the opening of a par- natestheelasticresponse,wehaveestablishedfrommea-
tial gap along the Fermi surface) has been discerned in surements of the 2D spin correlations that genuine co-
photoemission [8, 10], optical spectroscopy [9, 11], and existence of AF and SC order is essentially absent in
charge transport [9] experiments on NCCO crystals and Nd2−xCexCuO4±δ. On symmetry grounds, a possible
Pr2−xCexCuO4±δ films up to x=0.15 [8, 11]. First, our second-order quantum phase transition between these
finding that the AF phase terminates at xAF =0.134(4) two types of order would seem unlikely and exotic. One
refutes statements that a possible quantum phase tran- scenarioisthatanunderlyingfirst-ordertransitionisren-
sition at x ≈ 0.17 is related to the disappearance of AF dered second-order owing to microscopic disorder [23].
order [11, 17]. Second, we find that the spin-correlation Such disorder is found in most high-T superconductors
c
length changes smoothly across the pseudogap tempera- [24]and,inthe presentcase,itmightbe the randomness
ture T∗ and, remarkably, up to x = 0.145 it follows the associated with the Nd-Ce substitution. Alternatively,
simple relationship: such a phase transition may be an example of ‘decon-
ξ∗ C fined’ quantum criticality [7], a new paradigm for quan-
= (2) tumphasetransitions. Tofurtherelucidatethenatureof
a x −x
c the transition from AF to SC order, a detailed comple-
with fitting parameters C =0.96(12) and x =0.171(4). mentarystudy ofthe superconducting criticalproperties
c
One interpretation of the pseudogap is that it signifies on small samples with minimal oxygenand cerium inho-
a change in the spin scattering of the electrons as the mogeneities would be desirable.
AF correlationsexceed the carriermean free path [9] (ℓ) WethankN.Bontemps,S.Chakravarty,S.A.Kivelson,
or the single-particle thermal de Broglie wavelength [12] R.S. Markiewicz and A.-M.S. Tremblay for discussions.
(ξ = h¯v /πk T) upon cooling. Boltzmann transport TheworkatStanfordUniversitywassupportedbygrants
th F B
theory, which might be expected to qualitatively hold if fromtheDepartmentofEnergyandtheNationalScience
ℓ > a and T > T∗, applied to direct-current resistivity Foundation. E.M.M. acknowledges support through the
data for NCCO yields ℓ(T∗)≈2.4a and ℓ(T∗)≈25a for NSF Graduate Fellowship programme.
x = 0.125 and x = 0.15, respectively [9]. This trend is
qualitatively consistent with our results up to x=0.145
seen in Fig. 4c. However, given the approximately lin-
ear relationship T∗ ∝ (x∗ − x) (Fig. 1), the thermal
de Broglie wavelength at T∗ exhibits the same quanti- ∗ [email protected]
[1] B. Keimer et al.,Phys. Rev.B 46, 14034 (1992).
tative doping dependence as does equation (2). Using
[2] M. Matsuda et al.,Phys. Rev.B 45, 12548 (1992).
the value vF = 2.2 × 107cm/s for the bare Fermi ve- [3] H. Takagi, S. Uchida and Y. Tokura, Phys. Rev. Lett.
locity [12], we find that ξ∗ = 2.6(2)ξth. We conclude 62, 1197 (1989).
that T∗ is a crossovertemperature below which the spin [4] T. Uefuji et al., Physica C 357-360, 208 (2001).
correlations become longer than the thermal de Broglie [5] T. Uefuji et al., Physica C 378-381, 273 (2002).
[6] P. K. Mang et al.,Phys.Rev.Lett. 93, 027002 (2004).
wavelength,inagreementwiththeoreticalwork[12]. The
[7] T. Senthilet al.,Science 303, 1490 (2004).
pseudogapphenomenonintheelectron-dopedcopperox-
[8] N.P.Armitageetal.,Phys.Rev.Lett.88,257001(2002).
ides therefore results from 2D AF spin correlations, and
[9] Y.Onose,Y.Taguchi,K.Ishizakaand Y.Tokura,Phys.
does not appear to be a direct precursor to supercon- Rev. B 69, 024504 (2004).
ductivity. That ξ∗ ∝ ξth is obeyed so well suggests that [10] H. Matsui et al.,Phys. Rev.Lett.94, 047005 (2005).
5
[11] A.Zimmers et al.,Europhys.Lett. 70, 225 (2005). [18] P. K. Mang et al.,Phys.Rev.B 70, 094507 (2004).
[12] B.Kyung,V.Hankevych,A.-M.Dar´eandA.-M.S.Trem- [19] T. Park et al.,Nature440, 65 (2006).
blay,Phys. Rev.Lett. 93, 147004 (2004). [20] Y. Wang et al.,Science 299, 86 (2003).
[13] R.S. Markiewicz, Phys.Rev.B 70, 174518 (2004). [21] G. Blumberg et al.,Phys. Rev.Lett. 88, 107002 (2002).
[14] O.P. Vajk et al.,Science 295, 1691 (2002). [22] H. Matsui et al.,Phys. Rev.Lett.95, 017003 (2005).
[15] K.Yamada et al.,Phys. Rev.Lett. 90, 137004 (2003). [23] M. Aizenman and J. Wehr, Commun. Math. Phys. 130,
[16] E. M. Motoyama et al., Phys. Rev. Lett. 96, 137002 489 (1990).
(2006). [24] H. Eisaki et al.,Phys. Rev.B 69, 064512 (2004).
[17] Y.Dagan et al.,Phys.Rev.Lett. 94, 057005 (2005).