Vortex State of Tl$_2$Ba$_2$CuO$_{6+δ}$ via $^{205}$Tl NMR at 2 Tesla

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by  Y. Itoh

Vortex State of Tl Ba CuO via 205Tl NMR at 2 Tesla
2 2 6+δ
Y. Itoh,1 C. Michioka,1 K. Yoshimura,1 A. Hayashi,2 and Y. Ueda,2
1Department of Chemistry, Graduate School of Science,
Kyoto University, Kyoto 606-8502, Japan
2Institute for Solid State Physics, University of Tokyo, 5-1-15 Kashiwanoha,
5
Kashiwa, Chiba 277-8581, Japan
0
(February 2, 2008)
0
2

n
a II. EXPERIMENTS
Wereporta205TlNMRstudyofvortexstateforanaligned
J
polycrystalline sampleof an overdopedhigh-Tc superconduc-
10 torTl2Ba2CuO6+δ (Tc ∼85K)withmagneticfield2Talong The powder sample in the present study is the same
thecaxis. Weobservedanimperfect vortexlattice, so-called one as in the previous study [4], which was mixed with

] Braggglass atT=5K,coexistenceofvortexsolid withliquid Stycast1266epoxy and magneticallyalignedalongthe c
n between 10 and 60 K, and vortexmelting between 65 and 85 axis.
o K.Noevidenceforlocal antiferromagneticorderingatvortex A phase-coherent-type pulsed spectrometer was uti-
c cores was found for our sample. lized to perform the 205Tl NMR (spin I=1/2) experi-
-
r ments. All the measurements were done with magnetic
p 74.25.Nf, 74.72.Jt, 76.60.-k
field cooling. The NMR frequency spectra with quadra-
u
s turedetectionwereobtainedbyintegrationofthenuclear
t. spin-echoes with frequency ν. The width of the first ex-
a
m I. INTRODUCTION citingπ/2-pulsetwwas4µs(theexcitedfrequencyregion
ν ∼63 kHz). Because of no fine structure but moder-
1
-
ately broad NMR spectra, high spectral resolution [11]
d Coexistence of magnetism with the mixed state of
n type-IIsuperconductorshasattractedgreatinterests [1]. was not required in the present measurements.
o The nuclear spin-lattice relaxation curves p(t) ≡ 1−
Nearly antiferromagnetic spin fluctuation close to the
c M(t)/M(∞) (recovery curves) were measured by an in-
[ quantum criticalpoint has been a key to understandthe
magnetic correlation of high-Tc superconductors. Such versionrecovery technique, as functions of a time t after
1 aninversionpulse,wherethenuclearspin-echoamplitude
an underlying magnetic correlation may affect the local
v M(t), M(∞)[≡ M(10T )] and t were recorded. In con-
electronic structure at vortex cores. 1
0
trastto thepreviousstudy [5],thecombpulsetrainwas
0 Tl2Ba2CuO6+δ (Tl2201) is an overdoped high-Tc su-
not needed. The measurement of M(∞) was necessary
2 perconductor. TheoptimalT isabout85Kforareduced
c
1 oxygencontent. The early studies by Tl NMR with 4.26 to determine the function form of p(t).
0
T [2]and Cu NMR with 7 T [3] for Tl2201reportedan
5
obvious Redfiled pattern due to the vortex lattice. Al-
0
III. RESULTS AND DISCUSSION
/ though the magnetic ordering in the mixed state is not
t
a expected for Tl2201, because it is a typical overdoped
m electronic system away from antiferromagnetic instabil- A. NMR spectrum
- ity [4], the recent Tl NMR study with 2.1 T shows coex-
d istence of local antiferromagnetic ordering at the vortex Figure1shows205TlNMRspectrawithmagneticfield
n
cores [5]. ThespecificcharacteristicsofTl2201arecation of H0=2 T along the c axis at T=85 and 5 K. The
o
c disorderontheTlsite [6]andmagneticfielddependence bare resonance line ν0 given by 205γnH0 (205γn=24.567
: of the elementary excitations [7–9]. Disorder makes the MHz/T) is denoted by the dash line. Above Tc, the
v
i vortex phase rich [10]. The effect of these characteris- full width at half maximum of the spectrum is about
X ticsontheantiferromagneticvortexcoreispoorlyunder- 50 kHz, being nearly the same as the reported one [5].
r stood. The linewidth can be considered to result from a stag-
a
In this paper, we studied the vortex state of an over- gered spin susceptibility (the second moment) and from
doped high-T superconductor Tl2201 (T ∼85 K) with a Knight shift distribution (the first moment). The
c c
magneticfieldof2Talongthecaxisusinga205TlNMR enhancement of the static staggered spin susceptibility
spin-echo technique. We observed a Redfield pattern of alongthe c axisis estimatedfromthe 63Cunuclearspin-
the 205Tl NMR spectrum at 5 K due to the vortex lat- spin relaxationrate 1/T2G [12].
tice state without static antiferromagnetic order at the The 205Tl Knight shift is understood by the sum
vortex cores. of the spin shift Kc,spin due to the Cu-to-Tl super-
transferred hyperfine coupling and the temperature-
independentK due toresidualspindensitypolariza-
c,res
1
tion [9]. Below T , the spectrum peak is largely shifted results remind us of the in-plane impurity-substitution
c
into the negative shift side (low frequency region), while effect [17]. The nuclear moments close to an impurity
thetailisstillinthepositiveshiftside(highfrequencyre- show nonexponential relaxation, because of random im-
gion). Sinceforasingletdx2−y2-wavesuperconductor,lo- purity distribution.
caldensity ofstates ofelectronsis suppressedawayfrom Figure 3(b) shows temperature dependence of the re-
vortex cores but recovers at the cores [13], then we ex- covery curve at ν=49.18-49.20 MHz. One can see non-
pectthataRedfieldpatternofthespinshiftscK (ν) exponential curves below 30 K and a nearly exponential
c,spin
due to the electron density of states affects the NMR one at 40 K.
spectrum. However,theobservednegativeshiftindicates The solid curves in Fig. 3 are the least-squares fitting
thataRedfieldpatternofasuperconductingdiamagnetic results by
shift scK (ν) is predominant.
c,dia t t
The T=5 K NMR spectrum resembles the field distri- p(t)=p(0)exp[− − ], (3)
T rτ
bution due to a slightly distorted vortex lattice [14,15] 1 1
but not a Gaussian due to amorphous vortex or vortex where p(0), T and τ are the fitting parameters. Equa-
1 1
glass. We could not deduce from the NMR spectrum tion(3)isderivedfromanimpurity-inducedNMRrelax-
which the vortex lattice is, triangular or square. ation theory [18]. T is a nuclear spin-lattice relaxation
1
Thepeakfrequencycanbeassignedtothesaddlepoint time due to quasi-particlescattering or homogeneousre-
(S) in the field distribution of vortices, the highest fre- laxationprocess,whereasτ isaninducedrelaxationtime
1
quency edge to the vortex core (V), and the lowest fre- due to random distribution of impurity relaxation cen-
quency edge to the minimum field position (C) mostly ters. Since there are no literal localized moments, the
away from the vortex cores [13,16]. Site-selective NMR finiteτ mayresultfromanextendedstaggeredspinfluc-
1
is possible for our sample. tuation around the vortex core [19], Friedel oscillation
In Fig. 1, the Knight shift at the vortex core V at 5 around the core [20], or thermal vortex motion [21].
K is nearly the same as or larger than the normal shift For breakdown of the site-selective NMR, the recov-
at 85 K. An external magnetic field is squeezed at the erycurveofthe nuclearmagnetizationis nonexponential
vortex core. We notice that the squeezed magnetic flux in the mixed state [21]. In the case that the magnetic
density at the core yields a higher magnetic field than penetrationdepth λ is too long,a sharpNMR line with
c
an applied external field, so that the shift at the core- hierarchicalT componentsisobservedandthenthesite-
1
site V can be larger than the normal shift. Using the selectiveNMRdoesnotwork. Thesecondmomentofthe
additional positive vortex core shift scK (V) due to NMRspectruminthevortexlattice,aguidetobroaden-
c,field
the enhanced field and the negative shift scK (C)<0 ing, is given by
c,dia
due to the diamagnetic field, we obtain
<∆H2 >∝1/λ2, (4)
c c
ν(V)=ν0[1+scKc,spin(V)][1+scKc,field(V)] (1) where∆Hc isthepfielddistributionaroundthepeak [22].
For deeply underdoped andheavilyoverdopedsupercon-
with scK (V)≥ K (T ) [13], while
c,spin c,spin c ductors,thelongλ ’sareestimated [23]. Foroursample,
c
ν(C)=ν [1+scK (C)]. (2) theobservedRedfieldpatternindicatesashortλc. Thus,
0 c,dia
we suppose one-to-one correspondence of the site to the
These are illustrated in Fig. 2. A part of the NMR frequency shift.
signalsatν(V)≥49.18MHzisduetothecombinedeffect Let us briefly discuss the reason why the relaxation
of magnetic flux squeezing and of the finite positive spin curveisnonexponentialinspiteofsiteselectioninNMR.
shift at the vortex core. To our knowledge, no one has Figure 4(a) illustrates a perfect squarelattice of vortices
ever pointed out the importance of this effect. on a CuO2 plane for convenience. The recovery curve
No signalabove 49.4 MHz at 5 K, that is, no evidence at any nuclear site in Fig. 4(a) must be an exponential
forthe localantiferromagneticorderingeffectatthe vor- function, even if local moments or local staggered mo-
tex cores was found for our sample. The difference in ments are induced at the vortex cores. For example, the
imperfection or in the crystal symmetry [6] may affect vortex configurations around all the B sites in Fig. 4(a)
the local order. arethesame,sothatalltherecoverycurvesoftheB-site
nuclei would become the same. However, we observed
the nonexponential recovery curves at the selected sites.
B. Nuclear spin-lattice relaxation Thus, the vortex lattice is not perfect. One may call it
Bragg glass [24]. Figure 4(b) illustrates an imperfect
Figure 3(a) shows frequency distribution of the recov- vortex lattice with weak disorder. The vortex configura-
ery curves at 5 K. The recovery curve is close to an ex- tionaroundthe B site inFig. 4(b) is notunique, so that
ponential function at the peak frequency (S) but non- the assemble average on the vortex distribution leads to
exponential at lower and higher frequency sides. These nonexponential relaxation.
2
C. Coexistence of vortex solid with liquid
Figure 5(a) shows 205Tl NMR spectra with magnetic
field cooling. The narrow NMR lines between T =85 K
c
and T=65 K indicate motional narrowing effect, that is, [1] E. Demler, W. Hanke, and S. C. Zhang, cond-
vortex melting. The NMR spectra between T=60 and mat/0405038, and references therein.
10 K are composed of two peaks with a negative and a [2] M. Mehring, F. Hentsch, Hj. Mattausch, and A. Simon,
positive Knight shifts. These peaks indicate coexistence Solid State Commun. 75, 753 (1990).
of the vortex solid with liquid, that is, partial melting. [3] A.Goto, Y.Itoh,H.Yasuoka,A.Hayashi,and Y.Ueda,
At T=5K, the Redfield pattern indicates the vortexlat- InstituteforSolidStatePhysics(ISSP)ReportNo.2846
(1994).
tice. Thesimilar,butnarrow,coexistenceregionwasfirst
[4] S. Kambe, H. Yasuoka, A. Hayashi, and Y. Ueda, Phys.
reportedforYBa Cu O [25,26]. Thedetailedmeasure-
2 3 7
Rev. B 47, 2825 (1993).
mentofvortexphaseisinprogressforourTl2201sample.
[5] K. Kakuyanagi, K.Kumagai, Y. Matsuda, and M.
Figures5(b)and5(c)show1/τ and1/T asfunctions
1 1 Hasegawa, Phys. Rev.Lett. 90, 197003 (2003).
of temperature at C, S, and L on the solid lines in Fig.
[6] Y. Shimakawa, Physica C 204, 247 (1993).
5(a). In Fig. 5(b), the peak behavior of 1/τ1 at L is [7] S. Kambe, H. Yasuoka, A. Hayashi, and Y. Ueda, Phys.
observedat Tf=20 K. Since the signalL comes from the Rev. Lett.73, 197 (1994).
vortexliquidinthecoexistenceregion,thepeakbehavior [8] Oleg M. Vyaselev, and Igor F. Schegolev, Czechoslovak
indicatesslowingdownofvortexmotiontowardfreezing. J. of Phys. 46, 1137 (1996) Suppl.S2.
This is not due to the local antiferromagnetic ordering [9] S. Kambe, H. Yasuoka, A. Hayashi, and Y. Ueda, Phys.
aroundvortexcores. T is closeto the irreversibilityline Rev. B 48, 6593 (1993).
f
[10] K. Shibata, T. Nishizaki, T. Sasaki, and N. Kobayashi,
[27]. The temperature dependence of1/T atC and Sin
1
Phys. Rev.B 66, 214518 (2002).
Fig. 5(c) can be understood by the spatial dependence
[11] W.G.Clark,M.E.Hanson,F.Lefloch,andP.Segransan,
of local density of states of electrons [13].
Rev. Sci. Instrum.66(3), 2453 (1995).
Morethan ten yearshavepassedsince our samplewas
[12] Y. Itoh, H. Yasuoka, A. Hayashi, and Y. Ueda, J. Phys.
synthesized. The vortex phase is sensitive to crystalline
Soc. Jpn.B 63, 22 (1994).
imperfection. The aging effect, e.g. oxygen redistribu- [13] M. Takigawa, M. Ichioka, and and K.Machida, J. Phys.
tion, might realize the solid-liquid coexistence. The ef- Soc. Jpn.69, 3943 (2000).
fect, however,does not cause Tc distributionin our sam- [14] T.M.Riseman,J.H.Brewer,K.H.Chow,W.N.Hardy,
ple. Weexcludeapossibilitythatthe signalLisalower- R. F. Kiefl, S. R. Kreitzman, R. Liang, W. A. MacFar-
T part of the sample. The magnetic susceptibility does lane,P.Mendels,G.D.Morris,J.Rammer,J.W.Schnei-
c
not exhibit T distribution. The Cu nuclear quadrupole der, C. Niedermayer, and S. L. Lee, Phys. Rev. B 52,
c
10569 (1995).
resonancespectrumatT=4.2K,whichissensitivetothe
[15] E. H.Brandt, Phys. Rev.B 37, 2349 (1988).
oxygendistribution,isstillsimilartothe previousreport
[16] A. G. Redfield,Phys. Rev. 162, 367 (1967).
[28]. The temperature dependence of 1/τ of the signal
1 [17] Y.Itoh,T.Machi,C.Kasai,S.Adachi,N.Watanabe,N.
L is notconventionalbehavior ofsuperconducting onset.
Koshizuka, and M. Murakami, Phys. Rev. B 67, 064516
(2003).
[18] M. R. MacHenry, B. G. Silbernagel, and J. H. Wernick,
IV. CONCLUSION
Phys. Rev. Lett. 27, 426 (1971); Phys. Rev. 5, 2958
(1972).
To conclude, we observed a vortex lattice with weak [19] H. Tsuchiura, M. Ogata, Y. Tanaka, and S. Kashiwaya,
disorder for our sample Tl2201 (T ∼85 K) with 2 T Phys. Rev.68, 012509 (2003).
c
at 5 K, coexistence of vortex solid with liquid (T=10- [20] M. Machida, and T. Koyama, Phys. Rev. Lett. 90,
077003 (2003).
60 K), and vortex liquid (T=65-85K), but not the local
[21] G. B. Furman, E. M. Kunoff, and S. D. Goren, Physica
antiferromagnetic ordering at the vortex cores.
C 266, 203 (1996), and references therein.
[22] P. Pincus, A. G. Gossard, V. Jaccarino, and J. H. Wer-
nick, Phys.Lett. 13, 21 (1964).
ACKNOWLEDGMENTS
[23] Ch. Niedermayer, C. Bernhard, U. Binninger, H. Gluck-
ler, J.L. Tallon, E.J. Ansaldo, and J. I.Budnick,Phys.
We thank A. Goto for fruitful discussion, and M. Rev. Lett.71 (1993) 1764.
Kato and T. Waki for experimental supports. This was [24] T.Giamarchi, andP.LeDoussal,Phys.Rev.B52,1242
supported by a Grant-in-Aid on priority area ”Novel (1995).
QuantumPhenomenainTransitionMetalOxides,”from [25] A.P.Reyes,X.P.Tang,H.N.Bachman,W.P.Halperin,
Ministry of Education, Science, Sports and Culture J. A. Martindale, and P. C. Hammel, Phys. Rev. B 55,
R14737 (1997).
(12046241).
[26] H. N. Bachman, A. P. Reyes, V. F. Mitrovic, W. P.
3
Halperin, A. Kleinhammes, P. Kuhns, and W. G. Moul- FIG. 3. Recovery curves of 205Tl nuclear spin-echoes
ton, Phys.Rev.Lett. 80, 1726 (1998). against frequency at T=5 K (a) and those against temper-
[27] C. Bergemann, A. W. Tyler, A. P. Mackenzie, J. R. ature at ν=49.18-49.20 MHz (b). The solid curves are the
Cooper, S. R. Julian, and D. E. Farrell, Phys. Rev. B least-squares fits byEq. (3).
57, 14387 (1998).
[28] S.Kambe,Y.Yoshinari,H.Yasuoka,A.Hayashi,andY.
Ueda,Physica C 185-189, 1181 (1991).
(a) V (b) V
B B
S S S S
units) Kc, res →→ Kc, spiHn 0=2 T // c axis V B C B V V B C B V
arb. scKc, dia←→ Knight shift S B S S B S
(
o
ch T=
E V V
- 85 K
n
Spi 5 K FIG.4. IllustrationofvortexlatticesonaCuO2 plane,(a)
a perfect square lattice and (b) an imperfect square lattice.
49.0 ν 49.2 49.4 49.6 Opencirclesarethevortexcores. Thesitenotationconforms
0
to Ref. [13].
Frequency (MHz)
FIG. 1. 205Tl NMR spectra with field cooling (2 T along
the c axis) at T=85 and 5 K. ν0 is given by 205γnH0
(205γn=24.567 MHz/T). The small signal around 49.3 MHz 1000
at85Kisprobablyduetomisalignmentofsomeofthegrains. (a) H0=2.0 T (b) T↓f
250 K 100
e (arb. units) 111502000 KKK 205-1τ1/ (s)110 CL
R spin-echo scKdia(CS )↓ S↓← scKspin(ν) Echo Amplitud 7800 KK TLc~I6Q 85U5 KI KD 1000.101 (c)S
NM 0 ν10 FrequeV n c↓y2{ → 1 + ↓scKspin(V)}3V 205Tl Nuclear Spin- S 3214465500005050 KKKKKKKK←→ coexistence 205-1T1/ (s)1101001 CS
FIG. 2. Illustration of NMR spectrum in a vortex state. C L S5O KLID L
Superconductingdiamagneticshifts(dashcurve),d-wavespin 49.0 ν49.2 49.4 49.6 0.1
0 1 10 100
shifts (shaded region), and their combination (solid curve). Frequency (MHz) T (K)
FIG. 5. (a) 205Tl NMR frequency spectra, (b) 1/τ1, and
(c) 1/T1 with magnetic field cooling. Vortex melting (LIQ-
UID), coexistence of vortex solid with liquid (coexistence),
1 4499..0070 MMHHzz ((SC)) 1 T1=0 K and vortex lattice (SOLID) are denoted in (a). No appre-
49.12 MHz 20 K ciable frequency distribution of the 205Tl nuclear spin-echo
49.20 MHz (V) 30 K decay curve was found at any temperatures. The 205Tl nu-
49.30 MHz (V) 40 K
clearspin-latticerelaxation ratesweremeasuredatC,S,and
205pt() 0.1 (a) 0.1 (b) LT3ondutehetosoalisduplienrecsonindu(act)i.nTghgeapdawsihthlinlienseinno(dbe)s.and (c) are
0.01
T=5 K ν=49.18-49.20 MHz
0.01
0 1 2 0 20 40 60
t (s) t (ms)
4