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Physica B 280 (2000) 201}204
Static and dynamical magnetic characters in doped Cu oxides
Y. Endoh!,*, R.J. Birgeneau", M.A. Kastner", G. Shirane#, K. Yamada$
!Department of Physics, CREST, Tohoku University, Aramaki Aza-Aoba, Aoba-ku, Sendai 980-8578, Japan"Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
#Department of Physics, Brookhaven National Laboratory, Upton, NY 11973, USA$Institute for Chemical Research, Kyoto University, Uji, 611-0011, Japan
Abstract
The discovery of the spin density wave (SDW) state de"ned as stripe in the doped Cu oxides becomes a central issue inthe elucidation of the high-temperature superconducting mechanism. We present the coexistence of the stripe order andsuperconductivity, and the change of the stripe structure associated with the insultor}metal transition. Both static anddynamical SDW are robust of the high-temperature superconducting Cu oxides. ( 2000 Published by Elsevier ScienceB.V. All rights reserved.
Keywords: Ac susceptibility; Diagonal spin stripe; Vertical spin stripe
1. Introduction
The self-organized stripe phase formed in the two-dimensional (2D)-doped Mott-insulator [1] is recognizedto be the "rst realization of the charge and spin separ-ation in such highly correlated electron metals. The stripeorder is constructed by the best compromise of dominantforces of the strong short-range antiferromagnetic ex-change interactions competing with the long-rangeCoulomb interactions. In most cases, charges are con-"ned in the localized charge cluster intervened by theinsulating background and concomitantly the systembecomes a charge ordered insulator. However, sucha stripe order is a robust feature of the high-temperaturesuperconductors consisting of the layered Cu oxides bymostly charge transfer type hole doping.
A direct evidence of the existence of stripe phases in thedoped antiferromagnetic oxides has been revealed bydecisive neutron scattering experiments. Tranquada et al.discovered the spin density wave (SDW) in the dopedLa
2NiO
4[2], where the wave vector, e of SDW were
determined besides the charge modulation, 2e; more pre-cisely, the superlattice modulation due to the charge
*Corresponding author.E-mail address: [email protected] (Y. Endoh)
density wave (CDW) formation. The fact of the phasedi!erence between SDW and CDW indicates that theantiphase domain boundary exists in spin sections.
In early years just after the discovery of the high-temperature superconductivity [3], energy-integratedneutron scattering to determine the instantaneous spincorrelations from the doped La
2~xSr
xCuO
4(LSCO)
showed a double peaked structure in q centered at thecommensurate wave vector (n,n) in x'0.06 [4]. On theother hand, the spin correlation function was "tted tosingle Lorenzian line shape in the lightly doped region(x(0.04). This result in early days contains a robustfeature of the LSCO showing the inherent relation be-tween superconductivity and spin stripes. We will comeback to this particular point in the end of our discussion.
In this presentation, we "rst demonstrate a clear resultof the on-set of the diagonal spin stripe order in thelightly doped, insulating LSCO [5]. Since the stripe inlayered materials is 1D in nature, the di!raction patternof the stripe should hold a two-fold symmetry projectedon the reciprocal space for the CuO
2square lattice of the
four-fold symmetry in such layered copper oxides. In factwe proved it experimentally. Then we show the transitionfrom the diagonal to vertical stripe order associated withinsulating (spin glass) * metal (superconductor)transition near 0.05(x(0.06 by 453 rotation of thestripe modulation wave vector around (n,n) [6]. Finally,
0921-4526/00/$ - see front matter ( 2000 Published by Elsevier Science B.V. All rights reserved.PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 5 7 3 - 2
Fig. 1. Di!raction data at ¹!1.5 K from a single structuraltwin domain in LSCO (x"0.05). Scan trajectories of (a), (b) and(c) are in the insert (cited from Ref. [8]).
we present dynamical spin susceptibility in both diagonaland vertical stripe phases, which evolves the mechanismof the high-temperature superconductivity as the result ofan inherent coupling of spin and charge.
2. Diagonal spin stripes in the spin glass phase
Though the existence of a diagonal stripe in the dopedCu oxides was theoretically proposed in the early days[7], it is very recent that such a spin stripe order has beendirectly observed [8]. Furthermore, this experiment pro-vides, for the "rst time, a two-fold symmetry of the 1Ddiagonal stripe order in the quasi-2D real lattice byelaborate neutron di!raction measurements. The neu-tron di!raction experiments with well-tuned spectrom-eter control revealed the twin structure in the distortedlattice of the orthorhombic symmetry with unbalanceddomain distribution [6]. Using this symmetry breakingin the crystal structure, we could directly observe the 1Dfeature of SDW. Details have been described in severalpublications [5,6,8], and only an essence of the results issummarized here.
A pair of magnetic elastic scattering peaks split fromthe antiferromagnetic superlattice positions of both(1, 0, 0)
035)0and (0, 1, 0)
035)0, de"ned as the incommensur-
ate static SDW, which were observed in lightly dopedLSCO (x)0.05) at very low temperatures (Fig. 1). Judg-ing from the observed magnetic scattering patterns, thestripe order propagates along b
035)0-axis with the modu-
lation wave vector d, which is approximately linear to x.Unlike in the undoped La
2CuO
4, the antiferromagnetic
spin structure in each magnetic domain separated bycharge stripes is a mixture of two components with di!er-ent propagation vectors; a
035)0and b
035)0and di!erent
spin orientations as well. Then all the spins freeze ina spin glass manner at the lowest temperatures with the3D short-range ordered state [9,10].
It is emphasized here that the stripe modulation wavevector holds approximately a linear relation of d"x,which seems to follow a heuristic relation discovered inthe superconducting phase (de"ned Yamada's relation)[11]. It should be noticed that the Yamada's relation wasdetermined from a vertical stripe structure, which is dis-cussed in the following section.
3. Vertical stripe in the superconducting phase
Prior to our detailed studies on spin structure from thesuperconducting phase in the doped LSCO (x'0.06)[12] and La
2CuO
4`y(¹
#"42 K) (LCO) [13], there
have been reported extensive studies on Nd doped LSCO[14]. The superconductivity in the latter system is sup-pressed by Nd substitution. On the other hand, LSCO aswell as crystals studied here are genuine superconduc-
tors. As just introduced in the previous section, the SDWpropagates along atetra axes rotating 453 from the diag-onal stripe around (n, n) in the tetragonal notation, whichis de"ned the vertical stripe. Like preceding section wesummarize here the essence of the recent publications[12,13]. In LSCO with x"0.12 (close to x"1/8 ) as wellas LCO, the stripe structure has the two-fold symmetryin the reciprocal space for the 2D quasi square latticeshown in Fig. 2. It is obvious that the incommensuratepeaks form a rectangular structure (d
HOd
K) or a distinct
angle from the principal axes of the based lattice. Theelastic scattering from such a stripe phase is sharp withthe resolution limited or very narrow q-width indicat-ing a long-range order unlike those in the diagonalstripe phase. The elastic magnetic peak intensities ap-parently grows as the superconductivity sets in, sugges-ting the strong correlation between the two components.In particular, the temperature dependence of the orderparameter (the scattering peak intensities) in LCO ap-proximately follows the BCS order parameter (square).
x dependence of the vertical stripe order has beenextensively elucidated and then the static stripe order
202 Y. Endoh et al. / Physica B 280 (2000) 201}204
Fig. 2. Positions of the elastic incommensurate SDW in a singledomain in La
2CuO
4`y(¹
#"42 K). H and K are in ortho-
rhombic units. cited from Ref. [12].
Fig. 3. Energy-integrated scattering pro"les of LSCO with vari-ous hole concentration, p. Scans are across the orthorhombic(h,0, l) with k
¶llel to l. Cited from note made by
T.R.Thurston (1989).
seems to exist in the x range of 0.06(x(0.13. Moreprecisely, the stripe order is the most stable in x"0.12and it extends in the vicinity of this speci"c hole concen-tration near x"1
8. The modulation vector, d saturates at
around 0.125 with increasing x (x(0.15).
4. Dynamical magnetic susceptibility
The dynamical magnetic susceptibility from layeredCu oxide superconductors have extensively been studiedby mainly inelastic neutron scattering [15]. Here wediscuss the dynamical feature taking a related issue ofthe stripe phase into it. As described in the "rst section,the instantaneous spin correlation function measured byenergy-integrated scattering demonstrated the change ofthe scattering pro"le in the 2D momentum space orq2D
from the single Lorenzian to the double-peakedfeature associated with the insulator}metal transition(Fig. 3). Extensive studies show that the instantaneousspin correlation function of single-Lorenzian signalscould be analyzed under the basic notion that well-developed 2D antiferromagnetic short-range order oc-curs in the lightly doped Cu oxides [16,17]. It means thatspin #uctuations is likely antiferromagnetic spin wavessimilar to that of the undoped La
2CuO
4propagating
from the center of the commensurate position, (n,n).Indeed the inelastic neutron scattering has revealed theexistence of the spin wave in the lightly doped LSCO[18].
Then a basic change to the double peak feature in theinstantaneous spin correlations may coincide with the
change from diagonal to vertical stripe order nearx&0.06. According to very recent inelastic neutron scat-tering from the optimum doped LSCO (¹
#"37 K),
scattering pro"le is so unusual that the incommensuratepeaks persist at large transferred energies higher than 20meV at low temperatures [19]. Though these incommen-surate spin #uctuations were reported to behave like spinwave mode at higher energies, it is still uncertain that thiscross-over might be real. It should be clari"ed in thefuture experiments.
Finally, the fact of a linear relation of d of the dynam-ical SDW modulation vector in the vertical stripe phase(x'0.06) with respect to ¹
#(d"A¹
#) is discussed. This
linear relation deviates in x'0.12, and saturates atabout 0.15 (optimum) for LSCO. Eventually, ¹
#goes
away in over doped region (x'0.25) [11]. Though thedata points are a few, the similar linear relation of d ver-sus ¹
#holds in YBCO in which the doping is controlled
by oxygen concentration [20,21]. We can derive a scalefactor of 1.5 in order to superpose both linear lines.Then it is very important that d reaches 0.17 in YBCO
Y. Endoh et al. / Physica B 280 (2000) 201}204 203
suggesting that more charges are doped in the stripes.The fact indicates that incommensurate spin dynamics orthe dynamical SDW is also a robust feature of the high¹
#superconductivity in Cu oxide metals.
Acknowledgements
YE acknowledges the kind hospitality of BrookhavenNational Laboratory, where he wrote the main text dur-ing the summer program there. The main work wassupported by the US}Japan Cooperation Research Pro-gram on Neutron Scattering. The work at Tohoku andKyoto has been supported by a Grant-In-Aid for Scient-i"c Research of Monbusho and the Core Research forEvolutional Science and Technology (CREST) projectsponsored by the Japan Science and Technology Cor-poration. The work at MIT was supported by the US-NSF under Grant No. DMR97-04532 and by theMRSEC Program of the NSF under Award No.DMR98-08941. The work at BNL was carried out underContract No. DE-AC02-98CH10886, DMS, US-Depart-ment of Energy.
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