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江畔独步寻花其六b 2000Antiferromagneti乘法法则
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d Density in
La 2−x Sr x CuO 4C.Panagopoulos a ,B.D.Rainford b ,J.R.Cooper a ,C.A.Scott c a IRC in Superconductivity and Department of Physics,University of Cambridge,Cambridge CB30HE,United Kingdom b Department of Physics and Astronomy,University of Southampton,Southampton S0171BJ,United Kingdom c Rutherford Appleton Laboratory,ISIS Facility,Didcot,Oxon OX110QX,United Kingdom Abstract We have performed muon spin relaxation and low field ac -susceptibility measurements in a ries of high quality samples of La 2−x Sr x CuO 4(x =0.08−0.24)as a function of temperature.Superconductivity is found to co-exist with low temperature spin glass order up to the optimally doped region where the normal state pudogap also clos.The systematic depletion of the superfluid density with the enhancement of aniferromagnetic correlations with underdoping indicates a competition between antiferromagnetic correlations and superconductivity.Establishing and understanding the pha diagram of the high-T c superconductors (HTS)versus temperature and dopin规划人生
g has been one of the major challenges in modern solid state physics.The parent compound La 2CuO 4of the first HTS family to be discovered,
La 2−x Sr x CuO 4,is an insulator exhibiting long range antiferromagnetic (AF)order,which is eventually destroyed as carriers are doped into the CuO 2planes.After passing through a spin glass (SG)state superconductivity emerges near 0.06holes/planar-Cu-atom and follows an approximately parabolic doping dependence until it disappears at x ≃0.30.Spectroscopic evidence however,indicates that AF correlations do not ize to exist with the emergence
of superconductivity,but instead a short range ordered AF state persists in the supercon-ducting state[1,2].This obrvation rais fundamental questions as to how far into the superconducting regime of the pha diagram the AF correlations persist and how,if at all,the affect the superconductivity.
In this short paper we prent briefly new experimentalfindings in which the signatures of antiferromagnetic correlations is obrved to persist up to x≃0.17.Wefind a clo correlation between the doping dependence of the AF and the absolute value of the superfluid density,ρs(0).The latter is almost constant for approximately x>0.17and drops with the enhancement of the AFfluctuati
ons,undergoing an incread depletion in the vicinity of the stripe pha region(x=0.125).The results suggest that the AF order parameter competes with the superconducting counterpart in more than50%of the superconducting region of the pha diagram.
The samples studied were single-pha polycrystalline La2−x Sr x CuO4(LSCO)(x=0.08, 0.10,0.125,0.15,0.17,0.20,0.22,0.24)prepared using solid-state reaction procedures.No other phas were detected by powder x-ray diffraction and the pha purity is thought to be better than1%.Highfield magnetic susceptibility measurements showed no signatures of excess paramagnetic centres and the measured values of T c and lattice parameters are also in very good agreement with published work[3].The samples have been extensively char-acterid by veral transport,magnetic and spectroscopic techniques,all indicating their high quality.Zero-field(ZF)and transver-field(TF)µSR experiments were performed at the puld muon source,ISIS Facility,Rutherford Appleton Laboratory.The samples were mounted on a silver plate either on the cold stage of a dilution refrigerator or in a variable temperature helium cryostat,enabling spectra to be collected over the temperature range 40mK to50K.The in-plane magnetic penetration depth,λab,(λ−2ab∼ρs)was determined both by a low-field ac-susceptibility technique(typically at1G and333Hz)on grain-aligned powders and from the analysis of TF-cooledµSR measurements.The latt
er were carried out on unaligned powders in afield of400G.Details for derivingλab in HTS from the measured low-field ac-susceptibility and TF-µSR spectra can be found elwhere[4,5].
In Fig.1we prent the time evolution of the ZF muon asymmetry for x=0.08 (T c=21K)as a function of temperature.In all samples the high temperature form of the depolarisation is Gaussian,consistent with dipolar interactions between the muons and their near neighbour nuclear moments.This was verified by applying a50G longitudinal field,which completely suppresd the depolarisation.As the temperature is lowered the ont of dynamical relaxation process becomes apparent in the change in the shape of the depolarisation function.The samples with x=0.08,0.10and0.125follow the same pattern, which is indicative of the ont of spin glass ordering at low temperature.For simplicity, we have chon to parametri the form of the depolarisation function as a stretched ex-ponential,G z(t)=A1exp[−(λt)β]+A2.The constant term A2accounts for a small time independent background arising from muons stopping in the silver backing plate.At high temperatures wefind that the value ofβ≈2,but for samples with x<0.15it decreas smoothly to a value approaching0.5at low temperatures.This”root exponential”behaviour is widely found in the temperature regime just above the glass temperature in spin glass [6].The temperature dependence ofβfor the prent samples is shown in Fig.2.We have ud the temperature at which the value ofβdrops below2as the ont temp
erature for AF correlations T sf,and the temperature whereβ≈0.5as a measure of T sg the spin glass freezing temperature.Wefind that for the x<0.08sample for example,the relaxation rate parameterλβis peaked clo to T sg(Fig.3).At temperatures below T sg the form of the depolarisation function changes:there is an initial rapid decay of G z(t),followed by a slowly damped tail(e left hand panel in Fig.1).This behaviour is very characteristic of the behaviour of spin glass below T sg,and has been attributed by Uemura et al,[7]to the effects of the static distribution offield,combined with dynamical process in the frozen spin glass state.
The prent data show that SG freezing persists up to and beyond x=0.125.Indeed the ont of AF correlations for x=0.125occurs at a higher temperatures than for x= 0.10.This is probably associated with the formation of stripe domains in this range of concentration[1].For x=0.15and0.17the trends ofβ(T)suggest a very small value
of spin glass temperature T sg(<45mK)withfluctuations tting just below8K and2K, respectively.This suggests that for higher dopings the AF correlations are abnt or at least beyond experimental range.
In Fig.4we summari the esnce of this work by comparing the doping dependence of T sf and T s
g,(including data for T sg from ref.[2]),with that ofλab(0)−2∼ρs(0).We note that our vales of T sg for x=0.08and0.10are in excellent agreement with tho reported in ref.
[2].Figure4indicates that although the freezing of spins occurs at very low temperatures, T sg≪T c,magneticfluctuations are apparent at significantly higher , T sf≈0.5T c for x=0.10and T sf≈0.2T c for x=0.15).Therefore,a large fraction of the supeconducting region of the pha diagram coexists with AF picking up near x=1/8and eventually disappearing in the lightly overdoped region where the normal state(or pudo) gap,∆N,is known to clo[8],suggesting a connection between∆N and antiferromagnetic correlations.
As shown in Fig.4,the superfluid density is doping independent in the region where T sg =T sf=0and is gradually reduced with the incread evolution of AF correlations(ie.,for x<0.20),undergoing a local dip in the1/8region where AF is enhanced possibly due to the stripe pha.We would like to note the striking parallel changes inρs(0)with T sg,T sf emphasising the intimate connection ofρs(0)with the AF background rather than simply T c.
The prent results suggest that AF coexists with superconductivity in the underdoped and slightly overdoped samples and becomes undetectable in the heavily overdoped regime where the pudog
ap also disappears.The systematic depletion of the superfluid density with increasing AF correlations(Fig.4)indicates that the latter compete with superconductivity andρs(0)is not simply a function of T c
We are grateful to Dr A.D.Taylor of the ISIS Facility,Rutherford Appleton Laboratory for the allocation of muon beam time. C.P.thanks Tao Xiang for uful discussions and Trinity College,Cambridge forfinancial support.
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个人储蓄
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FIGURE CAPTIONS
Figure1.Typical zero-fieldµSR spectra of La2−x Sr x CuO4for x=0.08measured at 1.3,5and9K.The solid lines arefits of the stretched exponential,G z(t)=A1exp[−(λt)β] +A2(e text for details).
Figure 2.Temperature dependence of the exponentβof La2−x Sr x CuO4for x= 0.08,0.10,0.125,0.15,0.17.
Figure.3.Temperature dependence of the relaxation rate parameterλβof La2−x Sr x CuO4 for x=0.08,0.10,0.125,0.15,0.17.
Figure4.Pha diagram of La2−x Sr x CuO4showing the doping dependence of T c(clod lower triangles),T sg(clod circles),T sf(clod squares),andλab(0)−2∼ρs(0)(clod upper triangles).Open cirlces are data for T sg taken from ref.[2].A schematic variation of the Nell temperature T N is also shown as a broken line.
