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d-Wave symmetry in Bi2212 and TI2223 vortex states: an ME-μSR study
PHYSlCA ELSEVIER
Physica C 341 348 ( 2 0 0 0 ) 1 0 9 7 - 1 0 9 8 www.elsevier.nl/Iocate/physc
d - W a v e S y m m e t r y in B i 2 2 1 2 and T I 2 2 2 3 V o r t e x States: an M E - ~ S R S t u d y R.D. Santiago a, A.M. Krupski a, C. Boekema a,b and D.W. Cooke c aphysics Department, San Jose State University, San Jose CA 95192 - 0106 bNational High Magnetic Field Laboratory, Tallahassee FL 32310 CLos Alamos National Laboratory, Los Alamos NM 87545 The vortex states of Bi2212 and TI2223 have been studied by muon-spin resonance (I~SR). Similar to d-wave order predictions, and as recently found for M1237, twin-peak signatures in the main vortex signals have been observed at 5 kOe, below T/Tc = 0.8. The twin-peak splitting is proportional to {1 - (T/Tc)n} , with n about 3. 1. Introduction By muon-spin rotation (tISR) we have studied the cuprate vortex states. [1, 2] A MaximumEntropy (ME) technique has been used to analyze these p.SR data. ME is a sensitive timeseries data analysis method. [3] We have found [1, 4] that the main vortex signal for MBa2Cu307 (M1237; M, a magnetic rare-earth ion: Er, Gd, or Ho) shows a signature of two peaks in the vortex field distribution, similar to dwave order predictions. [5, 6] One question is if the observed twin peaks of the main vortex signal are caused or enhanced by the M-layer magnetism. We report on our ME analysis of the Bi2Sr2CaCu20 x (Bi2212) and TI2Ba2Ca2Cu3Ox (TI2223) vortex data [7], focusing on possible d-wave splitting in the vortex-pancake states, with no additional magnetism present. We need to know whether the twin peaks are present in Bi2212 and TI2223 vortex states, and if their splitting is temperature dependent. 2. ME-I~SR of Cuprate Vortex States Our polycrystalline cuprate samples are highquality single-phase ceramics, prepared at Los Alamos National Laboratory. The samples have been field cooled in transverse field (TF). TF-pSR data are analyzed using an ME-Burg method for minimizing noise in Si = T_,Ck Si-k + ni (1) where Si is the muon-spin polarization at time i, and ni is the assumed white noise term. [1-4] The auto-regressive coefficients Ck (k = 1 ..... p) are determined from the data, where p is the order of the ME-model description. Before ME transformation, Si is weighted by a Gaussian filter function with a filter time Tf. 0921-4534/00/$ - see front matter © 2000 Elsevier Science B.~ PII S0921-4534(00)00801-7
The following attributes for M1237 vortex states have been revealed by our I~SR studies: [1,2] a) A peak near the applied field originates from grain boundaries (GB). b) Below 25 K, a low field tail is present in the vortex field distribution; [8] ¢) A sharp fall-off in the field distribution below the applied field occurs at B*, the upper limit of the low field tail. B* decreases with increasing M magnetic moment; [2, 4] d) Below 10 K and for magnetic M ions, twin-peak signatures in the main M1237 vortex signals are observed in ME transforms, using long Tf's. [1] 3. Bi2212 and TI2223 ME-I~SR results In an earlier ME-pSR study [7] on Bi2212 (Tc = 80 K) and TI2223 (Tc = 105 K), we focused only on the comparison of the unusual M1237 vortex characteristics (b, c) using only short Tf's. Consistent with vortex-pancake formation, and with the absence of magnetic ions and CuO chains, none of these anomalies (b, c) were observed. [7] We ignored then to further study some structure seen for long Tf's in these vortex field distributions. To observe a twin peak, two criteria for determining the "best" Gaussian filter time compete: 1)to reduce the intensity of the long-living GB signal a short Tf (~ 1 IJS) is needed; 2) to measure a twin-peak splitting of ~ 0.5 MHz, the preferred "If is about 2 liS (or longer). In Fig. 1, ME transforms (Tf = 1.5 ItS, an optimum value) of Bi2212 and TI2223 #SR vortex data recorded at 10 K and 5 kOe are depicted. The twin peaks are between 4.91 and 4.95 kOe. The peak for Bi2212 and the change in slope for TI2223 both at 4.96 kOe originate from the reduced GB signals near the applied field. The slight shoulder at 4.90 kOe All rights reserved.
R.D. Santiago et aL/Pl~vsica C 341-348 (2000) 109~1098
1098
could be a similar fall-off observed for Y1237 (Y, a non-magnetic ion). [2, 4] The twin splittings (0.3 MHz) are consistent with those found for M1237 (0.45(9) MHz between 4 and 7 K [1]) and Y1237 (0.40(8) MHz between 3 and 10 K [4]). 0.6
/T12223 (o)
~
°']'"Oe''0"/ r'" ~03 4
II
~
/'~
I
i;
I
0.2 0.
4.86 4.88
I
0.4
4.9
4.92 4.94 4.96 4.98 B!j [kOe]
I
I
•
0.3-
5
I Bi2212 (.) TI2223 (o)
O
The twin-peak signatures observed in the Bi2212 and TI2223 5-kOe vortex states are clearer than those of the Y1237 1-kOe vortex states. [4] This is probably because of the higher frequency range of the 5-kOe ~SR data. The -0.3 MHz 'beat' signal due to the twin splitting is more easily resolved at higher (-67 MHz) frequencies. The ME estimates of the twin-peak splitting for Bi2212 and TI2223 are about twice than predicted. [5, 6] This large difference in twin splitting suggests that other (induced) s- and d- wave components besides dx2-y2 can be considered. Further, these cuprate vortex states may deviate from type-II behavior, as is assumed for the d-wave order calculations. The temperature dependence up to 0.8Tc substantiates the likely existence of the d-wave twin-peak signatures. The quasiclassical d-wave order modeling [5] predicts twin peaks for all temperatures below T c and H/Hc2 < 0.15. Thus, this ME-I~SR study supports the notion of d-wave symmetry in the Bi2212 and TI2223 vortex states. Acknowledgments
Research is supported by NSFoREU (PHY9605147), LANL-DOE, SJSU College of Science, WiSE@SJSU and SJSU Graduate Studies. AK, RS and CB thank LLNL for their summer hospitality. CB kindly acknowledges financial support and hospitality of the Physik Institut, Universit&t Z0rich and NHMFL during his sabbatical.
"~0.2 -
<-
0.1-
! 0.2
4. Discussion and Conclusion
5.
eo
z~
15 K. For Bi2212 and TI2223, this upper limit is about 0.8 T/T c.
References 014
0.16
0.18 TITc
In Fig. 2, the temperature dependence of the twin-peak splitting Atwin is shown. Fitting with Atwin = Atwin(0) { 1 -(T/Tc) n} (2) yields Atwin(0) = 0.31(1) MHz and n = 3.1(4). Below Tc, there are no major differences between the TI2223 and Bi2212 vortex signals. Near T c, the overlap of the vortex signal and GB signal is too large to observe both twin peaks. These overlap problems are major for M1237 and Y1237, such that for their vortex states twin-peak signatures can only be seen below
1] C. Boekema eta/, J Appl Phys 83 (1998) 6795. 2] S. Alves et al, Phys Rev B49 (1994) 12396; Hpf Interact 86 (1994) 513. 3] D.S. Stephenson, Progress in NMR Spectroscopy 20 (1988) 515; N. Wu, "The Maximum Entropy Method," Springer Berlin (1997). 4] C. Boekema et al, Phys Rev B in preparation. 5] M. Ichioka et al, Phys Rev B59 (1999) 8902. 6] M.H.S. Amin etal, Phys Rev B58 (1998) 5848; I. Affleck et al, Phys Rev B55 (1997) R704; D.L. Fedder and C. Kallin, Phys Rev B55 (1997) 559; J.H Xu etal, Phys Rev B53 (1996) R2991; M. Franz et al, Phys Rev B53 (1996) 5795. 7] C. Boekema et al, Physica C235-240 (1994) 2633. 8] C. Boekema et al, Physica 0282-287 (1997) 2069.
Physica C 341 348 ( 2 0 0 0 ) 1 0 9 7 - 1 0 9 8 www.elsevier.nl/Iocate/physc
d - W a v e S y m m e t r y in B i 2 2 1 2 and T I 2 2 2 3 V o r t e x States: an M E - ~ S R S t u d y R.D. Santiago a, A.M. Krupski a, C. Boekema a,b and D.W. Cooke c aphysics Department, San Jose State University, San Jose CA 95192 - 0106 bNational High Magnetic Field Laboratory, Tallahassee FL 32310 CLos Alamos National Laboratory, Los Alamos NM 87545 The vortex states of Bi2212 and TI2223 have been studied by muon-spin resonance (I~SR). Similar to d-wave order predictions, and as recently found for M1237, twin-peak signatures in the main vortex signals have been observed at 5 kOe, below T/Tc = 0.8. The twin-peak splitting is proportional to {1 - (T/Tc)n} , with n about 3. 1. Introduction By muon-spin rotation (tISR) we have studied the cuprate vortex states. [1, 2] A MaximumEntropy (ME) technique has been used to analyze these p.SR data. ME is a sensitive timeseries data analysis method. [3] We have found [1, 4] that the main vortex signal for MBa2Cu307 (M1237; M, a magnetic rare-earth ion: Er, Gd, or Ho) shows a signature of two peaks in the vortex field distribution, similar to dwave order predictions. [5, 6] One question is if the observed twin peaks of the main vortex signal are caused or enhanced by the M-layer magnetism. We report on our ME analysis of the Bi2Sr2CaCu20 x (Bi2212) and TI2Ba2Ca2Cu3Ox (TI2223) vortex data [7], focusing on possible d-wave splitting in the vortex-pancake states, with no additional magnetism present. We need to know whether the twin peaks are present in Bi2212 and TI2223 vortex states, and if their splitting is temperature dependent. 2. ME-I~SR of Cuprate Vortex States Our polycrystalline cuprate samples are highquality single-phase ceramics, prepared at Los Alamos National Laboratory. The samples have been field cooled in transverse field (TF). TF-pSR data are analyzed using an ME-Burg method for minimizing noise in Si = T_,Ck Si-k + ni (1) where Si is the muon-spin polarization at time i, and ni is the assumed white noise term. [1-4] The auto-regressive coefficients Ck (k = 1 ..... p) are determined from the data, where p is the order of the ME-model description. Before ME transformation, Si is weighted by a Gaussian filter function with a filter time Tf. 0921-4534/00/$ - see front matter © 2000 Elsevier Science B.~ PII S0921-4534(00)00801-7
The following attributes for M1237 vortex states have been revealed by our I~SR studies: [1,2] a) A peak near the applied field originates from grain boundaries (GB). b) Below 25 K, a low field tail is present in the vortex field distribution; [8] ¢) A sharp fall-off in the field distribution below the applied field occurs at B*, the upper limit of the low field tail. B* decreases with increasing M magnetic moment; [2, 4] d) Below 10 K and for magnetic M ions, twin-peak signatures in the main M1237 vortex signals are observed in ME transforms, using long Tf's. [1] 3. Bi2212 and TI2223 ME-I~SR results In an earlier ME-pSR study [7] on Bi2212 (Tc = 80 K) and TI2223 (Tc = 105 K), we focused only on the comparison of the unusual M1237 vortex characteristics (b, c) using only short Tf's. Consistent with vortex-pancake formation, and with the absence of magnetic ions and CuO chains, none of these anomalies (b, c) were observed. [7] We ignored then to further study some structure seen for long Tf's in these vortex field distributions. To observe a twin peak, two criteria for determining the "best" Gaussian filter time compete: 1)to reduce the intensity of the long-living GB signal a short Tf (~ 1 IJS) is needed; 2) to measure a twin-peak splitting of ~ 0.5 MHz, the preferred "If is about 2 liS (or longer). In Fig. 1, ME transforms (Tf = 1.5 ItS, an optimum value) of Bi2212 and TI2223 #SR vortex data recorded at 10 K and 5 kOe are depicted. The twin peaks are between 4.91 and 4.95 kOe. The peak for Bi2212 and the change in slope for TI2223 both at 4.96 kOe originate from the reduced GB signals near the applied field. The slight shoulder at 4.90 kOe All rights reserved.
R.D. Santiago et aL/Pl~vsica C 341-348 (2000) 109~1098
1098
could be a similar fall-off observed for Y1237 (Y, a non-magnetic ion). [2, 4] The twin splittings (0.3 MHz) are consistent with those found for M1237 (0.45(9) MHz between 4 and 7 K [1]) and Y1237 (0.40(8) MHz between 3 and 10 K [4]). 0.6
/T12223 (o)
~
°']'"Oe''0"/ r'" ~03 4
II
~
/'~
I
i;
I
0.2 0.
4.86 4.88
I
0.4
4.9
4.92 4.94 4.96 4.98 B!j [kOe]
I
I
•
0.3-
5
I Bi2212 (.) TI2223 (o)
O
The twin-peak signatures observed in the Bi2212 and TI2223 5-kOe vortex states are clearer than those of the Y1237 1-kOe vortex states. [4] This is probably because of the higher frequency range of the 5-kOe ~SR data. The -0.3 MHz 'beat' signal due to the twin splitting is more easily resolved at higher (-67 MHz) frequencies. The ME estimates of the twin-peak splitting for Bi2212 and TI2223 are about twice than predicted. [5, 6] This large difference in twin splitting suggests that other (induced) s- and d- wave components besides dx2-y2 can be considered. Further, these cuprate vortex states may deviate from type-II behavior, as is assumed for the d-wave order calculations. The temperature dependence up to 0.8Tc substantiates the likely existence of the d-wave twin-peak signatures. The quasiclassical d-wave order modeling [5] predicts twin peaks for all temperatures below T c and H/Hc2 < 0.15. Thus, this ME-I~SR study supports the notion of d-wave symmetry in the Bi2212 and TI2223 vortex states. Acknowledgments
Research is supported by NSFoREU (PHY9605147), LANL-DOE, SJSU College of Science, WiSE@SJSU and SJSU Graduate Studies. AK, RS and CB thank LLNL for their summer hospitality. CB kindly acknowledges financial support and hospitality of the Physik Institut, Universit&t Z0rich and NHMFL during his sabbatical.
"~0.2 -
<-
0.1-
! 0.2
4. Discussion and Conclusion
5.
eo
z~
15 K. For Bi2212 and TI2223, this upper limit is about 0.8 T/T c.
References 014
0.16
0.18 TITc
In Fig. 2, the temperature dependence of the twin-peak splitting Atwin is shown. Fitting with Atwin = Atwin(0) { 1 -(T/Tc) n} (2) yields Atwin(0) = 0.31(1) MHz and n = 3.1(4). Below Tc, there are no major differences between the TI2223 and Bi2212 vortex signals. Near T c, the overlap of the vortex signal and GB signal is too large to observe both twin peaks. These overlap problems are major for M1237 and Y1237, such that for their vortex states twin-peak signatures can only be seen below
1] C. Boekema eta/, J Appl Phys 83 (1998) 6795. 2] S. Alves et al, Phys Rev B49 (1994) 12396; Hpf Interact 86 (1994) 513. 3] D.S. Stephenson, Progress in NMR Spectroscopy 20 (1988) 515; N. Wu, "The Maximum Entropy Method," Springer Berlin (1997). 4] C. Boekema et al, Phys Rev B in preparation. 5] M. Ichioka et al, Phys Rev B59 (1999) 8902. 6] M.H.S. Amin etal, Phys Rev B58 (1998) 5848; I. Affleck et al, Phys Rev B55 (1997) R704; D.L. Fedder and C. Kallin, Phys Rev B55 (1997) 559; J.H Xu etal, Phys Rev B53 (1996) R2991; M. Franz et al, Phys Rev B53 (1996) 5795. 7] C. Boekema et al, Physica C235-240 (1994) 2633. 8] C. Boekema et al, Physica 0282-287 (1997) 2069.