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Spin susceptibility in underdoped YBaCuO single crystals from NMR
Physiea C 235-240 (1994) 1677-1678 North-Holland
PHYSlCA
Spin susceptibility in underdoped YBaCvO single crystals from NMR T. Auler a C. Berthier a,b, Y. Berthier a, P. Carretta ~,b, $. A. Gillet a, M. ttorvati6 b p. S~gransan a and J. Y. Henry e aLaboratoire de Spectrometric Physique, UJF Grenoble I, B.P. 87, 38402 St. Martin d'H~res, France bbaboratoire des Champs Magn~tiques Intenses, CNRS et MPI, B.P. 166X, 38042 Grenoble, France ¢D~partement de Recherche Fondamentale du CENG, 38401 Grenoble, France We report on Say, eaCu and 1tO NMR measurements in the normal state of YBaCuO single crystals (To = 91 K and T¢ = 48 K). A comprehensive description of all N M R results is obtained starting from a spin susceptibdity with a contribution from antiferromagnetic spin fluctuations delineated by the inelastic neutron scattering data, and a contribution from itinerant quasi-particles with a characteristic frequency increasing at low temperatures. For the first time a complete analysis is given for yttrium spin-lattice relaxation data.
NMR has yielded information of paramount importance on several aspects of the microscopic spin susceptibility X(~',w) in high T~ superconductors, both of static and of dynamical character [1]. However, a global description of all NMR results is still missing. We present an analysis of 89y, 6aCu and 170 NMR data obtained on underdoped YBal 928r0 0 s C u 3 0 6 5 ( T c : 48 K, sample 1) and YBal 92Sr0 0sCuaO6 9~ (T~ = 91 K, sample 2) single crystals, which offers new insights on the descriptmn of x(q',w) An accurate comparison with inelastic neutron scattering (INS) findings is made, especially in view of the INS measurements performed on sample 2. The x(q', w) is supposed to stem from two distinct contributions: XAF, arising from the correlated antiferromagnetic (AF) spin fluctuations (AFF), and XOt", describing the itinerant charges or quasi-parhcles [1,2] For XAF we take a phenomenological form dehneated by INS, whose basis rehes on the random phase approximatmn In the low frequency limit
_
rA -
xet_@fCq~_r)2+(q,_~r)2]]( 1 -- rcosfqz)).
(la) l+r where the AF correlation length ( ((/a = 2 66 for sample 1 and 1.33 for sample 2 [3]) and the coupling r between two CuO2 planes of one bilayer are derived from the INS results FAr" cor0921-4534/94/$07 00 © 1994 - F.lsevmr Scmncc B V All nghls re,ervcd 092 I- ~534(94)01405- !
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T ~K) Figure 1. Temperature dependence of 89R (open triangles), 63R (open circles) and lrR (open diamonds) in sample I for tlo [I e. The closed triangles show S9R calculated from Eqs. 1 and 2 without adjustable parameters, using the values of FAF and ro derived from 6aR and 17R.
responds to the w-width of the peak In X"(q',w) at ~'= QAF = (Tr, rr, q~), centered around 30 meV r,~ T~. _n'_e~qureI.o1 X~ t:,~ t ~ ' d A F , n~ u ! W a S estimated ,%:,m ....... ments (see Ref [4]) (for sample 1 we used the data reported m Ref [5]). For the quasl-pamcles contribution, in the w ---- 0 limit, we write x" Qe(¢, o~
_ x'(0, o) Fo
(lb)
where X'(0, 0) is derived either from ]70 or sgy hyperfine shifts (17K, s9K), and the charactens-
r AHer et al IPhyswa C 235-240 (1994) 1677-1678
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T (K) Figure 2. Temperature dependence of ['AF and F0 in sample 1, as derived from our analysis.
tic frequency F0 " E F / h "., 1 / h D ( E F ) . The 6 3 C u ( 2 ) and 170(2,3) hyperfine coupling constants [6] and form factors [2] used to estimate the nuclear spin lattice relaxation rate
n = ( T I T ) -1, 72kB X"aF(q", WL) + X"QP(q, WL) n = 21t2B E, f(q~) WL ' q
(2) are the usual ones, derived from the Mfla-Riee Hamiltoman The Sgy form factor for Ho II c
f(q) = 64[eo,,,2(q:/2)[D~co~2(q~/2)cos~'(%/2)+ D~d,s,n 2(q~:::2)sin 2(%/2)] + D~2sin2fq./2)x . q 2 x [cos2(qz/2)sm2(%/2) + sm'(q~/2)cos (qu/2)]]
takes into account the &polar couphng to Cu spins Ddl = 0-327 kOe and Da2 = 0.289 kOe. The hyperfine coupling D = 5 1 4- 0.2 kOe was deduced comparing the temperature (T-) dependence of SgK¢¢ and 17K~¢ m the same sample. Analysing S"R and SgK m sample 2, we find D to be isotropic, while the amsotropy of SgK ~s due to the amsotropy of the spin susceptlbd]ty (k¢/k~b = 1 13 + 0 06), whtch can be accounted for by a small anisotropy of Cu 2+ Landb factor [7] In contrast to Ref [2], we found the assumptton, of efliaent filtering of AFF m 17R and Tindependence of F0 incompatible with the experunental data The AFF contribution to IzR ts
always found to be substantial, whatever shape in q-dependence of X"af(q',w) we assume. Moreover, the effect of AFF is directly observable in the T-dependence of the 17R/SgR ratio, as a consequence of the different form (filtering) factors of the two nuclei. Only the minor part of this T-dependence could a priori be attributed to the variation of the inter-plane coupling r(T), but this is contradicted by the INS data for YBa2Cu306 .~ which show that r = 1 and is temperature independent [3]. The only way to explain 17R within the previously defined framework, is to suppose that a relative increase of the AFF contribution is compensated by a decrease of the quasi-particle term due to increasing F0, which is possibly related to sharp singularities in D(EF). A T-dependent P0 would also explain the observed non-linear relation between S9R and S9K [7]. Therefore, we used experimental 17R and 63R values and Eqs. 1 and 2 to deduce FAF and F0 (see Fig. 2) and thus define completely the spin susceptibility. 89R could then be calculated with no further parameters, and it is found to be m fine agreement with the expel nental values both m magnitude and Tdependence (Fig. 1) Moreover, FAF and its T-dependence are in satisfactory agreement with the one derived from INS [3]. It is interesting to note that in sample 1 we get F0 cx 1/X'(0, 0), indi,:atmg that for the quasi-particle contributmn a Korringa relation [1] holds with a Korrmga factor S,¢ "=_03. REFERENCES 1 Appl Mag. Resonance 3 (1992) 383-750. 2. M. HorvatK et al., Phys Re~. B 48 (1993) 13848 3 L. P Regnault el al, this conference 4 J A Gfllet et al, this conference 5 M Takigawd, Phys Rev. B 49 (1994) 4158. 6 The used couphng constants (m kOe) are B = 83, A ~ = 40, A~ = -332 for 63Cu, and C , ~ = 9 6 , ( ' ~ = 9 4 C b = 154 for 170 [1,2] 7 M Takmgawa, W L llults and J L. Smgh. Phys Rev Lett 71 (1993) 2650; tI. Ailoul c t a l , Phys Rev Left 70(1993), 117i.
PHYSlCA
Spin susceptibility in underdoped YBaCvO single crystals from NMR T. Auler a C. Berthier a,b, Y. Berthier a, P. Carretta ~,b, $. A. Gillet a, M. ttorvati6 b p. S~gransan a and J. Y. Henry e aLaboratoire de Spectrometric Physique, UJF Grenoble I, B.P. 87, 38402 St. Martin d'H~res, France bbaboratoire des Champs Magn~tiques Intenses, CNRS et MPI, B.P. 166X, 38042 Grenoble, France ¢D~partement de Recherche Fondamentale du CENG, 38401 Grenoble, France We report on Say, eaCu and 1tO NMR measurements in the normal state of YBaCuO single crystals (To = 91 K and T¢ = 48 K). A comprehensive description of all N M R results is obtained starting from a spin susceptibdity with a contribution from antiferromagnetic spin fluctuations delineated by the inelastic neutron scattering data, and a contribution from itinerant quasi-particles with a characteristic frequency increasing at low temperatures. For the first time a complete analysis is given for yttrium spin-lattice relaxation data.
NMR has yielded information of paramount importance on several aspects of the microscopic spin susceptibility X(~',w) in high T~ superconductors, both of static and of dynamical character [1]. However, a global description of all NMR results is still missing. We present an analysis of 89y, 6aCu and 170 NMR data obtained on underdoped YBal 928r0 0 s C u 3 0 6 5 ( T c : 48 K, sample 1) and YBal 92Sr0 0sCuaO6 9~ (T~ = 91 K, sample 2) single crystals, which offers new insights on the descriptmn of x(q',w) An accurate comparison with inelastic neutron scattering (INS) findings is made, especially in view of the INS measurements performed on sample 2. The x(q', w) is supposed to stem from two distinct contributions: XAF, arising from the correlated antiferromagnetic (AF) spin fluctuations (AFF), and XOt", describing the itinerant charges or quasi-parhcles [1,2] For XAF we take a phenomenological form dehneated by INS, whose basis rehes on the random phase approximatmn In the low frequency limit
_
rA -
xet_@fCq~_r)2+(q,_~r)2]]( 1 -- rcosfqz)).
(la) l+r where the AF correlation length ( ((/a = 2 66 for sample 1 and 1.33 for sample 2 [3]) and the coupling r between two CuO2 planes of one bilayer are derived from the INS results FAr" cor0921-4534/94/$07 00 © 1994 - F.lsevmr Scmncc B V All nghls re,ervcd 092 I- ~534(94)01405- !
SSDI
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.,,.,
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T ~K) Figure 1. Temperature dependence of 89R (open triangles), 63R (open circles) and lrR (open diamonds) in sample I for tlo [I e. The closed triangles show S9R calculated from Eqs. 1 and 2 without adjustable parameters, using the values of FAF and ro derived from 6aR and 17R.
responds to the w-width of the peak In X"(q',w) at ~'= QAF = (Tr, rr, q~), centered around 30 meV r,~ T~. _n'_e~qureI.o1 X~ t:,~ t ~ ' d A F , n~ u ! W a S estimated ,%:,m ....... ments (see Ref [4]) (for sample 1 we used the data reported m Ref [5]). For the quasl-pamcles contribution, in the w ---- 0 limit, we write x" Qe(¢, o~
_ x'(0, o) Fo
(lb)
where X'(0, 0) is derived either from ]70 or sgy hyperfine shifts (17K, s9K), and the charactens-
r AHer et al IPhyswa C 235-240 (1994) 1677-1678
1678
200
.....
.,.,,
....
l ....
40
nrl
,-.150
~ o
o o
oO E
, ....
n n
[]
100
o
30--1
[]
20 ,~,
o
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5o
I0~ i1|11
50
....
100
I . , , , l , . . , I . , , ,
150
200
250
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300
T (K) Figure 2. Temperature dependence of ['AF and F0 in sample 1, as derived from our analysis.
tic frequency F0 " E F / h "., 1 / h D ( E F ) . The 6 3 C u ( 2 ) and 170(2,3) hyperfine coupling constants [6] and form factors [2] used to estimate the nuclear spin lattice relaxation rate
n = ( T I T ) -1, 72kB X"aF(q", WL) + X"QP(q, WL) n = 21t2B E, f(q~) WL ' q
(2) are the usual ones, derived from the Mfla-Riee Hamiltoman The Sgy form factor for Ho II c
f(q) = 64[eo,,,2(q:/2)[D~co~2(q~/2)cos~'(%/2)+ D~d,s,n 2(q~:::2)sin 2(%/2)] + D~2sin2fq./2)x . q 2 x [cos2(qz/2)sm2(%/2) + sm'(q~/2)cos (qu/2)]]
takes into account the &polar couphng to Cu spins Ddl = 0-327 kOe and Da2 = 0.289 kOe. The hyperfine coupling D = 5 1 4- 0.2 kOe was deduced comparing the temperature (T-) dependence of SgK¢¢ and 17K~¢ m the same sample. Analysing S"R and SgK m sample 2, we find D to be isotropic, while the amsotropy of SgK ~s due to the amsotropy of the spin susceptlbd]ty (k¢/k~b = 1 13 + 0 06), whtch can be accounted for by a small anisotropy of Cu 2+ Landb factor [7] In contrast to Ref [2], we found the assumptton, of efliaent filtering of AFF m 17R and Tindependence of F0 incompatible with the experunental data The AFF contribution to IzR ts
always found to be substantial, whatever shape in q-dependence of X"af(q',w) we assume. Moreover, the effect of AFF is directly observable in the T-dependence of the 17R/SgR ratio, as a consequence of the different form (filtering) factors of the two nuclei. Only the minor part of this T-dependence could a priori be attributed to the variation of the inter-plane coupling r(T), but this is contradicted by the INS data for YBa2Cu306 .~ which show that r = 1 and is temperature independent [3]. The only way to explain 17R within the previously defined framework, is to suppose that a relative increase of the AFF contribution is compensated by a decrease of the quasi-particle term due to increasing F0, which is possibly related to sharp singularities in D(EF). A T-dependent P0 would also explain the observed non-linear relation between S9R and S9K [7]. Therefore, we used experimental 17R and 63R values and Eqs. 1 and 2 to deduce FAF and F0 (see Fig. 2) and thus define completely the spin susceptibility. 89R could then be calculated with no further parameters, and it is found to be m fine agreement with the expel nental values both m magnitude and Tdependence (Fig. 1) Moreover, FAF and its T-dependence are in satisfactory agreement with the one derived from INS [3]. It is interesting to note that in sample 1 we get F0 cx 1/X'(0, 0), indi,:atmg that for the quasi-particle contributmn a Korringa relation [1] holds with a Korrmga factor S,¢ "=_03. REFERENCES 1 Appl Mag. Resonance 3 (1992) 383-750. 2. M. HorvatK et al., Phys Re~. B 48 (1993) 13848 3 L. P Regnault el al, this conference 4 J A Gfllet et al, this conference 5 M Takigawd, Phys Rev. B 49 (1994) 4158. 6 The used couphng constants (m kOe) are B = 83, A ~ = 40, A~ = -332 for 63Cu, and C , ~ = 9 6 , ( ' ~ = 9 4 C b = 154 for 170 [1,2] 7 M Takmgawa, W L llults and J L. Smgh. Phys Rev Lett 71 (1993) 2650; tI. Ailoul c t a l , Phys Rev Left 70(1993), 117i.