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YBa2Cu3O7 electro-magnetic optic effects in Ba L2,3 X-ray absorption near Tc
Microchemical Journal 81 (2005) 98 – 107 www.elsevier.com/locate/microc
YBa2Cu3O7 electro-magnetic optic effects in Ba L2,3 X-ray absorption near Tc J.V. AcrivosT San Jose’ State University, One Washington Square, San Jose´, CA 95192-0101, United States Received 21 January 2005; accepted 22 January 2005 Available online 23 March 2005
Abstract The onset of electro-magnetic optic effects, observed at the Ba L2,3 edges synchrotron X-ray absorption by a YBa2Cu3O7 single crystal, 20 K above the transition temperature to superconductivity, Tc ~ 92 K is used to identify the role played by the Ba donor layer in the transition to superconductivity in the CuO2 layers. Negative permeability leads to Faraday rotation of the transmitted beam below T =112 to 56 K for the 22 Am thick single crystal (c-axis orientation of 8k/18 relative to EX-rays) and sharp changes in the density of empty final states lead to zero transmitted radiation in an interval DE at the given orientation. The temperature dependence: DE(L2) =1.4, 3.5 and 3.9 eV, while DE(L3) = 5.3, 6 and 7 eV at T =92, 74 and 63 K, respectively, indicates that the width of the empty final states bands increases as T decreases. DE(L3)/DE(L2)= 3.8 at 92 K to 1.8 at 63 K also indicates that the d5/2 symmetry bands fill faster than those of d3/2 symmetry below Tc, providing the first experimental evidence of unpaired spin-orbit states in the Ba donor layer of a superconductor. These effects, characteristic of ferromagnetic and anti-ferromagnetic materials near a resonance absorption, signal the onset of a Mott transition. The interaction between the layer states is described using 1D conjugate molecular orbitals. D 2005 Elsevier B.V. All rights reserved. Keywords: Cuprate superconductors; X-ray absorption; Alternant conjugate LCAO-MO
1. Introduction The purpose of this work is to determine how electromagnetic optic effects [1–5] if present in the layer superconductor YBa2Cu3O7 (YBCO7) (Fig. 1a,b) are related to the onset of the transition to superconductivity, at temperature Tc [6–11]. The magnetic properties of a metal are determined by an unbalance in the population of its spinorbit split conduction band states, and the X-ray absorption spectra, XAS at an element L2,3 edges measure the transition probabilities for the excitations to these states: 2 4 4 ð1sÞ2 ð2sÞ2 2p1=2 2p3=2 . . .fð1sÞ2 ð2sÞ2 2p1=2 2p3=2 . . . nd3=2 ; at the element L2 edge
T Tel.: +1 408 924 4972; fax: +1 408 924 4945. E-mail address: [email protected]. 0026-265X/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.microc.2005.01.020
2 4 2 ð1sÞ2 ð2sÞ2 2p1=2 2p3=2 . . .fð1sÞ2 ð2sÞ2 2p1=2 ð2p3=2 Þ3 . . . nd5=2 ; at the element L3 edge: These are split, by the spin orbit interactions in the core and in the conduction band state, i.e., DEL2;3 ¼ htL2 htL3 ¼ DE
final states
DE
core :
ð1Þ
DE L2,3 is dominated by the separation of core states, DE core c Z 42p,effective/32c 2 Hartree is the relativistic textbook relation for hydrogen like core states [12a]. Z 2p,effective is the 2p electron shielded atomic number (c 24 for Cu and c 50 for Ba is estimated from the L2,3 edge separation when DE final states b1) and c is the velocity of light in atomic units. Recent work has shown that the XAS by a YBCO7, 22 Am thick, single crystal at the Ba L2,3 edges [6,7] is enhanced below T = 112 K going from caxis^EX-ray =k/2 to 8k/18 for linearly polarized synchrotron X-rays (Fig. 2). Changes in the components of the index of refraction: n = 1 d ib (text book relation [12b,12c]) produce a
J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
a
99
b
DONOR LAYER c QL
Cu2 O3A Cu2 Ba O2
Y O3B
c
ε X-rays
CuO2 Layer
Cu: na,nb,0
Cu1
b
c
y
ρe
O1
θ
b
a
O3b
|k,g> =I0+Sample
a, b-axes
θ
Rg"g|k,g> |k,g"> =R
O3ax a
YBCO
sample x
=Is+Sample
|k,g'>=Tg'g|k,g>
=IT+Sample
Fig. 1. Schematic of sample and measurement parameters: (a) YBCO7 crystal structure. (b) CuO2 conduction layer intercalated between Ba and Y donor layers. (c) Scattered I s and transmitted I T beams of incident radiation I 0 by sample. I s/I 0 and I T/I 0 measure the change in the initial state |k,gi produced by complicated reflection and transmission operators R and T [1–5,12]. hV=c^EX-rays =8k/18 and h =ki^a where ki is the direction of incident X-rays and EX-rays the direction of their linear polarization and g represents the quantum state of the system.
Faraday/Kerr rotation if n + and n for the right and left the handed components of the incident linearly polarized radiation respectively, are not equal due to electro-magnetic interactions in the L2,3 edge transitions final states [1,2]. Since the population of the final states gives rise to the magnetic properties and d symmetry band states have been associated with superconductivity in YBCO7, the Ba L2,3 edge XAS data is used here to ascertain how changes in the d5/2, d3/2 symmetry empty final states, in the donor layer affect the CuO2 conduction layer states near Tc.
2. Materials and methods The XAS of a 22 Am thick single crystal YBCO7 grown at the IRC for Superconductivity, Cavendish Laboratory [6,7] were determined in transmission, T geometry (Fig. 1c) near the Ba L2,3 edges at the Stanford Radiation Laboratory, SSRL in the earth magnetic field. In order to evaluate the components of the complex index of refraction near Tc, detailed orientation measurements are required at a syn-
chrotron facility. These experiments report only the variation with temperature of the electro-magnetic optical effects at a single orientation in order to identify how the final states and their occupation vary near Tc. The onset of superconductivity was determined by the transparency induced by Abrikosov vortices at the Cu K edge [6,7,11]. 3. Results The raw data corrected only for a linear background subtraction gives the absorbance for the single crystal at T = 112 K (Fig. 2, insert): A ¼ lnðIT =I0 Þ=lnð10Þ in T geometry (Fig. 1c). The ratio A(T)/A(121–112 K) for T b112 K indicates up to a threefold enhancement as T decreases below Tc, at the orientation c^EX-rays = 8k/18. The temperature dependence of the interval DE where the transmission vanishes is indicated for the L2 and L3 edges, respectively (Fig. 2, inserts).
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4. Discussion The components of the response, scattered or transmitted light I s or I T respectively from an incident linearly polarized beam I 0 by atom a in YBCO7 (Fig. 1) are written [12b,c]: fa ¼ fa0 þ fa V þ i fa W:
ð2Þ
The matrix elements leading to (2) are the square of the vector potential A 2 acting once on the electron number density q(r) to give f a0 responsible for Bragg diffraction far from an element edge, and near an element edge the energy density jd A acts twice to give the anomalous Bragg diffraction: f aV (dispersion) and f aW (absorption), where j is the current density. Electric and magnetic field E, H rotations by u Kerr or u Faraday are observed in I s or I T for both ferromagnetic and antiferromagnetic materials [1,2,5]: uKerr ¼ Im½ðnþ n Þ=ðnþ n 1Þ with ellipticity eKerr ¼ Re½ðnþ nÞ=ðnþ n 1ÞuFaraday e Faraday ¼ ½pEz=hc Re ðnþ n Þ with ellipticity e Faraday ¼ tanh½ pEz=hc Imðnþ n Þ:
ð3Þ
These give rise to an elliptical polarization of the scattered and transmitted beams respectively. A non-zero ellipticity is caused by unequal changes in the complex n + and n versus photon energy, E, h is Planck constant and z the distance
YBCO Ba L2,3 Edge XAS: θ'=8π/18 3
Table of Extinction Interval =
92 5.3
74 6
63 7 eV
∆E (L2)
=
1.4
3.5
3.9 eV
∆E (L3)/∆E (L2)= 3.8
121.6-112.2 K 108.2-105.7 K 102.2-99.2 K 96.8-94.9 K 93.3-88 K 82.5-77.7 K 74.2-71.3 K 69-67.1 K 65.7-64.7 K 63.3-56 K
1.7
3
-4.1 E/10 -23.184 6
1.8
LnI0/IT(121 - 112 K)
T(K)
A L3(T=121 to 56 K)/A L3(121 K), A L2(T=121 to 56 K)/A L2(121 K)
∆E (L3)
195(121 - 112 K) Ln (I0/IT)
112.2-108.2 K 105.7-102.2 K 99.2-96.8 K 94.9-93.3 K 88-82.5 K 77.7-74.2 K 71.3-69 K 67.1-65.7 K 64.7-63.3 K
3
E (eV)
3 ∆E
0 5.247
E (keV)
E (keV)
5.257
0 5.623
E (keV)
5.633
5.75
5.85
0 5.25
5.35
5.45
5.55
5.65
Fig. 2. Ba L2,3 edge XAS for YBCO7 single crystal. A(T)/A(121 K) at the orientation h’=8k/18 near Tc of YBCO single crystal of 22 Am thick [6,7]. The raw data is corrected only for baseline (indicated in insert). The ratio A(T)/A(121 K) eliminates the effect of sample thickness, except for the magneto-optic effects. A(T)/A(121 K) does not change appreciably from room temperature to 56 K at h =k/2, but at h =8k/18 the complex index of refraction indicates the presence of magneto-optic effects 20 K above Tc. The transmission (Fig. 1c) vanishes in the interval DE near the indicated resonance absorptions and depends on T (inserts).
J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
101
a
53/54,74
63/64,74
Cu
56/57,74
O
O
C u
74/75,74
Cu
66/67,74
O
75,75
O
Cu
0
ε(H)
Cu4O4: 74 MO OCC No PLD
-1.06 57
m,74
75
b
O O
Cu
ρe > (.1/b)3
1/4{114,114}
O
1/4{113,113}
1/4{84,114}
1/4{101,114}
ε(H)
0.08 Cu4O12: 114 MO occupied
-0.82 m',114 80
97 3
3
114
Fig. 3. (CuO2)n electron density contours of q e N10 /bohr obtained for a TV-Nd2CuO4 nano-particle in the field of 18 unit cells [13]: (a) Cu4O4:v m,74, (b) x Cu4O12 :v mV,114, (c) tight binding SCF-MO approximation for k+ =(k, k, 0): WmVm ðr; kÞ ¼ N 1=2
X expði kR74 Þvm;74 ðr R74 Þ þ expði kR114 ÞvmV;114 ðr R114 Þ ¼ WmVm ðr; ðFp; Fp; 0ÞÞ R
¼ 1=MN
X vm;74 ðr R74 Þ þ vmV;114 ðr R114 Þ ; Ri
and the MO are centered at: R114 =2n(a Fb) and R74 =2(naF (n 1) b), n=0, 1, N/2.
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J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
c
delocalized
ρe
Unit Cell (CuO2)16 resonance
2 t 114-114
4 by 4 PLD
2 t 114-114
2 t 114-114
2 t 114-114
Fig. 3 (continued).
traversed inside the sample. The final density of states at the L2,3 edges, respectively, is responsible for the changes in d and the critical angle, (2d)1/2 for external reflection (textbook definition in [12c]) leads to sharp decreases/increases in the transmission over an interval DE (where the slope of the empty final density of states versus E diverges, i.e., dd/dE Z Fl). The limits determined by DE indicate where sharp changes occur in the density of empty final states, related to the L2 and L3 band widths. For 20 to 60 nm Fe ferromagnetic films (Fig. 8, [5]) DE(L3)~ 2 eV and DE(L2)~ 0.28 eV indicate that the empty states band width is 7.2 times greater for 3d5/2 than for 3d3/2, suggesting that the latter is the majority occupied band. The experimental results are discussed in three parts: A. The 22 Am YBCO7 crystal electro-magnetic properties determined by Ba L2,3 XAS are: (i) The sharp changes in the index of refraction in the interval DE, observed below 112 K, DE(L3)/DE(L2)= 3.8 at 92 K to 1.7 at 63 K (Fig. 2, table insert) indicate that the relative widths and/or population of the d5/2 and d3/2 symmetry final empty states bands have a different temperature dependence, which result in different magnetic properties. (ii) The ratio DE(L3)/DE(L2)= 3.8 near Tc is smaller than that for a ferromagnetic Fe film of 7.2 [8] at room temperature indicating a greater unbalance of spin-orbit states and therefore stronger magnetic properties for the latter. The unequal population of d5/2 and d3/2 symmetry final states does not distinguish between ferromagnetic and antiferromagnetic properties, but an equal probability for their occupation should obtain DE(L3)/DE(L2)= 1.5. (iii) Faraday rotation extends into the extended X-ray absorption, XAFS as indicated by the enhanced absorption over that at 121 K (Fig. 2). (iv) The unpaired spin states in the donor layer may be the cause and/or consequence of spin defects in the CuO2 conduction layer states that can lead to the formation of superconducting pairs at the onset of superconductivity described as follows.
J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
103
B. The molecular orbital, MO description of the material suggested by the data, is: (i) The wave functions [12a] involved in the transitions are: Ba initial core states: wBa;i : 2p3=2 : j3=2; F3=2i ¼ Y1;F1zA R2;1 ðrBa Þ;
h i j3=2; F1=2i ¼ 31=2 21=2 Y1;0zA þ Y1;F1 Az R2;1 ðrBa Þ
h i wBa;i : 2p1=2 : j1=2; F1=2i ¼ 31=2 Y1;0zA 21=2 Y1;F1 Az R2;1 ðrBa Þ and empty final band states band containing fractional character of:
wBa;f : 5d5=2 : j5=2; F5=2i ¼ Y2;F2zA R5;2 ðrBa Þ; j5=2; F3=2i ¼ 51=2 Y2;F2 Az þ 2Y2;F1zA R5;2 ðrBa Þ; h i j5=2; F1=2i ¼ 151=2 3Y2;0zA þ 61=2 Y2;F1 Az R5;2 ðrBa Þ:
wBa;f : 5d3=2 : j3=2; F3=2i¼51=2 2Y2;F2 Az Y2;F1zA R5;2 ðrBa Þ; h i j3=2; F1=2i ¼ 151=2 61=2 Y2;0zA 3Y2;F1 Az R5;2 ðrBa Þ:
ð4Þ
where Y l,m (r a,h a,u a) are spherical harmonics, the sub-indexes zA represent the spin S z = F 1/2 states and R n,1(r a) is the radial dependence when (r a,h a,u a) are the spherical polar coordinates of the electron relative to atom a. The LCAO-MO extended state wave functions for the [CuO2]n conduction layer obtained by a SCF analysis give the maps of electron density, q e N (0.1/bohr)3, indicating the direction of the extended electron overlap population along O3a :2pab –O3b :2pab the a,b and a, b diagonals (Fig. 3a,b) [13]. These are built with SCF, MO:v m,M = v m,74(Cu4O4) and v mV,114(Cu4O12)x (M is the total number of doubly occupied MO and m is the order of increasing energy, e m,M ) where the v m,74 are doubly degenerate with an overlap population along the ab or a, b diagonal (Fig. 3a, e.g., m = 53/54, 63, 64, etc.). The highest occupied SCF MO, HOMO q e (m =74/75) identifies the direction of electron overlap population at the Fermi level that agrees with the preferred direction of superconductivity along the a,b and a, b diagonals, determined experimentally by photoemission measurements [14] after the SCF analysis [13]. The experimental conduction electron state wave vectors in the first Brillouin zone, kF = (k y,k x ,k z )= F (k, Fk, 0) are used in a semi empirical tight binding approximation [12g] of the layers next. (ii) The extended states are usually built with kF and the SCF MO basis [13] (Fig. 3c). Here simple Alternant 1D conjugate orbitals [15] in a lattice with atom coordinates (Figs. 1a,b and 4): RCu : ð x=a; y=b; z=cÞ ¼ ðn þ na ; n þ nb ; 0Þ; RO3a : ðn þ na þ 1=2; n þ nb ; dÞ and RO3b : ðn þ na ; n þ nb 1=2; 0:02Þ and donor layers RBa=Y : ðn þ nb þ 1=2; n þ nb 1=2; 0:16Þ
are used. n a , n b =0, 1, etc. identify the chains with n =0, 1, N. k+ = F (k, k, 0) obtains the MO: vO;na ;nb ðr; p; p; kz Þ ¼ ð 2N Þ1=2 icosðpðna þ nb ÞÞRn ½wO ðr RO3a Þ wO ðrRO3b Þ; vCu;na ;nb ðr; p; p; 0Þ ¼ N 1=2 cosðpðna þ nb ÞÞRn wCu ðr RCu Þ; v
donor;na ;nb ðr;p; p;kzÞ¼N
1=2
ð5Þ
cosðpðna þnb ÞÞRn wdonor ðrR donorÞ:
N is the total number of Cu sites in a chain and w are atomic orbitals. Along the a, b diagonal, the 1D overlap occurs for k = F (k, k, 0). However, if k+ changes to k the O3a :2pab –O3b :2pab 1D overlap changes direction (Figs. 3c and 4a,b) creating anti-bonding states, which in turn give rise to periodic lattice distortions, PLD.
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J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
na , n b
chain Cu
n a +1, n b O3a
(kx,ky) = (π π,-π) O3b
Ba
(kx,ky) = (π, π)
(kx,ky) = (π,-π)
Fig. 4. Direction of extended orbital overlap population in conjugate MO in the CuO2 plane for kF. The O3a :2pab –O3b :2pab overlap is indicated by solid lines (for + 2p orbital phase) and dashed lines (for 2p orbital phase). The Cu:3d phase is indicated by solid lines (+) and dashed lines (), respectively. Antibonding states are created where k+ changes to k (blank). The PLD periodicity is produced by the repeat chevron symmetry.
(iii) A periodic repeat between broken bonds (Fig. 4) creates expansion and compression waves that can be detected by X-ray diffraction (XRD). A 1D PLD with k PLD = 24a has been observed in a 50 nm YBCO7 film (a =4.88 2 in [10]) but 4 by 4 PLD can also be explained by the interchange of k+ changes to k (Fig. 3c). The undistorted 1D chain length determines the conduction electron mean free path in the chain, and the defect unpaired spin states may be the cause and/or the result of the electro-magnetic optic property changes in the Ba donor layer 20 K before the onset to superconductivity. The energy cost for breaking a O3a :2pab –O3b :2pab bond is estimated from the SCF, LCAO-MO analysis. The difference in q e between v 54,74 and v 57,74 is due to subtle changes in the O3a :2pab –O3b :2pab overlap population (Fig. 3a). An additional resonance energy t due to O3a :2pab –O3b :2pab overlap is possible for v 54,74 but not for v 57,74 and obtains e 57,74e 54,74 = 0.16 eV ~ 2t [13]. Also the SCF energy difference (e 75,74e 74,74)/2 =0.95 eV between the Cu4O4:HOMO and LUMO is due to the difference in q e for v 74,74 and v 75,74: Two Cu:p-like in the HOMO q e symmetry are associated with a d10 closed shell, but addition of an electron gives two Cu:d-like in the LUMO q e symmetry, associated with an open d shell. This is in agreement with the higher heat of formation per mole for the 3d8 shell oxide, NiO over that for a 3d10 closed shell oxide, ZnO by 1.2 eV [12f]. The presence of broken O3a :2pab –O3b :2pab bond defects does
J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
105
not necessarily increase the ground state energy because of the degeneracy introduced by, e.g., v 54/53,74, v 57/56,74, v 64/63,74, v 66/67,74 and v 74/75,74 (Fig. 3a) [13,17]. This suggests that PLD are formed when k and k+ are interchanged by an excitation of 2t/N c 0.16 eV/N when one O3a :2pab :O3b :2pab becomes anti-bonding, in a chain of N atoms [15]. These excitations may be introduced at the onset of YBCO7 Ba lattice vibrations at T b 130 K [16], i.e., the YBCO7 50 nm film (k PLD/a =24) would require excitations of ~ 6 meV to change the spin state population. (iv) Electron pair states with J = 0, obeying Bose statistics can be formed by the interaction of an O:2p3/2 spin defect chain with another of Cu:3d3/2 symmetry (and/or Ba:5d3/2). The two electron pair states are eigenfunctions of J = J 1 + J 2 and J z
a
b
Fig. 5. Enhanced 001 scattering by 50 nm YBCO7, film on SrTiO3 with a 24 DEG grain boundary according to [8]: (a) f W near the Cu L2,3 edges at different T above and below Tc. (b) f W near the O K edge at different T above and below Tc.
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J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
but not S z . The parity of the product states P for the exchange operation P12 of electrons 1 and 2 of d3/2 (Cu or Ba) and p3/2 (O) orbital symmetry give the allowed |J,0i
| J,Jz> | 3,0> | 2,0> | 1,0> | 0,0>
Matrix
Coefficients
1/401/2 [ 1 1 3 3 ] 1/81/2 [-1 -1 1 1 ] 1/401/2 [ 3 3 -1 -1 ] 1/81/2 [ 1 -1 1 -1 ]
=
*
(I+ iPP12)* (I+e (I+eiPP12)* (I+ (I+eiPP12)* (I+ (I+eiPP12)* (I+
d3/2
p3/2
P
| 3/2 1/2>d1** | 3/2 -1/2>d1** | 3/2 3/2>d1** | 3/2 -3/2>d1**
| 3/2 -1/2>p2 | 3/2 1/2>p2 | 3/2 -3/2>p2 | 3/2 3/2>p2
2π π 2π 2π
ð6Þ where the matrix coefficients are obtained to satisfy the eigenvalues, J( J +1), J z and the raising and lowering angular momentum textbook operations [12a]. I is the identity operator and electrons 1 and 2 are identified by the position in the product. The principal axis of quantization in relation (4) is parallel to kF and the electron pair e2= states allowed by symmetry in (6) are: j0; 0iab
chain
¼ 51=2 ðI þ P12 Þ
Y1;0z Rn RO:2p ðr RO3a Þ RO:2p ðr RO3b Þ 1 Y2;0 A Rn RCu:3d ðr RCu Þ 2
Y1;0 A Rn RO:2p ðr RO3a Þ RO:2p ðr RO3b Þ 1 Y2;0zRn RCu:3d ðr RCu Þ 2 g:
ð7Þ
for J = 0. Electron pair states obeying Bose statistics are possible for J =3, 1, 0 in (6) through interactions between electron states in neighboring 1D chains along the diagonal a,b (Fig. 4), mediated by lattice vibrations in YBCO7 of ~ 10 to 80 meV [16b]. (vi) Equal superconducting properties along the a:b and a:b diagonals, in a perfect lattice may occur only in a crystal with k+ and k quantization in two different CuO2 layers (e.g., YBCO7, Fig. 1a) or when an equal probability of k+ and k quantization gives rise to bonding f anti-bonding excitations of 2t/N ~ 6 meV, causing the commonly observed PLD. C. Evidence for electro-magnetic optic effects below Tc has also been obtained in the enhanced 001 scattering by a 50 nm YBCO7 film on SrTiO3 with a 24 DEG grain boundary [8]. Near the Cu L2,3 edges both the raw data I s/I 0 and f W (obtained from the raw data by an inverse Kerr rotation of u K = 23.5 DEG) indicate that below Tc a decrease in the final empty band states contribution of Cu:3d3/2 symmetry (L2 edge) is greater than for the Cu:3d5/2 contribution to the empty final states (L3 edge) (Fig. 5a). Changes at the O K edge are difficult to measure because the spin-orbit energy separation in the final states bands is negligible (Fig. 5b). However, in a film with grain boundaries, magnetic states are also introduced by broken bonds at the grain boundary in the same manner as when k+ changes to k (Fig. 4). 5. Conclusions
Acknowledgements
The temperature dependence of the YBCO7, Ba L2,3 XAS indicate that the onset of electro-magnetic optic effects in the Ba layer ~ 20 K above Tc forecasts the Mott transition [18] associated with the transition to superconductivity. The valence of an alkaline earth metal changes near the metal insulator Mott transition in Sr(NH3)x as determined by XAS valence edge shifts [19]. The elegant work of Zhang et al. [20] helps to unravel the YBCO7 superconductivity– magnetism relation. They have shown that spin polarized transport is non-dissipating and that transport by a Bose condensate in the superconducting state is a sub-group of spin polarized transport. A question remains: are the spin polarized nd3/2 over the nd5/2 band states in YBCO7 a result of the Bose condensation, or does the uneven spin population in nearly 1D conjugate orbitals (5) cause the Bose condensation? Since Faraday rotations are observed above Tc, the latter appears closer to the truth.
Support for this work was given by an NSF/DMR grant 9612873 at SJSU and DOE at SSRL. Professor Yao W. Liang of the IRC for superconductivity, Cavendish Laboratory is thanked for the YBCO7 single crystal and for moral support. References [1] [2] [3] [4] [5] [6] [7]
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J.V. Acrivos / Microchemical Journal 81 (2005) 98–107 [9] J.B. Kortright, D.D. Awachalom, J. Stohr, S.D. Bader, Y.U. Idzerda, S.S.P. Parkin, I.K. Schuller, H.C. Seigmann, J. Magn. Magn. Mater. 207 (1999) 7. [10] M.A. Navacerrada, J.V. Acrivos, NanoTech 2003, vol. 1, 2003, p. 751. [11] J.G. Chigvinadze, G.I. Mamniashvilli, J.V. Acrivos, Bulletin of the American Physical Society Meeting: MAR04, K1.189 (to be submitted for publication). [12] (a) L.I. Schiff, Quantum Mechanics, McGraw Hill, New York, 1949, section 239; (b) D. Templeton, in: G. Brown, D.E. Moncton (Eds.), Handbook of Synchrotron Radiation, vol. 3, Elsevier, 1991, p. 201; (c) R.W. James, The Optical Principles of X-rays, Ox Bow Press, Woodbridge, CN, 1962, p. 172; (d) M.E. Rose, Elementary Theory of Angular Momentum, John Wiley and Sons, NY, 1953; (e) P.M. Morse, H. Feshbach, Methods if Theoretical Physics, McGraw Hill, New York, 1953; (f) R.C. Weast (Ed.), Handbook of Physics and Chemistry, 49th edition, The Chemical Rubber Co., 1969, pp. D-24e; (g) J. Callaway, Quantum Theory of Solids, Academic Press Inc., San Diego, 1974.
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[13] J.V. Acrivos, O. Stradella, Int. J. Quant. Chem. 46 (1993) 55. [14] Z.-X. Shen, W.E. Spicer, D.M. King, D.S. Dessau, B.O. Wells, Science 267 (1995) 343. [15] R. Pauncz, in: E.J. Br7ndas, E.S. Kryachko (Eds.), Fundamental World of Quantum Chemistry, Kluwer Academic Pub., Dordrecht, 2003, p. 155. [16] (a) N. Watanabe, N. Koshizuka, Advances in Superconductivity, vol. IX, Springer-Verlag, Tokyo, 1997, p. 153; (b) C. Thomsen, M. Cardona, in: D.M. Ginsberg (Ed.), Physical Properties of High Tc Superconductors, vol. I, World Scientific, 1988, p. 409. [17] H.S. Sahibudeen, J.V. Acrivos, 227th ACS National Meeting, Anaheim, CA, March 28–April 1, 2004 INOR 588 (to be submitted for publication). [18] (a) N.F. Mott, Metal Insulator Transitions, Taylor and Francis, Ltd., 1974; (b) A.S. Alexandrov, N.F. Mott, Polarons and Bipolarons, World Scientific, Singapore, 1995. [19] J.V. Acrivos, K. Hathaway, A. Robertson, M.P. Klein, J. Phys. Chem. 84 (1980) 1206. [20] S. Murakami, N. Nagaosa, C. Zhang, Science 301 (2003) 1348.
YBa2Cu3O7 electro-magnetic optic effects in Ba L2,3 X-ray absorption near Tc J.V. AcrivosT San Jose’ State University, One Washington Square, San Jose´, CA 95192-0101, United States Received 21 January 2005; accepted 22 January 2005 Available online 23 March 2005
Abstract The onset of electro-magnetic optic effects, observed at the Ba L2,3 edges synchrotron X-ray absorption by a YBa2Cu3O7 single crystal, 20 K above the transition temperature to superconductivity, Tc ~ 92 K is used to identify the role played by the Ba donor layer in the transition to superconductivity in the CuO2 layers. Negative permeability leads to Faraday rotation of the transmitted beam below T =112 to 56 K for the 22 Am thick single crystal (c-axis orientation of 8k/18 relative to EX-rays) and sharp changes in the density of empty final states lead to zero transmitted radiation in an interval DE at the given orientation. The temperature dependence: DE(L2) =1.4, 3.5 and 3.9 eV, while DE(L3) = 5.3, 6 and 7 eV at T =92, 74 and 63 K, respectively, indicates that the width of the empty final states bands increases as T decreases. DE(L3)/DE(L2)= 3.8 at 92 K to 1.8 at 63 K also indicates that the d5/2 symmetry bands fill faster than those of d3/2 symmetry below Tc, providing the first experimental evidence of unpaired spin-orbit states in the Ba donor layer of a superconductor. These effects, characteristic of ferromagnetic and anti-ferromagnetic materials near a resonance absorption, signal the onset of a Mott transition. The interaction between the layer states is described using 1D conjugate molecular orbitals. D 2005 Elsevier B.V. All rights reserved. Keywords: Cuprate superconductors; X-ray absorption; Alternant conjugate LCAO-MO
1. Introduction The purpose of this work is to determine how electromagnetic optic effects [1–5] if present in the layer superconductor YBa2Cu3O7 (YBCO7) (Fig. 1a,b) are related to the onset of the transition to superconductivity, at temperature Tc [6–11]. The magnetic properties of a metal are determined by an unbalance in the population of its spinorbit split conduction band states, and the X-ray absorption spectra, XAS at an element L2,3 edges measure the transition probabilities for the excitations to these states: 2 4 4 ð1sÞ2 ð2sÞ2 2p1=2 2p3=2 . . .fð1sÞ2 ð2sÞ2 2p1=2 2p3=2 . . . nd3=2 ; at the element L2 edge
T Tel.: +1 408 924 4972; fax: +1 408 924 4945. E-mail address: [email protected]. 0026-265X/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.microc.2005.01.020
2 4 2 ð1sÞ2 ð2sÞ2 2p1=2 2p3=2 . . .fð1sÞ2 ð2sÞ2 2p1=2 ð2p3=2 Þ3 . . . nd5=2 ; at the element L3 edge: These are split, by the spin orbit interactions in the core and in the conduction band state, i.e., DEL2;3 ¼ htL2 htL3 ¼ DE
final states
DE
core :
ð1Þ
DE L2,3 is dominated by the separation of core states, DE core c Z 42p,effective/32c 2 Hartree is the relativistic textbook relation for hydrogen like core states [12a]. Z 2p,effective is the 2p electron shielded atomic number (c 24 for Cu and c 50 for Ba is estimated from the L2,3 edge separation when DE final states b1) and c is the velocity of light in atomic units. Recent work has shown that the XAS by a YBCO7, 22 Am thick, single crystal at the Ba L2,3 edges [6,7] is enhanced below T = 112 K going from caxis^EX-ray =k/2 to 8k/18 for linearly polarized synchrotron X-rays (Fig. 2). Changes in the components of the index of refraction: n = 1 d ib (text book relation [12b,12c]) produce a
J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
a
99
b
DONOR LAYER c QL
Cu2 O3A Cu2 Ba O2
Y O3B
c
ε X-rays
CuO2 Layer
Cu: na,nb,0
Cu1
b
c
y
ρe
O1
θ
b
a
O3b
|k,g> =I0+Sample
a, b-axes
θ
Rg"g|k,g> |k,g"> =R
O3ax a
YBCO
sample x
=Is+Sample
|k,g'>=Tg'g|k,g>
=IT+Sample
Fig. 1. Schematic of sample and measurement parameters: (a) YBCO7 crystal structure. (b) CuO2 conduction layer intercalated between Ba and Y donor layers. (c) Scattered I s and transmitted I T beams of incident radiation I 0 by sample. I s/I 0 and I T/I 0 measure the change in the initial state |k,gi produced by complicated reflection and transmission operators R and T [1–5,12]. hV=c^EX-rays =8k/18 and h =ki^a where ki is the direction of incident X-rays and EX-rays the direction of their linear polarization and g represents the quantum state of the system.
Faraday/Kerr rotation if n + and n for the right and left the handed components of the incident linearly polarized radiation respectively, are not equal due to electro-magnetic interactions in the L2,3 edge transitions final states [1,2]. Since the population of the final states gives rise to the magnetic properties and d symmetry band states have been associated with superconductivity in YBCO7, the Ba L2,3 edge XAS data is used here to ascertain how changes in the d5/2, d3/2 symmetry empty final states, in the donor layer affect the CuO2 conduction layer states near Tc.
2. Materials and methods The XAS of a 22 Am thick single crystal YBCO7 grown at the IRC for Superconductivity, Cavendish Laboratory [6,7] were determined in transmission, T geometry (Fig. 1c) near the Ba L2,3 edges at the Stanford Radiation Laboratory, SSRL in the earth magnetic field. In order to evaluate the components of the complex index of refraction near Tc, detailed orientation measurements are required at a syn-
chrotron facility. These experiments report only the variation with temperature of the electro-magnetic optical effects at a single orientation in order to identify how the final states and their occupation vary near Tc. The onset of superconductivity was determined by the transparency induced by Abrikosov vortices at the Cu K edge [6,7,11]. 3. Results The raw data corrected only for a linear background subtraction gives the absorbance for the single crystal at T = 112 K (Fig. 2, insert): A ¼ lnðIT =I0 Þ=lnð10Þ in T geometry (Fig. 1c). The ratio A(T)/A(121–112 K) for T b112 K indicates up to a threefold enhancement as T decreases below Tc, at the orientation c^EX-rays = 8k/18. The temperature dependence of the interval DE where the transmission vanishes is indicated for the L2 and L3 edges, respectively (Fig. 2, inserts).
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J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
4. Discussion The components of the response, scattered or transmitted light I s or I T respectively from an incident linearly polarized beam I 0 by atom a in YBCO7 (Fig. 1) are written [12b,c]: fa ¼ fa0 þ fa V þ i fa W:
ð2Þ
The matrix elements leading to (2) are the square of the vector potential A 2 acting once on the electron number density q(r) to give f a0 responsible for Bragg diffraction far from an element edge, and near an element edge the energy density jd A acts twice to give the anomalous Bragg diffraction: f aV (dispersion) and f aW (absorption), where j is the current density. Electric and magnetic field E, H rotations by u Kerr or u Faraday are observed in I s or I T for both ferromagnetic and antiferromagnetic materials [1,2,5]: uKerr ¼ Im½ðnþ n Þ=ðnþ n 1Þ with ellipticity eKerr ¼ Re½ðnþ nÞ=ðnþ n 1ÞuFaraday e Faraday ¼ ½pEz=hc Re ðnþ n Þ with ellipticity e Faraday ¼ tanh½ pEz=hc Imðnþ n Þ:
ð3Þ
These give rise to an elliptical polarization of the scattered and transmitted beams respectively. A non-zero ellipticity is caused by unequal changes in the complex n + and n versus photon energy, E, h is Planck constant and z the distance
YBCO Ba L2,3 Edge XAS: θ'=8π/18 3
Table of Extinction Interval =
92 5.3
74 6
63 7 eV
∆E (L2)
=
1.4
3.5
3.9 eV
∆E (L3)/∆E (L2)= 3.8
121.6-112.2 K 108.2-105.7 K 102.2-99.2 K 96.8-94.9 K 93.3-88 K 82.5-77.7 K 74.2-71.3 K 69-67.1 K 65.7-64.7 K 63.3-56 K
1.7
3
-4.1 E/10 -23.184 6
1.8
LnI0/IT(121 - 112 K)
T(K)
A L3(T=121 to 56 K)/A L3(121 K), A L2(T=121 to 56 K)/A L2(121 K)
∆E (L3)
195(121 - 112 K) Ln (I0/IT)
112.2-108.2 K 105.7-102.2 K 99.2-96.8 K 94.9-93.3 K 88-82.5 K 77.7-74.2 K 71.3-69 K 67.1-65.7 K 64.7-63.3 K
3
E (eV)
3 ∆E
0 5.247
E (keV)
E (keV)
5.257
0 5.623
E (keV)
5.633
5.75
5.85
0 5.25
5.35
5.45
5.55
5.65
Fig. 2. Ba L2,3 edge XAS for YBCO7 single crystal. A(T)/A(121 K) at the orientation h’=8k/18 near Tc of YBCO single crystal of 22 Am thick [6,7]. The raw data is corrected only for baseline (indicated in insert). The ratio A(T)/A(121 K) eliminates the effect of sample thickness, except for the magneto-optic effects. A(T)/A(121 K) does not change appreciably from room temperature to 56 K at h =k/2, but at h =8k/18 the complex index of refraction indicates the presence of magneto-optic effects 20 K above Tc. The transmission (Fig. 1c) vanishes in the interval DE near the indicated resonance absorptions and depends on T (inserts).
J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
101
a
53/54,74
63/64,74
Cu
56/57,74
O
O
C u
74/75,74
Cu
66/67,74
O
75,75
O
Cu
0
ε(H)
Cu4O4: 74 MO OCC No PLD
-1.06 57
m,74
75
b
O O
Cu
ρe > (.1/b)3
1/4{114,114}
O
1/4{113,113}
1/4{84,114}
1/4{101,114}
ε(H)
0.08 Cu4O12: 114 MO occupied
-0.82 m',114 80
97 3
3
114
Fig. 3. (CuO2)n electron density contours of q e N10 /bohr obtained for a TV-Nd2CuO4 nano-particle in the field of 18 unit cells [13]: (a) Cu4O4:v m,74, (b) x Cu4O12 :v mV,114, (c) tight binding SCF-MO approximation for k+ =(k, k, 0): WmVm ðr; kÞ ¼ N 1=2
X expði kR74 Þvm;74 ðr R74 Þ þ expði kR114 ÞvmV;114 ðr R114 Þ ¼ WmVm ðr; ðFp; Fp; 0ÞÞ R
¼ 1=MN
X vm;74 ðr R74 Þ þ vmV;114 ðr R114 Þ ; Ri
and the MO are centered at: R114 =2n(a Fb) and R74 =2(naF (n 1) b), n=0, 1, N/2.
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J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
c
delocalized
ρe
Unit Cell (CuO2)16 resonance
2 t 114-114
4 by 4 PLD
2 t 114-114
2 t 114-114
2 t 114-114
Fig. 3 (continued).
traversed inside the sample. The final density of states at the L2,3 edges, respectively, is responsible for the changes in d and the critical angle, (2d)1/2 for external reflection (textbook definition in [12c]) leads to sharp decreases/increases in the transmission over an interval DE (where the slope of the empty final density of states versus E diverges, i.e., dd/dE Z Fl). The limits determined by DE indicate where sharp changes occur in the density of empty final states, related to the L2 and L3 band widths. For 20 to 60 nm Fe ferromagnetic films (Fig. 8, [5]) DE(L3)~ 2 eV and DE(L2)~ 0.28 eV indicate that the empty states band width is 7.2 times greater for 3d5/2 than for 3d3/2, suggesting that the latter is the majority occupied band. The experimental results are discussed in three parts: A. The 22 Am YBCO7 crystal electro-magnetic properties determined by Ba L2,3 XAS are: (i) The sharp changes in the index of refraction in the interval DE, observed below 112 K, DE(L3)/DE(L2)= 3.8 at 92 K to 1.7 at 63 K (Fig. 2, table insert) indicate that the relative widths and/or population of the d5/2 and d3/2 symmetry final empty states bands have a different temperature dependence, which result in different magnetic properties. (ii) The ratio DE(L3)/DE(L2)= 3.8 near Tc is smaller than that for a ferromagnetic Fe film of 7.2 [8] at room temperature indicating a greater unbalance of spin-orbit states and therefore stronger magnetic properties for the latter. The unequal population of d5/2 and d3/2 symmetry final states does not distinguish between ferromagnetic and antiferromagnetic properties, but an equal probability for their occupation should obtain DE(L3)/DE(L2)= 1.5. (iii) Faraday rotation extends into the extended X-ray absorption, XAFS as indicated by the enhanced absorption over that at 121 K (Fig. 2). (iv) The unpaired spin states in the donor layer may be the cause and/or consequence of spin defects in the CuO2 conduction layer states that can lead to the formation of superconducting pairs at the onset of superconductivity described as follows.
J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
103
B. The molecular orbital, MO description of the material suggested by the data, is: (i) The wave functions [12a] involved in the transitions are: Ba initial core states: wBa;i : 2p3=2 : j3=2; F3=2i ¼ Y1;F1zA R2;1 ðrBa Þ;
h i j3=2; F1=2i ¼ 31=2 21=2 Y1;0zA þ Y1;F1 Az R2;1 ðrBa Þ
h i wBa;i : 2p1=2 : j1=2; F1=2i ¼ 31=2 Y1;0zA 21=2 Y1;F1 Az R2;1 ðrBa Þ and empty final band states band containing fractional character of:
wBa;f : 5d5=2 : j5=2; F5=2i ¼ Y2;F2zA R5;2 ðrBa Þ; j5=2; F3=2i ¼ 51=2 Y2;F2 Az þ 2Y2;F1zA R5;2 ðrBa Þ; h i j5=2; F1=2i ¼ 151=2 3Y2;0zA þ 61=2 Y2;F1 Az R5;2 ðrBa Þ:
wBa;f : 5d3=2 : j3=2; F3=2i¼51=2 2Y2;F2 Az Y2;F1zA R5;2 ðrBa Þ; h i j3=2; F1=2i ¼ 151=2 61=2 Y2;0zA 3Y2;F1 Az R5;2 ðrBa Þ:
ð4Þ
where Y l,m (r a,h a,u a) are spherical harmonics, the sub-indexes zA represent the spin S z = F 1/2 states and R n,1(r a) is the radial dependence when (r a,h a,u a) are the spherical polar coordinates of the electron relative to atom a. The LCAO-MO extended state wave functions for the [CuO2]n conduction layer obtained by a SCF analysis give the maps of electron density, q e N (0.1/bohr)3, indicating the direction of the extended electron overlap population along O3a :2pab –O3b :2pab the a,b and a, b diagonals (Fig. 3a,b) [13]. These are built with SCF, MO:v m,M = v m,74(Cu4O4) and v mV,114(Cu4O12)x (M is the total number of doubly occupied MO and m is the order of increasing energy, e m,M ) where the v m,74 are doubly degenerate with an overlap population along the ab or a, b diagonal (Fig. 3a, e.g., m = 53/54, 63, 64, etc.). The highest occupied SCF MO, HOMO q e (m =74/75) identifies the direction of electron overlap population at the Fermi level that agrees with the preferred direction of superconductivity along the a,b and a, b diagonals, determined experimentally by photoemission measurements [14] after the SCF analysis [13]. The experimental conduction electron state wave vectors in the first Brillouin zone, kF = (k y,k x ,k z )= F (k, Fk, 0) are used in a semi empirical tight binding approximation [12g] of the layers next. (ii) The extended states are usually built with kF and the SCF MO basis [13] (Fig. 3c). Here simple Alternant 1D conjugate orbitals [15] in a lattice with atom coordinates (Figs. 1a,b and 4): RCu : ð x=a; y=b; z=cÞ ¼ ðn þ na ; n þ nb ; 0Þ; RO3a : ðn þ na þ 1=2; n þ nb ; dÞ and RO3b : ðn þ na ; n þ nb 1=2; 0:02Þ and donor layers RBa=Y : ðn þ nb þ 1=2; n þ nb 1=2; 0:16Þ
are used. n a , n b =0, 1, etc. identify the chains with n =0, 1, N. k+ = F (k, k, 0) obtains the MO: vO;na ;nb ðr; p; p; kz Þ ¼ ð 2N Þ1=2 icosðpðna þ nb ÞÞRn ½wO ðr RO3a Þ wO ðrRO3b Þ; vCu;na ;nb ðr; p; p; 0Þ ¼ N 1=2 cosðpðna þ nb ÞÞRn wCu ðr RCu Þ; v
donor;na ;nb ðr;p; p;kzÞ¼N
1=2
ð5Þ
cosðpðna þnb ÞÞRn wdonor ðrR donorÞ:
N is the total number of Cu sites in a chain and w are atomic orbitals. Along the a, b diagonal, the 1D overlap occurs for k = F (k, k, 0). However, if k+ changes to k the O3a :2pab –O3b :2pab 1D overlap changes direction (Figs. 3c and 4a,b) creating anti-bonding states, which in turn give rise to periodic lattice distortions, PLD.
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na , n b
chain Cu
n a +1, n b O3a
(kx,ky) = (π π,-π) O3b
Ba
(kx,ky) = (π, π)
(kx,ky) = (π,-π)
Fig. 4. Direction of extended orbital overlap population in conjugate MO in the CuO2 plane for kF. The O3a :2pab –O3b :2pab overlap is indicated by solid lines (for + 2p orbital phase) and dashed lines (for 2p orbital phase). The Cu:3d phase is indicated by solid lines (+) and dashed lines (), respectively. Antibonding states are created where k+ changes to k (blank). The PLD periodicity is produced by the repeat chevron symmetry.
(iii) A periodic repeat between broken bonds (Fig. 4) creates expansion and compression waves that can be detected by X-ray diffraction (XRD). A 1D PLD with k PLD = 24a has been observed in a 50 nm YBCO7 film (a =4.88 2 in [10]) but 4 by 4 PLD can also be explained by the interchange of k+ changes to k (Fig. 3c). The undistorted 1D chain length determines the conduction electron mean free path in the chain, and the defect unpaired spin states may be the cause and/or the result of the electro-magnetic optic property changes in the Ba donor layer 20 K before the onset to superconductivity. The energy cost for breaking a O3a :2pab –O3b :2pab bond is estimated from the SCF, LCAO-MO analysis. The difference in q e between v 54,74 and v 57,74 is due to subtle changes in the O3a :2pab –O3b :2pab overlap population (Fig. 3a). An additional resonance energy t due to O3a :2pab –O3b :2pab overlap is possible for v 54,74 but not for v 57,74 and obtains e 57,74e 54,74 = 0.16 eV ~ 2t [13]. Also the SCF energy difference (e 75,74e 74,74)/2 =0.95 eV between the Cu4O4:HOMO and LUMO is due to the difference in q e for v 74,74 and v 75,74: Two Cu:p-like in the HOMO q e symmetry are associated with a d10 closed shell, but addition of an electron gives two Cu:d-like in the LUMO q e symmetry, associated with an open d shell. This is in agreement with the higher heat of formation per mole for the 3d8 shell oxide, NiO over that for a 3d10 closed shell oxide, ZnO by 1.2 eV [12f]. The presence of broken O3a :2pab –O3b :2pab bond defects does
J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
105
not necessarily increase the ground state energy because of the degeneracy introduced by, e.g., v 54/53,74, v 57/56,74, v 64/63,74, v 66/67,74 and v 74/75,74 (Fig. 3a) [13,17]. This suggests that PLD are formed when k and k+ are interchanged by an excitation of 2t/N c 0.16 eV/N when one O3a :2pab :O3b :2pab becomes anti-bonding, in a chain of N atoms [15]. These excitations may be introduced at the onset of YBCO7 Ba lattice vibrations at T b 130 K [16], i.e., the YBCO7 50 nm film (k PLD/a =24) would require excitations of ~ 6 meV to change the spin state population. (iv) Electron pair states with J = 0, obeying Bose statistics can be formed by the interaction of an O:2p3/2 spin defect chain with another of Cu:3d3/2 symmetry (and/or Ba:5d3/2). The two electron pair states are eigenfunctions of J = J 1 + J 2 and J z
a
b
Fig. 5. Enhanced 001 scattering by 50 nm YBCO7, film on SrTiO3 with a 24 DEG grain boundary according to [8]: (a) f W near the Cu L2,3 edges at different T above and below Tc. (b) f W near the O K edge at different T above and below Tc.
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J.V. Acrivos / Microchemical Journal 81 (2005) 98–107
but not S z . The parity of the product states P for the exchange operation P12 of electrons 1 and 2 of d3/2 (Cu or Ba) and p3/2 (O) orbital symmetry give the allowed |J,0i
| J,Jz> | 3,0> | 2,0> | 1,0> | 0,0>
Matrix
Coefficients
1/401/2 [ 1 1 3 3 ] 1/81/2 [-1 -1 1 1 ] 1/401/2 [ 3 3 -1 -1 ] 1/81/2 [ 1 -1 1 -1 ]
=
*
(I+ iPP12)* (I+e (I+eiPP12)* (I+ (I+eiPP12)* (I+ (I+eiPP12)* (I+
d3/2
p3/2
P
| 3/2 1/2>d1** | 3/2 -1/2>d1** | 3/2 3/2>d1** | 3/2 -3/2>d1**
| 3/2 -1/2>p2 | 3/2 1/2>p2 | 3/2 -3/2>p2 | 3/2 3/2>p2
2π π 2π 2π
ð6Þ where the matrix coefficients are obtained to satisfy the eigenvalues, J( J +1), J z and the raising and lowering angular momentum textbook operations [12a]. I is the identity operator and electrons 1 and 2 are identified by the position in the product. The principal axis of quantization in relation (4) is parallel to kF and the electron pair e2= states allowed by symmetry in (6) are: j0; 0iab
chain
¼ 51=2 ðI þ P12 Þ
Y1;0z Rn RO:2p ðr RO3a Þ RO:2p ðr RO3b Þ 1 Y2;0 A Rn RCu:3d ðr RCu Þ 2
Y1;0 A Rn RO:2p ðr RO3a Þ RO:2p ðr RO3b Þ 1 Y2;0zRn RCu:3d ðr RCu Þ 2 g:
ð7Þ
for J = 0. Electron pair states obeying Bose statistics are possible for J =3, 1, 0 in (6) through interactions between electron states in neighboring 1D chains along the diagonal a,b (Fig. 4), mediated by lattice vibrations in YBCO7 of ~ 10 to 80 meV [16b]. (vi) Equal superconducting properties along the a:b and a:b diagonals, in a perfect lattice may occur only in a crystal with k+ and k quantization in two different CuO2 layers (e.g., YBCO7, Fig. 1a) or when an equal probability of k+ and k quantization gives rise to bonding f anti-bonding excitations of 2t/N ~ 6 meV, causing the commonly observed PLD. C. Evidence for electro-magnetic optic effects below Tc has also been obtained in the enhanced 001 scattering by a 50 nm YBCO7 film on SrTiO3 with a 24 DEG grain boundary [8]. Near the Cu L2,3 edges both the raw data I s/I 0 and f W (obtained from the raw data by an inverse Kerr rotation of u K = 23.5 DEG) indicate that below Tc a decrease in the final empty band states contribution of Cu:3d3/2 symmetry (L2 edge) is greater than for the Cu:3d5/2 contribution to the empty final states (L3 edge) (Fig. 5a). Changes at the O K edge are difficult to measure because the spin-orbit energy separation in the final states bands is negligible (Fig. 5b). However, in a film with grain boundaries, magnetic states are also introduced by broken bonds at the grain boundary in the same manner as when k+ changes to k (Fig. 4). 5. Conclusions
Acknowledgements
The temperature dependence of the YBCO7, Ba L2,3 XAS indicate that the onset of electro-magnetic optic effects in the Ba layer ~ 20 K above Tc forecasts the Mott transition [18] associated with the transition to superconductivity. The valence of an alkaline earth metal changes near the metal insulator Mott transition in Sr(NH3)x as determined by XAS valence edge shifts [19]. The elegant work of Zhang et al. [20] helps to unravel the YBCO7 superconductivity– magnetism relation. They have shown that spin polarized transport is non-dissipating and that transport by a Bose condensate in the superconducting state is a sub-group of spin polarized transport. A question remains: are the spin polarized nd3/2 over the nd5/2 band states in YBCO7 a result of the Bose condensation, or does the uneven spin population in nearly 1D conjugate orbitals (5) cause the Bose condensation? Since Faraday rotations are observed above Tc, the latter appears closer to the truth.
Support for this work was given by an NSF/DMR grant 9612873 at SJSU and DOE at SSRL. Professor Yao W. Liang of the IRC for superconductivity, Cavendish Laboratory is thanked for the YBCO7 single crystal and for moral support. References [1] [2] [3] [4] [5] [6] [7]
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