Knight shift vs hole concentration in Hg1201 and Hg1212

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by  Y. Itoh

Knight shift vs hole concentration in Hg1201 and Hg1212
Y. Itoh1
1Department of Physics, Graduate School of Science, Kyoto Sangyo University,
Kamigamo-Motoyama, Kita-ku Kyoto 603-8555, Japan
(Dated: January 13, 2015)
5 We studied the hole concentration dependences of 63Cu Knight shifts in single-CuO2-layer high-
1
Tc cupratesuperconductorsHgBa2CuO4+δ anddouble-layerHgBa2CaCu2O6+δ. Wefoundthatthe
0
spinKnightshiftatroomtemperatureasafunctionoftheholeconcentrationinthesingle-layersu-
2
perconductorisdifferentfromthatinthedouble-layersuperconductor. Twotyperelationsbetween

n thespin Knight shift and theholedopinglevelserveto estimate theindividualhole concentrations
a of thenon-equivalent CuO2 planes in a unit cell.
J

0 PACSnumbers:
1

] I. INTRODUCTION HgBa2CuO4+δ HgBa2CaCu2O6+ δ
n
o BaO BaO
c The doped hole carriers have been believed to dis- CuO2 CuO2
- tributenonuniformlyinthemulti-layercupratesupercon- BaO Ca
r CuO
p ductors. How to estimate the individual carrier doping HgOδ BaO2
u levels of the non-equivalent CuO2 planes in the multi-
s layer superconductors has been an issue. The bond HgOδ
.
t valence sum associated with a local ionic valence has
a
served to estimate the hole concentration [1–3]. The
m
bondvalencesumisamicroscopiccharacterizationbased
-
d on the nanometer-scale structural analysis of the ionic
n bonds. Although a bulk observable such as thermoelec-
o tricpower(Seebeckcoefficient)atroomtemperaturehas
c been proposed to estimate the hole concentration [4], no FIG. 1: Schematic crystal structures of Hg1201 (left) and
[
macroscopic observables enable us to estimate the layer- Hg1212 (right).

1 selective hole concentration in the multi-layer systems.
v Then, microscopic observables have been desired.
7 The ab-plane spin component of the plane-site 63Cu tal structures of Hg1201 and Hg1212. The oxygen con-
3 Knight shift 63Kab at room temperature was used to centrationintheHgOlayercontrolstheholedopinglevel
3 s
estimate the individual hole concentrations of the non- in the CuO2 plane. The crystal symmetry is tetragonal.
2
0 equivalent CuO2 planes in the multi-layer supercon- We believe that Hg1201 and Hg1212 are the canonical
. ductors [5, 6]. The hole concentration p is defined high-Tc cuprate superconductors.
1
0 by the fraction of holes per Cu2+p ion in the CuO2 Inthispaper,westudiedtheholeconcentrationdepen-
5 plane. A one-to-one correspondence between 63Ksab dences of the spin Knight shifts at room temperature in
1 and the hole concentration p has been proposed except the single-layersuperconductorsHg1201andthe double-
v: for La2−xSrxCuO4 (LSCO), YBa2Cu3O7−δ (Y1237)and layer Hg1212 in [9–11]. The present analysis is based
i YBa2Cu4O8 (Y1248)[5,6]. The singleuniversalrelation on the NMR results reported in [9–11]. The prepara-
X between63Kab andphasbeeadoptedforthemulti-layer tionmethods ofthe samples for the NMR measurements
s
r superconductors. However, the uniform spin susceptibil- are described in [9, 10, 12]. We emphasize that the spin
a ities per Cu spin in single-layer systems are known to Knight shift as a function of the hole concentration in
be larger than those in double-layer systems [7, 8]. It the single-layersuperconductors is different from that in
should be noted that the difference in 63Kab of single- the double-layer superconductors
s
CuO2-layersuperconductorHgBa2CuO4+δ(Hg1201)and
double-layer HgBa2CaCu2O6+δ (Hg1212) in [9–11] has
been overlooked. Thus, an issue how relevant the appli- II. EXPERIMENTAL KNIGHT SHIFTS OF
cationofthe singleuniversalrelationbetween63Kab and HG1201 AND HG1212
s
p is for the multi-layer systems should be addressed.
The optimal Tcs of Hg1201 and Hg1212 are the high- Figure 2 shows the 63Cu Knight shifts 63Kab’s of
est among the single-layerand the double-layer systems. Hg1201 (open symbols) and Hg1212 (closed symbols) in
The structural flatness of the CuO2 plane characterizes anexternalmagneticfieldalongthe abplanes,whichare
Hg1201andHg1212. Figure 1 showsthe schematic crys- reproduced from [9–11]. The doping levels are catego-
2
1.0 Tc = 50 K Tc = 96 K Tc = 30 K
T = 127 K
%) c
( T = 103 K
b c
aK
63 T = 93 K
c
0.5
K (a) (b) (c)
orb
0
0 200 0 200 0 200
T (K) T (K) T (K)
FIG.2: 63CuKnightshifts63KabforHg1201(opensymbols)andHg1212(closedsymbols)intheunderdoped(a),theoptimally
doped(b),andtheoverdopedregimes(c),whicharereproducedfrom[9–11]. ThedashedlinesindicatetheindividualTcs. The
sold lines in (c) are visual guides.
rized into underdoping (a), optimally doping (b), and
overdoped doping (c). 0.4 D1
The 63Cu Knight shift 63Kab is given by 63Kab =
63Kab(T) +63Kab , where 63Kab is the spin Knight shift S1
ands63Kab is tohreb orbital shifst. 63Kab is proportional 0.3
orb s
to the uniform spin susceptibility multiplied by the hy-
perfine coupling constant. 63Kab is proportional to the ph 0.2
orb
Van Vleck orbital susceptibility. The temperature de-
pendenceof63Kab inthecupratesuperconductorscomes 0.1
Hg1212
from that of the spin shift 63Kab. We have estimated
s Hg1201
63Kab ∼0.25%forHg1201and∼0.20%forHg1212[9–
orb 0.0
11]. As seen in Fig. 2, 63Kab of Hg1201 is larger than 0.0 0.2 0.4 0.6 0.8
s
63 ab
that of Hg1212 at each doping regime. K (RT) (%)
s
Figure3showstheholeconcentrationp in[12]against
h
63Kab (%) at room temperature of Hg1201 and Hg1212
s
in [9–11]. From the least squares fits, we obtained two
relationsofS1: p =0.6363Kab(RT)-0.13(Hg1201)and FIG.3: HoleconcentrationphagainstspinKnightshift63Ksab
h s atroom temperature(RT)in Hg1201 andHg1212. Thesolid
D1,ph =0.7463Ksab(RT)-0.04(Hg1212). Thesolidlines lines are the fit functions of S1: ph = 0.6363Ksab(RT) - 0.13
in Fig. 3 indicate the fit functions of S1 and D1. The (Hg1201) and D1, ph = 0.7463Ksab(RT) - 0.04 (Hg1212).
extrapolations of S1 and D1 to p = 0 lead to 63Kab
h s
= 0.21 % (Hg1201) and 63Kab = 0.05 % (Hg1212) at
s
the phase boundary. The empirical functions of S1 and
D1 are different from the previous fit functions F1 and linear extrapolation from the existing data in [13]. The
F2 (63Kab < 0.5 %) adopted for the multi-layer systems single-layer system LSCO is located close to S1. The
s
in [5]. double-layer systems of Y1237 and Y1248 are located
close to the line D1.
In Fig. 4(b), we estimated the hole concentrations
III. DISCUSSIONS
ps by the parabolic curve of Tc/Tc,max = 1 - 82.6(p -
0.16)2in[19]after[5]. Figure4(b)showspagainst63Kab
s
We discuss the hole concentration dependence upon (%)ofHg1201,LSCO[13],Tl2Ba2CuO6+δ (Tl2201)[20];
the spin Knight shift for the other cuprate superconduc- Hg1212,andBa2CaCu2O4(F,O)2 (0212F)[6]. Inspiteof
torsandthealternativeestimationoftheholeconcentra- the alternative estimation of the hole concentration, the
tion. pvs63KabdependenceofHg1201isdifferentfromthatof
s
Figure 4(a) shows p against 63Kab (%) of Hg1201, Hg1212. The reason why 63Kab’s of Hg1212 are smaller
h s s
LSCO [13]; Hg1212, Y1237 [14, 15] and Y1248 [16–18]. than those of Hg1201 at the respective doping levels in
We estimated 63Kab at room temperature for LSCO by Figs. 2and3maybeduetotheeffectofthemagneticbi-
s
3
(a) (b)
0.4 D1 0.4 0212F F1
Hg1212
S1 Hg1201
F2
0.3 0.3
Y1237
Y1237
ph 0.2 Y1248 p 0.2 LSCO
Tl2201
Hg1212
0.1 0.1
Hg1201
LSCO
0.0 0.0
0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8
63 ab 63 ab
K (RT) (%) K (RT) (%)
s s
FIG.4: (a)HoleconcentrationphagainstspinKnightshift63KsabofHg1201,LSCO[13];Hg1212,Y1237[14,15]andY1248[16–
18]. (b) Hole concentration p against spin Knight shift 63Ksab of Hg1201, LSCO [13], Tl2201 [20]; Hg1212, 0212F [6]. One
should note ph (a) and p (b) estimated from the different ways. In (b), F1 (dashed line) and F2 (sold line) are the previous
functions for 63Ksab < 0.5 % in [5].
layercoupling. Theeffectofthebilayercouplinghasalso conductors Hg1201 is different from that in the double-
been studied for the triple-layer superconductors. Thus, layer superconductors Hg1212. Since we believe that
one should take into considerationwhich type relationis Hg1201 and Hg1212 are the canonical systems, the p
h
relevantS1orD1toestimatetheindividualholeconcen- dependencesupon63KabatroomtemperatureinHg1201
s
trations of the non-equivalentCuO2 planes in the multi- and Hg1212 should be standard to estimate the indi-
layer superconductors. vidual hole concentrations of the non-equivalent CuO2
planes in a unit cell.
IV. CONCLUSION
We found that the spin Knight shift 63Kab as a func- V. REFERENCES
s
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