NMR Study on Copper-Oxide Superconductor Kitaoka Lab. Nozomu Shiki T. Goto et al., J. Phys. Soc. Jpn. 65(11), 3666-3671, 1996-11-15 T. Tsuda et al.,J. Phys. Soc. Jpn. 61, pp. 2109-2113 (1992) Contents • Introduction Copper-Oxide superconductor(LSCO) • Results NMR, NQR(Zero-field-NMR) technic NMR, Zero-field-NMR results on TlBa2YCu2O7-δ • Summary Introduction High-Tc Superconductor Charge Reservoir ＣｕＯ２ plane Charge Reservoir Cu2+ (3d9) La2CuO4 Mott Insulator Introduction High-Tc Superconductor Charge Reservoir ＣｕＯ２ plane La2CuO4 Mott Insulator Charge Reservoir Crystal field O2x2-y2 Cu2+ (3d9) 3z2-r2 xy O2- Cu2+ O2O2- yz zx O2- cubic symmetry O2- Introduction High-Tc Superconductor Charge Reservoir La2CuO4 ＣｕＯ２ plane Mott Insulator Charge Reservoir Jahn-Teller effect Crystal field Cu2+ (3d9) x2-y2 x2-y2 3z2-r2 3z2-r2 O2- xy xy yz yz zx zx O2- Cu2+ O2O2- O2- O2- Introduction High-Tc Superconductor Charge Reservoir La2CuO4 ＣｕＯ２ plane Mott Insulator Charge Reservoir Jahn-Teller effect Crystal field Cu2+ (3d9) U: coulomb energy t : hopping energy x2-y2 x2-y2 3z2-r2 3z2-r2 xy xy yz yz zx zx Antiferromagnetic interaction Ｊ t 𝒕𝟐 𝑱∝ 𝑼 Introduction High-Tc Superconductor Charge Reservoir La2CuO4 ＣｕＯ２ plane Mott Insulator Charge Reservoir Jahn-Teller effect Crystal field Cu2+ (3d9) U: coulomb energy t : hopping energy x2-y2 x2-y2 3z2-r2 3z2-r2 xy xy yz yz zx zx 𝒕𝟐 𝑱∝ 𝑼 Antiferromagnetic interaction Ｊ U t Introduction High-Tc Superconductor Charge Reservoir La2CuO4 ＣｕＯ２ plane Mott Insulator Charge Reservoir Jahn-Teller effect Crystal field Cu2+ (3d9) U: coulomb energy t : hopping energy x2-y2 x2-y2 3z2-r2 3z2-r2 xy xy yz yz zx zx 𝒕𝟐 𝑱∝ 𝑼 Antiferromagnetic interaction Ｊ U t Introduction High-Tc Superconductor Charge Reservoir La2-xSrxCuO4 ＣｕＯ２ plane Sr2+ Charge Reservoir Cu2+ (3d8) substitution La3+ x2-y2 x2-y2 3z2-r2 3z2-r2 xy xy yz yz zx zx Sr2+ Introduction Phase diagram Hole doping type (T-structure) Nd2-xCexCuO4 T La2-xSrxCuO4 Nd3+ → Ce4+ La3+ → Sr2+ Electron doping Hole doping Cu Cu O La (Sr) AFM La, Sr SC SC 0.15 0 0.15 A mother compound is a Mott insulator. La2-ｘSrxCuO4 La3+ Sr2+ As carriers increase , the ground state changes from AFM to SC. x Introduction Phase diagram Hole doping type (T-structure) Nd2-xCexCuO4 T La2-xSrxCuO4 Nd3+ → Ce4+ La3+ → Sr2+ Electron doping Hole doping Cu Cu O La (Sr) AFM La, Sr SC SC 0.15 0 0.15 A mother compound is a Mott insulator. La2-ｘSrxCuO4 La3+ Sr2+ As carriers increase , the ground state changes from AFM to SC. x Sample TlBa2YCu2O7-δ Tl1212 Tl Carrier density is controlled by changing oxygen deficiency. O Ba Cu ・Ca→Y ; atomic radius : Ca=197pm , Y=180pm (pm=10-12m) Y ・CuO2 planes in Tl1212 are pyramid type. ・Mott insulator (TN=320K) Experiment We performed NMR measurement of Tl1212. Experiment Nuclear Magnetic Resonance H1 cos t Ex. I=1/2 𝐻0 m=-1/2 I=1/2 ΔH ω= g H0 gℏ H0 H0 m=+1/2 H0＝0 Ｉ H0≠0 Zeemann splitting Zeeman interaction ℋ0 = −𝝁 ∙ 𝑯0 = −𝛾ℏ𝑰 ∙ 𝑯0 NMR Intensity e ΔH Em = −γℏ𝐻0𝑚 H res ω/γ ⊿H NMR (Nuclear Magnetic Resonance) 核磁気共鳴 γ (gyromagnetic ratio) 磁気回転比 H 0 ω/γ H Experiment Nuclear Magnetic Resonance ΔH Ex. I=1/2 𝐻0 m=-1/2 I=1/2 ω= g H0 gℏ H0 H0 m=+1/2 H0＝0 H0≠0 Zeemann splitting e NMR Intensity Antiferromagnetic state H0 Hint Hint H res ω/γ H H Ｉ Experiment Nuclear Magnetic Resonance ΔH Ex. I=1/2 𝐻0 m=-1/2 I=1/2 ω= g H0 gℏ H0 H0 m=+1/2 H0＝0 Ｉ H0≠0 Zeemann splitting e Antiferromagnetic state NMR Intensity Polycrystalline H0 Internal field H res ω/γ H H Experiment Nuclear Quadrupole Resonance ( H0 = 0 ) Cu nuclear spin ( I=3/2 ) + m=±3/2 + hνQ e 2 qQ 2 ΗQ 3I z I 2 4 I (2 I 1) f + νQ m=±1/2 + Different Electric field gradient OP IP IP Cu νQ(Cu : OP)～16 MHz Cu νQ(Cu : IP) ～ 8 MHz IP 8 MHz OP f 16 MHz NQR (Nuclear Quadrupole Resonance) 核四重極共鳴 、eQ (the nuclear quadrupole moment) 、 eq (the electric field gradient) Experiment NQR , Zero-field-NMR Different Electric field gradient OP IP IP Cu νQ(Cu : OP)～16 MHz Cu νQ(Cu : IP) ～ 8 MHz IP 8 MHz OP 16 MHz IP NQR (Nuclear Quadrupole Resonance) 核四重極共鳴 、eQ (the nuclear quadrupole moment) 、 eq (the electric field gradient) f Experiment NQR , Zero-field-NMR Different Electric field gradient OP IP Cu νQ(Cu : OP)～16 MHz Cu νQ(Cu : IP) ～ 8 MHz IP 8 MHz IP OP 16 MHz Shift!! When Hint occurs , IP signal shifts to high frequency. IP H g N I H int e 2 qQ (3I Z2 I ( I 1)) 4 I (2 I 1) Zeeman interaction Hint can be determined by frequency shift. Nuclear quadrupole interaction NQR (Nuclear Quadrupole Resonance) 核四重極共鳴 、eQ (the nuclear quadrupole moment) 、 eq (the electric field gradient) f Experiment NQR , Zero-field-NMR e2 qQ H g N I H int (3I Z2 I ( I 1)) 4I (2I 1) I=3/2 Zeeman interaction Hz only Nuclear quadrupole interaction HQ << Hz m 3 2 Δ m 1 2 -Δ 1 2 -Δ 3 m 2 Δ m f 0 g n H Effect of Hint is big Because of νQ～10MHz, Zeeman interaction is dominant when Hint is bigger than 1T. f 0 2 0 0 2 Results Tl1212 Cu-zero-field-NMR spectra Tl O Ba The signals of 63Cu and 65Cu are overlapped. Cu Y H g N I H int e 2 qQ (3I Z2 I ( I 1)) 4 I (2 I 1) Zeeman interaction Nuclear quadrupole interaction 0 2 Cu signal is resonant with higher frequency than νQ by the big internal field. f 0 0 2 Results Comparison of spectra YBa2Cu3O6 La2CuO4 TlBa2YCu2O7-δ O O Tl O Ba Ba Cu La Y ・CuO2 plane in Tl1212 is more ununiform than La2CuO4 and YBa2Cu3O6 . Cu Y Cu Determination of the values of MAFM Results Hint = | A – 4B | MAFM Cu AM O Onsite hyperfine field A ～ 3.7 T/μB 4BM The supertransferred hyperfine field B ≈ various value T/μB Results Experimental Results O Cu O O Tl O Ba Ba Cu AM Y Y La Cu 4BM TlBa2YCu2O7-δ YBa2Cu3O6 La2CuO4 20.44(±1.3) 22.87 31.9 Hint(T) 8.62 7.665 7.878 MAFM(μB)(theoretical value) 0.6 0.6 0.6 |A-4B|(T/μB) 14.3(±0.9) 12.78 13.13 B(T/μB) 2.66(±0.2) 2.27 2.36 63ν Q(MHz) Hint = | A – 4B | MAFM Cu Results Multi-layer cuprate superconductor S. Shimizu et al., Phys. Rev. B 85, 024528 (2012) Hidekazu Mukuda et al., J. Phys. Soc. Jpn. 81 (2012) 011008 Character of multi-layer cuprate OP : Outer Plane IP : Inner Plane Flatness of each layer is good!! CRL Carrier concentration; p Two types of CuO2 layer；OP and IP OP Carrier concentration varies in each layer. IP；low doping IP IP NMR IP n=2 OP CRL Madelung potential for hole doping n=5 OP IP Results (non-doped) 25MHz ZF-NMR Intensity Comparison of Cu-zero-field spectra TlBa2Ca4Cu5O12+δ (optimally-doped)1.5K 15MHz 10 O Cu Y Ba IP1 Ca Cu OP O 20 30 TlBa2Ca5Cu6O14+δ (optimally-doped) Tl Ba Tl 1.8K Tl Ba OP 10MHz 15MHz Ca Cu O IP1 IP2 Results Comparison of Results Tl O Cu O Tl Ba Ba Cu AM Ca Cu Y O 4BM TlBa2YCu2O7-δ TlBa2Ca4Cu5O12+δ TlBa2Ca5Cu6O14+δ 20.44(±1.3) 16.05(OP) , 8.37(IP) 16.6(OP) , 9.7(IP) Hint(T) 8.62 2.5(IP1) 2.1(IP1) , 3.6(IP2) MAFM(μB) 0.6(theoretical value) 0.1(IP1) |A-4B|(T/μB) 14.3(±0.9) 20.7(IP1) 21(IP1) , 21.17(IP) B(T/μB) 2.66(±0.2) 4.25(IP1) 4.33(IP1) , 4.37(IP2) 63ν Q(MHz) Hint = | A – 4B | MAFM 0.1(IP1) , 0.17(IP2) Results Comparison of Results Cu Wave functions of Cu 3d and O 2p are overlapped largely. So, Cu-O bonding in multi-layer is stronger. O AM Cu O 4BM Flatness is good in multi-layer. TlBa2YCu2O7-δ TlBa2Ca4Cu5O12+δ TlBa2Ca5Cu6O14+δ 20.44(±1.3) 16.05(OP) , 8.37(IP) 16.6(OP) , 9.7(IP) Hint(T) 8.62 2.5(IP1) 2.1(IP1) , 3.6(IP2) MAFM(μB) 0.6(theoretical value) 0.1(IP1) |A-4B|(T/μB) 14.3(±0.9) 20.7(IP1) 21(IP1) , 21.17(IP) B(T/μB) 2.66(±0.2) 4.25(IP1) 4.33(IP1) , 4.37(IP2) 63ν Q(MHz) Hint = | A – 4B | MAFM 0.1(IP1) , 0.17(IP2) Results Tl-NMR spectra TlBa2YCu2O7-δ O Tl Ba Cu Y Magnetic moment at Cu site induces the internal field at Tl site. Tl O Cu Tl-NMR spectra TlBa2Ca5Cu6O14+δ Tl 50K Ba 100K Ca Cu 0.3 150K FWHM(kOe) Cu H0⊥c 4.2K Tl Ba Y Tl1256 Echo Amplitude TlBa2YCu2O7-δ O 174.2MHz 200K 0.2 0.1 300K 205 7.00 O 203 Tl 7.05 7.10 Tl 0 7.15 100 7.20 Magnetic Field(T) ・Electronic state around Tl site is homogeneous. ・AFM order develops below TN. 200 Temperature(K) 300 7.25 Summary ・We investigated AFM in Tl1212 by Cu-zero-field-NMR. The AFM order of Mott insulating state is a common feature for CuO2 planes. Hint = | A – 4B | MAFM ・The transferred hyperfine field (B) is large in multi-layer, due to the strong covalency of Cu-O bonding and good flatness of CuO2 planes ・Internal field at Tl site is observed by Tl-NMR in Tl1212. because of magnetic order at CuO2 planes Cu O ゼロ磁場中での測定 NQR , zero-field-NMR ゼロ磁場中における核スピンのハミルトニアン e2 qQ H g N I H int (3I Z2 I ( I 1)) 4I (2I 1) ゼーマン相互作用 核四重極相互作用 i) 常磁性（内部磁場なし）の場合 四重極相互作用によるNQRスペクトルが得られる ii) 反強磁性秩序状態の場合 内部磁場（と四重極相互作用）によるゼロ磁場NMRスペクトルが得られる ゼロ磁場中でのスペクトルの解析により 磁性・非磁性状態を確認することができる ゼロ磁場中での測定 NQR , zero-field-NMR e2 qQ H g N I H int (3I Z2 I ( I 1)) 4I (2I 1) ゼーマン相互作用 HQ only 3 2 核四重極相互作用 Hz << HQ h Q 1 2 微小な内部磁場 3 2 1 2 3g NH 0 cos 0 g N H 0 [cos2 ( I 12 ) 2 sin 2 ] 1 2 HQ //c f 3e 2 qQ Q 2 I (2 I 1)h f Q 90 Experiment Knight Shift H0 Ｉ e ω= g (Hres+⊿H) = g Hres(1+K) NMR (Nuclear Magnetic Resonance) 核磁気共鳴 NMR Intensity ΔH ΔH H res ω/γ ⊿H H 0 ω/γ Knight shift K γ (gyromagnetic ratio) 磁気回転比 ΔH H res H
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