Anisotropic dispersion of the spin excitations in acuprate superconductor

Oleh Ivashko

Physik-Institut

Team

J. Chang
C. E. Matt
D. Destraz
C. Monney

N. B. Christensen

C. G. Fatuzzo
N. E. Shaik
H. M. Rønnow

P. G. Freeman

X. Lu
M. Dantz
D. E. McNally
T. Schmitt

T. Kurosawa
N. Momono
M. OdaOutline

Introduction• Resonant Inelastic X-ray Scattering (RIXS)• RIXS on cuprates
Magnetic excitations on LSCO 12%• Overview of the data
• Extraction of the magnetic-excitations dispersion• Hubbard model• LSCO vs. LCO comparison
Two orbital model & data interpretation
Conclusions

Oleh Ivashko

Introduction: RIXS

Adapted from L. J. P. Ament, et al., Rev. of Mod. Phys., 83 (2011)

Oleh Ivashko

Introduction: RIXS on cuprates

G. Ghiringhelli et al., Science 6096, 821 (2012)

M. Le Tacon et al., Nature Physics 7, 725–730 (2011)

L. Braicovich et al., PRL 104, 077002 (2010)
Oleh Ivashko

Magnetic excitations on LSCO 12%: Overview of the data

QCDW = (±δ1,δ2)
δ1 = 0.24(6) rlu
δ2 ≈ 0.01 rlu

V. Thampy et al., PRB 90, 100510 (2014)
T. P. Croft et al., PRB 89, 224513 (2014)
Oleh Ivashko

Magnetic excitations stronger for LH lightunder grazing exit scattering conditions
M. Le Tacon et al., Nature Physics 7, 725–730 (2011)

O. Ivashko et al., PRB 95, 214508 (2017)

Magnetic excitations on LSCO 12%: Paramagnons

Damped harmonic oscillator response functionγω''''χ =χ 0 22[ ω −ω 20 ] +ω2 γ 2Damping coefficient(γ /2)=√ ω20 −ω 21
Dynamical Stucture Factor
1S(Q , ω)=∗χ' ' (Q , ω)
1−exp (ħ ω /k B T )C. Monney, et al., PRB 93, 075103 (2016); J. Lamsal and W. Montfrooij, PRB 93, 214513 (2016)
Oleh Ivashko

O. Ivashko et al., PRB 95, 214508 (2017)

Magnetic excitations on LSCO 12%: Paramagnons

Oleh Ivashko

O. Ivashko et al., PRB 95, 214508 (2017)

Magnetic excitations on LSCO 12%: Hubbard model
Hamiltonian
H H =−t ∑ c i ,σ c j σ −t ∑ c i ,σ c j σ−t†i , j1 ; σ'1,†i , j 2 ;σ2,''∑ c †i ,σ c j σ +U ∑ ni ,↑ ni ,↓i , j 3 ;σ3,iDispersion relation

ω( q)=Z √ A (q) 2−B(q)2 , Z =1.219

Zone-boundary dispersion

11 1
E ZB =ω( , 0)−ω( , )24 444t
Case (1) E ZB =12 Z J B , J B= 3U
for t '=t ' ' =0

If t = 430 meV, U/t = 8EZB ≈ 50 meV
J.-Y. P. Delannoy et al., PRB 79, 235130 (2009); O. Ivashko et al., PRB 95, 214508 (2017)

Oleh Ivashko

Magnetic excitations on LSCO 12%: Hubbard model

U=8t

Zone-boundary dispersion

11 1
E ZB =ω( , 0)−ω( , )24 4E ZB
JA1≈1+112−
Case (2)12 Z J B
12JB(forOleh Ivashko

24t' 24t4t, J A=, J B= 3tUU)( )||Ut't''≃8, ⩽0.5,− =0.5ttt'
O. Ivashko et al., PRB 95, 214508 (2017)

Magnetic excitations on LSCO 12%: LSCO vs. LCO
ARPES4t = 1720 meV and -t’/t = 0.16 (-t”/t = 0.5)
C. G. Fatuzzo et al, PRB 89, 205104 (2014); J. Chang et al., Nat.
Comm. 4, 2559 (2013); T. Yoshida et al., PRB 74, 224510 (2006)

U/t ∼ 5 & Z ∼ 0.7

4t = 1720 meV and Z = 1.219 (-t”/t = 0.5)
Ref.
1233
1 N. S. Headings et al., PRL 105, 247001 (2010)
R. Coldea et al., PRL 86, 5377 (2001)
2 J.-Y. P. Delannoy et al., PRB 79, 235130 (2009)
3 O. Ivashko et al., PRB 95, 214508 (2017)

Oleh Ivashko

Two orbital model & data interpretation

H. Sakakibara et al., PRL 105, 057003 (2010)
H. Sakakibara et al., PRB 85, 064501 (2012)
Oleh Ivashko

Two orbital model & data interpretation

E z ↓⇒|t '| ,|t ' '|↑⇒ E ZB ↑2Oleh Ivashko

O. Ivashko et al., PRB 95, 214508 (2017)

Conclusions• Magnetic excitations in LSCO are strongly anisotropic
compared to the ones on LCO• Hubbard type model reveals a non negligible value of t’ (and t’’)in contrast with ARPES data
• This discrepancy between RIXS and ARPES data is solved within
the frame of two-orbital model• Cu dz2 orbital reveals to be important for the description of theantiferromagnetic zone-boundary dispersion of the magnetic excitations
O. Ivashko et al., PRB 95, 214508 (2017)
Oleh Ivashko