spin and charge excitations in stripe-ordered cuprates ... · schematic diagram of stripe order in...
TRANSCRIPT
![Page 1: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/1.jpg)
Spin and Charge Excitations in
Stripe-Ordered Cuprates
Takami Tohyama
Tokyo University of Science, Japan
Shigetoshi Sota RIKEN
Michiyasu Mori JAEA
Kenji Tsutsui QST
![Page 2: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/2.jpg)
Outline
- Charge stripes in hole-doped cuprates
- Dynamical density-matrix renormalization group
(DDMRG) calculations of dynamical spin and charge
structure factors for a 24x4 t-t’-J ladder
- Comparison with RIXS experiments and some implication
for electron-doped cuprates
T.T., M. Mori, and S. Sota, Phys. Rev. B 97, 235137 (2018)
- Effect of dimensionality on dynamical spin and charge
structure factors
- RIXS in one-dimensional extended Hubbard model
![Page 3: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/3.jpg)
Schematic diagram of stripe order in
1/8-doped La1.875La0.125CuO4
Review: M. Fujita et al., J. Phys. Soc. Jpn. 81, 011007 (2012)
![Page 4: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/4.jpg)
Spin dynamics in stripe-ordered hole-doped cuprates: experiments
M. Fujita et al., J. Phys. Soc. Jpn. 81, 011007 (2012)
Inelastic neutron scattering
“hourglass” around (p,p)
(p,p)(0.6p,p) (1.4p,p)
Resonant inelastic x-ray scattering
“plateau” around (0.5p,0)
stripe-ordered La1.875Ba0.125CuO4
H. Miao et al.,
PNAS 114, 12430
(2017)
(0.5p,0)
![Page 5: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/5.jpg)
Ground-state properties in the 1/8-hole-doped 12x4 t-t'-J ladder
S. White and D. J. Scalapino, PRB 60, R753 (1999)
J/t = 0.35
charge densityd-wave paring
correlation
![Page 6: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/6.jpg)
Hole-doped four-leg t-t'-J ladder gives a charge-stripe orderS. White and D. J. Scalapino, PRB 60, R753 (1999)
We calculate dynamical spin and charge structure factors
0
1 1, Im 0 0z z
tJ
S S SH E i
p
q qq
0
1 1, Im 0 0
tJ
N N NH E i
p
q qq
t-t’-J model
1 2 1
, , , ,
, , , , ,
1' h.c.
4tJ i j i j i j i j
i j i j i j
H t c c t c c J n n
S S
24x4 t-t’-J ladder
x (leg) direction open boundary
y (rung) direction periodic boundary
Dynamical density-matrix renormalization group (DDMRG)
J/t = 0.4
t’/t = -0.25
T.T., M. Mori, and S. Sota, Phys. Rev. B 97, 235137 (2018)
![Page 7: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/7.jpg)
Dynamical charge structure factor in the 24x4 t-t'-J ladder
hole doping x=1/12 x=1/8 x=1/6
0.0 0.2 0.4 0.6 0.8 1.00.0
0.4
0.8
1.2
1.6
2.0
xh=1/12
N(q,)
qy=0
24x4 t-t'-J hole x=8/96=0.083, m=4000, /t=0.08
qx/p
/t
0.00
0.04
0.08
0.12
0.0 0.2 0.4 0.6 0.8 1.00.0
0.4
0.8
1.2
1.6
2.0
xh=1/8
N(q,)
qy=0
24x4 t-t'-J hole x=12/96=0.125, m=4000, /t=0.08
qx/p
/t
0.00
0.04
0.08
0.12
0.0 0.2 0.4 0.6 0.8 1.00.0
0.4
0.8
1.2
1.6
2.0
xh=1/6
N(q,)
qy=0
24x4 t-t'-J hole x=16/96=0.167, m=4000, /t=0.08
qx/p
/t
0.00
0.04
0.08
0.12
Minimum-energy position is close to qx= p(1- 4x) as expected from stripe order.
(p,0)(0,0)
![Page 8: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/8.jpg)
0.0 0.4 0.80.0
0.2
0.4
0.6
0.8
1.0
S(q,)
qy=p
24x4 t-t'-J hole x=16/96=0.167, m=3000, /t=0.08
qx/p
/t
0.0
0.5
1.0
1.5
2.0
1.2 1.6 2.0
xh=1/6
0.0 0.4 0.80.0
0.2
0.4
0.6
0.8
1.0
S(q,)
qy=p
24x4 t-t'-J hole x=12/96=0.125, m=3000, /t=0.08
qx/p
/t
0.0
0.5
1.0
1.5
2.0
1.2 1.6 2.0
xh=1/8
Dynamical spin structure factor in the 24x4 t-t'-J ladder
0.0 0.4 0.80.0
0.2
0.4
0.6
0.8
1.0
S(q,)
qy=p
24x4 t-t'-J hole x=8/96=0.083, m=3000, /t=0.08
qx/p
/t
0.0
0.5
1.0
1.5
2.0
1.2 1.6 2.0
xh=1/12
hole dopingx=1/12 x=1/8 x=1/6
(p,p)(0.6p,p) (1.4p,p)
- Calculated q=(p,p) excitations
are higher in energy than the
experimental data.
- Incommensurate qx is p(1-2x).
(p,p)(0, p)
- Strong “outward” weight,
inconsistent with experiments
![Page 9: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/9.jpg)
Dynamical charge and spin structure factor in the 24x4 t-t'-J ladder
hole doping x=1/12 x=1/8 x=1/6
0.0 0.2 0.4 0.6 0.8 1.00.0
0.4
0.8
1.2
1.6
2.0
xh=1/12
N(q,)
qy=0
24x4 t-t'-J hole x=8/96=0.083, m=4000, /t=0.08
qx/p
/t
0.00
0.04
0.08
0.12
0.0 0.2 0.4 0.6 0.8 1.00.0
0.4
0.8
1.2
1.6
2.0
xh=1/8
N(q,)
qy=0
24x4 t-t'-J hole x=12/96=0.125, m=4000, /t=0.08
qx/p
/t
0.00
0.04
0.08
0.12
0.0 0.2 0.4 0.6 0.8 1.00.0
0.4
0.8
1.2
1.6
2.0
xh=1/6
N(q,)
qy=0
24x4 t-t'-J hole x=16/96=0.167, m=4000, /t=0.08
qx/p
/t
0.00
0.04
0.08
0.12
(p,0)(0,0)
- A step structure at the charge order vector qx for x=1/8 and 1/6
strong coupling between charge and spin; ferromagnetic coupling across the stripes
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
xh=1/12
S(q,)
qy=0
24x4 t-t'-J hole x=8/96=0.083, m=3000, /t=0.08
qx/p
/t
0.00
0.02
0.04
0.06
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
xh=1/8
S(q,)
qy=0
24x4 t-t'-J hole x=12/96=0.125, m=3000, /t=0.08
qx/p
/t
0.00
0.02
0.04
0.06
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
xh=1/6
S(q,)
qy=0
24x4 t-t'-J hole x=16/96=0.167, m=3000, /t=0.08
qx/p
/t
0.00
0.02
0.04
0.06
S(q,)
N(q,)
![Page 10: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/10.jpg)
Dynamical charge and spin structure factor in the 24x4 t-t'-J ladder
electron dopingx=1/12 x=1/8 x=1/6
- No step-like structure in contrast to hole doping because of weak stripe order
- A downward spectral weight toward (p,0) intrinsic for electron doping?
S(q,)
N(q,)
0.0 0.2 0.4 0.6 0.8 1.00.0
0.4
0.8
1.2
1.6
2.0
xe=1/12
N(q,)
qy=0
24x4 t-t'-J electron x=8/96=0.083, m=4000, /t=0.08
qx/p
/t
0.00
0.04
0.08
0.12
0.0 0.2 0.4 0.6 0.8 1.00.0
0.4
0.8
1.2
1.6
2.0
xe=1/8
N(q,)
qy=0
24x4 t-t'-J electron x=12/96=0.125, m=4000, /t=0.08
qx/p
/t
0.00
0.04
0.08
0.12
0.0 0.2 0.4 0.6 0.8 1.00.0
0.4
0.8
1.2
1.6
2.0
xe=1/6
N(q,)
qy=0
24x4 t-t'-J electron x=16/96=0.167, m=4000, /t=0.08
qx/p
/t
0.00
0.04
0.08
0.12
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
1.2
xe=1/12
S(q,)
qy=0
24x4 t-t'-J electron x=8/96=0.083, m=3000, /t=0.08
qx/p
/t
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
1.2
xe=1/8
S(q,)
qy=0
24x4 t-t'-J electron x=12/96=0.125, m=3000, /t=0.08
qx/p
/t
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
1.2
xe=1/6
S(q,)
qy=0
24x4 t-t'-J electron x=16/96=0.167, m=3000, /t=0.08
qx/p
/t
0.00
0.04
0.08
0.12
0.16
0.20
(p,0)(0,0)
![Page 11: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/11.jpg)
Doping dependence of magnetic excitation by RIXS
M. Le. Tacon et al., Nat. Phys. 7, 725 (2011);
PRB 88, 020501(R) (2013)
M. P. M. Dean, JMMM 376, 3 (2015)
Hole doping
K. Ishii, M. Fujita, T.T. et al., Nat. Commun.
5, 3714 (2014)
W. S. Lee et al., Nat. Phys. 10, 883 (2014)
Electron doping
![Page 12: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/12.jpg)
Dynamical spin structure factor in the t-t'-J model
J/t=0.4
t’/t=-0.25
4-leg
6-leg
8-leg
The two discrepancies are
resolved with increasing leg
number, i.e., toward square
lattice.
(p,p)(p/2, p)
S(q,)
toward square lattice
![Page 13: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/13.jpg)
Charge stripes from 4-leg to 8-leg ladders
N(q,)
Weakening of stripes from
4-leg to 8-leg systems
toward square lattice
![Page 14: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/14.jpg)
2p
3d
absorption process
(=XAS)
emission process
(=XES)intermediate stateground state
RIXS for L-edge
2
†, 0, i io o
i 0
i o
i o
1, ~ 0 f
f
I f D D E EH E i
kkq
q k k0 : ground state (no Cu2p hole)
f : ‘final’ state with momentum q
: dipole transition operatori(o) i(o) i(o), i(o) , , , ,
, ,
3 ; 2 ;z
z
K z j j
j
D d p jj d P
ε k k k
k
ε r
![Page 15: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/15.jpg)
RIXS for cuprates
†,, i io o
i 0
10 f 0
j j jN
jSf D N
E iSD
H
q qkk
Cu2+: 3d9 1 hole on x2-y2 orbital with in-plane spin orientation
1/2 3/i o
2o i
22
15
j jN N z z
ε ε ε ε 1/2 3/o
2i
2
15
j jS S z
i
ε ε
M. W. Haverkort, PRL 105, 167404 (2010)
J. Igarashi and T. Nagao, PRB 85, 064421 (2012)
S. Kourtis, J. van den Brink, and M. Daghofer, PRB 85, 064423 (2012)
1 3,
2 2j
Non spin-flip process
Spin-flip process
![Page 16: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/16.jpg)
Incident-photon energy i dependence of RIXS intensity
Spin-flip Non-spin-fliphole doping (11%)
YBCO
M. Minola et al., PRL 114, 217003 (2015)
18 sites t’=-0.25t
U=10t Ucore=12t =t
K. Tsutsui, T.T., PRB
94, 085144 (2016)
two-magnon
charge
A change from “two-magnon” to “charge”
fluorescence-like behavior
How do RIXS spectra behave
when attractive interactions are
explicitly taken into account?
![Page 17: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/17.jpg)
One-dimensional extended Hubbard model
†1 1 1
h.c.i i i i i i i ii i i
H t c c U n n V n n n n
F. Iemini, T. O. Maciel, and R. O. Vianna, Phys. Rev. B 92, 075423 (2015).
U/t
V/t
Singlet super
Half-filling
H. Q. Lin and J. E. Hirsch, Phys. Rev. B 33, 8155 (1983).
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PS
CDWV/t
RIXS for spin-flip process and S(q,)
CDW singlet super. (SS)
0 2 4 6 8 100
20
40
60
80
S(q
,)
(arb
. unit)
(t)
q=p
6p/7
5p/7
4p/7
3p/7
2p/7
p/7
U=-4, V=+0.25
0 2 4 6 8 100
20
40
60
80
S(q
,)
(arb
. unit)
(t)
q=p
6p/7
5p/7
4p/7
3p/7
2p/7
p/7
U=-4, V=-0.25
S(q,)
0 2 4 6 8 10
0
0.06
0.12
0.18
(t)
IS
=1 (
arb
. unit)
K=p
U=-4, V=+0.25
6p/7
5p/7
4p/7
3p/7
2p/7
p/7
0
Uc=4,i:edge
0 2 4 6 8 10
0
0.06
0.12
0.18
(t)
IS
=1 (
arb
. unit)
K=p
U=-4, V=-0.25
6p/7
5p/7
4p/7
3p/7
2p/7
p/7
0
Uc=4,i:edge
RIXS
☑ No difference
between CDW
and SS
☑ Excitations at
high-energy
Hubbard model at
half-filling
U<0
N(q,)
S(q,)
U>0
S(q,)
N(q,)
![Page 19: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/19.jpg)
PS
CDWV/t
RIXS for non-spin-flip process and N(q,)
RIXS
N(q,)CDW singlet super. (SS)
0 2 4 6 8 100
100
200
N(q
,)
(arb
. unit)
(t)
q=p6p/75p/74p/73p/72p/7p/7
U=-4, V=+0.25
0 2 4 6 8 100
20
40
60
80
N(q
,)
(arb
. unit)
(t)
q=p
6p/7
5p/7
4p/7
3p/7
2p/7
p/7
U=-4, V=-0.25
0 2 4 6 8 10
0
0.06
0.12
0.18
(t)I
S=
0 (
arb
. unit)
K=p
U=-4, V=-0.25
6p/7
5p/7
4p/7
3p/7
2p/7
p/7
0
Uc=4,i:edge
0 2 4 6 8 10
0
0.06
0.12
0.18
0.24
(t)
IS
=0 (
arb
. unit)
K=p
U=-4, V=+0.25
6p/7
5p/7
4p/7
3p/7
2p/7
p/7
0
Uc=4,i:edge
☑ CDW
RIXS and N(q,)
similar
☑ SS
RIXS detects
high-energy
excitations that
are the same as
spin-flip case.
More incoherent
nature in SS than
CDW
☑ Clear difference
between CDW
and SS
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PS
CDWV/t
Incident-photon-energy dependence of RIXS for SS
0 5 10
0
0.05
0.1
0.15
edge (t)
I XA
S (
arb
. unit)
U=-4, V=-0.25 Uc=4
XAS
0 2 4 6 8 10
0
0.06
0.12
0.18
(t)
IS
=0 (
arb
. unit)
K=p
U=-4, V=-0.25
6p/7
5p/7
4p/7
3p/7
2p/7
p/7
0
Uc=4,i:edge
non-spin-flip
0 2 4 6 8 10
0
0.06
0.12
0.18
(t)
IS
=1 (
arb
. unit)
K=p
U=-4, V=-0.25
6p/7
5p/7
4p/7
3p/7
2p/7
p/7
0
Uc=4,i:edge
spin-flipabsorption at singly
occupied sites
0 5 10
0
0.05
0.1
0.15
edge (t)
I XA
S (
arb
. unit)
U=-4, V=-0.25 Uc=4
0 2 4 6 8 10
0
0.06
0.12
0.18
(t)
IS
=1 (
arb
. unit)
K=p
U=-4, V=-0.25
6p/7
5p/7
4p/7
3p/7
2p/7
p/7
0
Uc=4,i:Uc
non-spin-flip spin-flip
XAS
absorption at
empty sites
0 2 4 6 8 10
0
0.06
0.12
0.18
(t)
IS
=0 (
arb
. unit)
K=p
6p/7
5p/7
4p/7
3p/7
2p/7
p/7
0
spin-flip: large intensity at low-energy XAS
non-spin-flip: large intensity at high-energy XAS
![Page 21: Spin and Charge Excitations in Stripe-Ordered Cuprates ... · Schematic diagram of stripe order in 1/8-doped La 1.875 La 0.125 CuO 4 Review: M. Fujita et al., J. Phys. Soc. Jpn. 81,](https://reader034.vdocument.in/reader034/viewer/2022050504/5f9602f6241fcc6ee9600ce3/html5/thumbnails/21.jpg)
Summary
☑ RIXS, S(q,), and N(q,) with charge-stripe order
- “hourglass” in S(q,)
- A step-like behavior with S(q,) along (0,0)-
(p,0)
hole doping: stripe order in the ground state
electron doping: weak stripe order in the ground state
- A downward behavior in S(q,) along (0,0)-(p,0).
← itinerant nature in strong antiferromagnetic correlation
T.T., M. Mori, and S. Sota, Phys. Rev. B 97, 235137 (2018)
☑ Dimensionality effect on S(q,)
T. T., S. Sota, S. Yunoki, in preparation
- Weakening of charge stripe change of “hourglass” behavior
☑ RIXS in 1D extended Hubbard model
K. Tsutsui, T. T., in preparation
- Comparison between CDW and singlet superconducting phases