Confinement of spin diffusion to single molecular layers in layered
organic conductor crystals
András Jánossy1
Ágnes Antal1
Titusz Fehér1
Richard Gaál2
Bálint Náfrádi1,2
László Forró2
Crystal growth: Erzsébet Tátrainé Szekeres1, Ferenc Fülöp1
special thanks to Natasha Kushch1Budapest University of Technology and Economics, Institute of Physics2Ecole Polytechnique Federale de Lausanne
I.F. Schegolev Memorial Conference “Low-Dimensional Metallic and Superconducting Systems”
October 11–16, 2009, Chernogolovka, Russia
Quasi 2D molecular layered compounds:
Independent currents in each layer?
Uncoupled magnetic order in each layer?
Aor MA
Bor MB
A
B
A
B
ac=0°
ac=90°
- ET2-X, layered organic crystalX = Cu[N(CN)2]Cl, Br 2D polymer
c
a
b
A
B
1 hole / ET2 dimer
X
c
a
b
A
B
1 hole / ET2 dimer
X
tII
ac=45°
t
t 0.1 meV
t// 100 meV
- ET2-X, layered organic crystalX = Cu[N(CN)2]Cl, Br 2D polymer
0,0 0,1 0,2 0,3 0,4 0,5 0,60
50
100
150
200
250
300
Tem
pera
ture
(K
)
Pressure (kbar)
Antiferromagnet Superconductor
Insulator Metal
"Bad" metal
Phase diagram-(BEDT-TTF)2CuN(CN)2Cl, Br
51 10
Mott transition
Goal:
Determine:
1. interlayer magnetic interaction in antiferromagnet
2. interlayer electron hopping frequency, in metallic phase
Method: high frequency ESR
1. Antiferromagnetic resonance, AFMR
2. Conduction electron spin resonance, CESR
0.33 0.34 0.35 0.36 0.37 0.38
7.96 7.97 7.98 7.99 8.00
Magnetic field (T)
9 GHz
222 GHz
9.4 GHz
BRUKER E500
420 GHz, Lausanne
222.4 GHz, Budapest
High frequency ESR spectrometer
high resolutionsame sensitivity0-12 kbar pressure
7,90 7,95 8,00 8,05
Magnetic field (T)
TEKCL7 ET2CuN(CN)
2Cl (a,b) plane ESR at 222.4GHz
250 K
A B Ref.
0,0 0,1 0,2 0,3 0,4 0,5 0,60
50
100
150
200
250
300
Tem
pera
ture
(K
)
Pressure (kbar)
Antiferromagnet Superconductor
Insulator Metal
"Bad" metal
Phase diagram-(BEDT-TTF)2CuN(CN)2Cl, Br
ET-Cl ET-Br
2. Conduction electron spin resonance
51 10
1. Antiferromagnetic resonance
D
y
z
BM1 M2
F = HZeeman + Hexchange + HDM + Hanisotropy
F = - B(M1 + M2 ) + M1 M2 + D(M1 x M2) + ½Kb(M1y2 +M2y
2)+½K(M1z2 + M2z
2)
Antiferromagnetic resonance
2 magnetizations 2 oscillation modes
First AFMR work: Ohta et al, Synth. Met, 86, (1997), 2079-2080
DA
MA1
MA2
DB
MB2
MB1
Magnetic structure
D. F. Smith and C. P. Slichter, Phys. Rev. Let. 93, 167002, 2004
A
B
AB =?
J = 600 T
F = FA + FB + ABMAMB
Antiferromagnetic resonancecalculation -(BEDT-TTF)2CuN(CN)2Cl
4 magnetizations : 4 modes:
ωαA , ωA
ωαB , ωA
F = FA + FB + ABMAMB
Antal et al., Phys. Rev. Lett. 102, 086404 (2009)
111.2 GHz
ωω
Magnetic field [T]
Fre
quen
cy [
GH
z]
B // b
Antiferromagnetic resonanceexperiment -(BEDT-TTF)2CuN(CN)2Cl
4 magnetizations : 4 modes:
ωαA , ωA
ωαB , ωA
F = FA + FB + ABMAMB
AFMR, 111.2 GHz, 4 K, H//b
Antal et al., Phys. Rev. Lett. 102, 086404 (2009)
-30 0 30 60 90 120 150 180 210
2
3
4
5
6
7
8
9
-aba
ab
(deg)
Reso
nance
field
(T
)
dB
dA
(a)
A
B
A and B modes do not cross!
intra-layer exchange: J = 600 T
inter-layer coupling: AB =1x 10-3 T
AB = AB exchange + AB dipole (same order of magnitude)
AB
Antiferromagnetic resonancemeasured and calculated
b
a
B, magnetic field
ab
Antal et al., Phys. Rev. Lett. 102, 086404 (2009)
0,0 0,1 0,2 0,3 0,4 0,5 0,60
50
100
150
200
250
300
Tem
pera
ture
(K
)
Pressure (kbar)
Antiferromagnet Superconductor
Insulator Metal
Metal
ET-Cl ET-Br
Conduction electron spin resonance
51 10
Conduction electron spin resonancein the metallic phase
A
B
2D spin diffusion
interlayer hopping rate
T1 spin life time
< 1/T1 2D spin diffusion
Expectation (300 K) :
ħ / t ≈ 10-11 s,
// ≈ 10-14 s
T1 ≈ 10-9 s
≈ 2x108 s < 1/T1 2D spin diffusion
2D spin diffusion
vF//= 1 nm spin ≈ 250 nmA
B
= (2t2 //) / ħ 2 blocked by short //
N. Kumar, A. M. Jayannavar, Phys. Rev. B 45, 5001 (1992)
t
A
B
A= gABB/h
B= gBBB/h
Measurement of interlayer hopping
ESR of 2 coupled spins
gA ≠ gB
A B
A B
A B
ESR
< I A – B I
≈ I A – B I
> I A – B I
Measurement of interlayer hopping
inte
rlaye
r ho
ppin
g fr
eque
ncy
7,90 7,95 8,00 8,05
A. Antal, BUTE, April 2008Magnetic field (T)
TEKCL7 ET2CuN(CN)
2Cl (a,b) plane ESR at 222.4GHz
250 K
BA
2 resolved ESR lines P=0, T=45-300 K
A
B
< I A – B I
< 3 x 108 Hz
Ref.
Antal et al., Phys. Rev. Lett. 102, 086404 (2009)
ESR g- factor anisotropy 45 -250 K
-(BEDT-TTF)2CuN(CN)2Cl
-180 -150 -120 -90 -60 -30 0 30 60
-38
-36
-34
-32
-30
-28
-26
-24
-22
-20
-18
-16
-14
A. Antal, BUTE, 2008
TEKCL7 ET2CuN(CN)
2Cl (a,b) plane 250K 222.4GHz
ES
R s
hift (
mT
)
angle, (o)
b
a A
B
b
a
B, magnetic field
Antal et al., Phys. Rev. Lett. 102, 086404 (2009)
A B
A B
A B
ESR
< I A – B I
≈ I A – B I
> I A – B I
Measurement of interlayer hopping
pres
sure
inte
rlaye
r ho
ppin
g fr
eque
ncy
7,42 7,44 7,46 7,48 7,50
0,0
0,1
0,2
0,3
0,4
0,5
Pre
ssur
e (G
Pa)
Magnetic field (T)
experiment7,42 7,44 7,46 7,48 7,50
0,0
0,1
0,2
0,3
0,4
0,5
fit
Magnetic field (T)
-ET2-Cl
< I A – B I
≈ I A – B I
> I A – B I
Measurement of interlayer hopping
Ref.
Motional narrowingunder pressure
210 GHz
T=250 K,B in (a,b) plane
Instr.
pres
sure
0 2 4 6 8 10
14,88
14,90
14,92
14,94
14,96
TEKCl8
Mag
netic
fiel
d (T
)
Pressure (kbar)
0
0,2
0,4
0,6
0,8
1,0
B
A
Measurement of interlayer hopping
Motional narrowingunder pressure
420 GHz
T=250 K,
= I A – B I = 1.0 x109 s-1
ES
R s
pec
tra
l in
ten
sity
0,0 0,5 1,0
1x109
1x1010
inte
rlaye
r ho
ppin
g ra
te, 2
(
Hz)
Pressure (GPa)
100
1000 C
onductivity (Ohm
cm) -1
= (2t2 //)/ħ2 blocked interlayer hopping
// parallel d.c. conductivity
pressure dependence
T=250 K
Measurement of interlayer hopping
0,0 0,1 0,2 0,3 0,4 0,5 0,60
50
100
150
200
250
300
Tem
pera
ture
(K
)
Pressure (kbar)
Antiferromagnet Superconductor
Insulator Metal
Metal
(P, T) interlayer hopping frequency
ET-Cl ET-Br
51 10
2x108 s-1 5x109 s-1
Summary
4,00 4,02 4,04 4,06 4,08 4,10
TEKCL8 ET2CuN(CN)
2Cl 0 kbar B//DM tempdep 111.2 GHz
Magnetic Field (Tesla)
250K
200K
150K
100K
50K
Measurement of interlayer hopping
temperature dependence
111.2 GHz
P=0
tem
pera
ture
Inte
rlaye
r ho
ppin
g fr
eque
ncy
antiferromagnet
metal
temperature dependence
111.2 GHz
P=4 kbar
Measurement of interlayer hopping
14,90 14,95 15,00
200
250
TEKCL8 ET2CuN(CN)
2Cl 4kbar B//DM tempdep 420 GHz
Magnetic Field (Tesla)
150
100
50
tem
pera
ture
Interlayer hopping frequencymetal
superconductor
Measurement 250 K, P=0 :
≈ 2x108 s-1 < 1/T1 2D spin diffusion
Electrons are confined to single molecular layers in regions of 350 nm radius
// = 10-14 - 10-13 s t = 0.1 meV - 0.03 meV
2D spin diffusion
= (2t2 //) / ħ 2 blocked by short //
vF//= 1 nmA
B
confinement ≈ 350 nm
t 0.1 meV
t// 100 meV
Anisotropy of resistivity
H. Ito et al J. Phys. Soc. Japan65 2987 (1996)
- / // nearly independent of T
- 100 cm
- / // 102 - 103
= (2t2 //) / ħ 2 blocking of interlayer tunnelling
1 / 1 / // , // 1 / //
/ // ( t// / t )2 (a/d)2 independent of T
H. Ito et al J. Phys. Soc. Japan65 2987 (1996)
Anisotropy of resistivity
Buravov et al. J. Phys. I 2 1257(1992)
-(BEDT-TTF)2CuN(CN)2Br-(BEDT-TTF)2CuN(CN)2Cl
Perpendicular dc resistivity: = 1/( e2 g(EF) d) g(EF) = two dimensinal density of states d: interlayer distance
-(BEDT-TTF)2CuN(CN)2Cl at 250 K, P=0:
Calculated: = 80 -300 cm
Typical measured: 100 cm
t 0.1 meV, t// 100 meV
/ // ( t// / t )2 (a/d)2
expected anisotropy: / // 106
measured: / // 102 - 103
: dc resistivity and DoS agree with CESR
// : measured is much less than calculated ?? unsolved
Anisotropy of resistivity
-(BEDT-TTF)2[Mn2Cl5(H2O)5]†
Zorina et al CrystEngComm, 2009, 11, 2102
MnLayer A
MnLayer B
14.80 14.85 14.90 14.95 15.00 15.05
measurement
simulation
MAGNETIC FIELD (T)
ES
R I
NT
EN
SIT
Y (
arb
. u
.)
ET
Mn
Ref. ESR spectrum in the a* direction at 420 GHz and 300 K. Resolved lines correspond to the Mn2+ ions and the ET molecules.
ESR in (ET)2CuMn[N(CN)2]4, a radical cation salt with quasi two dimensional magnetic layers in a three dimensional polymeric structure
K. L. Nagy1, B. Náfrádi2, N. D. Kushch3, E. B. Yagubskii3, Eberhardt Herdtweck4, T. Fehér1, L. F. Kiss5, L. Forró2, A. Jánossy1
Phys. Rev. B (2009)
Me-3.5-DIP)[Ni(dmit)2]2PS3-7 Yamamoto bi functional conductorPHYSICAL REVIEW B 77, 060403R 2008 PS3-10 Hazama transport under pressure
0,0 0,1 0,2 0,3 0,4 0,5 0,60
50
100
150
200
250
300
Tem
pera
ture
(K
)
Pressure (kbar)
Antiferromagnet Superconductor
Insulator Metal
Metal
(P, T) interlayer hopping frequency
ET-Cl ET-Br
51 10
2x108 s-1 5x109 s-1
Summary
Antiferromagnet
AB = exchange + AB dipole same order of magnitude
Maybe AB changes sign at Mott transition ?
AB
A
B
14,90 14,95 15,00
0,0
0,2
0,4
0,6
0,8
1,0
Pre
ssur
e (G
Pa)
Magnetic field (T)
experiment
14,90 14,95 15,00
0,0
0,2
0,4
0,6
0,8
1,0
fit
Magnetic field (T)
-ET2-Cl
1 < I A – B I
≈ I A – B I
> I A – B I
Measurement of interlayer hopping
Ref.
Motional narrowingunder pressure
420 GHz
T=250 K,B in (a,b) plane
Instr.
-30 0 30 60 90 120 150 180 210
2
3
4
5
6
7
8
9
A
A
-aba
ab
(deg)
Reso
nance
field
(T
)
dB
AA
dA
Aω
ω
„A” layers only
B
ab
Antiferromagnetic resonanceCalculated
B in (a,b) plane
-30 0 30 60 90 120 150 180 210
2
3
4
5
6
7
8
9
B A
B A
-aba
ab
(deg)
Reso
nance
field
(T
)
dB
BBAA
dA
A
B
Independent A and B layersA and B modes cross!
Antiferromagnetic resonanceCalculated
B in (a,b) plane
Ohta et al, Synth. Met, 86, (1997), 2079-2080
Antiferromagnetic resonance -(BEDT-TTF)2CuN(CN)2Cl
A. Antal et al 2008 (present work)
B // b
’-(BEDT-TTF)2CuN(CN)2Clresistivity
Zverev et al, Phys. Rev. B. 74, 104504 (2006)
0 50 100 150 200 2500
400
800
1200
0
2
4
6
8
10
12
14
16
18
Res
isti
vity
an
izo
tro
py,
b/
ac
Temperature (K)
b
ac
x400
b/
ac
(
Oh
m·c
m)
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