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)