Confinement of spin diffusion to single molecular layers in layered organic conductor crystals András Jánossy 1 Ágnes Antal 1 Titusz Fehér 1 Richard Gaál 2 Bálint Náfrádi 1,2 László Forró 2 Crystal growth: Erzsébet Tátrainé Szekeres 1, Ferenc Fülöp 1 special thanks to Natasha Kushch 1 Budapest University of Technology and Economics, Institute of Physics 2 Ecole 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?  A  or M A  B  or M B A B A B

 ac =0°  ac =90°  - ET 2 -X, layered organic crystal X = Cu[N(CN) 2 ]Cl, Br 2D polymer c a b A B 1 hole / ET 2 dimer X

c a b A B X t II  ac =45° tt t   0.1 meV t //  100 meV  - ET 2 -X, layered organic crystal X = Cu[N(CN) 2 ]Cl, Br 2D polymer

Phase diagram  -(BEDT-TTF) 2 CuN(CN) 2 Cl, Br 5110 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

9.4 GHz BRUKER E GHz, Lausanne GHz, Budapest High frequency ESR spectrometer high resolution same sensitivity 0-12 kbar pressure

Phase diagram  -(BEDT-TTF) 2 CuN(CN) 2 Cl, Br ET-Cl ET-Br 2. Conduction electron spin resonance Antiferromagnetic resonance

D y z B M1M1 M2M2 F = H Zeeman + H exchange + H DM + H anisotropy F = - B(M 1 + M 2 ) + M 1 M 2 + D(M 1 x M 2 ) + ½K b (M 1y 2 +M 2y 2 )+½K(M 1z 2 + M 2z 2 ) Antiferromagnetic resonance 2 magnetizations  2 oscillation modes First AFMR work: Ohta et al, Synth. Met, 86, (1997),

DADA M A1 M A2 DBDB M B2 M B1 Magnetic structure D. F. Smith and C. P. Slichter, Phys. Rev. Let. 93, , 2004 A B AB =? J = 600 T F = F A + F B + AB M A M B

Antiferromagnetic resonance calculation  -(BEDT-TTF) 2 CuN(CN) 2 Cl 4 magnetizations : 4 modes: ω αA, ω  A ω αB, ω  A F = F A + F B + AB M A M B Antal et al., Phys. Rev. Lett. 102, (2009) GHz ωω ωω Magnetic field [T] Frequency [GHz] B // b

Antiferromagnetic resonance experiment  -(BEDT-TTF) 2 CuN(CN) 2 Cl 4 magnetizations : 4 modes: ω αA, ω  A ω αB, ω  A F = F A + F B + AB M A M B AFMR, GHz, 4 K, H//b Antal et al., Phys. Rev. Lett. 102, (2009)

A B A and B modes do not cross! intra-layer exchange: J = 600 T inter-layer coupling: AB =1x T AB = AB exchange + AB dipole (same order of magnitude) AB Antiferromagnetic resonance measured and calculated b a B, magnetic field  ab Antal et al., Phys. Rev. Lett. 102, (2009)

ET-Cl ET-Br Conduction electron spin resonance 5110 Conduction electron spin resonance in the metallic phase

 A B 2D spin diffusion  interlayer hopping rate T 1 spin life time  < 1/T 1 2D spin diffusion

Expectation (300 K) : ħ / t  ≈ s,  // ≈ s T 1 ≈ s  ≈ 2x10 8 s < 1/T 1 2D spin diffusion 2D spin diffusion  v F  // = 1 nm  spin ≈ 250 nm A B  = (2t  2  // ) / ħ 2 blocked by short  // N. Kumar, A. M. Jayannavar, Phys. Rev. B 45, 5001 (1992) tt

A B A = g A  B B/h B = g B  B B/h  Measurement of interlayer hopping ESR of 2 coupled spins g A ≠ g B

A B A B A B ESR  < I A – B I  ≈ I A – B I  > I A – B I Measurement of interlayer hopping interlayer hopping frequency

B A 2 resolved ESR lines P=0, T= K A B  < I A – B I  < 3 x 10 8 Hz  Ref. Antal et al., Phys. Rev. Lett. 102, (2009)

ESR g- factor anisotropy K  -(BEDT-TTF) 2 CuN(CN) 2 Cl A B b a B, magnetic field   Antal et al., Phys. Rev. Lett. 102, (2009)

A B A B A B ESR  < I A – B I  ≈ I A – B I  > I A – B I Measurement of interlayer hopping pressure interlayer hopping frequency

 -ET 2 -Cl  < I A – B I  ≈ I A – B I  > I A – B I Measurement of interlayer hopping Ref. Motional narrowing under pressure 210 GHz T=250 K, B in (a,b) plane Instr. pressure

B A Measurement of interlayer hopping Motional narrowing under pressure 420 GHz T=250 K,  = I A – B I = 1.0 x10 9 s -1 ESR spectral intensity

 = (2t  2  // )/ħ 2 blocked interlayer hopping     // parallel d.c. conductivity pressure dependence T=250 K Measurement of interlayer hopping

 (P, T) interlayer hopping frequency ET-Cl ET-Br x10 8 s -1 5x10 9 s -1 Summary

Measurement of interlayer hopping temperature dependence GHz P=0 temperature Interlayer hopping frequency antiferromagnet metal

temperature dependence GHz P=4 kbar Measurement of interlayer hopping temperature Interlayer hopping frequency metal superconductor

Measurement 250 K, P=0 :  ≈ 2x10 8 s -1 < 1/T 1 2D spin diffusion Electrons are confined to single molecular layers in regions of 350 nm radius  // = s t  = 0.1 meV meV 2D spin diffusion  = (2t  2  // ) / ħ 2 blocked by short  //  v F  // = 1 nm A B  confinement ≈ 350 nm

t   0.1 meV t //  100 meV Anisotropy of resistivity H. Ito et al J. Phys. Soc. Japan (1996) -   /  // nearly independent of T -    100  cm -   /  // 

 = (2t  2  // ) / 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. Japan (1996) Anisotropy of resistivity Buravov et al. J. Phys. I (1992)  -(BEDT-TTF) 2 CuN(CN) 2 Br  -(BEDT-TTF) 2 CuN(CN) 2 Cl

Perpendicular dc resistivity:   = 1/( e 2 g(E F )  d) g(E F ) = two dimensinal density of states d: interlayer distance  -(BEDT-TTF) 2 CuN(CN) 2 Cl at 250 K, P=0: Calculated:   =  cm Typical measured: 100  cm

t   0.1 meV, t //  100 meV   /  //  ( t // / t  ) 2 (a/d) 2 expected anisotropy:   /  //  10 6 measured:   /  //    : dc resistivity and DoS agree with CESR  // : measured is much less than calculated ?? unsolved Anisotropy of resistivity

 -(BEDT-TTF) 2 [Mn 2 Cl 5 (H 2 O) 5 ] † Zorina et al CrystEngComm, 2009, 11, 2102 Mn Layer A Mn Layer B

ESR spectrum in the a* direction at 420 GHz and 300 K. Resolved lines correspond to the Mn 2+ ions and the ET molecules. ESR in (ET) 2 CuMn[N(CN) 2 ] 4, a radical cation salt with quasi two dimensional magnetic layers in a three dimensional polymeric structure K. L. Nagy 1, B. Náfrádi 2, N. D. Kushch 3, E. B. Yagubskii 3, Eberhardt Herdtweck 4, T. Fehér 1, L. F. Kiss 5, L. Forró 2, A. Jánossy 1 Phys. Rev. B (2009)

Me-3.5-DIP)[Ni(dmit)2]2 PS3-7 Yamamoto bi functional conductor PHYSICAL REVIEW B 77, R 2008 PS3-10 Hazama transport under pressure

 (P, T) interlayer hopping frequency ET-Cl ET-Br x10 8 s -1 5x10 9 s -1 Summary

Antiferromagnet AB =  exchange +  AB dipole same order of magnitude Maybe AB changes sign at Mott transition ? AB A B

 -ET 2 -Cl  1 < I A – B I  ≈ I A – B I  > I A – B I Measurement of interlayer hopping Ref. Motional narrowing under pressure 420 GHz T=250 K, B in (a,b) plane Instr.

A ωω ωω „A” layers only B  ab Antiferromagnetic resonance Calculated B in (a,b) plane

A B Independent A and B layers A and B modes cross! Antiferromagnetic resonance Calculated B in (a,b) plane

Ohta et al, Synth. Met, 86, (1997), Antiferromagnetic resonance  -(BEDT-TTF) 2 CuN(CN) 2 Cl A. Antal et al 2008 (present work) B // b

 ’-(BEDT-TTF) 2 CuN(CN) 2 Cl resistivity Zverev et al, Phys. Rev. B. 74, (2006)