“Quantum Limit in a Quasi-One-Dimensional System Under Pressure"

1. ISCOM 2005 – Key West NHMFL / FSU September 13, 2005 “Quantum Limit in a Quasi-One-Dimensional System Under Pressure" David E. Graf Experimental collaborators: J. S. Brooks - NHMFL E. S. Choi - NHMFL M. Almeida’s Group - Portugal Funding: NSF-DMR-95-27035 (NHMFL) NSF-DMR 02-03532 (Brooks) NSF GK-12 Fellowship Program

2. Outline: • Crystal structure of (Per)2M(mnt)2 • Theoretical predictions • Experimental results for M = Au, Pt from ambient pressure to 8 kbar • Conclusions

3. The Perylene systems (and a-(ET)2MHg(SCN)4) – CDWs in high fields are a topic of growing (continuing) interest: Theory: Zanchi, Bjelis, Montambaux, PRB 53 1240 (1996). A. G. Lebed, JETP Lett. 78 138 (2003). M. Fujita, K. Machida, and H. Nakanishi JPSJ 54 3820 (1985). P. Grigoriev, et al. cond-mat 0504779 (2005). T. Osada, ISCOM proceedings. R. McKenzie, cond-mat 9706235 (1998). a-(ET)2MHg(SCN)4: J. S. Qualls, et al. PRB 62 10008 (2000). D. Andres, M. Kartsovnik, et al. PRB 68 201101 (2003). D. Andres, M. Kartsovnik, et al. PRB 64 161104 (2001). Per. Exp. Work (high B): G. Bonfait, et al. SSC 80 391 (1991); Physica B 211 297 (1995). M. Matos, et al. PRB 54 15307 (1996). Brooks/Almeida groups, PRB 69 125113 (2004). Brooks/Almeida groups, PRL 93 076406 (2004). R. McDonald, et al. PRL 93 076406 (2004). R. McDonald, et al. PRL 94 106404 (2005).

4. (Per)2M(mnt)2M = Au, Pt • tb : ta : tc = 150 : 2 : 0.1 meV • Anisotropy 5-10 times greater than (TMTSF)2PF6 • CDW ground state observed through X-ray studies and IV-characteristics with TCDW ~ 8 K (M = Pt) and 12 K (M = Au) • Rice and Strassler predicted that a 1D conductor will have a low temperature energy gap which is similar to BCS • Dietrich and Fulde proposed that field dependence of the transition temperature due to the Zeeman effect would follow B2 E. Canadell, et al. Euro. J. Phys. B 42 453 (2004). R. T. Henriques, et al., J. Phys. C 19 4463 (1986). E. B. Lopes, et al., , J. Phys. I (Paris) 6 2141-2149 (1996). M. J. Rice and S. Strässler, Solid State Comm. 13 125 (1973). W. Dietrich and P. Fulde, Z. Physik 265 239 (1973). maleonitriledithiolene Perylene kBT ~ mBB ac-plane

5. Magnetoresistance of (Per)2Au(mnt)2 • The transition temperatures measured become strongly anisotropic at high fields in contrast to MFT predictions. • The behavior of D and transition temperatures indicate further fields are needed beyond 33 tesla to completely close the energy gap. B ^b-axis

6. b q 90o c a 0o (Per)2Au(mnt)2 • The b // c-axis orientation is perpendicular to the directions of the highest bandwidths, which suggests a contribution to the magnetoresistance from orbital motion. D. Graf, E. S. Choi, J. S. Brooks, S. Uji, J. C. Dias, M. Almeida, M. Matos, PRB 69 126113 (2004).

7. B // c - transverse B // b - longitudinal 0.5 K 0.5 K 9.0 K 9.0 K (Per)2Pt(mnt)2 Using the predicted critical field of the energy gap (~ 36 T) for M = Au and the ratio of transition temperatures (8 K / 12 K) we find that a prediction of 24 tesla for M = Pt is accurate. • The orbital contributions of a highly anisotropic system can stabilize high field density wave states by changing the nesting parameters. The FIDW states can be seen in any orientation of the magnetic field, with varying critical field values.

8. Why probe the systems further using pressure? FIDW CDWo Ambient pressure – nearly perfectly nested: D. Zanchi, A. Bjelis, and G. Montambaux, Phys. Rev. B 53 1240 (1996). • S. Kagoshima and R. Kondo, Chem. Rev. 104 5593 (2004). • J. Paglione, et al., Phys. Rev. B 65 220506 (2002). Young’s Modulus: Organics < 1010 N/m2 Ruthenates ~ BeCu ~ 1011 N/m2 They’re soft and small changes in pressure cause dramatic changes in the ground states. (TMTTF)2PF6 D. S. Chow, et al. Phys Rev Lett 81 3984 (1998).

9. 3.5 mm 2 1 Double-clamped BeCu pressure cell Range of pressure: Ambient – 12 kbar (room temperature) Pressure medium: Daphne oil 7373 Benefits: Rotation He gas pressure system Range of pressure: Ambient – 10 kbar Pressure medium: He gas Benefits: Hydrostatic pressure BeCu capillary tubing Gas Compressor U11 Helium Dewar Pressure cell D = ~ 9 m

10. Dependence of TCDW on pressure N. Mitsu, K. Yamaya, M. Almeida, R. T. Henriques, to be published. – Hokkaido U. Measurements using the resistance minimum and the transition temperature found from derivative of log(R) agree that a minimum occurs between 5 – 6 kbar. • TCDW can change for several reasons: • Electron-phonon interaction (lel-ph) • Nesting condition of the Fermi surface • Commensurability effects

11. Metallic Pressure dependence of the magnetoresistance of (Per)2Au(mnt)2 B//c-axis He gas pressure system Clamped BeCu pressure cell • Pressure moves the molecules closer together, increasing bandwidth via molecular orbital overlap. • It also changes the nesting of the Fermi surface, creating pockets between the FS sheets. T = 1.35 K

12. Magnetoresistance under pressure: 5.0 kbar • Effective mass ~ 0.3me • Frequency of the oscillations = 18 T Quantum limit? or CDWx? T = 0.5 K

13. (Per)2Au(mnt)2 8 kbar Angular and temperature dependence B q

14. b q c a b c a q (Per)2Pt(mnt)2 Rotation with a pressure of 6.2 kbar B//c-axis B//c-axis B//a-axis B//b-axis Magnetoresistance (arb. units) B//c-axis B//c-axis Magnetic Field (T)

15. kb ka kc kb E. Canadell, et al. Euro. J. Phys. B 42 453 (2004). Increasing Hydrostatic Pressure ka kc kb ka kc

16. (Per)2Pt(mnt)2 Under pressure • Suppression of the CDWo state is consistent with the Au sample. (TMTTF)2PF6 D. S. Chow, et al. Phys Rev Lett 81 3984 (1998). Pressure tuned SP  AFM transition via J^ (interchain spin coupling). • Stronger interaction between spin and conducting chains as proximity between them decreases with pressure.

17. Conclusions: • The behavior of the change in TCDW is consistent with the pressure dependence of inorganic MX2 or MX3 compounds. The increasingly rigid lattice results in a lower transition temperature. • Closed orbit oscillations have been observed in the Perylene systems under pressure. The oscillations are not consistent with LK formulism for a cylindrical Fermi surface, indicating that imperfect nesting creates a more complex ellipsoidal shape. • The indices of the SdH magnetoresistance peaks indicate the quantum limit of the pressure-induced pockets of the Fermi surface are reached at the high field limit of the hybrid magnet. • Initial measurements of the magnetoresistance of the M = Pt compound under pressure indicate that interactions between the spin and conducting chains may grower stronger with pressure and play a prominent role in finding a full explanation of this material. • Acknowledgements: • Eric Palm and Tim Murphy – mK rotation experiments • Unipress, Institute of High Pressure Physics – He gas pressure system • NHMFL Facilities – Electricians • Hybrid magnet operators / Helium group

20. SdH oscillations or FISDW? • Quantum oscillations and FISDW states both require Landau quantization. Observing peaks which are periodic in inverse field will not assist us in differentiating between the two. • With the previous observation, both follow 1/cos(q) behavior. • The FISDW requires a threshold field to meet the nesting condition to create FS pockets. SdH oscillations begin from B = 0. (TMTSF)2ClO4 W. Kang, et al., Physical Review Letters 70 3091 (1993)

21. Outline: • Ross will have already discussed the high field behavior, including their claims that Au and Pt are identical, except for the SP transition in Pt which provides the difference in the high field behavior. ESC suggested really looking at their 2nd paper for details about what he might be talking about. • Without even mentioning the controversial FIDW state stuff directly, I can give a 3 minute overview of why this systems are interesting and then proceed with the pressure work. Also make clear the focus is on M = Au, though we also have some high field work for M = Pt (shows hystersis where McD says the SP state has died) • Comparing with other systems, the temperature dependence follows what happens for h-Mo4O11 at the lower transition temperature (Tc lowers with additional pressure) • Have to look into the quantum limit. Will that y-axis have an intercept at – ½? If so, this make a good argument for quantum oscillations. • Need to have a reasonable explanation for why the M = Au or M = Pt SCM2 experiments haven’t shown only QO in the rotation data? • It is important to point out that the frequency of the QO increases slowly with pressure in 4 separate cases. • There is a quadratic rise in MR in almost all cases to the first easily observed oscillations. • IMPORTANT Note: In previous linear chain compounds (like NbSe3) the CDW and FS could be considered almost separately due to very different temperature regimes for the nest and imperfectly nested FS. The Per systems are interesting because of the low energy range we manipulate with temperature, pressure and magnetic field. • The general outline should be: • Brief intro to the materials (crystal structure, recent measurements) • Effect of pressure on the CDW state • Possible SdH on the system, leading to the idea of the quantum limit at 45 Tesla • Brooks’ comments: Start out with ambient pressure information: Rotation is a huge key to understanding these systems.

22. B // c - transverse B // b - longitudinal • The orbital contributions of a highly anisotropic system can stabilize high field states by changing the nesting conditions. • An lower resistance intervening state between density wave states was observed, which is not predicted by theory. • The FIDW states may be observed in any orientation (i.e. B // c or B // b) between the field and crystal axes, but the critical field values will shift with the orientation. • The predicted transition temperatures are lower than what has been observed. • In high enough fields CDWx and CDWy states will also be suppressed, in agreement with the observed activated state. Temperature – Magnetic Field Phase Diagrams of (Per)2Pt(mnt)2

23. b c a q The effects of nesting Q tb : ta : tc = 150 : 2 : 0.1 meV (354 : 8 : 0.5 meV) Under pressure, the transition temperature can drop by 50%. If ta and tb both double then the entire imperfect nesting parameter is four times larger. Zanchi, et al. Phys. Rev. B 53 1240 (1996). Note: Zanchi’s notation b is the a-axis in our work.

25. Lifshitz-Kosevich formula: Maple plot with “typical” parameters B(T) Magnetoresistance t-(P-(S,S)-DMEDT-TTF)2(AuBr2)1+y Pressure ~ 1 kbar

26. Magnetoresistance: • Rotation from B // c to B // b • There is weak angular dependence in the lower critical field • The onset of the FIDW shifts quickly to higher fields T = 0.5 K • MR results for B // b-axis (no possible orbital effects) • The FIDW is only observed below 3.5 K

27. Temperature dependence of M = Au • Zero-field energy gap ~ 86 K (7.4 meV) • The mean field predictions of the energy gap from comparison with BCS are too small. (D = 2 meV) • The CDW state is not completely suppressed, even at 33 tesla. G. Bonfait, et al., Solid State Commun., 80 391 (1991). G. Bonfait, et al., Physica B, 211 297 (1995). M. Matos, et al., Phys. Rev. B., 54 15307 (1996).

29. Q b c a q CDW in high magnetic fields:Zanchi, et al. Phys. Rev. B 53 1240 (1996). Pauli: h Orbital: B // c B // a B // b Ratio of SDW to CDW coupling: n