and of course, the Standard Model Supported by NSF-DMR & Mag Lab NSF DMR /DoE/State of Florida

Transcription

1 Magnetic field-induced transitions in organic conductors a perspective J. Brooks, and many more collaborators, colleagues, and competitors Chaikin, Naughton, Graf, Fortune, Swanson, Valfells,Tokumoto, Murata, Uji, Kobayashi (H & A), Kartsovnik, Singleton, Harrison, Mielke, Lebed, Wosnitza, Schlueter, Almeida, Yamada, Anzai, Cui, Yakavenko, Maki, Brown, Brill, Takahashi, Sarrao, Fisk, Perenboom, McKenzie, Montambaux, Steven, etc. and of course, the Standard Model Supported by NSF-DMR & Mag Lab NSF DMR /DoE/State of Florida

2 Field-induced, orbital, not SdH, true AF order, thermodynamic,. (TMTSF) 2 PF 6 Kwak K (TMTSF) 2 ClO 4 Bando 1982 T=1.1 K P = 7.4 kbar C el /T (TMTSF) 2 ClO 4 Pesty K 0.38 K 0.89 K threshold 0.49 K 77 Se 1 H Azevedo mk (TMTSF) 2 ClO 4 Naughton 1985

3 Outline: Review FIDW mechanism in Q1D Q1D : Q2D : FISDW systems CDW systems CDW and/or DW systems* t a ~ 250 mev t b ~ 25 mev t c ~ 1.5 mev Other (time permitting): Spin Peierls, Bronzes, τ-phases Conclusions: Some challenges for future {theoretical} work. *(Note: Mark Kartsovnik will treat this topic in detail.)

4 (a) (b) (c) (d) Physical and electronic structure of (TMTSF) 2 X. Thorup 1981; Grant 1983

5 General model representation of imperfectly nested Q1D FS t b t b2 /2t a 1.3 mev ε k = v F ħ( k x - k F ) + ε ( k ) ε (k ) = 2t b cos(bk y ) + 2t b cos(2bk y ) + 2t c cos(ck z ) + 2t c cos(2ck z ) Ishiguro, Yamaji, Saito

6 t b t b2 /2t a For FISDW, the trick is to start here. Let s assume we are here. For (TMTSF) 2 PF 6, pressure increases t b Ishiguro, Yamaji, Saito magnetic field brings you back

7 The key to everything: ε k = v F ħ( k x - k F ) + 2t b cos(bk y ) B = 0 ε k = v F ħ( k x - k F ) + 2t b cos(b(k y ebx/ħ)) A = (0,Bx,0): B z 0 The magnetic field introduces: A periodic 1D potential Real space motion with frequency ω b = ev F Bb/ħ wavelength λ = h/ebb amplitude A = 4t b b/ω b A Kronig-Penny dispersion with wave number G = 2π/λ = ebb/ħ bandwidth ħω b = ev F Bb

8 Chaikin 1996 A y = 4t b b/ħω b λ x = h/ebb real-space ω b = ebv F b/ħ k-space So, let s put this all together to see how the FISDW gap forms for imperfect nesting: Chaikin 1983

9 From the linear dispersion, t b = ħv F q = nev F Bb, so also t b =nħω b In general, Q = 2k F ± ng, so as the field increases, n will decrease (in jumps) to minimize the energy. k F q xcrit E F t b Detail of un-nested region Here, n = 1 When q xcrit = nebb/ħ ng gaps can appear in the non-nested FS.

10 (TMTSF) 2 PF 6 (TMTSF) 2 ClO 4 Kang 1993 T(K) 10 T(K) (TMTSF) 2 ReO (TMTSF) 2 NO 3 Kang 1991 P = 13.5 kbar B(T) P = 8.5 kbar B(T) Vignolles 2005

11 (DMET-TSeF) 2 AuCl 2 Oshima 1995 Biskup 1999 Ito 2006 (DMETTSeF) 2 CuCl 2 FISDW seems to be a general feature of TTF type materials where t a /t b ~ 10.

12 Main Points: ORBITAL 1) Q1D Electronic structure (in some form) appears necessary for orbital FIDW phenomena. 2) The Q1D system should be close to an instability with a characteristic imperfect nesting energy t b 3) The application of a magnetic field changes a Q2D plane wave system into a Q1D Kronig-Penny system. A new field-dependent periodicity G with bandwidth ħω c appears in the spectrum. 4) When ħω c becomes of order t b, the imperfectly nested Q1D bands can become gapped. 5) Since the Q1D spectrum has gaps that appear periodically as ng, orbital quantization of the imperfectly nested pockets appears. The quantum number n adjusts to lower values as G increases with field. Filled Landau levels always remain below E F. Main Points: SPIN 1) In materials without localized moments, an important effect of the Zeeman effect is to remove the degeneracy of the bands at the Fermi level. 2) In CDW systems, this degrades the good nesting condition Q, 2k F, but in SDW systems, the nesting condition is saved: Q, =2k F. 3) When µ B B> CDW, subbands can cross E F, and orbital effects are possible. (Mark Kartsovnik next talk)

13 Pre-existing ground states: What can happen? Pre-existing SDW: T SDW can go up with field. Naughton; Matsunaga; Maki; Audouard; Brooks etc. Question: can Q x = 2k F ± NG be important in other situations where there is Q1D electronic structure, and/or where Q1D and Q2D coexist? What about the CDW and FICDW prospects?

14 Start with a pre-existing CDW: (Dieterich, W. and P. Fulde, Magnetic field dependence of the Peierls instability in onedimensional conductors. Z. Physik, : p ) Field effects driven by Zeeman (Pauli) effects on bands. Low field behavior: δt c /T c ~ F(ε F /T c )(µ B H/kT c ) 2 Gap closes when µ B B~ CDW Nesting condition changes no longer 2k F.

15 Tiedje, T., J.F. Carolan, A.J. Berlinsky, and L. Weiler, Magnetoresistance of TTF-TCNQ. Can. J. of Phys., : p T c = 58 K (corresponds to a huge field!) δt c /T c ~ γ(µ B H/2kT c ) 2 δρ/ρ ~ -1/2 (µ B H/kT) 2 Same for other field directions

16 In (Per 2 )Au[mnt] 2 T CDW is not so high (of order 10 K), and magnetic fields can do something. How about the high field region? Graf, D., et al., Suppression of a charge density wave ground state in high magnetic fields: spin and orbital mechanisms. Phys. Rev. B, : p

17 Beyond Dieterich and Fulde: Anisotropic Hubbard model with SDW and CDW interactions. Key idea: nesting vector adjusts above the critical field both Pauli and Orbital effects are important. (Mark Kartsovnik will talk about this subject next.) Zanchi, D., A. Bjelis, and G. Montambaux, Phase diagram for charge-density waves in a magnetic field. Phys. Rev. B, : p

18 Lebed, A.G. and S. Wu, Soliton Wall Superlattice in the Quasi-One-Dimensional Conductor (Per) 2 Pt(mnt) 2. Phys. Rev. Lett., : p ? Graf, 2004 (Per) 2 Pt(mnt) 2

19 But what about inducing a CDW (FICDW) from a native metallic Q1D state? Note Pressure can in principle produce a metallic Q1D state from a CDW. T DW (H) = exp(-1/g eff (H)) Yes, but T FICDW will be at comparatively lower temperatures than T SDW λ = 2t c /ω c (H) ~ 1/H Lebed, A.G., Theory of Magnetic Field-Induced Charge-Density-Wave Phases. JETP Letters : p

20 Graphite: One possible FICDW example: (a) (c) (b) Yoshioka and Fukuyama, Electronic Phase Transition of Graphite in a Strong Magnetic Field. J. Phys. Soc. Jpn., : p. 725.

21 α-et 2 MHg(SCN) 4 β -ET 2 AuBr 2 Q2D? Assuming that you need Q1D to get a FIDW to occur, how does it manifest itself in a Q2D system? Materials of the α-et 2 X and β -ET 2 X have Fermi surfaces with both open (Q1D) and closed (Q2D) Fermi surface sections, where the open sheets are relatively flat, and in principle prone to nesting instabilities.

22 In some cases, the temperature dependent resistivity can show an anomaly when the Q1D band nests. Since the Q2D bands are not destroyed, but only reconstructed, the sample usually remains metallic at low temperatures. What happens when magnetic field is added? Kartsovnik, M.V., A.E. Kovalev, and N.D. Kushch, Magnetotransport investigation of the low-temperature state of (BEDT-TTF) 2 TlHg(SCN) 4. Journal Phys. I (France), : p Biskup 1998

23 Osada, 1990 Harrison, 2000 Qualls, 2000 (Also Andres, 2003) When the magnetic field is turned on, both spin and orbital effects can come into play!

24 Fermiology? AMRO? Uji, S. et al.,. Phys. Rev. B, (1): p Clear evidence for fieldinduced changes in the electronic structure. Caulfield, et al., J. Phys: Cond. Mat., : p. L155-L162.

25 How about the β -ET 2 X compounds? β -(BEDT-TTF) 2 AuBr 2

26 Field dependent SdH frequencies. β -(BEDT-TTF) 2 CsCd(SCN) 4 Kondo, R., J. Otsuji, S. Kagoshima, and Y. Nogami, J. Phys. Soc. Japan Lett., : p ; Kondo, R., J. Otsuji, and S. Kagoshima, Journal of Physics: Conference Series, : p

27 Small anomaly at 7 K in resistance anisotropy R. Kondo, private commun. β -(BEDT-TTF) 2 AuBr K 0.56 K Swanson 1990 House 1996 Field dependent SdH frequencies; background MR increases at Low T.

28 β - (BEDT-TTF) 2 SF 5 CH 2 CF 2 SO 3 Geiser, 1996 Background MR increases at low T. Wosnitza, 2001

29 Briefly, let s mention three other materials: Spin Peierls phases of (TMTTF) 2 PF 6 Tau phase system has a nearly isotropic metal-insulator transition at high fields. η-mo 4 O 11 crossed Q1D Fermi surfaces CDW

30 High field phases of the Spin-Peierls compound (TMTTF) 2 PF 6 As in other Peierls-type systems, there may be strange commensurate and incommensurate effects that arise as the instability vector deviates from its low field value. Brown, 1999

31 τ-(p-s,s-dmedt-ttf) 2 (AuBr 2 ) 1+y (Papavassiliou, Murata, etc.) Although many different measurements have confirmed the bulk nature of this dramatic field induced metal-insulator transition, there is no theory or model that treats this primarily Zeemandriven, 1 st order phenomenon. Storr 2001;, Graf 2003&2005

32 Spin and Orbital effects in the CDW system η-mo 4 O 11? M.-H. Whangbo, E. Canadell, P. Foury, and J.-P. Pouget, Hidden Fermi surface nesting and charge density wave instability in low-dimensional metals, Science 252, 96-98(1991). Hill, 1997& 1998

33 Conclusions: A magnetic field introduces a 1D periodicity in Q1D systems. This orbital effect can induce instabilities in Q1D metals: typically, Q x = 2k F ±ng The spin effect (Zeeman, Pauli) removes the degeneracy in bands and creates subbands: For SDW there is little effect, but CDW s are suppressed. In high fields, new effects may arise in both spin-peierls and CDW systems where the optimum nesting vector may start to change, creating new (soliton-like?) phases. When the CDW gap is closed, some subbands may cross the Fermi level. Hence orbital effects may again be possible. In materials where Q1D and Q2D structure coexists, instabilities due to the Q1D structure appear to be magnetic field dependent, undergoing both spin and orbital modifications with increasing magnetic field.

34 Some theoretical challenges: 1) Origin of the field induced metal-insulator transition in the τ-phase material - Many measurements, no theory! 2) Modeling of NMR spin relaxation behavior upon crossing SDW and FISDW phase boundaries. 3) Why does Q1D physics (including the anisotropic Hubbard model) work so well for Q2D α-(bedt-ttf) 2 MHg(SCN) 4? Lumata PRB (R)2008 =? 4) Modeling of the β systems: Reconstruction (or not) Spin and orbital contributions.

35 Relaxed (TMTSF) 2 ClO 4