Atomic Tunneling in Clathrates and Related Materials. Joseph H. Ross, Jr. Texas A&M University October 6, 2004

Transcription

1 Atomic Tunneling in Clathrates and Related Materials Joseph H. Ross, Jr. Texas A&M University October 6, 2004

2 Collaborators: TAMU: Yang Li Weiping Gou Ji Chi Venkatesh Goruganti Haidong Liu Farit Vagizov University of South Florida: George Nolas M. Beekman J. Martin Univ. of Science and Technology, Beijing: Zuxiong Xu Guohui Cao Yang Liu Nat l Lab. for Superconductivity, Inst. of Physics, Beijing: Cheng Dong University of Texas-Pan American: Zhaosheng Feng

3 Outline: 1. Clathrates and thermal-atomic motion 2. NMR measurements of Sr 8 Ga 16 Ge 30 clathrate Lineshapes and slow atomic motion Pulse techniques: echo and CPMG expts. Comparison to related materials 3. Al 2 Fe behavior: x-ray and Mössbauer measurements 4. Conclusions

4 Germanium clathrates Group-IV clathrates have extended tetrahedrally-bonded frameworks, and an ordered array of cage-centered ions. Type-I structure most common, occurs in hydrate clathrates and zeolites. Sr 8 Ga 16 Ge 30 : Sr ions held in cage-center positions

5 Thermal properties: Ba 8 Ga 16 Ge 30, Sr 8 Ga 16 Ge 30, Eu 8 Ga 16 Ge 30, are semiconductors, with high thermoelectric efficiencies, attributed to rattling cage-center atoms. Discovery: B. Eisenmann, et al., J. Less-Common Met. 118, 43 (1986). J. L. Cohn, G. S. Nolas, et al., PRL 1999: Glasslike thermal conductivity, κ T 2 Glass behavior: attributed to broad range of two-level system tunneling states.

6 Fourier maps of nuclear density at large-cage Ba, Sr, or Eu site for Ba 8 Ga 16 Ge 30 and Sr 8 Ga 16 Ge 30 (15 K) and Eu 8 Ga 16 Ge 30 (40 K) from neutron-diffraction data. Vertical axis is probability of finding the nucleus at a particular position. For all three figures, x-y plane area is Å 2. It is likely that the Sr and Eu atoms can tunnel among the four nearby sites that are located between 0.3 and 0.5 Å from cage center. Single-crystal neutrons B.C. Sales, B.C. Chakoumakos, R. Jin, J.R. Thompson, and D. Mandrus, Phys. Rev. B 63, (2001)

7 Atom displacements: Larger cages: four off-center positions in plane of cage. Sr displacement ~ 0.3 Å x-ray fit: Sales et al. PRB (2001) (However some uncertainty as to whether Sr has a true displacement.) Sr-ion low-frequency Einstein oscillator mode can be measured, several techniques, values K range. Examples: 46 K Raman measurement: Nolas and Kendziora PRB 62, 7157 (2000) 80 K x-ray thermal displacements: Sales PRB (2001)

8 71 Ga nuclear magnetic resonance (NMR) lineshapes I = 3/2 71 Ga NMR reference: aqueous 71 Ga(NO) 3. Pulse-length measurements: observed transitions are (1/2-1/2) transitions.

9 Ga site distribution Ba 8 Ga 16 Ge 30 Ga known to occupy all three framework sites: Y. Zhang, P. L. Lee, G. S. Nolas, and A. P. Wilkinson, Appl. Phys. Lett. 80, 2931 (2003) Leads to built-in disorder in the lattice Ga NMR line is superposition of signals from different sites. 3 framework sites

10 NMR lineshape: measures atomic dynamics Linewidth used to characterize T- dependence Activated fit includes Room-T point

11 Motional Narrowing large τ c τ c linewidth Given correlation time (τ c ) for random motion, hopping with 2 sites only, in motional narrowing limit (large τ) can show: (Linewidth) = (const.) + τ c /(2 T 22 ) (T 2 denotes intrinsic transverse relaxation time) small τ c Activated process: τ c = τ exp( / kt ) Sr Position A Position B Ga Hence Linewidth activated in high-t limit

12 NMR linewidth fit Fit assumes line splitting hidden in lineshape. Apparent activation barrier 7 K k B for atom hopping Below 50 K, hopping times comparable to inverse NMR linewidth (100 µs) Small attempt frequency

13 Models for clathrate hopping Zerec et al. PRL 92, (2004): resonant ultrasound. 4-well model for atomic hopping (best fit for Eu). Large hopping barrier (~50 K); tunnel splitting between 1st excited manifold ~ few K. details

14 Zerec et al. fits for Sr, Eu clathrate Zerec et al. Successful fit for Eu using v. small tunnel splittings (plotted: elastic constant from ultrasound) Sr best fit ignores tunnel barriers; Einstein quantized modes dominate.

15 Two pulse Hahn echo sequence 90x 180 τ τ Spin echo NMR frequency: ω = γ (B + B local ) γ is nuclear gyromagnetic ratio. B is external field B local is local field.* y Rotating-frame view. 90x 180y x Echo refocusing: requires same B local before & after 180 pulse. * Local field due to electric quadrupole effects, not a magnetic field, in present case.

16 Echo results Echo decay: Exponential at low T (motion dominates) Gaussian at high T (spin-spin interaction dominates): consistent with motional narrowing.

17 Stimulated Echo Sequence Spin Echo 90 x 90 x τ T mix 90 x τ x y x y z x z x x y x y 90 x 90 x 90 x Echo reduced by frequency jumps during T mix ; decay constant = T τ T 1 measurement Sequence Echo sequence 180 x T wait τ τ 1. Decay time T 1 ; refocusing not affected by frequency jumps during T wait. 2. With no motion, T τ same with T 1.

18 T 1 fit to Korringa law Korringa: K 2 T 1 T = constant (metals) NMR results good agreement with measured parameters, band mass, m* ~ 3 No evidence for ultranarrow electronic features, inferred from cage-center NMR in other clathrates. * Sr clathrate: native heavily-doped n-type semiconductor * J. Gryko, et al., Phys. Rev. B 57, 4172 (1998).

19 Stimulated echo results Echo decay rate falls below 1/T 1, not above, at low temperatures. Tentative explanation: wide distribution of echo decay rates at low T, small-t 2 signals suppressed by stimulated echo process.

20 Carr-Purcell-Meiboom-Gill (CPMG) sequence y τ x Spin echo 180 y Spin echo τ τ τ etc y f s δ 1 s y x f δ 1 x 90 - ( τ ) - [180 - ( τ ) - ECHO - ( τ )-] x y n

21 Hahn echo vs. CPMG sequence: Hahn echo τ Jump 90 x 180 y Spin Echo τ B loc ~ NMR frequency 2 π νt (Large phase difference) t T Spin Echo CPMG sequence 90 x 180 y 180 y 180 y 180 y τ 2τ 2τ t 2 π νt (Small phase difference) T CPMG reduces the effect of atom motion on echo decay. Commonly used to measure atomic diffusion.

22 CPMG results Hahn echo

23 CPMG analysis Data best fit in slow-motion limit; typically one jump per time τ (~ ms). Model calculation, echo strength S vs. time, in strongcoupling limit yields: 1 t S = Aexp( t /T 2 )exp( t / τ c )1+ πτ c ν tan 1 2π ντ 2τ

24 CPMG fitting Solid curves: 3- parameter fits, yield jump correlation times τ c.

25 Tunneling analysis Activated process: τ c = τ exp( / kt ) Fit gives /k B = 4.6 K; reasonably consistent with lineshape result. Attempt frequency (3 ms) extremely small; nominally should be Einstein frequency (10 13 Hz).

26 Slow atomic hopping processes Ralls and Buhrman, PRL 1988: Atom motion observed as noise in copper point-contact junctions. Extremely slow motion observed here. General case: observed tunnel systems cover range DC to >10 12 Hz (D. Cox, Adv. Phys. 47, 599 (1988)

27 TLS behavior in glassy systems: Zawadowski, cond/mat Parameters include o (bare tunnel splitting) and (effect of disorder); net tunnel barrier o With included, phonon-assisted tunneling required; can exhibit activated T-dependence. Clathrate system: very small attempt rate we attribute to cage-cage interactions.

28 Cage-Cage interactions o Interaction of cages: may also cause decrease of linewidth at lowest temperatures. Ferroelectric behavior?

29 Conclusions: clathrates Tunneling motion in Ge clathrates seen in Ga NMR Activation barrier: consistent values obtained by two different experiments Ultra-slow tunneling rate: best understood in terms of disorder, and cage-cage interactions

30 FeAl 2 FeAl 2 : Ordered intermetallic 18 atoms/cell monoclinic lattice near close-packing arrangement structural hole Lue et al. PRB 2001: Spin glass, T f = 35 K anomalous large Fe moment Fe Al

31 FeAl 2 Mössbauer: Spectral area increase at T f. (Sample density behavior extrapolates to nonzero intrinsic result.) T f Mössbauer spectroscopy: Fe gamma-spectroscopy measures Fe local fields, and phonon dynamics involving Fe.

32 FeAl 2 Mössbauer spectra and fit involving distribution of hyperfine magnetic fields.

33 FeAl 2 Mössbauer hyperfine fields develop at previously observed spin-glass freezing temperature (J. Chi et al., submitted to PRB)

34 FeAl 2 NMR T 1 : concentrated local moments exchange coupling dominates high-temperature dynamics. (J. Chi et al., submitted to PRB)

35 FeAl 2 New low-temperature x-ray measurements: confirm Mössbauer spectral area results.

36 FeAl 2 Reduction in x-ray scattering intensity: due to Debye- Waller factor: exp( 2W ) exp q u 2 Mössbauer spectral area (Lamb-Mössbauer factor, f) reduced by a similar factor: exp( 2W ) exp k u [ ] 2 Where u denotes atomic displacements; for x-rays q is difference wavevector; for Mössbauer, k is gamma-ray wavevector. Details: x-rays fast timescale, measures snapshot of displacements; Mössbauer slow (like NMR), f measures soft modes allowing hopping due to atom recoil.

37 FeAl 2 Mössbauer isomer shift: lack of large change at low T: soft modes are acoustic, not optical.

38 FeAl 2 X-rays: (u q ) rms ~ 0.07 Å, coupled to melting of spin glass. Global random motion or localized phason? Mössbauer: lattice softens at same temperature. Paramagnetic spin fluctuations above T f strongly coupled to localized atomic displacements.

39 FeAl 2 QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. Phason motions in quasicrystals: Abe, Nature 421, 347 (2003): direct TEM observation at high-t Also NMR: Doninsek, et al. PRB 65, (2002); low-t slow motions (may not be specific to quasicrystals?) QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture.

40 FeAl 2 Other materials with strong magnetic-lattice coupling: perovskite manganites: leads to textures and complex behavior see e.g. Mathur and Littlewood, Phys. Today (2003). giant magnetorestrictive materials (UFe2) e.g. McGuire and Herber, Solid State Commun. 48, 393 (83) FeAl 2 only one we are aware of with coupling to a random spinglass phase.

41 Summary / Thanks NMR, Mössbauer, x-ray diffraction used to probe atomic hopping behavior. Ge clathrates measure of hopping barrier, ultra-slow motion behavior. FeAl 2 coupled magnetic-structural softening confirmed by Mössbauer, x-rays. Lattice softening tied to spin-glass freezing. Acknowledgements: This work was supported by the Robert A. Welch Foundation (A-1526), National Science Foundation (DMR ), and Texas A&M University Telecommunications and Informatics Task Force. Support for the SQUID magnetometer was provided by the National Science Foundation (NSF ).