1. Recent NMR Results in NCKU C. S. Lue ( 呂欽山 ) Department of Physics, National Cheng Kung University ( 國立成功大學物理系 )

2. Outline: I: Fundamental NMR principles: (i) NMR frequency shifts (ii) Quadrupole interactions (ii) Spin-lattice relaxation rates II: Studied systems: (i) 27 Al NMR study of electronic structure of Al 3 M (ii) 51 V NMR study of spin gap nature of BaCu 2 V 2 O 8 (iii) 51 V NMR study of pseudogap characteristics of Fe 2 VAl

3. Bulk Properties: collective response of the system to an external perturbation Electronic property:  =  E/  J Magnetic property:  =  M/  H Thermal property: C =  U/  T Optical property:

4. Merits of NMR: local probe of electronic and magnetic features Site selected Impurity phase isolated Sensitive to the excitation near the Fermi-level

5. Central transition 71 Ga NMR line shape in NbGa 3 D0 22 crystal structure

6. Simple resonance theory: Zeeman energy:  E = o h =  n  H o Nuclear spin I: 2I +1 energy states For I = 3/2, (MHz) H = 0H = H o  

7. NMR in Solids: (i) Magnetic hyperfine interactions : couplings between nuclear magnetic moment  n and electronic magnetic moment  e Fermi-contact dipolar orbital s-like e - non-s-character e - K s K an K orb

8. NMR frequency shifts: Site-I o NMR signal Site-II  ( MHz )  Site-I Site-II

9. NMR Shift & Magnetic susceptibility (a) Simple metals: (s-electrons) (b) d-electron based materials: Note: Bulk diamagnetic term  L does not enter because of the small hyperfine field.

10. (ii) Electric hyperfine interactions: couplings between nuclear quadrupole moment eQ and electric field gradient (For I > 1/2 in the non-cubic environments with axial symmetry ) +q -q +q -q +q-q+q E a > E b

11. Satellite Lines: I = 3/2 EFG = 0 EFG  0 o o + Q /2 o - Q /2 o

12. 27 Al (I = 5/2) NMR powder pattern in Cr 2 AlC

13. Spin-lattice relaxation time (T 1 ): M(t) t

14. Recovery curve of 11 B in ZrB 2

15. T 1 & Electronic origins

16. Magnetic dipolar broadening of rigid lattices: (Simplest case: cubic) r ~ 2A and  ~ 10 -3  B H loc ~  /r 3 ~ 1 gauss H o = 1 T = 10 4 gauss H loc /H o =  / o ~ 10 -4 If o ~ 10 - 100 MHz, intrinsic line width  ~ 1 - 10 kHz Motional narrowing: motional effects narrow the line width in normal liquids.

17. Varian 300 Solid-State NMR Home-built NMR probe-head (Top-loaded) 7.05 T superconducting magnet

18. D0 23 -type Al 3 Zr & Al 3 Hf Potential aerospace applications: High melting point Low mass density Large elastic modulus Shortage: Poor ductility Interesting issues: Electronic properties Structural stability

19. 27 Al NMR central transitions of Al 3 Zr & Al 3 Hf Central transition line shapes: Anisotropic Knight shift & Quadrupole effects High-frequency peak: Al-III Low-frequency part: Al-I & Al-II

20. Satellite lines for the three Al sites in Al 3 Zr and Al 3 Hf

21. Partial 27 Al NMR results of Al 3 Zr & Al 3 Hf AlloyAl-IAl-IIAl-IIITotal Al 3 Zr0.01470.01460.02230.0172 Al 3 Hf0.01450.02320.03040.0227 Smaller Fermi-level DOS in Al 3 Zr → Al 3 Zr is more stable than Al 3 Hf with respect to the D0 23 structure, consistent with the fact that Al 3 Hf becomes more favorable with D0 22 as T > 650 C. Fermi-level s-DOS (states/eV atom) for each Al crystallographic site

22. Oxidation states: Magnetic Cu 2+ (S = ½) Nonmagnetic V 5+ Spin chains: CuO 4 square plaquette + edge-sharing V(I)O 4 tetrahedra Alternating coupling ratio J 2 /J 1 = 0.2 Spin gap  = 230 K

23. Bulk magnetic susceptibility of BaCu 2 V 2 O 8 Ghoshray et al. PRB 71 (2005)He et al. PRB 69 (2004)

24. Models for the S=1/2 one-dimensional spin chain compounds 1.Alternating-chain model 2.Dimer-chain model J1J1 J2J2 J JJ J1J1 J1J1 JJ JJ From the analyses of the bulk susceptibility and heat capacity, He et al. concluded that the alternating chain model is more suitable for the understanding of the gap characteristics of BaCu 2 V 2 O 8.

25. 51 V NMR investigation of BaCu 2 V 2 O 8

26. T-dependent NMR shifts of BaCu 2 V 2 O 8

27. T-dependent NMR T 1 of BaCu 2 V 2 O 8

28. NMR parameters of BaCu 2 V 2 O 8 Alternating-chain model:  K (I) = 360 K  K (II) = 370 K  R (II) = 440 K For V-II,  R /  K ~ 1.2 Dimer-chain model :  K (I) = 460 K  K (II) = 470 K  R (II) = 450 K For V-II,  R /  K ~ 1 Summary: Both models seem to be suitable for the understanding of the spin gap nature in BaCu 2 V 2 O 8.

30. L2 1 Heusler-type Fe 2 VAl Transport: semi-conducting behavior Magnetism: paramagnetic behavior (Pauli or Van-Vleck?) Low-T specific heat: possible 3d heavy fermion  = 14 mJ/mol K 2 mass enhancement m*/m ~ 20 -70) LiV 2 O 4 : 3d heavy fermion? FeSi: 3d Kondo insulator

31. Theoretical calculations on Fe 2 VAl G. Y. Guo, G. A. Botton, and Y. Nishino, J. Phys.: Condens. Matter 10, L119 (1998). D. J. Singh and I. I. Mazin, Phys. Rev. B 57, 14352 (1998). R. Weht and W. E. Pickett, Phys. Rev. B 58, 6855 (1998). M. Weinert and R. E. Watson, Phys. Rev. B 58, 9732 (1998). A. Bansil, S. Kaprzyk, P. E. Mijnarends, and J. Tobola, Phys. Rev. B 60, 13396 (1999).

32. 1. Narrow NMR line width: nonmagnetic 2. NMR shifts: For 51 V, K o = 0.61% is not likely due to the Pauli paramagnetism. → Van-Vleck mechanism dominated Band splitting: E g ~ 0.22 eV

33. T-dependent NMR T 1 of Fe 2 VAl E g ~ 0.27 eV Low-T data: V partial Fermi-level DOS D(E F ) = 0.023 states/eV atom Total Fermi-level DOS D(E F ) = 0.055 states/eV atom → Semi-metallic characteristics

34. 1. Sample-dependent heat capacity 2. Solid line: C(T) =  T +  T 3 +  T 5  Small  = 1.5 mJ/mol K 2 3. Magnetic cluster induced low-T upturn in 

35. Field-dependent specific heat in Fe 2 VAl Multi-level Schottky anomaly: Conclusions: the reported  enhancement is not intrinsic → Fe 2 VAl is a false d-electron heavy fermion.