Nuclear Magnetic Resonance to measure spin susceptibilities. NMR page 1 - M2 CFP Electronic properties of solids (F. Bert)

Transcription

1 Nuclear Magnetic Resonance to measure spin susceptibilities NMR page 1 - M2 CFP Electronic properties of solids (F. Bert)

2 Nobel Prizes related to NMR Zeeman, Physics 1902 Rabi, Physics 1944 Bloch & Purcell, Physics 1952 Ernst, Chemistry 1991 Wuthrich, Chemistry 2002 Lauterbur & Mansfeld, Medecine 2003 NMR page 2 - M2 CFP Electronic properties of solids (F. Bert)

3 First NMR signal in condensed matter NMR page 3 - M2 CFP Electronic properties of solids (F. Bert)

4 Imaging with NMR: MRI NMR page 4 - M2 CFP Electronic properties of solids (F. Bert)

5 NMR page 5 - M2 CFP Electronic properties of solids (F. Bert)

6 NMR for chemistry 14 Tesla 23 Tesla NMR page 6 - M2 CFP Electronic properties of solids (F. Bert)

7 Measurement of the uniform susceptibility with NMR NMR page 7 - M2 CFP Electronic properties of solids (F. Bert)

8 Interaction électron-noyau Orbital effect Weak-anisotropic Dipolar effect from unpaired spins Weak anisotropic Contact interaction (s Orbitals) Strong isotropic «chemical» shift In liquids, solids NMR in metals, magnetic materials NMR page 8 - M2 CFP Electronic properties of solids (F. Bert)

9 Nb of nuclei K total 0 0 reference 0 =H 0 /2 ix, y, z (1 2 K i orb K i dip K contact ) H 0 Gyromagnetic ratio: depends on the nucleus Orbital or chemical shift K spin Spin shift A hf spin ( q 0, 0) NMR page 9 - M2 CFP Electronic properties of solids (F. Bert)

10 Orbital or chemical shift Due to orbital moment of electrons in full shells unpaired valence electrons In general: independent of temperature weak anisotropic (tensorial form) gives informations on the nature of the orbitals proportional to orbital susceptibility NMR page 10 - M2 CFP Electronic properties of solids (F. Bert)

11 Orbital or Chemical Shift Used in chemistry to determine molecules structure gasoline Shift orbital NMR page 11 - M2 CFP Electronic properties of solids (F. Bert)

12 Orbital or Chemical Shift Used in chemistry to determine molecules structure gasoline Shift orbital NMR page 12 - M2 CFP Electronic properties of solids (F. Bert)

13 Spin shift electrons Kspin A hf 0 Why would one want (bother) to measure K spin and not directly spin of the electrons with standard magnetic measurements (SQUID)? intrinsic, not affected by impurities allows to distinguish different spin at various cristallographic sites does not sum up the various spin but gives an histogram : measurement of local variation of spin Price to pay : not always absolute values not as easy and quick as SQUID NMR page 13 - M2 CFP Electronic properties of solids (F. Bert)

14 K spin measures 0 High Tc superconductor cuprates YBa 2 Cu 3 O 6+x K T Alloul et al., PRL (1989) K proportional to : K NMR page 14 - M2 CFP Electronic properties of solids (F. Bert)

15 K spin measures 0 at various sites K s (%) YBa 2 Cu 3 O 6+x O Cu Y 0,20 0,16YBCO 0,12 0, K 61 K 89 K 95.7K 87.8K 75 K Takigawa et al., PRB (1991) 0,04 YBCO 0, T (K) Bobroff et al., PRL (1997) Alloul et al., PRL (1989) NMR page 15 - M2 CFP Electronic properties of solids (F. Bert)

16 Uniform susceptibilities in exotic systems Cobaltates Na x CoO 2 Very good ionic conductors (batteries) Non conventional superconductors Large thermoelectric power 0.10 Co 4+ supra antiferro magnétisme x Co Kc (%) 0.05 x=0.62 x=0.58 x=0.66 x=0.5 x=0.44 x=0.3 Co 3d 7 4s x= T (K) Lang et al., PRB NMR page 16 - M2 CFP Electronic properties of solids (F. Bert)

17 Kc (%) K spin measures the intrinsic 0 if K spin is different from macro, one should usually trust K spin cobaltate Na x CoO x=1 x=0.7 (1e6 emu/g) K x=0.5 x= T (K) T (K) NMR page 17 - M2 CFP Electronic properties of solids (F. Bert) Lang et al., PRB 09

18 K spin measures 0 at various sites cobaltates Na 0.7 CoO 2 NMR page 18 - M2 CFP Electronic properties of solids (F. Bert) Mukhamedchine et al., PRL (2006) 3 different Co with different charge state

19 K spin measures the intrinsic 0 Spin 1 chain YBa 2 NiO 5 K Shimizu et al., PRB (1995) K NMR page 19 - M2 CFP Electronic properties of solids (F. Bert)

20 Intensité (unités arbitraires) K spin provides a histogram of the : access to local variations of Impurity effect: YBa 2 NiO 5 spin 1 chain with Zn non magnetic impurities at site Ni Ni Ni Ni Ni Ni Ni Ni Zn Ni Ni Ni Ni Ni Y 2 Ba Ni 98% Zn 2% O 5 Zn 2% pur T = 200 K (khz) Tedoldi et al., PRL 99; Das et al.prb 04 NMR page 20 - M2 CFP Electronic properties of solids (F. Bert)

21 Nb of nuclei Zn 2% champ local <S Z > Zn Ni NMR page 21 - M2 CFP Electronic properties of solids (F. Bert)

22 line shift in % K spin measures the intrinsic 0 Geometrically frustrated antiferromagnet (Volborthite) K Paramagnetic impurities NMR Squid Volborthite 0.2 Intrinsic behavior Temperature (K) Mendels et al., PRL (2000) NMR page 22 - M2 CFP Electronic properties of solids (F. Bert)

23 K spin provides a histogram of the : access to local variations of Cu:Mn diluted alloy, Cu NMR Imaging the Friedel oscillation in a metal induced by magnetic impurities ν 0 MHz NMR page 23 - M2 CFP Electronic properties of solids (F. Bert)

24 K spin measures 0 at various sites Bi2212 Oxygene 17 NMR Trokiner et al., PRB (1991) Different susceptibilities so different doping on the different layers NMR page 24 - M2 CFP Electronic properties of solids (F. Bert)

25 K spin provides a histogram of the : access to local variations of example : cuprate Bi2212 STM NMR intensity inhomogeneous YBaCuO 6.6 homogeneous Bi2212 Cren et al., PRL 2000 Pan et al., Nature 2001 McElroy et al. Science dopage J Bobroff et al., PRL 02 NMR page 25 - M2 CFP Electronic properties of solids (F. Bert)

26 NMR technique NMR page 26 - M2 CFP Electronic properties of solids (F. Bert)

27 Principle of (pulsed) NMR measurement Static field H 0 Oscillating field H 1 (rf) NMR page 27 - M2 CFP Electronic properties of solids (F. Bert)

28 NMR lab spectrometre H 0 aimant Magnetic field: Good homogeneity (10-5 to 10-8 ), and strong (typically : 7 to 20 Tesla) H 0 spectrometer : In the radiofrequency range (typically : 10 to 500 MHz) NMR page 28 - M2 CFP Electronic properties of solids (F. Bert)

29 H 0 Radiofrequency pulse : msec and kw M H 0 NMR page 29 - M2 CFP Electronic properties of solids (F. Bert)

30 H 0 U t NMR page 30 - M2 CFP Electronic properties of solids (F. Bert)

31 Why pulsed NMR? Nb of nuclei frequency or local field T Dt 0 =1/T With one pulse a range of frequencies are iradiated at the same time. By Fourier transform of the signal, one gets the whole NMR spectrum. NMR page 31 - M2 CFP Electronic properties of solids (F. Bert)