1. NMR and  SR in 2D frustrated vanadates P. Carretta (Pavia) N. Papinutto R. Melzi (Bruker BioSpin) S. Aldrovandi E. Pavarini C.B. Azzoni M.C. Mozzati R.G.M. Caciuffo (Ancona) A. Bombardi (ESRF) P. Millet (Toulouse) S. Gonthier NMR,  SR, Cv, M(T) Band structure EPR Neutron scattering Sample preparation, chemical and structural characterization

2. [V 4+ ]=[Ar] 3d 1 S=1/2 c b a Magnetic ions V 4+ a b J2 J2 J1 J1 Li 2 VO(Si,Ge)O 4 structure

3. J 2 J1 J1 0 1 0.5 ? Néel Order I) II) Collinear Order 2D Vanadates J 1 -J 2 at T=0 P ? Li 2 VOSiO 4 J 1 +J 2  8.5 K Li 2 VOGeO 4 J 1 +J 2  6.0 K VOMoO 4 J 1 +J 2  155 K P. Chandra and B. Doucot PRB 38, 9335 (1988) H. J. Schulz and T.A.L.Ziman Europhys. Lett. 18 355 (1992) V.N. Kotov et al. PRB 60, 14613 (1999) L. Capriotti. and S. Sorella PRL 84, 3173 (2000) ; L. Capriotti, Int. J. Mod. Phys. B 14, 3386 (2000) V.N. Kotov et al. PRB 63, 064412 (2000); J 2 /J 1

4. How much frustated are the vanadates ?

5. CompoundJ 1 +J 2 T m  (K)T c (K)J 2 /J 1 J 2 /J 1 from band structure VOMoO 4 155  10 100 42  0.5 -0.15 Li 2 VOSiO 4 9191 5.35 2.85  0.05 1 - 512 Li 2 VOGeO 4 6.0  0.3 3.5 1.95  0.03 0.9 - 45 R. Melzi et al. PRL 85, 1318 (2000) R. Melzi et al. PRB 64, 024409 (2001) H. Rosner et al. PRB 67, 014416 (2003) G. Misguich et al. cond-mat/0302583

6. Li 2 VOSiO 4 H vs. T phase diagram NMR and NS showed that the magnetic order is collinear If x is the direction of V 4+ magnetic moments then Q=(  /a,0)

7. The collinear phase Critical exponent for the magnetization  0.24, both for Li2VOSiO4 and VOMoO4. At low-T the reduction of the order parameter is consistent with SWT with J   10 -3 -10 -4 (J1+J2) NS results in Li2VOSiO4 confirm that the order is collinear and yield  (T  0)  0.6  B

8. L. Siurakshina et al., PRB64, 104406 (2001) H.J. Schulz et al., J.Phys. I 6, 675 (1996) L. Capriotti cond-mat/0306679

9.  K=A  +  At T dist a modification in the hyperfine coupling A is evidenced The ratio T dist /(J 1 +J 2 ) is similar for both compounds, despite of the huge difference in J 1 +J 2.. Evidences of frustration driven distortions T dist /(J 1 +J 2 )  0.5 T dist /(J 1 +J 2 )  0.67

10. I. Shiozaki et al. Physica B 284-288, 1621 (2000) Distortion in VOMoO 4 from Raman scattering

11. Diffusive lattice distortion from 29 Si NMR in Li 2 VOSiO 4

12. 1/T 1 = (  2 /2N)  q |A q | 2 S(q,  R )    e 2  s/T Nuclear spin-lattice relaxation for T c <T<J 1 +J 2

15. Very-low-frequency excitations for k B T< J 1 +J 2  c  (1/  Heis ) P. Chandra, P. Coleman and A.I. Larkin PRL 64, 88 (1990) P. Carretta et al. PRL 88, 047601 (2002)

16. Collinear I Collinear II Domain wall motions

17. From the analysis of NMR shift one concludes that P sizeably reduces J2/J1 The transition temperature to the collinear phase is weakly affected, by about 0.2 K, by P Effect of pressure (P) on J 2 /J 1

18. Peierls-like transition induced by frustration in a 2D AF F. Becca and F. Mila, PRL89, 037204(2002) SP O T J 1,2 (d ij )  (d ij ) -  1

19. These vanadates are characterized by a collinear ground state and J 2 /J 1 >1. These vanadates are characterized by a collinear ground state and J 2 /J 1 >1. Sublattice magnetization is close to the one of a pure 2DQHAF. Sublattice magnetization is close to the one of a pure 2DQHAF. Frustration driven lattice distortions are observed by means of NMR. Frustration driven lattice distortions are observed by means of NMR. 7 Li 1/T1 is surprisingly nearly T independent down to T  Tc. 7 Li 1/T1 is surprisingly nearly T independent down to T  Tc. An anomalous very-low-frequency dynamics is observed by means of  SR. An anomalous very-low-frequency dynamics is observed by means of  SR. Pressure reduces J 2 /J 1 but the GS is little affected. What happens to the lattice distortion as J 2 /J 1 is reduced? Pressure reduces J 2 /J 1 but the GS is little affected. What happens to the lattice distortion as J 2 /J 1 is reduced? What happens to the lattice distortion when impurities or dilution (e.g. V 4+ for Ti 4+ ) is present? What happens to the lattice distortion when impurities or dilution (e.g. V 4+ for Ti 4+ ) is present? Conclusions and open questions