1. A review on the magnetism of 2D solid 3 He films Multiple-spin exchange in two dimensional systems CNRS - CRTBT Grenoble Ultra Low Temperature Group H. Godfrin, Yu. Bunkov, E. Collin C. Winkelmann, V. Goudon, T. Prouvé, J. Elbs COSLAB - ESF Chamrousse - December 17-22 2004

2. NMR experiments down to 100µK in the Nuclear Demagnetization Refrigerator DN1

3. Multi-spin exchange and Condensed Matter Physics Bulk solid 3 He Theory : Thouless, Roger, Delrieu, Hetherington, Ceperley, … Experiments : Osheroff, Adams, H.G., Greywall, Fukuyama… Two-dimensional 3 He Theory : Roger, Delrieu, Hetherington, Bernu, Misguich, … Experiments : H.G., Greywall, Saunders, Osheroff, Fukuyama, Ishimoto, … 3 He in porous media (Aerogel, Vycor, …) in the audience! Wigner solid : Okamoto, Kawaji, Roger Quantum Hall Effect : =1AsGa ferromagnetic heterostructures, Manfra et al 1996; Girvin, Sachdev, Brey, … HTc superconductors Theory : Roger, Gagliano, … Experiments : S. Hayden, … Phase transitions theory : Chubukov, Lhuillier, Misguich, Gagliano, Balseiro,…

4. Graphite substrates : Grafoil, Papyex, ZYX exfoliated graphites Large uniform platelets (5->50 nm) Strong adsorption potential Layer by layer absorption 2D - 3 He systems Adsorption isotherms, heat capacity, nuclear susceptibility, neutron scattering measurements. He-graphite adsorption potential 3 He adsorbed on graphite

5. Phase diagram of 2D - 3 He Data from Seattle (O. Vilches), revisited by H.G. (1988) and D.S. Greywall (1990)

6. Nuclear magnetism of two-dimensional solid 3 He 3 He atom : nuclear spin 1/2 Fermions! In the solid phases the atoms are quasi-localized Zero point energy is comparable to the potential well depth (about 10 K). Large tunneling of atoms (frequency of order MHz) Quantum exchange interactions J ~ 1 mK. He-He potential (Aziz)

7. on the triangular lattice of 2D - 3 He J2J2 J3J3 J4J4 The J n depend on the film density Multi-spin exchange interaction

8. Multi-spin exchange : a fundamental description of quasi-localized Fermions - Identical particles - Hamiltonian without explicit spin-dependent interactions Pauli principle: the spin state is coupled to the parity of the wave function Permutation of spins & particles: Dirac (1947) : Effective Hamiltonian on spin variables: H ex = -  P (-1) p J p P Two-particle permutations: P 2 = (1 +  i.  j ) Heisenberg Hamiltonian Multi-spin exchange in solid 3 He (Thouless, 1965) Three-particle exchange is also Heisenberg P 3 = (1 +  i.  j +  j.  k +  k.  i ) Four-spin exchange introduces a new physics: P 4 = (1 +  µ.  +  ((  i.  j ).(  k.  l ) + (  i.  l ).(  j.  k ) - (  i.  k ).(  j.  l ))) All exchange coefficients J are positive

9. Multi-spin exchange HTSE fits : thermodynamic data for T > J in solid 3 He films High temperature series expansions of order 5 in J/T for C and  (M. Roger, 1998) MSE Hamiltonian: H ex = J  P 2 + J 4  P 4 - J 5  P 5 + J 6  P 6 Effective pair exchange : J = J 2 -2 J 3 Leading order in specific heat : C v = 9/4 N k B ( J c / T ) 2 J c 2 = ( J 2 - 2 J 3 + 5/2 J 4 - 7/2 J 5 + 1/4 J 6 ) 2 +2 (J 4 - 2 J 5 +1/16 J 6 ) 2 + 23/8 J 5 2 -J 5 J 6 + 359/384 J 6 2 ) Leading order in susceptibility :  = N c / (T-  ) c = Curie constant  = 3 J  = Curie temperature J  = - ( J 2 - 2 J 3 - 3 J 4 - 5 J 5 - 5/8 J 6 )

10. STM image of Papyex U. of Tsukuba, 1996 The graphite substrate has a large homogeneous surface… + defects !

11. The substrate defects can trap 3 He atoms (essentially paramagnetic). These can be replaced by the non-magnetic isotope, by adding 4 He Adding 4 He changes the amount of liquid and solid 3 He (in the second layer, in the case shown) and it removes the paramagnetic defects (of the 4/7 phase, in this example)

12. Exchange in 2D-3He : first measurements (Grenoble, Bell Labs) and the concept of Quantum Frustration (M. Roger)

13. Effective exchange interactions in 2D- 3 He

14. 2D - Ferromagnetic Heisenberg Hamiltonian Godfrin, Ruel and Osheroff, 1988

15. 2D-Heisenberg ferromagnet : Stanford measurements

16. The 4/7 phase a family of registered phases

17. The 4/7 phase : a spin-liquid? Large entropy at low temperatures, well below J

18. Measurements of the susceptibility and heat capacity of the 4/7 phase : a frustrated quantum antiferromagnet

19. Intrinsic magnetization of the 4/7 phase 3 He/ 4 He/graphite Low field (30.51 mT) cw - NMR measurements Dots : clean regime (2D liquid subtracted) Circles : impurity regime (liquid and defects subtracted) Note the very low values of M! E. Collin, PhD Thesis Grenoble (2002)

20. High temperature (T > 2mK) MSE analysis We determine the main exchange constants with an accuracy of 0.1 mK : J2 = -2.8 mK, J4 = 1.4 mK, J5 = 0.45 mK, J6 = 1.25 mK. J  = 0.07 +/- 0.1 mK : strongly frustrated system! The Curie-Weiss temperature :  = 3J  = +0.2 mK is different from the “Curie-Weiss fit” and has the opposite sign “  ” “ = -0.9 mK as a result of the strong cancellation of the Heisenberg term due to multiple spin exchange. Our data for 3 He/ 3 He/ graphite (2000) J /J4 = -1.67 J5/J4 = 0.34 J6/J4 = 0.83 and (black dot) 3 He/ 4 He/ graphite (2001) J /J4 = -2 J5/J4 = 0.32 J6/J4 = 0.89

21. MSE coefficients for different 2D-3He 4/7 phases E. Collin, PhD Thesis, Grenoble 2002

22. Low temperature thermodynamics Test of the prediction of a spin-liquid state with a gap  in the triplet excitations (Misguich et al.) We assume that the excitations are spin-wave-like S=1 bosons, with a dispersion relation  =  + J. S (k-k 0 ) n + gµ N  B The low temperature, low field magnetization is then M(T)  (T  /  J.  S) ( 2/n - 1) exp(-   /  T) The logarithmic derivative of M(T) with respect to 1/T is -d lnM/ d (1/T) =  n).T (method suggested by Troyer et al., 1994)

23. Low temperature magnetization Gapped spin-waves with  = 75 µK and n = 6

24. Spin-gap = 75 µK

25. Tokyo susceptibility measurements : - No spin gap? - Impurities? New measurements needed!

26. Conclusions

27. Conclusions on the Spin-Liquid phase The 4/7 phase of 3 He/ 4 He/graphite displays unusual magnetic properties Dirac-Thouless multi-spin exchange describes well HT thermodynamics Magnetic phase-diagram (Misguich, Bernu, Lhuillier, Waldmann) : consistent with experiments Spin-liquid ground state? Several experimental indications! Magnetic impurities : can be reduced adequately (in this T range…) Heat capacity (Fukuyama) double peak structure, large density of states (dominated presumably by S=0 excitations) Susceptibility varying very slowly :  << J M ~ 3% of Msat at 100 µK Gap in the S=1 excitation spectrum of 75 µK (Grenoble), or no spin Gap (Tokyo)? Unusual (k 6 ) dispersion relation for magnetic excitations (seen by Momoi et al uuud phase…)

28. References P.A.M Dirac, The Principles of Quantum Mechanics (Oxford: Clarendon) (1947). D.J. Thouless, Proc. Phys. Soc. {86}, 893 (1965). M. Roger, J.H. Hetherington and J.M. Delrieu, Rev. Mod. Phys. {55}, 1 (1983). H. Franco, R. E. Rapp, and H. Godfrin, Phys. Rev. Lett. {57}, 1161 (1986). M. Roger, Phys. Rev. Lett. {64}, 297 (1990). D. Greywall, Phys. Rev. B {41}, 1842 (1990). P. Schiffer, M.T. O'Keefe, D.D. Osheroff, and H. Fukuyama, Phys. Rev. Lett. {71}, 1403 (1993). M. Siqueira, C.P. Lusher, B.P. Cowan, and J. Saunders, Phys. Rev. Lett. {71}, 1407 (1993). H. Godfrin and R. E. Rapp, Advances in Physics, {44}, 113-186 (1995). M. Roger, Phys. Rev. B. {56}, R2928 (1997). K. Ishida, M. Morishita, K. Yawata, and H. Fukuyama, Phys. Rev. Lett. {79}, 3451 (1997). M. Roger, C. Bauerle, Yu.M. Bunkov, A.S. Chen, and H. Godfrin, Phys. Rev. Lett. {80}, 1308 (1998). G. Misguich, B.Bernu, C. Lhuillier and C. Waldmann, Phys. Rev. Lett. {81}, 1098 (1998). A. Casey, H. Patel, J. Nyéki, B.P. Cowan, and J. Saunders, J. of Low Temp. Phys. {113}, 265 (1998). T. Momoi, H. Sakamoto, K. Kubo, Phys. Rev. B, {59}, 9491 (1999) C. Bauerle, Y. M. Bunkov, A.-S. Chen, D. J. Cousins, H. Godfrin, M. Roger, S. Triqueneaux, Physica B, {280}, 95 (2000) E. Collin, S. Triqueneaux, R. Harakaly, M. Roger, C. Bauerle, Yu.M. Bunkov and H. Godfrin, Phys. Rev. Lett. {86}, 2447 (2001). R. Masutomi, Y. Karaki, and H. Ishimoto, J. of Low Temp. Phys. {126}, 241 (2002) ) and Phys. Rev. Lett. 92, p? (2004). Spin Waves : M. Troyer, H. Tsunetsugu and D. Würtz, Phys. Rev. B. {50}, 13515 (1994). and special thanks to Grégoire Misguich, Bruce Normand and Michel Roger!