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A review on the magnetism of 2D solid 3 He films

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.

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A review on the magnetism of 2D solid 3 He films

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  1. A review on the magnetism of 2D solid 3He 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 3He Theory : Thouless, Roger, Delrieu, Hetherington, Ceperley, … Experiments :Osheroff, Adams, H.G., Greywall, Fukuyama… • Two-dimensional 3He Theory : Roger, Delrieu, Hetherington, Bernu, Misguich, … Experiments :H.G., Greywall, Saunders, Osheroff, Fukuyama, Ishimoto, … • 3He 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. 3He adsorbed on graphite Graphite substrates : Grafoil, Papyex, ZYX exfoliated graphites Large uniform platelets (5->50 nm) Strong adsorption potential Layer by layer absorption 2D - 3He systems Adsorption isotherms, heat capacity, nuclear susceptibility, neutron scattering measurements. He-graphite adsorption potential

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

  6. Nuclear magnetism of two-dimensional solid 3He • 3He 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 interactionsJ ~ 1 mK. He-He potential (Aziz)

  7. Multi-spin exchange interaction on the triangular lattice of 2D - 3He J2 J3 J4 The Jn depend on the film density

  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: Hex = -P(-1)p Jp P Two-particle permutations: P2 = (1 + i.j) Heisenberg Hamiltonian Multi-spin exchange in solid 3He (Thouless, 1965) Three-particle exchange is also Heisenberg P3 = (1 + i.j+ j.k+ k.i) Four-spin exchange introduces a new physics: P4 = (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 3He films High temperature series expansions of order 5 in J/T for C and  (M. Roger, 1998) MSE Hamiltonian: Hex = JP2 + J4P4 - J5P5 + J6P6 Effective pair exchange : J = J2 -2 J3 Leading order in specific heat : Cv = 9/4 N kB ( Jc/ T )2 Jc2= ( J2 - 2 J3 + 5/2 J4 - 7/2 J5 + 1/4 J6)2 +2 (J4 - 2 J5 +1/16 J6)2 + 23/8 J52 -J5 J6 + 359/384 J62) Leading order in susceptibility :  = N c / (T- ) c = Curie constant  = 3 J = Curie temperature J = -( J2 - 2 J3 - 3 J4 - 5 J5 - 5/8 J6)

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

  11. The substrate defects can trap 3He atoms (essentially paramagnetic). These can be replaced by the non-magnetic isotope, by adding 4He Adding 4He changes the amount of liquid and solid 3He (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-3He

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

  15. 2D-Heisenberg ferromagnet : Stanford measurements

  16. The 4/7 phasea 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 • 3He/4He/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. • Jc = 0.07 +/- 0.1 mK : strongly frustrated system! • The Curie-Weiss temperature : Q = 3Jc = +0.2 mK is different from the “Curie-Weiss fit” and has the opposite sign “Q”“ = -0.9 mK as a result of the strong cancellation of the Heisenberg term due to multiple spin exchange. Our data for 3He/ 3He/ graphite (2000) J /J4 = -1.67 J5/J4 = 0.34 J6/J4 = 0.83 and (black dot) 3He/ 4He/ graphite (2001) J /J4 = -2 J5/J4 = 0.32 J6/J4 = 0.89

  21. MSE coefficientsfor 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 D in the triplet excitations (Misguich et al.) • We assume that the excitations are spin-wave-like S=1 bosons, with a dispersion relation w = D + J.S(k-k0)n + gµNsB • The low temperature, low field magnetization is then M(T) a (T/J.S)(2/n - 1) exp(-D/T) • The logarithmic derivative of M(T) with respect to 1/T is -d lnM/ d (1/T) = - D (1-2/n).T (method suggested by Troyer et al., 1994)

  23. Low temperature magnetization Gapped spin-waves with D = 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 3He/4He/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 : Q << 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 (k6) 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!

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