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

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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

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

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3He adsorbed on graphite
Graphite substrates Grafoil, Papyex, ZYX
exfoliated graphites Large uniform platelets
(5-gt50 nm) Strong adsorption potential Layer by
layer absorption 2D - 3He systems
Adsorption isotherms, heat capacity, nuclear
susceptibility, neutron scattering measurements.
He-graphite adsorption potential
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Phase diagram of 2D -3He
Data from Seattle (O. Vilches), revisited by H.G.
(1988) and D.S. Greywall (1990)
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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 interactions
  J 1 mK.

He-He potential (Aziz)
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Multi-spin exchange interaction
on the triangular lattice of 2D - 3He
J2
J3
J4
The Jn depend on the film density
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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
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Multi-spin exchange HTSE fits thermodynamic
data for T gt 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)
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The graphite substrate has a large homogeneous
surface defects !
STM image of Papyex
U. of Tsukuba, 1996
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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)
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Exchange in 2D-3He first measurements (Grenoble,
Bell Labs) and the concept of Quantum
Frustration (M. Roger)
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Effective exchange interactions in 2D-3He
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2D - Ferromagnetic Heisenberg Hamiltonian
Godfrin, Ruel and Osheroff, 1988
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2D-Heisenberg ferromagnet Stanford measurements
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The 4/7 phasea family of registered phases
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The 4/7 phase a spin-liquid?Large entropy at
low temperatures, well below J
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Measurements of the susceptibility and heat
capacity of the 4/7 phase a frustrated
quantum antiferromagnet
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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)
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High temperature (T gt 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
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MSE coefficients for different 2D-3He 4/7 phases
E. Collin, PhD Thesis, Grenoble 2002
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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
  S1 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)
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Low temperature magnetization
Gapped spin-waves with D 75 µK and n 6
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Spin-gap 75 µK
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Tokyo susceptibility measurements - No spin
gap?- Impurities? New measurements needed!
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Conclusions
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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 S0 excitations)
• Susceptibility varying very slowly Q ltlt
  J M 3 of Msat at 100 µK
• Gap in the S1 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)

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References
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(Oxford Clarendon) (1947). D.J. Thouless, Proc.
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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.
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Saunders, Phys. Rev. Lett. 71, 1407 (1993). H.
Godfrin and R. E. Rapp, Advances in Physics,
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and C. Waldmann, Phys. Rev. Lett. 81, 1098
(1998). A. Casey, H. Patel, J. Nyéki, B.P.
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Kubo, Phys. Rev. B, 59, 9491 (1999) C.
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50, 13515 (1994). and special thanks to
Grégoire Misguich, Bruce Normand and Michel
Roger!