THE FASCINATING PHYSICS OF SOLID 3He

1
Le coche et la mouche Sur un chemin montant,
sablonneux, malaise, Et de tous les cotes au
soleil expose, Six forts chevaux tiraient un
coche Jean de La Fontaine
M. Roger
?
The coach and the fly Over a hilly, sandy and
difficult road, From every side exposed to the
sun, Six strong horses were pulling a coach
... Jean de La Fontaine
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THE FASCINATING PHYSICS OF SOLID 3He ITS IMPACT
IN OTHER FIELDS

• Michel Roger
• CEA DRECAM SPEC

3
Historical survey 1

• Theory
• 1926-1930
• Heisenberg1, Dirac2 general concept of an
  effective exchange Hamiltonian for almost
  localised identical fermions
• Hex ? (-1)p JP P?

• Experiment
• up to 1975
• No evidence for any experimental system for
  which permutations involving more than two
  particles
• are relevant
• (Nothing beyond the so-called Heisenberg model)

4
Historical survey 2

• Theory
• 1965
• Thouless3
• Puts forward the idea that three and four-spin
  exchange might be important in solid 3He and lay
  out the basis for a calculation of their
  frequencies JP from first principles
• Proves that 2, 4, particle cyclic exchanges are
  antiferromagnetic while 3, 5, particle cyclic
  exchanges are ferromagnetic.

• Experiment
• Nothing new!

5
Historical survey 3

• Theory
• 1975
• J. H. Hetherington5
• The data of D. Adams et al. are explained by
  significant four-particle exchange processes

• Experiment
• 1975
• D. Adams et al.4
• Experimental evidence of a first order
  transition at 1mK to some antiferromagnetic order
  in solid bcc 3He incompatible with a simple
  Heisenberg model

6
Historical survey 4

• Theory
• 1977-1980
• Delrieu, Hetherington, Roger9
• Quantitative interpretation of all experimental
  data with a multiple spin exchange Hamiltonian
• In particular, the competition between the two
  exotic phases is a signature of the  quantum
  frustration  resulting from the competition
  between ferromagnetic three-particle exchange and
  antiferromagnetic four-spin exchange

• Experiment
• 1977-1980
• Adams et al.6, Godfrin et al7
• Experimental evidence for a competition between
  two ordered phases.
• A low field phase
• A (moderately-high) -field phase with exotic
  properties.
• 1980
• Osheroff et al.8 Indirect proof byNMR of the
  unexpected symmetry  uudd  of the low-field
  phase

7
Historical survey 5

• Theory
• 1980
• J. M Delrieu10 prediction of the ferromagnetism
  of the hcp phase based on the argument that
  steric hinderance favor 3 particle exchange in a
  compact lattice.

• Experiment
• 1985
• Takano et al.11 measurement of the
  susceptibility of hcp solid 3He showing
  ferromagnetic behavior
• 1996
• Adams, Takano et al.12 reach the ferromagnetic
  phase by direct nuclear adiabatic demagnetization

8
Historical survey 6

• Theory
• 1981-84
• Delrieu13 Roger14 justification of the
  hierarchy of various exchange processes from
  first principles through WKB approximation
• 1987
• Ceperley Jacucci15 calculation of exchange
  frequencies from first principles though
  Monte-Carlo methods.

• Experiment
• 1985
• Benoit, Bossy et al16. direct observation of the
  low field  uudd  phase of bcc 3He through
  neutron diffraction

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Present situation

• A unique model system for which we are able to
  start from the first principles, predict
  quantitatively the expected thermodymamic
  properties and compare quantitatively with
  experimental results
• Most  indirect  consequences of the
  Multiple-Spin-Exchange model, as the behavior of
  a large number thermodynamic properties, have
  been verified experimentally.
• Nevertheless, the direct observation by neutron
  diffraction of the most important prediction
  which results from the intrisically  quantum
  frustrated  nature of the model the exotic high
  field phase, is missing.
• Neutron critical scattering also offer the most
  direct measurement of various exchange parameter,
  which should be interesting to compare with
  Monte-Carlo theoretical predictions.

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The role of Saclay Il semble que ce soit Un
sergent de bataille allant en chaque endroit
Faire avancer ses gens, et hater la victoire
.  (La Fontaine)

• Will be crucial in the last year of the project
  to participate with experimentalists to the
  quantitative interpretation of the results.
• ? A postdoctoral theoretician will be appointed
  from next october
• Preparation of the project of direct
  characterisation of exchange processes through
  inelastic neutron scattering, in close
  collaboration with HMI and the University of
  Liverpool.
• Spreading of our results to a large community,
  including physicists interested in other
  strongly interacting fermion systems where
  relevant four-particle exchange processes have
  been theoretically predicted.
• ? Organisation of a largely open spring school
  in April 2003

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Multiple-spin exchange in the Wigner Solid

• 1984
• Delrieu13 Roger14 WKB calculation of exchange
  processes in the two-dimensional Wigner Solid of
  electrons. Three-particle exchange is dominant
  near the classical limit (low density), four
  particle exchange might be also significant at
  higher densities.
• 2000
• Bernu Ceperley17 Ab initio Monte-Carlo
  calculation of exchange processes in the Wigner
  Solid. Confirmation of the WKB results near the
  classical limit. Close to melting the hierarchy
  of various exchange processe is similar to that
  calculated and observed for two-dimensional solid
  3He layers adsorbed on graphite.
• Present experimental situation
• A lot of excitement and controversies about the
  possible observation of the 2D Wigner solid in
  AgGa and Si MOSFET inversion layers!

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Four-spin exchange in the CuO2 planes of hight Tc
superconducting cuprates

• 1988
• Delrieu Roger18 theoretical prediction of
  significant four-spin exchange in the CuO2 planes
  of high Tc superconducting cuprates, based on a
  large U expansion of a three-band Hubbard model.
• 2000
• Calzado Malrieu19 same conclusion through
  ab-initio quantum-chemical calculations on finite
  clusters.
• Present experimental situation
• Although most experimental thermodynamic
  properties of the anti-ferromagnetic phase of
  these compounds are generally interpreted with a
  simple Heisenberg model, some results, which are
  in contradiction with the pure Heisenberg model
  can be explained with a small but significant
  amount of four-spin exchange
• - The susceptibility data M. Roger20
• - The anomalously broad two (and four?) magnon
  Raman spectra S. Sugai et al21, 1990
• - Magnon spectrum obtained through
  high-resolution inelastic neutron scattering
• Coldea et al22, 2000

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Conclusion

• Solid 3He a model system involving fundamental
  quantum mechanical processes
• Has long been considered, from theoretical point
  of view, as marginal.
• Should be now advertised as an archetype among
  other strongly interacting identical-fermion
  systems illustrating the same fundamental
  physics
• - Wigner solid
• - High Tc superconducting cuprates
• - Other magnetic systems (the list is open! )

14
References

• 1 Heisenberg, Z. Phys. 38, 411 (1926)
• 2 P.A.M Dirac, Proc. Roy. Soc. A123, 714
  (1929)
• 3 D.J. Thouless, Proc. Phys. Soc. 86, 893
  (1965)
• 4 R.B. Kummer, E.D. Adams, W.P. Kirk, A.S.
  Greenberg, R.M. Mueller, C.Y Britton
• and D.M. Lee, Phys. Rev. Lett. 34, 517 (1975)
• 5 J.H. Hetherington, Phys. Rev. Lett. 35, 1442
  (1975)
• 6 E.D. Adams, J.M. Delrieu and A. Landesman,
  J. Phys. Lett. 39, L190 (1978)
• 7 H. Godfrin, G. Frossati, A. Greenberg, B.
  Hebral and D. Thoulouze, Phys. Rev. Lett.
• 44, 1695 (1980).
• 8 D.D. Osheroff, M.C. Cross and D.E. Fisher,
  Phys. Rev. Lett. 44, 792 (1980)
• 9 M. Roger, J.M. Delrieu and J.H.
  Hetherington, Rev. Mod. Phys. 55, 1 (1980).
• 10 J.M. Delrieu et al. J. Low. Temp. Phys. 40,
  71 (1980)
• 11 Y. Takano, N. Nishida, Y. Miura, H.
  Fukuyama, H. Ishimoto and S. Ogawa,
• Phys. Rev. Lett. 55, 1490 (1985)

15
References

• 12 T. Lang, P.L. Moyland, D.A. Sergatskov,
  E.D. Adams and Y. Takano, Phys. Rev. Lett.
• 77, 322 (1996)
• 13 J.M. Delrieu, unpublished (1981)
• 14 M. Roger, Phys. Rev. B 30, 6432 (1984)
• 15 D.M. Ceperley and G. Jacucci, Phys. Rev.
  Lett. 58, 1648 (1987)
• 16 A. Benoit, J. Bossy, J. Flouquet, J.
  Schweizer, J. de Physique Lettres, L923 (1985)
• 17 B. Bernu, L. Candido, and D.M. Ceperley
  Phys. Rev. Lett. 86, 870 (2001)
• 18 M. Roger and J.M. Delrieu, Phys. Rev. B39,
  2299 (1989)
• 19 C.J. Calzado and J.P. Malrieu, Phys. Rev.
  B63, 214520 (2001)
• 20 M. Roger, to be published.
• 21 S. Sugai et al. Phys. Rev. B42, 1405 (1990)
• 22 R. Coldea et al. Phys. Rev. Lett. 86, 5377
  (2001)

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The moral of the fable

• Ainsi certaines gens, faisant les empresses,
• S introduisent dans les affaires,
• Ils font partout les nécessaires,
• Et, partout importuns, devraient être chasses.
• Jean de La Fontaine.