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

Multiple-spin exchangein two dimensional systems

CNRS - CRTBT

Grenoble

Ultra Low Temperature GroupH. Godfrin, Yu. Bunkov, E. Collin

C. Winkelmann, V. Goudon, T. Prouvé, J. Elbs

COSLAB - ESF Chamrousse - December 17-22 2004

NMR experiments down to 100µK

in the Nuclear Demagnetization Refrigerator DN1

Multi-spin exchange and Condensed Matter Physics

• Bulk solid 3HeTheory : 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 superconductorsTheory : Roger, Gagliano, …Experiments : S. Hayden, …

• Phase transitions theory : Chubukov, Lhuillier, Misguich, Gagliano, Balseiro,…

Graphite substrates : Grafoil, Papyex, ZYX exfoliated graphitesLarge uniform platelets (5->50 nm)

Strong adsorption potentialLayer by layer absorption

2D - 3He systems

Adsorption isotherms, heat capacity, nuclear susceptibility, neutron scattering measurements.

He-graphite adsorption potential

3He adsorbed on graphite

Phase diagram of 2D -3He

Data from Seattle (O. Vilches), revisited by H.G. (1988) and D.S. Greywall (1990)

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)

on the triangular lattice of 2D - 3He

J2

J3

J4

The Jn depend on the film density

Multi-spin exchange interaction

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 PTwo-particle permutations: P2 = (1 + i.j)

Heisenberg Hamiltonian

Multi-spin exchange in solid 3He (Thouless, 1965)

Three-particle exchange is also HeisenbergP3 = (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

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 J6

2)

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)

STM image of Papyex U. of Tsukuba, 1996

The graphite substrate has a large homogeneous surface… + defects !

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)

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

Effective exchange interactions in 2D-3He

2D - Ferromagnetic Heisenberg Hamiltonian

Godfrin, Ruel and Osheroff, 1988

2D-Heisenberg ferromagnet : Stanford measurements

The 4/7 phase

a family of registered

phases

The 4/7 phase :a spin-liquid?

Large entropy at low temperatures, well below J

Measurements of the susceptibility and heat capacity of the 4/7 phase :

a frustrated quantum

antiferromagnet

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)

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 3He/ 3He/ graphite (2000)J /J4 = -1.67J5/J4 = 0.34J6/J4 = 0.83

and (black dot) 3He/ 4He/ graphite (2001)J /J4 = -2J5/J4 = 0.32J6/J4 = 0.89

MSE coefficients for different 2D-3He 4/7 phases

E. Collin, PhD Thesis, Grenoble 2002

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-k0)n + gµNB

• 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)

Low temperature magnetization

Gapped spin-waves with = 75 µK and n = 6

Spin-gap = 75 µK

Tokyo susceptibility measurements :

- No spin gap?- Impurities?

New measurements needed!

Conclusions

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 : << 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…)

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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).

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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!