H. Godfrin et al- Multiple-spin exchange in two dimensional systems

8/3/2019 H. Godfrin et al- Multiple-spin exchange in two dimensional systems

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A review on the magnetism of

2D solid3

He films

Multiple-spin exchange

in two dimensional systems

CNRS - CRTBT

Grenoble

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

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

COSLAB - ESF

Chamrousse - December 17-22 2004


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NMR experiments down to 100K

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 : R=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,


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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

3He adsorbed on graphite


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Phase diagram of 2D -3He

Data from S

eattle (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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on the triangular lattice of 2D - 3He

J2

J3

J4

The Jn depend on the film density

Multi-spin exchange interaction


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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 = -7P (-1)p Jp P

Two-particle permutations: P2 = (1 + Wi.Wj)

Heisenberg Hamiltonian

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

Three-particle exchange is also HeisenbergP3 = (1 + Wi.Wj+ Wj.Wk+ Wk.Wi)

Four-spin exchange introduces a new physics:

P4 = (1 + 7W.WR + 7 ((Wi.Wj).(Wk.Wl) + (Wi.Wl).(Wj.Wk) -

(Wi.Wk).(Wj.Wl)))

All exchange coefficients J are positive


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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 G

(M. Roger, 1998)

MSE Hamiltonian: Hex = J 7P2 + J4 7P4 - J57P5 + J6 7P6

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 : G = N c / (T- 5)

c = Curie constant 5 = 3 JG = Curie temperature

JG = - ( J2 - 2 J3 - 3 J4 - 5 J5 - 5/8 J6)


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STM image of Papyex U. of Tsukuba, 1996

The graphite substrate has a large

homogeneous surface + defects !


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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

0

0.2

0.4

0.6

0.8

1

6 6.5 7 7.5 8 8.5 9

ccSTP3

He

ind

efects

amount of 4He ccSTP

L

F

D

-1,33

0

0.5

1

1.5

2

liqu

id

3He

(ccSTP)

L

F

D

+0,79

+1,00 +0,33

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 phase

a family of

registered

phases


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The 4/7 phase :

a spin-liquid?

Large entropy at low

temperatures, wellbelow J


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Measurements ofthe 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!0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.1 1 10 100

M/

Msat

T(mK)

E. Collin, PhD Thesis Grenoble (2002)


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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.

JG = 0.07 +/- 0.1 mK:strongly frustrated system!

The Curie-Weiss temperature :

5 = 3JG = +0.2 mKis different from the

Curie-Weiss fit and has the opposite

sign 5 = -0.9 mKas a result of the

strong cancellation of the Heisenberg

term due to multiple spin exchange.

Our data for3He/ 3He/ graphite (2000)

J /J4 = -1.67

J5/J4 = 0.34J6/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 ( 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 + gNWB

The low temperature, low field magnetization is then

M(T) E (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)


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Low temperature magnetization

0

0.02

0.04

0.06

0.08

0.1

0.12

0.01 0.1 1 10 100

MT

(arb.units)

Temperature (mK)

Curie Law

spin waves

0

0.05

0.1

0.15

0.01 0.1 1 10 100

M

T

Gapped spin-waves with ( = 75 K and n = 6


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Spin-gap = 75 K

-0,4

-0,3

-0,2

-0,1

0

0,1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

-dlnM/

d(1/T)

T (mK)


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Tokyo

susceptibility

measurements :

- No spin gap?

- Impurities?

New measurementsneeded!


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Conclusions


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Conclusions on the Spin-Liquid phase

The 4/7 phase of3He/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 ofstates (dominated presumably by S=0 excitations)

Susceptibility varying very slowly : 5


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ReferencesP.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. Nyki, 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. Wrtz, Phys. Rev. B. {50}, 13515 (1994).

and special thanks to Grgoire Misguich, Bruce Normand and Michel Roger!

H. Godfrin et al- Multiple-spin exchange in two dimensional systems

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