spin tunneling and inversion symmetry

Spin Tunneling and Inversion SymmetrySpin Tunneling and Inversion Symmetry

www.physics.ucf.edu/~delbarco

ENRIQUE DEL BARCO

Department of Physics – UCF Orlando

QCPS II 2009 - Vancouver

ENRIQUE DEL BARCO, CHRISTOPHER RAMSEY (UCF)

STEPHEN HILL (NHMFL and Physics Department, FSU – Tallahassee)

SONALI J. SHAH, CHRISTOPHER C. BEEDLE AND DAVID N. HENDRICKSON(Chemistry Department, UCSD – La Jolla-San Diego)

PHILIP C.E. STAMP AND IGOR TUPITSYN(PITP-Physics, UBC, Vancouver)

Nature Physics 4, 277-281 (2008)

Spin Tunneling and Inversion SymmetrySpin Tunneling and Inversion Symmetry

THE MOLECULETHE MOLECULE

[Mn12(Adea)8(CH3COO)14]·7CH3CN

Rumberger et al., Inorg. Chem. 43, 6531–6533 (2004).

2

2

22

2

2 5/2

5/2

5/2

5/2

5/2

5/2

SS=7=7

MAGNETIZATION - QTMMAGNETIZATION - QTM

-0.6 -0.3 0.0 0.3 0.6-1.0

-0.5

0.0

0.5

1.0 = 0.2 T/min

T = 0.90 KT = 0.80 KT = 0.70 KT = 0.65 KT = 0.60 KT = 0.50 KT = 0.41 KT = 0.27 K

M/M

s

H (T)

Tc ~0.3K

TB ~0.9K

S = 7D = 0.4K

T = 0.9K

S = 7, D = 0.4 K

50m

wheel axis

HL

mS = +7

+6

+5

+4

-7

-6

+3

+2

+1

BR gDkH /

MAGNETIZATION - QTMMAGNETIZATION - QTM

exc.

k =

0

0.00 0.29 0.580

5

10

15

exc.

k =

2k =

1(S

)

dM/d

H (

a.u.

)

H (T)

k =

1(A

)

S = 7, D = 0.4 K

0.00 0.29 0.58-25

-20

-15

-10

En

erg

y (K

)

H (T)

Ms =7

Ms =6

Ms =5

zzBz HSgDS 2 H

0.00 0.29 0.580

5

10

15

dM/d

H (

a.u.

)

H (T)0.00 0.29 0.58

0

5

10

15

dM/d

H (

a.u.

)

H (T)

?

HL

HT

[Mn12(Adea)8(CH3COO)14]·7CH3CN

Rumberger et al., Inorg. Chem. 43, 6531–6533 (2004).

2

2

22

2

2 5/2

5/2

5/2

5/2

5/2

5/2

SS=7=7

THE MOLECULETHE MOLECULE

THE MOLECULETHE MOLECULE

[Mn12(Adea)8(CH3COO)14]·7CH3CN

d*

d*

d

dd

dd

dd

dd

d

davg~3.17Å

d*~3.49Å

J ~2-5 cm-1

J* <<J Fo

gu

et-

Alb

iol,

D.

et

al.,

An

ge

w.

Ch

em

. In

t. E

dn

44

, 8

97

–9

01

(2

00

5)

Rumberger et al., Inorg. Chem. 43, 6531–6533 (2004).

THE MOLECULETHE MOLECULE

d*

d*

Rumberger et al., Inorg. Chem. 43, 6531–6533 (2004).

7/27/2

7/27/2

[Mn12(Adea)8(CH3COO)14]·7CH3CN

EXCHANGE-COUPLED SPINSEXCHANGE-COUPLED SPINS

QUANTUM TUNNELING BTW. STATES OF DIFFERENT SPIN LENGHQUANTUM TUNNELING BTW. STATES OF DIFFERENT SPIN LENGH

2121 SJSHHH

HS i gSSESDH Byixizii ˆ2,

2,2/7

2,2/7 2/7iS )2(~865.02/7 DKD )2(~156.02/7 EKE KJJ z 39.0

yyxxzzz SSSSJSSJ 212121

QUANTUM INTERFERENCEQUANTUM INTERFERENCEHARD

2,

2,2/7 yixi SSE

BERRY PHASE INTERFERENCE OF TWO COUPLED TUNNELING SPINSBERRY PHASE INTERFERENCE OF TWO COUPLED TUNNELING SPINS

HL

HT

NEW TOPOLOGICAL EFFECTNEW TOPOLOGICAL EFFECT

Quantum Tunneling Spin

Fe8: Wernsdorfer & Sessoli, Science (1999)Mn12: del Barco et al., PRL (2003)

Mn12 -tBuAc: da Silva Neto et al., (2008)

EXPERIMENT

THEORYLoss et al., PRL (1992)

Von Delft et al., PRL (1992)Garg, EPL (1993)

Coupled Tunneling Spins

SINGLE SPINClassical spin precession

i.e. Wagh et al., PRL (1998)

Pancharatnam (1956)(light interference)

Berry (1984)(quantal systems)

Aharanov and Anandan (1987)(generalization Hilbert space)

.

.

.

INTERACTING SPINSClassical coupled-spins precession

Sjoqvist, PRA (2000)

THEORY

(??)

Mn12 wheel: Ramsey et al., Nature Physics (2008)

EXPERIMENT

SYMMETRY RULESSYMMETRY RULES

ANTI-SYMMETRIC TERM NEEDED

Dzyaloshinskii–Moriya interaction

21 SSDHDM

2121 SJSHHH

NOT ALLOWED ON A DIMER MODEL with

INVERSION SYMMETRY

SYMMETRY RULESSYMMETRY RULES

7/27/2

7/27/2

Wernsdorfer, PRB (2008)a - Dimer model identically used in a Mn6 wheel (CI) b - DM interaction used to explain results

Wernsdorfer, PRL (2008)a - Dimer model used in an “identical” Mn12 wheelb – DM interaction used to explain results

Rejected by NP: See our response in arXiv:0806.1922

Wernsdorfer, arXiv:0804.1246v1,v2,v3a - Dimer model not valid

SYMMETRY RULESSYMMETRY RULES

7/27/2

7/27/2

Wernsdorfer, PRB (2008)a - Dimer model identically used in a Mn6 wheel (CI) b - DM interaction used to explain results

Wernsdorfer, PRL (2008)a - Dimer model used in an “identical” Mn12 wheelb – DM interaction used to explain results

Rejected by NP: See our response in arXiv:0806.1922

Wernsdorfer, arXiv:0804.1246v1,v2,v3a - Dimer model not valid

Wernsdorfer-justification:1)Disorder2)Local DM interactions are not forbidden

del Barco et al., PRL (2009)1)Disorder2)Local DM interactions are not forbidden

SYMMETRY RULESSYMMETRY RULES

2

2

2

2

2

25/25/2

5/2

5/25/2

5/2 d1center of inversion

middle point

7/2

7/2

middle point

center of inversionD = 0

SYMMETRY RULESSYMMETRY RULES

7/2

7/2

middle point

center of inversion

D 0 parallel to z-axis (Ramsey, Nature Physics)D 0 tilted (Wernsdorfer, PRL)

1221 HHHΗ

HgSSSEDSH iBiyixizi

ˆ222

The Hamiltonian of the coupled half-wheels:

Each half-wheel:

Exchange coupling:

2112 SJSΗ S

AS ΗΗΗ 121212

Symmetric exchange:

Antisymmetric exchange (DM interaction):

2112 SSDΗ A

SYMMETRY RULESSYMMETRY RULES

2

2

2

2

2

25/25/2

5/2

5/25/2

5/2 d1center of inversion

middle point

D

*

*

D

x

y

z

SYMMETRY RULESSYMMETRY RULES

2

2

2

2

2

25/25/2

5/2

5/25/2

5/2 d1center of inversion

middle point

D

x

y

z

D

x

y

z

SYMMETRY RULESSYMMETRY RULES

H

H

Center of Inversion

SYMMETRY RULESSYMMETRY RULES

2

2

2

2

2

25/25/2

5/2

5/25/2

5/2 d1center of inversion

middle point

D

x

y

z

D

x

y

z

2

2

3/2

3/2center of inversion

middle point

(d’<d ,J’>>J)

(d ,J)D

x

y

z

D

x

y

zD’’

’

x

y

z

D’’

’

x

y

z

SYMMETRY RULESSYMMETRY RULES

)(, jijiij

ii HHΗ

The Hamiltonian of 4 coupled quarter-wheels:

HgSSSEDSH iBiyixizi

ˆ222

Each quarter-wheel:

Exchange coupling:Aij

Sijij ΗΗΗ

Antisymmetric exchange (DM interaction):

jiijAij SSDΗ

jiijSij SSJΗ

Symmetric exchange:

wJJJ 3412 )(4123 ws JJJJ Center of inversion symmetry imposes:

*

*

k = 1(A) is degenerate

2

2

3/2

3/2center of inversion

middle point

(d’<d ,J’>>J)

(d ,J)D

x

y

z

D

x

y

zD’’

’

x

y

z

D’’

’

x

y

z

0.0 0.1 0.2 0.3 0.4

10-8

10-7

10-6

10-5

12

= 0o

34

= 1o

34

= 5o

34

= 10o

34

= 30o

34

= 90o

34

= 120o

34

= 150o

34

= 170o

34

= 180o

k=1(

A) (

K)

HT (T)

SYMMETRY RULESSYMMETRY RULES

10-7

10-6

10-5

10-4

med

ium

yk = 0

k = 1(A)

(K

)

x~30o

hard

k = 1(S)

-0.4 0.0 0.4 0.8

10-7

10-6

(K

)

HT (T)

12 = 0o

12 = 30o

12 = 60o

12 = 90o

SYMMETRY RULESSYMMETRY RULES

In a centro-symmetric molecule

local DM-interactions MUST BE related by inversion symmetry and

DO NOT BREAK THE DEGENERACY BETWEEN LEVELS OF OPPOSITIVE PARITY

independently of how complex the Hamiltonian is

because PARITY (good quantum number) MUST BE CONSERVED

SYMMETRY RULESSYMMETRY RULES

DM-interactions are important in S = 1/2 systems

ONLY SOURCE OF DEGENERACY BREAKING

but never mix states of opposite parity in a system with inversion symmetry

(Kagome lattice – weak ferromagnetism)

when inversion symmetry is not present

BOTH SYMMETRIC and ANTISYMMETRIC INTERACTIONSCAN BREAK DEGENERACIES

E. del Barco, S. Hill and D. N. Hendrickson, Phys. Rev. Lett. in press (2009)E. del Barco et al., In preparation

2

2

2

2

2

25/25/2

5/2

5/25/2

5/2 d1center of inversion

middle point

D

x

y

z

D

x

y

z

Dipolar fields? (Philip?)Dipolar fields? (Philip?)

CONCLUSIONSCONCLUSIONSQuantum superposition of states with different spin length in a SMMQuantum superposition of states with different spin length in a SMM

New topological effect: Quantum phase interference of two coupled tunneling spinsNew topological effect: Quantum phase interference of two coupled tunneling spins

Local DM interactions in a centro-symmetric SMM do not break the degeneracy Local DM interactions in a centro-symmetric SMM do not break the degeneracy between states of opposite paritybetween states of opposite parity

Del Barco LabDel Barco Lab

Low temperature nanomagnetismLow temperature nanomagnetismSingle-molecule magnetsFM thin films and nanowiresNanoparticles

Low temperature nanotransportLow temperature nanotransportMolecular spintronicsMolecular spintronicsSingle-electron transistorsSingle-electron transistorsLow-dimensional systems Low-dimensional systems i.e. graphene, nanowires, i.e. graphene, nanowires, nanoparticles, molecules,…nanoparticles, molecules,…

Physics collaborationsPhysics collaborationsStephen Hill (NHMFL-FSU)

Masa Ishigami, Robert Peale, Lee Chow (UCF)Agustin Camon, Fernando Luis (UZ-Spain)

Javier Tejada (UB-Spain)Oliver Waldmann (U.Freiburg-Germany)

Andrew Kent (NYU)XiXiang Zhang (KAUST)

Eduardo Mucciolo, Michael Leuenberger (UCF)Philip Stamp, Igor Tupitsyn (UBC-Canada)

Chemistry collaborationsChemistry collaborationsDavid Hendrickson (UCSD)

George Christou (UF)Eugenio Coronado (UV-Spain)

Florenzio Hernandez (UCF)Joel Miller (UU)

[Mn12(Adea)8(CH3COO)14].7CH3CN

0.00 0.29 0.580

5

10

15

dM

/dH

(a

.u.)

H (T)

S = 7/2 + 7/2

[Mn12(Edea)8(CH3CH2COO)14]

S = 7

[Mn12(Edea)8(CH3COO)2(CH3CH2COO)12]

S = 7

d*

d*

d

dd*

d*d*

d*

d

dd

d

d*/davg = 1.100d*/davg = 1.093 d*/davg = 1.091< >

SISTER MOLECULESSISTER MOLECULES

J*/Javg J*/Javg J*/Javg>> <<