Symmetry IssuesSymmetry Issues

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)

Nature Physics 4, 277-281 (2008)

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

yyxxzzz SSSSJSSJHHH 21212121

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

SYMMETRY RULES and DMSYMMETRY RULES and DM

SYMMETRY RULES and DMSYMMETRY RULES and DM

ANTI-SYMMETRIC TERM NEEDED

a) Hyperfine interaction / state mixing

AJJ

A

2

2

~

b) Dzyaloshinskii–Moriya interaction

xyyxDM SSSSJH 2121sin

JJ z cosJJ

o037.0

yyxxzzz SSSSJSSJHHH 21212121

NOT ALLOWED ON A DIMER MODELDUE TO INVERSION SYMMETRY

c) Tilts of easy axes?

SYMMETRY RULES and DMSYMMETRY RULES and DM

7/27/2

7/27/2

Wernsdorfer, arXiv:0804.1246v1a - Experiment invalidb - Dimer model not validc - DM interaction not possible

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

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

, v2perhaps invalid

, v3

clearly existingRejected by NP: See our response in arXiv:0806.1922

SYMMETRY RULES and DMSYMMETRY RULES and DM

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

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

7/2

7/2

middle point

center of inversionD = 0

SYMMETRY RULES and DMSYMMETRY RULES and DM

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:

21212112 2

1SSSSJSSJΗ xyzzz

S

AS ΗΗΗ 121212

Symmetric exchange:

Antisymmetric exchange (DM interaction):

2112 SSDΗ A

2

2

2

2

2

25/25/2

5/2

5/25/2

5/2 d1center of inversion

D

middle point

D

*

*

x

y

z

SYMMETRY RULES and DMSYMMETRY RULES and DM

2

2

3/2

3/2center of inversion

middle point

x

y

z

D

D

*

*

(d’<d ,J’>>J)

(d ,J)

SYMMETRY RULES and DMSYMMETRY RULES and DM

2

2

3/2

3/2center of inversion

middle point

x

y

z

D

D

*

*

(d’<d ,Js>>Jw)

(d ,Jw)413423124321 HHHHHHHHΗ

The Hamiltonian of 4 coupled quater-wheels:

HgSSSEDSH iBiyixizi

ˆ222

Each quarter-wheel:

Exchange coupling:Aij

Sijij ΗΗΗ

Antisymmetric exchange (DM interaction):

jiijAij SSDΗ

)sin(3412 wJDD

04123 DD

jijixyijjzizzij

Sij SSSSJSSJΗ

2

1

Symmetric exchange:

wJJJ 3412 )(4123 ws JJJJ

Center of inversion symmetry imposes:

180*

180*

hard x-axis

x

y

D

~30o

QUESTION 1

NEW TOPOLOGICAL EFFECTNEW TOPOLOGICAL EFFECT

Quantum Tunneling Spin

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

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 (1954)(quantal systems)

Aharanov and Anandan (1987)(generalization Hilbert space)

.

.

.

INTERACTING SPINSClassical coupled-spins precession

Sjoqvist, PRA (2000)

THEORY

(none yet?)

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

EXPERIMENT

QUESTION 2

SYMMETRY RULES and QTMSYMMETRY RULES and QTM

[NEt4]3[Mn3Zn2(salox)3O(N3)6Cl2]

2

2

2

(S=6)

SYMMETRY RULES and QTMSYMMETRY RULES and QTM

SYMMETRY RULES and QTMSYMMETRY RULES and QTM

SYMMETRY RULES and QTMSYMMETRY RULES and QTM

zzBzz HSgBSDS 42H HA

SYMMETRY RULES and QTMSYMMETRY RULES and QTM

zzBzz HSgBSDS 42H HA

SYMMETRY RULES and QTMSYMMETRY RULES and QTM

zzBzz HSgBSDS 42H

SYMMETRY RULES and QTMSYMMETRY RULES and QTM

SYMMETRY RULES and QTMSYMMETRY RULES and QTM 66

663333

4322

2242 ˆ SSCSSSSSSCSSCHgSBSDSH zzBzz

SYMMETRY RULES and QTMSYMMETRY RULES and QTM

QUESTION 3

0 90 180 270 3600.0

0.1

0.2

0.3

0.4

0.5

0.6

k = 1

Pro

babi

lity

(degrees)

HT = 0.25 T

k = 0