Internal Degrees of Freedomand Quantum Tunneling of the Magnetization

in Single-Molecule Magnets

ENRIQUE DEL BARCO

Department of Physics – UCF Orlando

In collaboration with: Steve Hill (FSU&NHMFL) and David N. Hendrickson (UCSD) SPONSORED BY: 1

SMMs and Giant Spin ApproximationGSA failure / multi-spin description / low-nuclearity SMMs

A low nuclearity SMM: Mn4

EPR and QTM Characterization

Asymmetric Berry Phase Interference Symmetry Considerations

Motion of Berry Phase PatternsInternal Degrees of Freedom

OUTLINE

2

SMMs and the GSA MODEL

8MnIII(S=2) = 16

-4MnIV(S=3/2) = 6~ S = 10

3

SMMs and the GSA MODEL

~ S = 10

up

downx

y

z

4

SMMs and the GSA MODEL

~ S = 10

up

downx

y

zM

ag

neti

c fi

eld

5

SMMs and the GSA MODEL

~ S = 10

up

downx

y

zon

-res

ona

nce

QT on (fast relaxation)

QT off (non relaxation)

off-

reso

nanc

eon

-res

ona

nce

2,5 3,0 3,5 4,0 4,5 5,0-1,0

-0,5

0,0

0,5

1,0

M/M

s

Hlong

(T)

6

SMMs and the GSA MODEL

7

FAILURE of the GSA MODEL

Anomalous term

Barra et al. (1997)

Low-lying excited states

Mukhin et al. (2001)

QTM btw. different spin lengths

Ramsey et al. (2008) observed before in AF molecules

Carreta et al. (2007)

8

MULTI-SPIN DESCRIPTION LOW NUCLEARITY SMMs

Connection between Dmol and dion

Higher-order molecular anisotropyConsequences of weak coupling and spin frustration

Internal degrees of freedom and QTM:(Symmetry lowering effects)

(Spin selection rules)

S. Hill et al., Dalton Transactions (2010).

Ni4 (S = 4)Mn6 (S = 4,12)Mn3 (S = 2,6)

9

MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM

[Mn4(Bet)4(mdea)4(Hmdea) 2] (BPh4)4

K. J. Heroux et al., unpublished.

S = 9 (at low-T)

MnII (S = 5/2)

MnIII (S = 2)

10

MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM

11

MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM

( )

12

test: k=1?

MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM

( )13

MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM

TIME REVERSAL INVARIANCE OF THE SPIN-ORBIT INTERACTION

HSgLSH B

SL

LS

H HS

=ODD

=ODD

=ODD

=EVEN

=EVEN

14

MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM

Second order anisotropy (symmetries):

a) 3 mutually orthogonal two-fold rotation axesb) 3 mutually orthogonal mirror planesc) Inversion center

(b) Guarantees invariance w.r.t. reversal of HT

IMPOSES SYMMETRIC BPI PATTERNS WHETHER HL=0 or HL0

xy-mirror symmetry must be broken TO ALLOW ASYMMETRIC BPI PATTERNS W.R.T. HT REVERSALTRI GUARANTEES THE TWO PATTERNS TO BE MIRROR IMAGES

15

MULTI-SPIN DESCRIPTION THE CASE OF Mn4 SMM

16

i

i

i

i

d

e

e

d

00

00

00�

gggg zzyyxx

JJJJ zzyyxx

MULTI-SPIN DESCRIPTION

iii ,,Euler angles:

17

MULTI-SPIN DESCRIPTION

(z - easy axis)

(x - hard axis)

CENTRAL ION (2)

EXTERNAL IONS (1,3)

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SOME RELAXATION ISSUES

19

SOME RELAXATION ISSUES

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SOME RELAXATION ISSUES

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SOME RELAXATION ISSUES

22

23

ACKNOWLEDGEMENTS

STUDENTS:

Hajrah M. Quddusi and Simran Singh (UCF)Junjie Liu (FSU)

Katie Heroux and Chris Beedle (UCSD)