Hysteresis and resonant MQTHysteresis and resonant MQT

2 2 2 ˆˆ ˆ .ˆ ˆˆ ˆ. (4) 'o z x y BH DS E B g SS S O H �

ResonanResonant t quantuquantum m tunnelintunnelingg

B//B//zz

Note: Note: resonant resonant tunneling tunneling strong at B = strong at B = 0 0

Hysteresis and resonant MQTHysteresis and resonant MQT

-6 -4 -2 0 2 4 6

-4

-2

0

2

4

0.5 K

1.4 K

1.8 K

2.2 K

2.8 K

Mag

neti

zati

on (

arb.

uni

ts)

Magnetic field (tesla)Resonant tunnelingResonant tunneling

The hysteresis is a property of each single moleculeThe hysteresis is a property of each single molecule

Hysteresis loops ofMn4 single-molecule magnets

Mn4O3(OSiMe3)(O2CMe)3(dbm)3 [Mn4(O2CMe)2(Hpdm)6][ClO4]2

S = 9/2 S = 8

Spin-parity dependent quantum tunnelingKramers theorem: No matter how unsymmetric the crystal field, a system possessing an odd

number of electrons must have a ground state that is at least doubly degenerate,even in the presence of crystal fields and spin-orbit interactions H. A. Kramers, Proc. Acad. Sci. Amsterdam 33, 959 (1930)

Mesoscopic systems: J.L. Van Hemmen and S. Süto, Europhys. Lett. 1, 481 (1986)D. Loss, D.P. DiVincenzo, and G. Grinstein, Phys. Rev. Lett., 69, 3232 (1992)J. von Delft and C. L. Hendey, Phys. Rev. Lett., 69, 3236 (1992)

Spin-parity dependent quantum tunneling

Environnemental effects• hyperfine interaction (nuclear spins)

• dipolar interaction between molecules• exchange interaction between molecules

etc.

Interests in Single Molecule MagnetsInterests in Single Molecule Magnets

•As single molecule magnetic memory devicesAs single molecule magnetic memory devices

•As magnetic quantum logic devicesAs magnetic quantum logic devices

•Fundamental studies of large spins, Fundamental studies of large spins, i.ei.e. quantum vs. . quantum vs. classical behaviorclassical behavior

•Studies of dynamics of nanomagnetsStudies of dynamics of nanomagnets

•Studies of quantum decoherence (environmental Studies of quantum decoherence (environmental couplings)couplings)Advantages:Advantages:

•Monodisperse magnetic unitMonodisperse magnetic unit

•Chemical control Chemical control "bottom-up" materials "bottom-up" materials engineeringengineering

•Tremendous control of the magnetic unit (the Tremendous control of the magnetic unit (the spin), as well as its coupling to the environmentspin), as well as its coupling to the environment

•Michael N. Leuenberger and Daniel Loss, Nature 410, 789 (2001).

HIGH FREQUENCY EPRHIGH FREQUENCY EPR

0 1 2 3 4 5

-500

-400

-300

-200

-100

0

100

200

300

400

MS = - 5

/2 to - 3

/2

MS = - 7

/2 to - 5

/2

MS = - 9

/2 to - 7

/2

S = 9/2

Freq

uenc

y (G

Hz)

Magnetic field (tesla)

Energy level diagram for Energy level diagram for DD < 0 system < 0 system2ˆ ˆˆ . .o z BH DS B g S

�

B // z-axis of molecule

Note frequency rangeNote frequency range

Cavity perturbationCavity perturbationCylindrical TE01Cylindrical TE01n n ((QQ ~~ 10104 4 -- 101055))ff = 16 = 16 250 GHz 250 GHzSingle crystal 0.2Single crystal 0.2×0.2×0.1 mm×0.2×0.1 mm33

T = 0.5 to 300 K, B up to 45 teslaT = 0.5 to 300 K, B up to 45 tesla

M. Mola M. Mola et alet al., Rev. Sci. Inst. ., Rev. Sci. Inst. 7171, 186 (2000), 186 (2000)

A u S S

B

More on the techniqueMore on the technique•We use a Millimeter-wave Vector Network We use a Millimeter-wave Vector Network Analyzer (MVNA, ABAnalyzer (MVNA, ABmmmm) as a spectrometer.) as a spectrometer.

•This device allows vector measurements with This device allows vector measurements with continuous frequency coverage from 8 to 600 continuous frequency coverage from 8 to 600 GHz.GHz.

•We currently use cavities up to 250 GHz and We currently use cavities up to 250 GHz and have a reflectivity probe working up to 450 GHz.have a reflectivity probe working up to 450 GHz.

•We use over-moded cavities when closely We use over-moded cavities when closely spaced frequencies are required.spaced frequencies are required.

•A A 33He capability has just been successfully He capability has just been successfully tested.tested.

•The cavity technique, in combination with the The cavity technique, in combination with the vector capability, is extremely important for line vector capability, is extremely important for line shape analysis; eliminates many instrumental shape analysis; eliminates many instrumental effects which plague single-pass scalar effects which plague single-pass scalar measurements.measurements.

•S. Hill, S. Maccagnano, K. Park, R. M. Achey, J. M. North and N. S. Dalal, Phys. S. Hill, S. Maccagnano, K. Park, R. M. Achey, J. M. North and N. S. Dalal, Phys. Rev. B Rev. B 6565, 224410 (2002)., 224410 (2002).

•M. Mola M. Mola et alet al., Rev. Sci. Inst. ., Rev. Sci. Inst. 7171, 186 (2000)., 186 (2000).

0 1 2 3 4 5

-500

-400

-300

-200

-100

0

100

200

300

400

MS = - 5

/2 to - 3

/2

MS = - 7

/2 to - 5

/2

MS = - 9

/2 to - 7

/2

S = 9/2

Freq

uenc

y (G

Hz)

Magnetic field (tesla)

Energy level diagram for S = Energy level diagram for S = 99//22, , DD < 0 system < 0 system2ˆ ˆˆ . .o z BH DS B g S

�

B // z-axis of molecule

0.0 1.0 2.0 3.0 4.0 5.0

24 K 18 K 14 K 8 K 6 K 4 K

1/2 to 1/

23/2 to 1/

2

5/2 to 3/

2

7/2 to 5/

2

9/2 to 7/

2f = 138 GHz

C

avit

y tr

ansm

issi

on (

arb.

uni

ts -

off

set)

Magnetic field (tesla)

HFEPR for high symmetry (HFEPR for high symmetry (CC3v3v) Mn) Mn44 cubane cubane

Field // Field // zz-axis of the molecule (-axis of the molecule (±0.2±0.2oo))InhomogeneouInhomogeneous lineshapes lineshape

0 1 2 3 4 5

0

50

100

150

S = 9/2

D = 0.484 cm-1

B0

4 = 0.000062 cm-1

gz = 2.00(1)

Freq

uenc

y (G

Hz)

Magnetic field (tesla)

2 0 0 0 2 2 44 4 4

ˆ ˆ ˆ ˆ ˆ ˆ ˆˆ , where o z B zz z z zH DS B O g BS O S S S

Fit to easy axis data - yields diagonal crystal field termsFit to easy axis data - yields diagonal crystal field terms