a first principles model for tunneling demagnetization in...

A first Principles Model for

Tunneling Demagnetization in

Single-Molecule Magnets

Daniel Aravena

Universidad de Santiago de Chile

daniel.aravena.p@usach.cl

Puerto Natales, December 17th, 2019

Single Molecule magnets

SMMs: molecules which retain their magnetic moment

orientation after the removal of a external magnetic field

Initially, SMM → paramagnet

Magnetic moment orientation

changes freely

Single Molecule magnets

SMMs: molecules which retain their magnetic moment

orientation after the removal of a external magnetic field

A external magnetic field will

orient SMM magnetic moment

in a parallel way

Single Molecule magnets

SMMs: molecules which retain their magnetic moment

orientation after the removal of a external magnetic field

After field removal, the molecule can quickly come back to the initial

situation of retain the magnetic moment orientation

Single Molecule magnets

SMMs: molecules which retain their magnetic moment

orientation after the removal of a external magnetic field

After field removal, the molecule can quickly come back to the initial

situation of retain the magnetic moment orientation

Single Molecule magnets

SMMs: molecules which retain their magnetic moment

orientation after the removal of a external magnetic field

After field removal, the molecule can quickly come back to the initial

situation of retain the magnetic moment orientation

Single Molecule Magnets and Molecular

Spin Qubits

Some examples

Thiele, S.; Balestro, F.; Ballou, R.; Klyatskaya, S.; Ruben, M.; Wernsdorfer, Science 2014, 344 (6188), 1135–1138. M. D. Jenkins, Y. Duan, B. Diosdado, J. J. García-Ripoll, A. Gaita-Ariño, C. Giménez-Saiz, P. J. Alonso, E. Coronado and F. Luis, Phys. Rev. B, 2017, 95, 064423; C. J. Yu, M. D. Krzyaniak, M. S. Fataftah, M. R. Wasielewski and D. E. Freedman, Chem. Sci., 2019, 10, 1702–1708. K. S. Pedersen, A.-M. Ariciu, S. McAdams, H. Weihe, J. Bendix, F. Tuna and S. Piligkos, J. Am. Chem. Soc., 2016, 138, 5801–5804. M. Atzori, E. Morra, L. Tesi, A. Albino, M. Chiesa, L. Sorace and R. Sessoli, J. Am. Chem. Soc., 2016, 138, 11234–11244.

Single Molecule Magnets and Molecular

Spin Qubits

SMMsMolecular Spin

Qubits

Spin-Orbit Coupling

High Low?

Key ParameterDemagnetization

time (𝜏. 𝑇1)Decoherence

time (𝑇𝑚)

Target time 100 s 𝜇𝑠 −𝑚𝑠

Double well scheme

To achieve blocking, magnetic anisotropy must lift ground

state degeneracy

D. Gatteschi, R. Sessoli; Angew. Chem. Int. Ed. 42, 268-297 (2003)

Ms = 1/2

Ms = 3/2

Ms = 5/2

Ms = -1/2

Ms = -3/2

Ms = -5/2

Double well scheme

To achieve blocking, magnetic anisotropy must lift ground

state degeneracy

Ms = 1/2

Ms = 3/2

Ms = 5/2

Ms = -1/2

Ms = -3/2

Ms = -5/2

D. Gatteschi, R. Sessoli; Angew. Chem. Int. Ed. 42, 268-297 (2003)

Ms = 1/2

Ms = 3/2

Ms = 5/2

D. Gatteschi, R. Sessoli; Angew. Chem. Int. Ed. 42, 268-297 (2003)

Ms = -1/2

Ms = -3/2

Ms = -5/2

Double well scheme

To achieve blocking, magnetic anisotropy must lift ground

state degeneracy

Ms = 1/2

Ms = 3/2

Ms = 5/2

D. Gatteschi, R. Sessoli; Angew. Chem. Int. Ed. 42, 268-297 (2003)

Ms = -1/2

Ms = -3/2

Ms = -5/2

Double well scheme

To achieve blocking, magnetic anisotropy must lift ground

state degeneracy

Ms = 1/2

Ms = 3/2

Ms = 5/2

D. Gatteschi, R. Sessoli; Angew. Chem. Int. Ed. 42, 268-297 (2003)

Ms = -1/2

Ms = -3/2

Ms = -5/2

Relaxation Pathways

To achieve blocking, magnetic anisotropy must lift ground

state degeneracy

Experimental data for Relaxation time

Low temperature region might show a plateau

related with tunneling relaxation

tQT

Experimental data for Relaxation time

Low temperature region might show a plateau

related with tunneling relaxation

Ueff

1 1

0 exp( / )eff BU k Tt t− −= −

Main theoretical descriptors for SMMs

Excitation energies, transition moments, g-tensor for the

ground state

Key parameters: ΔE, g, μ are related with Ueff and tQT,

but they are not directly comparable

A model for calculation of t, focused on the tunneling

regime

Our approach

1 10 1001E-6

1E-4

0.01

1

100

10000

t-1 (

s-1)

T (K)

Thermally activatedregime

Tunnelingregime

tQT

Our approach

For the calculation of tQT we need g-factors and g-

vectors from the ground state (ORCA/Molcas)

We also need the relative position of neighbor

spins (cif file)

Model for the prediction of tQT and Ueff

g-factors:

0.020118 0.026371 17.783088 iso = 5.943192

g-shifts:

-1.982201 -1.975948 15.780768 iso = 3.940873

Orientation:

X 0.4502222 0.4953585 -0.7429131

Y -0.7947483 0.6015746 -0.0805185

Z 0.4070321 0.6266801 0.6645276

We must include dipolar coupling in the model, as

magnetic dilution has a dramatic effect for supressing

tunneling (we must consider molecular orientation in the

crystal!)

Dipolar interaction

2 2

3 5

( )( )3a b a b

dip

r rH

r r

= −

Non-diagonal (spin-flip) matrix elements are

Two spin-flip terms (neglected)

Dipolar interaction

2

5

3 ( )ˆ

2

bz z ax bz ax x ay bz ay y

dip

g r g S S r ig S S rH

r

− + =

2 2 2 2

5

( ) 3 3 ( ) 3ˆ

4

ax bx ax bx ay by ay by ax bx ax bx x x y ax by ax by ay bx ay bx ay by ay by y

dip

r g g S S g g S S g g S S r ir r g g S S g g S S g g S S rH

r

− − + + + =

Interaction of the central ion with neighbor spins

Spin-flip matrix elements

The transition rate is predicted according to Fermi

Golden Rule

Tunneling rate

22sfk E

=

Mononuclear, half-integer Single Molecule

Magnets at zero field.

Tested for lathanides

May be restrictive, but best SMMs are DyIII

mononuclear compounds

Model scope

Tunneling Relaxation times

Selected 18 mononuclear LnIII SMMs with a clear

tunneling plateau (15 DyIII and 3 ErIII)

Tunneling Relaxation times

Aravena D, J Phys. Chem. Lett. 9, 5327 (2018)

Demagnetization pathways

,

exp( / )( ) i B

i QT i

E k Tk T k

Z

−

1

( )( )

Mi

eff i

i k

k TU T E

N=

=

Effective demagnetization barriers

Conrad A. P. Goodwin, Fabrizio Ortu, Daniel Reta, Nicholas F. Chilton, David P. Mills, Nature 548, 439–442 (2017)

REFCODE Ei (cm-1) log(tQT) (s) Ueff,exp (cm-1) Ueff,calc (cm-1)

MEKDOY 0 4.249 1223 1209

464.3 0.929

731.4 -1.938

906.2 -3.778

1063.2 -4.985

1210.9 -7.243

1327.4 -3.273

1397.6 -4.798

Effective demagnetization barriers

Conrad A. P. Goodwin, Fabrizio Ortu, Daniel Reta, Nicholas F. Chilton, David P. Mills, Nature 548, 439–442 (2017)

Liu J, Chen Y-C, Liu J-L, Vieru V, Ungur L, Jia J-H, Chibotaru LF, Lan Y, Wernsdorfer W, Gao S, Chen X-M, Tong

M-L; J. Am. Chem. Soc. 2016, 138, 5441−5450 (2016)

Effective demagnetization barriers

REFCODE Ei (cm-1) log(tQT) (s) Ueff,exp (cm-1) Ueff,calc (cm-1)

IMOTUB 0 -1.094 712 736

395.1 -5.409

630.5 -7.639

724.6 -0.585

775.8 -7.966

785.5 -6.492

797.9 -8.020

862.7 -6.084

Effective demagnetization barriers

Liu J, Chen Y-C, Liu J-L, Vieru V, Ungur L, Jia J-H, Chibotaru LF, Lan Y, Wernsdorfer W, Gao S, Chen X-M, Tong

M-L; J. Am. Chem. Soc. 2016, 138, 5441−5450 (2016)

Effective demagnetization barriers

REFCODE Ei (cm-1) log(tQT) (s) Ueff,exp (cm-1) Ueff,calc (cm-1)

RAPDUK 0 3.815 1261 1196

564.6 -0.599

946.3 -4.725

1151.3 -6.201

1180.8 -3.479

1208.6 -5.635

1227.3 -5.866

1243.6 -6.459

Ding Y-S, Chilton NF, Winpenny REP, Zheng Y-Z; Angew. Chem. Int. Ed. 55, 16071 –16074 (2016)

Effective demagnetization barriers

Ding Y-S, Chilton NF, Winpenny REP, Zheng Y-Z; Angew. Chem. Int. Ed. 55, 16071 –16074 (2016)

Magnetic Dilution

Is there any general trend regarding magnetic dilution?

Llanos L, Aravena D, J Magn. Magn. Mater. 489, 165456 (2019)

18-molecule benchmark set

Same trend for all compounds

Magnetic Dilution

0.01 0.1 1

-4

0

4

8

log(t

QT)/

s

Concentration (x)0.01 0.1 1

0

2

4

log(t

QT)/

s

Concentration (x)

Magnetic Dilution

0.01 0.1 11E-4

1E-3

0.01

0.1

1

10

t (s

)

Concentration (x)

[ErPOM2]9-: A well characterized system

F. Luis, M.J. Martínez-Pérez, O. Montero; E. Coronado, S. Cardona-Serra, C. Martí-Gastaldo, J.M. Clemente-

Juan, J. Sesé, D. Drung, T. Schurig; PHYSICAL REVIEW B 82, 060403(R) 2010

Computational implementation

A software for the calculation of tunneling relaxation

times is available (U&Tau)

It requires two input files:

- A cif file (ideally from the CCDC database)

- An input file (called .zdir) with state energies and g-

values/g-vectors obtained from an electronic structure

package

We distribute the binary upon request

to daniel.aravena.p@usach.cl