a first principles model for tunneling demagnetization in...
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A first Principles Model for
Tunneling Demagnetization in
Single-Molecule Magnets
Daniel Aravena
Universidad de Santiago de Chile
Puerto Natales, December 17th, 2019
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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
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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
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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
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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
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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
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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.
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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
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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
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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)
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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
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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
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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
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Experimental data for Relaxation time
Low temperature region might show a plateau
related with tunneling relaxation
tQT
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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− −= −
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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
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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
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Our approach
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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
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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
= −
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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
− − + + + =
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Interaction of the central ion with neighbor spins
Spin-flip matrix elements
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The transition rate is predicted according to Fermi
Golden Rule
Tunneling rate
22sfk E
=
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Mononuclear, half-integer Single Molecule
Magnets at zero field.
Tested for lathanides
May be restrictive, but best SMMs are DyIII
mononuclear compounds
Model scope
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Tunneling Relaxation times
Selected 18 mononuclear LnIII SMMs with a clear
tunneling plateau (15 DyIII and 3 ErIII)
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Tunneling Relaxation times
Aravena D, J Phys. Chem. Lett. 9, 5327 (2018)
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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=
=
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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
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Effective demagnetization barriers
Conrad A. P. Goodwin, Fabrizio Ortu, Daniel Reta, Nicholas F. Chilton, David P. Mills, Nature 548, 439–442 (2017)
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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
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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)
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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)
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Effective demagnetization barriers
Ding Y-S, Chilton NF, Winpenny REP, Zheng Y-Z; Angew. Chem. Int. Ed. 55, 16071 –16074 (2016)
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Magnetic Dilution
Is there any general trend regarding magnetic dilution?
Llanos L, Aravena D, J Magn. Magn. Mater. 489, 165456 (2019)
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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)
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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
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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