II Jornada científica NanoFrontMag - 12 de junio de 2018 - IMDEA Nanociencia Javier Tejada Universidad de Barcelona

1. Experiments on Quantum and Classical
magnetization reversal process
in nanomagnets
MADRID 2018
Professor Javier Tejada.
Dept. Física Fonamental, Universitat de Barcelona.

2. Contenidos
Single Domain Particles
Molecular Magnets
Quantum magnetic deflagration
Superradiance
Nanospheres and Mg-12 acetate triclinic
Effects of SAW: Classical reversal
Conclusions
Content

3. TítuloMacroscopic solid to single domain particles
53
1010 −≈
an
ex
E
E
• Domains and domain walls:
• Tipically
• If the particle has then no domain
wall can be formed. This is a SDP:
• The probabilty of an individual spin flip is:
with
The exchange energy is so high that it is
difficult to do any non-uniform rotation of
the magnetization ( ).
Hence, at low T, the magnetic moment is
a vector of constant modulus:

4. Single domain particles (SDP)
• Classical description: energy barrier of height
• Blocking temperature is defined via the condition
which leads to:
Analogously, we can also define the Blocking
volume:
Anisotropy
constant
Volume
( )TVU
e /)(−
=Γ ν
U
mt/1=Γ
( )mB tKVT νln/=
( )mB t
K
T
V νln=
Microscopic attempt frequency

5. Important aspects of SDPs

6. • The particles relax toward the equilibrium state:
SDP: magnetic relaxation
Initial remanent magnetization
• The dependence of S on T shows two
different regimes:
1) Thermal regime: at high temperatures it
is easier to “jump” the barrier. In this
regime,
2) Quantum regime: at low temperatures,
magnetic relaxation is due to tunnel
effect. In this regime S is of
T.
( ) ( ) ( )( )tSMtM RR νln10 −=

7. Quantum
Classical
Empirically, the magnetic moment is considered to behave quantumly if
|M| ≤ 100μB holds.
Quantum magnetic entities
• Their magnetic moment M is a quantum operator: it verifies the
commutation relation
which yields

8. [ ] 0,ˆ
,ˆˆ
10Spin
2
≠
+−=
=
⊥
⊥
z
z
SH
HDSΗ
S
Molecular Magnets (MM): example
of Mn12 acetate
Quantum counterpart of a SDP.
Discrete projection of the spin
onto the easy axis.
-3/2
+2
-3/2-3/2
-3/2
+2
+2
+2
+2
+2
+2
+2

9. Magnetic bistability of Mn12 acetate
Degenerate ground states for the
Mn12 acetate molecule.
There exists an anisotropy energy
barrier between these two spin
orientations.
The effect of an external magnetic field applied along the easy axis.

10. Título
• Application of an external field: adds a Zeeman term
Longitudinal component of the field (H // easy axis) Shifts the levels.
Transverse component of the field (H easy axis) Allows tunnel effect.
• The tunnel effect is possible for certain values of the field: the resonant
fields.
Resonant spin tunneling on MM

11. -10
-9
-8
-7
-6
-5
-4
-3
-2-10 1 2
3
4
5
6
7
8
9
10
H=0
Magnetic field
Resonant spin tunneling on MM

12. -10
-9
-8
-7
-6
-5
-4
-3-2-10 1 2
3
4
5
6
7
8
9
10
H = 0.5HR
Magnetic field
Resonant spin tunneling on MM

13. H = HR
-10
-9
-8
-7
-6
-5
-4
-3-2 1 2
3
4
5
6
7
8
9
10
Magnetic field
Resonant spin tunneling on MM

14. -10
-9
-8
-7
-6
-5
-4
-3-2-10 1
2
3
4
5
6
7
8
9
10
H = 2HR
Magnetic field
Resonant spin tunneling on MM

15. • As we only have a single barrier height, relaxation goes
exponential.
Relaxation MM
Mn12 Ac relaxation measurements
from the remanent state at different
temperatures.
( ) ( ) ( )[ ]
( )tH
eq eTMtM Γ−
−= 1

16. • Peaks of the relaxation rate Γ(H) at the resonant fields
Relaxation MM
Relaxation rates of
Mn12 acetate at
different fields

17. Landau-Zener effect
m 'm
tW
EEW mm
ν=
−= '
m m
m'm 'm
'm 'm
m
+E
−E
22
∆+=− −+ WEE
Permanence probability
Size of magnetization step
νπ h2/2
∆−
= eP
P−∝1

18. TítuloResonant spin tunneling on MM

19. 19
Energy released  ∆E
Ignition (barrier overcoming)  ∆U
Thermal diffusion  k
Characteristic length of propagation  δ
Two important characteristic timescales:
• Thermal diffusion
• Burning timescale
Metastable
State
∆ U
Deflagration is a technical term describing subsonic combustion that usually
propagates through thermal conductivity
∆ E
Stable
State
19
τb= τd Deflagration Flame width
What is a deflagration?

20. 20
Molecule magnets
Field jumps 1999
Deflagration-like description 2005
20
From magnetization jumps to magnetic
Deflagration (MD)

21. Magnetic deflagration:
Propagation of a front of reversing spins
at constant velocity along the crystal
Problem: Sweeping H we cannot
control the magnetic field at
which it occurs.
Y. Suzuki et. al. PRL 95, 147201 (2005)
A. Hernández-Mínguez et. al. PRL 95 17205 (2005)
H
ΔE
First evidences of MD

22. Avalanche ignition produced by SAW:
IDT
LiNbO3
substrate
Conducting
stripes
Coaxial cable
Mn12 crystal
c-axis
Hz
Coaxial cable connected to an Agilent microwave signal generator
Change in magnetic moment registered in a rf-SQUID magnetometer
Surface Acoustic Waves (SAW) are low frequency acoustic phonons
(below 1 GHz)
Quantum magnetic deflagration

23. • The speed of the avalanche
increases with the applied
magnetic field
• At resonant fields the
velocity of the flame front
presents peaks.
• The ignition time shows peaks at
the magnetic fields at which spin
levels become resonant.








−=
fB0 T2k
U(H)
exp
τ
κ
v
This velocity is well fitted:
κ = 0.8·10-5 m2/s
Tf (H = 4600 Oe) = 6.8 K
Tf (H = 9200 Oe) = 10.9 K
Quantum magnetic deflagration

24. Quantum Magnetic Deflagration

25. Quantum Magnetic Deflagration

26. I
t
τ1
Luminescence
Superradiance
I
t
τSR
This kind of emission (SR) has characteristic properties that make it
different from other more common phenomena like luminescence
L
λL ~ λ
Superradiance
Proposed by Robert H. Dicke in 1954.
NI ∝
2
NI ∝
N is the number of dipoles

27. All spins decay to the fundamental level coherently, with the
emission of photons.
-10
-9
-8
-7
-6
-5
-4-3-2-1012
3
4
5
6
7
8
9
10
B = 2B0
Superradiance

28. Superradiance??
Sharp peak shows a signal which is
equivalent to the sample being at 20 K
(the expected self heating is about 3 K).

29. Magnetic deflagration in pulsed fields
Δt
dB/dt (kT/s)
1.61.92.53.23.74.87.0
200 400
0
2
4
6
dM/dt
t (s)
coil 1
coil 2

30. 1000 2000 3000 4000 5000 6000 7000
-2
0
2
4
6
8
10
12
14
16
Time-difference between the observation of a
magnetisation-reversal in a coil on the left
and on the right of a Mn12Ac-sample in function
of (high) magnetic field-sweeprates.
All observations were done in pulsed fields
at a temperature of about 500mK (in liquid 3He).
∆t(µs)
dHz
/dt (T/s)
Quantum magnetic detonation
t∆

31. S. Lendínez et al., PRB 91, 024404
(2015)
Resonant spin tunneling in Mn12-acetate
nanospheres
Randomly oriented nanospheres
(nanospheres)

32. Resonant spin tunneling in Mn12-acetate
S. Lendínez et al., PRB 91, 024404
(2015)
Randomly oriented powder

33. Derivatives along descending
branches
1/H2 scaling
Derivatives vs. 1/H2 along
descending branches
S. Lendínez et al., PRB 91, 024404
(2015)
Resonant spin tunneling in Mn12-acetate
Randomly oriented powder

34. FE-SEM image
average length = 3.2
± 1.9 µm
average width = 0.8
± 0.3 µm
triclinic
crystallographic
structure
(ALBA synchrotron
beamline)
Resonant spin tunneling in Mn12-acetate
Ribbon-shaped particles
J.Espin et al.,JACS (2016)

35. Resonant spin tunneling in Mn12-acetate
Ribbon-shaped particles
The magnetic moments (arrows) do not form chains along a single magnetic
anisotropy axis

36. Resonant spin tunneling in Mn12-acetate
Ribbon-shaped particles
I. Imaz et al. JACS (2016),

37. Resonant spin tunneling in Mn12-acetate
Ribbon-shaped particles
I. Imaz et al.,JACS (2016)

38. m 'm
tW
EEW mm
ν=
−= '
m m
m'm 'm
'm 'm
m
+E
−E
22
∆+=− −+ WEE
Staying probability
Size of magnetization step
νπ h2/2
∆−
= eP
P−∝1
Resonant spin tunneling in Mn12-acetate
Ribbon-shaped particles
Landau-Zener
effect

39. Resonant spin tunneling in Mn12-acetate
Ribbon-shaped particles
J.Espin et al.,JACS(2016)
Landau-Zener
effect

40. EFFECTS OF SAW: CLASSICAL
REVERSAL
Fe3O4 nanoparticles
ZFC TEM

41. EFFECTS OF SAW: CLASSICAL
REVERSAL

42. EFFECTS OF SAW: CLASSICAL
REVERSAL

43. EFFECTS OF SAW: CLASSICAL
REVERSAL

44. • Energy barrier between opposite orientations of the magnetic moment is
formed by weak relativistic interactions whether stable molecular
magnets can ever break liquid nitrogen temperature of 77K.
• Making identical molecules comparable to mesoscopic magnetic particles will
be a challenging task for chemists.
• Another challenging question would be whether magnetic molecules can ever
become ultimate memory units of conventional computers or even elements
of quantum computers.
• We have demonstrated experimentally that surface acoustic waves accelerate
transitions between magnetic states of magnetite nanoparticles.
• The Einstein–de Haas mechanism of the magnetization reversal by SAWs
comes from the shear deformation of the substrate and the resulting rotation
of the particle as a whole when its size is small compared to the SAW
wavelength.
• I hope to see answers to these questions in the near future!!
Future

45. References
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(Cambridge Univ. Press, 1998).
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[4] A. Hernández-Mínguez et al. Phys. Rev. Lett. 95, 217205 (2005).
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(2012).
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