2. Qué es el magnetismo?
• Interacción electrostática+ Mecánica Cuántica
2
e
Solapamiento de
r12 las funciones de
onda
2
e
es diferente S 0 and S 1
r12 para
Heisenberg
s i s j Hamiltoniano Hamiltoniano
3. Interacción de intercambio
• Interacción en función de operadores de espín
Solapamiento de f.o. decae
exponencialmente
Suma se hace sobre
los primeros vecinos
J ~ TC
4. Anisotropía Magnética
• Origen relativista p
v
– Orden de magnitud , siendo p par.
c
• Clásicamente:
– Altura de la barrera de energía:
U kV
Constante de volumen
anisotropía
• Cuánticamente:
Eje fácil Eje difícil
5. Del sólido magnético a la partícula
monodominio
• Dominios y paredes de dominio E ex
a
EA
E ex 3 5
10 10
EA
nm
• Si tamaño partícula R<λ:
– No hay paredes de dominio
– Partícula monodominio!
– Probabilidad de invertir un espín
E ex
exp 0 Para T (<< TC): S=cte
T
6. ¿Realidad de SDP?
• Distribución de tamaños y de orientaciones:
f R f V f U
• Sus momentos magnéticos se alinean con el campo
magnético externo
• Si anulamos el campo, los momentos magnéticos
tienden a recuperar su orientación inicial y eso hace
que el valor de la magnetización que medimos
decrezca logarítmicamente con el tiempo:
7. Dependencia de la viscosidad con
la temperatura
• Partículas relajan hacia su estado de equlibrio:
M M0 1 S ln t
Viscosidad
magnética
• Comportamiento clásico S T
– A temperaturas elevadas es más fácil saltar la barrera
• Cuánticamente (independent of T)
– Relajación debida al efecto túnel
8. Blocking temperature
• Flipping between ↓ and ↑ states occurs in a
certain characteristic time that depends on
temperature:
U
tf t 0 exp
k BT
T > TB
• Below the blocking temperature TB the magnetic
T<T B
moment cannot flip above the barrier
• Above the blocking temperature the magnetic
moment can flip, following a Curie law:
SUPERPARAMAGNETIC state
10. Magnetization curve
• Application of an external field: Zeeman Term
H S
– Longitudinal field (H || easy axis)
• Moves levels
– Transverse field (H easy axis)
• Allows tunneling
• Tunneling is possible at resonant fields
12. Spin resonant tunnel effect
-1 0 1
-3-2 2
3
-4 4
-5
5
-6
6
-7
7
-8
8
-9
9
-10
10 Magnetic field
B = 0.5B0
13. Spin resonant tunnel effect
-3-2 12
-4 3
-5 4
-6 5
-7 6
-8 7
-9 8
-10 9
B = B0 10
Magnetic field
14. Spin resonant tunnel effect
-3-2-10 1
-4 2
-5 3
-6 4
-7 5
-8 6
-9 7
-10 8
9
B = 2B0 Magnetic field
10
15. Relaxation in Molecular Magnets
• After a certain time, relaxation goes
exponential
M t M eq
t 1 exp H t
• Peaks of the relaxation rate Γ(H) at
resonances
17. New trends in magnetism
• Magnetic deflagration
• Superradiance
• Rotational Doppler Shift
18. Magnetic Deflagration
Deflagration is a technical term describing subsonic combustion that
usually propagates through thermal conductivity
Energy Barrier
• There are two characteristic timescales which are
AF important here. The first is the thermal diffusion
timescale is approximately equal to
FM • The second is the burning timescale that strongly
decreases with temperature, typically as
Energy released
Thermal diffusion
Ignition
(barrier overcoming)
19. From Magnetisation jumps to magnetic
deflagration.
Manganites
Field jumps 1999
Deflagration-like description 2007
T=3K
1.0
Molecule magnets
Field jumps 1999
S
M/M
0.5
Deflagration-like description 2005
0.0
0 10 20 30
T = 1.8 K H (kOe)
1.0
0.5 Intermetallic compounds
Field jumps 2002
M/Ms
0.0
Deflagration-like description 2009
-0.5
1.0
-1.0
0.8
-30 -20 -10 0 10 20 30 0.6
H (kOe)
M/MS
0.4
0.2
0.0
0 5 10 15 20 25 30 35 40 45 50
H (kOe)
20. Molecule Magnets
H
ΔE
Magnetic deflagration:
Propagation of a front of reversing spins
at constant velocity along the crystal
A. Hernández-Mínguez et. al. PRL 95 17205 (2005)
Problem: Sweeping H we cannot
control the magnetic field at
which it occurs.
Y. Suzuki et. al. PRL 95, 147201 (2005)
21. Igniting avalanches with SAW
Surface acoustic waves (SAWs) are low frequency acoustic phonons (below 1 GHz)
The coaxial cable is connected to an Agilent microwave signal generator.
The change of the magnetic moment is registered by a rf-SQUID magnetometer.
Hz
coaxial cable
IDT Mn12 crystal
c-axis
conducting LiNbO3
stripes substrate
22. Quantum magnetic deflagration in nanomagnets
κ U(H)
v exp
τ0 2k B T f
This velocity is well fitted:
κ = 0.8·10-5 m2/s
• The speed of the avalanche Tf (H = 4600 Oe) = 6.8 K
Tf (H = 9200 Oe) = 10.9 K
increases with the applied
magnetic field.
• At resonant fields the • The ignition time shows peaks at the
velocity of the flame front magnetic fields at which spin levels
presents peaks. become resonant.
23. Associated to the deflagration...
• Superradiance emission (?)
– All spins decay to the fundamental level
coherently, with the emission of photons.
-3-2-10 1
-4 2
-5 3
-6 4
-7 5
-8 6
-9 7
-10 8
9
B = 2B0
10
24. Linear Doppler
Shift on frequency due to relative velocity between
emitter and observer (non relativistic case): Relative
velocity
v
1
Frequency c
seen by the
observer Frequency of
the emitter
v
c
25. Rotational Doppler
Shift on frequency due to relative rotation between
emitter and observer (circularly polarized light):
Relative rotation
Frequency
seen by the Frequency of
observer the emitter
29. Rotational Doppler Effect
2 B
FMR 0
H
n
I
n
Hn 0
I
2
H Hn 1
Hn
I 2 B
I
measured H ~ 2 . 5 Oe
produced by r ~ 1nm particles
30. Rotational Doppler Effect
Occupied states
L L 1
En n n 1 B
H
2I
2 En
n ~
B
H
1/ 2
k BT
E n ~ k BT n~
B
H
T ~ 2K
n 100
B
H ~ 0 . 17 mK
31. Rotational Doppler Effect
• Change in frequency observed due to rotation:
• RDE in GPS systems (resonance of an LC
circuit)
– Resonant frequency insensitive to magnetic fields
Resonance
• RDE in Magnetic Resonance systems
– Resonant frequency sensitive to magnetic fields
Resonance
32. Rotational Doppler Effect
• Article by S. Lendínez, E. M. Chudnovsy, and J.
Tejada:
arXiv:1008.2142v1 [cond-mat.other]
• Expression for ω’Res are found for ESR, NMR and
FMR.
Resonance
• Exact expression depends on type of resonance
(ESR, NMR or FMR)
• Depends on anisotropy
33. Rotational Doppler Effect
• Ω ≈ 100 kHz
• ESR and FMR: • ωRes ≈ GHz Ω << ωRes << Δω
• Δω ≈ MHz
BUT
Position of maximum can be
With free rotors: determined with accuracy of
100 kHz ≈ Ω
• ω Ω≈ 100 Ω ≈ Δω
≈ MHz MHz
• NMR: Res
• Δω ≈ kHz Gyromagnetic
ESR and tensor
• κ ≠ 1 needed anisotropy FMR: (shape,...)
NMR: Hyperfine
interactions
