Deflagration in Magnetism, J. Tejada, A. Hernández-Mínguez, F. Macià, S. Vélez and J.M. Hernández Grup de Magnetisme, Dept. de Física Fonamental, Universitat de Barcelona

1. J. Tejada, A. Hernández-Mínguez, F. Macià, S. Vélez and
J.M. Hernández
Grup de Magnetisme, Dept. de Física Fonamental, Universitat de Barcelona
V. Moschalkov, J. Vanacken, Wim Decelle
INPAC, Katholieke Universiteit Leuven
P. V. Santos
Paul-Drude-Institut für Festkörperelektronik, Berlin

2.  Introduction
 What is a deflagration?
 From Magnetisation jumps to magnetic deflagration.
 Molecule Magnets
 Manganese Oxides
 Intermetallic Compounds

3. Deflagration is a technical term describing subsonic combustion that usually propagates
through thermal conductivity
Energy released  E
Ignition (barrier overcoming)  U
Thermal diffusion 
Metastable U
Characteristic length of propagation 
State
 There are two characteristic timescales which are
important here. The first is the thermal diffusion
E timescale is approximately equal to
Estable
State
 The second is the burning timescale that strongly
decreases with temperature, typically as
 When the burning timescale greater exceed the difussion timescale, the huge
amount of energy realized by the metastable spins could lead to the ocurrence of
a Magnetic Deflagration.

4. Manganites
Field jumps 1999
Deflagration-like description 2007
T = 3 K
1.0
Molecule magnets
Field jumps 1999
M/M S
0.5
Deflagration-like description
2005
0.0
0 10 20 30
H (kOe)
T = 1.8 K
1.0
Intermetallic compounds
0.5
Field jumps 2002
s
Deflagration-like description 2010
M/M
0.0
-0.5
1.0
-1.0
0.8
-30 -20 -10 0 10 20 30
0.6
H (kOe)
M/M S
0.4
0.2
0.0
0 5 10 15 20 25 30 35 40 45 50

5. 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
Y. Suzuki et. al. PRL 95, 147201 (2005)
field at which it occurs.

6. 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

7. • The speed of the avalanche
increases with the applied
magnetic field.
• At resonant fields the • The ignition time shows peaks at
velocity of the flame front the magnetic fields at which spin
presents peaks. levels become resonant.

8. • Space is needed to place piezoelectric
devices and ignite avalanches
•NO cavities can be used
Optical detection
Frequency 150-350 GHz
f 9,8= 269 GHz
H=12 kOe
9.1
0.0
9.0
-0.1
8.9
-0.2
(arb.u.)
(arb.u.)
8.8
-0.3
8.7
E6,5 -0.4
Sign. Ampl.
Sign. Ampl.
8.6 E-10,-9
E7,6 -0.5
8.5
E8,7 -0.6
8.4
E9,8 -0.7
8.3
-0.8
0 10 20 30 40 50 60
H (kOe)
F. Macià et. al. PRB 77 020403R (2008)

9. • Surface Acoustic Waves allow us t (ms) t (ms)
to control magnetic avalanches 0 50 100 150 0 25 50
(arb. units)
(arb. units)
0.00
0.0
Sign. Ampl.
-0.05
Sign. Ampl.
-0.1
(a) (b)
-0.10
0.0 0.0
(arb. units)
(c) (d)
(arb. u.)
-0.2
Sign. Ampl.
Avalanche
Sign. Ampl.
-0.4
SAW pulse
Avalanche
SAW pulse
-0.4
0 50 100 150 0 50 100
t (ms) t (ms)

10. Very fast sweeping magnetic fields
Decelle et al. Phys. Rev. Lett. 102, 027203 (2009)

11. Superradiance
During the second of two field pulses with the same polarity.
During the second of two field pulses with opposite polarity.
0
-1
V ( mV )
-2
-3
-4
100 200 300 400 500 600 700 800
time ( s )
H-M. et al. Europhys. Lett. 69, 270 (2005)

12. • Is the described deflagration-like process in molecular clusters unique?
• Among the variety of compounds presenting steps in the magnetisation
curves… are there also spatial propagation involved?
PS Manganites
The fragility of the state shown here implies that
several perturbations besides magnetic fields should
induce dramatic changes, including pressure, strain, (La,Pr,Ca)-MnO3
and electric fields.
Antiferromagnetic and Isolating
Ferromagnetic and Conductor

13. T=3K
x = M / Mferro 1.0
x, fraction of the ferromagnetic phase
S
M/M
0.5
1.00 0.0
0 10 20 30
FM-CD final state H (kOe)
0.75
s
2.0
M/M
0.50 12
3.0 K
3.5 K 1.5
0.25 4.0 K
AF-CO initial state 4.5 K
M (emu)
1.0
5.0 K 36
0.00
H a (kOe)
32
0 20 40 0.5
H (kOe) 28
0.0 0 50 100
1 xa (%)
0 10 20 30 40 50
H (kOe)

14.  Commercial MPMS SQUID
magnetometer
 Three pick-up coils detect the magnetic
flux variation.
 Recorded by an oscilloscope
1.0
1.2
z = 4.0 cm z 0.8 cm
= 5.5 z = 6.5 cm
1.0
coil A
V coil / V coil,max
0.6
coil B
V coil / V coil,max
0.8
coil C
Sample 0.4
0.6
T = 3.5 K
0.4
0.2
0.2 0.0
0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0.2 t (ms)
 Evidence of propagation0.6 0.8 0.0 0.2 0.4 0.6 0.8
0.0 0.2 0.4 0.0 0.4 0.6 0.8
t (ms) t (ms) t (ms)
 Avalanche begins at the centre of the sample

15. T=3K
Energy Barrier 1.0
AF
S
M/M
0.5
?
Energy released
0.0
FM 0 10
H (kOe)
20 30
Energy released 1.00
12
10
0.75
Thermal diffusion 8
M (arb. u.)
T (K)
1.00
0.50
0.95 6
M (arb. u.)
0.25
Ignition 0.01
0.00
4
0.00
(barrier overcoming) 80 90 100
t (ms)
110 120
2
0 200 400 600
t (ms)

16. Initial FM fraction dependence H=28 kOe
2.0
12
600
(a)
1.5
400
M (emu)
t ig (ms)
1.0
36
200
H a (kOe)
32
0.5
28
0.0 0 50 100 0
1 xa (%)
0 10 20 30 40 50
H (kOe) 12 (b)
10
t d (ms)
The larger the initial FM phase
8
concentration, the slower the
deflagration velocity 6
20 25 30 35 40 45 50 55
x (%)
Macià et al. Phys. Rev. B 76, 174424 (2007)

17. T=2K T=3K T=4K
As the field increases the energy 600 (a)
barriers decrease and 500
t ig (ms)
deflagration becomes faster. 200
100
0
1.00
27.0 kOe 20 60
(b)
0.98 27.5 kOe
x (%)
40
28.0 kOe 20
M (arb.u.)
28.5 kOe 15
28 30 32
0.96 29.0 kOe
t d (ms)
H (kOe)
29.5 kOe
30.0 kOe
10
0.01 30.5 kOe
31.0 kOe
0.00 5
28 30 32
0 100 200 300 400
t (ms) H (kOe)

18. • Initially sample is in the AF-CO phase.
• As field increases FM-CD phase begins
to grow.
• At some time a conducting path
appears.
• It is not necessarily associated with the
magnetic avalanche
O.C. 1.0
0.8
100 T=3 K
0.6
M/M
resistance
(k )
10 magnetisation
s
0.4
1 0.2
0.1 0.0
0 10 20 30
H (kOe)

19. Initial FM-CD phase concentration smaller than 10%
AF-CO 8
(insulator) OC
750 O.C.
T = 2.5 K 6
R (k )
800
500 400
R (k )
T (K)
0
FM-CD -200 0 200 400 4
250 t ( s)
(metallic)
0
2
-2 -1 0 1
t (s)
Macià et al. Phys. Rev. B 77, 012403 (2008)

20. Initial FM-CD phase concentration larger than 10%
Zero field cooled Field cooled H = 15 kOe
140 6
T=3K 120
T=3K
100 5
80
R (k )
4
O.C. 60
6
1000 40
3
20
R (k )
T (K)
100
4 0
2
10 0 10 20 30 40 50
t (s)
1
2
-6 -4 -2 0 2
t (s)

21. Coax. Resonator f 3 GHz, Q 100
3.92
0.30
0.4
S 11 (a. u.)
0.25
3.88
S 11 (arb. units)
f (GHz)
0.20
0 1 2
0.2 t (ms)
f=3.88 GHz
3.84
T=3 K
0.0 3.80
10 20 30
H (kOe)
Macià et al. Europhys. Lett. 82, 37005 (2008)

22. Outline: Magnetic and crystallographic Properties
• At low temperatures, the field driven AFM FM
transition undergoes via an avalanche due to the arrest
• In the ac plane the spins are aligned of kinetics of the crystal structure.
ferromagnetically
• Two different crystal structures: AFM or FM
coupling between the spin layers along the b axis Dynamical study  It is a magnetic deflagration?

23. • Hability to control the initial FM phase (x) cooling the sample at different HFC
• Avalanches appear at HFC smaller than HFC ~11.0 kOe (x~0.5)
T=2K
Velez et al. Phys. Rev. B 81, 064437 (2010)

24. •Set-up •Ignited avalanche by sending a heat pulse:
•For spontaneous avalanches: The signals detected with the two coils are almost simultaneous:
The Nucleation should take place at the middle of the sample
•For ignited avalanches, a time diference is observed between the coils:
A phase deflagration front is generated an it propagates through the sample changing the magneto-
crystallographic structure of the system: Magnetostructural Deflagration.

25. Magnetic time-evolution of the sample for different ignition fields (Hign) at T=2 K
The quasi-linear time evolution of M(t) indicates that the phase-front traverses
the sample at a constant speed.

26. T = 2K Hign = 22 KOe T = 2K
Speed of the flame vs Hign at two dif. HFC Speed of the flame vs HFC  different xini
• The velocity increases with the Hign
• The velocity decreases with the initial FM phase x: losses of the flammability of the
system

27. U E U 200 K 1
4
D
5 (1 x) E
Tf 30 K
AFM 3k B D
D
120 K
ΔE
FM
4 1
Tf exp U / k BT f 10 s
1
v k BT f / U Tf Tf 2 0 . 1m / s
5 2
Tf 10 m /s

28. b
Hz c
coaxial 2.45 mm
cable Gd5Ge4 SC 1.04 mm
IDT
a 1.17 mm
Conducting LiNbO3
stripes substrate c a
1.07 mm 2.40 mm
b 1.29 mm
Magnetic deflagrations have been induced by means of controlled SAW pulses.
They were induced on Gd5Ge4 Single Crystals with diferent geometries and under different sample
configurations.
The magnetic time evolution of the sample was taken directly from the SQUID-voltmeter

29. Same direction of applied magnetic field + different sample configuration:
Anisotropic Magnetic Deflagration attributed to the Anisotropy of the Thermal Difussivity
30
S1 H b, SAW a
S1 H b, SAW c
S2 H a, SAW c
S2 H a, SAW b
20
Due to the sample’s
td~L/ vp(ms)
geometry, L is approx the
same for all cases
10
0
16 18 20 22 24 26 28 30
Hig (kOe)
Clear different speed for different crystallographic direction of the applied magnetic field +
Correlation with the magnetic anisotropy of the sample:
Anisotropic Magnetic Deflagration attributed to the Magnetic Anisotropy
Velez et al. Submitted

30.  Magnetic deflagration is observed in several magnetic
materials.
 Molecular magnets:
 New methods to study spin dynamics (SAW+HFEPR) and to
correlate experiments with theory.
 Radiation emission associated to deflagration and detonation
(SUPERRADIANCE  TASER)
 Manganites:
 Colossal MagnetoResistance associated to the phase deflagration
 Intermetallic compounds
 Fast Magnetostructural transitions
 Anisotropic Magnetic Deflagration: Magnetic and Thermal diffusivity