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

Introduction

What is a deflagration?

From Magnetisation jumps to magnetic deflagration.

Molecule Magnets

Manganese Oxides

Intermetallic Compounds

There are two characteristic timescales which are

important here. The first is the thermal diffusion

timescale is approximately equal to

The second is the burning timescale that strongly

decreases with temperature, typically as

Energy released E

Ignition (barrier overcoming) U

Thermal diffusion

Characteristic length of propagation Metastable

State

U

Deflagration is a technical term describing subsonic combustion that usually propagates

through thermal conductivity

E

Estable

State

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.

-30 -20 -10 0 10 20 30

-1.0

-0.5

0.0

0.5

1.0

M/M

s

H (kOe)

T = 1.8 K

Molecule magnets

Field jumps 1999

Deflagration-like description

2005

0 10 20 30

0.0

0.5

1.0

M/M

S

H (kOe)

T = 3 K

Manganites

Field jumps 1999

Deflagration-like description 2007

Intermetallic compounds

Field jumps 2002

Deflagration-like description 2010

0 5 10 15 20 25 30 35 40 45 50

0.0

0.2

0.4

0.6

0.8

1.0

M/M

S

H (kOe)

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

IDT

LiNbO3

substrate

conducting

stripes

coaxial cable

Mn12 crystalc-axis

Hz

The coaxial cable is connected to an Agilent microwave signal generator.

The change of the magnetic moment is registered by a rf-SQUID magnetometer.

Surface acoustic waves (SAWs) are low frequency acoustic phonons (below 1 GHz)

• 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.

Optical detection

Frequency 150-350 GHz

• Space is needed to place piezoelectric

devices and ignite avalanches

•NO cavities can be used

f 9,8= 269 GHz

H=12 kOe

0 10 20 30 40 50 60

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9.0

9.1

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

E-10,-9

E8,7

E6,5

E7,6

Sig

n. A

mpl

. (

arb.

u.)

H (kOe)

E9,8

Sig

n. A

mpl

. (

arb.

u.)

F. Macià et. al. PRB 77 020403R (2008)

(a)

(d)(c)

0 50 100

-0.4

-0.2

0.0

Sig

n. A

mpl

. (

arb.

u.)

t (ms)

Avalanche

SAW pulse

0 50 100 150

-0.4

0.0

Avalanche

SAW pulse

Sig

n. A

mpl

. (

arb.

uni

ts)

t (ms)

0 25 50

-0.10

-0.05

0.00

Sig

n. A

mpl

. (

arb.

uni

ts)

t (ms)

-0.1

0.0

0 50 100 150

t (ms)

Sig

n. A

mpl

. (

arb.

uni

ts)

(b)

• Surface Acoustic Waves allow us

to control magnetic avalanches

Very fast sweeping magnetic fields

Decelle et al. Phys. Rev. Lett. 102, 027203 (2009)

Superradiance

H-M. et al. Europhys. Lett. 69, 270 (2005)

100 200 300 400 500 600 700 800

-4

-3

-2

-1

0

V (

mV

)

time ( s )

During the second of two field pulses with the same polarity.

During the second of two field pulses with opposite polarity.

• 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?

Antiferromagnetic and Isolating

Ferromagnetic and Conductor

The fragility of the state shown here implies that

several perturbations besides magnetic fields should

induce dramatic changes, including pressure, strain,

and electric fields.

PS Manganites

(La,Pr,Ca)-MnO3

0 10 20 30

0.0

0.5

1.0

M/M

S

H (kOe)

T = 3 K

0 20 40

0.00

0.25

0.50

0.75

1.00

AF-CO initial state

FM-CD final state

M/M

s

H (kOe)

3.0 K

3.5 K

4.0 K

4.5 K

5.0 K

x = M / Mferro

x, fraction of the ferromagnetic phase

0 10 20 30 40 50

0.0

0.5

1.0

1.5

2.0

0 50 100

28

32

36

12

M (

emu)

H (kOe)

1

Ha (

kOe)

xa (%)

Commercial MPMS SQUID

magnetometer

Three pick-up coils detect the magnetic

flux variation.

Recorded by an oscilloscope

Sample

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.0

0.2

0.4

0.6

0.8

1.0

Vco

il /

Vco

il,m

ax

t (ms)

coil A

coil B

coil C

T = 3.5 K

Evidence of propagation

Avalanche begins at the centre of the sample

0.0 0.2 0.4 0.6 0.8

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8

Vco

il /

Vco

il,m

ax

t (ms)

z = 4.0 cm z = 5.5 cm

t (ms)

z = 6.5 cm

t (ms)

Energy released

Thermal diffusion

Ignition

(barrier overcoming)

0 10 20 30

0.0

0.5

1.0

M/M

S

H (kOe)

T = 3 K

AF

FM

Energy Barrier

Energy released

80 90 100 110 120

0.00

0.01

0.95

1.00

0 200 400 600

0.00

0.25

0.50

0.75

1.00

2

4

6

8

10

12

M (

arb.

u.)

t (ms)

t (ms)

M (

arb.

u.) T

(K)

?

The larger the initial FM phase concentration, the slower the deflagration velocity

0

200

400

600

20 25 30 35 40 45 50 55

6

8

10

12

t ig (

ms)

(a)

(b)

x (%)

t d (

ms)

H=28 kOeInitial FM fraction dependence

0 10 20 30 40 50

0.0

0.5

1.0

1.5

2.0

0 50 100

28

32

36

12

M (

emu)

H (kOe)

1

H

a (

kOe)

xa (%)

Macià et al. Phys. Rev. B 76, 174424 (2007)

As the field increases the energy

barriers decrease and

deflagration becomes faster.

28 30 32

5

10

15

20

0

100

200

500

600

28 30 32

20

40

60

t d (

ms)

H (kOe)

(b)

(a)

t ig (

ms)

x (

%)

H (kOe)

0 100 200 300 400

0.00

0.01

0.96

0.98

1.00

27.0 kOe

27.5 kOe

28.0 kOe

28.5 kOe

29.0 kOe

29.5 kOe

30.0 kOe

30.5 kOe

31.0 kOe

M (

arb

.u.)

t (ms)

T = 2 K T = 4 KT = 3 K

• 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

0 10 20 30

0.1

1

10

100

O.C.

0.0

0.2

0.4

0.6

0.8

1.0

resistance

(k

)

H (kOe)

T=3 K

magnetisation

M/M

s

AF-CO

(insulator)

FM-CD

(metallic)

Initial FM-CD phase concentration smaller than 10%

T = 2.5 K

-2 -1 0 1

0

250

500

750

OC

2

4

6

8

-200 0 200 400

0

400

800

O.C.

R (

k)

t (s)

T (

K)

R (

k)

t ( s)

Macià et al. Phys. Rev. B 77, 012403 (2008)

Initial FM-CD phase concentration larger than 10%

T = 3 K

0 10 20 30 40 50

0

20

40

60

80

100

120

140

2

3

4

5

6

R (

k)

t (s)

T (

K)

T = 3 K

Zero field cooled Field cooled H = 15 kOe

-6 -4 -2 0 2

1

10

100

1000

O.C.

2

4

6

R (

k)

t (s)

T (

K)

Coax. Resonator f 3 GHz, Q 100

10 20 30

0.0

0.2

0.4

3.80

3.84

3.88

3.92

0 1 2

0.20

0.25

0.30

S1

1 (

arb.

uni

ts)

H (kOe)

f (

GH

z)

T=3 K

S1

1 (

a. u

.)

t (ms)

f=3.88 GHz

Macià et al. Europhys. Lett. 82, 37005 (2008)

• In the ac plane the spins are aligned

ferromagnetically

• Two different crystal structures: AFM or FM

coupling between the spin layers along the b axis

• At low temperatures, the field driven AFM FM

transition undergoes via an avalanche due to the arrest

of kinetics of the crystal structure.

Dynamical study It is a magnetic deflagration?

Outline: Magnetic and crystallographic Properties

• 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 = 2 K

Velez et al. Phys. Rev. B 81, 064437 (2010)

•Set-up

•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.

•Ignited avalanche by sending a heat pulse:

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.

T = 2KHign = 22 KOe

Speed of the flame vs Hign at two dif. HFC Speed of the flame vs HFC different xini

T = 2K

• The velocity increases with the Hign

• The velocity decreases with the initial FM phase x: losses of the flammability of the

system

smTTUTkvfffB

/1.0/ 21

Kk

ExT

DB

D

f30

3

)1(54

1KUE 200

smTf

/1025

1410/exp sTkUT

fBf

KD

120

AFM

FM

U

ΔE

IDT

LiNbO3

substrate

Conducting

stripes

coaxial

cable Gd5Ge4 SC

Hz

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

a 1.17 mm

b

2.45 mm c

1.04 mm

c

1.07 mm

b 1.29 mm

a

2.40 mm

Velez et al. Submitted

16 18 20 22 24 26 28 300

10

20

30

S1 H b, SAW a

S1 H b, SAW c

S2 H a, SAW c

S2 H a, SAW b

t d~

L/ v

p(m

s)

Hig (kOe)

Same direction of applied magnetic field + different sample configuration:

Anisotropic Magnetic Deflagration attributed to the Anisotropy of the Thermal Difussivity

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

Due to the sample’s

geometry, L is approx the

same for all cases

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