Download Evidence for a Magnetic Seebeck Effect

Evidence for a Magnetic Seebeck Effect
Phys. Rev. Lett. ...
ICNM 2013, Istanbul : Wednesday, September 4th , 2013
Sylvain D. Brechet
Francesco A. Vetro and Jean-Philippe Ansermet
Institute of Condensed Matter Physics, EPFL, Lausanne,
Switzerland
Outline
1
Theory : Irreversible thermodynamics of a continuous medium
with magnetisation
2
Experiment : YIG slab excited at 4 GHz
Sylvain D. Brechet - EPFL
Magnetic Seebeck Effect
Irreversible thermodynamics of electron continua
Linear relation : (Eur. Phys. J. B 86, 318 (2013))
je = Les · (− ∇ T ) + Lee · (− ∇ µ − e ∇ V + m ∇ B)
Material : YIG (insulator)
je = 0
(no electronic transport)
∇V = 0
(no charge accumulation)
∇µ = 0
(uniform spatial distribution)
Stationary state :
M ∇ B = λ n kB ∇ T
where
Sylvain D. Brechet - EPFL
M = n m and
Magnetic Seebeck Effect
λ>0
Magnetic Seebeck Effect
Bulk identity :
M ∇ B = jM × B
where
jM = ∇ × M
Magnetic Seebeck effect
B = εM × ∇ T
where
Sylvain D. Brechet - EPFL
εM = − λ n kB (∇ × M)−1
Magnetic Seebeck Effect
Linear response (to RF excitation field)
Linearisation :
B ext = B0 + b
M = MS + m
where
m MS
Eigenmodes :
mkx,y = χkx,y bk
χkx,y = −
Ω=
1
p
Ω − Ω0 (Ω0 + 1) + i rx,y α Ω + kT · k−1
ω
,
γ µ 0 MS
Ω0 =
γ B0
,
γ µ0 MS
Sylvain D. Brechet - EPFL
kT =
Magnetic Seebeck Effect
λ n kB
∇T
µ0 MS2
Theoretical prediction
Magnetisation waves propagation (YIG) :
Magnetostatic backward volume modes
m(0)
Cold to Hot
−1
Cold to Hot : negative thermal damping (kT · k
k-1
< 0)
B0
k-1
Hot to Cold : positive thermal damping (kT · k−1
m(τ)> 0)
YIG
x
y
k T ∝∇ T
m(0)
k-1
Cold to Hot
m(0)
B0
k-1
m(τ)
YIG
x
y
k T ∝∇ T
m(0)
z
m(τ)
YIG
k T ∝∇ T
Hot to Cold
Sylvain D. Brechet - EPFL
Hot to Cold
k-1
k-1
Magnetic Seebeck Effect
z
B0
Transmission measurement of magnetisation waves
RF pulse
generator
Crystal
detector
Amplifier
Oscilloscope
Antennae
Peltier
element
B1
YIG
B0
Cu
Excitation frequency : 4 GHz
Distance between antennae : 8 mm
Thickness : 25 µm
Temperature gradient : 20 K /cm
Sylvain D. Brechet - EPFL
Magnetic Seebeck Effect
Magnetic Seebeck Effect (YIG slab at 4 GHz)
6.0
kT· k-1 < 0
4.0
86
Cold to Hot
84
kT· k-1 > 0
2.0
B0 (mT)
82
1.0
80
0.8
78
0.6
76
0.4
74
-20
0
20
40
60
-20
86
84
0
20
40
60
80
100
120
140
80
Time (ns)
Time (ns)
100
160
Hot to Cold
120
140
160
kT· k-1 < 0
2.0
kT· k-1 > 0
B0 (mT)
82
1.5
80
78
1.0
76
74
0.5
74
Sylvain D. Brechet - EPFL
76
78
Magnetic Seebeck Effect
80
B0 (mT)
82
84
86
Conclusion (Phys. Rev. Lett. ...)
Evidence for a Magnetic Seebeck Effect
Propagation of magnetisation waves from cold to hot
⇒ less attenuation
m(0)
Cold to Hot
Propagation of magnetisation waves from hot to cold
⇒ more attenuation
k-1
k-1
m(τ)
−1
Effect on propagation of magnetisation waves
∝k
YIG
x
y
k T ∝∇ T
m(0)
k-1
Cold to Hot
m(0)
B0
k-1
m(τ)
YIG
k T ∝∇ T
x
y
z
Hot to Cold
m(0)
Sylvain D. Brechet - EPFL
m(τ)
YIG
k T ∝∇ T
Magnetic Seebeck Effect
THANK YOU
z
Hot to Cold
k-1
k-1
B0
B0
Conclusion (Phys. Rev. Lett. ...)
Evidence for a Magnetic Seebeck Effect
Propagation of magnetisation waves from cold to hot
⇒ less attenuation
m(0)
Cold to Hot
Propagation of magnetisation waves from hot to cold
⇒ more attenuation
k-1
k-1
m(τ)
−1
Effect on propagation of magnetisation waves
∝k
YIG
x
y
k T ∝∇ T
m(0)
k-1
Cold to Hot
m(0)
B0
k-1
m(τ)
YIG
k T ∝∇ T
x
y
z
Hot to Cold
m(0)
Sylvain D. Brechet - EPFL
m(τ)
YIG
k T ∝∇ T
Magnetic Seebeck Effect
THANK YOU
z
Hot to Cold
k-1
k-1
B0
B0