modelling and simulation a physicist’s point of view part 2 school... · 2017-03-28 · sharvin g...
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1
Institute for Materials Research & WPI-AIMR, Tohoku UniversityKavli Institute of NanoScience, TU Delft
Modelling and Simulationa physicist’s point of view
Part 2
Who’s Afraid of YIG?
Barnett Newman, Who’s Afraid of Red, Yellow and Blue III, 1967-68
Contents
• YIG electronic and magnetic structure
• Spin Hall magnetoresistance of YIG|Pt• Spin Seebeck effect in YIG vs. GdIG
Yttrium Iron Garnet Y3(3+) Fe2
(3+) (Fe(3+)O4(2-))3
© A
.R. C
hakh
mou
radi
an
Yttrium Iron Garnet Y3(3+) Fe2
(3+) (Fe(3+)O4(2-))3
- 80 atoms & 20 moments/unit cell- ferrimagnetic insulator- Curie temperature 550 K- man-made near perfection with
Gilbert damping ~10-5
Tabuchiet al. (2014)
2
Spintronics with magnetic insulators
FINM T
T, V SMR, transverse spin Seebeck
Longitudinal spin Seebeck and Peltier effects, magnon Bose condensation
acoustic spin pumpingelectrically detected FMR
YIG band structure Jia et al., EPL (2011)
0.33eVGGAgE
1.4 eVUgE
Mixing conductance of YIG|Ag (Jia et al., 2011)
spin current absorption
Confirmed by experiments:Burrowes et al. (2012), Azevedo et al. 2012),Weiler et al. (2013) …
2 *
nm nm nmnm
eG r r
h
Sharvin
GG
2 2
Sharvinnm
nm
e eG N
h h
Spin waves in YIG
RT
(Plant, 1983)
Lars Onsager Memorial at NTNU Trondheim
Lars Onsager
The Nobel Prize in Chemistry 1968:“for the discovery of the reciprocal relations bearing his name, which are fundamental for the thermodynamics of irreversible processes”
Onsager symmetry (1931)
Xi
m mn nn
J L X linear responseiJ
generalized forcesgeneralized currents
i ii
S X J entropy creation rateIf:
ij jiL L Onsager relationsthen:
i = {mass, charge, energy, volume, (angular) momentum, …}
When time reversal symmetry is broken:
, ,ij ext i j ji extL L m H m H
1 even (charge) when variable 1 odd (spin)i i
3
Thermoelectrics
TV
T+TV+V
c
Q
V R S JJ K T
R = 1/G electrical resistanceK thermal conductanceS Seebeck coefficient Peltier coefficient= STOnsager-Thomson (Kelvin)relation
11 21
12 22
c
Q
VJ L LTJ L L
T
12 21L L Onsager reciprocity
Spin-dependent thermoelectrics
Johnson and Silsbee (1987)Hatami et al. (2009)Slachter et al. (2010)Flipse et al. (2012)
20
/ 211 / 2
/
c
s
Q
V VJ P STJ G P P ST V VJ ST P ST L T T T
F
E
E E
PGPG
spin-dependent Seebeck effectspin-dependent
Peltier effect
Contents
© Vadym Zayets
• YIG electronic and magnetic structure• Spin Hall magnetoresistance of YIG|Pt• Spin Seebeck effect in YIG vs. GdIG• Strong coupling with microwaves
SMR (Nakayama et al., 2013)
MR
PHE
Kato et al. (2004)
Ic
InGaAs
Spin current tensor, spin Hall angle
,
,
,
, ,s x
x y zs s s s s y
s z
J
JJ J J J
J
,ˆ
s SH c J J
xsJ
,s xJ
polarization of current x
current direction of polarization x
ˆc SH s
J J
4
3D spin Hall effect
ˆ ˆ ˆ1/ 2ˆ 1 0 0/ 2ˆ 0 1 0
ˆ 0 0 1 / 2
c SH SH SHx
sxs SHNy
sys SHzs SH sz
x y zVxVy
z V
Ejjjj
Onsager reciprocity in the spin Hall effect
spin Hall effect inverse spin Hall effect
Heterostructure
m
N FI
Exchange spin transfer torque
m
N FI
0FsI
Absorbed spin current = spin-transfer torque
2
2Re
2NS N N
F N N
Ge
Area k
IL
spin-mixing conductance
2 *
nm nm nmnm
eG r r
h
0NsI
A switchable mirror for spins
perfect mirror
*efficient absorber
Ferromagnetic insulator
F
Detection of spin current mirror
F
* 0, ˆz
s y SH cj j y SHE
SHE + ISHE
zx
5
Contents
• YIG electronic and magnetic structure
• Spin Hall magnetoresistance of YIG|Pt• Spin Seebeck effect in YIG vs. GdIG
(Longitudinal) spin Seebeck effect
Uchida et al. (2010/2011)
V [
V]
≠ spin-dependent Seebeck effect!
Spin currents cause magnetization motion(spin transfer torque, Slonczewski, 1996).
Spin torque and spin pumping
Magnetization motion causes spin currents (spin pumping, Tserkovnyak, 2002).
Onsager reciprocals(Brataas et al., 2011)
G~
© Kajiwara et al.
FM N
Noise-induced spin currents
Foros et al. (2005)Xiao et al. (2009)
FM N
Noise-induced spin currents
Xiao et al. (2010)Adachi et al. (2011)
pump J-N noise M es s s F NJ J J g T T
Spin Seebeck Onsager matrixTF
sV
TN
Q
sJJ
effM H
heat conductancespin Peltier effect
eff
/ 2/
mm ms mQ
sm ss sQ s
Qm Qs QQ Q
s
zL L L HL L L V
T TL LJM
LJ
thermal fieldspin Seebeck effect
magnon Peltier effect
ijL spin-spin correlation functions at the interface
6
Spin Peltier effect (Flipse et al., 2014)Pt (5 nm)
JQ JQ
YIG (200 nm)|GGG
200 m
VSPE
1st harmonic signals
Magnon transport
Corn
eliss
en e
t al.
(201
5)
(also Kajiwara et al. (2010))
RE-IG
Electroceramics: Materials, Properties, Applications, by A.J. Moulson & J. M. Herbert (Wiley, 2003) .
YIGGdIG
Geprägs et al. (2015)
Ohnuma et al. (2013)
Spin Seebeck effect and spin correlation
interface
, ,
, ,s
s
t tMJ V dt t
s ρ s ρρ
s ρ h ρ
, , ', 'ij i jS s t s t k r rFt
Spin-spin correlation power spectra: Equal time and position spin correlation function
Nxi ij i j
j iE J
S S
effi i i i i i S S B S S eff i
i ii
E t
B b
S
2 ik l kli
B
ib t b t tT t
Mk
Atomistic spin simulations:
Rare Earth Iron Garnets → GdIG
J. Barker (2015)
2
3 3
3
7
Geprägs et al. (2015)
H