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1
Magnetic Insulators(with emphasis on YIG)
ESM 2015, Gerrit Bauer, Part II
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)
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
2
Spin waves in insulators Spin waves in YIG
RT
(Plant, 1983)
Contents
Magnon-phonon coupling
© Vadym Zayets
[Spin Mechanics 4 in Banff (Ca), Feb. 2017]
Magnetoelastic coupling
- thermalization of lattice and spin- magnon-phonon drift- magnon-polarons (Kittel, 1958)
Dynamic effects of magnon-phonon interaction
Magnon-polarons
Kamra et al. (2015)
3
Magneto-polaron propagation (Shen, 2015)
Satoh et al. (2012)
Excitation by – Inverse Faraday effect– Heat
Detection by – Faraday or Kerr rotation
Femto-second optical excitation
Hashimoto et al. (unpublished).
Magneto-polaron propagation (Shen, 2015)
pumpprobe
xLine source excitation with IFE.
W
1 m spot excitation 5 ns coda
inverse Faraday excitation
Magneto-polaron propagation (Shen, 2015)
1 m spot excitation 5 ns coda
pressure wave excitation
Magneto-polaron propagation (Shen, 2015)
1 m spot excitation 5 ns coda
Shear deformationexcitation
Magneto-polaron propagation (Shen, 2015)
Strong coupling with microwaves
4
0B
1( ) i trfH t H e
0.1 meVFMR B B T
“precession cone”~ intensity of rf
~
r
0 0.01 in bulk metals, ~10-5 in best YIG
FerroMagnetic Resonance
m
Landau-Lifshitz-Gilbert equation; Gilbert damping constant
eff m m B m
Thin films in microwave cavities
Cao et al. (2015)Bai et al. (2015)
spin wave resonance electric readout
Ultra strong coupling with microwaves
Zhang et al.(2014)
Rameshti et al. (2015)[spherical cavity]
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
Contents
Spin Hall magnetoresistance
SMR (Nakayama et al., 2013)
MR
PHE
5
SMR vs. AMR (out of plane magnetization),
N
IF
x
yz
Nd
cj
0z N
IF
x
yz
Nd
cj
0z
SMR = 0
02SMRym 2AMR
xA m
AMR = 0
x
yz
cj
x
yz
cj
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
6
Spin Caloritronics 4
SPIN
CALO
RITR
ON
ICS
VI
Spin Caloritronics VII, Utrecht, The Netherlands, 11-15 July 2016
Spin Caloritronics
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 conductance
=T=0
F N
0
20 0 0 0 0
1 /1 /
/
c c
s s
Q
J P ST eJ G P P ST eJ ST P ST L T T T
F
E
E E
PGPG
,T ,T
spin-dependent Seebeck effect
spin-dependent Peltier effect
Landauer-Büttiker formalism (Butcher, 1990)
0
2
2
2
2222
0
2
2
2F
F
B F
B
B F
B
E
g E
g E
g E
eG dEh E
k E EeGS dEh e E k
g E
G EeLT
f
fT
k E EeS G dET h e E k T
E
S Gf LT
,
2n m E
nmnmg E t
nmt transmission amplitude
total transmission probability n
m
,f E T Fermi-Dirac function
Enhanced spin Seebeck effect
Hu e
t al.
(201
4)
V V72 22K Ks cS S
1P
Contents
Spin Seebeck effect in YIG
7
(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~
Collinear spin configuration
m
N F
0FsI N
sI
Spin current conversion
m
N F
0FSI N
sI
Spin current conversion
m
N F
0FSI N
sI
Small angle spin transfer
magnon creation
magnon annihilation
8
© 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
Spin Peltier effect (Flipse et al., 2014)Pt (5 nm)
JQ JQ
YIG (200 nm)|GGG20
0 m
VSPE
1st harmonic signals
Magnon transport
Corn
eliss
en e
t al.
(201
5)
(also Kajiwara et al. (2010)) Contents
Spin Seebeck effect in GIG
9
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
J. Barker (2015)
GdIG spin wave power spectrumand chirality.
Geprägs et al. (2015)
H
10
CollaboratorsSendaiOleg TretiakovAdam CahayaTakahiro ChibaSaburo TakahashiJoe Barker
DelftPeng YanYunshan CaoAkashdeep KamraYaroslav BlanterKa ShenYang Zhou
EuropeRembert DuineArne BrataasHans SkarsvågPaul Kelly
SendaiEiji SaitohDazhi HouHiroyasu NakayamaKoki TakanashiKenichi UchidaSubrojati Bosu
GermanyStefan GeprägsSebastian GönnenweinMathias AlthammerMichael SchreierMathias Kläui
AsiaKe XiaJiang XiaoBabak Zare RameshtiHedyeh KeshtgarSadamichi MaekawaYanting Chen
GroningenBart van WeesJoost FlipseFasil DejeneNynke Vlietstra
AmerikasYaroslav TserkovnyakAxel HoffmannIsaac Acosta