Upload
oriolespinal
View
563
Download
2
Tags:
Embed Size (px)
Citation preview
NANOMAGNETISM
Javier Tejada
University of Barcelona
Earth Magnetic Field Magnetotactic Bacterium
Einstein – de Haas Effect - 1915
constSLJ
momentumangular total
theconserve tonecessary
rotation mechanical
causesbody suspended
freely a ofmoment
magnetic in the Change
Einstein in a letter to a student, May 31,1915, (quoted by K. Selig): “Any boy could do the work on magnetism, but the general theory of relativity is quite a different matter.”
magnmagnmech
magnmagnmech
MMe
mcM
e
mc
MMM
)1.01(1057.0
:(1920s)result Correct
1013.12
)1.01(1011.1
:1916) (Berlin, Haas de -Einstein
7
7
7
ninteractio Exchange
moleculeHydrogen
ij ji
ji
e rr
m
pp
||42
1
2
ˆˆˆ
0
22
21
21ˆˆˆ :(1926) Dirac ssJeff
jiji
ij ssJ ˆˆ2
1ˆ :(1926) Heisenberg
tismferromagne agnetismantiferrom tismferrimagne
0S 1S
)22ln41(2
1J- Energy
:1932 - Bethe )2/ˆS( 2/1for only
and 1Din only known issolution - spins Quantum
:matrices vector to vectorsfrom Transition
NJS- Energy :spins Classical (AFM) 0
ˆˆ ˆ
2
2
N
S
J
SSJHik
ki
Anisotropy Magnetic
E
v Bsg
EvB
Belocal
ˆˆ
...ˆ sssscssbA
... ,c ,42
c
v
c
vb
},{},{},{ˆ :Cubic
)(ˆ :Biaxial
ˆ :Uniaxial
222222A
222A
2
zyzxyx
yxz
zA
SSSSSSC
SSEDS
DS
Small particles
Distribution of sizes
364 10210
600
erg/cmK~
K~~TE Cex
agnetismSuperparamM
H
particle magnetic
domain -single
solid ain particles ofArray
2/32/32/3Azy HHH
M
H
Cobalt 3nm
FC and ZFC Magnetization Curves
Free Rotors – Rotational Doppler Effect
?detectable L ofon quantizati Is
L/I ,'
Free Rotors - Experiment (Tejada et al., 2010)
Quantum Steps in the Microwave Absorption
:acetate Mn ofy bistabilit Magnetic 12
10 S
ˆˆˆ 2zSD
0],ˆ[ zS crystal acetate Mn12
nm 731.
nm 24.1
nm 731.
O4HCOOH2CH]O)(HCOO)(CHO[Mn 23421631212
t
t
e
z
ti
cos
)0( , 102
1)(
2
11 ,
2
10 /
Quantum Magnetization Curve J. Friedman, M. Sarachik, J. Tejada, R. Ziolo (PRL - 1996)
EC and Javier Tejada (Barcelona – Spain)
Milestone 22
(1996) Mesoscopic tunnelling of magnetization
Karl Ziemelis, Chief Editor Physical Sciences, Nature28 February 2008 | doi:10.1038/nphys877
ˆˆˆ0
zzBz BSgDS 20
ˆ
zBm mBgDmE 2
acetate Mnin lingspin tunneResonant 12
zS
E
)/( : Bzmm gDkBEE
,...2,1,0 mmk
effectZener -Landau
m m m
mm
m
m
mm
m
22 WvtW
W mm
:yprobabilit Transition
vP
2exp1
2
8Fein ies trajector tunnelingof ceInterferen
zzBzx BSgaSDS 22ˆ
zB
S
S
10
zB
-1
-0.5
0
0.5
1
0 0.25 0.5 0.75 1 1.25
140 mT/s14 mT/s2.8 mT/s
M/M
S
µ0H(T)
T=40 mK
array of SQUIDs
B
sample
array of SQUIDs
0k
1k
2k
m = 1 to m = 2 transition: f = 0.08 THz
m = 9 to m = 10 transition: f = 0.35 THz
12Mn
Experiment: J. Tejada, E. M. Chudnovsky, J.-M. Hernandez, R. Amigo (2003)
Avalanches in Mn-12 Acetate
Magnetic Deflagration (Chudnovsky et al - 2005)
fBTk
BUv
2
)(exp
2/1
0
Quantum Magnetic Deflagration [Tejada et al - 2005]
Lectures on Magnetism(with 128 Problems)
Eugene M. ChudnovskyJavier Tejada
Rinton Press
Lectu
res on M
agnetism
with 128 P
roblems
Lectures on Magnetismwith 128 Problems
This book is intended as a compact one-semester course for graduate and upper-level undergraduate students. It teaches basic language and ideas that are used by researchers working in the field of magnetism of solids. In selecting the material the preference has been given to simple mathematically rigorous models that explain magnetic phenomena qualitatively. The book consists of three chapters, twenty four sections; each section being accompanied by homework problems. Magnetism at the nanometer scale of individual atoms and molecules is discussed in the first chapter. Magnetic order at the mesoscopic scale of many interacting atoms and itinerant electrons is studied in the second chapter. Magnetism at the macroscopic scale of magnetic domains is considered in the third chapter. The chapters are connected through demonstration of the fact that same magnetic phenomena can be looked at from different angles and described by models that use different techniques. The book should be useful for students who plan to work in condensed matter physics and material science. It can also be of interest to students specializing in other fields because many ideas and methods initially developed to describe magnetism of solids subsequently entered other areas of physics.
Visit Rinton Press on the World Wide Web at: http://www.rintonpress.com
E. M
. Ch
ud
novsk
yJ. T
ejada
M
H
Domains and domain walls
Topology: Magnetic Skyrmions and Magnetic Instantons
GMR