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

qq

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