hydrogen molecule tutorial magnetic phenomena in …schnack/molmag/... · 2020. 7. 27. ·...

12
APS March Meeting, Baltimore, 12 March 2006 TUTORIAL MAGNETIC PHENOMENA IN CRYSTALS OF HIGH-SPIN MOLECULES Eugene M. Chudnovsky CUNY Lehman College and Graduate School n interactio Exchange molecule Hydrogen + + ! ! ! " + + = # ij j i j i e r r q q m p p | | 4 2 1 2 ˆ ˆ ˆ 0 2 2 2 1 r r r r $% 2 1 ˆ ˆ ˆ : (1926) Dirac s s J eff r r ! " = # j i j i ij s s J ˆ ˆ 2 1 ˆ : (1926) Heisenberg r r ! " = # $ % & tism ferromagne agnetism antiferrom tism ferrimagne 0 = S 1 = S

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Page 1: Hydrogen molecule TUTORIAL MAGNETIC PHENOMENA IN …schnack/molmag/... · 2020. 7. 27. · magnetism of solids. In selecting the material the preference has been given to simple mathematically

APS March Meeting, Baltimore, 12 March 2006

TUTORIAL

MAGNETIC PHENOMENA IN CRYSTALS

OF HIGH-SPIN MOLECULES

Eugene M. Chudnovsky

CUNY Lehman College and Graduate School

ninteractio Exchange

moleculeHydrogen + +

!!

!"

++

=#ij ji

ji

err

qq

m

pp

||42

1

2

ˆˆˆ

0

2

2

2

1rr

rr

$%21

ˆˆˆ :(1926) Dirac ssJeff

rr!"=#

ji

ji

ij ssJ ˆˆ2

1ˆ :(1926) Heisenbergrr!"=# $

%&'

tismferromagne agnetismantiferrom tismferrimagne

0=S 1=S

Page 2: Hydrogen molecule TUTORIAL MAGNETIC PHENOMENA IN …schnack/molmag/... · 2020. 7. 27. · magnetism of solids. In selecting the material the preference has been given to simple mathematically

Anisotropy Magnetic

E

r

vr Bsg

EvB

Belocal

rr

rrr

!"=#

$=

ˆˆ

µ

...ˆ ++=! "#$%%$#"$%%$ sssscssbA

... ,c ,

42

!"

#$%

&'!

"

#$%

&'

c

v

c

vb ()*+()

[ ]},{},{},{ˆ :Cubic

)(ˆ :Biaxial

ˆ :Uniaxial

222222

A

222

A

2

zyzxyx

yxz

zA

SSSSSSC

SSEDS

DS

++=!

"+"=!

"=!

agnetismSuperparamM

r

H

r

particle magnetic

domain -single

solid ain particles ofArray

2/32/32/3

Azy HHH =+2001-rWernsdorfe

M

H

!

Cobalt 3nm

Page 3: Hydrogen molecule TUTORIAL MAGNETIC PHENOMENA IN …schnack/molmag/... · 2020. 7. 27. · magnetism of solids. In selecting the material the preference has been given to simple mathematically

s1990'early al.,et Sessoli :acetate Mn ofy bistabilit Magnetic 12

10 S=

!"+#=" ˆˆˆ 2

zSD

0],ˆ[ !"# zS

crystal acetate Mn12

nm 731.

nm 24.1

nm 731.

O4HCOOH2CH]O)(HCOO)(CHO[Mn 23421631212 !!

Magnetic clusters:

Mn, Mn2, Mn3, Mn4, [Mn4]2, Mn5, Mn6, Mn7, Mn8, Mn9, Mn10,

Mn11, Mn12, Mn13, Mn16, Mn18, Mn21, Mn24, Mn26, Mn30, Mn84

Fe2, Fe3, Fe4, Fe5, Fe6, Fe7, Fe8, Fe10, Fe11, Fe13, Fe17/19, Fe19

Co4, Co6, Co10

Ni4, Ni5, Ni6, Ni8, Ni12, Ni21, Ni24

Co2Gd2, Co2Dy2, Cr12, CrNi6, CrNi2, CrCo3, Fe10Na2, Fe2Ni3,

Mn2Dy2, Mn2Nd2, V15, Ho, ...

• • • • • •

S = 0, 1/2, 1, 3/2, 2, 5/2, 4, 9/2, 5, …………. 33/2

Page 4: Hydrogen molecule TUTORIAL MAGNETIC PHENOMENA IN …schnack/molmag/... · 2020. 7. 27. · magnetism of solids. In selecting the material the preference has been given to simple mathematically

Quantum Magnetization CurveJ. Friedman, M. Sarachik, J. Tejada, R. Ziolo (PRL - 1996)

Magnetization curve of Fe-8 (W. Wernsdorfer)

-1

-0.5

0

0.5

1

0 0.25 0.5 0.75 1 1.25

140 mT/s

14 mT/s

2.8 mT/s

M/M

S

µ0H(T)

T=40 mK

array of SQUIDs

B

sample

array of SQUIDs

Page 5: Hydrogen molecule TUTORIAL MAGNETIC PHENOMENA IN …schnack/molmag/... · 2020. 7. 27. · magnetism of solids. In selecting the material the preference has been given to simple mathematically

AFM dimer [Mn4]2 , S=±9/2 , Wernsdorfer et al., Nature-2002; Hill et al., Science-2003

!"+"=" ˆˆˆ0

zzBz BSgDS !""=# µ2

zBm mBgDmE µ!!= 2

acetate Mnin lingspin tunneResonant 12

zS

E

)/( : Bzmm gDkBEE µ== !

,...2,1,0 ±±=!""= mmk

Page 6: Hydrogen molecule TUTORIAL MAGNETIC PHENOMENA IN …schnack/molmag/... · 2020. 7. 27. · magnetism of solids. In selecting the material the preference has been given to simple mathematically

effectZener -Landau

m m!m!

m!m

m

m

mm!

m!

22!+="#" #+ WvtW

Wmm

=

!"!# $

:yprobabilit Transition

!!"

#$$%

& '((=

vP

h2exp1

2)

8Fein ies trajector tunnelingof ceInterferen

zzBzx BSgaSDS µ!+!="22ˆ

zB

S

r

S

r

Page 7: Hydrogen molecule TUTORIAL MAGNETIC PHENOMENA IN …schnack/molmag/... · 2020. 7. 27. · magnetism of solids. In selecting the material the preference has been given to simple mathematically

10!

zB

-1

-0.5

0

0.5

1

0 0.25 0.5 0.75 1 1.25

140 mT/s

14 mT/s

2.8 mT/s

M/M

S

µ0H(T)

T=40 mK

array of SQUIDs

B

sample

array of SQUIDs

1993-Garg:Theory

0=k

1=k

2=k

1999-Science

Sessoli &r Wernsdorfe

:Experiment

Effect of polarized microwaves on the magnetization curve of Fe-8

L. Sorace, W. Wernsdorfer, C. Thirion, A.-L. Barra, M. Pacchioni, D. Mailly, and

B. Barbara, Phys. Rev. B 68, 220407 (2003)

-10 -5 0 5 10

Energ

y

quantum number m

!M = +1h!

tunnelingh!

!M = -1

H = 0

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

0

0.119

0.151

0.190

0.237

0.256

0.320

0.458

M/M

s

µ0Hz (T)

60 mK

115 GHz

0.007 T/s

P/P0 =

Page 8: Hydrogen molecule TUTORIAL MAGNETIC PHENOMENA IN …schnack/molmag/... · 2020. 7. 27. · magnetism of solids. In selecting the material the preference has been given to simple mathematically

m = 1 to m = 2 transition: f = 0.08 THz

m = 9 to m = 10 transition: f = 0.35 THz

12Mn

Page 9: Hydrogen molecule TUTORIAL MAGNETIC PHENOMENA IN …schnack/molmag/... · 2020. 7. 27. · magnetism of solids. In selecting the material the preference has been given to simple mathematically

Avalanches in Mn-12 Acetate

CCNY Experiment – 2005, Suzuki et al.

Page 10: Hydrogen molecule TUTORIAL MAGNETIC PHENOMENA IN …schnack/molmag/... · 2020. 7. 27. · magnetism of solids. In selecting the material the preference has been given to simple mathematically

Magnetic Deflagration

Magnetic Deflagration

Page 11: Hydrogen molecule TUTORIAL MAGNETIC PHENOMENA IN …schnack/molmag/... · 2020. 7. 27. · magnetism of solids. In selecting the material the preference has been given to simple mathematically

!!"

#

$$%

&=

fBTk

BUB

)(exp)( 0''

Tt

T 2!=

"

"#

!!"

#

$$%

&'((

)

*++,

-=

fBTk

BUv

2

)(exp

2/1

0.

/

2005)September - Lett. Rev. Phys. al.,et Suzuki (Y.

acetate Mn in ondeflagrati Magnetic 12

Quantum Magnetic Deflagration

[A. Hernandez-Minguez et al, PRL – November 2005]

Page 12: Hydrogen molecule TUTORIAL MAGNETIC PHENOMENA IN …schnack/molmag/... · 2020. 7. 27. · magnetism of solids. In selecting the material the preference has been given to simple mathematically

Lectures on Magnetism(with 128 Problems)

Eugene M. Chudnovsky

Javier Tejada

!" Rinton Press

Lectu

res on

Magn

etis mw

i th 1

28 P

roblem

s

!"

Lectures on Magnetism

with 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

novs k

y

J. T

eja

da

M

H