This document provides an overview of nanomagnetism and the key developments in the field over time. It discusses early experiments and models from Einstein, de Haas, Heisenberg, and others. Key concepts covered include magnetic anisotropy, superparamagnetism, quantum tunneling of magnetization, and magnetic deflagration. Experimental work is highlighted from various researchers, including observations of quantum steps in microwave absorption and avalanches in Mn-12 acetate.

1. NANOMAGNETISM
Javier Tejada
University of Barcelona

2. Earth Magnetic Magnetotactic
Field Bacterium

3. Einstein – de Haas Effect - 1915
  
J = L + S = const
Change in the magnetic
moment of a freely
suspended body causes
mechanical rotation
necessary to conserve the
total angular momentum

4. 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.”
Einstein - de Haas (Berlin, 1916) :
M mech = λM magn = −1.11×10 −7 (1 ± 0.1) M magn
2mc
= −1.13 ×10 −7
e
Correct result (1920s) :
mc
M mech = M magn = −0.57 × 10 −7 (1 ± 0.1) M magn
e

5. Exchange interaction
− − S =0 S =1
+ Hydrogen molecule +

ˆ 2
ˆ
p12 + p2 1 qi q j  
ˆ =
Η + ∑   ˆ ˆ ˆ
Dirac (1926) : Η eff = − Js1 ⋅ s2
2me 2 ij 4πε 0 | ri − rj |
ˆ = − 1 ∑J s ⋅s
Heisenberg (1926) : Η
 
ˆ ˆ
ij i j
2 〈i≠ j〉
ferromagnetism antiferromagnetism ferrimagnetism

6. 
ˆ ˆ
ˆ = J ∑S S
H i k
ik
J > 0 (AFM) Classical spins : Energy = - JS N
2
Transition from vectors to vector matrices :
Quantum spins - solution is known only in 1D and
 
ˆ
only for S = 1 / 2 (S = σ / 2) Bethe - 1932 :
2
1
Energy = - J  N (1 + 4 ln 2 − 2)
2

7. Magnetic Anisotropy
   
B =v×E
E
ˆ  
ˆ
 Η local = − ge µB s ⋅ B
v
ˆ
Η A = bαβ sα sβ + cαβγδ sα sβ sγ sδ + ...
2 4
v v
bαβ ∝   , cαβγδ ∝  , ...
c c
Uniaxial : ˆ
Η A = − DS z2
Biaxial : ˆ
Η A = − DS z2 + E ( S x2 − S y )
2
Cubic : ˆ [ ]
Η A = C {S x2 , S y } + {S x2 , S z2 } + {S y , S z2 }
2 2

9. Small particles
Eex ~TC ~ 600 K
K~10 4 − 2 ⋅106 erg/cm 3
Distribution of sizes

10. Superparamagnetism 
M
single - domain 
H
magnetic particle
3nm Cobalt
H y / 2 + H z3 / 2 = H A/ 2
3 3
M
⇒
H
Array of particles in a solid

11. FC and ZFC Magnetization Curves

12. Free Rotors – Rotational Doppler Effect
ω ' = ω ± Ω, Ω = L/I
Is quantization of L detectable?

13. Free Rotors - Experiment (Tejada et al., 2010)

14. Quantum Steps in the Microwave Absorption

15. Magnetic bistability of Mn12 acetate :
[Mn12 O12 (CH 3COO)16 (H 2 O) 4 ] ⋅ 2CH 3COOH ⋅ 4H 2 O
1.73 nm
S = 10 1.73 nm
ˆ ˆ ˆ
Η = − DS z2 + Η ⊥ 1.24 nm
ˆ
[Η ⊥ , S z ] ≠ 0 Mn12 acetate crystal

16. ↑ ↓
0 =
1
(
2
↑ + ↓ ,) 1 =
1
2
(
↑ −↓ e )
−i∆t / 
Ψ (t ) =
1
( 0 + 1 ), Ψ (0) = ↑
2
∆ 
Ψ σ z Ψ = cos t 
 

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

18. EC and Javier Tejada (Barcelona –
Spain)

19. Milestone 22
(1996) Mesoscopic tunnelling of magnetization
Karl Ziemelis, Chief Editor Physical Sciences, Nature
28 February 2008 | doi:10.1038/nphys877

20. Resonant spin tunneling in Mn12 acetate
ˆ ˆ ˆ
Η = Η0 + Η⊥
ˆ
Η 0 = − DS z2 − gµ B S z ⋅ Bz
E
Em = − Dm − gµ B mBz
2
Sz
Em = Em′ : Bz = k ( D / gµ B )
k = −m − m′ = 0,±1,±2,...

21. Landau - Zener effect
m′ m
m m′ m′ m
m m′
W ≡ Ε m − Ε m′ m m′
W = vt Ε + − Ε − = W 2 + ∆2
Transition probability :
 π∆2 
P = 1 − exp −
 2v 

 

22. Interference of tunneling trajectories in Fe8
Bz

S

S
ˆ
Η = − DS x2 + aS z2 − gµ B S z Bz

23. k =2
∆10 k =1
k =0
Bz
1
140 mT/s
14 mT/s
0.5
2.8 mT/s
sample
S
0 T=40 mK
M/M
B
-0.5
array of SQUIDs
-1
0 0.25 0.5 0.75 1 1.25
µ 0 H(T)

24. Mn12
m = 1 to m = 2 transition: f = 0.08 THz
m = 9 to m = 10 transition: f = 0.35 THz

25. Experiment: J. Tejada, E. M. Chudnovsky, J.-M. Hernandez, R. Amigo (2003)

27. Avalanches in Mn-12 Acetate

28. Magnetic Deflagration (Chudnovsky et al - 2005)

29. 1/ 2
κ   U ( B) 
v= 
τ  exp − 
 0  2 k BT f 
 

30. Quantum Magnetic Deflagration
[Tejada et al - 2005]

31. 
with 128 Problems
Lectures on Magnetism
Lectures on Magnetism Lectures on Magnetism
with 128 Problems (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
Eugene M. Chudnovsky
magnetism of solids. In selecting the material the preference has
been given to simple mathematically rigorous models that explain
Javier Tejada
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
J. Tejada M
E. M. Chudnovsky
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
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 Rinton Press

32. Domains and domain walls

33. Topology: Magnetic Skyrmions
and Magnetic Instantons

34. GMR