http://www.citeulike.org/user/ase_tut_finland/article/12017420

1. “Coercivity weighted Langevin magnetisation: A new approach to
interpret superparamagnetic and nonsuperparamagnetic behaviour in
single domain magnetic nanoparticles”
Dhanesh Rajana and Jukka Lekkalab
a,b
Department of Automation Science and Engineering,
Tampere University of Technology, Finland

2. Presentation Outline
Introduction
A few words on…
Coercivity weighted Langevin magnetisation: A new approach to
interpret superparamagnetic and nonsuperparamagnetic behaviour
in single domain magnetic nanoparticles
Motivation for this work
Results
How is it useful ?

3. -- Ferromagnetism
MR - remanence MS - saturation magnetisation
susceptibility, χ = M H
M - magnetisation (A/m)
Hc - coercivity
H - applied field (A/m)

4. -- Ferromagnetism
-- Paramagnetism
MS - saturation magnetisation
susceptibility, χ = M H
M - magnetisation (A/m)
H - applied field (A/m)

5. -- Ferromagnetism
-- Paramagnetism
-- Superparamagnetism (SPM)
MS - saturation magnetisation
χ SPM χ PM Super-paramagnetism (SPM)
M - magnetisation (A/m) >>
H - applied field (A/m)

6. -- Superparamagnetism (SPM)
MS - saturation magnetisation
MR (remanence ) =0
χ SPM χ PM Super-paramagnetism (SPM)
M - magnetisation (A/m) >>
H - applied field (A/m)
Langevin approach

7. -- Superparamagnetism (SPM)
-- A few application areas..
 Functionalised particles , Drug delivery and gene transfection
Separation: Cell, DNA, protein, RNA fishing
 As contrast agent in MRI (magnetic resonance imaging ) & (MRA)
magnetic resonance angiography
 Ferrofluid (magnetic fluid) & Sensors
 Hyperthermia treatment
 MPI (magnetic particle imaging)
Tomographic imaging using the nonlinear response of magnetic
particles, Nature 435, Bernhard Gleich & Jürgen Weizenecker

8. -- Motivation (1/2)
When, What factors actually determine SPM behaviour
Magnetic particle imaging using a field free
line J. Weizenecker, B. Gleich and J. Borgert,
J. Phys. D: Appl. Phys. 41
Magnetisation response spectroscopy of
SD superparamagnetic nanoparticles for MPI S.Biederer,
T Knopp et al. J. Phys. D: Appl. Phys. 42
SPM
Tomographic imaging using the nonlinear response of magnetic particles
B. Gleich & J.Weizenecker, Nature Letter 435, 1214-1217

9. -- Motivation (2/2)
When, What factors actually determine SPM behaviour
 SPM particles are SD particles but not all SD particles are SPM particles
 The SPM behaviour depends on a few parameters including
material type, temperature, time period & magneto crystalline
anisotropy
 There can be remanence and coercivity in SD regime (= can act like
ferromagnetic)
 Limitation of classical Langevin equations:- Langevin approach
Its applicability is limited to pure SD-SPM
behaviour; Lacks parameters to predict
remanence and coercivity in SD regime.
 To solve this issue, we propose a new model by modifying the classical
Langevin equations.

10. -- Results
KA
dSD = 72
µ 0 Ms 2
6kbT
dSPM = 2 3
K
[Check the article references]
Single domain critical diameter dSD, superparamagnetic diameter dSPM as a
function of temperature for magnetite and maghemite particles
Table 1: Anisotropy and crystalline parameters defining SD and SPM critical diameters at 300K

11. -- Results
 1

 kbT  τ m   2 
Hc = Hco 1 −  ln
  KV  τ O ÷÷ 
 
 
where 1/τm is measurement frequency.
1/τo is attempt frequency characteristic
to material
Coercivity as a function of particle diameter a) at different temperatures and b) at different field
frequencies. The zero coercivity corresponds to the superparamagnetic transition which is clearly a
function of temperature (blocking temperature) and measurement frequency.

12. -- Results
 1  1  ωτ eff  1 
MAC = φ Ms   coth(α eff cos ωt ) − ÷+  coth(α eff sin ωt ) − ÷
1 + ω τ eff
2 2  α eff cos ω t ÷ 1 + ω 2τ eff
2  α eff sin ω t ÷
    
πµ Msd
3
(H x ± Hc )
α eff =
0
6k T b
The magnetisation plots for a) SD magnetite and b) SD maghemite particles at different
temperatures. Two diameters 10% above and below the critical d SPM are considered. (For
computations, f = 10Hz, particle concentration = 0.1mmol/L, suspension medium = distilled water)

13. -- Results
 1 α 
χ DC = φ Ms  − eff ( coth 2 (α eff ) − 1) 
 α eff Heff Heff
 

φ Ms  1 α 
χ'=  − eff ( coth 2 (α eff ) − 1) 
1 + w2τ eff
2
 α eff Heff Heff
 

wτφ Ms  1 α eff 
χ '' =
1 + w2τ eff
 − ( coth 2 (α eff ) − 1) 
The χʹ and χ” plots for SD- SPM and SD- nonSPM particles for
 α eff Heff Heff
2
 

magnetite and maghemite at different frequencies.
The cusp observed in experimental χʹ
versus T plots
χʹ versus T curve for magnetite for a given SPM diameter

14. -- Conclusions
 The new model
1) Combines steady / time varying magnetisation dynamics and
considers all known factors affecting the SPM state
2) Directly calculates coercivity compensated magnetisations
and susceptibilities.
3) Covers full spectrum of SD diameters
4) Defines the switching between SPM and non-SPM (= can act
like ferromagnetic) states more accurately.
 Direct calculation of coercivity weighted magnetisation and susceptibility
would be helpful in biomedical areas where magnetic particles have been
used for eg. calculating magnetisation dependent voltage, magnetisation
dependent polarisation, magneto optic effect etc.
 Further work: Next stage : inclusion of ‘log normal diameter distribution’ of
particles to accommodate polydispersity, and validation experiments.

15.  For more details please check the conference article...
Thank you !
Questions ??