Dhanesh Rajana and Jukka Lekkalab

a,b Department of Automation Science and Engineering,Tampere University of Technology, Finland

“Coercivity weighted Langevin magnetisation: A new approach to interpret superparamagnetic and nonsuperparamagnetic behaviour in single domain magnetic nanoparticles” 

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 ?

MR - remanence MS - saturation magnetisation

-- Ferromagnetism

Hc - coercivity

MH susceptibility,

M - magnetisation (A/m)

H - applied field (A/m)

-- Ferromagnetism -- Paramagnetism

MS - saturation magnetisation

MH susceptibility,

M - magnetisation (A/m)

H - applied field (A/m)

-- Ferromagnetism -- Paramagnetism -- Superparamagnetism (SPM)

MS - saturation magnetisation

M - magnetisation (A/m)

H - applied field (A/m)

Super-paramagnetism (SPM) SPM >> PM

-- Superparamagnetism (SPM)

MS - saturation magnetisation

M - magnetisation (A/m)

H - applied field (A/m)

MR (remanence ) =0

Langevin approach

Super-paramagnetism (SPM) SPM >> PM

-- Superparamagnetism (SPM) -- A few application areas..

Functionalised particles , Drug delivery and gene transfectionSeparation: 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

-- Motivation (1/2) When, What factors actually determine SPM behaviour

SPM

SD

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 superparamagnetic nanoparticles for MPI S.Biederer, T Knopp et al. J. Phys. D: Appl. Phys. 42

Tomographic imaging using the nonlinear response of magnetic particles B. Gleich & J.Weizenecker, Nature Letter 435, 1214-1217

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:- 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.

-- Motivation (2/2) When, What factors actually determine SPM behaviour

Langevin approach

-- Results

20

72s

SDKA

Md

36

2b

SPMk T

Kd

Table 1: Anisotropy and crystalline parameters defining SD and SPM critical diameters at 300K

Single domain critical diameter dSD, superparamagnetic diameter dSPM as a function of temperature for magnetite and maghemite particles

[Check the article references]

1

2

1 lnm

O

bc co

k TH H

KV

where 1/m is measurement frequency. 1/o is attempt frequency characteristicto 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.

-- Results

3

0

6 b

s x

eff

M d H Hc

k T

The magnetisation plots for a) SD magnetite and b) SD maghemite particles at different temperatures. Two diameters 10% above and below the critical dSPM are considered. (For computations, f = 10Hz, particle concentration = 0.1mmol/L, suspension medium = distilled water)

2 2 2 2

1 1 1coth( cos ) coth( sin )

1 cos 1 sineff

AC s eff effeff eff eff eff

M M t tt t

-- Results

21coth ( ) 1

eff eff

effsDC eff

eff

MH H

22 2

1' coth ( ) 11 eff eff

s effeff

eff eff

M

w H H

22 2

1'' coth ( ) 11 eff eff

s effeff

eff eff

w M

w H H

The ʹ and ” plots for SD- SPM and SD- nonSPM particles for magnetite and maghemite at different frequencies.

ʹ versus T curve for magnetite for a given SPM diameter

The cusp observed in experimental ʹ versus T plots

-- Results

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.

-- Conclusions

For more details please check the conference article...

Thank you !Questions ??