coercivity weighted langevin magnetisation: a new approach to interpret superparamagnetic and...
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http://www.citeulike.org/user/ase_tut_finland/article/12017420TRANSCRIPT
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 ??