scaling relations and magnetic properties of nanoparticles

8/14/2019 Scaling relations and magnetic properties of nanoparticles

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Scaling relations and magneticproperties of nanoparticles

Universidade Federal do Rio de JaneiroInstituto de Fsica

Jos dAlbuquerque e Castro

PAN AMERICAN ADVANCED STUDIES INSTITUTEUltrafast and Ultrasmall; New Frontiers and AMO Physics

March 30 - April 11, 2008


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polycrystalline alloys of Co, Cr, and Ptwith B or Ta

segregation of the non-magnetic elements:reduction of the coupling between grains

net magnetization

grain size 10 nm

Problem:superparamagnetism limit

100 Gbit in -2

areal density: 50 Gbit in -2 ( year 2000)

Magnetic storage media: thin films


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Superparamagnetism

m

magnetic particle

energy barrier E B


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Superparamagnetism

m

magnetic particle

energy barrier E B


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Superparamagnetism

volume: V net anisotropy: K

m energy barrier for reversal: E B = KV

rate of switching: 1/ = f 0 exp(- E B /kT)

f 0 10 9 s-1

storage time 10 years E B ~ 40 kT


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Patterned thin films

Nanoimprint lithography

arrays of circular nanomagnets

cylinders with diameter D and height H

5 nm H 150 nm

50 nm D 500 nm Lebib et al., JAP 89, 3892 (2001)


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particles cannot accommodate a domain wall

patterned thin films as recording media

200-260 Gbit in -2

Patterned thin films

grains within particles are strongly coupled

1 Tbit in-2

periodicity 25 nm

(periodicity 50 nm)


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R. P. Cowburn et al. , Phys. Rev. Lett 83, 1042 (99)


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A. Lebib et al. , J. Appl. Phys. 89, 3892 (01)

MFM

vortex

single-domain


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R. P. Cowburn et al. , Phys. Rev. Lett. 83, 1042 (99)

experimental phase diagram

R. P. Cowburn et al. , Phys. Rev. Lett. 83, 1042 (99)


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IIIIII

in-plane out-of-plane vortex

Configurations

core


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Theoretical approach

E ij = classical dipolar interaction

i = magnetic moment on site i

J ij = exchange coupling

K = anisotropy constant

{ 1, 2, 3} = angles between i and theprincipal (easy) crystalline axes

i

configuration of lowest energy ?


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For smaller systems ( e.g. N ~ 10 6)

single domain configurations only Reason: strength of the exchange interaction J

Scaling approach

J. dA. e C., D. Altbir, J. C. Retamal, and P. Vargas, Phys. Rev. Lett. (2002)

J = x J with x < 1


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x = 0.04


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x = 0.04 x = 0.06


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x = 0.04 x = 0.06

x = 0.08


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x = 0.04 x = 0.06

x = 0.08

x = 0.10


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triple point


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H t (x) = H t (1) x with = 0.55


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Scaling relations

H(1) = H(x) / x

D(1) = D(x) / x

J = x J

From the relation

H t (x) = H t (1) x H t (1) = H t (x)/ x

we expect to find


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Truncated conical particles

C. A. Ross et al., Phys. Rev. B 62, 14252 (2000)

C. A. Ross et al., J. Appl. Phys. 89, 1310 (2001)


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= 0.3

x = 0.010

x = 0.015

x = 0.020

J. Escrig, P. Landeros, J.C. Retamal, D. Altbir, and J. dA. C., Appl. Phys. Lett. (2003)

Calculation for Ni particles


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= 0.3

= 0.55

Calculation for Ni particles

J. Escrig, P. Landeros, J.C. Retamal, D. Altbir, and J. dA. C., Appl. Phys. Lett. (2003)


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Important point: value of

Scaling relations for magnetized nanoparticles P. Landeros, J. Escrig, D. Altbir, D. Laroze, J. dA.C., and P. Vargas Phys. Rev. B 71, 094435 (2005)

value of may depend on the model for the magneticconfigurations!

vortex core

model for the core


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Fast Monte-Carlo method

http://www.ctcms.nist.gov/~rdm/mumag.org.html

Fast Monte-Carlo method for magnetic nanoparticles P. Vargas, D. Altbir and J. d'Albuquerque e Castro Phys. Rev. B, 73, 092417 (2006)

Could we combine the scaling technique and theMonte-Carlo method?

Single domain limit:size L for which the flower and vortex states haveequal energy.


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Mag group (NIST)

L 8 l ex where l ex = (2A/ 0 M 0 )1/2

Co: l ex = 3.6 nm a 0 = 0.2 nm J 0 =2.35 x10 3 kOe/ B

L 29 nm and N 3x10 6 atoms !

A = exchange stiffness constant J


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For given L (small): Monte-Carlo J

Calculations: L 1 = 5 a 0 x 1 = 2.240 10 -3

L 2 = 7 a 0 x 2 = 4.125

10-3

L 3 = 9 a 0 x 3 = 6.509 10 -3

x = J/J 0 L = L/ x

?


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Results

L = 8.02 l ex = 0.551

Conclusion

It is possible to combine the Monte-Carlo methodwith the scaling technique

fast and reliable method for investigatingthe equilibrium properties of magnetic nanoparticles

scaling relations and magnetic properties of nanoparticles

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