Introduction to nanomaterials Magnetic properties H.Hofmann 2009

Chapter treated • 8.1 Introduction – 8.1.1 – 8.1.2

Concept Phenomena

• Magnetic Properties of small atom cluster – 8.2.1 – 8.2.2

Introduction Size dependents

• Small Particle Magnetism – 8.3.1 – 8.3.2 – 8.3.3

Classification of magnetic nanomaterials Anisotropy Single domain particles

• 8.5 Giant Magneto Resistance • 8.6 Storage devices

Magnetism The basic magnetic properties of a material are often described by a “B-H curve.” (B Magnetic flux density or mag. Induction (Gauss or Tesla), H Magnetic field strength (Oe or A/m) Materials either slightly reject magnetic fields (diamagnetism) or reinforce them (paramagnetism). A limited set of materials (Fe,Co,Ni,Gd and some transition metal oxides) exhibit ferromagnetism, i.e. spontaneous alignment of atomic spins.

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Magnetism

Field

Balance (a ) P a r a m a g n e tic D i s o r d e r e d s p in ( 2 D )

Force, F

( b ) F e r r o m a g n e t ic O rd e r e d (a lig n ) s p in (2 D )

Magnetic Material

( c ) A n t if e r r o m a g n e t ( d ) F e r r im a g n e t O r d e r e d ( o p p o s e d ) s p in s ( 2 D )

F= VχH dH/dx µ= 1+4πχ ( e ) C a n te d a n tife r ro m a g n e ts o r w e a k fe r r o m a g n e t ( 2 D )

χ= Susceptipility µ= Permeability

χ < 1 : Diamagnetic χ> 1 Paramagnetic χ>> 1 Ferromagnetic, Ferrimagnetic

(a) The ferromagnetic hysteresis M-H loop showing the effect of the magnetic field on inductance or magnetization. The dipole alignment leads to saturation magnetization (point 3), a remanance (point 4), and a coercive field (point 5). (b) The corresponding B-H loop. Notice the end of the B-H loop, the B value does not saturate since B = µ0H + µ0M. (Source: Adapted from Permanent Magnetism, by R. Skomski and J.M.D. Coey, p. 3, Fig. 1-1. Edited by J.M.D. Coey and D.R. Tilley. Copyright © 1999 Institute of Physics Publishing.

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Magnetism

B= H+ 4πM where M is called the magnetisation of the material. For a material in which the magnetisation is thought to be proportional to the applied field strength we define

M

Saturation Magnetization, M s

Reminent Magnetization, M R Coercivity, Hc

M = χH

H

Combining the above two equations we get: B = H(1+4πχ) =µH Finally , we need to define the magnetic moment ,µ µm, through the following equation: M = µ m/ V that is the magnetisation is the magnetic moment per unit volume.

Metal

4π πMS (Maxwells/cm2)

Tc(K)

Fe

2.2 x 104

1043

Co

1082 x 104

1404

Gd

7.11 x 104

289

Ni

0.64 x 104

631

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Cluster and surface atoms

1

2

3

4

5 45 %

92% 100000 10000 Surface atoms (%)

Total no. of atoms

120

1000 100 10 1

100 80 60 40 20 0

0

10 20 Cluster size (nm)

30

0

5

10

15

Size of cluster (nm)

20

25

Magnetic moment per atom in units of Bohr magnetron for iron, cobalt, nickel and rodium clusters as a function of cluster size

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Fe-clusters

Ni: 550 – 600 Co : 400- 500

Magnetic moment per atom

3

2.5

Bulk Fe

2

Fe complicated behaviour (f(N, T)

Co-clusters Bulk Co

1.5 1

Ni-clusters Bulk Ni

0.5 Rh-clusters 0 0

100

200

300

400

Cluster Size (N)

500

600

700

800

Magnetic propertiesof nanostructured materials Single domain Multi domain

Hc

Super Paramagnetic

D Dc

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Blocking Temperature and Relaxation Time

τ = τ 0 .exp (CV k T ) B τ0

=10-9s, kB=106erg/cm3, and T=300K

CV TB = k B ln(τ i τ 0 )

Particles of diameter of 4 nm will have a relaxation time of 0.1 s. Increasing the particle diameter to 14.6 nm increases τ to 108s.

Application: Drug delivery, Hyperthermia, cell separation, ….

(mH ωτ ) P= 2 2  2τ k BTV (1 + ω τ )  2

1.E+11

200 MHz 1.E+10

Loss power (W/m3 Fe2O3)

20 MHz 1.E+09 1.E+08

2 MHz 1.E+07 1.E+06

200 kHz

Néel and Brownian relaxation Field amplitude 6.5 kA/m γ-Fe2O3 particles Ms = 74 Am2/kg

1.E+05 1.E+04

η= 0.001 Pa s Hydraulic radius = rparticle +10 nm

20 kHz

1.E+03 1.E+02 2

4

6

8

Particle radius (nm)

10

12

14

50

Tumor site temperature (°C)

48 46 12 mT 44 11 mT 42

10.5 mT

40

10 mT 9 mT

38 36 34 32 0

5

10

15

20

Time (min)

P.-E. Le Renard, 1 A Thermograms representing the tumor temperature as a function of time, during a single 20 min treatment in a 141 kHz alternating magnetic field for magnetic field strengths of 9 mT (n = 5), 10 mT (n = 4), 10.5 mT (n = 5), 11 mT (n = 3), 12 mT (n = 5).

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2R

S

Ferrofluids

σ ,µ ,µ

Sample Volume Electrical conductivity of particles

1.7 x 10-6 m3 σ f = 3 × 10 6 (Ω m ) −1

Electrical conductivity of ferrofluid

σ fluid < 10 −7 (Ω m ) −1

Volume percentage of particles Initial magnetic permeability of particles

3% by volume

Particle mean radius Density of magnetic particles Fluid density Fluid viscosity of carrier fluid

R10-8 m ρ = 7.8 g/cm3 ρ = 1 g/cm3 ρ =1 cp = 0.01 g/cm. sec

µ ≈ 100 µ 0

•rotary shaft seals •magnetic liquid seals, to form a seal between region of different pressures •cooling and resonance damping for loudspeaker coils •printing with magnetic inks •inertial damping, by adjusting the mixture of the ferrofluid, the fluid viscosity may be change to critically damp resonances accelerometers, •level and attribute sensors •electromagnetically triggered drug delivery

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Forces acting on a particle in a magnetic field

Fm= = 1/2 V grad( M*B) Assumptions: •the particle is free to rotate to the position of lowest potential energy, (M and B are parallel) • M is substantially constant over the particle its volume, F m= 1/2 V M δB/δ δx For the migrating particle in the Stokes regime, the opposing drag force is Fd = Π η r umag Fm : force on the particle M: inducible magnetization (paramagnetic) V: particle volume V B: mag Field r is the particle radius, u magnetic field-induced velocity, η is the viscosity.

Fd

Fm X Fg

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Velocity of a magnetic particle in a blood stream

Umag=

Vm M 12 Π η r particle

dB dx

Vm: magnetic active volume (Σ(Vcrystal –V dead layer) ) rparticle: « Stoke diameter » of the particle η of blood = 4mPa s

r

r

Vm < 0.64 Vparticle Random densed packed

Single particle Vm < 4/3 Π r3 Min. separation of the mag. particles: Diamaeter of the magnetic particle

When a external field is applied, dispersed magnetic particles are exposed to one dominant force, namely the attraction to zones of denser magnetic flux densities B:

corresponding to the energy of a magnetic particle in a magnetic field

In order to calculate the force that acts on a particle, it is important to consider the magnetic flux density of an external magnet, Be, as well as that of the other particles in the dispersion, Bp:

BE causes an orientation of the particles’ magnetic moments parallel to the magnetic field lines. Therefore the interaction between two particles with the same magnetic moment m is :

Using equation one can derive the limit between attractive and repulsing arrays. With angles β smaller than 54.7 ° (=arccos%(1/3)), particles with parallel magnetic moments are attracted, otherwise repulsed. In a „head-to-tail“-position, the attraction between two particles is maximal; in a „side-by-side“-position the repulsion is maximal.

Transport of SPION

Artificial fiber matrix of polysacharides with defined pore size model for extracellular matrix pore diffusion of nanoparticles Pluen A. et al., Biophys. J.,1999 Used concentrations: 0.25% wt, 0.2% wt -

-estimated value of z(t=t0) 2s-1 diffusion coefficient 1 · 10-7 cmz(t=t 0) z(t=t1) z(t=t2)

Diffusion coefficient, D [cm2s-1]

Agarose

rh = 20 nm

Hydrodynamic radius, rh [nm] (Pluen A. et al., Biophys. J.,1999)

20

Spintronics

An mehrlagigen Fe/Cr-Schichten entdeckte Grünberg 1986, daß sich die Magnetisierungen benachbarter Fe-Schichten bei Cr-Lagendicken um 1 nm antiparallel ausrichten. Eine weitere Entdeckung von Baibich et al. an derartigen Schichtsystemen aus ferro-magnetischen und nicht-magnetischen Metallen führte dann zur Definition des Riesenmagnetowiderstandseffektes oder GMR-Effektes ("Giant Magnetoresistance"): Wird durch ein äußeres Magnetfeld die Magnetisierung der einzelnen Lagen parallel ausgerichtet, so sinkt der elektrische Widerstand des Systems erheblich. Der GMR-Effekt ist auf spinabhängige Streuung an den Phasengrenzen - intrinsischer GMR - und an Verunreinigungen - extrinsischer GMR zurückzuführen. Bereits bei Raumtemperatur erhält man Widerstandsänderungen von bis zu 50 % bei Feldstärken von etwa 2 Tesla. Nobel Price 2007

The probability of spin-flip scattering processes in metals is normally small as compared to the probability of the scattering processes in which the spin is conserved. This means that the upspin and down-spin electrons do not mix over long distances and, therefore, the electrical conduction occurs in parallel for the two spin channels. Second, in ferromagnetic metals the scattering rates of the up-spin and down-spin electrons are quite different, whatever the nature of the scattering centers is. The band structure in a ferromagnet is is not the same for up-spin and down-spin electrons at the Fermi level. Scattering rates are proportional to the density of states, so the scattering rates and therefore resistivities are different for electrons of different spin. physics.unl.edu/.../tsymbal_files/GMR/gmr.html.

Streuung in GMR-aktiven Schichten wwwiap.physik.uni-giessen.de/ mfs/magnetfeldsensoren.htm

GMR

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cap layer AF F(pinned) cap layer

cap layer

NM

AF

F(free)

NM

F(free) NM F(pinned)

F(free) buffer layer

AF buffer layer

AF buffer layer

substrate

substrate

substrate

F(pinned)

(a)

(b)

NM F(pinned)

(c)

Schematic cross-section of a top (a), bottom (b) and a symmetric (c) exchangebiased spin-valve structure. If the current direction is parallel to the easy axis of the free F layer, the magnetoresistance is given by:

∆R(H)=

∆R(GMR)(1-cosθ ) +∆R(AMR) sin 2θ 2

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GMR

RRequirements for F/NM combinations with a high GMR ratio are (a) 293 K (i) the F and NM materials possess, for one spin direction, very similar electronic structures, whereas for the other spin direction the electronic structures are very dissimilar, (ii) the electron transmission probability (transmission without diffusive scattering) through the F/NM interfaces is large for the type of electrons for which the electronic structure in the F and NM layers are very similar, and (b) 5 K (iii) the crystal structures of the F and NM materials match very well.

R/R sat (%)

8 6 4 2 0 12 R/R sat (%)

10 8 6 4 2 0 0

20

40

free F-layer thickness (nm)

Dependence of the MR ratio on the free magnetic layer thickness, measured at 293 K (a) and at 5K (b), for (X/Cu/X/Fe50Mn50) spin 60 valves, grown on 3nm Ta buffer layer on Si(100) substracts, with X=Co (squares), X=Ni66Fe16Co18 (traingles) and (X= Ni80Fe20) (+), measured at 5K. Layer thickness: tCu = 3nm (but 2.5 for F=(X= Ni80Fe20); tF(pinned layer)=5nm (but 6nm for F= Ni66Fe16Co18)[i].[i]

utep.el.utwente.nl/.../magel/ spinvalvetransistor.html