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7 Current-Induced Domain Wall Motion in Magnetic Nanostructures

7 Current-Induced Domain Wall Motion in Magnetic Nanostructures

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Current-Induced Domain Wall Motion in Magnetic Nanostructures


Fig. 8.36 Magnetic domain walls in nanowires, their motion, and their deformation. (a) Magnetic

domain wall in a constriction in a 7.5-nm thick Fe20 Ni80 film as measured by spin-polarized scanning electron microscopy (spin SEM). The color code shows the in-plane magnetization component

along the +y (left) and the −y (right) directions. The arrows give the in-plane magnetization

directions. The magnetization configuration is asymmetric, showing a wall that is wider toward

the top than the bottom constriction (colored yellow for vanishing magnetization component in

y-direction). (b–c) Fe20 Ni80 nanowires with a width of 500 nm, a thickness of 10 nm, and a length

of the central straight segment of 20 μm. The spin-SEM studies yield the black and white magnetization contrasts according to the magnetization directions given by the black and white arrows.

The walls move from the initial positions at the bends shown in (b) to a position in the straight

wire shown in (c), after injection of a 10 μs long current pulse with the current direction indicated by the red arrow. Current density, 2.2 × 1012 A/m2 . (d–f) Arrow images constructed from

high-resolution experimental images of the spin structure of a domain wall in a Fe20 Ni80 wire of a

width of 500 nm and a thickness of 20 nm after subsequent current injections. The wall transforms

from (d) the initial vortex state to (e) a vortex core with a large transverse component and (f) to a

transverse wall. This wall no longer moves with a current density of 2.2 × 1012 A/m2 . The arrow

images are constructed from the spin-SEM studies. Image size: 1600 nm × 500 nm. (Reprinted

with permission from [8.117]. © 2006 Materials Research Society)


8 Nanomagnetism

to oscillations by a high-frequency current. From this experiment quasi-particle

domain wall masses between 5.6 × 10−25 kg and 6.2 × 10−24 kg were derived,

depending on the type of wall [8.131]. The pinning potential can be completely

characterized [8.132].

In analogy to the current-induced domain wall motion, the motion of a domain

wall by a magnetic field can generate a current [8.133].

8.8 Single Molecule Magnets

The observation of a magnetic memory effect [8.134] in single molecule magnets

(SMMs) has opened the perspective of exploiting the information storage capability

of individual SMMs. In fact, the combination of a large spin of the molecule with

an easy-axis magnetic anisotropy results in an energy barrier for the reversal of the

magnetization, although the barrier can be cross-cut by a tunneling mechanism for

some particular values of the magnetic field [8.135–8.137]. Anchoring SMMs on

conducting surfaces is required to make them individually addressable. Evidence

that SMMs retain molecular magnetic hysteresis has been presented [8.138].

SMMs comprising four high-spin iron(III) ions, Fe4 (Fig. 8.37a, b), and having

a diameter of ∼ 2.5 nm [8.138] are stable and robust. The outer three individual

s = 5/2 spins interact antiferromagnetically with the center spin to give a ground

state S = 5 spin state with an anisotropy barrier of about 15 K to be overcome

for magnetization reversal. At low temperatures of 0.5 K a magnetic hysteresis

(Fig. 8.37c) of purely molecular origin is observed. This may open the possibility to

control magnetization reversal by conduction electrons in a metal–molecule–metal

nanojunction which would mimic at the molecular scale the current-induced motion

of domain walls for memory nanostructures (see Sect. 9.4).

8.9 Multiferroic Nanostructures

Three forms of ferroic order are widely known: ferromagnetism, a spontaneous

magnetization; ferroelectricity, a spontaneous polarization; and ferroelasticity, a

spontaneous strain. It is currently debated whether to include an ordered arrangement of magnetic vortices as a fourth form of ferroic order, termed ferrotoroidicity


Multiferroic materials that display simultaneously ferromagnetic and ferroelectric ordering have recently gained interest [8.140–8.142] because they couple

magnetic and electric behavior. In these materials the electrical polarization P can

be reoriented by means of magnetic fields H and the magnetization M by electrical fields E as predicted more than 100 years ago [8.143]. Since E fields can be

generated in integrated circuits more easily than H fields, it would be of interest to switch (write) magnetic multiferroic bits by E fields, whereas for reading,

the magnetization could be more convenient [8.144]. The coupling of ferroelectric


Multiferroic Nanostructures


Fig. 8.37 (a) Schematic diagram of the anchoring on a gold surface of the Fe4 derivative molecule

through its thiolate-terminated aliphatic chains (Fe atoms in large green spheres, oxygen in red,

carbon in gray, and sulfur in light yellow). Inset: A view of the magnetic core structure of the Fe4

molecule, with the ground-state spin arrangement (white arrows). (b) Room-temperature scanning

tunneling micrograph (STM) of a monolayer of Fe4 molecules. (c) Magnetic hysteresis of the Fe4

monolayer monitored through the x-ray magnetic circular dichroism (XMCD) intensity. (Reprinted

with permission from [8.138]. © 2009 Nature Publishing Group)


8 Nanomagnetism

Fig. 8.38 (a) Epitaxial alignment of a spinel (top left) and a perovskite (top right) on a perovskite

substrate (bottom). (b) Schematic illustration of a self-assembled nanostructured columnar thin

film formed on a substrate. (Reprinted with permission from [8.145]. © 2004 AAAS)

and magnetic order parameters in a two-phase nanostructured BaTiO3 –CoFe2 O4

multiferroic ferroelectromagnet has been demonstrated [8.145]. The intrinsic similarities in crystal chemistry (i.e., oxygen coordination) between the perovskite

(BaTiO3 ) and the spinel (CoFe2 O4 ) families lead to lattice dimensions that are

compatible. This presents the possibility of heteroepitaxy in three dimensions,

e.g., of nanopillars of the ferromagnetic spinel in a ferroelectric perovskite matrix

(Fig. 8.38).

The connection between the polarization P and the magnetization M as well

as P(H) and M(E) dependences can be derived from the minimization of the free


F = (1 − α) [φP (P) − EP] + α [φM (M) − HM] + e ε0P (P), ε0M (M)

where α is the fraction of the ferromagnetic phase, φP (φM ) the specific free energy

of uniform ferroelectrics (ferromagnets), e the energy of elastic interaction, ε0P (P) =

QP2 the spontaneous ferroelectric strain with Q the electrostriction coefficient, and

ε0M (M) the spontaneous magnetostriction (see [8.145]). It is clear from the above

equation that a strong magnetoelectric coupling requires a strong interphase elastic


The two-phase oxide films with self-assembled CoFe2 O4 nanopillars (30 nm

in diameter; volume fraction 35%; Fig. 8.39a, b) in a BaTiO3 matrix are prepared by pulsed laser deposition. The nanopillars exhibit a compressive out-of-plane

strain of 0.8% due to a vertical heteroepitaxial mismatch between CoFe2 O4 and

BaTiO3 [8.145]. In quasi-static ferroelectric measurements a ferroelectric hysteresis is observed with a dielectric constant of 350 (normalized to the BaTiO3 fraction)

at 100 kHz. In magnetometry measurements a saturation magnetization (normalized

to the CoFe2 O4 fraction) of ∼350 electromagnetic units (emu)/cm3 are found.

Temperature-dependent magnetization measurements (Fig. 8.38c; upper curve)

show coupling between the electric and magnetic order parameters in a CoFe2 O4 –

BaTiO3 films as manifested by a drop in the magnetization of ∼16 emu/cm3


Multiferroic Nanostructures


Fig. 8.39 (a) AFM topography image of a film showing a quasi-hexagonal arrangement of

CoFe2 O4 nanopillars in a BaTiO3 matrix. (b) TEM planar view image of the CoFe2 O4 nanopillars in the BaTiO3 matrix. The heteroepitaxy of the two structures can be shown by electron

diffraction. (c) Temperature dependence of the magnetization of the CoFe2 O4 –BaTiO3 film

at H = 100 Oe, showing a drop in magnetization at the ferroelectric Curie temperature

TC ∼ 390 K for the vertically self-assembled nanostructure (upper curve); a multilayered nanostructure (lower curve) shows negligible change in magnetization. (Reprinted with permission from

[8.145]. © 2004 AAAS)

around the ferroelectric Curie temperature TC ∼ 390 K upon cooling. At temperatures >TC , the CoFe2 O4 is compressed due to the lattice mismatch with BaTiO3 .

At temperatures
reduction of the magnetization as experimentally observed [8.145].

A number of applications are envisaged for multiferroic materials. Composite

multiferroics with strong magnetostriction and large piezoelectric coefficients

enable the creation of tiny magnetic sensors with the sensitivity exceeding that of

even superconducting quantum interference devices (SQUIDs) [8.146].

Domain walls in multiferroics, intrinsically nanoscopic because of their small

thickness, could be used as active device components [8.147]. In the insulating room-temperature multiferroic BiFeO3 , domain walls separating regions with

polarization orientations differing by 180◦ or 109◦ show the signature of electric conductance [8.148] which is correlated to a local structural distortion in the


8 Nanomagnetism

otherwise insulating material. This distortion reduces the electronic band gap in the

region of the domain wall. A possible application could be as a highly sensitive local

strain sensor.

In a Néel magnetic domain wall of a multiferroic an electric polarization could

form [8.141]. This domain wall can be moved by an inhomogeneous electric field

exerted, e.g., by a voltage pulse on a Cu tip [8.149]. This interaction could be a

means of controlling the domain structure, and consequently a magnetic memory,

by applying a voltage rather than electric currents (see Sect. 8.7 and 9.4) or magnetic

fields (see [8.141]).

8.10 Magnetically Tunable Photonic Crystals

of Superparamagnetic Colloids

Colloidal crystals, i.e., periodic structures typically self-assembled from monodisperse colloidal building blocks, are a low-cost photonic band gap material. In

analogy to the electronic band gaps of semiconductor crystals, photonic crystals

exhibit photonic band gaps giving rise to the disappearance of the transparency for

radiation with particular wavelengths. For application it is desirable that the tunability of the photonic band gap (stop band) can be conveniently controlled by external


As building blocks for a photonic crystals, polyacrylate-capped superparamagnetic magnetite (Fe3 O4 ) colloidal nanocrystal clusters (CNCs) with a diameter of

120 nm have been synthesized [8.150] (see Fig. 8.40). The CNCs consist of 10-nm

superparamagnetic primary particles (Fig. 8.40a). The polyacrylate binds to the particle surface through a strong coordination of the carboxylate groups with iron

cations, whereas the non-coordinated carboxylate groups of the polymer chains

extend into the aqueous solution and render the particle surface highly charged

(Fig. 8.40b). The Fe3 O4 CNCs readily self-assemble in deionized water into colloidal photonic crystals upon application of a magnetic field. Figure 8.40d, e shows

the photos and reflection spectra of an aqueous solution of 120-nm CNCs (ca. 8.6 mg

mL−1 ) in response to a varying magnetic field achieved by controlling the distance

between a NdFeB magnet and the sample. The peaks resulting from the diffraction of the (111) planes blue shift from 730 to below 450 nm as the magnetic field

increases from 8.8 to 35.2 mT moving the magnet toward the sample (3.7–2.0 cm).

The blue shift corresponds to a decrease of the interplanar spacing from 274 to

169 nm. The 3D order of the colloidal photonic crystal formed within ∼ 200 ms

[8.150] in the magnetic field is the balanced result of the interparticle electrostatic

repulsive force and the magnetic forces [8.151]. The above studies demonstrate that

medium-sized superparamagnetic clusters can reversibly form stable colloidal photonic crystals in a magnetic field with tunable stop bands and therefore tunable

colors covering the whole visible spectrum [8.150].


Nanomagnets in Bacteria


Fig. 8.40 (a) Transmission electron micrograph and (b) schematic illustration of polyacrylatecapped Fe3 O4 colloidal nanocrystal clusters (CNCs) with a nanocrystal size of ∼ 10 nm; scale bar:

100 nm. (c) Magnetization curve of CNCs measured at room temperature exhibiting superparamagnetic behavior. (d) Photographs of solutions of colloidal photonic crystals formed in response

to an external magnetic field; the magnet–sample distance decreases gradually from right to left.

(e) Variation of the reflectance spectra at normal incidence on the colloidal photonic crystals with

the magnet–sample distance. Diffraction peaks blue shift (from right to left) as the magnet–sample

distance decreases from 3.7 to 2.0 cm in steps of 0.1 cm. (Reprinted with permission from [8.150].

© 2007 Wiley-VCH)

8.11 Nanomagnets in Bacteria

Magnetotactic bacteria, such as the bacterium Magnetospirillum magnetotacticum,

biomineralize iron into magnetite (Fe3 O4 ) nanoparticles (“magnetosomes”), which

enable the bacteria to respond to magnetic fields in their environments. These magnetosomes have considerable potential for use in nanotechnological, biotechnical,

and medical application because of their narrow size distribution and inherent biocompatibility (see [8.152]). Furthermore, magnetotactic bacteria are the simplest

single-cell organisms in which biomineralization occurs and, as such, offer a model

system to study biomineralization mechanisms. Models of the biomineralization of

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