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5 Antiferromagnetic and Complex Magnetic Nanostructures

5 Antiferromagnetic and Complex Magnetic Nanostructures

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8 Nanomagnetism

Fig. 8.29 (a) Schematic representation of the microstructure in 2:17 Sm–Co magnets. (b) Typical

cellular and lamellar microstructure in 2:17 Sm–Co magnets parallel to the c-axis. (c) Typical

magnetic domain structure in the 2:17 Sm–Co magnets; Foucault mode of Lorentz microscopy for

imaging. (Reprinted with permission from [8.85]. © 2007 Wiley Interscience)


Antiferromagnetic and Complex Magnetic Nanostructures


8.5.1 Spin Structure of Antiferromagnetic Domain Walls

Antiferromagnetic surfaces play an important role in information technology as they

are used to pin the magnetization direction of bistable thin ferromagnetic films by

the exchange bias (EB) effect in spin valves (see Sect. 1.4) and in magnetic storage

devices (see [8.105]). Only a few uncompensated spins are thought to contribute

to the effect. Uncompensated moments of phase domain walls in antiferromagnetic

surfaces – in addition to moments that arise from known sources as grain size, step

edges, and non-magnetic defect sites (see [8.105]) – may contribute to EB.

Domain walls were studied by spin-polarized scanning tunneling microscopy

(SP-STM) in the perpendicular antiferromagnet of a Fe monolayer on W (001)

where the magnetic moments of nearest-neighbor atoms are pointing alternately

up and down (see Fig. 8.30b, inset). Segments of a phase domain wall (p-DW) are

shown in Fig. 8.30c. In the p-DW (Fig. 8.30a) the phase of the magnetic lattice

shifts at the position of the wall by one atomic site. Within the p-DW, which is

only a few lattice sites wide (Fig. 8.30c), the magnetic signal appears to be rather

blurred because here the magnetic moments of the tip and the sample are orthogonal. According to Monte Carlo (MC) simulations, the [110]-oriented p-DWs carry

a finite perpendicular magnetic moment of about 0.6 μB per nm DW length. As

sketched in Fig. 8.30 the wall is 6–8 atomic rows wide and Bloch-like; the in-plane

component of rows 4 and 5 is already very small. In Fig. 8.30e and f calculated and

experimental SP-STM images of such a wall are shown.

8.5.2 Antiferromagnetic Monatomic Chains

In monatomic chains of manganese atoms on an insulating CuN layer on Cu (100),

the ground-state spin of the chain can be determined by measuring the conductivity dI/dU in inelastic tunneling spectroscopy by means of a scanning tunneling

microscope (Fig. 8.31a). The alternation of the ground-state spin between zero for

even-length chains (2, 4, 6, 8, 10 Mn atoms) and non-zero values for odd-length

chains (1, 3, 5, 7, 9 Mn atoms) indicates antiferromagnetic coupling between the

atomic spins (Fig. 8.31b). Theoretical studies [8.107] by means of the Korringa–

Kohn–Rostoker (KKR) Green function method based on density functional theory

(DFT) and local spin density approximation (LSDA) show that even-numbered

antiferromagnetic Mn chains on Ni (001) exhibit a non-collinear structure whereas

odd-atom chains have a collinear ferromagnetic structure.

8.5.3 Antiferromagnetic Nanoparticles

Nanoparticles of antiferromagnetic materials may have applications in new types

of hard-magnetic materials consisting of composites of antiferromagnetic and ferromagnetic nanoparticles (see [8.108]). In the following, the properties and the


8 Nanomagnetism

Fig. 8.30 Schematic representation of domain walls (DWs) at antiferromagnetic surfaces, experimental observations, and theoretical spin structure. (a) Scheme of an orientational domain wall

(o-DW) and a phase domain wall (p-DW). (b) Spin-polarized scanning tunneling micrograph (SPSTM) of a 1.1 Fe monolayer on W (001). The antiferromagnetic structure (higher resolution in

the inset) exhibits long-range periodicity without any DWs. (c) p-DWs (dashed lines) at higher

defect densities (double-layer islands). (d) Theoretical spin structure of a <110>-oriented p-DW.

(e) Simulated and (f) experimental SP-STM image of a p-DW in the out-of-plane antiferromagnetic

Fe monolayer on W (001). (Reprinted with permission from [8.105]. © 2006 Nature Publishing



Antiferromagnetic and Complex Magnetic Nanostructures


Fig. 8.31 Mn chains on CuN. (a) Scanning tunneling micrograph (STM) perspective rendering

of a chain of 10 Mn atoms. The observed double-peak structure suggests the existence of 1D

delocalized electronic states as seen in metallic chains constructed on metal surfaces (see [8.106]).

(b) Schematic of the antiferromagnetic coupling of three atomic spins described by the Heisenberg

model [8.106]. (Reprinted with permission from [8.106]. © 2007 Institute of Physics)

interaction of antiferromagnetic nanoparticles will be discussed which can be studied by magnetization measurements, by Mössbauer spectroscopy, or by neutron


In contrast to bulk antiferromagnets with a zero magnetic moment, nanocrystalline antiferromagnets have a non-zero magnetic moment because of imperfections

or finite size effects. Nanoparticles of antiferromagnetic NiO exhibit spin canting

and a reduction of the antiferromagnetic ordering temperature (Néel temperature – TN ). From neutron diffraction data it has been deduced that 15 nm hematite

(α-Fe2 O3 ) nanoparticles are single domain particles. In bulk α-Fe2 O3 , the sublattice

magnetization changes at the Morin temperature TM ≈ 263 K from a direction in

the (001) plane to the hexagonal [001] direction because of a change of sign of the

magnetocrystalline anisotropy constant, K. In nanocrystalline α-Fe2 O3 , however,

TM decreases with decreasing particle size and disappears for sizes below 20 nm

because of a size-dependent K (see [8.108]). The magnetization of NiO nanoparticles appears to be proportional to N1/3 , where N is the total number of spins in a

particle, which has been theoretically suggested for a random occupation of surface

sites (see [8.108]). From temperature-dependent measurements, values of the magnetic anisotropy constant K can be derived for ferritin, an iron storage protein with

an antiferromagnetic 8-nm iron oxyhydroxite core (K = 25 kJ/m3 ) [8.109], and for

α-Fe2 O3 nanoparticles (K ≈ 4 kJ/m3 ) (see [8.108]).

Uncoated antiferromagnetic α-Fe2 O3 nanoparticles show a strong interaction as

shown in their Mössbauer spectra (Fig. 8.32) as compared to the spectra of coated,

weakly interacting particles. In the weakly interacting particles, the low-temperature

Mössbauer sextet disappears at 240 K which is characteristic for fast superparamagnetic relaxation above this temperature. In contrast to that, the sextet is maintained


8 Nanomagnetism

Fig. 8.32 Mössbauer spectra of (a) 20 nm α-Fe2 O3 nanoparticles coated with oleic acid (weakly

interacting) and (b) uncoated (strongly interacting) nanoparticles, measured at the temperatures

indicated. The lowest spectrum in each panel is measured in an external magnetic field. (Reprinted

with permission from [8.111]. © 2000 American Physical Society)

in the uncoated, strongly interacting particles to temperatures above 360 K. The

strong interaction is ascribed to a magnetic exchange interaction of the nanoparticles

because the magnetic dipole interaction is negligible due to the very small magnetic

moments of the antiferromagnetic particles. Exchange interaction implies that the

particles are in such a close proximity that the electronic wave functions of atoms at

the interfaces overlap (see [8.108]). Neutron diffraction experiments suggest [8.112]

that about three α-Fe2 O3 nanoparticles may be aligned in chains with common crystallographic orientation and a magnetic correlation in the [001] direction, which has

been confirmed by high-resolution electron microscopy [8.112].


Ferromagnetic Nanorings


8.5.4 Complex Magnetic Structure of an Iron

Monolayer on Ir (111)

Using spin polarized scanning tunneling microscopy, a nanometer-sized 2D magnetic unit cell of Fe atoms on Ir (111) is observed which is also favored by

first-principles calculations. A collinear magnetic structure is proposed for the magnetic unit cell (Fig. 8.33) consisting of 15 atoms with 7 magnetic moments pointing

in one and 8 moments in the opposite direction. This structure is induced by the

strong Fe–Ir hybridization. The Fe atoms in the mosaic structure have a magnetic

moment of m

¯ Fe = 2.96 μB and the Ir atoms a value of ∼ 0.1 μB .

Fig. 8.33 Magnetism of the face-centered cubic (fcc) Fe monolayer on fcc Ir (111). (a) Spinpolarized scanning tunneling micrograph (SP-STM) of the Fe monolayer in a magnetic field of

B = 2 T. (b) Structural model based on the experimental data. (c) Calculated SP-STM image for

the 7:8 domain of the Fe magnetic mosaic structure. (Reprinted with permission from [8.110].

© 2006 American Physical Society)

8.6 Ferromagnetic Nanorings

Ferromagnetic rings with a diameter of 1–3 μm and of nanometer widths and thicknesses exhibit new spin states (Fig. 8.10), switching behavior, and spin dynamics

which can be controlled via geometry, materials composition, and applied field.


8 Nanomagnetism

Fig. 8.34 Hysteresis loop of

an array of polycrystalline Co

rings with an outer diameter

of 1.65 μm, a width of

350 nm, and a thickness of

16 nm. The insets show

schematic diagrams of the

onion and vortex states of a

ring which are attained during

the magnetization reversal

process. (Reprinted with

permission from [8.9].

© 2007 Institute of Physics)

These characteristics make the rings an attractive geometry for devices, including

MRAMs (magnetic random access memories) and magnetic sensors [8.9]. These

nanorings are prepared by a combination of electron beam lithography (EBL), metal

molecular beam epitaxy, and lift-off techniques (see [8.9]).

A hysteresis loop of an array of micrometer-sized magnetic nanorings (Fig. 8.34)

is characterized by the “onion” magnetization state from positive saturation down

to zero field. As the magnetic field is reversed, a jump of the magnetization to a

state close to zero remanence is characteristic for the transition from the “onion”

to the “vortex” state. When the reverse field is further increased, the transition to

the reverse onion state occurs. The equilibrium magnetic configuration of nanorings

is determined by the exchange energy and the magnetostatic energy, where in 3d

transition metal ferromagnets the magnetocrystalline anisotropy plays a minor role

(see [8.9]).

In field-induced magnetic switching of ring elements, the switching time and

switching field amplitude depend on the particular reversal mechanisms favored by

the magnetic system. In the case of double switching, from onion to vortex and

vortex to reverse onion, domain wall propagation, and domain nucleation plus wall

propagation are prevalent. In the transition from the onion to the vortex state one

of the 180◦ walls is displaced and propagates along one half of the ring (annihilating the other domain wall or forming metastable 360◦ domain walls, depending

on the relative winding [8.113]), where the onion-to-vortex switching field strongly

depends on the ring width (see [8.9]). The magnetic switching properties of ring

elements have been studied by using resistance measurements, yielding jumps in

resistance when a domain wall is located within or outside the measuring section

(see Fig. 8.35a, c).

Magnetization dynamics in confined geometries have also been studied by

means of Brillouin light scattering for investigating the spin wave modes (see, e.g.,

[8.115]), showing in the case of 1 μm permalloy rings 2D quantization of spin waves

in radial and azimuthal direction which partially disappears in larger rings.


Ferromagnetic Nanorings


Fig. 8.35 (a) Resistance response of a permalloy nanoring due to domain wall movement by an

applied magnetic field; level A corresponds to the presence of the domain wall in between the

voltage contacts (see (c)), while for level B the domain wall is outside the voltage contacts (for

these measurements, the ring is severed to exclude contributions from other portions of the ring).

(b) Resistance across the voltage contacts after successive positive and negative current pulses

(width: 20 μs, amplitude: 5×1012 Am−2 ), demonstrating current-induced domain wall motion. (c)

Schematic diagrams of the voltage contacts and of the domain wall position [8.114]. (d) Scanning

electron microscopy (SEM) of a pseudo-spin valve ring with a diameter of 5 μm and the structure

Au (4 nm)/Co (7 nm)/Cu (5 nm)/NiFe (4 nm)/SiOx /Si (001). (e) Magnetoresistive characteristics

for the ring in (d). The magnetic field is applied in the direction of the current contacts [8.9].

(Reprinted with permission from [8.114] (a–c) and [8.9] (d) (e). © 2005 American Physical Society

(a–c) and © 2007 Institute of Physics (d) (e))

Current-induced magnetic switching can be performed by switching the magnetization or by displacing domain walls by means of a spin polarized current. This is of

much interest for the switching of magnetic memory elements with the advantage of

much simplified wiring as compared to conventional magnetic field switching. The

ring geometry has been used for the study of current-induced domain wall propagation. A domain wall initially outside two voltage contacts (Fig. 8.35c) can be

positioned by a current pulse into the region between the two voltage contacts which

is monitored by a lowering of the resistance (Fig. 8.35b). A reverse current pulse can

move the wall back.

Pseudo-spin-valve multilayer ring structures of the type Au (4 nm)/Co (7 nm)/Cu

(5 nm)/NiFe (4 nm)/SiOx /Si (001) (Fig. 8.35d) exhibiting giant magnetoresistance (GMR; see Sect. 1.4) have been fabricated and their magnetization reversal

investigated using magnetoresistance measurements and micromagnetic modeling


8 Nanomagnetism

[8.116]. The GMR data for the ring show a flat baseline interrupted by jumps

(Fig. 8.35e) as domain walls are created and move through the ring; this leads to an

increase in resistance as the parallel arrangement of the magnetization of the NiFe

and the Co at high fields (both in the same onion state) changes to an antiparallel

spin arrangement following the reversal of the NiFe layer to the reverse onion state.

8.7 Current-Induced Domain Wall Motion in Magnetic


Domain walls in nanoscale ferromagnetic structures exhibit complex spin arrangements that strongly deviate from the wall types in bulk and thin film systems [8.117].

Recently, a new aspect of magnetic domain walls has been attracting attention, i.e.,

the domain walls are considered as possible objects for high-speed logic, where

each wall represents a single bit [8.118]. The pioneering prediction [8.119–8.121]

and confirmation [8.122, 8.123] that domain walls cannot only be moved by magnetic fields but also by spin-polarized electrical current offer an attractive alternative

in designing novel devices such as sensors and magnetic non-volatile memories

[8.124, 8.125].

The transition of the magnetization direction in one ferromagnetic domain to the

opposite direction in the adjacent domain occurs in the domain wall between the two

domains. The width of the wall in a bulk system is governed by the magnetocrystalline anisotropy energy and the quantum mechanical magnetic exchange energy.

Lateral confinement in nanostructured films (see Fig. 8.36a) leads to pronounced

geometrical effects, i.e., to modifications of the domain wall structure because of the

demagnetization energy at the edges. This in turn offers the possibility to finely tune

the wall properties, such as the wall width from a few nanometers to several hundred

nanometers which determines, e.g., the electrical resistance and the dynamic properties of the domain wall (see [8.117, 8.126, 8.127]). Wall positions can be detected by

anisotropic or giant magnetoresistance, by induced Hall voltage, by magnetic force

microscopy, by magneto-optical Kerr effect, or by spin-polarized scanning electron

microscopy (see [8.117]).

An electrical current flowing in a magnetic element can be used, instead of

a magnetic field, to move a domain wall. This was first observed in continuous

films [8.128, 8.129]. The predominant mechanism for this process is believed to

be the exchange interaction between the 3d electrons in the ferromagnet and the

spin-polarized conduction electrons which results in a torque and a transfer of spin

momentum from the drifting electrons to the domain wall. In theoretical treatments

the underlying Landau–Lifshitz–Gilbert equation has been extended by additional

torque terms (see [8.117]).

For the movement of a domain wall, relatively high current densities of

1011 – 1012 A/m2 are required (Fig. 8.36b, c). Domain wall velocities up to 80 m/s

have been observed [8.130], a value similar to that expected theoretically (100 m/s;

see [8.117]). Domain walls pinned at notches of a ferromagnetic wire can be excited


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 ì 500 nm. (Reprinted

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

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