soft x-ray microscopy of nanomagnetism

Investigating magnetic properties of matter on the nanoscale is a

very active area in modern solid-state physics1-3. Exciting

phenomena, e.g. interlayer exchange coupling4 or the giant

magnetoresistance effect5, occur in low-dimensional systems

where characteristic length scales, i.e. magnetic exchange lengths,

become relevant. Magnetic exchange lengths can be derived from

intrinsic material parameters such as anisotropy (K) and exchange

(A) constants, giving values <10 nm for typical magnetic materials,

e.g. permalloy (Ni80Fe20) or the hard magnetic system6,7 Nd2Fe14B.

Generally, the energetic ground state of a ferromagnetic system is

not a single-domain state, but exhibits a characteristic microscopic

magnetic domain structure that reflects the interplay between

competing energies, such as anisotropy, exchange, Zeeman, and

magnetostatic energies8. In order to understand the origin of

macroscopic magnetic properties, this microstructure is the target

of experimental9-16 and theoretical studies17-23. Moreover, the

corresponding dynamics of the magnetic microstructure on a

subnanosecond time scale is an emerging field, both for scientific

and applied reasons, and numerous activities are currently being

developed.

Nanomagnetism is of utmost importance to current technological

developments. The dramatic increase in magnetic storage density over

the last decade24-27, various applications of miniaturized magnetic

sensor devices based on the giant magnetoresistance effect28-30, and

the development of spintronics, a new generation of computing

technology31-34, require a thorough understanding of magnetism on the

nanometer scale. Spintronics considers the spin of an electron as an

additional degree of freedom, which can be manipulated to obtain

particular functionalities. Recent concepts for spintronic logical elements

discuss domain walls35,36, i.e. the intermediate region of spin

inhomogeneity between two domains with opposite magnetization

directions in nanowired elements.

The magnetic nanoscale systems that exhibit the largest activity,

both in fundamental and applied research, are multilayers37,38 and

oxides39,40, nanoparticles41,42, nanostructures25,43, semiconductors44,45,

multiferroic heterostructures46,47, and spintronic materials48-51. Several

key questions in these systems depend on the dynamics of the

magnetization and the associated magnetic microstructure52-55:

• How does the magnetization reverse, i.e. how does it switch its

orientation on a short length and fast time scale?

Magnetic materials with dimensions of a few tens of nanometers areimportant for the development of ultrahigh-density magnetic storage andsensor devices. Magnetic microstructure largely determinesfunctionality, and imaging of magnetic domains and magnetizationreversal behavior is an outstanding challenge. Magnetic X-raymicroscopy makes it possible to investigate magnetization phenomenawith elemental specificity and high spatial and temporal resolution.

Peter Fischer*, Dong-Hyun Kim, Weilun Chao, J. Alexander Liddle, Erik H. Anderson, and David T. Attwood

Center for X-ray Optics, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley CA 94720, USA

*E-mail: [email protected]

ISSN:1369 7021 © Elsevier Ltd 2006JAN-FEB 2006 | VOLUME 9 | NUMBER 1-2 26

Soft X-ray microscopyof nanomagnetism

mailto:[email protected]

• Does the magnetic microstructure remember its history or is

magnetization reversal a purely stochastic process56,57?

• Is there a limit as to how fast the magnetization can switch58?

Technologically, several concepts have been developed by which

magnetization can be reversed. Besides conventional magnetic switching

(i.e. applying an external magnetic field in opposite direction, which

does not permit a similar increase in switching time as in storage

density), thermally assisted magnetic-switching phenomena59-61,

switching through a spin-polarized current62-64, and precessional

switching mechanisms65,66 are being investigated with relevant time

scales in the subnanosecond regime.

To image magnetic domains, an abundance of techniques have been

developed, which can be categorized according to the probes they use8.

There are electron microscopies, like scanning electron microscopy with

polarization analysis and transmission electron microscopy acting as

Lorentz microscopy. There are optical microscopies, like near-field

scanning optical microscopies or Kerr microscopies. And, finally, there

are scanning probe microscopies, such as magnetic force microscopy or

spin-polarized scanning tunneling microscopies. The task for any modern

magnetic imaging technique is to visualize on a nanometer length scale

the ultrafast dynamics of magnetization in a complex, often

multicomponent, system.

In the follow sections, we show that magnetic X-ray microscopy is a

promising experimental tool that allows the study of magnetic

nanostructures with high lateral and temporal resolution, magnetic

elemental sensitivity, and can be carried out in external magnetic

fields.

Nanotechnology enables nanoscienceSince 1994, the Center for X-ray Optics (CXRO) has operated the full-

field, soft transmission X-ray microscope XM-1 at the Advanced Light

Source (ALS) in Berkeley, California67-69. Its optical design is similar to

a conventional microscope using visible light and follows the concept

of the first soft X-ray microscope that was developed by Schmahl and

coworkers in Göttingen, Germany (Fig. 1). X-rays are emitted from a

bending magnet source and there is a condenser, an objective lens, and

a detector. However, because the refractive index of soft X-rays is close

to one, conventional lenses or mirrors cannot be used. Rather, Fresnel

zone plates (FZPs), i.e. circular gratings with a radially increasing line

density, can be used to build an X-ray microscope70-72. The optical

elements of XM-1 are therefore two FZPs: a condenser zone plate

(CZP) and a ‘micro’ zone plate (MZP) that serves as the objective lens.

The CZP with a central stop provides a partially coherent hollow-

cone illumination of the sample. Together with a pinhole close to the

specimen, and because of the wavelength dependence of its focal

length, it acts as linear monochromator with a spectral resolution of

E/∆E ~ 500. For the Fe L-absorption edges with a photon energy E of

~700 eV, this spectral resolution is sufficient to distinguish the L3 and L2

edges separated by a spin-orbit coupling of ~13 eV. The current CZP

has an outer diameter of ~9 mm with 50 000 rings and an outermost

zone width ∆r of ~40 nm.

The MZP, positioned near its focal length downstream from the

sample, projects a full-field image onto an X-ray-sensitive charge

coupled device (CCD) with 2048 x 2048 pixels, where a typical image

exposure time is only a few seconds. The field of view is typically

Fig. 1 Schematic of the soft X-ray microscopy beamline XM-1 at the ALS used for magnetic imaging. Off-orbit emitted radiation provides elliptically polarized

X-rays. The micro zone plate projects a full field image onto a CCD camera that is sensitive to soft X-rays. Partially coherent, hollow-cone illumination of the

sample is provided by a condenser zone plate. A central stop and a pinhole provide monochromatization. Magnetic fields generated by a solenoid allow the

magnetic microstructure to be changed in situ.

JAN-FEB 2006 | VOLUME 9 | NUMBER 1-2 27

Soft X-ray microscopy of nanomagnetism REVIEW FEATURE

10 x 10 µm2, corresponding to a magnification of about 2500. The

MZP typically has a diameter of ~30-60 µm, 500 rings, and an

outermost zone width ∆r down to 15 nm. These optical elements

largely determine the spatial resolution that can be obtained in the

X-ray microscope.

The spatial resolution of a zone-plate-based microscope is equal to

k1λ/NAMZP, where λ is the wavelength, NAMZP is the MZP numerical

aperture, and k1 is an illumination-dependent constant that ranges73

from 0.3 to 0.61. For a zone-plate lens used at high magnification,

NAMZP = λ/2∆rMZP. Since the condenser forms the image of the

bending magnet source on the sample, the illumination is partially

coherent and the degree of partial coherence74 σ is given by the ratio of

the numerical aperture of the MZP to that of the CZP. In our case,

σ ~ 0.4 and k1~ 0.4 (Fig. 2).

Nanotechnology is the cornerstone in the fabrication of X-ray optical

components of the highest quality and, thus, is crucial in achieving

optimum performance in X-ray microscopy. The successful realization of

a 15 nm zone plate was reported recently75. It has an outermost zone

width ∆rMZP of 15 nm, 500 zones, and a diameter of 30 µm. A new

overlay technique for zone-plate fabrication using electron-beam

lithography was developed to overcome nanofabrication limits resulting

from electron-beam broadening in high-feature-density patterning and

inherently low resist contrast. Since semi-isolated features are less

sensitive to these issues, the successful strategy was to divide the dense

zone pattern into two, less-dense patterns and overlay them in

subsequent lithography steps (Fig. 3). The spatial resolution achieved

can easily be seen by imaging a test pattern with 15 nm lines and

spaces with the high-resolution X-ray optics (Fig. 4).

It is essential to achieve a high placement accuracy of typically one-

third of the smallest features with the electron-beam writer. Since

electron-beam lithography systems with high beam control and overlay

accuracy have been demonstrated (the CXRO Nanowriter has a zone

placement accuracy of better than 2 nm across the two-dimensional

field), further zone plate developments and, therefore, spatial resolutions

in the 10 nm regime can be foreseen in the near future.

Fig. 2 Calculated modulation of a dense line binary pattern for a 15 nm zone

plate and the dependence on partial coherence. The graph shows the shift of

the Rayleigh criterion toward smaller half periods, i.e. better spatial resolution

can be obtained with partially incoherent light.

JAN-FEB 2006 | VOLUME 9 | NUMBER 1-228

REVIEW FEATURE Soft X-ray microscopy of nanomagnetism

Fig. 3 (a) Overlay nanofabrication technique for MZP fabrication. The zone

plate is composed of even-numbered opaque zones and odd-numbered

transparent zones. Set I, containing zones 2, 6, 10,… , and its complement,

set II, are fabricated sequentially to form the desired overlaid MZP.

(b) Scanning electron micrograph of a zone plate with a 15 nm outer zone.

Inset shows a more detailed view of the outer zones. The zonal period, as

indicated by the two black lines, is 30 nm. The zone placement accuracy is

1.7 nm75.

Fig. 4 Soft X-ray images of 15.1 nm half-period test objects using a zone plate

with outer zone widths of (a) 25 nm and (b) 15 nm. The test object consists of

Cr/Si multilayers, with 15.1 nm half-periods, respectively. No modulation is

seen with the 25 nm zone plate, while the image obtained with the 15 nm zone

plate shows excellent modulation. Images (a) was obtained at a wavelength of

2.07 nm (600 eV photon energy); (b) was obtained at a wavelength of

1.52 nm (815 eV). The equivalent object plane pixel size for image (a)

is 4.3 nm; the size for (b) is 1.6 nm75.

(a)

(b)

(a) (b)

Magnetic X-ray microscopyMagnetic contrast in X-ray microscopy is provided by X-ray magnetic

circular dichroism (X-MCD). That is, the dependence of the X-ray

absorption cross section on the relative orientation between the

helicity of the photon beam and the projection of the magnetization in

a ferromagnetic specimen onto the photon propagation direction.

X-MCD is used as contrast mechanism by both photoemission electron

microscopy (X-PEEM)76, where secondary electrons created in the

absorption process are detected with electron optics, and by X-ray

microscopes based on zone-plate optics. The latter can be operated in

an imaging mode (transmission X-ray microscopy, TXM)77, which is

described here, and also in scanning mode (scanning transmission X-ray

microscopy, STXM)78,79. Large values of X-MCD up to several tens of

percent are observed in the vicinity of L-absorption edges of transition

metals such as Fe, Co, and Ni80. Here, the photon energy matches the

binding energy of inner-core atomic levels, such as p3/2 and p1/2

electrons, which correspond to the L3 and L2 absorption edges,

respectively. Besides magnetic absorption contrast, which can be

described by an additional contribution to the imaginary part of the

scattering amplitude, magnetic phase contrast has also been observed

recently81. This is the result of a corresponding magnetic contribution

in the real part of the scattering amplitude82. From X-MCD

spectroscopy, magnetic spin83 and orbital84 moments can be derived

and, therefore, X-ray microscopy is able to resolve these contributions

laterally. Results obtained with a photoemission electron microscope

have also been reported85.

Circularly polarized X-rays, which are essential to observe X-MCD

contrast, are abundantly available at synchrotron storage rings, either at

helical undulators or at bending magnet sources. For the latter, the

radiation emitted at an angle of a few milliradians with respect to the

orbital plane exhibits a degree of polarization of ~70%, with reversed

polarity above and below86. Therefore, a modulation of the polarization

in an X-ray microscope located at a bending magnet is easily achieved

by suitable apertures to distinguish, for example, magnetic from

topological structures in the images.

Magnetic TXM is a pure photon-in, photon-out based technique.

Therefore, in principle, any magnetic field in any direction can be

applied during the imaging, which gives access to microscopic studies of

magnetization reversal processes87.

In the following sections, typical examples of magnetic X-ray

imaging at XM-1 demonstrate how the intrinsic features of this

technique contribute new insights into problems in nanomagnetism.

Local magnetic hysteresis loops CoCr-based alloy films and, in particular, CoCrPt alloy films have

received attention as possible high-density magnetic recording media.

This is because of their strong perpendicular magnetic anisotropy

(PMA) and low media noise resulting from the decoupling of the

exchange interaction between magnetically isolated grains via

compositional segregation at grain boundaries88,89. Insight into the

magnetization reversal behavior on a nanogranular length scale is

crucial, since it is closely related to the size, irregularity, and stability of

written domains.

A 50 nm thick (Co83Cr17)87Pt13 alloy film was prepared using

dc magnetron cosputtering of a CoCr alloy target with Pt chips at a base

pressure of better than 8 × 10-7 torr, and a sputtering Ar pressure of

3 mtorr. To achieve a better (002) hexagonal close-packed

crystallographic alignment of the CoCrPt alloy film, a 40 nm Ti buffer

layer was first deposited onto a 200 nm thick Si3N4 membrane used as

an X-ray transparent substrate. The average grain size of the sample90,

determined by analyzing transmission electron microscopy images

using particle-analysis software, was ~25-35 nm. Magnetic X-ray

images were recorded at the Co L3 absorption edge at 777 eV using an

MZP with a 15 nm outermost zone width and various external magnetic

fields91.

Fig. 5 shows X-ray images of the magnetic domain structure. The

dark and white areas correspond to regions where the Co magnetization

is pointing in and out of the paper plane, respectively. The variation of

these patterns within the hysteresis loop is clearly visible. Since the

magnetic contrast is a direct and element-specific measure of Co

magnetization, integrating the grayscale intensity in the X-ray images

allows the macroscopic hysteresis behavior of the films to be derived.

The results are in full agreement with the measured behavior

(Fig. 5, top). Three typical images are displayed (Fig. 5, center), where

the arrows indicate the position of each image within the hysteresis

loop. The high spatial resolution, which is comparable to the granular

size in these systems, allows one to zoom in on the details of

magnetization reversal for each grain (Fig. 5, bottom). From these

measurements, one can deduce the microscopic hysteresis behavior.

Image analysis provides direct information on return-point-memory

effects and the stochastical character of the nucleation process, which is

both scientifically interesting and technologically relevant.

Magnetic nanoparticlesWith the continuing increase in storage density in modern magnetic-

recording materials, the ‘superparamagnetic limit’ is becoming more

important92. This limit arises because the thermal stability of the

magnetic orientation of magnetically decoupled grains scales with

magnetic anisotropy strength Ku and grain volume V. As grain size

decreases, the magnetization of the grains becomes unstable. One

approach to delay this effect is to increase Ku by introducing

monodisperse nanoparticles with high magnetic anisotropy93. Another

approach for creating monodisperse, magnetically isolated single-

domain elements uses substrates with a corrugated surface94, such as

close-packed spherical polymer particles, onto which magnetic

multilayer films are deposited by standard film-deposition techniques.

The advantages are that the thickness of the magnetic ‘caps’ decreases

toward the edge of the spheres, leading to magnetic decoupling of the



elements, and self-assembly of the spheres allows large-scale

fabrication of the nanostructured magnetic arrays.

For our X-ray microscopy studies, monodisperse spherical

polystyrene (PS) particles were deposited on a Si3N4 membrane, where

they self-assembled upon slow evaporation of the solvent under

ambient conditions. A magnetic multilayer, consisting of

1 nm Cr / 5 nm Pd / [0.28 nm Co / 0.8 nm Pd]7 / 0.28 nm Co /

20 nm NiFe / [0.28 nm Co / 0.8 nm Pd]8 / 1 nm Pd, exhibiting a strong

PMA was deposited onto the PS spheres by electron-beam evaporation

of Co and Pd at room temperature.

X-ray images were recorded at the Co L3 edge. A particle diameter of

~50 nm can be derived from the X-ray images. Fig. 6 shows the

magnetic patterns in a field of view divided between a monolayer (top)

and an area with more than one monolayer of PS particles (bottom).

Although this image was taken with 35 nm spatial resolution, details in

the magnetic pattern arrangement can be clearly distinguished.

Arrays of microelementsArrays of magnetic micro- and nanoelements are expected to form the

basic components for future spintronic applications such as magnetic

random access memory95,96. Dipolar interactions in dense arrays are

Fig. 5 (Top) Hysteresis loop of a nanogranular (Co83Cr17)87Pt13 alloy thin film derived from an integration of the grayscale intensity in magnetic X-ray images taken

at the Co L3 absorption edge. The total observation area corresponds to ~2.1 x 1.6 µm2 (300 x 240 pixels). (Center) Field-dependent magnetic domain patterns at

various magnetic fields (indicated by the arrows) during the field cycle. A 75 x 75 pixel region is denoted and divided into a 5 x 5 grid pattern used for the

determination of local hysteresis loops. Each grid has 15 x 15 pixels (equivalent to 100 x 100 nm2). (Reprinted with permission from91. © 2005 American Institute of

Physics.)



Fig. 6 Magnetic domain structure in monodisperse spherical PS particles

covered by a magnetic multilayer consisting of 1 nm Cr / 5 nm Pd /

[0.28 nm Co / 0.8 nm Pd]7 / 0.28 nm Co / 20 nm NiFe / [0.28nm Co /

Pd 0.8 nm]8 / 1 nm Pd. The image was recorded at the Co L3 absorption edge

(777eV). Two areas with different PS particle coverage can be seen.

important because magnetic properties, such as magnetization process,

remanence, and coercive field, can be significantly different from those

of noninteracting systems. The field of view of X-ray microscopy, and

the ability to tessellate even larger areas while maintaining high spatial

resolution, makes it a perfect tool for such studies97.

Arrays of Fe microelements98, consisting of a 5 nm Al seed layer,

20 nm Fe ferromagnetic layer, and 3 nm Al protective cap layer, were

defined by electron-beam lithography and fabricated by electron-beam

evaporation of the Fe layer and lift-off processing on Si3N4 membranes.

Fig. 7 shows representative X-ray images of various arrays of

micron-sized elements, where the influence of the spacing between

neighboring elements on the magnetic domain structure and switching

behavior was studied systematically. Unlike the PMA systems

mentioned above, these magnetic systems with a pronounced in-plane

magnetization have to be tilted at an axis perpendicular to the photon

beam direction to achieve a projection of the magnetization99.

Therefore, the dark and white regions have magnetizations that point

left and right in the images, respectively, while the magnetization of the

regions of intermediate gray intensity point up or down along the plane

so as to fulfill the flux closure condition in squared elements. A strong

dipolar coupling is observed with interelement spacings up to >600 nm.

This agrees with theoretical calculations, which predict significant field

strengths for the spacings discussed here100. Micromagnetic simulations

are able to calculate the domain configuration in a few elements101.

However, both the stray-field coupling and micromagnetic simulation in

real arrays, i.e. systems with inhomogeneities in shape and composition

as well as a larger number of elements, are very time and resource-

consuming tasks.

Investigating the static properties of magnetic-domain structures

and their magnetization reversal behavior with magnetic X-ray

microscopy is an important step. Directly measuring the reversal

dynamics of magnetic microstructures by time-resolved magnetic X-ray

microscopy is a very appealing further step.

Magnetization dynamicsSpin dynamics, i.e. the temporal development of magnetization, is

described by the Landau-Lifshitz-Gilbert (LLG) equation of motion102,103:

(1)

where the first term accounts for the precession of the magnetization

in an external magnetic field Heff with γ being the gyromagnetic ratio,

and the second term describes the relaxation and damping of the

system with α being a damping constant depending strongly on the

local geometry, anisotropy, and morphology. The mechanisms

governing the relaxation processes are currently only poorly

understood. Typical precession frequencies for micron-sized elements

are in the gigahertz regime, while the relaxation time can extend to

several hundred picoseconds.

The intrinsic, pulsed time structure of synchrotron radiation is

determined by the length of the electron bunches circulating in the

storage ring, i.e. about 70 ps at the ALS. While the normal operation

mode of the storage ring runs at a repetition frequency of 500 MHz, it

can also be operated in a so-called ‘two-bunch’ mode with only two

electron bunches circulating in the ring.

Time-resolved X-ray microscopy uses a pump-probe scheme with a

stroboscopic illumination of the sample’s magnetization (Fig. 8)104.

Short electronic pulses (rise time < 100 ps) launched into microcoils or

waveguide structures (the pump) generate short magnetic field pulses

either perpendicular or along the surface of the magnetic elements.



Fig. 7 Magnetic X-ray microscopy images of arrays of Fe microelements with

(a) 200 nm, (b) 600 nm, (c) 800 nm, and (d) 2000 nm interelement spacing

in a magnetic field of µ0H = +8.7 mT. The magnetic field direction is indicated

by the arrow. The inset in (d) is an enlarged image of one microelement in this

array with the magnetization indicated by arrows. (Reprinted with permission

from98. © 2005 American Institute of Physics.)

Fig. 8 Stroboscopic pump-and-probe experimental setup for investigating fast

magnetization dynamics in micron-sized magnetic elements. Electronic pulses

launched into a microcoil generate a magnetic pump pulse on the sample’s

magnetization. Two electron bunches circulating in the storage ring at 3 MHz

provide the X-ray probe pulse. Varying the delay between the pump and probe

pulses allows the temporal evolution of the z-component of the magnetization

to be followed.

(a) (c)

(d)(b)

2 µm

H

The probe pulses are X-ray flashes, which can be delayed up to several

nanoseconds to follow the temporal evolution of the local

magnetization.

A typical series of images reflecting the temporal evolution of the

magnetization in a 4 x 4 µm2 [3 nm Al / 50 nm Ni80Fe20 / 2 nm Cu /

50 nm Co] element are shown in Fig. 9105. The contrast seen shows the

temporal variation of the z-component of the magnetization of the Fe

into and out of the paper plane. Several hundred images were

accumulated per time step, since the rather weak field pulse amplitude

tips the magnetization only into a cone of a few degrees. Two different

precession modes in the square element can be observed, one of them

located along the domain walls. These results are in agreement with

micromagnetic simulations proving that the magnetization dynamics in

these elements can be described by eq 1.

OutlookMagnetic TXM is a novel technique that allows the study of

nanomagnetism with elemental selectivity. Current X-ray optical

elements have achieved a spatial resolution better than 15 nm, and

nanofabrication techniques now available should open the path for

zone plates with spatial resolution in the 10 nm regime. Unique

diffractive optical elements106, with special emphasis on magnetic

phase contrast imaging, will allow a focus on the regions of spin

inhomogeneities, such as domain wall structures. Advanced

source and detection schemes for improving the time resolution

of X-ray microscopy toward the picosecond regime are being

discussed at third-generation synchrotron sources. With the

construction of free electron X-ray lasers, investigations of

femtosecond spin dynamics with X-ray microscopy might also become

feasible in the future107,108.

A fundamental understanding of the physics of nanomagnetism

and further technological development of nanoscale magnetic systems

require experimental tools that are able to image magnetic

nanostructures at high spatial and temporal resolution. Magnetic X-ray

microscopy might also become feasible in the future.

AcknowledgmentsThe continuous help of the technical staff of CXRO and the ALS is highly

appreciated. We highly appreciate fruitful collaborations with M.-Y. Im and

S.-C. Shin (KAIST Taejeon, South Korea) on nanogranular films, M. Albrecht

(University of Konstanz, Germany) on curved surfaces, and G. Meier,

M. Barthelmes, R. Eiselt, and M. Bolte (University of Hamburg, Germany) on

magnetic arrays. Time-resolved studies were performed in collaboration with

H. Stoll, A. Puzic, and B. v. Waeyenberge (Max Planck Institute, Stuttgart,

Germany), and J. Raabe, M. Buess, T. Haug, R. Höllinger, C.H. Back, and

D. Weiss (University of Regensburg, Germany). This work was supported by the

Director, Office of Science, Office of Basic Energy Sciences, of the US

Department of Energy under Contract No. DE-AC03-76SF00098, the German

Research Foundation (DFG) within the priority program ‘Ultrafast

Magnetization Processes’ (FI 542/3-1,2), and partially supported by the

National Science Foundation under grant EEC-0310717.



Fig. 9 (a) The z component of the dynamic magnetization at selected time delays obtained from micromagnetic simulations using the object-oriented

micromagnetic framework (OOMMF). (b) Magnetic X-ray images of the temporal evolution of the z-component of the magnetization at delay times varying from

400 ps before the pump pulse up to 2400 ps after the pump. (Reprinted with permission from105. © 2004 American Institute of Physics.)

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soft x-ray microscopy of nanomagnetism

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