New Journal of Physics
The open–access journal for physics

Spin polarization vectors of field emitted electrons
from Fe/W tips
T Irisawa1 , T K Yamada1,2,3 and T Mizoguchi1
1
Faculty of Science, Gakushuin University, 1-5-1 Mejiro, Toshima,
171-8588 Tokyo, Japan2
Physikalisches Institut, Universität Karlsruhe, Wolfgang-Gaede Strasse 1,
Geb.30.23, 76131 Karlsruhe, Germany
E-mail: Toyokazu.Yamada@pi.uka.de
New Journal of Physics 11 (2009) 113031 (11pp)

Received 08 July 2009
Published 17 November 2009
Online at http://www.njp.org/
doi:10.1088/1367-2630/11/11/113031

The atomic and electronic structures at the apex of W tips werestudied by means of field ion microscopy and field emission microscopy, before
and after the thermal deposition of a 5 nm Fe film. Two geometries of W tip, aconventional hemi-spherical type and a chisel (flat needle) type, were prepared.
The hemispherical and the chisel W tips had a h110i direction parallel andperpendicular to the tip axis, respectively. The coated Fe films were found to be
most likely in a non-crystalline phase, and to have a lower work function leading
to a drastic change in electron emission from the apexes. The spin-polarization
vectors of field-emitted electrons from these Fe/W tips were investigated witha Mott detector with a rotatable mechanism of tips. A similar absolute value ofthe spin-polarization vector | PE tip | = 0.415 ± 0.025 was obtained for each Fe/W,
while the direction of the spin-polarization vector was dependent on the shapeof the apex. The angle from the tip axis was θ = 45◦ for the hemispherical apexand θ = 66◦ for the chisel apex. A spin-polarized scanning tunneling microscopy
setup with a rotation mechanism of such Fe/W tips made it possible to detect boththe in-plane and the out-of-plane spin component of a sample magnetization.
Abstract.

3

Author to whom any correspondence should be addressed.

New Journal of Physics 11 (2009) 113031
1367-2630/09/113031+11$30.00© IOP Publishing Ltd and Deutsche Physikalische Gesellschaft

2Contents

1. Introduction
2. Results and discussion
3. Conclusions
Acknowledgments
References

2
2
9
10
10

1. Introduction

The field emission microscope (FEM) invented by Müller in 1936 was the first tunnelingmicroscope [1], while the field ion microscope (FIM) invented later by him gave the first direct
atomic image of tungsten (W) crystals in real space. These microscopes visualize the atomic
arrangements at the apex of a sharp W tip. It is rather strange that, as far as we know, not verymuch information about the spin polarization of field-emitting electrons has been reported formagnetic tips; to date only for Ni tips, Fe tips, or EuS-coated W tips [2]–[6]. The apex of the tip
is known to be an attractive regime since atoms at a sharp apex are not only found at the surfaceof the material, but exist at a singular point of the surface with less coordination, which may
have unique electronic states connecting a single atom to the bulk material.
Spin-polarized scanning tunneling microscopy/spectroscopy (SP-STM/STS) is one of thetechniques for investigating atomic-scale magnetism, which has been rapidly developed fromthe beginning of this century [7]–[30]. Magnetic images obtained with SP-STM/STS are basedon a contrast, which is proportional to an inner product of the spin-polarization vector of amagnetic tip PE tip and that of a sample PE sample [26, 27]. In order to obtain the spin-polarizationof a sample quantitatively it is essential to know the magnitude and direction of the spinpolarization vector of tunneling electrons from the tip used in the measurement. No direct
measurement of the spin-polarization vector of a magnetic tip for SP-STM was reported, which
limited measurement of the quantitative information from the SP-STM/STS data.
So far W tips coated with magnetic thin films are mostly used for SP-STM/STS. The
most popular Fe(2–10 nm)-coated W tips are a sensitive to in-plane magnetic moments of thesample surface [7]–[10], [15], [20]–[22], [25]–[32], while other kinds of tips, e.g. Cr(5–10 nm)coated W tips, Gd(2 nm)-coated W tips and Gd90 Fe10 (2–3 nm)-coated W tips, have out-of-planesensitivity at low temperatures [11, 13, 19, 23, 32]. The amplitude of the spin polarization wasreported for a Fe/Al2 O3 /Al tunnel junction to be 0.44, which is the same for flat Fe films on
W [33]. For SP-STM/STS measurements, dull tips with an apex of 1 µm radius were reported
to be appropriate [32], since there will be an almost flat apex and therefore the spin polarization
vector of the Fe films follows the magnetic shape anisotropy and is aligned in-plane.
In this study, we investigated the atomic, electronic and spin structures of Fe films with athickness of 5 nm grown on two types of W tips: (1) a conventional hemispherical type tip and(2) a chisel (flat needle) type tip by means of FIM, FEM, microbeam x-ray diffraction, scanningelectron microscopy (SEM), and a custom-built instrument including a Mott detector.
2. Results and discussion

Two types of W tips were prepared, one by means of chemical etching from a wire, and theother from a narrow thin foil cut out perpendicularly to the roll direction. The W wires or foils
New Journal of Physics 11 (2009) 113031 (http://www.njp.org/)

3

Figure 1. Investigations of the hemispherical W tip. (a) and (b) SEM images of
the apex of the tip. A side (a) and a top (b) view. (c) X-ray Debye–Scherrer image(Cu target) obtained from the wire. (d) FIM image (+5 kV, He+ ). (e) Solid-spheremodel. (f) FEM image (−0.4 kV).

most usually available are highly oriented polycrystals, as the slip planes of crystalline grains areparallel to the h110i direction which follows the elongated direction, i.e. the wire direction or rolldirection. SEM images of a hemisphere-type tip made from the wire and a chisel-type tip madefrom the foil are shown in figures 1(a) and (b) and 2(a)–(c), respectively. It was confirmed by
x-ray diffraction measurements with a focused beam of 5 µm, that the tip axes are parallel orperpendicular to Wh110i at the top part of the tips, as shown in figures 1(c) and 2(d). These W
tips were installed in our ultra-high vacuum (UHV) chamber and the apexes of the tips werecleaned by field evaporation. The atomic structure of the obtained clean apexes of the W tips
was investigated by FIM.
FIM measurements were taken at room temperature in a UHV chamber (∼10−8 Pa) toinvestigate the atomic and electronic structures of the tip apex. He+ ions of ∼10−3 Pa fromthe apex were accelerated to a multi-channel plate (MCP) which enhanced incoming signals
and showed features on a fluorescent screen imaged by a CCD camera. Single dots in the FIM
image corresponded to single atoms at atomic steps. Our FIM setup had a magnification of
about 106 , i.e. a 1 nm-size structure at the apex of the tip appeared as a size of 1 mm on thescreen. The FIM image of the hemispherical tip is shown in figure 1(d). Concentric circles ofthe spots can be observed around the center of the image. The bright spot in the center of theimage shows the remaining atoms in the uppermost atomic plane after the field evaporation. Our
FIM measurements were taken at room temperature, and the spots are not as clear as those froman FIM operated at low temperatures. To understand the atomic structure of the tip apex, a solid
sphere model was used (figure 1(e)). By comparing the model and the obtained FIM image we
could identify the atomic planes around the apex of the hemispherical tip. In the center of the
New Journal of Physics 11 (2009) 113031 (http://www.njp.org/)

4

Figure 2. Investigations of the chisel-type W tip. (a)–(c) SEM images of the apexof the tip. Side views (a, c) and a top view (b). (d) X-ray Debye–Scherrer image(Cu target) obtained from the tip. (e) FIM image (+9.9 kV, He+ ). (f) FEM image(−4.2 kV).
FIM image, the area within a diameter of about 10 nm has a (110) plane. {112} and {100} atomic
planes are seen around the (110) plane.
FEM measurements were performed under UHV conditions with the same experimental
setup by changing the applied bias from positive to negative. In this way, we obtained theelectronic structure of the same apex. The FEM image of the hemispherical tip shows four brightspots (figure 1(f)), whose positions correspond to the areas of {100} and {211} planes in the FIM
image. The central plane (110), which has the highest work function [34], appears darker.
On the other hand, the chisel-type tip showed a completely different FIM image (seefigure 2(e)). There were several spots in the FIM image before the tip was cleaned by the fieldevaporation, and only one bright spot was left after the field evaporation. Several chisel-type
W tips showed the same behavior. Only bright spots instead of atomic planes were observed,
which indicates a protuberance of about 3 nm at the apex. The FEM image of the same apex isshown in figure 2(f). One bright spot is observed at exactly the same position of the protuberance
observed in the FIM image, i.e. electrons emit from this protuberance.
After these FIM/FEM measurements, the W tips were moved in front of an Fe evaporator
in the same UHV chamber. An Fe film with a thickness of 5 nm was grown on the apex of the
W tip at room temperature with an evaporation rate of ∼1 nm min−1 calibrated with a quartz
New Journal of Physics 11 (2009) 113031 (http://www.njp.org/)5

Figure 3. (a) and (b) show an FIM and an FEM image, respectively, obtained

from the 5 nm Fe film coated on the hemisphere-type W tip. (c) F–N plot of thehemispherical W tip shifts to a lower voltage side after the deposition of a 5 nm
Fe film. (d) and (e) show an FIM and an FEM image, respectively, obtained
from the 5 nm Fe film coated on the chisel-type W tip. (f) F–N plot of thehemispherical W tip shifts to a higher voltage side after the deposition of a 5 nm
Fe film.
thickness monitor. After the deposition, the tip was not annealed and there was no external field
applied. Thus, the tips were moved back to the position for the FIM/FEM measurements.
Figure 3(a) shows the FIM image obtained from the hemispherical W tip coated by the
Fe film. Many bright spots were observed, without an ordered arrangement. Also, anotherhemispherical W tip coated by the Fe film appeared different in FIM images, which indicatesthat the atomic structure of the Fe film on the hemispherical W tip with the (110) plane does
not have a reproducible ordered arrangement, i.e. it probably has a non-crystalline structure.
The FEM image obtained from the same apex is shown in figure 3(b). The character of
the FEM image also drastically changed after the deposition of Fe (cf figure 1(f)). Fourbright spots were observed around the apex, which seem not to be related to any particularatomic planes.
We took FIM/FEM measurements for the Fe-coated chisel-type W tips as well. The FIM
image (figure 3(d)) shows several bright spots near the protuberance observed in the FIM imageof figure 2(e). Again, no clear atomic structure was observed. Due to the curved W substrate
the Fe film is not assumed to grow epitaxially, but in a non-crystalline phase. The FEM image
obtained from the same apex is shown in figure 3(e). One bright spot is observed, whose positionis the same as the position of the protuberance shown in figure 2(f). Electrons emit from the same
position before and after the Fe deposition.
From these experiments, we conclude the following for the W tips and Fe-coated W
tips. (1) The hemispherical W tip has a clean (110) plane at the apex due to the preferred
New Journal of Physics 11 (2009) 113031 (http://www.njp.org/)

6
Table 1. Obtained parameters from the F–N plots. r denotes the radius of the tip,

8 the work function. Details are described in the text.
A

B (V) r (nm) 8 (eV)Hemi-spherical W tip
175.1 −6265 13.4
Hemi-spherical Fe/W tip 192.8 −3891 18.4
Chisel-type W tip
1150 −48941
Chisel-type Fe/W tip
25 −56970

α

kr

kα

5.84 0.786 × 108 67.0
3.93 × 108
8
3.38 1.632 × 10
92.1
8.16 × 108(5.84)(510.1) (2.99 × 1010 )(3.38)(1348.2) (0.45 × 1010 )h110i orientation parallel to the tip axis. Electrons emit mainly from the surrounding W{100}and W{211} atomic planes, while electrons emit from no clear atomic planes after the depositionof Fe. (2) The chisel-type W tip has a nanometer-scale protuberance at the apex. Electrons
emit mainly from here before and after the deposition of Fe. (3) The Fe films on thehemispherical as well as the chisel-type W tips probably have a non-crystalline structure.
We measured the total electron emission curves as a function of the bias voltage by bringing
a metal ball in front of the apexes of the W tips before and after the deposition of Fe (figure 3(c)for the hemispherical tip and figure 3(f) for the chisel-type tip).
The emission characteristics are expressed in the scheme of Fowler and Nordheim(F–N) [34, 38], where Y = log(I /V 2 ) is plotted as a function of X = V −1 , as shown infigure 3(c) for hemispherical tips and in figure 3(f) for chisel-type tips. All curves are shown
to be well fitted with a straight line, i.e. Y = A + B X with negative slopes (B < 0) regardlessthe shape or materials at the apexes (W or Fe/W). Experimentally obtained fitted parameters
A and B are summarized in table 1. From the F–N equation, those are related as A = α/(kr )2and B = ckr 83/2 , where 8 denotes the work function of the apex, k represents a geometricconstant which is about 5 for a hemispherical apex, α is proportional to a discharge area andobtained experimentally, and c = −0.68 is calculated from physical constants using the unit of
nm for length and nA for current.
The radius of the hemispherical W tips is estimated from the FIM image in figure 1(d)with a combination of the solid-sphere model in figure 1(e), where eight steps of the W(110)atomic planes are observed between the central(110) pole and the {211} poles. Since the√angle between h110i and h211i is cos−1 (3/ 12) = 30◦ , and inter-plane distance of {110} in
W is d110 = 0.224 nm, a radius of curvature of the hemisphere-type tip apex is r = 8d110 /(1 −cos θ) = 13.4 nm. This value for the hemispherical W apex and the observed B value in table 1
give a work function, 8 = 5.84 eV, which is consistent with values given in the literature [34].
For a hemispherical Fe/W apex, the radius of curvature is, r = 18.4(= 13.4 + 5) nm and the
reduced B value give us the reduced work function, 8 = 3.38 eV. Thus, more emission current
flows and the F–N line shifts upward.
For the chisel-type apex there is no theoretical derivation, nevertheless the F–N plots ofobserved data show straight lines for both the W and Fe/W apex as shown in figure 3(f). It
is interesting that the F–N line for the Fe/W apex shifts downward relative to that for the W
apex after deposition of Fe. If we assume the same work functions for W and Fe/W as for thehemispherical tip, the observed parameters, B and A(kr )2 , give us kr and kα as shown in table 1.
They are much larger than those in the hemispherical tips, suggesting the effective curvature of
apex for the chisel-type tip is much larger. The apex is considered to become smoother after
deposition of Fe, shifting the F–N line downward.
New Journal of Physics 11 (2009) 113031 (http://www.njp.org/)

7
The spin-polarization vectors of the emission current from these Fe-coated W tips were
measured by our purpose-built instrument, inclusive of a Mott detector. Field-emission electrons
were mainly emitted from the Fermi level of the tip. It is certain that field-emitted electrons
from the Fe-coated W tip were spin-polarized as this tip shows spin contrast in SP-STM/STS
images [7]–[10], [15], [20]–[22], [25]–[32]; however, as far as we know, the spin-polarization
vector has not been definitely measured so far. For a standard polarization measurement of theelectron beam, a calibrated Mott detector was used [35]. It detects only components of spinpolarization perpendicular to the incident direction. In order to measure three components ofthe spin-polarization vector, the field-emitted electrons in the z-direction were deflected electrostatically by 90◦ without changing spin direction, as shown in figure 4(a), before going into theMott detector, which gave a constant Pz (polarization component parallel to the tip axis) and asinusoidal variation of P y (polarization component perpendicular to the tip axis) as a function of
the rotating angle of the tip around its axis. A schematic sketch of this system with the definitionof the x-, y-, and z-axes is shown in figure 4(a). The Mott detector was calibrated using 30%
spin-polarized photo-electrons from negative electron affinity (NEA)-GaAs{110} illuminatedwith circularly polarized light, as shown in figure 4(b). The Shaman function (the ratio of theasymmetry As measured with our Mott detector to the spin polarization P) was measured to be
S = As /P = 0.12.
Components (Pz and P y ) of the spin-polarization vectors were obtained from theasymmetries of the measured emission current from the Fe-coated W tips with the Mott detector
by rotating the tip by an angle φ around its axis. The x, y and z components of the spinpolarized vector are expressed in polar coordinates as Px = Psin θsin φ, P y = Psin θ cos φ,and Pz = Pcos θ , where θ is an angle between the polarization vector and the z-axis (the tip
direction) and φ is the angle between the polarization vector and y-axis. When we rotate thetip around the z-axis, P y shows sinusoidal variation with the maximum value, P y:max , which isthe component of the spin-polarization vector
q perpendicular to the tip axis. The absolute valueof the vector can be obtained as | PE tip | = P y:max 2 + Pz 2 . The direction of the spin-polarization
vector of emitted electrons from the Fe-coated W tip is expressed by θ = tan−1 (P y:max /Pz ) andφ at which P y shows the maximum value. The experimentally obtained components of thespin-polarization vector of electrons emitted from the hemispherical Fe/W apex are shown infigure 4(c). We obtain P y:max = 0.31, Pz = 0.31 and then the absolute value of the spin-polarized
vector turns out to be | PE tip | = 0.44 and θ = 45◦ . The components of the spin-polarization vectorof the electrons emitted from the chisel-type Fe-coated W tip are shown in figure 4(d), fromwhich we obtain P y:max = 0.36, Pz = 0.16 and then the absolute value of the spin-polarized
vector turns out to be | PE tip | = 0.39, θ = 66◦ , and the angle between the polarization vector
and the edge direction, which is set initially in y-axis, of the chisel-type tip is 28◦ . Notethat the absolute value of the spin polarization of electrons emitted from the Fe-coated W
tips is | PE tip | = 0.415 ± 0.025, which is close to the value obtained for a Fe/Al2 O3 /Al tunnel
junction [33], regardless of apex shape. With this value we can directly obtain the sample spinpolarization from the experimentally obtained maximum spin contrast in SP-STM/STS data, i.e.
| PE sample | = ASTM /| PE tip |.
The direction of the vector is, however, different from tip to tip, suggesting that the local
direction of magnetization at the point of electron emission from an Fe film at the apex of a
tip is indefinite. However, it is worth noting that an Fe/W apex, which is typically used fornormal STM measurement, has an almost constant absolute value of spin-polarization vector,
and has not only a perpendicular, but also a parallel component, to the tip axis for a sharp tip.
New Journal of Physics 11 (2009) 113031 (http://www.njp.org/)

8

Figure 4. (a) Schematic sketch of our experimental setup. The gray line shows

the path of the emission current beam from the apex of the tip. (b) Experimentallyobtained asymmetry at each channeltron (black dots) with ±30% spin-polarized
current from the NEA-GaAs surface excited by a left/right circular polarized
light, giving the maximum asymmetry at exactly 0◦ parallel to the y-axis.
(c) and (d) Components (Pz and P y ) of the spin-polarization vectors of fieldemitted electrons from the Fe-coated W apex as a function of a rotating angleof the tip around the z-axis (φ). White and black dots denote experimentallyobtained P y and Pz , respectively. Plots (c) and (d) were obtained from thehemispherical tip and the chisel-type tip, respectively.
If SP-STM/STS measurements are performed with such a tip rotatable around the tip axis, allcomponents of sample spin-polarization vector can be obtained. The amplitude of the sinusoidal
variation of magnetic contrast with the tip rotation angle gives the in-plane components to
New Journal of Physics 11 (2009) 113031 (http://www.njp.org/)

9
Table 2. Obtained values of spin polarization vectors of the Fe/W tips.
P y:max
Hemi-spherical Fe/W apex
Chisel-type Fe/W apex

0.31
0.36

Pz
0.31
0.16

| PE tip |
0.44
0.39

θ

φ
◦

45
66◦

−30◦
−28◦

a sample surface and the average gives the out-of-plane component. Calibration of the spinpolarization vector of the tip apex with a standard sample, e.g. Fe whiskers or photo-excited
GaAs{110} cleaved in UHV [28], would be desirable for quantitative discussions.
The tips used for field emission are sharper than an ordinary SP-STM/STS tip whose apex
has a radius of curvature of a few hundred nm, as described before [28, 32]. Fe thin film 5 nm
thick on such a flat apex probably has in-plain magnetization, i.e. θ = 90◦ , and therefore in-plain
sensitivity. Even in such a flat thin magnetic film, there is the possibility of magnetic domains
and domain walls, which are easily identified by a slight dent or protuberance where electroemission probably occurs. In this study sharp tips with a hemispheric or ellipsoid apex coatedby Fe were used. The magnetic anisotropy, which is one of the important factors in determining
domain wall width, may be weaker than that in a bulk bcc-Fe crystal since the evaporated Fethin film on the apex of a W tip probably has a non-crystalline structure, which leads to a more
gradual change of spin direction in a domain wall. Micro-magnetic simulations for magnetic
domain structures of such a complex thin film have to be performed. Shape anisotropy may
play an important role, as the magnetic dipole interaction is long ranged. We expected different
magnetic shape anisotropies for the hemispherical apex and the chisel-type (edge-like) apex oftips.
In our previous work [26, 27] with Fe-coated W tips with a radius of about 100–200 nm, we
demonstrated an in-plane sample spin polarization | PE sample | = 0.67 on Mn(001) surface from theobserved maximum contrast of Astm = 0.1 by SP-STS. We required two assumptions. Firstly,that the in-plane tip and sample spin-polarization vectors were parallel and, secondly, that theamplitude of the in-plane tip spin polarization vector was 0.15, which value was estimated by
a comparison between observed spin-resolved local density of states (LDOS) and theoreticallycalculated LDOS [26]. Now we know that the Fe-coated W tip has | PE tip | ∼ 0.415. With thisvalue the angle of the polarization vector of the tip that we used can be estimated to be θ = 21◦ .
3. Conclusions

When viewing the atomic image of materials by field ion microscopy, the apex of the tip isseen to be an attractive regime since atoms at a sharp apex are not only at the surface of asolid state, but exist at a singular point of the surface with less coordination, which may haveunique electronic states connecting a single atom to a solid state of materials. Iron is one of
the most popular magnetic materials and many important physical properties have been foundin its bulk and surface. We focused on the study of iron in the regime of the apex. There had
been, to date, no direct measurement of spin-polarization vectors at the apex of magnetic tips,
in spite of the fact that such magnetic tips have been widely used for SP-STM/STS, which
limited the quantitative information obtainable from the experimentally obtained spin contrast
in SP-STM/STS data.
In this study, we investigated the atomic, electronic and spin structures of Fe films witha thickness of 5 nm grown on the apex of the W tips. Two kinds of W tips were prepared to
New Journal of Physics 11 (2009) 113031 (http://www.njp.org/)

10
study the influence of different magnetic shape anisotropy at the apex: the hemispherical W tip
with a (110) plane at the apex and the chisel-type W tip (the h110i direction is perpendicular
to the tip axis). FIM showed that the Fe films are in non-crystalline phase. The emission ofelectrons from the tip was drastically changed before and after the deposition of Fe, which
may be due to a great variation of the work function at the apex. All three components ofthe spin-polarization vector of the field-emitted electrons from Fe/W apex of two kinds of tips
were measured with an instrument specially designed and constructed in-house. As shown intable 2, the absolute value of the spin-polarization vector of emitted electrons from both thehemispherical apex and the chisel-type apex were almost the same as | PE tip | = 0.415 ± 0.025,
while the direction of polarization vectors was found to be different. The angle from the tip axisis θ = 45◦ for the hemispherical apex and θ = 66◦ for the chisel apex. A SP-STM setup withrotation mechanism of such Fe/W tips makes possible the detection of both in-plane and out-of
plane spin components of a sample magnetization.
Acknowledgments

We thank Dr Hono for his advice in performing FIM experiments. We acknowledge Dr J Cole,Dr A Bork, Dr L Gerhard and Dr W Wulfhekel for their careful reading of the manuscript andfor their helpful discussions.
References[1] Müller E W 1937 Z. Phys. 106 132[2] Müller N, Eckstein W, Heiland W and Zinn W 1972 Phys. Rev. Lett. 29 1651
[3] Chrobok G, Hofmann M, Regenfus G and Sizmann R 1977 Phys. Rev. B 15 429[4] Landolt M and Campagna M 1977 Phys. Rev. Lett. 38 663
Landolt M and Campagna M 1978 Surf. Sci. 70 197[5] Landolt M and Yafet Y 1978 Phys. Rev. Lett. 40 1401
[6] Nagai S, Fujiwara Y and Hata K 2009 Ultramicroscopy 109 395[7] Wiesendanger R, Bode M and Getzlaff M 1999 Appl. Phys. Lett. 75 124[8] Heinze S, Bode M, Kubetzka A, Pietzsch O, Nie X, Blügel S and Wiesendanger R 2000 Science 288 1805
[9] Kleiber M, Bode M, Ravlić R and Wiesendanger R 2000 Phys. Rev. Lett. 85 4606
[10] Pietzsch O, Kubetzka A, Bode M and Wiesendanger R 2001 Science 292 2053
[11] Krause S, Berbil-Bautista L, Herzog G, Bode M and Wiesendanger R 2007 Science 317 1537
[12] Bode M, Heide M, von Bergmann K, Ferriani P, Heinze S, Bihlmayer G, Kubetzka A, Pietzsch O, Blügel S
and Wiesendanger R 2007 Nature 447 190[13] Meier F, Zhou L, Wiebe J and Wiesendanger R 2008 Science 320 82[14] Wulfhekel W, Ding H F, Lutzke W, Steierl G, Vazquez M, Marin P, Hernando A and Kirschner J 2001 Appl.
Phys. A 72 463[15] Yamasaki A, Wulfhekel W, Hertel R, Suga S and Kirschner J 2003 Phys. Rev. Lett. 91 127201[16] Schlickum U, Wulfhekel W and Kirschner J 2003 Appl. Phys. Lett. 83 2016[17] Schlickum U, Janke-Gilman N, Wulfhekel W and Kirschner J 2004 Phys. Rev. Lett. 92 107203[18] Gao C L, Schlickum U, Wulfhekel W and Kirschner J 2007 Phys. Rev. Lett. 98 107203[19] Gao C L, Wulfhekel W and Kirschner J 2008 Phys. Rev. Lett. 101 267205[20] Yang H, Smith A R, Prikhodko M and Lambrecht W R L 2002 Phys. Rev. Lett. 89 226101[21] Okuno S N, Kishi T and Tanaka K 2002 Phys. Rev. Lett. 88 066803[22] Kawagoe T, Iguchi Y, Yamasaki A, Suzuki Y, Koike K and Suga S 2005 Phys. Rev. B 71 014427

New Journal of Physics 11 (2009) 113031 (http://www.njp.org/)

11[23] Yayon Y, Brar V W, Senapati L, Erwin S C and Crommie M F 2007 Phys. Rev. Lett. 99 067202[24] Prokop J, Kukunin A and Elmers H J 2006 Phys. Rev. B 73 014428[25] Yamada T K, Bischoff M M J, Mizoguchi T and van Kempen H 2003 Appl. Phys. Lett. 82 1437
[26] Yamada T K, Bischoff M M J, Heijnen G M M, Mizoguchi T and van Kempen H 2003 Japan. J. Appl. Phys.
42 4688[27] Yamada T K, Bischoff M M J, Heijnen G M M, Mizoguchi T and van Kempen H 2003 Phys. Rev. Lett. 90
056803[28] Matsuda T, Tonomura A, Yamada T K, Okuyama D, Mizuno N, Vazquez de Parga A L, van Kempen H and
Mizoguchi T 2005 IEEE Trans. Magn. 41 3727
[29] Yamada T K, Robles R, Martinez E, Bischoff M M J, Vega A, Vazquez de Parga A L, Mizoguchi T and van
Kempen H 2005 Phys. Rev. B 72 014410[30] Yamada T K, Martinez E, Vega A, Robles R, Stoeffler D, Vazquez de Parga A L, Mizoguchi T and van
Kempen H 2007 Nanotechnology 18 235702[31] Balashov T, Takacs A F, Wulfhekel W and Kirschner J 2006 Phys. Rev. Lett. 97 187201[32] Bode M 2003 Rep. Prog. Phys. 66 523[33] Tedrow P M and Meservey R 1973 Phys. Rev. B 7 318[34] van Tol M F H, Hondsmerk F A, Bekker J W and Nieuwenhuys B E 1992 Surf. Sci. 266 529[35] Oshima Y, Yamada T, Fujii J and Mizoguchi T 2001 Trans. Magn. Soc. Japan 1 16
[36] Dyke W P, Trolan J K, Dolan W W and Barnes G 1953 J. Appl. Phys. 24 570[37] Pierce D T and Meier F 1976 Phys. Rev. B 13 55484
Pierce D T, Celotta R J, Wang G C, Unertl W N, Galejs A, Kuyatt C E and Mielczarek S R 1980 Rev. Sci.
Instrum. 51 478[38] Fowler R H and Nordheim L W 1928 Proc. R. Soc. Lond. A 119 173

New Journal of Physics 11 (2009) 113031 (http://www.njp.org/)