MICROSCOPY RESEARCH AND TECHNIQUE 66:93–104 (2005)

Evaluation of Sample Spin-Polarization From Spin-Polarized
Scanning Tunneling Spectroscopy Experiments
T.K. YAMADA,1,2* A.L. VÁZQUEZ DE PARGA,3 M.M.J. BISCHOFF,1 T. MIZOGUCHI,2 AND H. VAN KEMPEN1
1

Institute for Molecules and Materials, Radboud University Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands
Department of Physics, Faculty of Science, Gakushuin University, 1-5-1 Mejiro, Tokyo, Japan
Departamento de Fı́sica de la Materia Condensada e Instituto de Ciencia de Materiales ‘‘Nicolás Cabrera,’’Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid, Spain

2
3

KEY WORDS

antiferromagnetic coupling; manganese; iron; screw dislocation; tip magnetization

ABSTRACT
Spin-polarized scanning tunneling microscopy has produced a great amount ofimages presenting magnetic contrast between different magnetic domains with an unsurpassed
spatial resolution but getting values like the surface polarization has proven to be a difﬁcult task.
We will discuss in detail how to extract this information for the case of manganese layers grown on
Fe(001) whiskers. Mn layers adopt a body-centered-tetragonal (bct) structure when they are grownon the Fe(001) surface at room temperature. The Mn layers show an antiferromagnetic coupling
between the layers. Comparing our spin-polarized scanning tunneling spectra measured with
Fe-coated W tips with spin-resolved band structure calculations, we are able to ﬁnd the value ofthe sample surface polarization. Also discussed is a method to change the tip magnetization.
Finally, the magnetic structure around a screw dislocation on the surface is reviewed. Microsc. Res.
Tech. 66:93–104, 2005. ' 2005 Wiley-Liss, Inc.
INTRODUCTION
Since its invention by Binnig et al. (1982), the scanning tunneling microscope (STM) has revolutionizedsurface physics research due to its unprecedented spatial resolution combined with its spectroscopic capabilities. Very soon after, there were some ﬁrst attempts todevelop an STM with spin sensitivity. The knowledge
about the magnetic structures on very small scales isbelieved to be crucial for the fundamental understanding of micromagnetism and the controlling of magnetic
media and devices in the future. To overcome the
obstacles of the established magnetic imaging techniques, the development of the spin-polarized scanningtunneling microscope (SP-STM) to map the spin structure at surfaces down to the atomic level has been theaim of many studies in the past. An instrument withthis high resolution would offer fundamentally new
insights into the real space order of antiferromagnets,
ferromagnets, and ferrimagnets at irregular defects
such as dislocations, steps, or atomic point defects,
which are inaccessible to scattering techniques, or thetransmission of spin-polarized electrons across ferromagnetic/nonferromagnetic interfaces.
The ﬁrst SP-STM experiments in ultra-high vacuum(UHV) on a clean and well-characterized surface weredone by Wiesendanger et al. (1990) using a CrO2 tip.
Since then, several experimental approaches to perform SP-STM measurements have been proposed(Alvarado and Renaud, 1992; Bode et al., 1998; Prins
et al., 1996; Suzuki et al., 1997; Vázquez de Parga andAlvarado, 1994; Wulfhekel and Kirschner, 1999). The
more successful approach so far is the one proposed by
Bode et al. (1998). In this approach, a clean tungsten
tip is covered with a layer of magnetic material (ferromagnetic or antiferromagnetic) and the tunneling current depends on the relative orientation of the'2005 WILEY-LISS, INC.

magnetization of tip and sample. With this method, it
has been possible to take images of magnetic structures
down to the atomic level (Heinze et al., 2000) surpassing the lateral resolution of any other magnetic sensitive technique. The main limitation in the SP-STM
experiments until now is that it is very difﬁcult toobtain quantitative information about the surface magnetism. In this article, we will discuss how to overcome
this difﬁculty using as sample Mn layers grown on anFe(001) whisker. We will compare our spin-polarized
spectra measured with the STM with spin-resolved
band structure calculations in order to ﬁnd the polarization of the sample surface. We will also discuss indetail an experimental procedure to change the tip
magnetization. Finally, we will discuss the magnetic
structure of the Mn layers around a screw dislocation
present on the surface. Comparing the results obtained
for the ﬂat areas of the Mn ﬁlms with the ones obtained
around the screw dislocation, we are able to determine
the magnetization directions on the surface.
EXPERIMENTAL PROCEDURES
STM and scanning tunneling spectroscopy (STS) measurements were performed in UHV (*5  1011 mbar)
at room temperature (RT). The UHV chamber isequipped with a cylindrical mirror analyzer that allows*Correspondence to: Dr. T.K. Yamada, Department of Physics, Faculty of
Science, Gakushuin University, 1-5-1 Mejiro, Toshima-ku 171-8588, Tokyo,
Japan. E-mail: toyokazu.yamada@gakushuin.ac.jp
Received 30 September 2004; accepted in revised form16 December 2004
Contract grant sponsor: Ministerio de Educación y Ciencia; Contract grant
number: FIS2004-01026; Contract grant sponsor: JSPS Fellows; Contract grantsponsor: International Research Center for Experimental Physics (IRCEP) at the
Queen’s University, Belfast, Ireland; Contract grant sponsor: Stichting voor
Fundamenteel Onderzoek der Materie (FOM).
DOI 10.1002/jemt.20149
Published online in Wiley InterScience (www.interscience.wiley.com).

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T.K. YAMADA ET AL.

us to do Auger electron spectroscopy measurements,
ion gun, sample and tip heating facilities, low-energy
electron diffraction optics (LEED), and different evaporators cooled with liquid nitrogen that allow us todeposit material on the sample or tip, keeping the pressure below 5  1010 mbar.
An Fe(001) whisker was used as a substrate and wascleaned by cycles of Arþ sputtering (750 eV) andannealing (up to 7308C). After this cleaning process,around 1% oxygen contaminants were measured byAuger spectroscopy and also in atomically and chemically resolved STM images.
In order to produce a clean Mn(001) surface, about
7 mono-layers (ML) of Mn (purity 99.999%) were grownon the Fe(001) whisker, which was kept at 370 K. The
evaporation rate was 0.06 nm/min. After the deposition, more than two Mn layers were exposed on the surface. Using atomically and chemically resolved STM
images, we determined that the level of contaminants
was below 1% on the Mn surface. Mn layers grown on
Fe(001) have a bct structure with the same in-planelattice constant as Fe(001) and an interlayer distanceof 0.165 nm (Yamada et al., 2002).
In this study, we use W tips that were prepared asfollows. A W polycrystalline wire (purity 99.99%) witha diameter of 0.5 mm was chemically etched with
5 M KOH aq., then washed with distilled water andintroduced in UHV. Once in UHV, the tips were sputtered with Arþ (1 kV) and heated by electron-bombardment (2300 K). After this procedure, a clean and blunt
W tip is produced.
To get spectroscopic information from the sample surface, STS measurements were performed at every pixelof a constant current topographic image by opening the
feedback loop. In a typical measurement, the STM tip
stays at every pixel around 100 ms. During 20 ms, thefeedback loop is connected and the tip height is recorded
to construct the topographic image. During 80 ms, thefeedback loop is disconnected and the tunneling current
as function of the bias voltage is measured. The voltage
range explored was from 2 V up to þ3 V with a voltage
step of at least 25 mV. The dI/dV curves were obtainedby numerically differentiation of the I(V) curves.
THEORETICAL MODEL
STM is based on the quantum mechanical tunnel
effect. The ﬁrst and most simple approximation to get aquantitative understanding of the STM is a one-dimensional model. Let’s consider two metallic electrodes (tipand sample) separated by a vacuum gap of a few ångstroms. We will assume that the work function of both
metals is identical, that their electronic states can be
described in terms of a free electron gas and the temperature is 0 K. The probability density of an electronof one electrode to be located at the position of theother, i.e., at z ¼ d with d being the barrier width, isgiven by the square of its wave function:
w ¼ j ðdÞj2 ¼ j ð0Þj2 expð2kdÞ
The tunneling current ﬂowing between both electrodes is proportional to the sum of all electron states available within the energy interval relevant for tunneling:Iðd; VÞ / expð2kdÞ

EF
X

j

i ð0Þj2

Ei ¼ EF eV

The sum is taken over the different electronic statesi of one of the electrodes and the energy interval is set
by the voltage applied between the electrodes. Thisequation is expressed in terms of the local density ofstates (LDOS) by replacing the summation over discrete states by energy integration:
Iðd; VÞ /Z EF
dE
EF eVXdðEi  EÞj

2i ðdÞji¼

Z EFnðd; EÞdE
EF eVThe quantity n(d,E) is the LDOS of one electrode at
the position d of the other. If we differentiate the previous equation with respect to the energy, we see thatthe differential conductivity (dI/dV) is related to the
LDOS of one of the electrodes:dIðd; VÞ / nðd; EF þ eVÞdV
In the 1960s, Bardeen (1961) developed a theoreticalmethod for treating more realistic the tunnelingprocess between two planar electrodes. The basic
idea was that the interaction between the electrodes
was very weak and the electronic structure of bothcan be calculated independently. Following thisapproach, the tunneling current between two weakly
bounded electrodes using ﬁrst-order perturbation
theory is:Iðz; VÞ ¼

2pe X
jMt;s j2 dðEt  Es Þ½ f ðEt  eVÞ  f ðEs Þh t;swhere V is the sample bias voltage, z is the tip-sample
separation, Mt,s is the tunneling matrix element
between states of the tip and of the sample, f (E) is the
Fermi-Dirac function and Et and Es are the energy ofthe states on the tip and sample, respectively. In thesemi-classical WKB approximation, the density of thetunneling current between two planar electrodes canbe written as follows:
!2 Z
1
2pe 
h2
Tðz; V; EÞ½ f ðE  eVÞJðz; VÞ ﬃ
h 2m
1 f ðEÞrs ðEÞrt ðE  eVÞdE
where T(z,V,E) is the tunneling transmission probability, rs ðEÞ and rt ðEÞ are the sample and tip density ofstates, respectively. For low surface temperature theexpression for the density of tunneling current can be
written as follows:

95

EVALUATION OF SP-STM/STS EXPERIMENTS

Fig. 2. dI/dV curves measured at layers above the third layer (dots).
The set point of Vs ¼ 0.5 V, I ¼ 0.5 nA was used and the curve is anaverage of typically 20 single curves. A ﬁt of the tunneling probability
function to the dI/dV curve is also shown (T: grey solid curve). The
dI/dV curve normalized by this T, i.e., (dI/dV)/T (black solid curve),
reveals a strong peak around þ0.8 eV. Also, besides this þ0.8 eV peak,a weak peak at 0.6 eV is observed in the (dI/dV)/T curve.

!2 Z
eV
2pe 
h2
Jðz; VÞ ﬃ
Tðz; V; EÞrs ðEÞrt ðE  eVÞdE
h 2m

0

Assuming a strong preference for tunneling of electrons with the parallel component of the wave vector
equal to zero, the transmission probability can be written in the following way:sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
#
2m  eVTðz; V; EÞ ﬃ exp 2z
E
fþ
2
h2

"

 is the tip and sample average work function,
where fand E is the electron energy.
The dI/dV curves reﬂect not only the sample surface
LDOS but also the tip LDOS and the tunneling probability. In the dI/dV curves, these two contributions
show up as an exponential background if the tip LDOS
is featureless in the energy range measured. The exact
energy position of the LDOS peaks obtained from thismethod depends strongly on the exponential background. Several methods have been proposed to overcome this problem (Lang, 1986). Ukraintsev (1996)
proposed to normalize the dI/dV curves with a tunneling probability function (T) given by:

Fig. 1. STS measurement on Fe(001) covered with 7.2 ML Mn at
370 K. (a) Topographic image obtained at a set point of Vs ¼ 0.5 V,
I ¼ 0.5 nA. Scan size is 150  150 nm2. Five different levels are
exposed on the surface. (b) The dI/dV map at þ0.2 V measured at thesame area as a. Numbers in a and b denote the stacking number ofthe Mn layers. (c) The dI/dV curves representative of each level.
These curves are averages of typically 10 single curves.

96

T.K. YAMADA ET AL.

Fig. 4. dI/dV curves normalized by the voltage-dependent tunneling probability function, which were obtained with an Fe-coated W tip
on Mn ﬁlms thicker than three layers. Solid and dotted curves are thedI/dV and the (dI/dV)/T curves, respectively. Tunneling probability
function (dashed curves) was obtained by a ﬁt to the dI/dV curve.
Black and grey curves are representatives of the odd and the evenlayers, respectively.

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
#
2m  eVf
T ¼ at exp 2z
2
h2

"

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
#
2m  eVfþþ as exp 2z
2
h2

"

where z ¼ d (a constant tip-sample separation) since
the separation is ﬁxed during a spectroscopy measurement. The ﬁrst (second) term of T describes tunnelingfrom the tip (sample) Fermi level to unoccupied sample(tip) states. at and as are proportionality coefﬁcients
related to the tip-surface effective contact area and areproportional to the tip and sample LDOS at the Fermi
level, respectively. Normalizing the dI/dV curves withthe function T, we found two different expressions for
positive and negative bias voltages:

Fig. 3. SP-STM and SP-STS measurements on Fe(001) covered
with about 10 ML Mn at 370 K. These measurements were performed
with an Fe-coated W tip. (a) The topographic image that was obtainedat Vs ¼ 0.5 V, I ¼ 0.5 nA. Scan size is 100  100 nm2. Five layers are
exposed. The numbers in a and b denote the local thickness of the Mnﬁlm. (b) The dI/dV map at þ0.2 V measured at the same area as a.
(c) dI/dV curves as a function of the sample bias voltage obtained on
the area shown in a. dI/dV curves obtained on even (odd) Mn layers
are shown as solid (dashed) curves, which were numerically obtained
from I(V) curves measured at a set point of Vs ¼ 0.5 V, I ¼ 0.5 nA.

ðdI=dVÞ
ﬃ rs ðeVÞrt ð0Þ forT
ðdI=dVÞ
ﬃ rs ð0Þrt ðeVÞ for
T

V>0
V<0

This result means that STS is mainly useful to ﬁnd
the empty density of states of the tip or sample while
for the occupied density of states the technique quickly
looses sensitivity going below the Fermi level.
In order to get magnetic information from the sample
surface it is necessary to include the spin orientation ofsample and tip in the tunneling current expressions.

EVALUATION OF SP-STM/STS EXPERIMENTShi
ðdI=dVÞ 1
ﬃ rs ðeVÞrt ð0Þ 1 þ Ps ðeVÞPt ð0Þ forT2hi
ðdI=dVÞ 1
ﬃ rs ð0Þrt ðeVÞ 1 þ Ps ð0ÞPt ðeVÞ for
T
2

97
V>0
V<0

These equations demonstrate that from the (dI/dV)/
T curves it is possible to get not only qualitative information about the sample polarization, for example taking images with contrast between different magnetic
domains, but it is also possible to get quantitative
information. In the following, we will discuss how to
get quantitative information about the sample polarization and the inﬂuence of the tip magnetic structureon the SP-STM experiments.

Fig. 5. (a) Band structure of an eight-layer Mn(001) slab. The plotshows both ‘‘majority’’ and ‘‘minority’’ bands, which are equivalent forthis even-layered antiferromagnetically ordered slab. The magnetization for each layer is deﬁned by the difference in integrated local DOSof the majority and minority bands. Thick black lines: d2z -like statesaround G; dashed line: the Fermi level. a, b, and g could contribute to
the experimentally observed þ0.8 V peak. (b,c) The isocharge density
distributions of the a and the b state at the G point for two different
energies, 0.27 eV and 0.50 eV. Dots and dashed lines indicate atom
positions and the boundary between vacuum and bulk, respectively.

The spin-polarization is deﬁned by the difference
between the number of electrons in the minority andmajority bands integrated up to the Fermi level divided
by the total number of electrons. Let us assume thatthe sample polarization vector (Ps) deﬁnes the x-axis
and lies within the sample surface plane. Then Ps and
Pt (tip polarization vector) can be described as follows:Ps ¼ ðPs ; 0; 0Þ
Pt ¼ ðPt cos f cos y; Pt cos f sin y; Pt sin fÞ
where 0  f  p/2 is the angle between the tip
polarization vector and the sample surface, y is theangle between the projection of the tip polarization
vector on the sample surface and the sample polarization vector. The modulus of the polarization vectors are deﬁned as: jPi j  ðri"  ri# Þ=ðri" þ ri# Þ where
i represents tip or sample. Finally, rs" ðrt" Þ and rs# ðrt# Þ
denote spin-up and spin-down sample (tip) LDOS,
respectively. The x-y plane is deﬁned by the sample
surface and the z axis is perpendicular to it. Now thetunneling current depends also on the dot product ofthe polarization vectors, Ps  Pt ¼ jPs jjPt j cos f cos y.
After including this effect in the differential tunnelingconductance, the new expressions for the normalized
differential tunneling conductance are:MAGNETIC STRUCTURE AND POLARIZATION
OF THE SURFACE OF Mn(001) THIN FILM
SP-STS measurements contain information about
the DOS and the relative orientation of the magnetizations of both tip and sample. Therefore, in order tostudy the magnetic structure of samples, it is favorable
to know their electronic structure as measured with a
non-magnetic tip. For this purpose, we use a clean
W tip. STM/STS measurements on Mn ﬁlms thicker
than four layers are shown in Figure 1. Figure 1ashows an STM topographic image obtained on Fe(001)covered by 7.2 ML of Mn. At each pixel of the
topographic image, I(V) curves were measured. The
resulting curves are shown in Figure 1c. All curves
obtained above the third Mn layer are identical, indicating that the DOS does not change from one layer tothe other. This is also clear from Figure 1b, where thedI/dV map shows no contrast between the different
terraces.
In order to better identify the different contributions
to the dI/dV curves, we performed measurements in awide voltage range (from 2.0 V up to þ3.0 V). ThesedI/dV curves can be ﬁtted quite accurately by a tunneling probability function (T) (Ukraintsev, 1996). T was
obtained by a ﬁt to the curves above þ2 V and below 1
V, where the dI/dV curves increase exponentially. The
main feature present on the (dI/dV)/T curves is abroad peak at 0.8 eV above the Fermi level and a lesspronounced peak below, as can be seen in Figure 2.
For the SP-STS measurements, we deposited between 7–10 nm of Fe at room temperature on the apexof the tips. Figure 3 shows SP-STM/SP-STS measurements obtained with an Fe-coated tip on 10 ML of Mngrown on an Fe whisker. At each pixel of the image,ﬁrst the tip-sample separation is ﬁxed with a set pointof Vs ¼ 0.5 V and I ¼ 0.5 nA and the topographic
information was measured (Fig. 3a). The numbers on
the topographic image denote the local Mn thickness.
Subsequently, an I(V) curve was measured. dI/dV
curves were obtained numerically. The result is plottedin Figure 3c. The solid and dotted curves were measured on the odd and even layers, respectively. Contrary
to the case of the curves measured with a clean W tip,where all the layers show the same amplitude of thedI/dV curves, for the curves measured with Fe-coatedtips there is a clear change in the amplitude above the98

T.K. YAMADA ET AL.

Fig. 6. (a) The asymmetry of the (dI/dV)/T curves obtained on
the even and odd Mn layers as a function of the sample bias voltage. The black solid curve is obtained from the calculated spinresolved DOS. (b) The asymmetry of the (dI/dV)/T curves obtainedwith different set points and different Fe-coated tips. Black dots
and triangles were obtained by the same Fe-coated W tip. White
dots were obtained by a different Fe-coated W tip. Black and white
dots were obtained at a negative voltage set point (Vs ¼ 0.5 V,

I ¼ 0.5 nA). Triangles were obtained at a positive voltage set point(Vs ¼ þ0.5 V, I ¼ 0.5 nA). (c) The majority (grey) and minority(black) LDOS of Mn(001) were obtained by experimentally obtained(dI/dV)/T curves with a tip polarization at the Fermi level of 10,15, and 44%, respectively. (d) The majority (grey) and minority(black) LDOS of Mn(001) obtained by band structure calculations.
SS, SR, and B denote surface states, a surface resonance, and bulk
states, respectively.

Fermi level between the curves measured on the evenand odd layers.
In Figure 3b, we show a dI/dV map constructed withthe value of the dI/dV curves at þ0.2 V. This map
clearly shows that the contrast oscillates with a periodof two layers. Although the odd layers (9 and 11) are
darker than the even layers (8, 10, and 12) in this particular dI/dV map, this is not always the case; withother tips the contrast is reversed. With the actual
experimental setup, it is not possible to determine theabsolute magnetization orientation of the tip. We
explain the alternating contrast in the dI/dV maps
obtained with the Fe-coated tips by the layered antiferromagnetic magnetization of the Mn(001) layers.
We will apply the normalization procedure by thefunction T explained previously with the dI/dV curves
measured with the Fe-coated tips. Figure 4 shows (dI/
dV)/T curves averaged over 30 single curves measured
with an Fe-coated tip. The curves measured on evenlayers (grey line) and odd layers (black line) show two
peaks at the same energies as the peaks obtained withthe clean W tips. The main difference of the curves
measured with the clean W tips is that now the amplitude of both peaks oscillates with a period of two layers
and the curves measured on the even and odd layers
cross at the Fermi level.
Natural occurring 3d metals with bcc structure such
Fe and Cr have a surface state at the (001) surface. On
the other hand, Mn, which is between Fe and Cr in the
periodic table, has a complicated bulk structure. An
open question is whether an artiﬁcial bct Mn(001) thinﬁlm also shows a surface state. In order to determine
the nature of the spin-dependent peaks present in the(dI/dV)/T curves (Fig. 4), band structure calculations
were carried out by Heijnen (Yamada et al., 2003b) of
the Theoretical Physics Department at the Radboud
University of Nijmegen using the Vienna Ab initio Simulation Program (VASP). It is based on spin density
functional theory and the projected augmented wave
(PAW) method (Blöchel, 1994; Kresse and Joubert,1999) with non-local corrections to the exchange andcorrelation taken into account by a generalized gra-

EVALUATION OF SP-STM/STS EXPERIMENTS

99

Fig. 7. SP-STS measurements on Fe(001) covered with 9.5 ML Mn
at 370 K showing a reversal of the magnetic contrast after pulsing thetip. (a) A topographic image measured at a set point of Vs ¼ 0.5 V, I
¼ 0.5 nA. Scan size is 100  80 nm2. Five different levels are exposedon the surface; the numbers denote the local thickness of the Mn ﬁlm.
(b–d) dI/dV maps at þ0.2 V measured at the same area as a. Between
b–d, the tip was moved 500 nm away from this area and a voltage
pulse was applied.

dient approximation (GGA). An eight-layer slab withthe experimental values for the in-plane (2.87 Å) andout-of-plane (2  1.64 Å) lattice constants was used; anantiferromagnetic stacking of Mn(001) layers was
assumed (Tulchinsky et al., 2000). Figure 5a shows the‘‘majority’’ and ‘‘minority’’ bands obtained in the calculation for 8-Mn layers. In the plot, the bands with thelargest dz2 character at the G point are marked withthick black lines.
Three bands are possible candidates for the experimentally observed empty state peak; the band called a
at 0.27 eV, b at 0.50 eV, and g at 0.87 eV above the Fermi
level. The calculations show the DOS at the Mn(001)surface while the tip detects the DOS in the vacuum at
the tip position. To check the distribution of each statein the vacuum, the surface charge density distribution
was calculated and is shown in Figure 5b and c forbands a and b, which exhibit a surface state–like behavior. The g band displays a strong decay into the vacuum.
The width of the þ0.8 V peak in (dI/dV)/T is about
1 V (Fig. 4). This width is larger than the peak obtainedon Fe(001) (0.13 eV) (Stroscio et al., 1995) and Cr(001)(0.2 eV at RT) (Kleiber et al., 2000). One possible
explanation is that in our case the peak at þ0.8 eV is
produced by two surface states a and b. The difference
between the calculated peak energies and the experimental peak energy is attributed to the limitations of
the calculation.

Once the spin-polarized tunneling contributions to
the electronic spectra have been identiﬁed, we will try
to extract quantitative information from them. Since
the (dI/dV)/T shows the sample (tip) DOS multipliedby the tip (sample) DOS at the Fermi energy for V > 0(V < 0), in principle it is possible to obtain the sample
polarization. The asymmetry of the normalized tunneling conductance, A(dI/dV)/T, deﬁned as follows:AðdI=dVÞ=T ¼

ðdI=dVÞeven =Teven  ðdI=dVÞodd =Todd
ðdI=dVÞeven =Teven þ ðdI=dVÞodd =Toddcorresponds to the sample (tip) polarization as a functionof the sample bias voltage multiplied by the tip (sample)
polarization at the Fermi energy for V > 0 (V < 0), i.e.
A(dI/dV)/T ¼ Ps(V)Ptip(EF) for V > 0 and Ptip(V)Ps(EF) for
V < 0 (Yamada et al., 2003a). Also, Todd and Tevendenote the tunneling probability functions obtained
from dI/dVodd and dI/dVeven, respectively. Todd andTeven are not identical. By the ﬁtting different tip-sample separations are obtained due to spin-polarized tunneling, e.g., 0.90 nm for Todd and 0.92 nm for Teven,assuming the same averaged work function on bothterraces.
The asymmetry curves shown in Figure 6a,b wereobtained from dI/dV curves showing spin-dependent
peaks with the maximum magnetic contrast, which

100

T.K. YAMADA ET AL.

were obtained from different voltage set points and different Fe-coated W tips. The A(dI/dV)/T is at maximum
10% below and above the Fermi energy, while the signchanges at the Fermi level. The changes in the ﬁtting
parameters for T produce errors in the asymmetry of
2% (error bars in Fig. 6a). The calculated polarizationof the Mn(001) surface divided by a 15% tip polarization is shown as a solid curve in Figure 6a. The calculated curve ﬁts to the experimentally obtained
asymmetry curve except around þ2 V where the calculation include bulk states while SP-STS only detects
surface LDOS. In order to show the reproducibility ofthis method, we show in Figure 6b the asymmetry
obtained in different experiments. The asymmetries
plotted with dots and triangles were obtained with thesame Fe-coated W tip and different set points (positive
and negative bias voltage respectively); the one represented by circles was measured with a different
Fe-coated W tip. These tips showed the maximum
value on the asymmetry of the (dI/dV)/T curves, which
are assumed to be parallel (or anti-parallel) between
the tip and the sample magnetization direction. This
plot demonstrates that the asymmetry obtained by thenormalized conductance does not depend on the set
point or on the tip.
We will focus now on the analysis of the asymmetries
above the Fermi level that is the energy range where
STS is sensitive to the sample DOS. For the positive
sample bias voltage, the (dI/dV)/T curves for the odd
and even layers can be described as follows:ðdI=dVÞeven  "maj#¼ Dtip ðEF ÞDmin
Mn ðVÞ þ Dtip ðEF ÞDMn ðVÞTeven
ðdI=dVÞodd  "#min¼ Dtip ðEF ÞDmaj
Mn ðVÞ þ Dtip ðEF ÞDMn ðVÞ
Todd
D"tip ðEF ÞðD#tip ðEF ÞÞ indicates the LDOS at the Fermi
level for the majority (minority) bands of the Fe-coated
W tips. Since the tip is ferromagnetic, majority-spin
and minority-spin bands of the Fe-coated W tips aremindeﬁned as spin-up and spin-down. Dmaj
Mn ðVÞ ðDMn ðVÞÞindicates the LDOS at the energy V above the Fermi
level for the majority (minority) bands of the sublattices of antiferromagnetic bct Mn ﬁlms. For a layered
antiferromagnetic material, the occupation of the
majority and minority band switches from spin-up to
spin-down electrons in every layer. For this reason wewill use majority and minority for the sample. Assuming that spin-up (-down) electrons from the tip will tunnel into the minority (majority) spin bands of the odd
Mn layers and into the majority (minority) spin bandsof the even Mn layers without spin ﬂipping, we candescribe the asymmetry asAðdI=dVÞ=T ¼ PT ðEF ÞPs ðEF þ eVÞ;where V > 0

Fig. 8. (a) An STM topographic image (70  70 nm2) obtained on
the Fe(001) whisker clean surface at a screw dislocation. (b) The STM
image of a in a three-dimensional mode. (c) dI/dV map at þ0.2 V
obtained simultaneously with the image shown in a taken with a set
point of Vs ¼ 0.6 V, I ¼ 0.5 nA.

EVALUATION OF SP-STM/STS EXPERIMENTS

101

Using these three equations the spin-resolved LDOS of
the Mn(001) can be experimentally obtained as follows:AðdI=dVÞ=T ðdI=dVÞ
1
1
C
T
PT
ave


A
1
ðdI=dVÞ
ðdI=dVÞ=T
min
1þ
DMn ¼
C
T
PT
ave
Dmaj
Mn ¼

where [(dI/dV)/ T]ave is the average of (dI/dV)odd /Toddand (dI/dV)even /Teven. C is the sum of D"tip and D#tip andPT is the tip polarization. Using the experimentallyobtained (dI/dV)/T and A(dI/dV)/T, the spin-resolved
sample LDOS can be obtained as is shown in Figure 6cfor three different tip polarizations. For comparison,
the calculated spin-resolved LDOS for the sample isshown in Figure 6d. Comparing the experimentallyobtained results with different tip polarizations, weconclude that the best ﬁt between the experimentallyobtained majority LDOS and the calculated majority
LDOS is obtained with a tip polarization of 18  5%.
With this tip polarization, we obtain a Mn surface
polarization of 60  16% at þ0.8 eV.
MODIFICATION OF THE TIP MAGNETIZATIONIn the present section, we will describe a method tochange the magnetization of the tip by applying voltage
pulses (Yamada et al., 2003c). During constant current
STM topographic measurements (typically, Vs ¼ þ1 V,
I ¼ 0.1 nA), we increased the bias voltage from 1 to 10 V
in 60 ms with the feedback on. The feedback loop is too
slow to keep the tunneling current constant and it
needs around 15 ms to recover the original value of thetunneling current (0.1 nA). During these 15 ms, the I/Vconverter is saturated and the output is at the maximum value that it is able to measure (3.7 nA); during
this time, the current density increases drastically andthe tip structure is modiﬁed.
Figure 7 shows the dependence of the alternating contrast in the dI/dV maps on the tip condition. Figure 7ashows a topographic image; the numbers denote thelocal thickness of the Mn ﬁlm. Figure 7b shows the original contrast (5%) obtained with the spin-polarized tip.
The alternating contrast between the even and odd Mnlayers is clear in the dI/dV map. After taking this dI/dV
map, we moved the tip 0.5 mm away from this area ofthe sample and we applied a voltage pulse. Then the tip
was moved back to the original area and another dI/dV
map was measured; the result is shown in Figure 7c; inthis case, the contrast is almost negligible (<1%). After
this measurement, we moved the tip away from the area
and we applied another voltage pulse. Figure 7d wasmeasured after this second voltage pulse. In this dI/dV
map the contrast is recovered but is inverted (6%) withrespect to the one originally obtained (Fig. 7b). From
this experiment, it is clear that the magnetic contrast
depends strongly on the tip condition and this can bealtered in a random way with voltage pulses.
MAGNETIC STRUCTURE AROUND A SCREWDISLOCATION IN AN
ANTIFERROMAGNETIC FILM
Occasionally, we found screw dislocations on theFe(001) surface. In Figure 8a,b, we show STM images

Fig. 9. An STM topographic image obtained on an Fe(001)-screwdislocation covered with 4.5 ML Mn at 370 K at a set point of Vs ¼
0.5 V, I ¼ 0.5 nA (100  100 nm2). The arrows indicates the positionof the screw dislocation on the Fe(001) surface. Numbers denote local
thickness of the Mn ﬁlm.

obtained at a screw dislocation on the Fe(001) surface.
The Fe(001) surface exhibits a surface state of dz2 character at 0.17 eV above the Fermi level (Bischoff et al.,
2003; Stroscio et al., 1995). Figure 8c shows a dI/dV
map at þ0.2 V obtained in the same area as the topography shown in Figure 8a. A black line is observed at
the position of the step edge indicating the disappearance of the iron surface state; the small black dots on
the terraces indicate the position of contaminants.
Since Fe has a ferromagnetic character, no magnetic
structure is observed around the screw dislocation incontrast to the screw dislocation on the antiferromagnetic Cr(001) surface (Ravlic et al., 2003).
This lack of magnetic structure changes when antiferromagnetic Mn layers are deposited on the screw
dislocation. The Mn layers grow with a spiral structure. In Figure 9, we show an STM image taken on
4.5 ML of Mn deposited on an Fe screw dislocation.
The numbers indicate the Mn local coverage and were
determined by measuring STS spectra since the third
Mn layer has a characteristic dI/dV curve (Yamada
et al., 2002).
The dI/dV map at þ0.4 V obtained around the screw
dislocation shows magnetic contrast as can be seen in
Figure 10a. A detailed analysis of the dI/dV map
reveals that several amplitudes of magnetic contrast
are present (marked from A to G in Fig. 10a).
In Figure 10b, we show individual dI/dV curves
obtained at the areas marked ‘‘A–G’’ in Figure 10a. The
maximum magnetic contrast is obtained between the
dI/dV curves measured on the fourth (A) and ﬁfth (B)102

T.K. YAMADA ET AL.



dI
dV


¼
even

dI0
ð1 þ Ptip Ps cosðy þ pÞÞdV expð2kz cosðy þ pÞÞ

Fig. 10. (a) SP-STS image (a dI/dV map at þ0.4 V) obtained at
the same area as Figure 9 at a set point of Vs ¼ 0.5 V, I ¼ 0.5 nA
with a magnetic tip (100  100 nm2). Numbers of 4–6 denote stacking
numbers of Mn layers. (b,c) dI/dV curves obtained at each area of
A–G in a.

Mn layers (i.e., AAB ¼ ((dI/dV)B(dI/dV)A)/((dI/dV)B þ(dI/dV)A)*20% for V > 0). Conversely, the minimum
contrast is obtained between the dI/dV curves measured on C and D areas (ACD*12% for V > 0).
It is very difﬁcult to calculate the magnetic structureof the Mn layers around the screw dislocation but wecan estimate the relative orientation of the in-planemagnetization of the different areas marked from A to
G. The dI/dV curves measured in the odd and even Mn
layers can be described as follows


dI
dV


¼
odd

dI0
ð1 þ Ptip Ps cos yÞ expð2kz cos yÞ
dV

ð1Þ

ð2Þ

where dI0/dV denotes the non-spin polarized term of
dI/dV, i.e., dI0 =dV ¼ 12 rtip rs expð2kzÞ, where rtip ðrs Þ
denotes the tip (sample) DOS, z the tip-sample distance, k the decay length. Ptip (Ps) denotes the tip (sample) polarization, y the angle between the tip and thesample magnetizations, and Dz the spin-dependent tipsample separation. Although Ptip and Ps are functionsof the sample bias voltage only, Dz depends on the spinpolarization in the whole energy window set by the bias
voltage, as well as on the spin-polarization of the tip
and the relative angle of the magnetization vectors.
Experimentally it has been determined that the spindependent tip-sample separation (Dz) is 0.1 Å (Yamada etal., 2003b) for the curves showing the maximum contrast.
Using equations (1) and (2) and assuming that the tip
and sample magnetizations are parallel (y ¼ 0), the calculated asymmetry (Acal¼ ((dI/dV)odd – (dI/dV)even)/((dI/dV)oddþ(dI/dV)even) is 0.2 for the dI/dV curves presenting
the highest contrast on Mn layers grown on ﬂat areas of
the Fe whisker. For the Mn layers grown on the screw
dislocation, we found that the maximum contrast occurs
between the areas marked as A and B and the value ofthe asymmetry is *0.2, which is the maximum value ofthe magnetic contrast obtained on the Mn(001) layers,
for a bias voltage of þ0.3 V. Using these values, we canassume that the magnetizations in areas A and B are
parallel (antiparallel) to the tip magnetization. Regions
marked in Figure 10a as A, C, and G are on the even Mn
layers (fourth and sixth), and areas marked as B, D, E, F
are on the odd Mn layers (ﬁfth). We also know that theeven and odd Mn layer tend to be antiferromagneticallycoupled. In order to estimate the relative orientation of
the magnetization in the different areas (C–G) in relation
to B, we can deﬁne a function f(a)¼(dI/dV)i/(dI/dV)B,
where a is the angle between the magnetization of thedifferent domains and i denotes the domain (C–G). Dueto the tendency of antiferromagnetic coupling between
the odd and even Mn layers, a will change by p from theareas in the even and odd layers. Therefore, we will have
two functions f (a), one for the odd layers:
fodd ðaÞ ¼

ðdI=dVÞi
ðdI=dVÞB
ð1 þ 0:1 cos aÞ expð0:2k cos aÞ¼
1:1 expð0:2kÞ
where i ¼ D, E, F

and one for the even layers:
ðdI=dVÞi
ðdI=dVÞB
ð1 þ 0:1 cosða þ pÞÞ expð0:2k cosða þ pÞÞ¼
1:1 expð0:2kÞ
where i ¼ C; G

feven ðaÞ ¼

Using the dI/dV curves measured experimentally inthe different areas, we can determine the value of theEVALUATION OF SP-STM/STS EXPERIMENTS

103

Fig. 11. The same dI/dV map shown in Figure 10 with local magnetization directions calculated from the asymmetry of the dI/dV
curves.

f(a) functions and from that value we can extract thevalue of the angle a. We found that the magnetizationin area C makes an angle of 2398 with respect to themagnetization in B. For D, we found 478, 1038 for E,
638 for F, and 2358 for G. The obtained magnetizations
are plotted by arrows in Figure 11.
Figure 12a shows a topographic image of 400 
333 nm2 represented in a differentiated mode in orderto make visible all the structural details. The numbers
denote the local Mn thickness. Fe steps, with a stepheight of 0.02 nm, show up on the surface as whitefaint lines, which have been surrounded by black thinlines to guide the eye. In Figure 12b, we show a mosaic
composed by 12 dI/dV maps at þ0.1 V obtained in several areas of the topography shown in Figure 12a. The
third Mn layer appears brighter than the other layers
due to a different DOS not related to the magnetic
properties. The obtained magnetization directions areshown with arrows on the topography presented in
Figure 12a. Although the right-hand side of the image
reveals a true antiferromagnetic coupling between thelayers, the presence of the screw dislocation rotates themagnetization directions. A clear example of this inﬂuence are the two islands marked with white squares in
Figure 12a. Both islands are 5-ML-thick but the magnetization directions of these islands make a 908 angle.
CONCLUSIONS
We have shown that by combining a detailed analysis of the SP-STS measurements with spin-resolved
band structure calculations, it is possible to obtain
quantitative information about the polarization of
surfaces with very high resolution. We also discussed
an experimental approach for modifying the tip magnetization direction. Finally, we have shown that
SP-STM/SP-STS experiments allow us to study in

Fig. 12. (a) SP-STM topographic image in a differential mode
obtained with a magnetic tip on 4.5 ML Mn on Fe(001) at 370 K at a
set point of Vs ¼ 0.5 V, I ¼ 0.5 nA (400  333 nm2). Hidden Fe steps
and a hidden Fe dislocation are observed as white curves surroundedby black curves. Numbers in a denote the stacking numbers of the Mn
layers. Arrows denote relative angles of magnetization directions.
Boxes show ﬁfth Mn layers with different magnetization directions.
(b) Twelve dI/dV maps at þ0.1 V obtained at several areas in a. Dueto the thermal drift, the 12 dI/dV maps were not connected perfectly.

detail the magnetic structure around isolated defects
on surfaces, like a screw dislocation. These defects are
not accessible with other spatially averaging techniques. We have shown that, even for a complicated situation like a screw dislocation in an antiferromagnetic
ﬁlm, the direction of the sample magnetization can be
determined.
ACKNOWLEDGMENTS
A.L.V.P. acknowledges the ﬁnancial support by the
Ministerio de Educación y Ciencia (MEC) through Project
No. FIS2004-01026. T.K.Y. acknowledges Grant-in-Aid
for JSPS Fellows. H.v.K. acknowledges a DVF from the104

T.K. YAMADA ET AL.

International Research Center for Experimental
Physics (IRCEP) at the Queen’s University, Belfast(Ireland).The authors thank Dr. D.T. Pierce for supplying the Fe whiskers. This work was supported by the
Stichting voor Fundamenteel Onderzoek der Materie(FOM), which is funded by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek.
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