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7XQQHOLQJ6SHFWURVFRS\0HDVXUHPHQWVT.K. Yamada1, A.L. Vázquez de Parga2, M.M.J. Bischoff1, T. Mizoguchi3and H. van Kempen1
165,08QLYHUVLW\RI1LMPHJHQ1/('1LMPHJHQ7KH1HWKHUODQGV'SWRGH)tVLFDGHOD0DWHULD&RQGHQVDGD8QLYHUVLGDG$XWyQRPDGH0DGULG&DQWREODQFR
0DGULG6SDLQ)DFXOW\RI6FLHQFH*DNXVKXLQ8QLYHUVLW\0HMLUR7RN\R-DSDQ$EVWUDFW Spin-polarized scanning tunneling spectroscopy measurements have been done on
ultrathin bct Mn films grown on Fe(001)-whiskers. Emphasis is placed on the relationshipbetween the feedback setpoint chosen for the tunneling spectroscopy measurements and thenormalization procedures for the data, and the values obtained for the spin polarization of thesurface electronic structure.

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The first observation of the spectral density of electronic states was made by Giaver[1] in metal-oxide-superconductor tunneling experiments. This work lead to theintroduction to the new many-body transfer Hamiltonian approach in tunneling current
calculation by Bardeen [2]. The invention of Scanning Tunneling Microscopy (STM)
by G. Binnig and H. Rohrer [3] stimulated additional interest in the theory oftunneling. Using the transfer Hamiltonian formalism, tunneling in the STM wasstudied by Tersoff and Hamann [4] and other authors [5,6]. It was concluded that thetunneling current can be expressed as a simple convolution of the sample Density ofStates (DOS) and tip DOS with the effective matrix element for tunneling. A simple
relation between the tunneling current and the sample DOS can be obtained in the onedimensional and semiclassical Wentzel, Kramers and Brillouin (WKB) approximation.
For a three dimensional problem the calculation of the effective matrix elements fortunneling is still an open question.
From the first experimental observation of the spectral density of the sample
electronic states by STM, the first derivative of tunneling current over tip-sample
voltage or differential conductivity, d,/d9, was used as measure of the sample DOS.
This approach presents two problems, one is the influence of the tip DOS and theother is the effect of the tunneling transmission probability on the observed
dependence of the tunneling current on sample voltage. These two problems are still
mainly unsolved.
Since its introduction [7] Spin-Polarized Scanning Tunneling Microscopy (SPSTM) and Spectroscopy (SP-STS) has proven very powerful tools for studying surface
magnetism with spatial resolution at atomic scale [8,9]. One of the most importantissues is to understand the origin of the magnetic contrast in SP-STS images takenwith magnetic tips. Although it has been reported that this magnetic contrast is related
to the existence of spin-polarized surface states, this relation is not straightforward dueto the influence of the tunneling probability.
In this paper we will discuss how to get quantitative information concerning thepolarization of the sample and the influence of the setpoint bias voltage.

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STM and STS measurements were performed in ultra-high vacuum (∼5×10-11 mbar)
at room temperature (RT). Mn layers with a body-centered tetragonal (bct) structure
were grown on an Fe(001)-whisker at 370 K. Details of the sample preparation andcharacterization are given in refs [10,11]. The tips used in the present study were W
tips covered with 7-10 nm Fe at RT. The magnetic contrast obtained with these tips
depends on the factor cosθ, where θ is the angle between the magnetization directionof the Fe-coated tip and the Mn layers. In the chamber we cannot apply any magnetic
field to the tip or the sample. Therefore, the tip magnetization direction is randomly
orientated with respect to the magnetization of the Mn layers and is different from tip
to tip. The tip was carefully brought close to the sample to exclude any mass transport
between tip and sample. STS measurements were performed at every pixel of aconstant current topographic image by opening the STM feedback loop at a given
voltage and current (setpoint). d,/d9, (dln,/dln9) and (d,/d9)/T curves were obtainedby numerical calculation from the original I(V) curves.

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The growth mode of Mn layers on Fe(001) has been studied before [10,11]. For a
Mn nominal thickness of 7 ML there are 4 different layers exposed on the surface, as it
is shown in Figure 1a. Previous results showed that the intermixing between Fe andMn takes place for the firsts Mn layers, but above 3 ML the intermixing of Fe on theMn film can be neglected. At this surface, I(V) curves were measured with Fe-coatedtips at every pixel of the topographic image using a setpoint of Vs=-0.5V and I=0.5nA.
Every I(V) curve was numerically differentiated to obtain the d,/d9 curve. In order tocheck the magnetic contrast in the spectroscopy data, d,/d9 maps were obtained.
Figure 1b shows the d,/d9 map at +0.2V, the strong contrast in the spectroscopic
image between layers is clear. The contrast oscillates with a periodicity of two layers.
This contrast is also present on the step height measured on the topographic image
with a sample voltage of +0.2 V as is shown in Figure 1c. This contrast is neverobserved with clean W tips [10]. With the help of Ab initio calculations the origin of
this contrast was trace back to the existence of minority bands at the Γ point above theFermi level in the surface Density of States (DOS) [12].

),*85( (a) STM topography, 70x70 nm2 of the surface of 7ML Mn film on Fe(001) measured witha Fe-coated tip at a setpoint of Vs=-0.5V, I=0.5 nA. (b) d,/d9 map at +0.2 V of the same area. A I(V)curve was measured in every pixel of the topography shown in (a) and them numerically differentiated.
(c) Line profile measured on the Mn layers with an Fe-coated tip.

Various methods for extracting the sample polarization from SP-STS measurements
have been reported [13,14]. However, these methods include a certain ambiguity. In
all of them is necessary to know the polarization of the magnetic tips used to make themeasurements. Other problem is that for a given setpoint voltage the tip-sample
distance can change (and so the tunneling probability) between different Mn layers
due to changes in the electronic structure. This is not something unexpected due to thespin-polarization of the DOS close to the Fermi level in magnetic materials andtherefore, the spin-polarized component of the current changes for the different layers.

),*85( (a) I(V) curves measured in the odd (solid black curve) and even (solid grey curve) layersof 7ML of Mn grown on Fe(001) with an Fe-coated tip using a negative sample voltage setpoint (Vs= 0.5V, I= =0.5 nA). (b) ) I(V) curves measured in the odd (solid black curve) and even (solid grey curve)
layers of 7ML of Mn grown on Fe(001) with an Fe-coated tip using a positive sample voltage setpoint(Vs= +0.5V, I= =0.5 nA). (c) Asymmetry in the I(V) curves. Black solid line if for the I(V) curves
measured with a negative voltage setpoint and the grey solid line is measured with a positive voltage
setpoint. The asymmetry is defined as AI(V)=[I(V)odd-I(V)even]/[I(V)odd+I(V)even].

Figure 2 shows the I(V) curves measured with a Fe-coated tip on the even and odd
Mn layers at negative (Fig. 2a, Vs= -0.5V) and positive (Fig. 2b, Vs= +0.5V) voltage
and with the same current (I= 0.5 nA) setpoint. In both cases the I(V) curves show adifference between the even and odd Mn layers as is expected due to the different
tunneling probability for the spin-polarized electrons. This difference in the tunnelingprobability allows us to take magnetic resolve images of the surface as shown in
Figure 1b. The problem arises when we try to extract quantitative information about
the sample polarization. Figure 2c shows the asymmetry obtained from the I(V) curves
measured on different Mn layers. The asymmetry is defined as AI(V)=[I(V)oddI(V)even]/[I(V)odd+I(V)even]. The asymmetry obtained is strongly influenced by thevoltage setpoint and can lead to wrong conclusions about the sample polarization.
This dependence is due to different tip-sample distance for the different voltage
setpoints and also to the fact that both I(V) curves has the same intensity value for thevoltage setpoint. The change in the tip-sample distance with the sample voltage isshown in Figure 1c where the apparent step height measured with a Fe-coated tipchanges from terrace to terrace due to the changes in the sample magnetization and its
influence in the tunneling transmission probability.
To get rid off this problem we numerically differentiate the I(V) curves. Panels (a)and (b) of Figure 3 show the results. The tunneling conductance also showsdifferences between the odd and even Mn layers. The shape of the d,/d9 curves does
not change depending on the voltage setpoint choose but it is clear that the energy
range where the differences between the d,/d9 curves measured in the odd and evenlayers are present depends strongly on the setpoint voltage.
),*85( (a) d,/d9 curves measured in the odd (solid black curve) and even (solid grey curve) layersof 7ML of Mn grown on Fe(001) with an Fe-coated tip using a negative sample voltage setpoint (Vs= 0.5V, I= =0.5 nA). (b) ) d,/d9 curves measured in the odd (solid black curve) and even (solid grey
curve) layers of 7ML of Mn grown on Fe(001) with an Fe-coated tip using a positive sample voltage
setpoint (Vs= +0.5V, I= 0.5 nA). (c) Asymmetry in the d,/d9 curves. Grey dots are for the d,/d9 curves
obtained from measurements taken with a negative voltage setpoint and the black dots are for the
positive
voltage
setpoint.
Theasymmetryisdefinedas
AdI/dV=[(d,/d9)odd(d,/d9)even]/[(d,/d9)odd+(d,/d9)even].

In a very simple approximation the tunneling conductance in STS can be related to
the DOS of both tip and sample [15]. Figure 3 is a clear example of how this very
simple approximation is not enough and it is necessary to take into account thetunneling transmission probability. In panel (c) of the Figure 3 we present theasymmetry of the d,/d9 curves defined in the same way than before. The result on theasymmetry depends strongly on the setpoint chosen to stabilize the feedback in
between the I(V) curves.

In general it is accepted that the tunneling conductance can be approximated interm of the DOS of the sample at a voltage V, plus a background term for positive
sample voltage. For negative sample voltage the tunneling conductance is dominatedby the electronic structure of the tip close to the Fermi level with a background. In
both cases the background is given by the tunneling transmission probability that
depends exponentially with the bias voltage [16]. In order to get best approximation to
the DOS of the sample is necessary to remove the background given by the tunnelingtransmission probability and prepare tips with a featureless density of states around the
Fermi level [17]. In order to remove the exponential background present on thetunneling conductance, Feenstra et al. [18] proposed the use of dln,/dln9 as a functionthat is a relatively direct measure of the DOS of the sample. This method was tested
extensively in many experiments and demonstrated reasonable agreement with someexperimental and theoretical data.

),*85( (a) (d,/d9)/(,/9) curves obtained on the odd (solid black curve) and even (solid grey curve)
layers of 7ML of Mn grown on Fe(001) with an Fe-coated tip using a negative sample voltage setpoint(Vs= -0.5V, I= =0.5 nA). (b) ) (d,/d9)/(,/9) curves obtained in the odd (solid black curve) and even(solid grey curve) layers of 7ML of Mn grown on Fe(001) with an Fe-coated tip using a positive sample
voltage setpoint (Vs= +0.5V, I= 0.5 nA). (c) Asymmetry in the (d,/d9)/(,/9) curves. Solid line is for thed,/d9 curves obtained from measurements taken with a negative voltage setpoint and the dotted line isfor the positive voltage setpoint.

In panels (a) and (b) of Figure 4 we show normalized tunneling conductivity(d,/d9)/(,/9) obtained at a negative and positive voltage setpoint. The normalization
removes almost completely any dependence of the asymmetry on the voltage setpoint.
Unfortunately the asymmetry values obtained are not correct. From previous studies it
is known that the electronic structure of the Mn(001) surface above the Fermi level isdominated by three “minority” bands located in energy between the Fermi level and+1.0 eV [12]. These bands produce a broad feature in the tunneling conductanceinstead of a well define peak. This particular electronic structure makes thisnormalization procedure unsuitable to recover the surface DOS. It is also well known
that the (d,/d9)/(,/9) normalization cannot exclude completely the exponential
background [16] and by definition should be 1 at 0 V. These limitations have an
influence on the asymmetry obtained from those curves.
To deal with these limitations Ukraintsev [16] proposed in 1996 that normalizing
d,/d9 with a fitted tunneling probability functions leads to the best recovery of thesample DOS within a one dimensional WKB approach [16]. The tunneling probability
function is:
1/ 2 
1/ 2 


 2m

 2m








T = a t exp − 2S(Φ − V / 2) + a s exp − 2S 2 ( Φ + V / 2  
2




!


!






The first term of T describes tunneling from the tip Fermi level to unocuupied
sample states, and the second term describes the tunneling from the sample Fermi
level to unocuupied tip states. at and as are proportionality coefficients related to thetip-surface effective contact area and are proportional to the tip and the sample DOS at
the Fermi level, respectively. Φ is the average of sample and tip work functions, 6 isthe tip sample separation and P the electron mass. In order to use this normalization
procedure is necessary to measure the I(V) curves over a long voltage range to haveenough data to make a good estimation of the exponential background. For this reason
our I(V) curves are measured in a energy range between -2V and +3V, as shown in
Figure 2.
),*85( (a) d,/d9 curves normalized by T obtained on the odd (solid black curve) and even (solid
grey curve) layers of 7ML of Mn grown on Fe(001) with an Fe-coated tip using a negative sample
voltage setpoint (Vs= -0.5V, I= =0.5 nA). In dotted lines we show again the d,/d9 curves, the black andgrey colors represents different Mn layers and the dashed black line is the function T. (b) ) d,/d9 curves
normalized by T obtained on the odd (solid black curve) and even (solid grey curve) layers of 7ML ofMn grown on Fe(001) with an Fe-coated tip using a positive sample voltage setpoint (Vs= +0.5V, I= 0.5nA). In dotted lines we show again the d,/d9 curves the black and grey colors represents different Mnlayers and the dashed black line is the function T. (c) Asymmetry in the (d,/d9)/T curves. The solid dots
are for the d,/d9 curves obtained from measurements taken with a negative voltage setpoint and theempty dots are for the positive voltage setpoint.

The result of this normalization is shown in Figure 5a and 5b. In this case thenormalized tunneling conductance shows again a clear difference between the curves
measured in the even and odd layers (black and grey solid line), the differences are notdependent on the voltage setpoint chosen to stabilize the feedback loop. With newnormalization method the normalized conductance resembles better the surface densityof states [12]. Above the Fermi level it presents a broad peak centered around +0.8 V
that changes its intensity depending on the sample magnetization. Figure 5c shows theasymmetry obtained from these curves. The asymmetry obtained with the differentsetpoints is identical within the error bars above the Fermi level. Below the Fermi
level the results reflects mainly the contribution of the tip DOS [12].
In summary in this paper we have explored the influence of the setpoint chose tostabilize the feedback loop during Spin-Polarized Scanning Tunneling Spectroscopy
measurements. We have shown that the setpoint has a strong influence and we
discussed the different approach to the analysis of I(V) curves in order to recover thesurface DOS.

$&.12:/('*0(176This work was supported by the Stichting voor Fundamenteel Onderzoek deMaterie (FOM), which is funded by the Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO), and the European Growth Project
MAGNETUDE. We are especially grateful to D.T. Pierce for supplying us with the Fe
whiskers. One of us, ALVP, thanks the Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO) and Ministerio de Ciencia y Tecnología for thefinancial support.

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