Temperature and Magnetic Field Dependenc

Thin Solid Films 509 (2006) 168 – 172
www.elsevier.com/locate/tsf

Temperature and magnetic field dependence of the Yosida–Kondo resonance
for a single magnetic atom adsorbed on a surfaceB
Wilson Agerico Din˜o a,b,c,d, Hideaki Kasai c,*, Emmanuel Tapas Rodulfo d, Mayuko Nishi a
b

a
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
Center for the Promotion of Research in Nanoscience and Nanotechnology, Osaka University, Toyonaka, Osaka 560-8531, Japan
c
Department of Applied Physics, Osaka University, Suita, Osaka 565-0871, Japan
d
Physics Department, De La Salle University, Manila 1004, Philippines

Available online 9 November 2005

Abstract
Manifestations of the Kondo effect on an atomic length scale on and around a magnetic atom adsorbed on a nonmagnetic surface differ
depending on the spectroscopic mode of operation of the scanning tunneling microscope. Two prominent signatures of the Kondo effect that can

be observed at surfaces are the development of a sharp resonance (Yosida – Kondo resonance) at the Fermi level, which broadens with increasing
temperature, and the splitting of this sharp resonance upon application of an external magnetic field. Until recently, observing the temperature and
magnetic field dependence has been a challenge, because the experimental conditions strongly depend on the system’s critical temperature, the socalled Kondo temperature T K. In order to clearly observe the temperature dependence, one needs to choose a system with a large T K. One can thus
perform the experiments at temperatures T b T K. However, because the applied external magnetic field necessary to observe the magnetic field
dependence scales with T K, one needs to choose a system with a very small T K. This in turn means that one should perform the experiments at
very low temperatures, e.g., in the mK range. Here we discuss the temperature and magnetic field dependence of the Yosida – Kondo resonance for
a single magnetic atom on a metal surface, in relation to recent experimental developments.
D 2005 Elsevier B.V. All rights reserved.
PACS: 73.20.At; 73.20.Hb; 72.10.Fk; 61.16.Ch
Keywords: Many-body effects; Kondo effect; Yosida – Kondo resonance; Dilute magnetic alloys; Metallic surfaces; Scanning tunneling microscopy; Mn; NiAl;
Al2O3

1. Introduction
Magnetic materials are key components in today’s information technology. Large amounts of data are stored in thin
magnetic films on computer hard disks. Magnetic multilayer
structures also serve as miniaturized, extremely sensitive
magnetization sensors. Integrated magnetic elements may even
compete with traditional semiconductor technology, for example, as fast nonvolatile random access memory (RAM). To
meet these ever-increasing demands on storage density,
processing speed, and device complexity, it is imperative that

B
This manuscript is dedicated to Dr. Jun Kondo, in commemoration of the
40th anniversary of his definitive explanation of the resistance minimum
phenomenon, now known as the Kondo effect.
* Corresponding author. Fax: +81 6 6879 7859.
E-mail address: kasai@dyn.ap.eng.osaka-u.ac.jp (H. Kasai).

0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.tsf.2005.09.183

we find ways to control the structure, composition, and
magnetic properties of these candidate materials on a sub100-nm scale. Obviously, we need new concepts, leading us to
new basic technologies that would allow us to go further
beyond mere miniaturization of classical devices. One notable
concept is that of NANOSPINTRONICS (cf., e.g., [1,2]),
which focuses on the utilization of the spin degree-of-freedom
of conduction electrons, on top of the conventional charge.
However, for the resulting devices (e.g., MRAM) to function
properly, the spin of the (e.g., tunneling) electrons have to be
conserved, because they contain information. But impurities

embedded at the surfaces/interfaces lead to unwanted spin-flip
processes, i.e., inelastic electron scattering and Kondo interactions of magnetic impurities with tunneling electrons. Thus, a
detailed understanding of magnetic interaction is not only
of academic interest, but is essential for future advances
in technology.

W.A. Din˜o et al. / Thin Solid Films 509 (2006) 168 – 172

In recent years, we have seen great progress, not only in
the ability to prepare well-characterized surfaces, but also in
the ability to manipulate individual atoms and molecules,
esp., with the use of the scanning probe microscope [4 –6].
We are also seeing great progress in terms of the ability to
detect and control the spin degrees-of-freedom of the charge
carriers in nanoscale materials. The resulting technology will
eventually allow us to create well-defined nanostructures on
surfaces, providing us with a means to design novel,
functionalized materials that exhibit novel physical properties,
which can be controlled and/or manipulated, and that do not
exist in the bulk phase. Thus, it would not be an exaggeration

to say that surfaces serve as playgrounds for physicists,
providing us with a stage to study the dynamics of complex
systems [3].
One physically significant phenomena that we can play
around with on surfaces is the observation of the Kondo
effect [7 – 16], in real space [17 – 31]. Two prominent
signatures of the Kondo effect that can be observed at
surfaces are the development of a sharp resonance (Yosida –
Kondo resonance [17 – 25]) at the Fermi level, and the
splitting of this resonance upon the application of an external
magnetic field [17 – 19,22]. True to our predictions [20 –24],
starting with Fe/Cu(111) [25], the real-space image of
Yosida – Kondo peak has since been observed [26], together
with the corresponding hallmarks associated with the Kondo
effect, viz., the spectroscopic profile [27 – 29], and the
temperature dependence [29]. However, the magnetic field
dependence has, until recently [30], eluded direct observation.
The main deterrence being the Kondo temperature T K. The
magnetic field necessary to observe the splitting of the
Yosida – Kondo is directly proportional to T K, and this

depends strongly on the hybridization of the conduction
electrons with the localized electrons at the magnetic
impurities, as determined by the Fano parameter [17 –
24,32,33]. Thus, in order to observe the magnetic field
dependence, one needs to drive down T K so as to be able to
apply magnetic fields of manageable magnitudes (a few
Teslas), at the cost of needing to perform the experiments at
much lower temperature conditions (mK range). This has
been achieved in a recent study using a low-temperature (as
low as 0.6 K), high magnetic field (as high as 7 T) scanning
tunneling microscope [30], and taking advantage of the
unique conditions provided by surfaces. In the following
sections, we focus on the two signatures of the Yosida –
Kondo resonance, viz., its behavior when the temperature of
the corresponding (Kondo) system under study is increased
(Section 2), and when an external magnetic field is applied
(Section 3). We also discuss an alternative experimental
means to determine the corresponding Kondo temperature T K
for the system under study (Section 2).
2. Temperature dependence of the Yosida –Kondo resonance for a single magnetic atom adsorbed on a surface

It has been shown that the energy width of the dI/dV(V)
spectra, at the vicinity of E F, observed in experiments is

169

directly related to the Kondo temperature T K (cf., e.g.,
[17,18,21– 24]. Thus, the energy width of the dI/dV(V)
spectra, i.e., the corresponding peak or dip structure at the
vicinity of E F, should give us an estimate of the
corresponding T K of the adsorbate – metal system. However,
determining the corresponding T K from the energy width of
the dI/dV(V) spectra at the vicinity of E F is non-trivial and
not so straightforward. Because the Fano parameter q
[32,33] (which gives us a measure of the spatial extent of
the wave function for the localized orbital – how far it
protrudes –out of the surface, for a particular adsorbate –
metal system) determines whether the dI/dV vs. V curve
around V = 0 (i.e., at the vicinity of E F) would be symmetric
or asymmetric, or whether a dip structure or a peak
structure would be observed. Recently, we proposed an

alternative means to experimentally determine T K, and to
check that the resonance observed experimentally does have
the temperature dependence [10 – 12] characteristic of the
Kondo effect, i.e., by measuring the peak height of the
second-derivative of the dI/dV(V) spectra at the vicinity of
E F—d2I/dV 2(V).
Briefly, let us consider a system where there is,
essentially, a single magnetic impurity sitting on a metal
surface (a single magnetic adatom). Let us further assume
that the system can be described by the Anderson model
(non-degenerate, single orbital, symmetric case). Thus, the
density of states distribution can be cast into the form (cf.,
e.g., [17,18,20 –24]).
2jbx; y; zjdj2
pq2 ½D  Im~ðx þ i0þ Þ
"
#
ðe þ qÞ2
Im~ðx þ i0þ Þ


;

D
e2 þ 1

qð x; y; z; xÞ,

ð1Þ

where the reduced energy parameter
e¼

x  Re~ðx þ i0þ Þ
;
D  Im~ðx þ i0þ Þ

ð2Þ

and the Fano parameter [32,33]
q¼

bx; y; zjd
:
pV ¯q ðeF Þbx; y; zj/kx ;ky kz 

ð3Þ

The factor (e + q)2 / (e 2 + 1) characterizes the shape of the dI/
dV spectra (the Fano line shape). From Eq. (1), we then
derive for d2I/dV 2(V) (”flq/flx), obtaining
Bqð x; y; z; xÞ
 4jbx; y; zjdj2
Bx


B
Re~ðx þ i0þ Þ
1  Bx
:


2
pq½D  Im~ðx þ i0þ Þ

ð4Þ

The peak height of the d2I/dV 2(V) (”(flq/flx)) spectra
would then be proportional to the product of the terms
explicitly dependent on the resonance level width D and the
self-energy R(x + i0+). For T b T K [17,18,20 –24],

170

W.A. Din˜o et al. / Thin Solid Films 509 (2006) 168 – 172

(

x
i
~ðx þ i0 Þ ¼  D
þ

TK
2
þ

"

x
TK

2

þ

and for T  T K [17,18,20 –24]
  rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
 
ln TTK þ ln2 TTK þ a
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
~ði0þ Þ ¼ iD
;
 
ln TTK  ln2 TTK þ a



pT
TK

2 #)

;

ð5Þ

ð6Þ

where a = 3p 2/4.
In Fig. 1 we plot the renormalized peak height given in Eq.
(4) as a function of the system temperature T, for various
corresponding T K. Thus, one could, by measuring the peak
height of the second-derivative of the dI/dV(V) spectra, and
plotting it as a function of the system temperature, not only
verify whether the observed resonance exhibits the temperature
dependence characteristic of a Yosida – Kondo resonance, but
also determine the corresponding Kondo temperature T K for
the system.
Fig. 1 suggests a corresponding Kondo temperature
T K å 100 K, within the experimental error bars, for the Ti/
Ag(100) system. This is higher than the experimental finding
(cf., [29], with a fitted T K å 40 K). To understand the origin of
the difference, we need to take into account how we view the
system in terms of what is being observed experimentally.
Based on Eq. (1), because of the spatial extent of the STM tip,
in the experiments, one measures not only electrons tunneling

through the magnetic impurity/adatom, but also (conduction/
surface) electrons tunneling from the surface without passing
through the magnetic impurity/adatom. Hence, the dependence
of the density of states distribution q(x, y, z, x) on the Fano
parameter q is shown in Eq. (1), and in turn the corresponding
T K for the system (through Eqs. (1) – (6)) [17,18,20 –24]. This
is how we determined the Kondo temperature for the system
under study. On the other hand, one could also choose to
neglect the q-dependent contributions (cf., Figs. 2 and 3, Eq.
(8), and corresponding discussion in [29]), in which case one
ends up with a much lower Kondo temperature. Heinrich et al.
[30] have recently applied this idea in a ingenious way to
observe the magnetic field dependence of the Yosida –Kondo
peak for Mn on NiAl(110) (cf., Section 3).
3. Magnetic dependence of the Yosida – Kondo resonance
for a single magnetic atom adsorbed on a surface
In order to perform the experiments under practically
reasonable (i.e., accessible) magnetic field magnitudes, one
needs to have a system with a low T K, as the magnetic field
necessary to observe Zeeman splitting scales with T K
[11,12,22]. What Heinrich et al. [30] did was deposit an oxide
layer on NiAl(110) before placing the Mn atoms, in effect
manipulating the Fano parameter q.
Again, invoking the same assumption as that presented in
Section 2, and following previous studies [17,18,20– 24], the
charge density near a magnetic adatom at temperature T å 0 K,
for spin r and under an external magnetic field B,
qð x; y; z; xÞ ¼ Ar ð x; y; z; xÞ þ Br ð x; y; z; xÞ
þ Cr ð x; y; z; xÞ

ð7Þ

is given as a sum of the contributions from the conduction
electrons |k
Ar ð x; y; z; xÞ ¼ ~ bx; y; zjkbkj
kkV



1
ImGr ðxÞjkVbkVjx; y; z;
p

ð8Þ

from the localized (d) electrons |d
Br ð x; y; z; xÞ ¼ bx; y; zjdbdj 
Fig. 1. Temperature dependence of the Yosida – Kondo resonance at B = 0
magnetic field. Shown is the peak height of the second derivative of the bias
voltage dependent differential conductance d2I/dV 2(V) as a function of the
system temperature T, for different corresponding Kondo temperatures T K.
Data points for the case of Ti/Ag(100) [29] in the region T b T K are also
shown. Experimental data all fall in the region T b T K [34]! (from [31]). Note
that there is some arbitrariness in the interpolation between the curve in the
low-temperature limit (i.e., T b T K) and the curve at temperatures around and
higher than the Kondo temperature (i.e., T  T K). As is to be expected, this part
or region cannot be used in comparison with the experimental points. The only
important part here would be the region considerably lower that T K. It should
also be noted that there are no available experimental data to compare with
theory for temperatures near the vicinity of T K or greater. The experimental data
shown in this figure all fall in the region T b T K. Whenever necessary, instead
of doing perturbation calculations, one could always resort to obtaining exact
solutions [14 – 16] valid for all temperature range [13].

1
ImGr ðxÞjdbdjx; y; z;
p

ð9Þ

and the hybridization of the conduction and the localized
electrons
Cr ð x; y; z; xÞ ¼ ~ bx; y; zjdbdj
k



1
ImGr ðxÞjkbkjx; y; z
p

þ ~ bx; y; zjkbkj
k



1
ImGr ðxÞjdbdjx; y; z:
p

ð10Þ

r = j(,) = +(). (x, y, z)gives the tip position relative to the

W.A. Din˜o et al. / Thin Solid Films 509 (2006) 168 – 172

171

height of the second derivative of the dI/dV(V) spectra at the
vicinity of E F—d2I/dV 2(V). We also discussed how, by
manipulating the hybridization between the conduction electrons and the localized electron at the magnetic impurity, one is
able to derive the Kondo temperature of the system so as to
reach manageable magnetic fields, and observe the Zeeman
splitting of the Yosida –Kondo resonance.
Acknowledgement

Fig. 2. The differential conductance dI/dV (”~r q(x, y, z, V) calculated for a
˚ from Mn under an applied magnetic
constant perpendicular distance of z = 10 A
field B = 0, 5.3, 6, 7 T.

adatom. x gives the electron energy with respect to the Fermi
level E F.
Because of the presence of the insulating oxide layer
between the Mn adatom and NiAl(110), the main contribution
to the charge density would come from the localized (d)
electrons |d. B j(x,y,z;x) is explicitly given by
Br ð x; y; z ; xÞ ¼ jbajx; y; zj2

1
p


D
2

References
x
TK

2

þD
  
2
 
2


o 2
x
D x
d
þ 2 TK þ D
x þ D TK þ Dtan prSz

n

This work is partly supported by a Grant-in-Aid for
Scientific Research from the Ministry of Education, Culture,
Sports, Science and Technology of Japan (MEXT); the 21st
Century Center of Excellence (COE) Program ‘‘Core Research
and Advance Education Center for Materials Science and NanoEngineering’’ supported by the Japan Society for the Promotion
of Science (JSPS); and the New Energy and Industrial
Technology Development Organization (NEDO) Materials
and Nanotechnology program. Some of the calculations were
done using the facilities of the Yukawa Institute Computer
Facility (Kyoto University), the Institute for Solid State Physics
(ISSP) Supercomputer Center (University of Tokyo), the
Information Technology Based Laboratories Project of the
Japan Atomic Energy Research Institute (ITBL, JAERI).

ð11Þ

S zd

is the z-component of the localized electron spin moment
and calculated as a function of the external field in the so-called
s – d limit [10 – 16].
Upon application of an external magnetic field, depending
on the magnitude of the applied external field, because of the
Zeeman effect, the q j(x, y, z, V) å B j (Eqs. (7),(9) and (11))
spectra shows a peak structure at ca.  Dtan(pS zd )  E F < 0, and
the q ,(x, y, z, V) å B , (Eqs. (7),(9) and (11)) spectra shows a
peak structure at ca. Dtan(pS zd )  E F > 0. Thus, in Fig. 2, we see
that the differential conductance dI/dV spectra (”~r q(x, y, z,
V), corresponding to an Mn atom on a thin film of Al2O3
deposited on NiAl(110), under an external applied magnetic
field of B = 0, 5, 3, 6, 7 T, shows two peak structures about E F
(due to the Zeeman effect) for B = 5.3, 6, 7 T.
4. Summary
In summary, we considered the temperature and magnetic
field dependence of the Yosida – Kondo resonance for a single
magnetic atoms adsorbed on a surface, in light of recent
experimental developments. We presented an alternative means
to experimentally determine the corresponding Kondo temperature T K for a system consisting of a magnetic atom adsorbed
on a non-magnetic metal surface, i.e., by measuring the peak

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