Temperature and magnetic field dependence of the Yosida–Kondo resonance
for a single magnetic atom adsorbed on a surface
B
Wilson Agerico Din˜o
a,b,c,d, Hideaki Kasai
c,*, Emmanuel Tapas Rodulfo
d, Mayuko Nishi
aa
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan b
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 so-called Kondo temperatureTK. In order to clearly observe the temperature dependence, one needs to choose a system with a largeTK. One can thus
perform the experiments at temperaturesTbTK. However, because the applied external magnetic field necessary to observe the magnetic field
dependence scales withTK, one needs to choose a system with a very smallTK. 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.
D2005 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 informa-tion 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 exam-ple, 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
we find ways to control the structure, composition, and magnetic properties of these candidate materials on a sub-100-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 interac-tions 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.
0040-6090/$ - see front matterD2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.tsf.2005.09.183
BThis 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.
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 TK. The magnetic field necessary to observe the splitting of the Yosida – Kondo is directly proportional to TK, 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 downTK 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 temperatureTK for the system under study (Section 2).
2. Temperature dependence of the Yosida – Kondo reso-nance 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 EF, observed in experiments is
directly related to the Kondo temperature TK (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 EF, should give us an estimate of the corresponding TK of the adsorbate – metal system. However, determining the corresponding TK from the energy width of the dI/dV(V) spectra at the vicinity of EF 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 EF) 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 TK, 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
EF—d2I/dV2(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]).
where the reduced energy parameter
e¼xRe~xþi0
þ
ð Þ
DIm~ðxþi0þÞ; ð2Þ
and the Fano parameter [32,33]
q¼ bx;y;zjd
pVq¯ðeFÞbx;y;zj/kx;kykz
: ð3Þ
~ðxþi0þÞ ¼ D x
InFig. 1we plot the renormalized peak height given in Eq. (4) as a function of the system temperature T, for various corresponding TK. 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 TK for the system.
Fig. 1 suggests a corresponding Kondo temperature
TKå100 K, within the experimental error bars, for the Ti/ Ag(100) system. This is higher than the experimental finding (cf.,[29], with a fittedTKå40 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 distributionq(x,y,z, x) on the Fano parameterq is shown in Eq. (1), and in turn the corresponding
TKfor 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 theq-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 lowTK, as the magnetic field necessary to observe Zeeman splitting scales with TK
[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 parameterq.
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 temperatureTå0 K, for spinr and under an external magnetic field B,
qðx;y;z;xÞ ¼Arðx;y;z;xÞ þBrðx;y;z;xÞ
þCrðx;y;z;xÞ ð7Þ
is given as a sum of the contributions from the conduction electrons |k
and the hybridization of the conduction and the localized electrons
adatom.xgives the electron energy with respect to the Fermi levelEF.
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.Bj(x,y,z;x)is explicitly given by
Szd is thez-component of the localized electron spin moment and calculated as a function of the external field in the so-called
s – dlimit[10 – 16].
Upon application of an external magnetic field, depending on the magnitude of the applied external field, because of the Zeeman effect, the qj(x,y,z,V)åBj (Eqs. (7),(9) and (11)) deposited on NiAl(110), under an external applied magnetic field ofB= 0, 5, 3, 6, 7 T, shows two peak structures aboutEF (due to the Zeeman effect) forB= 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 temper-atureTKfor a system consisting of a magnetic atom adsorbed on a non-magnetic metal surface, i.e., by measuring the peak
height of the second derivative of the dI/dV(V) spectra at the vicinity of EF—d2I/dV2(V). We also discussed how, by manipulating the hybridization between the conduction elec-trons 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
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 Nano-Engineering’’ 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).
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