Excitation of local magnetic moments by tunneling electrons

Abstract

The advent of milli-kelvin scanning tunneling microscopes (STM) with inbuilt magnetic fields has opened access to the study of magnetic phenomena with atomic resolution at surfaces. In the case of single atoms adsorbed on a surface, the existence of different magnetic energy levels localized on the adsorbate is due to the breaking of the rotational invariance of the adsorbate spin by the interaction with its environment, leading to energy terms in the meV range. These structures were revealed by STM experiments in IBM Almaden in the early 2000s for atomic adsorbates on CuN surfaces. The experiments consisted in the study of the changes in conductance caused by inelastic tunneling of electrons (IETS, inelastic electron tunneling spectroscopy). Manganese and Iron adatoms were shown to have different magnetic anisotropies induced by the substrate. More experiments by other groups followed up, showing that magnetic excitations could be detected in a variety of systems: e.g. complex organic molecules showed that their magnetic anisotropy was dependent on the molecular environment, piles of magnetic molecules showed that they interact via intermolecular exchange interaction, spin waves were excited on ferromagnetic surfaces and in Mn chains, and magnetic impurities have been analyzed on semiconductors. These experiments brought up some intriguing questions: the efficiency of magnetic excitations was very high, the excitations could or could not involve spin flip of the exciting electron and singular-like behavior was sometimes found at the excitation thresholds. These facts called for extended theoretical analysis; perturbation theories, sudden-approximation approaches and a strong coupling scheme successfully explained most of the magnetic inelastic processes. In addition, many-body approaches were also used to decipher the interplay between inelastic processes and the Kondo effect. Spin torque transfer has been shown to be effective in changing spin orientations of an adsorbate in theoretical works, and soon after it was shown experimentally. More recently, the previously mentioned strong coupling approach was extended to treat the excitation of spin waves in atomic chains and the ubiquitous role of electron–hole pair creation in de-exciting spins on surfaces has been analyzed. This review article expounds these works, presenting the theoretical approach by the authors while trying to thoroughly review parallel theoretical and experimental works.

Introduction

Tunneling phenomena is a purely quantal phenomena with great impact in current basic and applied research. The advent of solid-state devices led to the study of electron tunneling through insulating barriers in order to create a plethora of device designs based on electron tunneling [1]. From the fundamental point of view, tunneling offered many interesting phenomena and applications from imaging of surface structure and topography [2] to Josephson effect [3] and to inelastic electron tunneling spectroscopy (IETS) [4].

Inelastic electron tunneling spectroscopy was discovered when studying electron tunneling through an insulating thin film between two metallic electrodes. Jaklevic and Lambe [4] recorded differential conductance traces where a rich structure appeared at certain well-defined voltages. Their analysis led to the conclusion that they were measuring the change in conductance due to the excitation of vibrations of unknown impurities in the insulating layer. This finding led to the creation of a new type of spectroscopy, IETS, that was much developed in the 70s and 80s. Hansma [5] summarizes in a very interesting review article many of the molecular species studied in this way in different types of tunneling barriers, and on-going research efforts are currently undertaken in the IETS of insulating layer interfaces [6].

The advent of the scanning tunneling microscope (STM) started the search of IETS in the tunneling junction of the STM [7]. The stakes were high: on the one hand-side, STM would be able to detect the vibrational signatures of the species in the junction making it possible to develop a chemical sensitivity absent in the usual STM operational modes; on the other hand-side, the extreme local sensitivity of the STM would permit to have a single-molecule spectroscopy. Despite theoretical evaluations that IETS was within reach in STM [7], [8], experimental proof only came in 1998 when Stipe et al. showed the vibrational IETS of a single acetylene molecule adsorbed on a Cu (1 0 0) surface [9]. There are excellent review articles that describe the physics and history of IETS with the STM [10], [11].

The sophistication of STM opens the possibility of addressing lower energy scales. Very low temperatures and extreme sensitivity equipment appear along the 90s. Once that vibrational IETS was proven with the STM, lower-energy excitations became available. In 2004, Heinrich and co-workers [12] showed that magnetic excitations on a single magnetic atom were detected using a milli-Kelvin STM with a built-in magnetic field. This seminal experiment has given rise to a lot of activity in magnetic IETS on the atomic scale.

Both vibrational and magnetic IETS consist in a measurable change of conductance due to an excitation of an atom, molecule or general atomic structure under the tip of an STM. Hence, the tunneling current is both the exciting and the measuring probe. This dual behavior of the tunneling current makes IETS a complex technique where a simple-minded picture is surely error prone. However, a first-order approximation of how the excitation of an atom or molecule changes the conductance can be easily found in terms of the opening of new conduction channels linked to the excited molecular states [4], [5], see Fig. 1. Indeed, when the tip-sample bias is larger than the excitation energy, the tunneling electron can cede part of its energy to the molecule and still end up in a state above the Fermi energy of the corresponding electrode, thus contributing to the tunneling current as part of an inelastic current. For bias below this threshold, the tunneling current is just formed of elastic electrons. When the new channel opens at the bias matching the excitation energy, the tunneling current increases because it now contains elastic as well as inelastic electrons. This abrupt change in the current leads to a jump in the differential conductance, and to a peak in the second derivative of the current with respect to bias, centered about the excitation energy in eV.

As announced, the previous picture is simplistic and it does not take into account the complexities of the many-body character of the excitation process. There are cases where the conductance decreases instead of increasing. This was shown by Hahn et al. [13] in the case of O₂ adsorbed on Ag (1 1 0) where the IETS shows dips instead of peaks. The study of this system showed that the appearance of dips can be associated with the mixed-valence electronic structure character of O₂ on Ag (1 1 0) [14].

A big difference between vibrational and magnetic IETS was quickly revealed. While vibrational IETS rarely implies increases of the conductance of more than 10%, magnetic IETS easily reaches 100% or more of change in conductance. This behavior can be traced back to the strengths of the interactions at play: while electron–vibration couplings are weak, electron–spin couplings are very large. The first consequence of this fact is that the perturbational approaches developed for vibrational IETS [8], [15], [16], [17], [18] are no longer valid. A second consequence is that multiple successive excitations are easily accessible in magnetic IETS [19] in the case of strong currents. Finally, vibrational IETS is very sensitive to the symmetry and to the particular system and thus, only a few modes are detectable which has led to the creation of propensity rules for mode analysis [20], [21]. Similarly, not all excited states in a magnetic system can be excited by a tunneling electrons (see e.g. below the discussion on spin wave excitation in Heisenberg chains) and this can be easily rationalized in terms of angular momentum conservation and spin-coupling coefficients [22].

Magnetic IETS has not been confined to a small number of atomic systems, but it has also been extended to spinwave excitation [23] and itinerant magnetism [24]. Moreover, the use of spin-polarized STM has made a natural connection of magnetic excitations with spin torque of magnetic atomic systems. The reversal of the magnetization of atomic structures by the tunneling current has been shown on magnetic islands [25], [26] and also on single atoms both at the experimental [19] and theoretical [27], [28] levels.

Finally, magnetic IETS is intrinsically linked to the Kondo effect. Indeed, Kondo effect is induced by spin-flip transitions in an impurity induced by collisions with the substrate electrons; this is exactly the same process as the one at play in magnetic IETS and one can expect strong links between the two phenomena, as well as the possible emergence of many-body effects (Kondo-like effects) in magnetic IETS.

Hence, despite its short life, magnetic IETS is a well established technique that we will expound in the present article. First, we will review the main experimental results that have been briefly mentioned above, together with other results to give the reader a vision of the breadth of the field. Second, we will review and explain the main theoretical approaches trying to emphasize the main features of magnetic IETS. Finally, we will conclude and try to outline some perspectives of this powerful technique.