Reversible 2D Phase Transition Driven By an Electric Field: Visualization and Control on the Atomic Scale

We report on a reversible structural phase transition of a two-dimensional system that can be locally induced by an external electric field. Two different structural configurations may coexist within a CO monolayer on Cu(111). The balance between the two phases can be shifted by an external electric field, causing the domain boundaries to move, increasing the area of the favored phase controllable both in location and size. If the field is further enhanced new domains nucleate. The arrangement of the CO molecules on the Cu surface is observed in real time and real space with atomic resolution while the electric field driving the phase transition is easily varied over a broad range. Together with the well-known molecular manipulation of CO adlayers, our findings open exciting prospects for combining spontaneous long-range order with man-made CO structures such as "molecule cascades" or "molecular graphene". Our new manipulation mode permits us to bridge the gap between fundamental concepts and the fabrication of arbitrary atomic patterns in large scale, by providing unprecedented insight into the physics of structural phase transitions on the atomic scale.


I. Introduction
Phase transitions are ubiquitous in science from fundamental physics, chemistry or biology to ecological or social systems, and have a broad range of applications, e.g. data storage, drug delivery, etc. [2][3][4][5][6][7]. Arising from an ensemble of a huge number of microscopic objects, like atoms or molecules, phase transitions manifest themselves as changes of a macroscopic order parameter, like conductivity or magnetization. For a detailed understanding of the different phases as well as the mechanism of phase transitions, knowledge about the individual objects is required. Various techniques based on microscopy or diffraction have been applied to analyze the structure of different phases [8][9][10][11][12][13][14][15][16][17].
The arrangement of adsorbates on a surface is governed by interactions between the adsorbate and the atoms of the supporting surface as well as between the adsorbates themselves. The geometric structure, these adsorbates assemble into, can be studied by ensemble averaging techniques like electron diffraction [8] or real space imaging techniques like low electron energy microscopy (LEEM) [9], electron microscopy [10], scanning tunneling microscopy (STM) [11] and atomic force microscopy (AFM) [12]. The latter two allow for the determination of the positions of individual atoms or molecules on the atomic scale.
Moreover, the tip of an STM or AFM may act as a local probe to provide a stimulus to induce phase changes. Despite the finite size attained by individual manipulation of molecules, manmade structures have proven to be of great interest [1,2]. The combination of STM-induced manipulations and the long-range ordering of phase transition is a promising route that needs to be explored.
Phase transitions induced by a change of the temperature have been analyzed by STM or high resolution electron microscopy, for example for Pb on Si(111) [13], Sn on Si(111) [14], for self-assembled monolayers [15], for roughening transitions of Au(110) and Pt(110) [16] or for the semiconducting to metallic phase transition of a MoS 2 layer [17]. External electric fields may prompt 3D-phase transitions in ferroelectric materials [18,19] or the freezing of thin layers of water [20,21]. Similarly, the potential in an electrochemical environment or a liquid solid interface can induce transitions between different phases of molecular layers on surfaces [22,23]. Furthermore, mechanical strain is predicted to induce a transition, for example from a non-metallic to a metallic phase [24]. Due to short range forces between the apex of the tip and the surface, the tip of an STM or AFM can be used to induce changes of a very small area, e.g. a transition between two different reconstructions of the Si(100) surface at low temperature [25,26] or a change of the H induced reconstruction on Si(100) [27]. However, these modifications do not persist if the tip is retracted from that area of the surface. On the other hand by increasing the bias voltage and the tunneling current of an STM, modification of a phase [28] or nucleation of crystallites of inorganic [29] and organic layers [30] can be induced.
Our experiment reveals a new aspect of adsorbed layers of CO on Cu(111). We use the tip of an STM to induce a structural phase transition between two phases of a monolayer of CO on a Cu(111) surface. As will be shown, the reversible transitions between an α-phase ( 7 7× superstructure) and a β-phase (  3  3  3 3 × ) R30° are caused by the electric field between the tip and the sample surface.

II. Geometric structure of the two phases
The surface is prepared by dosing CO in excess onto a clean Cu(111) surface at 80K. At saturation, the α-phase is formed covering the entire surface. The molecular ordering appears to be stable if the surface is imaged by the STM using a negative bias at the sample. However, if a high enough positive bias is applied for an extended period of time, patches of a new phase, referred to as β-phase appear and grow continuously. At 80K, the two phases may coexist on the surface.  Both structures were previously studied by electron diffraction [31]. A 7 7 × superstructure was proposed for the α-phase [32] which is now confirmed by our observations. However, the combination of DFT calculations and measured data reveals the individual positions of the CO molecules which differ from the original model. Fig. 2   A careful analysis for the β-phase based on our STM observations at high resolution reveals a 3 3 3 3 × unit cell rotated by 30° with respect to the substrate, instead of the c(4x2) or structures which were originally proposed based on electron diffraction data [34]. Since the real space configuration we have found will lead to an almost identical diffraction pattern as observed in [34] and the experimental parameters are very similar, we conclude that the β-phase is identical to the one previously identified as . Our data also correspond well to the experimental results of a previous STM study [35], although a different structural model was proposed.
DFT calculations reveal a delicate balance between the α-and the β-phase for the given experimental parameters (see calculations). The corresponding simulated STM images, displayed in Fig. 2 b and 2 e respectively, agree well with the experimental observations.

III. Phase transition between the two phases
Once coexisting domains of both phases are present on the surface, we can locally and reversibly induce the phase transition by changing the bias voltage. Fig. 3 shows that the transition between the α-and the β-phase can be simply induced by the external electric field of the STM tip. Fig. 3 a displays three Cu(111) terraces covered with the β-phase of CO. c-f show the area marked in a with higher resolution. Between the images, the tip was placed at the center of the dashed frame and the bias voltage applied to the sample was ramped to -3V to switch from β-to α-phase (prior to c and e) and to 1V to switch from α-to β-phase (prior to d and f). This process was repeated more than 50 times. All images were acquired at a bias of -0.5V, a parameter which does not alter the distribution of the phases. As displayed in Fig. 3 b, the dynamics of the process are revealed by monitoring the tunneling current while the voltage is varied. The phase transition can be identified by a discontinuity in the tunneling current marking the thresholds of the electric field required for the transition.
The upper part of Fig. 3 b displays the tunneling current as function of bias in a range between -3 V and +1 V; the insets provide a close up of the small kinks in the curve indicating the phase transitions. One clearly sees a hysteresis between the threshold for the formation of the β-phase going from negative to positive voltage (red) and the one for the formation of the αphase going from positive to negative voltage (black). This indicates a first order phase transition which requires an activation energy.
In the lower part of Fig. 3  The experiments have been repeated with tips of different shape but also different material (chromium tips as well as platinum-iridium tips). In all cases, the phase transition is induced by the electric field. However, the threshold values for the required bias voltage vary from tip to tip and also as a function of time and coverage.

IV. Calculations
Our calculations confirm the findings by vibrational spectroscopy about the adsorption sites of the molecules: for the β-phase all the molecules adsorb on top sites, while for the α-phase bridge and eventually hollow sites are occupied as well. This leads to non-trivial dipole distributions on the surface. Both experimentally and theoretically, the work function for the α−phase is about 0.1 eV higher than for the β−phase despite the slightly higher coverage [36,37] reflecting the complexity of the dipolar arrangement on the surface.

Fig. 4
Change in the Gibbs free energy due to the formation of adsorbate monolayers. The orange and the magenta lines show the results for the α-and the β-phase respectively. The lowest Gibbs free energy corresponds to the stable phase. The two dashed lines mark the phase transitions as a function of the reservoir's chemical potential, ∆µ(T,P). If a small electrical field of 0.3 V/Å is applied such that the molecular dipole is more stable, the stability domain of the β-phase greatly increases. However, as soon as the field decreases, the α-phase is favored. The key finding is that the two available phases are extremely close both in mean adsorption energy per molecule and in molecular density. As a consequence, the Gibbs free energies of the two phases are very close for a wide range of the CO gas-phase temperatures and pressures, and a small perturbation can easily change the stable phase. In agreement with the larger work function, the α-phase dipole is slightly larger. At the positive applied bias, this leads to a destabilization of roughly 10 meV of the molecular dipoles seen as the adsorptionenergy difference between both phases. Since the destabilization is lower for the beta-phase (4 meV), this small perturbation is enough to induce a sizable increase of the stabilization domain of the β−phase, so that it becomes the prevailing phase. As the field is reversed, the α-phase becomes more stable due to its slightly larger molecular density.

V. Details of the phase transition
While the experiments can be repeated many times for several hours, there is a temporal evolution on the time scale of days due to a very slow but not completely negligible desorption of the CO molecules at the given temperature of 80 K. Thus, within days the relative contribution of the β-phase slightly increases.
Since the coverage of CO molecules in the α-phase is higher, the question arises where the redundant molecules go to after switching to the β-phase. Since the process can be reversed they apparently have to stay in close vicinity. A possible explanation is found if a larger area of the β-phase is studied after switching from the α-phase. As can be seen in Fig  The hysteresis observed in Fig. 3 b between switching back and forth suggests that an activation energy has to be overcome to start the conversion of the phases. The relatively constant value of the threshold indicates that this energy is required for one specific initial process starting a chain reaction which continues until the reaction comes to a stop at a defect or a boundary, e.g. an atomic step. We tested this concept by analyzing the threshold as a function of the size of the transformed area and do not find any correlation. However, the hysteresis is rate dependent, i.e. the thresholds for switching depend on the dwelling time.
Hence, the barrier given by the activation energy is overcome by thermal activation. If the tunneling current is measured as function of bias as shown in Fig. 3 b, the width of the hysteresis shrinks if the slew rate of the voltage is decreased. As discussed in more detail (see appendix B Fig. 8b), we use this to evaluate the impact of the electric field on the activation energy. The hysteresis of the phase transition enables us to create arbitrary pattern of patches of the two phases, which are long lived if the appropriate electric field for coexistence is used after the formation (see appendix B Fig. 9).

VI. Conclusions
Our experiments reveal a structural 2D phase transition between two rather complex molecular arrangements of CO on Cu(111), which is reversible despite the slightly different coverages. Since the transition is efficiently triggered by the electric field of an STM tip using voltages in the range of +/-3 V it opens a new field of research, especially due to the excellent control of the experimental conditions. In contrast to thermally induced transitions, very localized areas can be reversibly transformed and patterns of the two phases may be written on a small scale. Since the phases differ in their electric surface potential, well defined structures in the electric potential (field) above the surface can be designed. The switching times can be very fast since the bias can be changed rapidly (If the bias is chosen high enough, the dwelling time for the thermal activation can be reduced substantially.). In contrast to the common observation of phase transitions, not only macroscopic quantities of a large ensemble may be studied, but the position of every element of the system is directly accessed.
Given the ease of the experiment, it is an ideal model system providing unprecedented insight into the physics of structural phase transitions on the atomic scale. Additionally, it opens an unforeseen development in the field of atomic manipulation. Future bottom-up strategies will combine atom-manipulation technics with phase transitions physics so as to generate new macroscopic structures.