On the magnetic bistability of small iron clusters used in scanning tunneling microscopy tip preparation

The combination of electron spin resonance with scanning tunneling microscopy has resulted in a unique surface probe with sub-nm spatial and neV energy resolution. The preparation of a stable magnetic microtip is of central importance, yet, at the same time remains one of the hardest tasks. In this work, we rationalize why creating such microtips by picking up a few iron atoms often results in magnetically stable probes with two distinct magnetic states. By using density functional theory, we show that randomly formed clusters of five iron atoms can exhibit this behavior with magnetic anisotropy barriers of up to 73 meV. We explore the dependence of the magnetic behavior of such clusters on the geometrical arrangement and find a strong correlation between magnetic and geometric anisotropy—the less regular the cluster the higher its magnetic anisotropy barrier. Finally, our work rationalizes the experimental strategy of obtaining stable magnetic microtips.


Introduction
Since spin-polarized scanning tunneling microscopy (SP-STM) and spin-polarized scanning tunneling spectroscopy are a powerful method for exploring the foundations of magnetic interactions at atomic scale [1,2], our work is aimed at shedding some light on tips for this type of techniques.As we know, a good tip must simultaneously offer high spatial resolution, high spin polarization, and non-destructive magnetic imaging.Ideally, controlling the orientation of the spin at the tip is desired.Basically three types of tips can be prepared [3]: bulk magnetic tips, magnetic thin film tips and tips made magnetic by picking up small magnetic clusters.
The use of bulk magnetic tips has proven in SP-STM, both at room temperature [4] and at low temperatures [5].In particular antiferromagnetic (AFM) probe tips are preferred since they have negligible stray magnetic fields.In contrast, the use of bulk iron (Fe) tips has a high saturation magnetization and substantial stray magnetic fields, which could potentially interfere with the samples.The second option is the preparation of magnetic thin film tips.In this way of tip preparation, when a thin magnetic layer is applied to such probe tips, the orientation of the magnetization is determined by the unique characteristics of the surface and interface of the material.This occurs because the thickness of the deposited magnetic layer, typically in the range of 1-3 nm, is significantly smaller than the radius of the tip, which is about 1 µm [6,7].
The key advantage of selecting thin-film ferromagnetic (FM) tips lies in the ability to apply an additional external magnetic field, and obtain highly precise SP-STM measurements in both the surface plane and perpendicular to it, all with the same tip.One of the drawbacks is that the preparation of such tips involves the use of high temperatures, which often necessitates their manufacturing outside from the STM device.
The third method, which is relevant for the present work, involves creating a non-magnetic tip with a cluster of magnetic material at the tip's front end.This method is the simplest and can be carried out in-situ without the need for elevated temperatures.This makes it the most widely employed approach, especially in electron spin resonance scanning tunneling microscopy (ESR-STM) [8][9][10], an emerging technique capable of detecting single spin precession that is increasingly gaining popularity.The typical value of atoms to create the magnetic tip varies, but usually lies between 1 to 6 atoms [11][12][13].Once this is accomplished, the resulting few-atoms cluster can be magnetized in an external magnetic field in a certain direction.At the low temperatures typically involved in these experiments (usually < 4 K), the cluster magnetization can remain stable for a significant amount of time unless perturbed by large current or voltage pulses or by being structurally modified, e.g. by unintentionally picking up another atom from the surface.Such tips have been employed in the study of ESR in STM of Fe, Ti, Na 2 dimers, Fe-phthalocyanine molecules just to name a few [11][12][13][14][15].A common feature of such tips that has been reported in various publications is that the tip possesses two orthogonal ('up' , 'down') magnetic states [16,17].In all instances, the magnetic behavior of the cluster resembles that of a macroscopic spin [14].The process leading to such tips is stochastic, often involving repeated dropping off and picking up of atoms until the desired stable spin-polarized tip is obtained.
In order to provide additional insight into the nature of magnetic tips, we study the magnetic behavior of small clusters by using density functional theory (DFT) and randomly generated Fe clusters of five atoms (i.e.Fe 5 clusters).Furthermore, we study the magnetic stability of such clusters and the magnetic anisotropy energy to understand why some tip clusters are apparently better to measure ESR signal from STM junction than others.Here, we focus on the minimum energy barrier defined by the MAE value between two orthogonal magnetic axes, i.e. a flip of the magnetization axis by 180 • .If this barrier value is small, minor thermal or other fluctuation could randomly flip the tip magnetization, leading to a bistable tip behavior [18].Finally, we explore the effect of the non-magnetic bulk part of the tip, by adsorbing the magnetic cluster on a non-magnetic silver slab.

Method
We used DFT as implemented in quantum espresso, using pseudopotentials and plane wave basis [19,20].All our calculations use norm-conserving pseudopotentials from the ONCV library with a cutoff of 100 Ry [21].The workflow is schematically depicted in figure 1(a).Fe 5 clusters are generated randomly to sample a large parameter space of geometric arrangements and placed in a vacuum box of size 20 × 20× 20 Angstrom.Based on convergence tests we estimate the uncertainty of ∆MAE ⩽ 5 meV.All systems were relaxed until the energy and force thresholds 10 −4 Ry and 10 −3 Ry/Bohr are reached.We note that many clusters relax to the same lowest energy configuration, which agrees with previous studies on Fe clusters [22].
In this work noncollinear treatment of spins are not indeed necessary, we treat the Fe 5 cluster as collinear and ferromagnetically coupled spins.This is justified based on previous works [23,24].
We proceeded by calculating the MAE of all clusters using the force theorem [25,26].As a convention, we first rotated all clusters such that their longest axis is aligned with the z-axis.Finally, we placed a cluster on a 4-layer slab of Ag(001) where the silver slab plays the role of a non-magnetic bulk background of the tip.

Results and discussion
We find that the total energies of randomly generated Fe 5 clusters before structure relaxation are in good approximation normally distributed within a standard deviation of 1.2 eV (blue curve figure 1(b)).This is an indication that our clusters are sufficiently randomly generated to sample a large part of the geometry phase space.After structural optimization, the clusters generally fall into three categories, which are narrowly defined by the total energy as well as volume, bond lengths and bond angles (orange bars in figure 1(b)).We then rotate all clusters with their longest axis in the z-direction and make the second longest axis parallel to the x-direction.This is a convention that does not affect the outcome of our study (figure S1).We subsequently filter out all clusters that can be classified as duplicates based on their shape parameters and total energy.Out of 115 optimized clusters, 93 unique clusters remained after this filtering (green bars in figure 1(b)).We chose 49 random samples across the three categories for the MAE calculation.Since the orbital angular momentum in small Fe clusters are known to be severely quenched to about 1% of the free atom value [23,27], spin-orbit effects were omitted in our calculations.
Figure 2 presents the structure of three representative clusters and their MAE.One can identify the preferred (low total energy) direction of the magnetization as well as the minimum energy barrier (MAE barrier) between two 180 • separated orientations, which is the value indicative of the magnetic stability of the cluster.The lowest energy clusters have the appearance of regular double-tetrahedrons (figure 2(a)), whilst the highest energy solutions exhibit a W-like shape (figure 2(c)) [28].In figure 2, we observe the presence of two poles in all instances.In cases (a) and (c), these poles are aligned with the z-axis, while in case (b), the hard axis is tilted.From the value of the MAE barrier in figure 2, we find that the coordination number plays a pivotal role in governing the magnetic anisotropy of each system.The highest MAE barrier value occurred in the cluster with the lowest number of first neighbors.
A more thorough analysis of this relationship is shown in figure 3  barrier is strongly dependent on the coordination number, which also holds true when considering the standard deviation (shaded area).However, as can be expected from the random sampling, some outliers with high MAE barrier value exist even in systems with a high coordination number.Furthermore, figure 3(b) demonstrates an interesting trend: systems with the lowest coordination number exhibit the highest total energy and largest MAE.The maximum obtained MAE barrier value is 73 meV, whilst the lowest cases show less than 1 meV, which makes them essentially not magnetically stable.
Additionally, we have calculated the magnitude and sign of the exchange coupling constant by calculating the energy of flipping one spin in the Fe 5 cluster and applying the Noodleman formula (table S1 in the supporting information).In our calculations, we mostly found a FM coupling of the Fe spins with a maximum exchange coupling constant of J = 41 meV (see figure S5).We note that the sign as well as the magnitude in small Fe clusters or chains is known to vary depending on the specifics of the system [29,30].We note that we observe AFM coupling between the spins in only a few configurations with low coordination number, which leads to a reduced total magnetic moment for these clusters as shown in figures 3(c) and (d).We estimate the maximum blocking temperature T B [31] for our clusters with a maximum MAE value of 130 meV, to be at most T B = 43 K.
Finally, we studied the effect of the non-magnetic tip background modeled as an Ag(001) slab.To understand the effect that the silver slab has we contrast three scenarios: First, an unrelaxed Fe 5 cluster in vacuum (figure 4(a)), the fully relaxed cluster on Ag(001) (figure 4(c)) and the same cluster, but with the silver removed (figure 4(b)).The influence of the relaxation can be understood by comparing figures 4(a) and (b).In our calculations, the relaxation caused in increase of the MAE by roughly a factor of 2. The combined effect of relaxation and metallic background on the cluster MAE can be understood by comparing figures 4(a) and (c).After the geometry optimization, the increased by almost a factor of 10 compared to the same cluster in vacuum (figure 4(b)).The overall magnetic energy landscape remains unchanged, but the minima become narrower and deeper.This indicates that a non-magnetic metallic bulk background together with the relaxation of the Fe 5 cluster can significantly stabilize the magnetic behavior of a magnetic cluster at the tip apex [32,33], which is in line with the experimental observations of tips with magnetic stability up to several Kelvin [34].We do not observe any significant charge transfer between the Fe 5 cluster and the slab in any of the cases indicating that charge transfer does not play a major role in the change of MAE observed here (table S2).
Finally, we note that the behavior of the magnetic anisotropy of Fe 5 clusters is comparable to the one of clusters formed by 3 and 4 Fe atoms, as shown in figure S4, which is also supported by the different choices for making magnetic microtips in the experiments.

Conclusion
In conclusion, our DFT study rationalizes the experimental observation that stable magnetic tips can be reliably generated by picking up Fe 5 atoms.The lack of consistent magnetic stability in the so-obtained magnetic tip can be attributed to the relatively small MAE barrier observed in the clusters with the lowest total energy.The stochastic nature of the tip making process could randomly generate such tips with high probability.However, our findings also indicate that by dropping off and picking up only one or two atoms to create a Fe 5 cluster on the tip one should be able to generate tips that have a sizable MAE barrier value up to 130 meV (blocking temperature T B ∼ 40 K).We found that clusters with the lowest coordination number emerge as the most promising candidates for creating a stable magnetic tip.Notably, these clusters exhibit the highest barrier value aligning with the previously observed trend in lanthanides and single ions magnets [35,36].With the recent increase in ESR-STM studies adopting the same strategy to make a tip [16,17,34,[37][38][39][40][41][42][43][44], we anticipate that our work helps to rationalize why this approach is successful.

Figure 1 .
Figure 1.(a) Flowchart showing the procedure to study magnetic anisotropy of Fe5 clusters from random generation, relaxation, filtering of duplicates and the calculation of magnetic anisotropy energy (b) energy distribution of different Fe5 clusters in three different stages, which are randomly generated structures (blue), after optimization (orange), after filtering all duplicates (green), respectively.∆E is the difference in total energy from the mean value of the total energy for all Fe5 cluster.The inset shows an Fe5 cluster with the coordinate system used.

Figure 2 .
Figure 2. Representative results for three types of clusters: In each line, from left to right we show the cluster geometry, the magnetic anisotropy of such clusters obtained in a 3D and 2D representation, respectively.From top (a) to bottom (c) the total energy of the cluster increases, as does their geometric anisotropy, when the number of first neighbors decreases from 9 in (a) to 7 in (c) .
(a) where the MAE barrier values are shown as a function of the coordination number for all clusters.The mean value (solid line) of the MAE

Figure 3 .
Figure 3. MAE barrier analysis (a) and (c) The MAE barrier and total magnetic moment per unit cell with respect to the number of nearest neighboring atoms, respectively.Shown are all individual data points, the mean (solid line) and standard deviation (shaded area).The values of magnetic moment are in Bohr.(b) and (d) Correlation between total energy and barrier value of Fe cluster, and the total magnetic moment per unit cell, depending on the number of nearest neighbors.The total number of Fe5 clusters used was N = 49.