Remote detection and recording of atomic-scale spin dynamics

Atomic spin structures assembled by means of scanning tunneling microscopy (STM) provide valuable insight into the understanding of atomic-scale magnetism. Among the major challenges are the detection and subsequent read-out of ultrafast spin dynamics due to a dichotomy in travel speed of these dynamics and the probe tip. Here, we present a device composed of individual Fe atoms that allows for remote detection of spin dynamics. We have characterized the device and used it to detect the presence of spin waves originating from an excitation induced by the STM tip several nanometres away; this may be extended to much longer distances. The device contains a memory element that can be consulted seconds after detection, similar in functionality to e.g. a single photon detector. We performed statistical analysis of the responsiveness to remote spin excitations and corroborated the results using basic calculations of the free evolution of coupled quantum spins.

S pin waves, quantum-mechanically described as magnons, are collective magnetic excitations that, due to their longdistance coherence 1 , are considered promising candidates for future spintronic devices [2][3][4][5] . In light of the intrinsic quantum nature of these waves, their exact behavior is difficult to predict. Scanning tunneling microscopy (STM)-based atom manipulation allows for the assembly of artificial spin structures 6,7 : a technique that has enabled studies of collective magnetism ranging from the emergence of magnetic bistability [8][9][10] to spin waves 11 , phase transitions 12,13 and topologically protected edge states [14][15][16] . More recently, the implementation of electron spin resonance (ESR) 17 has led to coherent manipulation of combined atomic spin states 18 . However, by nature of the STM design, in each of these studies the effect of local tip-induced stimuli can only be probed there where they are generated.
For atomic structures that have a static spin state, remote detection schemes exist that make use of a nearby atomic probe [19][20][21] . In order to remotely probe the dynamic response occurring faster than the tip travel time, one would need to implement a memory unit that stores this response until the tip has had time to arrive. Such memory-based remote detection schemes have been implemented for dynamic processes not based on spin 22,23 . In this work, we present a device that provides memory-based remote detection of spin dynamics in atomic spin structures. By comparing experimental results to calculations we show that the triggering of the detector correlates with the probability of a magnetic excitation induced elsewhere reaching the detector due to free quantum evolution.

Results
Design of spin wave detector. The general design of the spin wave detector, shown in Fig. 1a, is based on Fe atoms on top of Cu 2 N. All structures are built in a line along a nitrogen row of the Cu 2 N molecular network. This direction coincides with the easy axis of the Fe atom spins, which we treat as effective S = 2 24 . During the experiment, we apply a magnetic field B = 0.5-1.0 T along this direction in order to maintain spin-polarized tunneling contrast 8 . Structures consist of three parts: an input lead, an output lead and a reset lead. The length of these parts are given as n in , n out and n reset , respectively. For reasons discussed below, the output lead is required to have an even length, whereas the input and reset leads are required to be odd. Throughout this paper, we will use n out = 8, n reset = 3 and 3 ≤ n in ≤ 9. To describe the structures, we will use the shorthand "n in -n out -n reset "; for example, the structure shown in Fig. 1 will be referred to as "3-8-3".
Neighboring atoms that are part of the same lead are separated by two unit cells of the Cu 2 N lattice, which is known to result in an antiferromagnetic coupling with coupling constant J = 0.7 meV 25 . Adjacent atoms from different leads are separated by three unit cells. We have determined through inelastic electron tunneling spectroscopy and spin-polarized STM that this separation results in a ferromagnetic coupling −0.05 meV < J 0 < 0 meV. We will use J 0 ¼ À0:05 meV throughout the rest of this paper. See Supplementary Note 1 for a detailed description of the Hamiltonian.
As demonstrated by means of spin-polarized STM in Fig. 1b, the output lead will at any time be in either of two Néel states N A and N B . For n out = 8, both these states have a lifetime upward of several seconds 8 . We define N A to be the state where the output atom closest to the input lead is aligned with the field. As n in and n reset are odd, atoms A and A′ (Fig. 1a) will also prefer to align with the field. As a result, when neither the input nor the reset lead is excited, the N A -state will have a favoured ("happy") coupling to the input lead and an unfavoured ("unhappy") coupling to the reset lead. In this situation, N A and N B are degenerate.
An operation cycle consists of the five steps outlined in Fig. 1c.
(1) First, the output lead is set to N A . If this is not the case, the output can be initialized by starting the cycle at step 3. (2) A spin excitation is induced in the input lead, affecting the spin state of atom A. The resulting energy splitting between N A and N B causes the system to fall to its ground state N B . (3) The output lead, consulted by the STM tip, retains its state N B after the input lead relaxes to its original state. Further actuation on the input lead does not change the output state. (4) A reset is performed by means of a similar excitation on the reset lead, after which (5) the system returns to its initial state N A . This design provides a ratchet behavior, where the output lead should switch only if the coupling configuration on the input side is "happy", and never if it is "unhappy". In the following experiments, we always start with the tip on the input lead. We then define P H as the measured probability for the output lead to switch from N A to N B , and P U the probability to switch from N B to N A .
In the figure, the input and reset leads are shown to fully invert. However, we emphasize that switching of the output lead would also occur if atom A in step 2 is only partially inverted due to a spin excitation. In fact, as we will discuss below, switches of the output lead can occur already if the magnetization of atom A is changed from S z = +2 to S z = +1, i.e., due to a single short-lived |ΔS z | = 1 excitation.
Triggering by means of voltage pulses. We have tested the functionality of the device by switching the input lead in two different ways: by means of local spin excitations in the input lead and by means of tip field-induced static inversion of the input lead as a whole. In the first method, we perform voltage pulses on input atoms, and we characterize the response of the output lead as a function of pulse parameters. Figure 2a shows the switching efficiency after applying voltage pulses of varying height on atom C. Pulse width and tunneling current are kept constant at 550 ms and 20 pA to ensure the same number of electrons for all pulses.
We note that this current is too low for the input trimer to spend a significant amount of time in the inverted state. Statistics throughout this paper are based on N ≳ 100 attempts. During readout of the output lead, the tunnel junction is set to 10 pA at 2 mV, i.e. below the excitation energy. For small pulse amplitudes, measured switching probabilities are close to zero. However, from~7 mV, which corresponds to the energy of a spin excitation on atom C from its S z = +2 to its S z = +1 state, increased values are found. Switching probability P H , for switches originating from the state where the input lead is in the "happy" configuration, reaches 80%. Note that switching probability P U from the "unhappy" configuration remains much lower, consistent with the expected behavior of the device. For even larger pulse voltages, P U increases while at the same time P H decreases. This can be explained in terms of secondary switches during a single pulse back towards the "happy" state. Hence, P H + P U ≤ 1. Figure 2b, c shows P H and P U as a function of pulse width and tip height, respectively. For the settings used in Fig. 2b, we find an approximate switching time τ = 25 ms. As I depends exponentially on tip-sample distance, both graphs show an equivalent range of number of electrons per pulse, IΔt ≈ [10 4 , 10 8 ]. Although both graphs behave similar for small IΔt, they diverge at higher values: when increasing pulse width, P H and P U are found to plateau, while increasing I eventually increases P U (thus reducing P H ). This suggests a path for switching from the "unhappy" configuration which is based on a multi-excitation process, presumably due to magnon excitations tunneling into the output lead (Supplementary Note 2).
Triggering by means of tip exchange field. In order to exclude the possibility of tunneling magnons, the second method to switch the output lead involves reversing the input lead via controlled exchange coupling with the tip 26 . In this experiment, the voltage is kept below the excitation threshold and the tip is held over an input atom at a certain target height for a certain duration. Figure 3a shows the switching probabilities P H and P U as a function of duration for a fixed target height of 10 pm (as compared to regulating at 1 mV, 3 pA on Cu 2 N). For this target height we find τ ≈ 5 s.
A more detailed investigation is shown in Fig. 3b, c, which shows P H (P U ) on the different atoms of the input lead as a function of target height. For sufficiently large tip separation, no switching is observed. Bringing the tip closer to the input lead induces switches of the output lead, suggesting that the tip field causes the predominant state of the input lead to switch from ðS C z ; S B z ; S A z Þ ¼ ðþ2; À2; þ2Þ to (−2, +2, −2). For target heights down to −100 pm, P H on atoms A and C increases, whereas P U does not increase significantly. Likewise, P H on atom B does not increase significantly beyond P U . Closer tip extensions are explored in Supplementary Note 3.
We emphasize that the essence of the switching mechanism is different in this second method compared to the first: here the input lead spends a significant amount of time in the fully inverted state, whereas in the first case, |ΔS z | = 1 excitations on one side of the barrier are the dominant cause for the reduction of the time averaged S A z .
Extended input lead and comparison with calculations. Having characterized the sensitivity of the detector to spin excitations on the input lead as described in Fig. 2, we now consider the effect of introducing these excitations at different distances. In Fig. 4a, b, we compare switching measurements for various tip locations on the input lead for n in = 3 and 5. Although the measurements on the 5-8-3 indicate a monotonous decrease of the switching probability as a function of distance to the output lead, both for switches from the "happy" and "unhappy" states, measurements on the 3-8-3 show a marked reduction in P H , and corresponding increase in P U , when the tip is located on atom B.   Fig. 3 Switching the input by tip exchange field. a Switching probabilities P H and P U as a function of duration at a target tip height of 10 pm, using a bias voltage of 1 mV. Arrows indicate data points that also appear in b and c. b P H for atoms A, B and C, for a duration of 2 s. Note how atom B is less sensitive to the tip field than atoms A and C. c Same as b but for P U . Data in all three subpanels is taken at 1.5 K, 1 T. The error bars show 1.5σ for a binomial distribution with μ at the recorded rate. Dashed lines are guides to the eye.
In order to gain insight into this behavior, we performed timedependent Schrödinger equation calculations simulating the dynamics of the input lead upon an excitation (Fig. 4c, d). In these calculations, we model only the input lead. The coupling to the output lead is modeled by an effective magnetic field on atom A (Supplementary Note 2). First, we initialize the system by finding the ground state of the Hamiltonian. Next, we perform a single spin excitation on one of the input atoms (i.e., we apply thê S þ orŜ À operator depending on the position in the antiferromagnetic input lead), after which we apply the time-dependent Schrödinger equation to the resulting state. Plotted are the values S A z ðαÞ after an excitation on atom α. Dissipation effects are not considered in these calculations. Figure 4c, d shows the results of calculations for the first 100 ps on a trimer and pentamer, respectively. As expected, S A z values never reach much lower than +1, so a full inversion of the input lead does not occur in these calculations. We estimate the lifetime of an excitation to be~10 ps (see Supplementary Note 2, not to be confused with the~1 μs lifetime of the inverted state, see Supplementary Note 4). Therefore, we took the averaged values of S A z ðαÞ over the first 20 ps and plotted these as open circled in Fig. 4a, b. As in the experimental data, this results in a deviation from S A z ¼ 2 that alternates for the trimer, whereas it decreases monotonously for the pentamer. These results suggest that the spin wave detector is able to register unitary spin dynamics.
Finally, in Fig. 4e, we show switching experiments on a 9-8-3 device. Here we find that it is possible to switch the output lead from as far away as 6.8 nm (19 Cu 2 N lattice sites). We find that as the current increases, the distance where P H ≈ 50%, the maximum value for this structure, also increases: from 7 lattice sites for z = 180 pm to at least 19 lattice sites for z = 30 pm. For this structure, the results are compared with a background measurement (V = 1 mV, z = 180 pm), which yields a minimum switching rate of~20%. We attribute this increased base switching probability to łonger lifetime of the input lead (in the order of 1 s), therefore spending extended periods of time in the inverted state, even in the absence of excitations.

Discussion
In summary, we have developed an atomic device that can be used to detect dynamic and nonlocal spin phenomena such as magnons. We have tested the device for its sensitivity to spin excitations, as well as a complete inversion of the input lead. We have shown that the device is sensitive to spin excitations originating up to 9 atoms away. In subsequent experiments, the input lead may be replaced by more exotic spin architectures. This method thereby provides a tool in studying dynamic spin processes on the atomic scale.

Methods
We used a UNISOKU USM-1300s 3 He STM system, operating at 1.5 K and B = 0.5-1 T in the plane of the sample, along the axis of the structures. The Cu 2 N/ Cu 3 Au(100) sample was prepared as described by Gobeil et al. 27 . The tip is prepared as in Loth et al. 8 . Fe atoms were picked up from the Cu 2 N by using bias pulses of 1 V at (regulation 100 pA, 20 mV, then move −300 pm) and dropped at −600 μV with the tip gradually nearing the surface until a change in current is observed. The Fe was subsequently maneuvered into place with a pulse of~1 V at (100 pA, 20 mV). Calculations were performed using QuTip 28,29 , a library for Python. See Supplementary Note 6 for a more detailed description of the data acquisition technique, and Supplementary Note 5 for possibilities on even faster data acquisition.

Data availability
All data presented in this paper is publicly available via digital object identifier (DOI) 10.5281/zenodo.3759448. Included in the open data folder are the raw data and the Python scripts to process the data, to reproduce Figs. 2, 3 and 4. Figure 1 does not include experimental data.