### Corresponding author

Sebastian Loth

Max Planck Institute for Solid State Research

### References

1.
Schmidt, R.; Lazo, C.; Kaiser, U.; Schwarz, A.; Heinze, S.; Wiesendanger, R.
Quantitative Measurement of the Magnetic Exchange Interaction across a Vacuum Gap
2.
Tao, K. ; Stepanyuk, V.S.; Hergert, W.; Rungger, L.; Sanvito, S.; Bruno, P.
Switching a single spin on metal surfaces by a STM tip: ab initio studies
3.
Loth, S.; Etzkorn, M.; Lutz, C.P.; Eigler, D.M.; Heinrich, A.J.
Measurement of fast electron spin relaxation times with atomic resolution

# Atomic exchange bias control of individual quantum magnets

## Authors

S. Yan, D.-J. Choi, J. A. J. Burgess, S. Rolf-Pissarczyk, and S. Loth

## Departments

Research Group "Dynamics of Nanoelectronic Systems"

Variable magnetic fields are crucial for modern data storage and spintronic applications but scaling magnetic fields to match the dimensions of individual nanomagnets is challenging. Exchange bias fields arising from the orbital overlap of magnetic atoms have been proposed as mechanism for local control of individual quantum magnets. We demonstrate that exchange coupling with a magnetic atom on the tip of a scanning tunneling microscope can be used to tune the spin state mixing of few-atom nanomagnets and thus yields complete control over nanomagnetism at atomic dimensions.

Miniaturizing magnetic elements to a point where their magnetization becomes quantized is a possible avenue to achieve quantum-limited spintronic devices. The ability to exert local control over such devices is important and can be achieved via short-ranged coupling mechanisms. The exchange interaction between magnetic atoms is localized to just a few angströms. Static exchange bias is used in thin-film devices for pinning of magnetic layers. Variable exchange interaction has been observed between the magnetic tip of an atomic force microscope and an antiferromagnetic surface [1] and the possibility of using this interaction for the control of atomic spins has been predicted [2].

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Fig. 1: Schematic of the local exchange bias interaction between a magnetic Scanning Tunneling Microscope (STM) tip and a quantum magnet consisting of three Fe atoms on a Cu2N/Cu(100) surface. Image is a 3D rendering of a constant current topograph. Red arrows indicate the spin orientation of the atoms on the surface and the STM tip.

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We used a low-temperature Scanning Tunneling Microscope (STM) to construct an individual nanomagnet and approach it with a magnetic STM tip (Fig. 1). We found that the magnetic interaction with the tip can be observed as variations in the nanomagnet’s spin relaxation time.

We focus on a small nanomagnet consisting of a linear chain of three Fe atoms assembled on a monatomically thin copper nitride, Cu2N, layer on Cu(100). This Fe trimer exhibits discrete spin states and magnetic contrast in spin-polarized imaging (Fig. 2(a)). We perform electronic pump probe spectroscopy [3] to measure the spin relaxation time of the Fe trimer (Fig. 2(b)). A sequence of alternating pump and probe voltage pulses with typical widths between 50 ns and 200 ns periodically promotes the Fe trimer into excited spin states and measures the subsequent relaxation towards the spin ground state by spin-polarized tunneling (Fig. 2(b) inset). To ensure minimal influence of thermal excitations and transverse magnetic fields the experiments are performed at 0.5 K temperature and in a vector magnetic field that was aligned to the easy magnetic axis of Fe atoms on the Cu2N surface with an accuracy of ±3 degrees.

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Fig. 2: Variation of the spin relaxation time of the Fe trimer with tip-sample distance. (a) Constant current topograph of the Fe trimer recorded with a spin polarized STM tip. Antiferromagnetic order of the Fe atoms is visible as height difference between center and side atoms. Image size, (3.2 × 2.2) nm2. (b) Pump probe spectra recorded on a side atom of the Fe trimer shown in a. Slow decay is observed with large tip-sample distance (purple curve, setpoint 10 mV, 1.25 nA) and fast decay with small tip-sample distance (blue curve, setpoint 10 mV, 2.5 nA). Inset depicts pump-probe pulse sequence with 35 mV pump pulse (red) and 5 mV probe pulse (orange). The pump probe sequence is repeated at > 100 kHz and the delay time, Dt, between pump and probe pulses is varied slowly. External magnetic field 2 T and temperature 0.5 K. (c) Schematic of the avoided level crossing of the two lowest spin states of the Fe trimer that leads to the observed variations in spin relaxation time. The two states |φ+> and |φ> evolve into the antiferromagnetic Néel-like states |+2 –2 +2> and |–2 +2 –2> in the presence of a magnetic field. External, Bext, and local, Bloc, magnetic fields can add (counteract) each other such that spin relaxation time is decreased (increased). (d) Local exchange bias field of the magnetic STM tip extracted from fitting a series of pump-probe spectra (see Fig. 3) on side (blue dots) and center atom (green dots). The solid blue is an exponential fit to the experimental measurements. [less]

The key observation of the experiment is that the Fe trimer’s spin relaxation time, T1, varies with the tip-sample distance. Spin relaxation becomes faster if the tip is approached to a side atom of the trimer and slower as the tip is approached to the center atom. By comparing spin relaxation times measured on side and center atoms we find that the tip’s influence becomes negligible at a tunnel junction conductance below 2.5 nS. At this tip position the spin relaxation time measured on side and center atoms converges to the same value 2.63 ms. We chose the point with tunnel conductance of 2.5 nS as z = 0. We quantified the distance-dependence of T1 by approaching the tip in small picometer-sized steps and monitoring the resulting changes in T1. With 1 T external magnetic field, T1 vanishes for an approach of 204 pm on either side atom. This short-range character strongly implicates exchange interaction as the source of the tip-induced variations in T1.

Other interaction mechanisms between tip and sample are possible but negligible here. Spin transfer torque arising from spin-polarized tunneling current can be excluded as no voltage is applied between pump and probe pulses. In addition, we could not observe changes in T1 when varying the voltage of either pump or probe pulses. Inelastic tunneling spectra recorded with a non-magnetic tip show that the spin excitations do not vary with tip-sample distance. Hence, tip-induced variations in the magnetic anisotropy that have been observed previously for magnetic molecules can also be excluded.

In order to deduce the strength of the tip-induced exchange bias we model the trimer and the influence of the tip-induced interaction by an effective spin Hamiltonian.

$\\&space;\hat{H}&=\sum_{i=A,B,C}{\hat{H}_i}&space;+J\left&space;(\vec{S}_A\vec{S}_B+\vec{S}_B\vec{S}_C&space;\right&space;)+J_{ts}\vec{S}_t\vec{S}_{A,B,C}\\&space;\hat{H}_i=-g_{i}\mu_B\vec{B_{ext}}\cdot\vec{S_i}+D_i\hat{S}_i^z^2+E_i\left&space;(&space;\hat{S}_i^x^2&space;-\hat{S}_i^y^2\right&space;)$

The model accounts for Zeeman energy from the external magnetic field (Bext), uniaxial and transverse magnetic anisotropy of the Fe atoms of the trimer (D(i) and E(i)), Heisenberg exchange interaction (J) between the atoms (A, B and C denote the Fe atoms in the trimer) and exchange interaction (Jts) between the tip spin and the coupled Fe atom in the trimer. The model parameters are adjusted such that the inelastic tunneling spectra and the spin relaxation time in the absence of the tip are reproduced. The model shows that only two spin states, |φ+> and |φ->, are at low energy with all other spin states being separated by an energy gap of ~7.5 meV. These two states dominate the observable spin relaxation in the microsecond range (Fig. 2(c)). Spin relaxation on the Cu2N/Cu(100) surface is dominated by Kondo-type electron scattering. It can be approximated as:

$(T_1)^{-1}=r_s\sum_{i}{\left&space;|&space;\left&space;\langle&space;\varphi_+\left&space;|&space;\vec{\sigma}\vec{S_i}&space;\right&space;|&space;\varphi_-&space;\right&space;\rangle&space;\right&space;|^2}\int{f(E)\cdot&space;(1-f(E+\Delta))dE}$

where σ is the vector spin operator of the scattering electron and Si is that of the trimer’s Fe atoms, f(E) is the Fermi function, and Δ is the energy difference between |φ+> and |φ>. rs sets the strength of the electron scattering from the substrate and it’s an empirical parameter in this model.

The two low-lying spin states feature an avoid-ed level crossing. In the absence of external perturbations they are equal superpositions of the |φ+> and |φ-> states (where ±2 denotes the magnetic quantum number of each Fe atom) resulting in fast spin relaxation. An external magnetic field removes the avoided level crossing and spin relaxation becomes slower. The key finding is that the exchange interaction with the magnetic tip acts just like a local magnetic field that is applied only to one atom of the trimer. This tip-induced exchange bias field adds to the external magnetic field if the tip is approached to the center atom. The spin system is pushed further away from the avoided level crossing and the nanomagnet stabilizes. By approaching either side atom, the tip-induced exchange bias counteracts the external magnetic field and the spin system approaches the avoided level crossing and the spin relaxation becomes faster.

By comparing the change in spin relaxation time with external magnetic field to the change with tip-induced exchange bias it is possible to deduce the absolute strength of the exchange bias field from the STM tip (Fig. 2(d)). Surprisingly, it can reach strengths of several tesla even under moderate tunneling conditions with tunneling conductance less than 1mS.

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Fig. 3: Spin state control using the local exchange bias field of the magnetic STM tip. Graphs show a series of pump probe spectra recorded on a side atom of the Fe trimer for different tip-sample distances. Negative pump probe signals for Δt > 0 indicate that the Fe trimer’s ground state is |+2 –2 +2> because the external magnetic field (blue lines and bottom sketch). At a tip movement of z = –204 pm the tip-induced exchange bias field exactly compensates the external field and spin-dependent signal vanishes (green curve and middle sketch). For z < –204 pm the pump probe signal becomes positive indicating a reversal of the trimer’s ground state (red curves and top sketch). External magnetic field Bext = 1 T, temperature 0.5 K. [less]

With the ability to counteract the external magnetic field it becomes possible to control the spin state mixing, i.e., the magnetic structure, of the Fe trimer. Figure 3 shows that the spin states of the Fe trimer can be tuned smoothly through the avoided level crossing. The tip-induced exchange bias field fully compensates the 1 T external field at the position z = –204 pm. At this point the two low-energy spin states are the symmetric and antisymmetric superposition states of |+2 –2 +2> and |–2 +2 –2>. In this point the spin polarization of the trimer is expected to vanish and indeed no pump-probe signal is detected (middle sketch, Fig. 3). For smaller tip-induced exchange bias fields (z > –204 pm) the trimer’s ground state carries most weight in the |+2 –2 +2> state leading to a negative pump-probe signal at Dt > 0 (bottom sketch, Fig. 3). For stronger exchange bias the ground state has most weight in |–2 +2 –2> and consequently features positive pump-probe signal at Δt > 0 (top sketch, Fig. 3).

In summary, this experiment demonstrates that exchange interaction with a magnetic STM tip can be used to fully control quantum spins by tuning of their spin state mixing. The strength of the exchange bias field from the magnetic STM tip is set by the tip-sample distance and can, in principle, be extended to other quantum systems exposed on the surface.