SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI:.38/NPHYS2299 Atom-by-atom engineering and magnetometry of tailored nanomagnets Wiebe_supplementary.pdf: The supplementary contains details of the experimental methods and a description of the Ising model (Supplementary Methods), a discussion of the zero magnetic field anomaly for threeatom chains (Supplementary Discussion), the legend of the Supplementary Movie, references (Supplementary Notes), and two Supplementary Figures S and S2 with legends (Adobe PDF; 3.8 MB). Supplementary Movie: This movie shows a sequence of magnetic images of several nanomagnets and illustrates the raw data for the acquisition of the magnetization curves (QuickTime; 4.9 MB). NATURE PHYSICS

2 Supplementary Information: Atom-by-atom engineering and magnetometry of tailored nanomagnets Alexander Ako Khajetoorians,, Jens Wiebe,, Bruno Chilian, Samir Lounis, 2, Stefan Blügel, 2 and Roland Wiesendanger Institute of Applied Physics, Hamburg University, Jungiusstrasse, D-2355 Hamburg, Germany 2 Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, D Jülich, Germany (Dated: February 22, 22)

3 Supplementary Methods The sample consists of a cleaned Cu() substrate covered with a random distribution of triangular Co islands and Fe atoms [, 2]. Topographs of the sample are taken in constant current mode at a current I stab with a voltage V stab applied to the sample. The tungsten STM tips were coated by several tens of monolayers of Cr [3, 4], in situ prepared by pulsing on and dipping into the Co islands. Spin-sensitivity was checked by monitoring the B-field dependent magnetization of the Co islands [, 2]. Magnetic images (di/ dv maps) are taken simultaneously to topographs via lock-in technique (AC voltage V mod, f = 4. khz added to the sample bias V stab ). Within the Ising model, the magnetization curve of the i-th atom in an N atom nanomagnet is calculated by: Mz(B) i s = M z {±} s N z {±} si ze E(s z,...,s N z )/k B T sat s z {±} s, () Nz {±} e E(s z,...,sn z )/k BT where ( ) N N E(s z,..., s N z ) = Bm i z J ij s i zs j z, (2) i= j=i+ m i z = m s i z = 3.5 µ B s i z and s i z = ± corresponding to the spin states up ( ) and down ( ). Supplementary Discussion: anti-ferromagnetic three-atom chains Fig. illustrates the magnetization curves for three different three-atom chains as the coupling is decreased from J NN 35 µev (a to c), over J NN µev (d to f), to J NN 8 µev (g to i). As can be seen, the magnetization curves outside the marked gray region are described reasonably well by the pair-kkr Ising model. However, as for the chains in the main manuscript, there is a range close to B = where the magnetization deviates strongly from the Ising model regardless of the exchange energy sets used. It is interesting to note that this region (gray) is nearly identical for all atoms in a given chain and is heavily dependent on J NN where the width of the region is stronger for larger coupling energies. Furthermore, the critical magnetic field, where this anomaly is broken for the three illustrated chains, scales nearly linearly with J NN (see width of gray shaded area). The role of the geometry on the low field anomaly for a given chain is exemplified in Fig. 2 where kinked chains are investigated. In Fig. 2 a to c, the chain is kinked but the exchange interaction is identical to the chain presented in Fig. d to f. As can be seen, the overall shape 2

4 of the curves as well as the width of the low field anomaly are identical to the case of the straight chain. This suggests that only the magnitude of the exchange interaction determines the low field anomaly. In Fig. 2 d to f another kinked chain is illustrated where the left pair is more weakly coupled (J NN µev) than the right pair (J NN 35 µev). Again, the low field anomaly for the atom in Fig. 2 d shows nearly identical width as compared to that of Fig. d and f which have identical coupling. Likewise the low field anomaly for the atom in Fig. 2 f, which has a different width than that of Fig. 2 d, shows nearly identical width as compared to that of Fig. a and c where the atoms have the same exchange coupling. Therefore, we conclude that the dominating parameter which determines the width of the low field anomaly is the strength of J NN while it is less sensitive to the exact shape of the chain. Supplementary Movie Legend The movie shows a sequence of magnetic images of several nanomagnets, and illustrates the raw data for the acquisition of the magnetization curves. Two individual Fe atoms, two pairs of Fe atoms, a three-atom, a four-atom, and a five-atom chain of Fe atoms adsorbed on the Cu() surface are visible. Acquisition of each individual magnetic image (I stab = 6 pa, V stab = mv, V mod = 5 mv) of the sequence took 2 minutes. Each image was recorded at the magnetic field value B indicated on the top left corner, which has been incrementally ramped from B =.5 T to B =.5 T, and back. Such magnetic images were used to extract the magnetization curves by averaging the signal in a small area on top of each Fe atom and on several substrate spots. 3

5 Supplementary Notes address: corresponding author address: address: [] Khajetoorians, A. A., Lounis, S., Chilian, B., Costa, A. T., Zhou, L., Mills, D. L., Wiebe, J., and Wiesendanger, R. Phys. Rev. Lett. 6(3), 3725 Jan (2). [2] Khajetoorians, A. A., Wiebe, J., Chilian, B., and Wiesendanger, R. Science 332(633), (2). [3] Wiebe, J., Wachowiak, A., Meier, F., Haude, D., Foster, T., Morgenstern, M., and Wiesendanger, R. Rev. Sci. Instrum. 75, (24). [4] Meier, F., Zhou, L., Wiebe, J., and Wiesendanger, R. Science 32, (28). 4

6 5.8 (a) (b) (c) di / dv (a.u.) (d) (e) (f) (h) 5.9 (g) (i) FIG. : (Supplementary Figure S) Three-atom chains with varying anti-ferromagnetic coupling. Magnetization curves (circles) measured on the atoms of three different antiferromagnetic chains with dnn =.887 nm corresponding to JNN 35 µev (a to c), dnn =.922 nm corresponding to JNN µev (d to f), and dnn =.2 nm corresponding to JNN 8 µev (g to i). The curves are coloured corresponding to the positions of the Fe atoms within each chain shown in the insets. Solid lines are calculated from the pair-kkr Ising model. The gray shaded area indicates the magnetic field range, where the experimental magnetization curves deviate qualitatively from the Ising model, which scales with JNN in width. 5

7 di / dv (a.u.) 5.9 (a) (b) (c) (d) (e) (f) 5.9 FIG. 2: (Supplementary Figure S2) Kinked anti-ferromagnetic three-atom chains. Magnetization curves (circles) measured on the atoms of two differently kinked antiferromagnetic chains with dnn =.922 nm corresponding to JNN µev (a to c), and d2 =.922 nm corresponding to JNN µev, d23 =.887 nm corresponding to JNN 35 µev (d to f). The curves are coloured corresponding to the positions of the Fe atoms within each chain shown in the insets. Solid lines are calculated from the pair-kkr Ising model. The gray shaded area indicates the magnetic field range, where the experimental magnetization curves deviate qualitatively from the Ising model. 6