Spin-Polarized Scanning Tunneling Microscopy with Quantitative

Phark and Sander Nano Convergence (2017) 4:8 DOI 10.1186/s40580-017-0102-5

REVIEW Open Access Spin‑polarized scanning tunneling microscopy with quantitative insights into magnetic probes Soo‑hyon Phark1,2* and Dirk Sander3

Abstract Spin-polarized scanning tunneling microscopy and spectroscopy (spin-STM/S) have been successfully applied to magnetic characterizations of individual nanostructures. Spin-STM/S is often performed in magnetic felds of up to some Tesla, which may strongly infuence the tip state. In spite of the pivotal role of the tip in spin-STM/S, the con‑ tribution of the tip to the diferential conductance dI/dV signal in an external feld has rarely been investigated in detail. In this review, an advanced analysis of spin-STM/S data measured on magnetic nanoislands, which relies on a quantitative magnetic characterization of tips, is discussed. Taking advantage of the uniaxial out-of-plane magnetic anisotropy of Co bilayer nanoisland on Cu(111), in-feld spin-STM on this system has enabled a quantitative determi‑ nation, and thereby, a categorization of the magnetic states of the tips. The resulting in-depth and conclusive analysis of magnetic characterization of the tip opens new venues for a clear-cut sub-nanometer scale spin ordering and spin- dependent electronic structure of the non-collinear magnetic state in bilayer high Fe nanoislands on Cu(111). Keywords: Spin-polarized scanning tunneling microscopy, Nanomagnetism, Magnetic anisotropy, Non-collinear magnetic order

1 Background to use spin-STM, undoubtedly, to perform a ‘magnetic 1.1 Nanoscopic magnetic tunnel junction in STM tunneling junction’ (MTJ) experiment on the single atom Spin-polarized scanning tunneling microscopy and spec- level. troscopy (spin-STM/S) is a magnetic imaging technique A spatially resolved measurement of the diferential with an ultimate lateral resolution on the atomic scale conductance dI/dV of the tunnel current provides a spa- [1–4], which is suitable for probing magnetism in fer- tial map of electronic information relevant to the local romagnetic nanostructures [5–7] and in antiferromag- magnetic order. Figure 1b, c are schematics describing nets [8–10]. Figure 1a schematically describes electron the spin-dependent tunneling in (b) parallel (P) and (c) tunneling in spin-STM. Electrons carry spin as well as antiparallel (AP) confgurations between MT and MS. Te charge, thus the electron tunneling is spin dependent electronic density of states (DOS) of ferromagnets splits [11–13]. When magnetically ordered materials are used up into majority (n↑)- and minority (n↓)-spin DOSs due for both tip and sample, the tunneling current depends to exchange interaction between electrons [14], giving on the magnetic order parameters of both tip and sample rise to the spin polarization P(E) at a given energy E. (here the local magnetization, M and M , respectively). T S n↑(E) n↓(E) In addition, spin-STM under an external feld μ0H allows P(E) − (1) = n↑(E) n↓(E) to control the orientations of MT and MS. Tis is the basis + Assuming (a) identical DOSs for both sample and tip and (b) conservation of spin orientation during the tun- *Correspondence: [email protected] neling process, the schematic implies that the tunneling 1 Center for Quantum Nanoscience, Institute for Basic Science, Seoul 03760, Republic of Korea current will depend on the magnetization confgurations Full list of author information is available at the end of the article (P or AP), as depicted by the thickness of the curved black

© Korea Nano Technology Research Society 2017. This article is distributed under the terms of the Creative Commons Attribu‑ tion 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Phark and Sander Nano Convergence (2017) 4:8 Page 2 of 17

a b MT MS c MT MS tip P AP

Vb g

T E

IT()x,y

sample

S Fig. 1 Tunneling in spin-polarized scanning tunneling microscopy. a A schematic illustration of the tunneling current between a magnetic sample

and a magnetic tip in scanning tunneling microscopy (STM) in an external magnetic feld μ0H. b, c A simplifed picture of spin-polarized tunneling within a hypothetical spin-split density of states model in parallel (P) and antiparallel (AP) magnetization orientations. The spin orientation of the tunneling electrons is assumed to be conserved during tunneling, i.e., spin-up electrons always tunnel into spin-up states and spin-down electrons always tunnel into spin-down states. Arrows (bottom) indicate the DOS of spin-up and spin-down electrons. The spin direction is antiparallel to the

magnetic moment [64]. MT and MS (top arrows) denote the magnetization orientation of tip and sample, respectively. b P and c AP alignment of tip and sample magnetization (Reprinted from [4] with permission from American Physical Society (Copyright 2014))

arrows. It is plausible that one can derive the contribu- Te authors also introduced the ‘magnetization density tion arising from the spin-polarization P(E) explicitly in of states’ m(E) to account for the decisive role of the rela- the mathematical formula of the tunneling phenomena. tive orientation between MT and MS in the tunneling of Tereby, it is instructive to write the tunneling current at spin-STM, the tip position RT as m(E) n↑ n↓ eM nP(E)eM, (5) I(RT V θ) I0(RT V ) IP(RT V θ), (2) = − ˆ = ˆ ; ; = ; + ; ; ↑ ↓ where I0 and IP denote the non-spin-polarized and spin- where n (n ) is the spin-up (-down) DOS at energy E, θ( θ θ ) e polarized currents, respectively, and ≡ T− S is the and ˆM is the unit vector of the magnetization. Assum- angle between MT and MS, as depicted in Fig. 1a. ing spin-conserved tunneling and constant tip DOS [17], substitution of the spinors (Eq. 5) leads to 1.2 Spin‑dependent diferential conductance dI/dV in spin‑STS 8π 3C2 3e I(RT, V , θ) dε[f (ε εF ) f (ε eV εF )] = κ2m2 − − + − Wortmann et al. developed a theoretical description of 2 2 the tunneling current in spin-STM [15]. According to ε ε S R S R δ( F ) nT↑ ψµ ( T) nT↓ ψµ ( T) , × − × ↑ + ↓ Bardeen’s approach [16], the tunneling current is written µ as (6)

2πe S T I(RT, V ) f ε εF f ε εF θ(R , V ) µ µ where T denotes the angle between MT and MS. = µ,v − − − Te diferential conductance dI/dV measurement in εT εS R 2 (3) δ ν µ eV Mν,µ( T) , the spin-STS provides a quantity which is directly cor- × − − related to the projection of the spin-DOS of the sample f (ε) εT/S ε where RT, V, , µ/v, and F are the tip position, the onto that of the tip at the tip position RT. Recalling the bias voltage, the Fermi function, the tip/sample energy description of Eq. 2, and using a set of algebraic processes states, and the Fermi energy, respectively. To calcu- [15], the Eq. 6 gives T S Mν,µ(RT) Ψ UT Ψ , late the matrix elements =� ν | µ� the dI (RT, V ) nTnS(RT, εF eV ) mT mS(RT, εF eV ), authors introduced the two component spinors for the d T S V ∝ + + · + tip and sample wave functions Ψν and Ψμ, respectively, (7)

T S T ψ T 0 S ψµ which exhibits a non-magnetic (1st term; dI/dV| Ψ ν or Ψ T , Ψ 0) and ν 0↑ ν ψ µ ψS↑ (4) = = ν = µ magnetic (2nd term; dI/dV|mag) term explicitly. Note, that ↓ ↓ n n P P eT eS the second (magnetic) term results in T S T S ˆM · ˆM , Phark and Sander Nano Convergence (2017) 4:8 Page 3 of 17

which is proportional to the projection of MS to MT at 1st 2nd the tip position. a b Co Fe 1.3 Experimental approach Co Fe Co Te experiments were performed in situ in an ultra- Fe −11 high vacuum (UHV) chamber (base pressure <1 × 10 Cu mbar) equipped with a liquid He cooled scanning tunneling microscope operating at 10–30 K and a super- cd Cu conducting magnet for feld of up to 7 T normal to the Co(0.5 ML) 1 Co(0.24 ML) & Fe(0.28 ML) sample surface [4, 18]. Co 3 5 Fe|Co 4 1.3.1 Co and Fe nanostructures on Cu(111) 4A 4A 2 Fe Cu Here we focus on biatomic-layer-high (BLH) Co, Fe, Fe nm 10 nm

and Fe-decorated Co (Fe|Co) islands on Cu(111) [7, 0.6

18–20]. Figure 2a schematically illustrates the sam- Cu ple preparation procedure. It results in 3 types of BLH islands schematically depicted in Fig. 2b: First, a sub- e 10 -0.39 V -0.31 V monolayer (ML)-equivalent Co deposition at room 1: Cu temperature (RT) forms Co islands as shown in Fig. 2c. 2: Fe Constant current STM (CC-STM) image of the sam- -0.24 V 8 3: Co ple surface formed by 0.5 ML-equivalent Co reveals an )

S 4: Fe island height of ~4 Å, indicative of BLH Co. Te islands n ( -0.03 V 5: Fe have a lateral dimension ranging from 5 to 30 nm. Sec- V

d 4

/ ond, the sequential deposition of frst sub-MLs of Co I (0.24 ML) and then Fe (0.28 ML) at RT formed two d types of islands (Fig. 2d): (1) pure BLH Fe island; (2) 0 BLH Fe|Co island, where Co forms the core and Fe sur- -0.4 V rounds the Co perimeter. We performed spin-polarized STM and STS on individual islands for all three types -0.8 -0.6 -0.4 -0.2 0.00.2 0.4 of islands. bias voltage (V) Fig. 2 Preparation of biatomic-layer-high Co and Fe nanoislands 1.3.2 Spectroscopic identifcation of element‑specifc on Cu(111). a An illustration showing the sample preparation. A electronic structures of nanoislands submonolayer (sub-ML) of Co was deposited frst on the Cu(111) substrate. Then a sub-ML of Fe was deposited subsequently. b CC- We discriminate diferent surface regions (Co, Fe, and STM image of the sample surface after Co deposition of an amount equivalent to 0.5 ML. (50 50 nm2; V 0.1 V; I 2 nA). c STM Cu) in the STM images (Fig. 2c and d) by diferences × b = set = in apparent heights. Tose regions are also identifed image of the sample surface after 0.24 ML Co deposition followed by subsequent 0.28 ML Fe deposition. (50 50 nm2; V –0.3 V; I 3 spectroscopically by local STS measurements. Fig- × b = set = nA). d A cartoon showing the lateral structures of 3 types of the ure 2e shows fve STS spectra measured at the posi- nanoislands obtained by the sample preparation process illustrated tions indicated by the numbers 1–5 in Fig. 2d, where in a. e, Diferential conductance dI/dV curves measured by scan‑ the same color code is used. Spectra 1 and 3 exhibit ning tunneling spectroscopy (STS) at the positions marked 1–5 in c. the onsets of the surface states of Cu(111) [21] and the Position mark in c and corresponding dI/dV curve in d of each STS measurement share the same color code 3dz2-minority state of Co [22] at the respective charac- teristic bias voltages Vb = −0.4 and −0.3 V. STS identifes two electronically diferent Fe regions. BLH Fe on Cu(111) has two structurally and electronically dif- 1.3.3 Spin‑polarized STM/S and dI/dV mapping ferent phases [23, 24]. Spectrum 4 shows a dominant For non-magnetic STM/S measurements, we used elec- peak at −0.39 V and a small peak at −0.03 V. Tis is the trochemically etched W tips. For spin-STM/S, we used signature of the electronic structure of BLH Fe in fcc- either Fe-coated W tips [19] or Cr/Co-coated W tips stacking [24]. Spectrum 5 shows a peak at −0.22 V, and [5, 7, 25]. Details of the sample and tip preparations are it is almost indistinguishable from the spectrum meas- described in Refs. [7] and [19]. STS spectra were measured at position 2 in the pure Fe island. Tese spectra ured by employing a lock-in technique with a modula- indicate BLH Fe in bridge-site-stacking of topmost Fe tion Vb at a frequency v = 4 kHz and a root-mean-square atoms [23, 24]. amplitude of 20 mV to detect the tunnel current I(V) and Phark and Sander Nano Convergence (2017) 4:8 Page 4 of 17

the diferential conductance dI/dV simultaneously. In 0.6nm order to obtain the switching feld Hsw of an individual a b island, the diferential conductance magnetic hysteresis Cu W loop dI/dV(H) was measured at the center of the Co core 0 0H Co of the island with an external feld μ0H sweep up to 3 T. 2 x Fe Te H of the island was extracted from the sharp drop sw x 1 of the signal in the dI/dV(H) hysteresis loop. For a simul- Fe taneous measurement of CC-STM and spin-polarized dI/ Co dV images, we utilized the spectroscopic mapping technique under an external magnetic feld. Te feld value and the feld history is chosen such that at the same 0 c 0.05 feld value AP and P magnetization confgurations are 1 0.1 0.2

) t sweep positive 0.3

u realized. After taking STS spectrum at each location of ) 0.5

a o field values

s 1 a scan for varying the bias voltage, we extract the dI/dV n

e i 1.5

( k 1.6

signal for every pixel at a given energy. Tus, we obtain c

H 2.5

l energy-resolved dI/dV maps of an island for both AP and ( 1.5 1 V -0.87 V

d 0.5

P magnetization confgurations. To obtain a spatial reso- /

I 0.2 lution on the atomic scale (<2 Å), we chose a pixel num- d 0.1 2 0 ber larger than 150 × 150 for a 25 × 25 nm image size. Tis corresponds to a measurement time of 12 h order for a spectroscopic map. -1.0 -0.8 -0.6 -0.4 -0.2 0.00.2 0.4 bias voltage (V) 2 Field dependence of diferential conductance d 3.0 in spin‑stm 2.9

2.1 Spin‑STM of Co nanoislands on Cu(111) )

o 2.8 Figure 3a shows a STM image of typical BLH Fe|Co islands V=b

- -0.87 V on Cu(111). Te Co core regions of the islands are enclosed k 2.7 dI/dV c ~ 2m m o T S

l 0SH W 0SH W

by dotted lines and labeled by ‘1’ and ‘2’, [19]. Te crosses ( 2.6 mark the location of the dI/dV measurements. Spin-STM V

d MTMS

/ I 2.5 measurements were carried out using Fe-coated W tips in d an external magnetic feld μ0H, as schematically illustrated 2.4 in Fig. 3b, at a sample temperature of 10 K. -3 -2 -1 0123 Figure 3c shows the STS spectra measured at the center Field (T) of Co core 1, as marked by the red cross in Fig. 3a, under Fig. 3 Magnetic hysteresis of dI/dV in spin-polarized STM/S. a STM varying μ0H along the surface normal. Te STS spectra image of two triangular Co cores of Fe-decorated Co islands on show at all feld values the sharp 3dz2-related electronic which the magnetic-feld-dependent dI/dV were measured. The inset shows the apparent STM height profle along the white solid line. state of Co near Vb 0.3 V [22], as indicated by the = − (V 0.2 V; I 1 nA). b A schematic of spin-STM measurement black vertical arrow. Shape and amplitude of the spectra b = − set = on a bilayer Co island in an external magnetic feld μ H. c A set of dI/ change with magnetic feld. We identify a bias voltage 0 dV curves measured under a varying μ0Hext at the position “1” marked Vb 0.87 V, which gives a clear feld-dependent change in a. (V 0.5 V; I 1 nA). d Magnetic hysteresis extracted from = − stab = stab = of the dI/dV signal. Figure 3d shows the dI/dV hysteresis the feld dependence of dI/dV values at V 0.85 V (c) (Reprinted b = − from [19] with permission from American Institute of Physics (Copy‑ loop extracted from the dI/dV values at Vb = −0.87 V. Te hysteresis loop consists of butterfy-shaped curves, right 2013)) which are symmetric about the vertical axis [25, 26]. Te sudden drop of the signal at ±1.6 T indicates the switching of the magnetization direction of the Co core [6]. A 2.2 Probing methods of spin‑STM gradual change of the dI/dV signal is observed in the feld 2.2.1 Spin‑polarized tips range below the switching feld Hsw, implying that the Spin-polarized tips are an important ingredient for spin- out-of-plane component of the tip magnetization varies STM. Several experimental schemes for obtaining spin- with the external feld [25]. polarized tips have been proposed, which were already Phark and Sander Nano Convergence (2017) 4:8 Page 5 of 17

realized in planar tunnel junctions: (1) magnetic mate- W tip at a temperature above 2200 °C under UHV con- rials [13, 27–29], (2) optically pumped GaAs [30], and ditions to remove contaminants and W-oxides, and (3) superconducting materials in magnetic felds [11, to partially crystallize the tip apex. (3) deposition of 12, 31, 32] have been used in spin-dependent transport magnetic materials, such as Fe (40 AL-equivalent), Cr measurements. (20–100 AL-equivalent), or Co (40 AL-equivalent) followed by Cr (40 AL-equivalent) onto W tip apices for 2.2.2 Modulation of tip magnetization method Fe-W, Cr-W, or Cr/Co-W tips, respectively. Tis deposi- A mode of spin-STM operation, where a tiny coil is used tion is followed by post-annealing at a mild temperature for periodically switching the tip magnetization back and around 400 °C to recrystallize each magnetic coating forth, was introduced by Wulfhekel et al. [33]. If the mod- for a stable structural phase at the tip apex. (4) in situ ulation frequency exceeds the cutof frequency of the microscopic preparation by application of voltage feedback loop, the measured signal becomes proportional pulses between tip and sample with a duration of typi- to the local magnetization of the sample. Tis method cally a few ms to shape the tip apex. Just after each volt- can efectively separate topographic and electronic from age pulse, the tip was tested by STS measurement on a magnetic contrast efects for a given sample bias. How- surface with well-known spectroscopic features, such ever, this approach appears to be highly demanding and as the surface states of Cu(111) and bilayer Co island. time consuming compared to the simple measure of the Te proper dI/dV signal indicates that the tip is usable STM signal using a spin-polarized tip. Another limita- in spin-STM measurements. tion of this method is that ferromagnetic tips have to be used, which is not free from the efect of its stray feld on 2.3.2 Cr‑bulk tips the measured magnetic contrast. Despite, recently near- Te tip was made of polycrystalline Cr rods with a nearly 2 atomic resolution has been achieved on a reconstructed square cross section of 0.7 × 0.7 mm obtained by cut- Mn flm epitaxially grown on a Fe(001) substrate using ting a 99.99% Cr foil (from Super Conductor Materials). the modulated tip magnetization mode [34]. Te Cr rod was electrochemically etched in 1.5 M NaOH solution, following the procedure reported in Ref. [38] 2.2.3 Tunneling anisotropic magnetoresistance (TAMR) and then it was directly transferred into the STM. Te efect only in situ preparation step was the application of volt- Tere are some reports which claim to observe spin- age pulses on the Cu(111) surface to shape the apex [26]. contrast for tips with no spin-polarization [35–37]. In principle the tunnel current—even from a non-spin- 2.3.3 Characterization of tips by feld emission microscopy polarized tip—depends on the magnetization direction (FEM) of the sample and a magnetic contrast is feasible. Tis In the feld emission microscopy (FEM), the electrons are tunneling anisotropic magnetoresistance (TAMR) has extracted from the metal tip to the vacuum [44], thus, been reported for W-tips. Te signifcance of TAMR for their spin polarization is proportional to that of the sur- spin-STM is difcult to judge, as material exchange form face at the metal tip. Nagai et al. investigated the atomic the magnetic sample onto the tip cannot be excluded structures and spin polarizations at the apex of Fe/W and exclusively. Cr/W tips used in spin-STM by means of FEM and feld ion microscopy (FIM) [45]. FIM has been used to inves- 2.3 Tips made of magnetic materials tigate atomic structures at the apex of metal tips [46]. All results presented in this review were obtained using Tus, FEM combined with FIM can provide information tips of magnetic materials. Common ways of prepar- of spin polarization of a tip correlated to its atomic struc- ing tips of magnetic materials are either coating W-tips ture. Te FIM of the Fe/W tip showed that the deposited with magnetic materials or direct electrochemical etch- Fe layers form a single crystalline structure over the apex, ing of bulk magnetic materials [38, 39]. Using a bulk except for the frst few layers. Te spin polarization at the antiferromagnetic material such as Cr [25, 26] or MnNi surface is as high as 41.2%, which is attributed to the sin- diminishes the magnetic stray feld emanating from the gle crystalline structure of Fe. On the other hand, a FIM tip [40–43]. image of the Cr/W tip showed that the Cr layer was not well-ordered crystalline, although some hints of crystal- 2.3.1 W tips coated by magnetic materials line order were observed because of the Cr islands. Con- A few sequential steps are applied to obtain Fe [19, sequently, the spin polarization is as low as 10.3%. Tese 20], Cr [25], Cr/Co [5, 7, 25] -coated W tips: (1) ex situ results may allow one to prepare and characterize the preparation of W tips through electrochemical etching structure of the magnetic tips and to quantify their spin in 1.5 M NaOH solution. (2) fash heating of the etched polarization for use in spin-STM. Phark and Sander Nano Convergence (2017) 4:8 Page 6 of 17

7.5 Cr-W M a f T W d BLH Co Cr on Cu(111) 7.0 0H H

T S Co 6.5 8 Cu Cr-W ) 7 b MT S W g

( 6 Cr

V 5 T S H

/ e out-of-plane I 4 d magnetic anisotropy 3 M 25 co c Cr/Co-W H SW M W h T 20 Co Cr 15 T S H H 10 -4 -3 -2 -1 01234 Field (T) Fig. 4 Magnetic response of tips in spin-STM. a–c dI/dV magnetic hysteresis loops measured on bilayer Co islands, with 3 diferent tips as denoted at the top-left corner of each fgure. The black arrows show the feld sweep directions for data acquisition. The red and green arrows represent the magnetization directions of tip and sample, respectively, at feld values for dI/dV signal saturation. For the loop in a, a fxed tip magnetization direc‑ tion is expected, however, its direction cannot be decided and the two possibilities are shown. d, e Schematics for local magnetic moments (d) and magnetization hysteretic response (e) of a bilayer Co island on Cu(111). f–h Field response of the tip magnetization extracted from the dI/dV hysteresis loops shown in a–c, respectively, in regard to the magnetic response of the Co island described in e (Reprinted from [25] with permission from American Institute of Physics (Copyright 2009))

2.4 Magnetic responses of tips to the external feld does not change in response to the external feld, as Figure 4a–c show magnetic hysteresis loops of the dI/ sketched in Fig. 4f. On the other hand, the symmetric dV signal measured at the center of bilayer Co islands hysteresis curves in Fig. 4b and c indicate that here the on Cu(111) using (a and b) Cr-W and (c) Cr/Co-W tips magnetization direction of the tip apex has changed in [25]. A frst inspection of the data reveals a striking unex- response to the external feld. Te magnetic response in pected result that the same macroscopic preparation Fig. 4g indicates a gradual increase with external feld procedure of tips gives rise to vastly diferent hysteresis of the out-of-plane component of the tip magnetization curves (compare Fig. 4a, b). To appreciate the shape of MT,⏊ along the feld direction, starting from 0 at zero the hysteresis curves in Fig. 4a–c, it is important to real- feld, and reaching saturation before the BLH Co core ize that the feld-driven change of the dI/dV signal is switches. A non-hysteretic feld dependence of dI/dV(H) ascribed to a corresponding change of the relative orien- results for H < Hsw. Figure 4h represents a ferromagnetic tation between the MT and MS [1]. state of the tip, where a switching of tip and sample at dif- Te observed hysteresis curves are either (a) asymmet- ferent feld magnitudes is observed. Te results presented ric or (b and c) symmetric about the vertical dI/dV axis. in Fig. 4 imply a complex magnetic behavior of the tips, Figure 4d, e are schematic illustrations of the local mag- which even varies under the same macroscopic prepara- netization confgurations and of the magnetic response tion. Tis indicates that, in addition to the macroscopic of a bilayer Co island to the external feld, respectively. preparation, also the in situ microscopic tip preparation Due to the uniaxial out-of-plane magnetic anisotropy, the by voltage pulses is a further decisive aspect which deter- Co island exhibits only a bistable single domain magneti- mines the magnetic contrast in spin-STM. zation state. Te Wortmann formula (Eq. 7) consequently Note that only the tips characterized by curves in points at the response of the tip to the applied feld, Fig. 4a, c give rise to a magnetic contrast for an out-of- as schematically illustrated in Fig. 4f–h, respectively. plane magnetized sample at zero feld. Tips represented Accordingly, the shape of the curve in Fig. 4a is ascribed by the curve in Fig. 4b require an out-of-plane feld to to a fxed magnetization direction of the tip apex, which provide magnetic contrast for out-of-plane magnetized Phark and Sander Nano Convergence (2017) 4:8 Page 7 of 17

samples. Terefore, the results of Fig. 4 indicate that the magnetic contrast in spin-STM changes diferently for a a b change of magnetic confguration of the tip. B W It has been tacitly assumed that a high signal of the dI/ A Cr(40ML)/ 0H dV in spin-STM corresponds to a P confguration, while Co(40ML) a low signal corresponds to an AP confguration [47– 49]. However, the results presented in Fig. 4 show that Co only in connection with a feld sweep, a reliable deduc- tion of the magnetic confgurations from the dI/dV signal is warranted. A closer inspection of Fig. 4 reveals c d V = -0.58 V that the value of the dI/dV and its variation upon a change of the magnetic confguration varies from curve to curve, and it also difers for the same macroscopic MS MT preparation. Te considerable diference of the magnetically induced signal ΔdI/dV (refer Fig. 3d; ~0.6 nS MS MT for Fig. 4a, ~3 nS for Fig. 4b) also refects that a specifc magnetic behavior is not necessarily linked to a -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 certain macroscopic tip preparation. All the observa- Magnetic field (T) tions in Fig. 4 indicate that neither the material at the Fig. 5 dI/dV hysteresis loops of Co islands measured with a ferro‑ magnetic tip. a CC-STM image of Co islands on Cu(111) (V 0.1 V, tip apex, nor its thickness, nor its spectroscopic features b = − I 1 nA). b Schematic illustration for the spin-STM measurements are parameters which are sufcient to determine the set = shown in c and d. Note the tip material confguration. c, dI/dV magnetic properties of the tip, but only feld-dependent hysteresis loops at the center of the Co islands A and B marked by the measurements do so. red and black dashed circles, respectively, in a. The red (blue) color is for the measurements on the island A and corresponds to forward (back- 3 Magnetic characterization of tips in spin‑stm ward) sweep of the magnetic feld. The black dashed line presents To understand the tip contribution to the a dI/dV(H) a dI/dV hysteresis loop of the island B in a. d, Minor hysteresis loop taken at the center of island A, with the sample magnetization MS signal requires a plausible physical description of MT. pointing down as indicated (Reprinted from [4] with permission from We introduced in Sect. 2.4 various types of magnetic American Physical Society (Copyright 2014)) response of MT to the applied feld. However, it is still not sufcient due to the following complications: (1) Te non-hysteretic feld response illustrated in Fig. 4g can be performed with a Cr/Co-coated W tip, as schematically caused by either a feld-driven continuous rotation of MT, described in Fig. 5b. Diferential conductance spectra which is originally in-plane oriented at zero-feld, or by a were measured at the center of two Co islands, marked superparamagnetic (SPM) response of MT. In both cases by the dashed circles (red and black) in Fig. 5a. A pro- the out-of-plane component of the tip magnetization nounced magnetic feld dependence of the dI/dV signal MT,⏊ increases with feld, and a non-hysteretic and sat- is observed [5], in the dI/dV hysteresis loops. Note the urated feld dependence of dI/dV(H) results. (2) Te tip sharp signal drop at μ0H 0.5 T is observed on both can also have an out-of-plane magnetic anisotropy with = ± islands. Te steep jumps at μ0H 1.3 and 0.8 T dif- a large magnetic moment and exhibits a ferromagnetic = ± ± fers for red and black island. Te switching feld Hsw of response to the applied feld, as illustrated in Fig. 4h. Tis the magnetization reversal of the BLH Co islands on reasoning can be applied to all cases shown in Fig. 4. Tis Cu(111) strongly depends on the size of the islands [6, implies that the sharp change in all three dI/dV(H) curves 47]. On the other hand, the Hsw of the tip would be the could alternatively stem from the switching of the bista- same provided the dI/dV measurements are performed ble along the applied feld direction instead of that MT with the tip apex. Tus, the sharp signal drop at μ0H of . In this section, we introduce some experimental MCo 0.5 T must be ascribed to the reversal of MT, and approaches of resolving the abovementioned open issue = ± the steep increase at μ0H = ±1.3 and ±0.8 T is ascribed and, thus, advancing spin-STM to be a tool for the quan- to the reversal of the magnetization of the larger (black) titative measurement of nanomagnetism in samples by and the smaller (red) Co islands, respectively. Te minor specifc control of the external feld. hysteresis loop in Fig. 5d, obtained under a feld sweep between 1.2 and 1.2 T, where M keeps its direc- 3.1 Ferromagnetic tip − + S tion pointing down, corroborates the discussion on the Figure 5a is a CC-STM image of bilayer Co islands response of MT to the external feld. Here, a ferromag- on Cu(111) [50, 51]. Spin-STM of the Co islands was netic tip with a switching feld of ±0.5 T is observed. Phark and Sander Nano Convergence (2017) 4:8 Page 8 of 17

3.2 Superparamagnetic tips Magnetism on a nanometer scale strongly depends on 1.0 a the measurement temperature due to the impact of thermal fuctuations. Tis is described by the so called 0.5 1 ‘superparamagnetic criterion’ 25kBT ≥ KaV, where kBT and KaV represent the thermal energy and the magnetic 0.0

) anisotropy energy, respectively [52]. If the tip response MS MT 10 K, 661±31

d B shown in Fig. 4g is caused by the feld-driven rotation of e -0.5

z 20 K, 663±26 B

i the MT from in-plane to out-of-plane, the magnetic ani- l a 30 K, 641±56 -1.0 B sotropy energy should be large enough to maintain the m

r given magnetic state against thermal fuctuations. On o

n the other hand, the feld dependence of the dI/dV signal ( 1.0 b

V will depend strongly on the measurement temperature in d

I 0.5 case of a tip in the superparamagnetic state. d 2 To address this ambiguity and to elucidate the physical 0.0 origin of the tip response shown in the butterfy-shaped 10 K, 635±31 dI/dV(H) in Fig. 4b, we measured dI/dV(H) hysteresis -0.5 B curves at diferent temperature, where MCo retains a 20 K, 676±45 B 30 K, 650±40 fxed orientation (here pointing down). Figure 6a, b pre- -1.0 B sent the feld dependence of dI/dV data measured at the center of the Co cores of the islands 1 and 2 shown in -2 -1 012 Fig. 3, respectively. We used a Fe-W tip at three temper- Field (T) atures, 10 K (black), 20 K (red), and 30 K (green). Note that the slope of the dI/dV signal at 0 T gets smaller with ) 1.0 c increasing temperature. At a fxed orientation of MCo, we d e 1 (10 K)

z ascribe the observed change of the dI/dV(H) signal to the i l 0.5 1 (20 K) m=tip 657±9 B response of the tip to both feld and temperature. Each a 1 (30 K)

m data set of the same color code shows a saturation with r 0.0 2 (10 K) o 0.5 n 2 (20 K) increasing feld, but the saturation feld increases with ( 2 (30 K) 0.0 increasing temperature. Tis suggests a superparamag- V -0.5

/ -0.5 netic response of the tip. I

d To support and quantify this assertion, we analyze the -1.0 -0.020.000.02 temperature dependences of the dI/dV signal in Fig. 6a and b within the framework of superparamagnetism [52] -0.2 -0.10.0 0.1 0.2 by ftting each set of dI/dV data to a Langevin function 0(H-Hoff) /T(T/K) Fig. 6 Superparamagnetic tip. a, b Magnetic-feld-dependent dI/ dI dI m µ (H H ) dV plots in a and b extracted from the hysteresis loops of Fig. 2c, d ( ) tip 0 oﬀ H coth − respectively. The dI/dV curves at each temperature are normalized dV = dV sat kBT (8) by fts using Eq. 8, as shown by the solid curves. The legend gives the kBT dI . measurement temperature and the total magnetic moment in μB, as −mtipµ0(H H ) − dV extracted from the ft of the data with the Eq. 8. c, Plots of all dI/dV − oﬀ C values as a function of reduced magnetic feld (μ0H/T). The inset is a close-up of the plots around μ (H–H )/T 0. The gray curve shows We introduce the saturation of the diferential con- 0 of = the Langevin ft in one curve for all data (Reprinted from [19] with ductance (dI/dV) and the diferential conductance of- sat permission from American Institute of Physics (Copyright 2013)) set (dI/dV)C, which determines the average of the two dI/dV saturation values for the P and AP magnetization confgurations. We also introduce the ofset feld Hof, to consider the shift of the curves by 60 mT to the positive Te convincing description of the experimental data by feld direction, which tentatively ascribed to the stray the Langevin approach is further corroborated by plot- feld induced by MCo. Te dI/dV data are normalized ting all data points as a function of μ0H/T. Te conden- sation of all data on a single curve, as shown in Fig. 6c, to a saturation value of ±1. Te solid curves through the data points of Fig. 6a, b are fts using Eq. 8, result- is the hallmark of a superparamagnetic response [52]. In a frst approximation, we ascribe the extracted magnetic ing in a magnetic moment mtip = 660 ± 30 μB for all measurements. moment to a macrospin, where all individual spins at the Phark and Sander Nano Convergence (2017) 4:8 Page 9 of 17

tip apex respond in unison to the external feld. Assum- 9 ing a magnetic moment of 2.2–3 μ per single Fe atom 0.4nm B a b 8

in Fe nanoclusters [53] leads us to speculate that a nano- ) MT MCo

0 S 7

apex of approximately 220–300 Fe atoms determines the ( 6 x V Co sweep

magnetic response of this tip. d / -0.75V sweep

I We use the ‘superparamagnetic criterion’ [52], to esti- Fe|Co d 5 mate the upper limit for the magnetic anisotropy as Fe 4 Cu Ka 0.07–0.1 meV/atom for 300–220 Fe atoms, respec- 3 ≤ -3 -2 -1 0123 tively. Tus, even a considerably increased magnetic ani- Field (T) sotropy per Fe atom of the nano-apex as compared to 9 bulk Fe (~0.0035 meV/atom) [54] would still fulfll the c 1.0 ) d

8 d H superparamagnetic criterion. In spite of the convincing = e

o MT MCo 0.5 i

)

7 a description of our data with a macrospin model, we can- S 55±1 n MT

(

0.0 o not exclude a more complicated arrangement of the mag- V 6

(

d netic structure at the nano-apex, which could also result 5 S -0.5 easy dI/dV M in the same magnetic moment of 660 μB. We analyzed dI/dV / axis 4 M M/M seven Fe-coated W tips, which were prepared under Sat -1.0 3 Stoner-Wohlfarth the same conditions as described above. In all cases we -1.5 -1.0 -0.5 0.00.5 1.01.5 magnet found a very good description of the experimental data 0H (T) by a superparamagnetic response. Te analysis revealed Fig. 7 Stoner-Wohlfarth response of spin-STM tip. a A STM image showing a Fe|Co island and Fe island (V 0.3 V, I 3 nA). The a magnetic moment between 100 and 2000 μB for the b = − set = black dashed curve encloses the Co core. b and c Magnetic hysteresis diferent tips. Tis fnding suggests that the same mac- loops of dI/dV signals (V 0.75 V) of the STS spectra measured at b = − roscopic tip preparation by Fe deposition followed by the center (marked by the cross) of the Co core of the island A (feld annealing may lead to diferent nano-apices with 30–900 sweep between 3 T and 3 T for b; feld sweep between 1 T and − + − 1 T for c). Red (blue) color code denotes the dI/dV values meas‑ Fe atoms, and these microstructures at the tip apex deter- + mine the magnetic response of the tip. ured for the forward (backward) feld sweep. The purple and green arrows indicate the directions of the magnetizations of the tip and Co core, respectively. Note that the Co magnetization M retains its 3.3 Tips with a Stoner‑Wohlfarth‑like magnetization Co orientation in c. The dashed curves in c are fts according to the SW response model of the data with as a ft parameter. The solid (dashed) red arrows Figure 7a shows a CC-STM image of a BLH Co island indicate the magnetization switching of the tip (the SW-magnet). d in contact with a Fe bilayer rim (Fe|Co island) [18, 19] Description of the tip magnetization vector MT based on a SW model. α and θ represent the polar angles of the magnetic easy axis and the and a pure Fe island. We performed feld-dependent dI/ magnetization vector, respectively, with respect to the direction of dV measurements at the center of the Co core, which is the external magnetic feld (along the z-axis) (Reprinted from [7] with indicated by the black dashed curve of the island A. We permission from Nature Publishing Group (Copyright 2014)) used a Cr/Co-coated W tip under an external feld sweep between −3 and +3 T [7]. Figure 7b shows the dI/dV hysteresis loop, extracted from the dI/dV values of the Co spectra. It clearly shows two distinctive groups of dI/ solely the response of MT to the applied feld. Besides the dV values, corresponding to the AP (intermediate feld magnetization switching at ±0.24 T, we note a mono- values) and P (high feld values) magnetization confgu- tonic dI/dV signal increase (decrease) for the backward rations [5]. Te changes of the dI/dV signal at ±0.24 T (forward) feld sweep. Based on the constant MCo ori- and ±1.1 T indicate the magnetization reversals of the ented in the out-of-plane direction, the feld-dependence tip and of the Co core, respectively, as discussed in the of the dI/dV signals in Fig. 7c implies a gradual increase Sect. 3.1. Interestingly, a close inspection of the curve of the out-of-plane component of the MT for an increas- after subtraction of the signal change due to sample and ing external feld. tip reversal reveals a monotonic change of the dI/dV sig- To obtain a quantitative insight into the tip magnetiza- nal, which saturates at ∼ ±1.5 T. tion MT, we apply a Stoner-Wohlfarth (SW) model [55] To identify the magnetic state of the tip, we obtained (Fig. 7d) to the dI/dV hysteresis in Fig. 7c. Te SW-model a dI/dV hysteresis loop with a feld sweep between −1 employs two angles α and θ, which represent the tilting and +1 T, as shown by red and blue squares in Fig. 7c. of the magnetic easy axis and of the magnetization vec- Tis feld regime is smaller than the switching feld of the tor, respectively, from the axis of the external feld. Te Co core, thus leaving the MCo unchanged. Terefore, the feld-dependence of the magnetization in the SW-model feld dependence of the dI/dV signal in Fig. 7c refects is described by the equation Phark and Sander Nano Convergence (2017) 4:8 Page 10 of 17

Am√1 m2 B 1 2m2 h(m) − + − , (9) =− √1 m2 a b 0T − MT MCo 2 2 B where A = cos α − sin α and B = cosα·sinα. Here the Fe|Co reduced magnetization m M/M cosθ and the 1 ≡ sat = 2 A A’ reduced external magnetic feld h ≡ μ0MsatVH/2Ka, Cu where M , V, and K represent the saturation magnetiza- sat a C’ tion, particle volume, and magnetic anisotropy constant, c y B’ respectively, are used. Te ft of the dI/dV hysteresis in 17nS Fig. 7c to Eq. 9 (dotted curves with dotted arrows) results V x 3 I

d /d in α 55 1°. Tis implies that MT is tilted by 55 1° at = ± ± 8nS zero-feld, away from the sample normal, as shown sche- C matically in Fig. 7d. d

4 Spin‑stm with quantitatively characterized ) 15 1

n (AA’)

(

magnetic tips a

14 l

/ 1.22 ± 0.05 nm In this section, we introduce some recent applications I

d 13 of spin-STM to unravel non-collinear spin ordering and 012345 spin-dependent electronic structures in nanometer scale distance (nm) magnetic structures, based on the quantitative character- e izations of tips as discussed in the last section. 15.0 1.5T 1.0T 4.1 Non‑collinear spin order probed by feld‑tuned tips 0.5T 14.5 4.1.1 Experimental proof of noncollineartiy of a periodic 0.1T spin‑dependent dI/dV pattern 0.05T P ~0.18nm A spatially periodic magnetic state could originate from 1.5T 0T 0.0T 14.0 either a collinear [56, 57] or non-collinear [9] spin-den- 1 1.522.5 sity wave (SDW). A collinear-SDW is characterized by a Fig. 8 In-feld spin-STS of a biatomic-layer-high Fe nanoisland with periodic change of the magnitude of the spin moments, a Stoner-Wohlfarth tip. a CC-STM image of a Fe|Co island on Cu(111). while the spin orientation is fxed. On the other hand, a Scale bar is 4 nm long. b Hard sphere model of the atomic stacking non-collinear SDW is composed of spin moments of con- in a Fe|Co island. The gray, red, and yellow spheres are the Cu, bottom layer Fe, and top layer Fe, respectively. c dI/dV map of the Fe|Co island stant magnitude but with changing orientation. Te dI/ e e shown in a measured at 0 T, where both magnetizations of tip MT and dV signal in spin-STS depends on T S (Eq. 7) [15]. If Co core M point up (V 0.3 V, I 3 nA). The island edges and ˆ · ˆ Co b = − set = one uses a tip of in-plane oriented MT at zero feld, as Co core are indicated by the grey and black dashed lines. The stripe induced by an in-plane magnetic anisotropy, the tip is patterns in three (1, 2, 3) regions originate from the non-collinear sensitive only to the in-plane component of M (M ) cycloidal spin orders in the bridge-stacked bilayer Fe on Cu(111). The S S,|| black, red and blue solid lines (arrows) indicate the directions of the at zero feld. On the other hand, the tip will be sensitive stripes (wave vectors of the cycloidal spin orders), in the regions 1, 2 MS, only to the out-of-plane component of MS ( ⊥) at a and 3, respectively. d Field-dependence of dI/dV profles along the feld large enough to saturate MT along the feld direc- arrow 1 in a, measured with the feld sweep of 0–1.5 T. e Magnifed tion. Accordingly, magnetic-feld-dependent dI/dV meas- view of the grey dashed box in d and is shown for a clarity of feld- urement for a collinear-SDW will result only in a change dependent shifts of the location of the maxima in d. The black and purple dotted lines denote the peak positions of the profles measured of magnitude, but not of the phase, with changing feld. at 0 and 1.5 T, respectively (Reprinted from [7] with permission from In contrast, measurement of a non-collinear SDW with Nature Publishing Group (Copyright 2014)) the same tip will show a feld-dependent phase shift of the stripe pattern of the dI/dV signal, since the tip gets MS, more sensitive to ⊥ as the feld increases [9]. stripe contrast along three diferent directions as indi- 4.1.2 Revealing noncollinearity of stripe patterns in BLH Fe cated by the solid lines superposed along the stripes with nanoisland the labels 1–3. To resolve the spin ordering in the stripe Figure 8a, b show CC-STM and dI/dV images of a Fe|Co patterns, we perform in-feld spin-STS with the SW tip island, measured at 0 T. Figure 8c is a hard sphere model as characterized by spin-STM on a BLH Co on Cu(111) representing the atomic stacking in Fe region 1 of b. (Fig. 7). In this tip the direction of MT is tuned by an Te Fe regions at the three corners of the island show a external feld. Te magnetic easy axis of the tip is canted Phark and Sander Nano Convergence (2017) 4:8 Page 11 of 17

by 55 ± 1° from the sample normal. Terefore, it is sensi- dependent out-of-plane (black dotted) and in-plane (red MS, MS, tive to both ⊥ MT,|| and ⊥ at 0 T, while it is sensi- dotted) components of MS(x) (upper fgure). Figure 9c MS, tive only to the ⊥ at a feld large enough to saturate shows the results of the corresponding calculation but for MS, . Figure 8d shows the feld dependence of the dI/ a LR-cycloid. Note the left-to-right (right-to-left) shift of ⊥ M M dV profle along the line AA’ perpendicular to the stripe the maxima of T · S|norm from 0 to 1.5 T for the RR- direction of region 1 in Fig. 8b. Te wavelength of the (LR-) cycloid for the given azimuthal angle of MT. For stripe pattern, as denoted, is identical with that (1.28 nm) the stripe contrast in region 1 of the island in Fig. 8, we observed in the pure Fe island [7, 20]. Figure 8e shows a observe that the extrema of the dI/dV curves shift from zoom-in of the feld dependence between two maxima right to left. Interestingly, the three cases show diferent in the profles, as shown within the grey dashed line in amounts of phase shifts with increasing feld (Supple- Fig. 8d, for clarity. With increasing magnetic feld, the mentary Information of [7]). We perform a quantitative positions of maxima and minima move monotonically analysis of the phase shift and its dependence on stripe from right to left, while the distance between the extrema orientation and feld. An excellent agreement between remains constant. A phase shift of ∆P ~ 0.18 nm is meas- the experiments and simulations reveals that the feld ured upon a change of the magnetic feld from 0 to 1.5 dependence of the phase shifts is determined by a given T. Tis observation rules out a collinear SDW. Rather, in- orientation of the tip magnetization. feld spin-STS identifes a non-collinear-SDW as the spin texture of the stripe contrast. 4.2 Spin‑STM of a non‑collinear magnetic state with a superparamagnetic tip 4.1.3 Simulation of phase shift in the feld dependence of the Figure 10a is CC-STM image of a BLH Fe island on stripe pattern Cu(111) in bridge-site stacking of the topmost atoms, Based on Wortmann et al.’s discussion [15], the dI/ measured with a Fe-coated W tip. Figures 10b–d are dI/ dV|mag (Eq. 7) signal is proportional to the projection of dV images of the same island as that of Fig. 10a meas- eT eS MS to MT at the tip position, i.e., ˆ · ˆ . Here we calcu- ured at 0 T, +1.5 T, and −1.5 T, respectively. Te stripe M M MT MS late a normalized T · S ( · |norm) with respect patterns in Fig. 10c, d indicate a cycloidal spin order as to the external feld. We model MT as a SW magnet of a discussed in the text above describing Figs. 8 and 9. How- magnetic easy axis canted by α = 55° from the external ever, no stripe contrast is observed in the dI/dV map at feld direction, as discussed in Fig. 7c and d. An ab ini- zero feld. We obtained dI/dV images under an external tio study of the sample confguration [7] predicted a feld from −3 to +3 T along the sample normal. We show Néel-type non-collinearity, where the plane of the spin in Fig. 10e the stripe contrast at 5 feld values, measured rotation is parallel with the wave vector of a periodic- along a direction perpendicular to the stripe patterns ity λSH = 1.28 nm. Tereby, we call this spin order a as indicated by the white lines in Fig. 10b–d. Figure 10f “spin-cycloid” in the rest of the paper. Ten both the shows the feld dependence of the stripe contrast (red), out-of-plane (MS,z) and in-plane (MS,x) components of peak-to-peak amplitude of the contrast oscillation at the M show a sinusoidal position dependence along each feld followed by a normalization with the satura- S e e the x-axis. Tus, ˆS,z and ˆS,x can be described by the tion value from the Langevin ftting (Eq. 8). Te inspec- equations tion of Fig. 10e reveals two aspects: (1) Te contrast at a 2πx 2πx π given position increases for increasing applied feld. No eS,z sin , eS,x sin , (10) ˆ = ˆ = ∓ 2 stripe contrast is observed at zero feld. Te stripe con- SH SH trast saturates at ~±1.5 T. (2) Te contrast depends only eS,x where the signs ‘−’ and ‘+’ in the formula of ˆ indi- on the magnitude of the feld, but not on the sign of the cate a right-rotating (RR) and left- rotating (LR) feld. Te extrema positions of the stripe patterns as indi- cycloid, respectively. cated by the yellow and blue dashed lines in Fig. 10c and We calculate the signal induced by the stripe pattern d remain unchanged. To obtain a quantitative insight into in region 1 in Fig. 8b. Figure 9a shows a description of the feld dependence of the stripe contrast (red curve in MT, with the polar (θT) and azimuthal (φT) angles, in the Fig. 10f), we also obtained the feld dependence of dI/dV Cartesian coordinate system. A sketch of the geomet- signals measured at the center of the Co core of a Fe|Co ric relation between the in-plane component of the tip island (inset) with the same tip. Tis measurement on magnetization MT,|| and the wave vector k1 of the stripe the Co reference sample defnitely refects the response pattern for region 1 in Fig. 8b is presented. Figure 9b of the tip to the applied feld (blue in Fig. 10f). Tis tip M M shows the feld dependence T · S|norm as a func- behaves as a superparamagnetic particle. Te larger slope tion of position x (lower fgure), calculated with α = 55° near zero feld for measurements on Co (blue curve) as and φT = 170° for a RR-cycloid, with the x-position compared to measurements on Fe (red curve), clearly Phark and Sander Nano Convergence (2017) 4:8 Page 12 of 17

z a y MT M T,|| k1 T z x

y x T

= 1.28 nm b 1

norm MSS,z

S 0 MSS,x

M -1 ‘RR’ /4 =0.32nm 1.5T P=0.16 nm 1T 1

norm 0.5T

| S 0.1T

M 0 0.05 T

• T 0T

M -1 0T 1.5T = 55oo&= 170 -0.1 T T -0.2 T 0.00.5 1.01.5 2.02.5 3.0 3.5 distance (nm)

c = 1.28 nm 1

norm MSS,z

S 0 MSS,x

M -1 ‘LR’ /4 =0.32nm 1.5T P=0.16 nm 1T 1

norm

| 0.5T S 0.1T

M 0 0.05 T

• T 0T M -1 1.5T 0T oo-0.1 T = 55 &=T 170 -0.2 T 0.00.5 1.01.5 2.02.5 3.0 3.5 distance (nm) Fig. 9 Probing non-collinear cycloidal spin order with a feld-tuned tip with Stoner-Wohlfarth magnetization behavior. a A description of the tip

magnetization MT of a “Stoner-Wohlfarth tip”, with the polar (θT) and azimuthal (φT) angles, in the Cartesian coordinate system and a sketch of the geometric relation between the in-plane component of the tip magnetization MT, and the wave vector k1 of the stripe pattern for the region 1 in Fig. 8c. The black bars indicate the stripe pattern. b, c The upper fgure of b (c) shows the x-position dependence of out-of-plane and in-plane com‑ ponents of local magnetization of the RR- (LR-) order. The lower fgure of b (c) shows the feld dependence of the MT · MS|norm curves as a function of the position x, calculated with θ 55° and φ 170° for a RR- (LR-) order. The in-plane (red dotted) and out-of-plane (black dotted) components T = T = of the spin cycloidal order are shown in the coordinate system illustrated in a. The green arrows in the upper fgure of b (c) indicate the local magnetization variation in space for a RR- (LR-) order. Reprinted from [7] with permission from Nature Publishing Group (Copyright 2014) (Reprinted from [7] with permission from Nature Publishing Group (Copyright 2014))

implies a sizable contribution of the response of the sam- Te feld dependence of the magnetization ple magnetic order to the measured quantity of the dI/dV MT of a superparamagnetic tip can be written as signal (red). In addition, the results imply a ‘non-hyster- MT(H) = −MT(−H) (blue curve in Fig. 10f). Te feld etic’ and ‘monotonic’ response of the Fe magnetic order dependence of the dI/dV signal of the pure Fe island to the applied feld. shown in Fig. 10 reveals a relation of dI/dV (−H) = dI/ Phark and Sander Nano Convergence (2017) 4:8 Page 13 of 17

dV (H) (red). Ten, the relation given by Wortmann et al., -0.5 V, 1nA +1.5 T a c dI/dV|mag = mT · mFe, resolves the infuence of the sign reversal in H on the magnetization density of state mFe (see Sect. 1.2) through a simple calculation

dI dI ( H) mT( H) mFe( H) (H) dV − = − · − ⇔ dV mag mag -0.5V mT(H) mFe(H), = · (11) 0T -1.5 T b d which leads to a relation mS(−Hext) = −mS(Hext). Tis, concurrent with the above-mentioned ‘non-hysteretic’ 2nS x and ‘monotonic’ feld dependence, provides an important conclusion on the magnetic property of the non-collinear spin order in the Fe island. Te stripe order in Fe island -1nS responds to the external feld as an efective magnetic -0.5V -0.5V moment, which is thermally fuctuating at a given measurement temperature. We show in the next section the e 1.2 V = -0.5V signifcance of this aspect to obtain a spin-polarization 1.0 b map of the Fe stripe phase from the data set shown in

)

S 0.8 Fig. 10a–c.

( 0.6 V 4.3 Spin‑polarization of magnetically ordered

d -1.5 T

/ I 0.4 -0.5 T nanostructures

d 0T 4.3.1 Diferential conductance asymmetry 0.2 +0.5 T +1.5 T 0.0 Te magnetic confguration of a sample is determined 4681012 by its spin-dependent electronic structure, giving rise to distance (nm) spin polarization of the electronic density of states. To investigate the spin polarization of a sample with spin- f 1.0 STM, the asymmetry of the diferential conductance, AdI/

) x , is introduced. Te asymmetry is defned as [5]

d dV

z 0.5 -0.5V, 1 nA

i l dI/dV dI/dV a AP P Tip AdI/dV − (12)

m r Tip (fit) = dI/dV AP dI/dV P

o 0.0 0.2nm x + n Fe-b ( Fe-b (fit)

V In case of a ferromagnetic sample of bistable mag-

/ -0.5 I netization, AdI/dV is calculated from the dI/dV signals d recorded under P and AP to the unit vector of magnetiza- -1.0 tion confgurations, i.e. êT·êS = ±1, as schematically illus- -4 -3 -2 -1 01234 trated in Fig. 11a. As introduced in Sect. 1.2, Wortmann et al. derived the description of the dI/dV signal meas- Field (T) ured by spin-STM [15] (Eq. 7). Substitution of their result Fig. 10 Spin-STM of thermally fuctuating magnetic order with a feld-tuned superparamagnetic tip. a–d CC-STM (a) and dI/dV maps into the Eq. 12 leads to at 0 T (b), 1.5 T (c), and 1.5 T (d) of a bilayer bridge-stacked Fe + − AdI/dV PTPS, (13) nanoisland measured with a superparamagnetic Fe-coated W tip =− at 10 K. (V 0.5 V, I 1 nA). e dI/dV profles along the line b = − set = which links the dI/dV asymmetry, AdI/dV, to the spin depicted in the CC-STM image in a, measured at 1.5 T (black), 0.5 − − polarization of the sample at the tip apex position, P ( ). T (red), 0 (green), 0.5 T (blue), 1.5 T (cyan). f Field dependence S RT + + of dI/dV contrast of the stripe pattern (red) measured at a bright Equations 11 and 12 were applied to the Co island ‘A’ center as marked by the cross in d. Field dependence of the dI/dV in Fig. 5a to extract the spatial distribution of its spin- contrast measured at the center of the Co (blue) of the Fe|Co island as polarization. Figure 11a, b are two dI/dV images on the indicated in the inset, with the same tip as used for measuring the Fe island measured at μ0H = −1.1 T, with (b) AP and (c) P island. The solid curves are fts of the data to the Langevin equation, magnetization confgurations, as indicated in Fig. 5c. for the Fe (red) and Fe|Co (blue) nanoislands. All the data are normal‑ ized with the saturation values obtained from the Langevin fts Figure 11d is the AdI/dV map, at the given bias voltage Vb, calculated from the dI/dV images in Fig. 11b and c. Phark and Sander Nano Convergence (2017) 4:8 Page 14 of 17

a ferromagnec order b c d

MT MS (AP) Co 6nS +0.04 (P) Cu

mT·mS(r)|AP = –mT·mS(r)|P 1nS -0.04

e cycloidal order f g h MT MS () Fe 7nS +0.2 () Cu 3 nm mT·mS(r)| = –mT·mS(r)| 0 T11nS .5 T -0.2

Fig. 11 Diferential conductance asymmetry AdI/dV. a Two magnetic confgurations in spin-STM measurements, AP and P, corresponding to two distinct magnetic states of a bilayer Co nanoisland, pointing up and down, respectively. b, c dI/dV images of the Co nanoisland ‘A’ in Fig. 5a measured at μ H 1 T and V 0.03 V for AP (b) and P (c) states. d A map calculated from the dI/dV images of b and c. e Two relative 0 ext = − b = + dI/dV magnetization confgurations of spin-STM measurements, corresponding to two distinct magnetic states of a bilayer Fe nanoisland, α and β. f, g dI/ dV images of a Fe nanoisland, measured at external felds of (b) 0 T and (c) a value H . h A map calculated from the dI/dV images of f and g. ≥ sat dI/dV b–d Reprinted from [18] with permission from Institute of Physics (Copyright 2014). f–h Reprinted from [20] with permission from Nature Publishing Group (Copyright 2016)

Oka et al. extracted a set of energy-resolved A maps dI/dV dI/dV dI/dV α − β of this Co island, which led to the disclosure of the elec- AdI/dV (14) = dI/dV dI/dV tronic nature of “spin-dependent quantum interference α + β within a single nanostructure” [5]. With substitution of the Eqs. 7, 14 becomes 4.3.2 Diferential conductance asymmetry of non‑collinear nTnS mT mS,α nTnS mT mS,β magnetic order AdI/dV + · − − · = nTnS mT mS,α nTnS mT mS,β In case of a helical (or cycloidal) spin order, the local m +m · + + · T S,α (15) magnetization rotates with a spatial period. Tus, the · =− nTnS spatially averaged magnetization is zero. As discussed in Sect. 4.2, a sign reversal of the external feld induces Tis leads to a link between the symmetry AdI/dV and the a corresponding reversal in that of the local magnetiza- spin polarization of the sample at the tip apex position, tion, MS(r; −H) = −MS(r; H), indicative of two distinct PS(RT) in the form antiparallel magnetic states at each position r. In addi- R AdI/dV PTPS( T) cos θ, (16) tion, the power of spin-STM, which allows to resolve the =− local magnetic signal down to the atomic scale, makes where θ is the angle between MT and MS (see Fig. 1a). a study on the local spin-polarization of the cycloidal Te asymmetry AdI/dV corresponds to the projection of order in the bilayer Fe island feasible. Although the def- PS onto the tip magnetization direction. nition of AP and P confgurations is not applicable to If a superparamagnetic tip (Fig. 6) is used in spin- this case due to the periodic change of the local mag- STM/S of the cycloidal spin order in the bilayer Fe island, netization, one can clearly distinguish two distinct mag- one is not able to have the above-mentioned two magnetic states, as sketched in Fig. 11e. Combined with the netization confgurations (α and β) because the tip mag- tip magnetic state, we introduce two magnetic confgu- netization will also be reversed by the sign reversal of the rations α and β, hence MS,(r) = −MS,β(r), analogous to applied feld, as discussed in Fig. 10. Tis always results the AP and P confgurations in the case of Fig. 11a. Te in the numerator of the Eq. (14) to be zero. We introduce asymmetry AdI/dV for the cycloidal spin order in the Fe a procedure to overcome this obstacle in the following island is defned as discussion. A careful inspection of the right hand side Phark and Sander Nano Convergence (2017) 4:8 Page 15 of 17

of Eq. 15 indicates that the denominator and numerator parallel confgurations of tip and sample magnetizations, are no other than non-magnetic and magnetic terms of provides diferential conductance asymmetry maps, the dI/dV signals for the confguration α, respectively. which directly link spin-STS data to the local spin-polari- Tese two contributions are provided by the dI/dV| zation within a single nanostructure. H=0 and dI/dV| – dI/dV| data, respectively. Figure 11f, In spite of the remarkable advances to date in the char- α H=0 g show the dI/dV| and dI/dV| maps of a bilayer Fe acterization of the tip states by exploiting external feld H=0 α nanoisland measured with a superparamagnetic tip, and control, the spin-STM research feld still requires more Fig. 11h is its AdI/dV map, derived from Fig. 11f and g as efort to overcome the following existing barriers. It is a given by Eq. 15. Fischer et al. extracted a set of energy- goal to defne the tip apex to maintain a specifc structural resolved AdI/dV maps of this Fe island, which were suc- confguration on the atomic scale during a set of meas- cessfully utilized to reveal the “spinor nature of electronic urements over periods ranging from days to months. states in nanosize non-collinear magnets” [20]. However, a specifc recipe of macroscopic (or ex situ) tip preparation does not seem to play a decisive role for the 5 Concluding remarks resulting magnetic behavior, as we demonstrated in this In the recent two decades, spin-STM has evolved into review (Fig. 4). Up to now, preparation and tuning of a tip a reliable and versatile tool for spatial mapping of local is extremely tricky. Key ingredients are in situ treatments magnetic structures of collinear and non-collinear spin by voltage pulses. Te tip never comes back to its original textures on the nano-scale. Te unsurpassed lateral reso- form once the tip loses its microscopic confguration by lution turned spin-STM into a unique tool to collect the crashes with the sample, which is unfortunately common magnetic information down to the atomic scale of single in STM measurement. Manipulation technique of single nanostructures. Te tunneling nature of STM/S inevi- atoms on a surface using STM tips [10, 58–61] has been tably couples contributions from both tip and sample in advanced signifcantly through precise estimation of the the measured signals, I(V) and dI/dV(V). Understand- force required to move an individual atom on a surface ing the tip contribution has been a challenging issue for [62, 63]. Tis allows to reliably attach/detach individual a reliable analysis of the sample properties. Undoubtedly, atoms to/from the tip apex without any change of the this is also true in the spin-STM/S measurements. In rest of the tip. In addition, complete control of the vec- this review, we introduced some examples of tip charac- tor nature of the tip and sample magnetizations call for a terization in spin-STM/S experiments. Tis analysis has “vector magnet feld”, which comes with a high price tag. advanced the quantitative physical understanding of spin Future advance in spin-STM is guaranteed by the combi- textures in nanostructures. nation of these advanced techniques. Based on in situ reference measurements on the bista- Authors’ contributions ble out-of-plane magnetization of biatomic-layer-high SHP and DS conceived and designed the contents of the paper. All authors Co nanoislands on Cu (111), we characterized magnetic discussed and wrote the paper. Both authors read and approved the fnal manuscript. states of spin-STM tips quantitatively. Temperature- dependent in-feld spin-STM/S gives a quantitative char- Author details acterization of tips in the superparamagnetic state. Te 1 Center for Quantum Nanoscience, Institute for Basic Science, Seoul 03760, Republic of Korea. 2 Department of Physics, Ewha Womans University, analysis reveals stray feld at the tip position induced by Seoul 03760, Republic of Korea. 3 Max-Planck-Institut für Mikrostrukturphysik, the sample magnetization. In-feld spin-STM/S combined 06120 Halle, Germany. with the Stoner-Wohlfarth (SW) model [55] for tip mag- Acknowledgements netization elucidates the orientation of the magnetic ani- S. Phark acknowledges support from IBS-R027-D1. D. Sander acknowledges sotropy of bistable ferromagnetic tips. Our studies show partial fnancial support by DFG SFB762. All the experiments were performed that the SW model within the framework of the super- using the low-temperature STM of the Max-Planck-Institute of Microstruc‑ ture Physics at Halle, Germany. S. Phark heartfully thanks Y. J. Chang and A. J. paramagnetic criterion indeed explains the magnetic Heinrich for careful reading, sophisticated discussion, and useful corrections of response of tips of various types, which give rise to dis- the manuscript. tinctly diferent feld-dependence of the spin-STS signal. Competing interests In-feld STM/S in combination, such sophisticated tip The authors declare that they have no competing interests. characterization allows to characterize the local magnetic order and local spin-dependent electronic structure of Availability of data and materials The datasets supporting the conclusions of this article are included within the magnetic nanostructures. Field-tuning of the orientation article. of a magnetically bistable tip was applied to reveal the non-collinearity of the one-dimensional periodic mag- Funding DFG SFB762 partially supports the design and experiments of the study in netic order in Fe nanoislands. Te spin-dependent dI/dV the manuscript. IBS-R027-D1 supports the interpretation of data and writing mapping of Co and Fe nanostructures, in antiparallel and process of the manuscript. Phark and Sander Nano Convergence (2017) 4:8 Page 16 of 17

Publisher’s Note 24. L. Gerhard et al., Magnetoelectric coupling at metal surfaces. Nat Nano‑ Springer Nature remains neutral with regard to jurisdictional claims in pub‑ tech. 5, 792–797 (2010) lished maps and institutional afliations. 25. G. Rodary, S. Wedekind, H. Oka, D. Sander, J. Kirschner, Characterization of tips for spin-polarized scanning tunneling microscopy. Appl. Phys. Lett. Received: 7 February 2017 Accepted: 29 March 2017 95, 152513 (2009) 26. M. Corbetta, S. Ouazi, J. Borme, Y. Nahas, F. Donati, H. Oka, S. Wedekind, D. Sander, J. Kirschner, Magnetic response and spin polarization of bulk Cr tips for in-feld spin-polarized scanning tunneling microscopy. Jpn. J. Appl. Phys. 51, 208 (2012) 27. S. Maekawa, U. Gäfvert, Electron tunneling between ferromagnetic flms. References IEEE Trans. Magn. 18, 707 (1982) 1. M. Bode, Spin-polarized scanning tunnelling microscopy. Rep. Prog. Phys. 28. T. Miyazaki, N. Tezuka, Giant magnetic tunneling efect in Fe/Al2O3/Fe 66, 523 (2003) junction. J. Magn. Magn. Mater. 139, L231 (1995) 2. W. Wulfhekel, J. Kirschner, Spin-polarized scanning tunneling microscopy 29. J.S. Moodera, L.R. Kinder, T.M. Wong, R. Meservey, Large magnetoresist‑ of magnetic structures and antiferromagnetic thin flms. Annu. Rev. ance at room temperature in ferromagnetic thin flm tunnel junctions. Mater. Res. 37, 69 (2007) Phys. Rev. Lett. 74, 3273 (1995) 3. R. Wiesendanger, Spin mapping at the nanoscale and atomic scale. Rev. 30. M.W.J. Prins, D.L. Abraham, H. van Kempen, Spin-dependent transmission Mod. Phys. 81, 1495 (2009) at ferromagnet/semiconductor interfaces. J. Magn. Magn. Mater. 121, 152 4. H. Oka, O.O. Brovko, M. Corbetta, V.S. Stepanyuk, D. Sander, J. Kirschner, (1993) Spin-polarized quantum confnement in nanostructures: scanning tun‑ 31. P.M. Tedrow, R. Meservey, Direct observation of spin-state mixing in neling microscopy. Rev. Mod. Phys. 86, 1127–1168 (2014) superconductors. Phys. Rev. Lett. 27, 919 (1971) 5. H. Oka, P.A. Ignatiev, S. Wedekind, G. Rodary, L. Niebergall, V.S. Stepanyuk, 32. P.M. Tedrow, R. Meservey, Spin-dependent tunneling into ferromagnetic D. Sander, J. Kirschner, Spin-dependent quantum interference within a nickel. Phys. Rev. Lett. 26, 192 (1971) single magnetic nanostructure. Science 327, 843 (2010) 33. W. Wulfhekel, J. Kirschner, Spin-polarized scanning tunneling microscopy 6. S. Ouazi, S. Wedekind, G. Rodary, H. Oka, D. Sander, J. Kirschner, Magneti‑ on ferromagnets. Appl. Phys. Lett. 75, 1944–1946 (1999) zation reversal of individual co nanoislands. Phys. Rev. Lett. 108, 107206 34. C.L. Gao, U. Schlickum, W. Wulfhekel, J. Kirschner, Mapping the surface (2012) spin structure of large unit cells: reconstructed Mn flms on Fe(001). Phys. 7. S.H. Phark, J.A. Fischer, M. Corbetta, D. Sander, K. Nakamura, J. Kirschner, Rev. Lett. 98, 107203 (2007) Reduced-dimensionality-induced helimagnetism in iron nanoislands. 35. K. von Bergmann, M. Menzel, D. Serrate, Y. Yoshida, S. Schröder, P. Ferriani, Nat. Commun. 5, 5183 (2014) A. Kubetzka, R. Wiesendanger, S. Heinze, Tunneling anisotropic magne‑ 8. S. Heinze, M. Bode, A. Kubetzka, O. Pietzsch, X. Nie, S. Blügel, R. Wiesen‑ toresistance on the atomic scale. Phys. Rev. B 86, 134422 (2012) danger, Real-space imaging of two-dimensional antiferromagnetism on 36. N. Néel, S. Schröder, N. Ruppelt, P. Ferriani, J. Kröger, R. Berndt, S. Heinze, the atomic scale. Science 288, 1805 (2000) Tunneling tunneling anisotropic magnetoresistance on the atomic scale. 9. M. Bode et al., Chiral magnetic order at surfaces driven by inversion asym‑ Phys. Rev. Lett. 110, 037202 (2013) metry. Nature 447, 190–193 (2007) 37. N.M. Cafrey, S. Schröder, S.Heinze Ferriani, Tunneling anisotropic magne‑ 10. S. Loth, S. Baumann, C.P. Lutz, D.M. Eigler, A.J. Heinrich, Bistability in toresistance efect of single adatoms on a noncollinear magnetic surface. atomic-scale antiferromagnets. Science 335, 196–199 (2012) J. Phys.: Condens. Matter 26, 394010 (2014) 11. P.M. Tedrow, R. Meservey, Spin polarization of electrons tunneling from 38. M. Cavallini, F. Biscarini, Electrochemically etched nickel tips for spin flms of Fe Co, Ni, and Gd. Phys. Rev. B 7, 318 (1973) polarized scanning tunneling microscopy. Rev. Sci. Instr. 71, 4457–4460 12. R. Meservey, P.M. Tedrow, P. Fulde, Magnetic feld splitting of the quasipar‑ (2000) ticle states in superconducting aluminum flms. Phys. Rev. Lett. 25, 1270 39. A.L. Bassi, C.S. Casari, D. Cattaneo, F. Donati, S. Foglio, M. Passoni, C.E. Bot‑ (1970) tani, P. Biagioni, A. Brambilla, M. Finazzi, F. Ciccacci, L. Duò, Appl. Phys. Lett. 13. M. Julliere, Tunneling between ferromagnetic flms. Phys. Lett. 54A, 225 (1975) 91, 173120 (2007) 14. C. Kittel, Physical theory of ferromagnetic domains. Rev. Mod. Phys. 21, 40. A.A. Minakov, I.V. Shvets, On the possibility of resolving quantization axes 541 (1949) of surface spins by means of a scanning tunneling microscope with a 15. D. Wortmann, S. Heinze, P. Kurz, G. Bihlmayer, S. Blügel, Resolving complex magnetic tip. Surf. Sci. 236, L377–L381 (1990) atomic-scale spin structures by spin-polarized scanning tunneling 41. S. Murphy, J. Osing, I.V. Shvets, Fabrication of submicron-scale manga‑ microscopy. Phys. Rev. Lett. 86, 4132 (2001) nese-nickel tips for spin-polarized STM studies. Appl. Surf. Sci. 144–145, 16. J. Bardeen, Tunneling from a many-particle point of view. Phys. Rev. Lett. 497–500 (1999) 6, 57–59 (1961) 42. G. Mariotto, S. Murphy, I.V. Shvets, Charge ordering on the surface of 17. J. Tersof, D.R. Hamann, Theory of the scanning tunneling microscope. Fe3O4(001). Phys. Rev. B 66, 245426 (2002) Phys. Rev. B 31, 805 (1985) 43. S.F. Ceballos, G. Mariotto, S. Murphy IV, I.V. Shvets, Fabrication of magnetic 18. D. Sander, S.H. Phark, M. Corbetta, J.A. Fischer, H. Oka, J. Kirschner, The STM probes and their application to studies of the Fe3O4(001) surface. impact of structural relaxation on spin polarization and magnetization Surf. Sci. 523, 131–140 (2003) reversal of individual nano structures studied by spin-polarized scanning 44. T.E. Feuchtwang, P.H. Cutler, J. Schmit, Surf. Sci. 75, 401 (1978) tunneling microscopy. J. Phys.: Condens. Matter 26, 394008 (2014) 45. S. Nagai, K. Hata, H. Oka, D. Sander, J. Kirschner, Atomic structure and spin 19. S.H. Phark, J.A. Fischer, M. Corbetta, D. Sander, J. Kirschner, Superparamag‑ polarization at the apex of tips used in spin-polarized scanning tunneling netic response of Fe-coated W tips in spin-polarized scanning tunneling microscopy. Appl. Phys. Exp. 7, 025204 (2014) microscopy. Appl. Phys. Lett. 103, 032407 (2013) 46. T. Hashizume, Y. Hasegawa, I. Kamiya, T. Ide, I. Sumita, S. Hyodo, T. 20. J.A. Fischer, L.M. Sandratskii, S.H. Phark, S. Ouazi, A.A. Pasa, D. Sander, S.S.P. Sakurai, H. Tochihara, M. Kubota, Y. Murata, J. Vac. Sci. Technol., A 8, 233 Parkin, Probing the spinor nature of electronic states in nanosize non- (1990) collinear magnets. Nat. Commun. (2016). doi:10.1038/ncomms13000 47. O. Pietzsch, A. Kubetzka, M. Bode, R. Wiesendanger, Spin-polarized scan‑ 21. M.F. Crommie, C.P. Lutz, D.M. Eigler, Imaging standing waves in a two- ning tunneling spectroscopy of nanoscale cobalt islands on Cu(111). dimensional electron gas. Nature (London) 363, 524 (1993) Phys. Rev. Lett. 92, 057202 (2004) 22. L. Diekhöner, M.A. Schneider, A.N. Baranov, V.S. Stepanyuk, P. Bruno, K. 48. Y. Yayon, V.W. Brar, L. Senapati, S.C. Erwin, M.F. Crommie, Observing spin Kern, Surface states of cobalt nanoislands on Cu(111). Phys. Rev. Lett. 90, polarization of individual magnetic adatoms. Phys. Rev. Lett. 99, 067202 236801 (2003) (2007) 23. A. Biedermann, W. Rupp, M. Schmid, P. Varga, Coexistence of fcc- and bcc- 49. C. Iacovita, M.V. Rastei, B.W. Heinrich, T. Brumme, J. Kortus, L. Limot, J.P. like crystal structures in ultrathin Fe flms grown on Cu(111). Phys. Rev. B Bucher, Visualizing the spin of individual cobalt-phthalocyanine mol‑ 73, 165418 (2006) ecules. Phys. Rev. Lett. 101, 116602 (2008) Phark and Sander Nano Convergence (2017) 4:8 Page 17 of 17

50. J. de la Figuera, J.E. Prieto, C. Ocal, R. Miranda, Scanning-tunneling-micros‑ 57. E. Fawcett, Spin-density-wave antiferromagnetism in chromium. Rev. copy study of the growth of cobalt on Cu(111). Phys. Rev. B 47, 13043(R) Mod. Phys. 60, 209–283 (1988) (1993) 58. M.F. Crommie, C.P. Lutz, D.M. Eigler, Confnement of electrons to quantum 51. N.N. Negulyaev, V.S. Stepanyuk, P. Bruno, L. Diekhöner, P. Wahl, K. Kern, corrals on a metal surface. Science 262, 218–220 (1993) Bilayer growth of nanoscale Co islands on Cu(111). Phys. Rev. B 77, 59. H.C. Manoharan, C.P. Lutz, D.M. Eigler, Quantum mirages formed by 125437 (2008) coherent projection of electronic structure. Nature 403, 512–515 (2000) 52. C.P. Bean, J.D. Livingston, Superparamagnetism. J. Appl. Phys. 30, S120 60. A.J. Heinrich, C.P. Lutz, J.A. Gupta, D.M. Eigler, Molecule cascades. Science (1959) 298, 1381–1387 (2002) 53. I.M.L. Billas, J.A. Becker, A. Chârelain, W.A. de Heer, Magnetic moments of 61. C.F. Hirjibehedin, C.P. Lutz, A.J. Heinrich, Spin coupling in engineered iron clusters with 25 to 700 atoms and their dependence on tempera‑ atomic structures. Science 312, 1021–1024 (2006) ture. Phys. Rev. Lett. 71, 4067 (1993) 62. M. Ternes, C.P. Lutz, C.F. Hirjibehedin, F.J. Giessibl, A.J. Heinrich, The force 54. M.B. Stearns, Magnetic properties of 3d, 4d, and 5d elements alloys and needed to move an atom on a surface. Science 319, 1066–1069 (2008) compounds (Landolt-Bornstein numerical data and functional relationships 63. M. Ternes, C. González, C.P. Lutz, P. Hapala, F.J. Giessibl, P. Jelínek, A.J. Hein‑ in science and technology group III) (Springer, Berlin, 1986) rich, Interplay of conductance, force, and structural change in metallic 55. E. Stoner, E. Wohlfarth, A mechanism of magnetic hysteresis in heteroge‑ point contacts. Phys. Rev. Lett. 106, 016802 (2011) neous alloys. Philos Trans R Soc A Phys Mech Eng Sci 240, 599–642 (1948) 64. S. Chikazumi, Physics of ferromagnetism, international series of monographs 56. A.W. Overhauser, Spin density waves in an electron gas. Phys. Rev. 128, on physics, 2nd edn. (Oxford University Press, New York, 1997) 1437–1452 (1962)