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pulse was applied. A new disclination defect
(branch point) appeared in the subsequent SP-
STM image (Fig. 4B, red circle), which repre-
sents a discrete change in the topological charge
density within this region. The core center also
shifted by ~5 nm with respect to the fixed back-
ground of atomic defects. Subsequent pulsing
shifted the disclination defect closer to the core,
which itself changed contrast and size (Fig. 4C).
A final cycle of pulsing annihilated the dis-
clination defect and further shifted the core
(Fig. 4D). Although this series of images was
taken with different atomic tip terminations
(and thus possibly different magnetic con-
trast), the topology of the final state was iden-
tical to the starting state (Fig. 4A). This indicates
that the target texture had been reversibly ma-
nipulated through a landscape of metastable
topological states.
We also observed hysteretic behavior of the
target texture with applied out-of-plane mag-
netic field, as shown in Fig. 4E. After acquir-
ingtheSP-STMimageatzerofield(image4in
Fig. 4D), the magnetic field was ramped up to
+1T.AsshowninSP-STMimage5inFig.4E,
the core region is reduced in size and shows
faintly dark contrast (dashed lines). Ramping
the field back down to 0 T (image 6) shows an
expansion of the wrapping and increased dark
contrast of the core region. The core region
flips back to bright contrast and shrinks when
the field is ramped to–1T(image7),andthen

expands again when the field is ramped back

down to 0 T (image 8). Comparing images 4

and 6 reveals a clear hysteresis effect, and the

identical magnetic contrast in images 4 and

8 indicate that this effect is reversible. Con-

sistent with previous SP-STM studies using

bulk Cr tips ( 30 ), this hysteretic behavior

cannot be explained as a field-dependent

polarization of the tip. In fig. S17 we show

SP-STM simulations indicating that if the

tip polarization vector were changing with

applied field, there would be changes in stripe

contrast and/or anisotropy, which are not ob-

served in Fig. 4E. Instead, our micromagnetic

modeling explains the contrast reversal as

arising from a net magnetic moment associated

with the finite-volume texture, which aligns

with the applied magnetic field. Apphase shift

is induced when the magnetic field switches

direction, leading to a reversal of contrast in

the SP-STM images (fig. S10).

The topological spin textures observed in

our thin films are distinct from those in bulk

samples, which raises questions concerning

the interplay of bulk and surface magnetism

( 32 ). How, or whether, the textures we ob-

served extend into the bulk of the films can be

further explored by comparing bulk measure-

ments of topological Hall effect with magnetic

imaging techniques such as (surface-sensitive)

SP-STM and (volumetric) Lorentz transmis-

sion electron microscopy. Although additional

study is needed to establish quantitative cor-

relation, the association of these textures with

local strain may reflect an interplay of magne-

tostriction effects, which have been studied in

B20 materials ( 33 – 35 ), and further advances

strain as an additional tuning parameter in

thin-film devices for future memory and logic

applications ( 12 , 31 , 36 ).

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    ACKNOWLEDGMENTS
    We thank S. Mueller for helpful discussions on the data analysis.
    Funding:Primary support was provided by DARPA grant D18AP00008.
    Partial support was provided by US Department of Energy grant
    DE-SC0016379 for SP-STM technique development. J.G.S. and N.T.
    thank DGAPA-UNAM projects IN101019 and IA100920 and CONACyT
    grant A1-S9070 of the Call of Proposals for Basic Scientific Research
    2017 – 2018 for partial financial support. Calculations were performed
    in the DGCTIC-UNAM Supercomputing Center, project LANCAD-
    UNAMDGTIC-368.Author contributions:J.R. and J.P.C. performed
    SP-STM experiments and analyzed data; T.L.,T.Z., S.C., and A.S.A. grew
    the thin films and characterized the structural and magnetic properties;
    P.-K.W. and M.R. performed theoretical modeling; N.T. and J.G.-S.
    performed density functional theory calculations for the surface
    structural study; and R.K.K., M.R., and J.A.G. helped in writing the
    manuscript and analyzing the results.Competing interests:The authors
    declare no competing interests.Data and materials availability:See ( 37 ).
    SUPPLEMENTARY MATERIALS
    science.org/doi/10.1126/science.abd9225
    Materials and Methods
    Supplementary Text
    Figs. S1 to S19
    References ( 38 – 43 )
    Movie S1
    20 July 2020; accepted 19 October 2021
    10.1126/science.abd9225

SCIENCEscience.org 17 DECEMBER 2021•VOL 374 ISSUE 6574 1487

Fig. 4. STM tip and magnetic field manipulation of a target texture.(AtoD) SP-STM images of the target
spin texture in different configurations. Between each image, current/voltage pulses were applied with the STM tip
(~2.0 V, 0.5 s,I≲ 1 mA due to 300-pm approach). White dashed lines are guides to the eye showing wrapping around
the core region. The red circle in (B) and (C) indicates a disclination defect that is generated, moved, and then
annihilated. The blue dot represents the same atomically registered fixed point in the images, showing motion of the
core. (E) SP-STM images showing the magnetic field dependence of the texture. Image 5, taken after image 4 with
an out-of-plane magnetic field of +1 T, shows reversed contrast. Subsequent imaging (images 6 to 8) was performed in
the indicated loop, with a clear hysteresis effect evident upon comparison of images 6 and 8. All images were
taken under conditions of–0.3V,0.2nA,andT= 5 K and are shown without any additional processing.

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