Magnetic antiskyrmions above room temperature in tetragonal Heusler materials

19 Pages·2017·13.43 MB·English

by  Ajaya K. Nayak

LEttER
doi:10.1038/nature23466
Magnetic antiskyrmions above room temperature in
tetragonal Heusler materials
ajaya K. Nayak1†, Vivek Kumar2, tianping Ma1, Peter Werner1, Eckhard Pippel1, Roshnee sahoo2, Fran oise Damay3,
ulrich K. Rößler4, Claudia Felser2 & stuart s. P. Parkin1
Magnetic skyrmions are topologically stable, vortex-like objects broken inversion symmetry, in which the skyrmions were discovered
surrounded by chiral boundaries that separate a region of reversed only in a very small range of temperatures and magnetic fields near
magnetization from the surrounding magnetized material1–3. They the magnetic ordering temperature in their respective magnetic phase
are closely related to nanoscopic chiral magnetic domain walls, which diagrams7. The skyrmionic phase was later stabilized over a wider tem-
could be used as memory and logic elements for conventional and perature range in thin plates of certain chiral magnets8,10. Depending
neuromorphic computing applications that go beyond Moore’s law. on the spin rotation, two distinct types of skyrmion have so far been
Of particular interest is ‘racetrack memory’, which is composed observed experimentally, referred to as Bloch and Néel skyrmions
of vertical magnetic nanowires, each accommodating of the order by analogy with the two fundamental types of domain wall. Another
of 100 domain walls, and that shows promise as a solid state, non- distinct type of skyrmion—an antiskyrmion—has been predicted in
volatile memory with exceptional capacity and performance4,5. certain tetragonal materials with acentric crystal structures and D
2d
Its performance is derived from the very high speeds (up to one symmetry16–18, but has not yet been found as either an isolated object
kilometre per second) at which chiral domain walls can be moved or in a lattice. Antiskyrmions reported to exist19 in engineered Co/Pt
with nanosecond current pulses in synthetic antiferromagnet multilayers are instead achiral spin textures without skyrmionic prop-
racetracks. Because skyrmions are essentially composed of a pair erties. Similarly, complex spin textures in the B20 compound MnGe are
of chiral domain walls closed in on themselves, but are, in principle, simulated to be arrays of skyrmions and antiskyrmions20, but the sym-
more stable to perturbations than the component domain walls metry of this compound intrinsically precludes antiskyrmions. Here we
themselves, they are attractive for use in spintronic applications, report, using Lorentz transmission electron microscopy, the observa-
notably racetrack memory. Stabilization of skyrmions has generally tion of antiskyrmions in the Mn–Pt–Sn inverse Heusler compound.
been achieved in systems with broken inversion symmetry, in Figure 1a–c illustrates the spin textures of the three classes of
which the asymmetric Dzyaloshinskii–Moriya interaction modifies skyrmion: Bloch skyrmion, antiskyrmion and Néel skyrmion. The
the uniform magnetic state to a swirling state6,7. Depending on corresponding helimagnetic structures from which these vari-
the crystal symmetry, two distinct types of skyrmions have been ous skyrmionic states emerge are shown schematically in Fig. 1d–f.
observed experimentally, namely, Bloch7,8 and Néel skyrmions9. Chiral magnets with the cubic B20 crystal structure and tetrahedral
Here we present the experimental manifestation of another type symmetry exhibit Bloch-type skyrmions7,8,10–12. When imaged using
of skyrmion—the magnetic antiskyrmion—in acentric tetragonal Lorentz transmission electron microscopy (LTEM), such skyrmions
Heusler compounds with D crystal symmetry. Antiskyrmions are should appear as a ring-like pattern (Fig. 1g). Unlike Bloch skyrmi-
2d
characterized by boundary walls that have alternating Bloch and Néel ons, a cross-sectional view of the spin arrangement in a Néel skyrmion
type as one traces around the boundary. A spiral magnetic ground- reveals a cycloid, whereby spins rotate in a plane along the direction
state, which propagates in the tetragonal basal plane, is transformed of propagation (Fig. 1f). In the case of Néel skyrmions viewed using
into an antiskyrmion lattice state under magnetic fields applied LTEM, the deflected electrons make a closed loop; hence, no intensity
along the tetragonal axis over a wide range of temperatures. Direct modulation is expected, as depicted in the simulated LTEM pattern in
imaging by Lorentz transmission electron microscopy shows field- Fig. 1i (lower panel). Polar magnets with C symmetry9 and multi-
nv
stabilized antiskyrmion lattices and isolated antiskyrmions from layer films with interfacial Dzyaloshinskii–Moriya interaction host Néel
100 kelvin to well beyond room temperature, and zero-field skyrmions14,15,21–23. Schematics of cross-sections along four different
metastable antiskyrmions at low temperatures. These results directions reveal both helicoid and cycloid spin propagations in an
enlarge the family of magnetic skyrmions and pave the way to the antiskyrmion (Fig. 1b, e). This rotation of the spin is expected to result
engineering of complex bespoke designed skyrmionic structures. in a distinct LTEM pattern. In the present spin notation, the transmitted
Skyrmions—topologically stable vortex-like objects with swirling electron beam will converge towards the centre of the antiskyrmion in
spin configurations—have recently been observed in several bulk the vertical direction, whereas it will diverge in the horizontal direction.
materials and thin films6–15. They were predicted to exist in extended Therefore, a single antiskyrmion is expected to form two bright and two
magnets with acentric crystalline structures more than 25 years ago16. dark lobes in an LTEM image; this is verified by the simulated LTEM
In these magnets, the magnetization, twisted by relativistic spin–orbit pattern shown in the lower panel in Fig. 1h.
coupling in the magnetic ground state, is usually a one-dimensional Because antiskyrmions break the cylindrical symmetry and have a
helix—a Dzyaloshinskii spiral. The pitch of the helix, which also quadrupolar moment of magnetostatic charges, their properties may
determines the size of the skyrmions, is governed by the ratio of the differ from those of Bloch and Néel skyrmions. In a broader perspec-
Heisenberg exchange constant to the magnitude of the Dzyaloshinskii– tive, acentric magnets bearing skyrmions are of interest for spintronic
Moriya interaction6. Evidence of the existence of skyrmions emerged applications. Heusler compounds (XYZ, where X, Y are transition met-
2
from experiments on a small class of chiral magnetic systems with als and Z is a main-group element) are well known for their potential
1Max Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany. 2Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Strasse 40, 01187 Dresden, Germany.
3Laboratoire Léon Brillouin, CEA-CNRS, CEA Saclay, 91191 Gif-sur-Yvette, France. 4IFW Dresden, PO Box 270116, 01171 Dresden, Germany. †Present address: School of Physical Sciences,
National Institute of Science Education and Research (NISER) Bhubaneswar, Jatni 752050, India.
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reSeArCH letter
a b c
d e f
g h i
(cid:126) (cid:126) (cid:126) (cid:126) (cid:126) (cid:126)
Figure 1 | Skyrmions and antiskyrmions. a–c, Spin textures of a Bloch arrows) and the Lorentz deflections of the transmitted electrons (red
skyrmion (a), an antiskyrmion (b) and a Néel skyrmion (c). In all cases arrows) is shown in the upper panel. The corresponding simulated LTEM
the magnetization is double-twisted along both the azimuthal and radial pattern of the deflected electrons is shown in the lower panel. h, The
directions. d, f, Cross-sections of Bloch (d) and Néel (f) skyrmions along in-plane spin arrangement of an antiskyrmion is shown in the upper
the radial directions indicated by the dashed rectangles in a and c. A panel. In this case the spins deflect towards the centre in the vertical
transverse helix with an anticlockwise spin rotation is evident for the Block direction, whereas the deflection is outward in the horizontal direction.
skyrmion, whereas the magnetization is anticlockwise-rotated in a spin The corresponding simulated LTEM pattern with two bright and two dark
cycloid for the Néel skyrmion. e, For an antiskyrmion, the magnetization lobes is shown in the lower panel. i, In-plane spin arrangement of a Néel
rotates both as a transverse helix (within the black dashed rectangles in skyrmion (upper panel) and the corresponding simulated LTEM pattern
b) and as a cycloid (within the red dotted rectangles in b). g, A schematic (lower panel).
of the in-plane arrangement of the moments in a Bloch skyrmion (green
a b c
2.0 Mn1.4PtSn (1) (2)
Mn Pt Pd Sn
a unit) 1.5 1.4 0.9 0.1 [100] [010]
ul
m
er for 1.0 (112) 500 nm c
M ( p(cid:80)B0.5 (101) (10(030)4)(20(02)11) 004 020 400 220 040 a
300400
0.020 320(cid:84) (°)40 50 100200T (K)
0 100 200 300 400
T (K) 5 nm–1 [100] 10 nm–1 [001] [100] 1 nm
d e f
M contrast 135 nm
E
LT
0 100 200 300 400
Distance (nm)
[010] [010]
[010]
[100] [100]
[100]
500 nm 500 nm 500 nm
Figure 2 | Structural and magnetic properties. a, Temperature scanning transmission electron microscopy image taken on the
dependence of low-field (0.1 T) magnetization, M(T), for Mn1.4PtSn (filled [100]-oriented platelet. The left inset shows an enlarged view of the atomic
circles) and Mn1.4Pt0.9Pd0.1Sn (filled squares). Powder neutron diffraction arrangement, whereas the right inset displays the crystal structure of the
measurements at different temperatures for Mn1.4PtSn are shown in the Mn–Pt(Pd)–Sn system. d, Focused LTEM image showing the twinned
inset. Here μB and θ represent the Bohr magneton and the scattering microstructure, as in c, at 300 K and 0 T. e, f, Room-temperature (300 K)
angle, respectively. b, TEM image of Mn1.4Pt0.9Pd0.1Sn showing a twinned under-focused LTEM images taken at zero field (e) and in a field of
microstructure (upper panel). The platelet labelled ‘(1)’ has a crystal 0.24 T (f), demonstrating the existence of helical magnetic structure and
orientation of [100], whereas that labelled ‘(2)’ has a [001] orientation. antiskyrmions, respectively. The inset of e depicts the sinusoidal change in
Selected-area diffraction patterns taken on platelets (1) and (2) are shown the LTEM contrast with distance. The scanned region is marked by a white
in the left and right lower panels, respectively. c, High-resolution line in the main panel.
562 | NatuRE | VOL 548 | 31 august 2017
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letter reSeArCH
a b c d
M contrast 1.0
LTE 50 100 150
l (nm) 0.5 n
o
ati
[110][010] 0 netiz
g
a
–0.5 M
[010] M contrast [010] [010] 150 nm –1.0
[100] LTE 40l(8n0m1)20160 [100] 50 nm [100] 150 nm
e [001] H f g h
(cid:84)
[110]
[110]
500 nm 500 nm 500 nm 500 nm
i j k l
[010] [010] [010] [010]
[100] 500 nm [100] 500 nm [100] 500 nm [100] 500 nm
Figure 3 | Room-temperature antiskyrmions in Mn1.4Pt0.9Pd0.1Sn. antiskyrmions. d, Theoretical simulation of an antiskyrmion lattice in an
a, Under-focused LTEM image of a single antiskyrmion at 300 K and with oblique field. The colour represents the magnetization component normal
a field (0.29 T) applied along [001]. The lower and upper insets show the to the sample plane. e–h, Under-focused LTEM images of antiskyrmions
intensity profiles of the in-plane magnetization along [010] and [100], taken at 300 K and in H = 0.24 T with rotation angles (θ; as shown
respectively. The corresponding scanned regions are marked by lines. schematically in the inset of e) of θ = 20° (e), θ = 13° (f), θ = 8° (g) and
I, distance. b, Over-focused LTEM image of the single antiskyrmion θ = −5 ° (h). i–l, Under-focused LTEM images of antiskyrmions taken at
shown in a. c, Under-focused LTEM image showing a hexagonal lattice of fields applied along [001] of 0.29 T (i), 0.33 T (j), 0.24 T (k) and 0.49 T (l).
applications in spintronics, especially in tunnelling-based devices24. of acentric cubic helimagnets, in which the applied field favours
Mn YZ-based magnetic Heusler compounds are ideal for the design conical helices propagating along the field direction7,8.
2
of tetragonal materials with flexible magnetic configurations25. The The magnetization versus temperature (M(T)) data measured in a
subset of Heusler compounds that have a tetragonal inverse structure field of 0.1 T for Mn PtSn and Mn Pt Pd Sn are plotted in Fig. 2a.
1.4 1.4 0.9 0.1
also have the correct symmetry (D ) for hosting antiskyrmion phases26. The parent compound Mn PtSn has a Curie temperature T of about
2d 1.4 C
Moreover, these materials can have very high magnetic ordering tem- 400 K and a second transition to a state with higher magnetization
peratures (well above room temperature), so antiskyrmions could be occurs at about 160 K. This second transition suggests that the change
stabilized over an extended temperature range. From a technological in temperature leads to a reorientation of the moments of the Mn sub-
perspective, the tetragonal symmetry ensures that the antiskyrmions are lattices. Neutron diffraction studies on powdered samples of Mn PtSn
1.4
located in one plane (the basal plane), thereby simplifying their control. demonstrate a considerable change in the intensity of the (101) and
A non-collinear spin configuration was recently observed26 in the (004) ferromagnetic peaks around the spin-reorientation transition,
acentric tetragonal Heusler compound Mn RhSn. Here we focus on signifying a change in the magnetic structure at this temperature (inset
2
the inverse tetragonal Heusler compound Mn Pt Pd Sn. In this of Fig. 2a). Mn Pt Pd Sn has a similar T to that of Mn PtSn;
1.4 0.9 0.1 1.4 0.9 0.1 C 1.4
compound, the direct magnetic exchange sets the basic magnetic however, the low-temperature spin-reorientation transition is decreased
configuration of the Mn moments in the unit cell; there are two to approximately 125 K in the Pd-doped sample.
distinct Mn sublattices, each with their own magnetic moment. The A bright-field transmission electron microscopy (TEM) study
Dzyaloshinskii–Moriya interaction twists this basic magnetic moment shows a martensitic-like twinned microstructure for Mn Pt Pd Sn
1.4 0.9 0.1
configuration along one given propagation direction, thereby giving (Fig. 2b, upper panel). Most interestingly, the adjacent twin platelets ori-
rise to a long-range helimagnetic structure (Extended Data Fig. 2). ent at an angle of almost 90° to each other: the platelet labelled ‘(1)’ has
However, because the crystal structure of this material belongs to a a [100] orientation, whereas that labelled ‘(2)’ has a [001] orientation.
crystal class with D point symmetry, the twisting of the ferromag- The corresponding selected-area diffraction patterns from each indi-
2d
netic order takes place only in the tetragonal basal plane. For this vidual platelet are shown in the lower panels of Fig. 2b. The high-res-
symmetry, theoretical considerations have shown that a field applied olution scanning transmission electron microscopy image taken on
close to the tetragonal c axis stabilizes an antiskyrmion lattice state the [100]-oriented platelet shows alternating bright and dark atoms,
because there is no competing conical spiral state in the magnetic corresponding to the columns with Mn–Pt(Pd) and Mn–Sn atoms,
phase diagram26. This behaviour is completely different from that respectively (Fig. 2c). An enlarged view of the atomic arrangements and
31 august 2017 | VOL 548 | NatuRE | 563
© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
reSeArCH letter
a b c
[010]
[010] [010]
[100] 500 nm [100] 500 nm [100] 150 nm
d e f
450
Magnetization 00001.....24680 11233 05005 000002 KKKKKK Field (T) 0000....0246 skx skHx ++ FsPkx H Lattice spacing (nm) 223340505000000 Antiskyrmion density–2(m)μ1234500000 0.2 F ie10l.0d3 0(T )K 0.4 200 K 335000 KK
150 150 K 250 K 368 K
0.0
0.0 0.2 0.4 0.6 0.8 1.0 100 150 200 250 300 350 400 0.15 0.20 0.25 0.30 0.35 0.40 0.45
Field (T) Temperature (K) Field (T)
Figure 4 | Temperature dependence of antiskyrmions and phase diagram. stars), a mixed helical and antiskyrmion phase (‘H + skx’), a field-polarized
a–c, Under-focused LTEM images taken at 350 K in a field of 0.22 T (a), state (‘FP’; open stars) and a mixed antiskyrmion and field-polarized
100 K and 0.33 T (b) and 100 K and zero field (c). A single antiskyrmion phase (‘skx + FP’). The various symbols and corresponding coloured
in zero field is shown inside the dashed circle. d, Magnetic isotherms at regions indicate distinct magnetic phase regions, as indicated in the figure.
different temperatures for Mn1.4Pt0.9Pd0.1Sn. The data are normalized by f, Field-dependent antiskyrmion–antiskyrmion lattice spacing at various
dividing by the magnetization at 1 T. e, Field–temperature phase diagrams temperatures. The error bars correspond to the standard deviation of the
for Mn1.4PtSn derived from the LTEM measurements with the field applied spacing distribution. The inset shows the variation in the antiskyrmion
along [001]. The phase diagram represents different phases at different fields density with magnetic field.
and temperatures: a helical phase (‘H’; asterisks), antiskyrmions (‘skx’; filled
the crystal structure of the system are shown in the left and right insets remains locked to the tetragonal axis, and that the antiskyrmions are
of Fig. 2c, respectively. Overviews of the sample taken in focused and consequently distorted, with the perfectly radial core shifting from the
under-focused LTEM modes and at zero magnetic field are depicted in centres of the cells of the hexagonal densely packed lattice.
Fig. 2d and e, respectively. Although the focused LTEM image does not A theoretical simulation of the antiskyrmion lattice in a small oblique
show any change in contrast in comparison to the TEM image in Fig. 2c, field is shown in Fig. 3d, illustrating the skewed appearance of the
additional contrast modulation is observed for the [001]-oriented antiskyrmions. This effect occurs because the in-plane component
platelet in the under-focused LTEM image. These stripe-like features of the magnetic field favours and broadens one edge of the circulat-
correspond to a helimagnetic structure propagating in the basal plane ing magnetization along the field, at the cost of the opposite edge. As
of the tetragonal crystal structure. The sinusoidal variation of the LTEM can be seen in Fig. 3e, when a magnetic field was applied at an angle
contrast with the helix period of about 135 nm is shown in the inset of of about 20 degrees to [001] by rotating the sample along [110], the
Fig. 2e. Applying a magnetic field along [001] modifies the helimag- antiskyrmions become distorted. We find that the antiskyrmions are
netic stripes into antiskyrmions (Fig. 2f). stable up to this maximum possible tilt angle. They appear as ellipti-
To examine the nature of the antiskyrmions in our system in detail, cal shapes in the LTEM images, with the centre of the antiskyrmions
an under-focused LTEM image of a single antiskyrmion taken at a field having moved off-centre with application of the in-plane field. This
of 0.29 T applied parallel to the [001] direction is displayed in Fig. 3a. distortion results from a combination of the tilting of the antiskyr-
Most interestingly, it exhibits two bright spots and two dark spots along mions themselves and the contributions to the LTEM images from
the [010] and [100] directions, respectively. The modulation of the con- tilted moments. Micromagnetic simulations show that antiskyrmions
trast can be discerned from the appearance of two peaks with a trough are stable to large tilted magnetic fields (see Methods). The appear-
in the middle of the line profile taken along [010] (lower inset) and ance of double-skyrmion-like features results from the projection of
two troughs with a peak in the middle of the line profile taken along the antiskyrmion tubes that are oriented obliquely to the illuminating
[100] (upper inset). These results agree well with the expected LTEM electron beam and to the applied field. As the rotation angle decreases
pattern shown in Fig. 1h, signifying the presence of antiskyrmions. A (Fig. 3e–g), the original quadrupole-like internal magnetization dis-
complete reversal of the contrast is observed in the over-focused LTEM tribution of the antiskyrmions is revealed. Strong bright spots can be
image (Fig. 3b). The formation of a hexagonal lattice of antiskyrmions seen at the upper half of the antiskyrmions for a rotation angle of θ = 8°
is depicted in Fig. 3c. A slight distortion of the lattice along [010] might (Fig. 3g), whereas they appear at the lower half for θ = − 5° (Fig. 3h).
be related to the presence of a small amount of in-plane field due to a In both cases, the antiskyrmion lattice exhibits a large distortion along
slight misorientation (by approximately ±3 °) of the sample away from [010]. Nearly symmetric bright and dark spots in an almost hexagonal
the exact [001] direction. At low in-plane fields, the distortion is mostly lattice can be seen in Fig. 3i, for an applied field of 0.29 T along [001]
in the [010] direction as the helix propagates along [100]. Owing to (within the ± 3° limit). A small increase in the field to 0.33 T perturbs
the tetragonal D symmetry, we expect that the antiskyrmion lattices the regular arrangement of the antiskyrmions in the lattice (Fig. 3j).
2d
undergo characteristic distortions in oblique fields, because their axis This field corresponds to the stability limit of the equilibrium lattice
564 | NatuRE | VOL 548 | 31 august 2017
© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
letter reSeArCH
phase. Owing to their topological stability, a large number of antiskyr- the crystal structure, and thereby the magnetocrystalline anisotropy and
mions remain as metastable excitations in the homogeneous field- the magnetization. To find antiskyrmions in other systems, we propose
polarized collinear state. For even higher fields, antiskyrmions disap- the exploration of tetragonal inverse structures that have the correct
pear from the relatively thinner region of the sample and are stabilized symmetry (D ) for stabilizing antiskyrmion rather than skyrmion
2d
only in the thicker region (Fig. 3k). Finally, the antiskyrmion lattice phases. The presence of more than one magnetic sublattice in Heusler
evolves into an array of single antiskyrmions, which disappear for fields compounds makes it possible to tune the total magnetic moment to
above 0.49 T at room temperature (Fig. 3l). zero25, potentially giving rise to antiferromagnetic antiskyrmions.
Because Mn Pt Pd Sn has a T of about 400 K, we expect it to Such skyrmions are predicted to move in a straight line in response to
1.4 0.9 0.1 C
display antiskyrmions up to 400 K. Under-focused LTEM patterns an applied current, in contrast to the curved motion of conventional
taken at 350 K in the presence of a field of 0.22 T show a lattice of skyrmions30. The quadrupole moment of the magnetostatic charge dis-
antiskyrmions (Fig. 4a). At higher temperatures, the antiskyrmion tribution in the antiskyrmions of acentric magnets enables their motion
phase can be stabilized at lower fields. At temperatures below the to be controlled by applying inhomogeneous magnetic fields.
spin-reorientation transition of the material, it was difficult to nucle-
ate an antiskyrmion lattice by applying a magnetic field, even at an Online Content Methods, along with any additional Extended Data display items and
Source Data, are available in the online version of the paper; references unique to
angle to [001] after cooling the sample in zero field (see Methods).
these sections appear only in the online paper.
Figure 4b shows antiskyrmions at 100 K for a field of 0.33 T applied
along [001]. By reducing the field to zero, each antiskyrmion can be
received 4 February; accepted 21 June 2017.
seen with two symmetric bright spots along [010], whereas the black
Published online 23 August 2017.
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(see Methods, Extended Data Fig. 3), the observed effect is unlikely to magnetic nanostructures. Nat. Nanotechnol. 11, 449–454 (2016).
arise from the intrinsic hysteretic behaviour of the material. The role 22. Woo, S. et al. Observation of room-temperature magnetic skyrmions and their
of disorder has also been discussed in the context of achieving stable current-driven dynamics in ultrathin metallic ferromagnets. Nat. Mater. 15,
zero-field skyrmions in a cubic magnet using a field-cooling process28. 501–506 (2016).
23. Jiang, W. et al. Blowing magnetic skyrmion bubbles. Science 349, 283–286
However, the stabilization of antiskyrmions at lower fields, without (2015).
any field-cooling or quenching29 processes, makes our system distinct 24. Jeong, J. et al. Termination layer compensated tunnelling magnetoresistance in
ferrimagnetic Heusler compounds with high perpendicular magnetic
from other skyrmion systems.
anisotropy. Nat. Commun. 7, 10276 (2016).
Although we have demonstrated the formation of antiskyrmions in 25. Nayak, A. K. et al. Design of compensated ferrimagnetic Heusler alloys for giant
Mn Pt Pd Sn, we also found evidence of antiskyrmions in Mn PtSn. tunable exchange bias. Nat. Mater. 14, 679–684 (2015).
1.4 0.9 0.1 1.4
26. Meshcheriakova, O. et al. Large noncollinearity and spin reorientation in the
We anticipate that the tunable nature of Heusler compounds will enable
novel Mn2RhSn Heusler magnet. Phys. Rev. Lett. 113, 087203 (2014).
the formation of a wide range of skyrmionic structures, by varying the 27. Li, Y. F. et al. Robust formation of skyrmions and topological Hall effect
number of valence electrons, the spin–orbit coupling, the symmetry of anomaly in epitaxial thin films of MnSi. Phys. Rev. Lett. 110, 117202 (2013).
31 august 2017 | VOL 548 | NatuRE | 565
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reSeArCH letter
28. Karube, K. et al. Robust metastable skyrmions and their triangular–square and P.W. The bulk materials were synthesized by V.K. and A.K.N. F.D. and
lattice structural transition in a high-temperature chiral magnet. Nat. Mater. R.S. carried out the neutron diffraction study. A.K.N. and R.S. performed
15, 1237–1242 (2016). the magnetic measurements. T.M. performed the micromagnetic and LTEM
29. Oike, H. et al. Interplay between topological and thermodynamic stability in a image simulations. A.K.N. and S.S.P.P. wrote the manuscript with substantial
metastable magnetic skyrmion lattice. Nat. Phys. 12, 62–66 (2016). contributions from all authors.
30. Barker, J. & Tretiakov, O. A. Static and dynamical properties of
antiferromagnetic skyrmions in the presence of applied current and Author Information Reprints and permissions information is available at
temperature. Phys. Rev. Lett. 116, 147203 (2016). www.nature.com/reprints. The authors declare no competing financial
interests. Readers are welcome to comment on the online version of the
Acknowledgements We thank H. Blumtritt and N. Schammelt for their help in paper. Publisher’s note: Springer Nature remains neutral with regard
preparing TEM lamellae for this study. This work was financially supported by to jurisdictional claims in published maps and institutional affiliations.
the ERC Advanced Grant No. 670166 “SORBET” and the ERC Advanced Grant Correspondence and requests for materials should be addressed to
No. 291472 “Idea Heusler”. S.S.P.P. ([email protected]).
Author Contributions A.K.N., C.F. and S.S.P.P. conceived the original idea for reviewer Information Nature thanks A. Hirohata and the other anonymous
the project. A.K.N. performed the LTEM investigations with the help of E.P. reviewer(s) for their contribution to the peer review of this work.
566 | NatuRE | VOL 548 | 31 august 2017
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letter reSeArCH
MethOds Magnetic characterization. M(H) loops measured at 2 K for Mn1.4PtSn and
Key requirements for the application of skyrmions in spintronics are a material Mn1.4Pt0.9Pd0.1Sn exhibit nearly the same saturation moment of about 4.5μB (μB is
with above-room-temperature magnetic ordering, stability of skyrmion states over the Bohr magneton; Extended Data Fig. 3), and both samples display soft magnetic
an extended temperature range and the ability to integrate films of such materials behaviour. These samples show slightly different hysteretic behaviour at 300 K,
into magnetic devices. Of especial importance is the control of magnetic anisot- above the spin-reorientation transition. At 300 K, the saturation magnetization is
ropy, which can influence the competition between a spiral magnetic state, skyr- obtained at lower fields than at 2 K.
mionic textures and collinear spin structures. Here we focused on the inverse LTEM. The under-focused LTEM images taken at 200 K and various magnetic
tetragonal Heusler compound Mn1.4Pt0.9Pd0.1Sn, in which Pt provides substantial fields are shown in Extended Data Fig. 4a–f. At this temperature, a field-polarized
spin–orbit coupling and thus a Dzyaloshinskii–Moriya interaction. We find that state is obtained for an applied magnetic field of 0.7 T and an array of antiskyrmi-
Mn2PtSn cannot be stabilized without the introduction of substantial Mn vacan- ons at 0.6 T. A lattice of antiskyrmions is found at 0.32 T. By reducing the field to
cies. Single-phase Mn1.4PtSn that crystallizes in an acentric tetragonal structure zero, metastable antiskyrmions and helical stripes are found to coexist.
with space group I42m can be obtained with uniformly distributed Mn vacancies Extended Data Fig. 4g–i shows under-focused LTEM images taken at 368 K at
exclusively in the Mn–Pt NaCl-type substructure. In addition, we found that a various magnetic fields. As mentioned in the main text, the antiskyrmion lattice is
small amount of Pd substituted in place of Pt enhances the tetragonality. stabilized by applying a field at an angle of 10°–20° to the [001] direction. We find
Polycrystalline ingots of Mn1.4PtSn and Mn1.4Pt0.9Pd0.1Sn were prepared by that with increasing temperature the stabilization of an antiskyrmion lattice can
arc-melting stoichiometric amounts of the constituent elements in a high-purity be obtained with a lower tilt. At 368 K, the stabilization of an antiskyrmion lattice
argon atmosphere. The as-prepared ingots were annealed for one week at 1,073 K is obtained at an even lower tilt angle of about 5°. This finding indicates that by
and subsequently quenched in an ice–water mixture. The samples were structur- approaching TC it should be possible to obtain the antiskyrmion lattice by applying
ally characterized by X-ray powder diffraction (XRD) using a Cu Kα source. The the field directly parallel to [001].
homogeneity and composition of the sample were analysed by scanning electron Extended Data Fig. 5 shows the image taken in zero magnetic field after the
microscopy (SEM), including energy-dispersive X-ray spectroscopy (EDS) and antiskyrmion lattice was stabilized in the sample at room temperature at a finite tilt
optical microscopy. The magnetization measurements were carried out in a vibrat- angle in a magnetic field. The tilt angle was then reduced to zero without chang-
ing sample SQUID magnetometer (MPMS 3, Quantum Design). Powder neutron ing the field. The sample was then cooled to 100 K in the same field and, after
diffraction studies were performed using a two-axis diffractometer equipped with stabilizing the temperature, the field was reduced to zero. We found a metastable
a vertical focusing pyrolytic graphite monochromator and a cold neutron guide. antiskyrmion phase with the presence of some helimagnetic stripes.
The sample was encapsulated in a vanadium crucible. Simulation of different types of skyrmion and their LTEM images. Here, we
Specimens for transmission electron microscopy (TEM) were prepared from describe the method used to simulate LTEM images of different types of skyrmion.
the polycrystalline Mn1.4Pt0.9Pd0.1Sn ingots by Ga focused ion beam (FIB) milling. The method is based on a Fourier approach31–34. The magnetization configuration
The thickness of the TEM specimen is about 100 nm in the flat, thicker region of of different types of skyrmion is calculated using the micromagnetic simulation
the sample and about 50–70 nm at the thinner end. The TEM investigations were code OOMMF35. The exchange energy and Dzyaloshinskii–Moriya interaction are
carried out using a FEI TITAN G2 80-300 microscope equipped with a Lorentz taken into account to simulate the skyrmions. The Dzyaloshinskii–Moriya interac-
lens, operated at 300 kV. For the antiskyrmion investigations the TEM observation tion included within the OOMMF code is modified according to the symmetry of
was made in Lorentz mode. The vertical magnetic field was controlled by applying the host compound36, thereby enabling calculation for different types of skyrmion.
currents in the objective lens. The in-plane magnetic field was applied by tilting Typical magnetization configurations of Bloch skyrmions, antiskyrmions and Néel
the sample using a double tilt sample holder. In our thin crystalline foils, ‘bend- skyrmions in the skyrmion lattice phase are shown in Extended Data Fig. 6.
contours’ occur when observing the TEM samples at the pole position, which The magnetization configurations are then used to calculate the induced phase
disturbs the visibility of antiskyrmions. Therefore, the sample was tilted slightly change in LTEM. In LTEM, the electrons experience a Lorentz force because of the
(about 3°) along the [001] direction for LTEM imaging. Variable-temperature local magnetization, which induces a phase change:
LTEM investigations were performed using a GATAN double tilt liquid nitrogen
π
sample holder. At all temperatures (except 100 K), the antiskyrmion phase was ϕ=− ∫Azdz
better nucleated when the field was applied at some angle to [001] (10°–20°). Once Φ0
the antiskyrmion lattice phase was stabilized with an oblique field, the sample was
rotated to apply the field along the [001] direction, where a stable antiskyrmion where Φ0 is the magnetic flux quantum and Az is the z component of the magnetic
lattice was formed. As the temperature approaches TC (368 K), the antiskyrmion vector potential. The magnetic phase component in reciprocal space is
phase can be nucleated for fields applied closer to [001] (about 5°). At 100 K,
tshame LpTleE aMt r oimomag etesm wpeerrea ttaukreen a ta aft efirn tihtee t ailnt tainskgyler mini oa nm laagttniceet iwc faise lsdta. bTihliez etidlt i ann tghlee ϕ(cid:31)=iπμΦ00Mstm∼xkk2xy−+mk∼2yykx
was then reduced to zero without changing the field. The sample was then cooled
troed 1u0c0e Kd itno tzheer os a(more i nficerlde aasnedd, taof toebr tsatainb iali fziienldg -tphoe ltaermizpeder sattautree), itnh ed iffifeeldre wnta ss tselposw tloy w∼here μ∼0 is the permeability of free space, Ms is the saturation magnetization,
mx and my are the x and y components of the unit vector of magnetization in
record the LTEM images.
reciprocal space, kx and ky are the x and y components of the reciprocal lattice
Structural characterization. The phase purity of the samples was studied with
k-vector, and t is the thickness of the specimen. Entering the back focal plane of
the help of XRD measurements at room temperature. As shown in Extended Data
the objective lens, the electron disturbance is
Fig. 1, the Rietveld refinement of the experimental pattern clearly shows that
M(nunm1.4bPetrS 1n2 c1r)y. sTtahlel irzeefsin inem anen atc reensutrlitcs itnet lraatgtiocne apla srtarmucettuerrse owf iat h= s 6p.a3c5e3 8g r±o u0.p0 0I0422 mÅ g(kx,ky)=∬exp[iϕ(x,y)]exp[−2iπ(yky+xkx)]dxdy
and c = 12.2142 ± 0.0007 Å with c/a = 1.9223. In our sample, Mn atoms fully
occupy the 8i and 2b positions and partially occupy the 4d position, the 4c and 4e where kx and ky are the x and y components of the spatial frequency, and are directly
positions are occupied by Pt, and the second 8i position is occupied by Sn. Hence, proportional to displacements within the back focal plane. As the electrons propa-
a complete Mn vacancy is found at position 2a. In the case of Mn1.4Pt0.9Pd0.1Sn, we gate from the back focal plane, we need to consider the ‘transfer function’:
suppose that the small number of Pd atoms statistically replace the Pt atoms in
ba o=t h6. 3t4h3e5 34 ±c 0a.n0d00 419e Åp,o cs =it 1io2n.2s4.0 A44 ±sm 0a.0l0l 0c3h7a Ån ganed i nc/ al a=t t1i.c9e2 9p6a wraams foeutenrds fotor t(kx,ky)=A(kx,ky)exp−2iπCsλ3(k42x+k2y)−Δzλ(k22x+k2y)
Mn1.4Pt0.9Pd0.1Sn.
A schematic of the alignment of the magnetic moments in our system is shown
in Extended Data Fig. 2. Mn atoms that occupy three different sublattices are shown where the λ is the electron wavelength, A(kx, ky) is the pupil function, Cs is the
spherical aberration of the objective lens, and Δz is the defocus distance. So, finally,
as Mn2b, Mn4d and Mn8c. Mn8c, which exhibits a larger magnetic moment,
we calculate the inverse Fourier transform to obtain the LTEM image intensity:
orients antiparallel to the relatively smaller moments of Mn2b and Mn4d
(Extended Data Fig. 2b). This results in an net effective ferromagnetic moment 2
(Extended Data Fig. 2c). The Dzyaloshinskii–Moriya interaction modifies the I(x′,y′)= ∬g(kx,ky)t(kx,ky)exp[−2iπ(y′ky+x′kx)]dkxdky
basic magnetic structure to a helimagnetic state that propagates along the a axis
(Extended Data Fig. 2d, upper panel) or a spin cycloid along [110] (Extended Data The calculated LTEM images at different defocus distances Δ z are shown in
Fig. 2d, lower panel). Extended Data Fig. 7.
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reSeArCH letter
To obtain the ground-state antiskyrmion phase, we first use high temperatures The variation of the antiskyrmion size with magnetic field and temperature is
to overcome local energy barriers. We then relax the magnetization while the shown in Extended Data Fig. 11a. In this case, the size corresponds to the diameter
temperature is gradually decreased to zero. By using this method, we calculate of the antiskyrmions when the field is applied along the [001] direction. The size
the evolution of the antiskyrmion phase under different fields. The parameters remains almost the same over a large temperature and magnetic field range. At very
used here are: exchange stiffness A = 1.2 × 10−10 J m−1, Dzyaloshinskii–Moriya high temperatures, we observe a considerable decrease in the antiskyrmion size.
interaction D = 6 × 10−3 J m−2 and saturation magnetization Ms = 445 kA m−1. The mean angle of the antiskyrmion lattice is shown in Extended Data Fig. 11b.
The antiskyrmion phases under different perpendicular field strengths are shown A mean angle of 60° indicates a hexagonal lattice. The inset shows the standard
in Extended Data Fig. 8a–f. In our simulations we use the experimentally mea- deviation of the antiskyrmion lattice angle, which reflects the degree of uniformity
sured value of Ms. We estimate the values of A and D from our experimental results of the hexagonal lattice. At the critical field for the transition of the hexagonal
for the size of the antiskyrmions and the magnetic fields over which the anti- lattice to the spin-polarized state, the standard deviation increases, indicating the
skyrmions are observed. Because we have not considered the quadrupole moment breakdown of the antiskyrmion lattice.
of the antiskyrmions here, the values of A and D used in the simulations are Data availability. The data that support the findings of this study are available
approximate. from the corresponding author on request.
We also used OOMMF to simulate the antiskyrmion lattice under an oblique
field. The field amplitude is kept at 0.24 T and the field is tilted by 20°, 10°,
31. Chapman, J. N. The investigation of magnetic domain structures in thin foils by
0°, − 10° or − 20° with respect to the [110] axis, as shown in Extended Data electron microscopy. J. Phys. D 17, 623–647 (1984).
Fig. 9a–e. Initially, the state at zero tilt angle in 0.24 T was calculated by field cooling 32. Beleggia, M. et al. A Fourier approach to fields and electron optical phase-shifts
from high temperature, as discussed above. This state was then used as the initial calculations. Ultramicroscopy 96, 93–103 (2003).
state for the simulation at a tilt angle of − 20° at zero temperature. The tilt angle 33. Beleggia, M. et al. Quantitative study of magnetic field distribution by electron
holography and micromagnetic simulations. Appl. Phys. Lett. 83, 1435–1437
was subsequently changed in 2° increments using the initial state from the previous
(2003).
tilt angle at zero temperature. 34. Walton, S. K. et al. MALTS: A tool to simulate Lorentz Transmission Electron
Antiskyrmion lattice analysis. We study the density, size, lattice length and Microscopy from micromagnetic simulations. IEEE Trans. Magn. 49,
lattice angle of the antiskyrmion lattice for various temperatures and magnetic 4795–4800 (2013).
fields. Extended Data Fig. 10 shows one example of such an image analysis. The 35. Donahue, M. J. & Porter, D. G. OOMMF User’s Guide, version 1.0, Interagency
Report NISTIR 6376 (National Institute of Standards and Technology,
red circles show the position and size of the antiskyrmions. The green lines that
Gaithersburg, 1999); available at http://math.nist.gov/oommf.
connect nearby antiskyrmions indicate a hexagonal lattice. The blue numbers are 36. Rohart, S. & Thiaville, A. Skyrmion confinement in ultrathin film nanostructures
the lengths of the green lines (in nanometres). The red numbers indicate the angles in the presence of Dzyaloshinskii–Moriya interaction. Phys. Rev. B 88, 184422
between the green lines (in degrees). (2013).
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letter reSeArCH
Extended Data Figure 1 | Structural characterization at room temperature. a, b, Room-temperature XRD pattern with Rietveld refinement for Mn1.4PtSn (a)
and Mn1.4Pt0.9Pd0.1Sn (b). The circles represent the experimental data (IExpt), the red line corresponds to a simulation (Ical) and the blue line shows the
difference (‘Diff’) between the two.
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reSeArCH letter
Extended Data Figure 2 | Schematic representations of crystal and magnetic sublattices. c, Effective ferromagnetic moment in the unit cell.
magnetic structures. a, Crystal structure of Mn1.4Pt0.9Pd0.1Sn with d, Helical modification of the spin arrangement due to Dzyaloshinskii–
different atoms shown in different colours. Pd randomly occupies the Moriya interaction along [100] (upper panel) and spin cycloid along [110]
Pt position. b, Ferrimagnetic arrangement of Mn atoms from different (lower panel).
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