Nanoscale imaging and control of altermagnetism in MnTe

Abstract

Nanoscale detection and control of the magnetic order underpins a spectrum of condensed-matter research and device functionalities involving magnetism. The key principle involved is the breaking of time-reversal symmetry, which in ferromagnets is generated by an internal magnetization. However, the presence of a net magnetization limits device scalability and compatibility with phases, such as superconductors and topological insulators. Recently, altermagnetism has been proposed as a solution to these restrictions, as it shares the enabling time-reversal-symmetry-breaking characteristic of ferromagnetism, combined with the antiferromagnetic-like vanishing net magnetization1, 2, 3–4. So far, altermagnetic ordering has been inferred from spatially averaged probes4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18–19. Here we demonstrate nanoscale imaging of altermagnetic states from 100-nanometre-scale vortices and domain walls to 10-micrometre-scale single-domain states in manganese telluride (MnTe)2,7,9,14, 15–16,18,20,21. We combine the time-reversal-symmetry-breaking sensitivity of X-ray magnetic circular dichroism¹² with magnetic linear dichroism and photoemission electron microscopy to achieve maps of the local altermagnetic ordering vector. A variety of spin configurations are imposed using microstructure patterning and thermal cycling in magnetic fields. The demonstrated detection and controlled formation of altermagnetic spin configurations paves the way for future experimental studies across the theoretically predicted research landscape of altermagnetism, including unconventional spin-polarization phenomena, the interplay of altermagnetism with superconducting and topological phases, and highly scalable digital and neuromorphic spintronic devices3,14,22, 23–24.

Full text

348 | Nature | Vol 636 | 12 December 2024
Article
Nanoscale imaging and control of
altermagnetism in MnTe
O. J. Amin1,12 ✉, A. Dal Din1,12 ✉, E. Golias2, Y. Niu2, A. Zakharov2, S. C. Fromage1, C. J. B. Fields1,3,
S. L. Heywood1, R. B. Cousins4, F. Maccherozzi3, J. Krempaský5, J. H. Dil5,6, D. Kriegner7,
B. Kiraly1, R. P. Campion1, A. W. Rushforth1, K. W. Edmonds1, S. S. Dhesi3, L. Šmejkal7,8,9,10,
T. Jungwirth1,11 & P. Wadley1 ✉
Nanoscale detection and control of the magnetic order underpins a spectrum of
condensed-matter research and device functionalities involving magnetism.
The key principle involved is the breaking of time-reversal symmetry, which in
ferromagnets is generated by an internal magnetization. However, the presence
of a net magnetization limits device scalability and compatibility with phases,
such as superconductors and topological insulators. Recently, altermagnetism
has been proposed as a solution to these restrictions, as it shares the enabling
time-reversal-symmetry-breaking characteristic of ferromagnetism, combined
with the antiferromagnetic-like vanishing net magnetization1–4. So far, altermagnetic
ordering has been inferred from spatially averaged probes4–19. Here we demonstrate
nanoscale imaging of altermagnetic states from 100-nanometre-scale vortices and
domain walls to 10-micrometre-scale single-domain states in manganese telluride
(MnTe)2,7,9,14–16,18,20,21. We combine the time-reversal-symmetry-breaking sensitivity
of X-ray magnetic circular dichroism12 with magnetic linear dichroism and
photoemission electron microscopy to achieve maps of the local altermagnetic
ordering vector. A variety of spin congurations are imposed using microstructure
patterning and thermal cycling in magnetic elds. The demonstrated detection and
controlled formation of altermagnetic spin congurations paves the way for future
experimental studies across the theoretically predicted research landscape of
altermagnetism, including unconventional spin-polarization phenomena, the
interplay of altermagnetism with superconducting and topological phases, and
highly scalable digital and neuromorphic spintronic devices3,14,22–24.
For condensed-matter physics, the d-wave (or higher even-parity wave)
spin-polarization order in altermagnets represents the sought-after, but
for many decades elusive, counterpart in magnetism of the unconven-
tional d-wave order parameter in high-temperature superconductivity
3
.
For spintronics, altermagnets can merge favourable characteristics of
conventional ferromagnets and antiferromagnets, considered for a
century as mutually exclusive3. They can combine strong spin-current
effects, which underpin reading and writing functionalities in com-
mercial ferromagnetic memory bits, with vanishing net magnetization,
enabling demonstrations of high spatial, temporal and energy scal-
ability in experimental antiferromagnetic bits insensitive to external
magnetic-field perturbations. These examples, as well as the predicted
abundance of altermagnetic materials, ranging from insulators and
semiconductors to metals and superconductors, illustrate the expected
broad impact of this field on modern science and technology3.
So far, however, the unconventional properties of altermagnets have
been experimentally detected using spatially averaging electronic
transport4–11 or spectroscopy probes12–19. Here we report mapping of the
altermagnetic order vector and demonstrate the controlled formation,
from nanoscale to microscale, of a rich landscape of altermagnetic tex-
tures, including vortices, domain walls and domains. We use polarized
X-ray photoemission electron microscopy (PEEM), which is a powerful
tool in magnetism, allowing for, in addition to element specificity and
magnetic sensitivity, concurrent full-field real-space imaging at the
microscale with nanoscale resolution.
The measurements were performed at 100 K on a 30-nm-thick film
of α-MnTe(0001) deposited on an InP(111)A substrate. Manganese
telluride (MnTe) is one of the prototypical materials in altermagnetic
research
2,7,9,12,14–16,18,20
. Below the transition temperature of 310 K, the
magnetic order is within the a–b plane of the film. The unit cell, shown
https://doi.org/10.1038/s41586-024-08234-x
Received: 3 May 2024
Accepted: 16 October 2024
Published online: 11 December 2024
Open access
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1School of Physics and Astronomy, University of Nottingham, Nottingham, UK. 2MAX IV Laboratory, Lund, Sweden. 3Diamond Light Source, Harwell Science and Innovation Campus, Didcot, UK.
4Nanoscale and Microscale Research Centre, University of Nottingham, Nottingham, UK. 5Photon Science Division, Paul Scherrer Institut, Villigen, Switzerland. 6Institut de Physique, École
Polytechnique Fédérale de Lausanne, Lausanne, Switzerland. 7Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic. 8Max Planck Institute for the Physics of Complex
Systems, Dresden, Germany. 9Max Planck Institute for Chemical Physics of Solids, Dresden, Germany. 10Institute of Physics, Johannes Gutenberg University, Mainz, Germany. 11Present address:
Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic. 12These authors contributed equally: O. J. Amin, A. Dal Din. ✉e-mail: oliver.amin@nottingham.ac.uk; alfred.daldin@
nottingham.ac.uk; peter.wadley@nottingham.ac.uk
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Nature | Vol 636 | 12 December 2024 | 349
in Fig.1a, contains two Mn atoms carrying magnetic moments M1 and
M2 of equal magnitude and opposite direction. The two MnTe sublat-
tices containing the opposite magnetic moments are connected by a
spin symmetry combining a spin-space two-fold rotation with a
real-space non-symmorphic six-fold screw-axis rotation ([C
2
∥C
6
t
1/2
]),
and not by translation or inversion2,7. This non-relativistic spin sym-
metry of the crystal structure generates an altermagnetic (g-wave)
spin polarization, which breaks the time-reversal (
T
)-symmetry of the
electronic structure
2
. The perturbative relativistic spin–orbit coupling
generates a weak magnetization along the [0001] axis which, in zero
external magnetic field, reaches a scale of only 10−3 μB per Mn atom,
whereμBis the Bohr magneton2,9,12.
Mapping the local altermagnetic order
Our vector mapping includes the local real-space detection of the ori-
entation of the altermagnetic order vector, L = M
1
− M
2
, with respect
to the MnTe crystal axes in the (0001)-plane by X-ray magnetic linear
dichroism (XMLD)-PEEM, and of the sign of L for a given crystal orien-
tation by including X-ray magnetic circular dichroism (XMCD)-PEEM.
In antiferromagnets with opposite spin sublattices connected by trans-
lation or inversion, the
T
-odd XMCD is excluded by symmetry. In such
cases, only the L axis can be detected by the
T
-even XMLD-PEEM, but
the sign of L remains unresolved
25–30
. Contrary to this, the recent theo-
retical and experimental spectroscopic study of altermagnetic MnTe
has demonstrated the presence of a sizable XMCD, reflecting the
T
-symmetry breaking in the electronic structure by the altermagnetic
g-wave spin polarization
12
. Furthermore, the XMCD spectral shape
owing to L pointing in the (0001) plane is qualitatively distinct from
the XMCD spectral shape owing to a net magnetization M = M
1
+ M
2
along the [0001] axis12. This was demonstrated in ref. 12 by comparing
the measured XMCD spectral shapes at a zero magnetic field and at a
6-T field applied along the [0001] axis. In the former case, M is weak
and the measured spectral shape agrees with the predicted spectral
shape due to L. In the latter case, M is sizable and qualitatively modifies
the spectral shape, again in agreement with theory. We performed
c
a
XMCD XMLD Vector
map
Néel
vector
b
XMLD
XMCD
+L−L
[C2||C6t1/2]
[1100]
Te
Mn
635 640645 650655 660
0
0.5
1.0 Mn L2,3 XAS
XMCD
Energy (eV)
Intensity (a.u.)
g
×50
I
def
I
Fig. 1 | Mapp ing of the alter magneti c order vector i n MnTe. a, Unit cell of
α-MnTe with Mn spin s collinear to the
[11
¯00]
magneti c easy axis. A pplying
T
transform s the left unit ce ll into the right . The unit cells w ith opposite L ve ctor
produce the s ame XMLD but in equivalent XM CD owing to
T
-symmetry
breaking i n altermagne tic MnTe. b, Illustration of the vec tor mapping proc ess.
The colour w heels show the an gular depende nce of the XMCD, thre e-colour
XMLD and si x-colour vector map on t he in-plane L-vector dire ction. Th e XMCD
acts on th e three-colou r XMLD, with light X MCD regions c hanging the co lour
and dark XMCD r egions leavi ng it unchanged t o produce the six-colo ur
L-vector map. In th e XMLD and vecto r map, coloured seg ments indic ate the
magneti c easy axes orie nted along the
⟨1100⟩
crystallographic directions .
c–e, XMCD-PE EM (c), XMLD-PEEM (d) and vector m ap (e) of a 25-μm2 reg ion of
unpatter ned MnTe film. f, An expanded v iew of the boxed reg ion in e in which a
vortex–antivort ex pair is identif ied. The vor tex–antivortex core pos itions are
highlight ed by the magenta–w hite and cyan–white c ircles, respe ctively. The
combinati on of XMLD-PE EM and XMCD-PE EM imaging allows for u nambiguous
determin ation of the helic ity of the swirli ng textures of the a ltermagne tic order
vector, indicate d by the six colours a nd overlaid vector plo t. Scale bars, 1 μ m (c)
and 250 nm (f).g, X-ray absor ption spec trum (XAS), plot ted in black,and XM CD
spectr um, plotted in re d,measuredacross t he Mn L2,3 resonan t edges. The
XMCD spe ctrum isscale d by×50. a.u., arbitrar y units.
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350 | Nature | Vol 636 | 12 December 2024
Article
normal incidence X-ray PEEM, which is the optimum geometry for
measuring both the in-plane Néel axis in the XMLD, and the alterma-
gnetic XMCD. Images are taken at zero external field, where the XMCD
signal owing to the weak relativistic remnant M is negligible compared
with the altermagnetic XMCD owing to
∥⟨1100⟩L
directions in the
(0001) plane12. The latter gives rise to our measured XMCD-PEEM con-
trast as confirmed by its spectral dependence (Methods and Extended
Data Fig.1). In analogy to the d.c. anomalous Hall effect, the XMCD can
be described by the Hall vector,
σσσ=( ,,)
zy
axz
ayx
a
h
, where σ
ij
= −σ
ji
are
the antisymmetric components of the frequency-dependent conduc-
tivity tensor. For L in the (0001) plane of MnTe, h points along the [0001]
axis, that is,
σ σ==0
zy
axz
a
and
σ≠0
yx
a
, with the exception of
⟨2110⟩∥L
axes
where
σ=0
yx
a
by symmetry.
The method of combining the XMCD-PEEM and XMLD-PEEM images
into the vector map of L is illustrated in Fig.1b. As the L vector subtends
the angle, ϕ, in the MnTe (0001) plane relative to the
[1100]
axis, the
XMCD is proportional to cos(3ϕ), with maximum magnitude for
∥L⟨1100⟩
-axes and vanishing for
L∥⟨2110⟩
axes
12
. An XMCD-PEEM image
〈1100 〉
〈1100〉
Before eld cool
After eld cool
After eld cool
Before eld cool
After eld cool
a
bc
de
gf
ih
jkl
Fig. 2 | Controlled formation of altermagnetic vortex nanotextures.
a, Schemat ic of a hexagon micros tructure wi th edges along the
⟨1100⟩
axes.
b,c, XMCD-PEE M map (b) and 6-colo ur vector map (c) of the virg in state of a
2-μm-wide hexa gon. The L-vector axis preferentially aligns parallel to the
hexagon edge s with domain wall s forming at the hexa gon corners. d,e, T he
same as in b and c, r espective ly, but after cooling in a 0.4 -T field applied alon g
the [0001] axis, re sulting in forma tion of only three do main type s with 120°
domain walls s eparating the m at the hexagon cor ners. An anti vortex pair
forms in the ce ntre of the struc ture, with core p ositions indi cated by cyan–
white circles. f–i, The same as in b–e, resp ectively, but for a 4-μm h exagon.
j, Schemat ic of a pair of triang les with edge s along the
⟨1100⟩
axes. k,l, T he same
as in d and e, resp ectively, but for a pair of 4- μm triangle mic rostructure s, with
a single vort ex at the centre of ea ch structure i ndicated by the m agenta–white
circles. S cale bars, 30 nm (a and j),1 μm ( b–i, k and l).
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Nature | Vol 636 | 12 December 2024 | 351
of a 25-μm
2
unpatterned area of MnTe is shown in Fig.1c, where positive
and negative XMCD appear as light and dark contrast, respectively.
The corresponding three-colour XMLD-PEEM map, shown in Fig.1d,
was obtained from a set of PEEM images taken with the X-ray linear
polarization rotated, within the MnTe (0001) plane, in 10° steps from
−90° to +90° relative to the horizontal [
1100
] axis. In this image, the
local L-vector axis is distinguished (by red–green–blue colours), but
the absolute direction remains unresolved. This information is included
by combining the XMCD-PEEM and XMLD-PEEM in a six-colour vector
map, shown in Fig.1e,f, where positive XMCD regions change the colour
(red–green–blue to orange–yellow–purple) of the XMLD-PEEM map
and negative XMCD regions leave it unchanged. The Mn L2,3 X-ray
absorption and altermagnetic XMCD spectra are shown in Fig.1g. The
XMCD-PEEM images are obtained at fixed energy corresponding to
the peak in the altermagnetic XMCD at the L
2
edge. The XMCD contrast
reverses between positive and negative peaks of the XMCD spectrum,
as shown in Extended Data Fig.1, and vanishes at elevated temperatures
where the spontaneous anomalous Hall effect is absent, as shown in
Extended Data Fig.2.
The characteristic vector mapping of L in our unpatterned MnTe
film, shown in Fig.1e,f, shows a rich landscape of (meta)stable tex-
tures akin to earlier reports in compensated magnets26–30. There
exist 60° and 120° domain walls separating domains with L aligned
along the different easy axes, as well as vortex-like textures. High-
lighted in Fig.1f is an example of an altermagnetic vortex–antivortex
pair, analogous to magnetic textures previously detected in anti-
ferromagnets such as CuMnAs (ref. 30). However, only the XMLD-
PEEM was available in the antiferromagnet
30
, that is, only the spatially
varying Néel-vector axis could be identified, similar to our XMLD-
PEEM image in Fig.1d. In our altermagnetic case, we can add the
information from the measured XMCD-PEEM (Fig.1c). This allows
us to plot the vector map of L, as shown in Fig.1e,f. We directly
experimentally determine that the L vector makes a clockwise
rotation by 360° around the first vortex nanotexture, indicated
by the magenta–white circle, whereas the other nanotexture is an
antivortex with an opposite winding of the L vector, indicated by the
cyan–white circle.
Controlled formation of vortices
In Fig.2, we show the designed formation of vortices with predeter-
mined winding and position. We utilize a known edge effect, arising
from an elastic energy term owing to magnetostriction of the film and
film–substrate clamping, which can result in alignment of the L vector
with respect to a patterned edge of a compensated magnet
31–34
. The
edge effect is large enough to overcome the intrinsic magnetocrystal-
line anisotropy over a distance up to about1.7 μm from the edge
(Extended Data Fig.3), where the length scale is governed by the inter-
play of anisotropy, exchange and destressing energies34. We leverage
this by patterning, using electron beam lithography and argon ion
Before eld cool After +0.4-T eld cool After –0.4-T eld cool
XMLD
a
XMCD
bdf
ceg
Fig. 3 | Larg e single- domain alte rmagneti c states con trolled by
micropatterning and field cooling. a–g, Ima ges of an unfille d hexagon shape
with arms , of 10 μm length an d 2 μm width, align ed along the
⟨1100⟩
easy axes,
before fie ld cooling (a–c) and afte r field cooli ng with +0.4 T and −0.4 T (d–g).
a, XMLD-P EEM images of the hex agon before fie ld cooling for three di rections
of the X-ray linear polar ization, ind icated by the doub le-headed ar row in the
top right co rner of each ima ge. The XMLD -PEEM contras t (double-headed
arrows at the ce ntre of each image) app ears as light w hen L is perpendicular to
the X-ray polarizat ion, indicati ng large single spin a xis domains in e ach arm,
parallel to the a rm edge. The 18 0° domain walls c an be seen as thi n, contrastin g
lines, sep arating domain s with opposit e direction of L. b, The c orrespondin g
XMCD-PE EM image reveals the dir ection of L alon g the spin axis par allel to the
hexagon arm s. c, A combinatio n of the XMLD-P EEM and XMCD-P EEM images
produces a si x-colour vector map. T he white arrows sh ow the directio n of L in
the coloured domains. d,e, Repeat of b (d) and c (e) after f ield cooling the
hexagon in a +0.4 -T external m agnetic f ield. f,g, Repeat of d (f) and e ( g) after
field co oling with the op posite-sig n magnetic f ield. Scale b ars, 5 μm.
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352 | Nature | Vol 636 | 12 December 2024
Article
milling, MnTe structures of filled hexagon and triangleshapes with
edges along the
⟨1100⟩
easy axes.
In a virgin state, the interior of the hexagon splits into six wedge-shape
domains with the L-vector axes aligned parallel to the hexagon edges,
and with domain walls extending from the hexagon corners towards
the centre of the structure (Fig.2b,c). Two domains from opposite edges
of the hexagon can have their L vectors parallel (one pair in Fig.2b,c)
or antiparallel (two pairs in Fig.2b,c). In the next step, we select one sign
of the L vector in each domain pair by first warming the structure above
the MnTe magnetic transition temperature, and then cooling it back to
100 K in an external magnetic field of 0.4 T applied along the [0001]
axis. In agreement with earlier spatially averaging measurements of
the anomalous Hall effect and XMCD spectra
7,12
, and explained by the
coupling of the external field to M and of M to L (ref. 9), this procedure
results in the population of only one sign of L in each pair of the
⟨1100⟩
easy-axis domains (Fig.2d,e). The formation of an antivortex pair in the
centre of the hexagon is then required to resolve the total winding angle
of the L vector through 720°. In Fig.2f–i, we show analogous measure-
ments in a larger hexagon. The observed magnetic configurations in
the virgin state and after field cooling are similar to those in Fig.2b–e
near the hexagon edges, whereas in the central region they contain
more complex textures reminiscent of the unpatterned film from Fig.1.
In Fig.2j–l, we show that the field-cooled state of triangle micro-
structures can stabilize isolated Bloch-type vortices, whose chirality
is controlled by the triangle orientation. The different topolog-
ical textures arise owing to the combination of the edge effect align-
ing the Néel vectorparallel to the edge, and the external magnetic
field selecting its sign. As the three edges of the triangle are 120°-
separated, the L vector completes a total winding of 360°, which is
facilitated by the formation of a single Bloch-type vortex.In Fig.2k,l,
mirrored triangle microstructures nucleate vortices with opposite
chirality.
Single-domain states
Moving from the nanoscale vortices to the opposite, large-scale limit
of the real-space control and detection of the altermagnetic states, we
show in Fig.3 a designed formation of single-domain states in MnTe.
Here we focus on a patterned unfilled hexagon shape with 10-μm arm
length and 2-μm arm width and arms along the
⟨1100⟩
easy axes. In the
virgin state, the patterning alone generates large domain states with
the axis of the L vector determined by the crystal direction of the
hexagon arm. This is seen in the XMLD-PEEM images in Fig.3a. The
arms also show narrow 180° domain-wall lines with opposite contrast
to the domains. In Fig.3b, we show the XMCD-PEEM image of the hex-
agon and in Fig.3c, we show the vector map obtained from the com-
bined XMCD and XMLD-PEEM images. Regions within the hexagon
arms where the XMCD-PEEM contrast reverses confirm the presence
1
2
3
–5
0
5
XMCD (a.u.)
00.5 1.
0
–20
0
20
40
60
80
d (μm)
00.5 1.
0
d (
μ
m)
XMLD (a.u.)
XMCD
XMLD
a
c
d
b
w = 134 ± 5 nm
w = 122 ± 13 nm
Fig. 4 | The 18 0° domain-wa ll widths mea sured in the vi rgin state o f an
unfil led easy-axes h exagon with 2-μm -wide bars. a, XM LD-PEEM image of
the unfil led hexagon. Vert ical bars cont aining 180° dom ain walls are shown as
zoomed in in sets. Line pro files acros s the domain walls ar e identifie d by red
boxes labelle d 1–3. b, Average domain-wall profil e (black), measure d in the
XMLD and overla id sech2 fi t line (red). The calcula ted domain-wall w idth is
w = 134 ± 5 nm. c,d, Th e same as in a and b, but me asured in the cor responding
XMCD-PE EM image. The avera ge line profile, f rom dark to light dom ains, is
fitt ed with a tanh fu nction and the c alculated wid th is w = 122 ± 13 nm.
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Nature | Vol 636 | 12 December 2024 | 353
of 180° domain walls separating opposite L-vector domains. Similarly,
at the corners of the hexagon, XMCD-PEEM contrast reversal indicates
60° domain walls separating the L-vector domains in adjacent arms,
and no contrast reversal indicates 120° domain walls.
To turn each arm into a micrometre-scale single-domain state, we
apply the field-cooling procedure as in Fig.2. The removal of the domain
walls and the formation of the single-domain states in the arms is shown
in the XMCD-PEEM image and vector map in Fig.3d,e, respectively. In
Fig.3f,g, we show that reversing the direction of the magnetic field
applied during cooling results in a reversal of the direction of L in each
of the single-domain states. We show, in Extended Data Fig.4, similar
behaviour in a hexagon with 4-μm-wide arms, which represents the
upper limit of device size to achieve single-domain states.
Domain-wall profiles
In Fig.4, we examine the domain-wall profiles in the zero-field-cooled
state of the unfilled hexagon. For the XMLD and XMCD measurements,
the dependence of the signal on distance d across a 180° domain wall
is described by functions sech
2
(2d/w) and tanh(d/w), respectively. The
domain-wall width parameter obtained for the fitted curves in Fig.4b,d
is w = (134 ± 5) nm for the XMLD image and w = (122 ± 13) nm for the
XMCD image. Further analysis of domain-wall profiles in unpatterned
regions is included in Extended Data Fig.5.
Outlook
The vector imaging and controlled formation of altermagnetic con-
figurations ranging from nanoscale vortices and domain walls to
microscale domains, demonstrated in this work, has broad science
and technology implications. It is the basis on which the experimental
field can develop, leveraging the
T
-symmetry-breaking phenomenol-
ogy, vanishing magnetization, ultrafast dynamics, and predicted
compatibility of the altermagnetic order with the full range of conduc-
tion types from insulators to superconductors3. The X-ray dichroism
vector mapping used here can be combined with other imaging tech-
niques, such as X-ray laminography or ptychography, potentially
offering depth sensitivity and even higher spatial resolution
35
. The
ability to image and control the formation of microscale single-domain
states will be highly relevant in the experimental research of funda-
mental electronic-structure properties of altermagnets, including
the predicted unconventional non-relativistic and relativistic
spin-polarization and topological phenomena, or interplay with other
order parameters such as superconductivity3,14,22–24. Similarly, the
controlled spatial uniformity of the altermagnetic states is an impor-
tant step for the experimental research of digital spintronic devices.
Multidomain states with spatially varying magnetic configurations
represent a complementary area that can leverage the unique phe-
nomenology of altermagnets in the research of topological skyrmions,
merons and other magnetic textures, and in the related field of neu-
romorphic spintronic devices. Our demonstration of the vector map-
ping and controlled formation of the altermagnetic textures opens
this experimental research front.
Online content
Any methods, additional references, Nature Portfolio reporting summa-
ries, source data, extended data, supplementary information, acknowl-
edgements, peer review information; details of author contributions
and competing interests; and statements of data and code availability
are available at https://doi.org/10.1038/s41586-024-08234-x.
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2. Šmejkal, L., Sinova, J. & Jungwirth, T. Beyond conventional ferromagnetism and
antiferromagnetism: a phase with nonrelativistic spin and crystal rotation symmetry.
Phys. Rev. X 12, 031042 (2022).
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Article
Methods
Sample fabrication
The 30-nm α-MnTe films used for this study were grown at about700 K
by molecular beam epitaxy (MBE) on InP(111)A substrates. The MnTe
c axis was oriented parallel to the normal of the substrate surface. We
confirmed the correct crystallographic phase and growth orienta-
tion of our MnTe films using X-ray diffraction, shown in Extended Data
Fig.6. Although MBE is a standard technique for growing epitaxial thin
films, we note that sputtering has also been used to grow high-quality
altermagnets, such as CrSb (ref. 17).
In this study, we present X-ray PEEM measurements on two epitaxial
MnTe samples. Sample A (Fig.1) was an uncapped α-MnTe film kept
under ultrahigh-vacuum conditions and transported between the MBE
and the PEEM in a custom-built vacuum suitcase. Sample B (Figs.2 and 3)
was an α-MnTe film capped with 2 nm of aluminium to prevent surface
oxidation of the MnTe layer. We carried out microfabrication on sample B
by coating with a 200-nm layer of polymethyl methacrylate (PMMA)
photoresist then exposing by electron-beam lithography and devel-
oping in methyl isobutyl ketone (MIBK) mixed with isopropyl alcohol
(IPA). Argon ion milling was used to fully remove the MnTe layer in
the exposed areas before any residual resist was removed in acetone.
PEEM imaging and Néel-vector mapping
The X-ray PEEM measurements were performed at the MAXPEEM
beamline of the MAX IV Laboratory synchrotron. The X-ray beam was
incident normal to the sample surface, with the X-ray linear polariza-
tion vector in-plane and the helicity vector out-of-plane. The linear
dichroism asymmetry, XMLD = (I(E
1
) − I(E
2
))/(I(E
1
) + I(E
2
)),where I is
the measured pixel intensity, was calculated between images obtained
at energies, E1 and E2, which correspond to maximum and minimum
points in the magnetic linear dichroism spectra at the Mn L
3
absorp-
tion peak. The circular dichroism asymmetry, XMCD = (I(μ
+
) − I(μ
−
))/
(I(μ+) + I(μ−)), was calculated between images obtained with opposite
helicity polarizations, μ±, for a fixed energy corresponding to a maxi-
mum in the magnetic circular dichroism at the Mn L
2
absorption peak.
The X-ray absorption spectroscopy and XMCD spectra shown in Fig.1g
were obtained at beamline I06-1 of Diamond Light Source, from a dif-
ferent chip cut from the same wafer of MnTe material.
XMLD maps were produced from dichroism asymmetry images
with X-ray linear polarization at angles, θ = −90° to θ = 90°, relative
to the horizontal axis, in steps of 10°. The angular dependence of the
XMLD was fitted with a sin(2(θ + φ)) function, where the phase offset,
φ, encodes information about the local Néel-vector axis. The symme-
try along the axis is broken by the XMCD, which is used as a mask to
produce the vector maps. More details of the vector mapping process
are included in Extended Data Fig.7.
Field cooling
Field-cooling cycles were done within the PEEM chamber at the MAX-
PEEM beamline of the MAX-IV Laboratory synchrotron. Extended Data
Fig.8 shows a photograph of the set-up during field cooling. The sample
was retracted to maximum distance from the microscope objective.
A sample flag plate with attached permanent magnets was brought
into proximity (about300 μm) with the sample surface. We used
1.2-T neodymium–iron–boron magnets (N40EH) with dimensions of
12 mm × 12 mm × 3 mm, stacked in two pairs. We measured the field
strength, normal to the sample surface, at about 300 μm to be 0.45 T.
The sign of the field was reversed by flipping the permanent magnet
flag plate.
To carry out a field-cool cycle, we heated the sample using a fila-
ment on the sample holder to 350 K. This was above the 300-K Néel
temperature of our samples. With the permanent magnet in proximity
to the sample surface, we cooled the sample from 350 K to 100 K using
liquid nitrogen.
Analysis of easy- and hard-axes domains
XMLD- and XMCD-PEEM images of the easy-axes and hard-axes hexa-
gons after zero field cooling are shown in Extended Data Fig.9. The
XMLD-PEEM images were taken with the X-ray linear polarization col-
linear to the horizontal axis of the image. Light and dark contrast cor-
responds to in-plane Néel domains aligned perpendicular and parallel
to the X-ray linear polarization, respectively.
From the regions of single contrast in the XMLD-PEEM images, we
determined that the device patterning aligns the Néel vector parallel
to the edge, and that the 2-μm bar width is narrow enough to induce
large single domains. A comparison between the hexagon patterned
with edges parallel to the MnTe magnetic easy axes (Extended Data
Fig.9a) and hard axes (Extended Data Fig.9c) reveals a similar domain
morphology, from which we conclude that the magnetic anisotropy
induced by the edges is dominant over the intrinsic magnetocrystalline
anisotropy of the MnTe film.
The XMCD-PEEM image of the easy-axes hexagon (Extended Data
Fig.9b) shows clear dark and light domains, which are well correlated
with the domain walls observed in the corresponding XMLD image
(Extended Data Fig.9a). For the hard-axes hexagon, the contrast in the
XMCD image is significantly weaker with a much smaller length scale.
This is as expected as the XMCD is disallowed by symmetry when the
magnetic moments are aligned with the
⟨2110⟩
axes
12
. The distribution
histogram of the XMCD-PEEM image pixel values within the outlined
regions (blue area of Extended Data Fig.9b and red area of Extended
Data Fig.9d) is shown in Extended Data Fig.9e. The small XMCD con-
trast visible in Extended Data Fig.9d most likely arises from small local
variations in the magnetic moment orientation.
Data availability
The data supporting the findings of this study are available from the
corresponding authors upon request.
Acknowledgements We thank MAX IV Laboratory for time on Beamline MaxPEEM under proposal
20231714 (O.J.A.). Research conducted at MAX IV, a Swedish national user facility, is supported
by the Swedish Research Council under contract 2018-07152, the Swedish Governmental
Agency for Innovation Systems under contract 2018-04969, and Formas under contract
2019-02496. We thank Diamond Light Source for the provision of beamtime under proposal
number MM36317. Electron-beam lithography was carried out at the nanoscale and microscale
research centre supported by EPSRC Grant P/M000583/1.O.J.A. acknowledges support from
the Leverhulme Trust Grant ECF-2023-755. D.K. acknowledges the Czech Science Foundation
(Grant 22-22000M) as well as Lumina Quaeruntur fellowship LQ100102201 of the Czech
Academy of Sciences. L.S. acknowledges funding by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation)-TRR288-422213477 (projects A09 and B05).
T.J. acknowledges the Ministry of Education of the Czech Republic GrantCZ.02.01.01/00/
22008/0004594 andERC Advanced Grant101095925. P.W. acknowledges support from the
Royal Society through a University Research Fellowship. The work was supported by the
EPSRC grant EP/V031201/1.
Author contributions O.J.A., A.D.D., K.W.E.,S.S.D., L.S., T.J. and P.W. conceived and led the
project. O.J.A., A.D.D., R.P.C., S.L.H., R.B.C. and A.W.R. contributed to growth and fabrication of
materials and devices. O.J.A., A.D.D., P.W., K.W.E., B.K., C.J.B.F., S.C.F., E.G., Y.N., A.Z., S.S.D. and
F.M. performed the XPEEM experiments and data analysis. O.J.A., A.D.D., P.W., K.W.E ., C.J.B.F.,
S.C.F., S.S.D., D.K., J.K. and J.H.D. performed sample characterization. P.W., T.J., S.S.D., O.J.A.,
A.D.D. and K.W.E. wrote the paper with feedback from all authors.
Competing interests The authors declare no competing interests.
Additional information
Supplementary information The online version contains supplementary material available at
https://doi.org/10.1038/s41586-024-08234-x.
Correspondence and requests for materials should be addressed to O. J. Amin, A. Dal Din or
P. Wadley.
Peer review information Nature thanks Kyung-Jin Lee and the other, anonymous, reviewer(s)
for their contribution to the peer review of this work. Peer reviewer reports are available.
Reprints and permissions information is available at http://www.nature.com/reprints.
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multiplet.
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Article
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Extende d Data Fig. 2 | XM CD-PEEM i mages taken a t low and high
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magneti c contrast in op en-space regi on in proximity to a pa tterned ed ge.
b, The same re gion re-imaged at T=25 0 K, where the XMCD m agnetic con trast
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on a 100 μm Hall bar a t T=150 K and 250 K, res pectively, showing t hat the
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Extende d Data Fig. 3 | Len gth scale o f domains ind uced by patte rned edge s
along mag netic easy a nd hard direc tions. a, XML D-PEEM image, t aken with
X-ray polarizatio n parallel to the hor izontal axis , of an open space re gion of
MnTe in proximity to a patter ned corner ed ge. b, Line profile m easurement s of
the XMLD as a f unction of di stance, d, from th e patterne d edge, parallel to th e
⟨1100⟩
magneti c easy axis (red) and
⟨2110⟩
magneti c hard axis (blue). Soli d lines
are the average lin e profiles me asured within t he boxed regions i n (a), with
the stand ard deviation plot ted as an envelop e. The dashe d vertical line
indicate s the nucleatio n length (1.7 μm) of t he edge-induce d domain, where
the XMLD b ecomes compa rable for easy and har d axis edges. c , d, Same as a, b,
respectively, for the corresponding XMCD-PEEM image.
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Article
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images take n with X-ray linear polari zation (blue d ouble-heade d arrow) 0°,60°,
120° to t he horizontal a xis, respec tively. d, Virgin st ate XMCD-PEE M image.
e-g, Same as a- c, for field-co oled state. h, F ield-cooled s tate XMCD- PEEM
image.
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a, XMLD-P EEM image of vortex-antivor tex. The pos ition of the cyan an d white
circle is at the c entre of the antivo rtex. Ortho gonal line prof iles are taken
following the re d and blue dashed l ines. b, XMLD me asured along the r ed and
blue line prof iles. A sech 2 fit gives t he vortex profi le width as w=132±14 nm
(red) and w=95±15 nm (blue). c, Colour map of in- plane Néel vect or direction .
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phase variation, Δϕ, acros s 60° domain walls ( black) and tanh f it line (red). The
measured d omain wall width i s w = 70 ± 4 nm.
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Article
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text, for X-ray linear pola rization vec tor (blue double -headed arrow) at
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Article
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cycling.
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