# Time-dependent multistate switching of topological antiferromagnetic order
in Mn3Sn

Gunasheel Kauwtilyaa Krishnaswamy  Department of Materials, ETH Zurich, 8093
Zurich, Switzerland  Giacomo Sala  Department of Materials, ETH Zurich, 8093
Zurich, Switzerland  Benjamin Jacot  Department of Materials, ETH Zurich, 8093
Zurich, Switzerland  Charles-Henri Lambert  Department of Materials, ETH
Zurich, 8093 Zurich, Switzerland  Richard Schlitz  Department of Materials,
ETH Zurich, 8093 Zurich, Switzerland  Marta D. Rossell  Electron Microscopy
Center, Empa, Swiss Federal Laboratories for Material Science and Technology,
Dübendorf, Switzerland  Paul Nöel  Department of Materials, ETH Zurich, 8093
Zurich, Switzerland  Pietro Gambardella  Department of Materials, ETH Zurich,
8093 Zurich, Switzerland

###### Abstract

The manipulation of antiferromagnetic order by means of spin-orbit torques
opens unprecedented opportunities to exploit the dynamics of antiferromagnets
in spintronic devices. In this work, we investigate the current-induced
switching of the magnetic octupole vector in the Weyl antiferromagnet Mn3Sn as
a function of pulse shape, magnetic field, temperature, and time. We find that
the switching behavior can be either bistable or tristable depending on the
temporal structure of the current pulses. Time-resolved Hall effect
measurements performed during the current pulsing reveal that Mn3Sn switching
proceeds via a two-step demagnetization-remagnetization process caused by
self-heating over a timescale of tens of ns followed by cooling in the
presence of spin-orbit torques. Single-shot switching measurements with 50 ps
temporal resolution indicate that chiral spin rotation is either damped or
incoherent in polycrystalline Mn3Sn. Our results shed light on the switching
dynamics of Mn3Sn and prove the existence of extrinsic limits on its switching
speed.

##  I Introduction

Electric control of magnetic order in antiferromagnets has raised prospects
for realizing high-speed and high-density magnetoelectric devices using
materials with zero net magnetization [1, 2, 3, 4, 5, 6]. The switching of the
order parameter in antiferromagnets is achieved by either injecting spin
currents from an adjacent heavy metal layer or current-induced spin-orbit
torques intrinsic to noncentrosymmetric crystals [7]. Electrical readout,
however, is problematic because of the small magnetoresistance [8], resistive
artefacts [9, 10, 11], and absence of Hall effect in most conventional
antiferromagnets. This problem can be elegantly solved by turning to
noncollinear antiferromagnets, which combine topologically nontrivial
electronic properties with chiral magnetic order. In these systems, the broken
time-reversal symmetry and large Berry curvature in momentum space give rise
to strong anomalous Hall effect (AHE) [12, 13] and magneto-optical responses
[14, 15, 16, 17], similar to ferromagnets but in the absence of significant
magnetization. Theoretical work shows that these materials can even exhibit a
large tunneling magnetoresistance [18], whereas the emergence of exotic
phenomena such as the chiral anomaly [19] and magnetic spin Hall effect [20,
21, 22, 23] makes them a very interesting playground for investigating the
interplay of topology, electron transport, and magnetism [24, 25, 26].

A prime candidate of this material class is Mn3Sn, a hexagonal Weyl metal in
which the Mn atoms form kagome lattice planes stacked along the $c$-axis with
an inverse-triangular spin structure and all the spins oriented in-plane [27,
28, 29, 12, 30]. The non-collinear antiferromagnetic order is best described
by the magnetic octupole moment g of the six Mn spins that reside in two
stacked inverted triangles on adjacent kagome layers [green arrow in Fig. 1
(a)]. Magnetic anisotropy defines six possible orientations of the g-vector in
the kagome plane [Fig. 1 (b)]. The almost perfect 120∘ non-collinear spin
alignment is slightly distorted by magnetic anisotropy, which leads to a weak
ferromagnetic moment of $\sim 0.002$ $\mu_{B}$ per Mn atom in the direction of
the g-vector. This conveniently allows for the manipulation of
antiferromagnetic order by external magnetic fields, whereas the large AHE and
anomalous Nernst effect (ANE) of Mn3Sn provide direct information on the
orientation of g [31, 32, 33, 34]. Importantly for applications, the
topological properties of Mn3Sn emerge in both polycrystalline and epitaxial
thin films [35, 36, 37, 33, 38, 39, 34, 40].

Figure 1: (a) Cross-section of the Mn3Sn/Pt bilayer. The inverted triangular
spin structure is shown in the center: white and black arrows represent the Mn
spins and the green arrow the octupole vector g. (b) Possible orientations of
g and corresponding AHE signal. (c) Microscope image of a Hall bar device and
(d) Hall cross used for switching and time-resolved measurements. (e) AHE of
Mn3Sn/Pt as a function of magnetic field along $z$ and (f) current density for
10 $\mu$s-long pulses and $B_{\rm x}=+200$ mT. Figure 2: (a) Switching loops
of Mn3Sn/Pt as a function of pulse voltage with rise and fall time increasing
from left to right. (b) Corresponding pulse shape. (c) Schematic showing the
$-z$, $+z$ and intermediate states and the possible orientations of the
g-vector in each state.

Pioneering work on Mn3Sn/heavy metal bilayers has demonstrated switching of
antiferromagnetic order by current-induced spin-orbit torques [41, 42, 43,
44]. In these experiments, a change of the AHE as a function of current
reveals the reorientation of g in crystal grains with $c$-axis oriented in-
plane. Switching only occurs in the presence of a symmetry-breaking magnetic
field collinear with the current, with the final state determined by the
relative orientation of current and field and by the sign of the spin Hall
angle in the heavy metal [41, 42, 45]. These observations suggest a switching
mechanism very similar to ferromagnet/heavy metal bilayers [46, 47, 7]. Within
this picture, however, different magnetization dynamics can be expected
depending on whether the torques rotate the moments in or out of the kagome
plane [48, 49, 41, 43]. New effects such as chiral spin rotation have been
proposed, whereby the Mn moments undergo continuous rotation in the kagome
plane with time periods in the tens of ns [48, 43, 50]. Thus far, however,
switching experiments relied on electrical pulses with pulse duration of 100
ms, which yield no information about the fast switching dynamics expected of
antiferromagnets.

In this work, we explore the chiral switching dynamics of Mn3Sn/Pt bilayers.
We observe that the switching behavior varies characteristically with the
pulse length and shape: conventional bistable switching between $\pm z$ states
is observed for pulses with fall times longer than 400 ns whereas tristable
switching is observed for pulses with shorter fall times, leading to a
demagnetized state with zero AHE. By studying the switching dependence on the
temporal shape of the pulses, applied field, temperature, and time we show
that the reversal of the g-vector occurs through two phases, namely current-
induced partial demagnetization lasting several ns followed by cooling in the
presence of spin-orbit torques at the end of a current pulse. This mechanism
is similar to the setting of exchange bias during field cooling in coupled
antiferromagnetic/ferromagnetic systems [51]. However, it differs from the
thermally-activated switching observed in collinear ferromagnets [52] and
antiferromagnets [3], in which Joule heating reduces the magnetic anisotropy
energy barrier while the sample remains magnetic. Time-resolved measurements
during pulsing indicate that the reversal of chiral antiferromagnetic order is
incoherent and that chiral spin rotation is either damped or averaged out in
polycrystalline Mn3Sn. Our measurements also set a limit on the reversal speed
attainable by the interplay of current-induced heating and spin-orbit torques
in chiral antiferromagnets.

##  II Methods

Our samples are polycrystalline Mn3Sn(50 nm)/Pt(5 nm) bilayers grown by
magnetron sputtering patterned into 3 to 6-$\mu$m-wide Hall bars and Hall
crosses [Fig. 1 (c,d)] [53]. High-resolution transmission electron microscopy
reveals the presence of columnar grains of about 250 nm width, different
orientations and excellent crystalline order [53]. Measurements of the
longitudinal ($R_{\rm xx}$) and transverse Hall resistance ($R_{\rm xy}$) are
consistent with previous work on similar samples [14, 41, 42, 45, 50, 53]. We
used a quasi-static pulse-probe protocol for characterizing the switching
properties as a function of pulse shape and field [46] and performed the time-
resolved measurements of the AHE using the split-pulse technique described in
Ref. 54. In the pulse-probe method we inject a current pulse of up to 20 mA to
induce switching followed by an alternate current of 1 mA, which allows for
probing the first and second harmonic contributions to Rxy that are
proportional to the AHE and ANE, respectively [53, 55]. In the time-resolved
measurements, we probe the change in AHE during a current pulse with about 50
ps temporal resolution [54]. Hall bars are used for quasi-static switching and
Hall crosses for the time-resolved measurements. Given the structure of our
samples, the AHE (ANE) reflects the out-of-plane (in-plane) component of g
averaged over different crystal grains in the region sensed by the Hall
resistance [53, 35, 31, 38]. Comparative switching measurements on Mn3Sn/W and
W/Mn3Sn/Pt samples are reported in Ref. 53.

##  III Results

###  III.1 Multistate switching determined by the pulse fall time

Figure 3: Field dependence of the current-induced switching for (a) long and
(b) short fall time pulses of 10 $\mu$s length. Switching amplitude $\Delta
R_{\rm xy}$ between $\pm 2$V (black squares) and $\pm 20$V (purple circles) as
a function of $B_{\rm x}$ for (c) long and (d) short fall time.

Figures 1 (e) and (f) show the field- and current-induced switching of the
g-vector, respectively, as measured by the AHE. In agreement with previous
reports [35, 41, 42], we observe switching of about 30% of the total AHE upon
injecting 10-$\mu$s-long current pulses with a fall time $\tau=420$ ns. This
bistable behavior is interpreted as g switching between the $+z$ and $-z$
states. Surprisingly, however, we find that gradually reducing $\tau$ to below
100 ns changes the switching from bistable to tristable, leading to the
appearance of states with high and low AHE at intermediate current values and
zero AHE at high current [Fig. 2]. Because the pulse length is constant, the
gradual shift of the endpoint $R_{\rm xy}$ in Fig. 2 (a) demonstrates that the
fall time determines the switching regime. Importantly, the magnetic state set
by the current pulse and magnetic field remains constant after the pulse. The
occurrence of multistate switching has been reported before in Mn3Sn [43], but
the role of the transient dynamic effects that determine the final orientation
of the g-vector has not been elucidated. These effects can be of two types,
thermal, due to Joule heating, and magnetic due to spin-orbit torques.

###  III.2 Switching as a function of in-plane field

To exclude a purely thermal origin of the switching, we study its dependence
on the external in-plane magnetic field $B_{\rm x}$. Figures 3 (a) and (b)
show the current-induced switching loops for 10-$\mu$s-long pulses with
$\tau=35$ ns and $420$ ns, respectively, for increasing values of $B_{\rm x}$.
The reversal of the switching direction upon inversion of $B_{\rm x}$
indicates that switching is due to spin-orbit torques in the entire range of
fall times. We also find that the switching amplitude between $+z$ and $-z$
states, $\Delta R_{\rm xy}=R_{\rm xy}(2~{}{\rm V})-R_{\rm xy}(-2~{}\rm{V})$,
increases up to $B_{\rm x}\approx 100$ mT, consistently with previous reports
[41, 42, 45, 35, 43] and the standard model of spin-orbit torque switching in
ferromagnets [46, 7]. However, $\Delta R_{\rm xy}$ decreases in the high field
limit [black squares in Fig. 3 (c,d)], indicating that another mechanism comes
into play. We also note that the offset of $R_{\rm xy}$ and the sign of the
switching amplitude $\Delta R_{\rm xy}(\pm\rm 20V)$ in the short pulse regime
are very sensitive to the presence of an out-of-plane external field [53].

###  III.3 Switching by current-induced heating and cooling in the presence of
spin-orbit torques

To understand the role played by heating we measured the AHE as a function of
temperature [Fig. 4 (a,b)]. The AHE vanishes at $T_{\rm N}=390$ K, close to
the Néel temperature of bulk Mn3Sn (420 K) [30, 43]. The longitudinal
resistance $R_{\rm xx}$ has a nonlinear temperature behavior as it is a
mixture of the resistance due to Pt and Mn3Sn. Measuring $R_{\rm xx}$ as a
function of current allows us to gauge the extent of Joule heating, which
shows that the sample temperature reaches $T_{\rm N}$ for pulse currents
larger than 14 mA (16 V) [53]. We thus propose a model to explain the
multistate switching behaviour in which the interplay of temperature and spin-
orbit torques is governed by $\tau$. Consider a generic voltage pulse that
heats up the sample and provides a current density $j$ to exert a torque, as
shown in Fig. 4 (c). As the pulse starts, the temperature increases
quadratically with the current at a rate determined by the longest between the
pulse rise time and the heat diffusion time. For pulses longer than a few tens
of ns, the sample temperature approaches $T_{\rm N}$, leading to a
demagnetized state until cool down begins at the end of the pulse.
Deterministic switching to a final state $+z$ or $-z$ can be achieved only if
$j$ is larger than a critical current density $j_{\rm c}$ as the temperature
has dropped below $T_{\rm N}$, i.e., for long $\tau$. If, on the other hand,
the current drops abruptly below $j_{\rm c}$ when the temperature is still
close to $T_{\rm N}$, the Mn3Sn grains freeze in a mixed multidomain
configuration, which leads to the intermediate state with no AHE for short
$\tau$. Our simultaneous measurements of the AHE and ANE show that this
intermediate state consists of domains along $\pm z$, which give a net zero
AHE, and grains that are oriented along $+x$ and $-x$ for $B_{\rm x}>0$ and
$B_{\rm x}<0$, respectively [53]. The fraction of grains oriented along $\pm
x$ during cool down increases with $B_{\rm x}$, which explains the non-
monotonic field dependence of the switching amplitude in Fig. 3. Thus, by
gradually modifying $\tau$, we tune the fraction of grains that switch and
those that remain demagnetized at the end of the pulse.

Figure 4: (a) AHE switching as a function of pulse voltage at different
temperatures for 10-$\mu$s-long pulses. (b) Temperature dependence of $R_{\rm
xy}$ (bottom panel) and $R_{\rm xx}$ (middle panel) of Mn3Sn/Pt. $R_{\rm xx}$
vs direct current and calibrated temperature (top panel). (c) Schematic
current pulse with temperature profile indicated by the red shading. (d) Step-
wise switching sequences: $R_{\rm xy}$ vs pulse amplitude starting from $\pm
18$ V in steps of 2 V (black, red), 4 V (blue) and 8 V (green).

This model also explains why the $\pm z$ final states with large/low AHE can
be reached starting from the intermediate state with zero AHE upon reducing
the pulse voltage in small incremental steps, as seen in Fig. 2 even for short
$\tau$. Figure 4 (d) shows $R_{\rm xy}$ recorded by sweeping the pulse
amplitude from +18 V to -18 V and back in steps of 2 V (black dots). Starting
from the intermediate state obtained by pulsing at +18 V with $\tau=35$ ns,
the AHE changes progressively to the low state upon reducing the pulse
amplitude. However, if the pulse amplitude is abruptly decreased from +18 to
+10 V, no switching occurs (green dots). The type of switching thus depends on
the initial state and on the decremental step size, which is different from
the change of switching amplitude as a function of current reported for
bistable switching in Ref. 41. Our observation is consistent with different
Mn3Sn grains having a distribution of $T_{\rm N}$ due to their varying sizes,
which are selectively switched to the $\pm z$ final states upon decreasing the
pulse amplitude from the intermediate state. This is essentially a step-wise
version of the long fall time scenario described above.

Overall, our results show that the switching of antiferromagnetic order in
Mn3Sn occurs due to heat-assisted demagnetization followed by reorientation of
the g-vector induced by spin-orbit torques during cool down. The fall time of
the current pulses determines the final magnetic configuration of the Mn3Sn
domains. Additionally, switching loops measured for 21 V pulses of decreasing
length, from 50 to 5 ns, evidence that the switching amplitude vanishes in the
limit of short pulses [Fig. 5 (a)]. These findings show that switching of
antiferromagnetic order in Mn3Sn by spin-orbit torques has a composite
temporal dependence and a different dynamics relative to ferromagnets [54, 56]
and collinear antiferromagnets [3, 57, 58].

###  III.4 Time-resolved measurements

To determine the transient dynamics, we performed time-resolved measurements
of $R_{\rm xy}$ during the current pulses using the setup shown in Fig. 5 (b).
The temporal evolution of the AHE voltage $V_{\rm H}$ during the switching
process is determined by taking the difference of the Hall voltage trace
measured during switching relative to a reference trace in the absence of
switching [54]. Figure 5 (c) shows the average of 20 differential time traces
of $V_{\rm H}$ taken during pulses with +21 V amplitude, 75 ns duration and
$\tau=0.3$ ns, separated by a 1 s delay. The decrease (increase) of $V_{\rm
H}$ following the onset of the pulse at $t=0$ for $B_{\rm x}=+250$ mT ($-250$
mT) reflects the decrease (increase) of the AHE from the initial $-z$ ($+z$)
state to the intermediate state with no AHE. It takes about 35 ns for $\lvert
V_{\rm H}\rvert$ to reduce to 0, after which no further changes of $V_{\rm H}$
are observed until the end of the pulse. Measurements performed for 20 ns-long
pulses as a function of $B_{\rm x}$, reported in Fig. 5 (d), further reveal
that the amplitude of the transient switching signal scales with $B_{\rm x}$
and that the timescale over which $\lvert V_{\rm H}\rvert$ reduces to 0 is
independent of $B_{\rm x}$. We thus associate the decrease of $\lvert V_{\rm
H}\rvert$ with the time it takes for the device to reach a temperature close
to $T_{\rm N}$, in line with the switching mechanism proposed above. This time
depends only on $j$ and not on $B_{\rm x}$, which shows that the switching
speed of Mn3Sn is ultimately limited by the heating rate.

Recent studies propose a coherent chiral spin reversal mechanism in
noncollinear antiferromagnets where the g-vector continuously rotates above a
given current density threshold [48, 43, 50]. The rotation period is estimated
in a range of 1-30 ns, depending on the current density. Inirect evidence for
this effect has been reported both in epitaxial and polycrystalline thin films
[43, 50].

The experimental evidence for such a mechanism, however, lacks insight into
the time-dependent dynamics that is the hallmark of coherent switching. Our
time-resolved traces shown in Fig. 5 (c,d) evidence a monotonic decrease of
$\lvert V_{\rm H}\rvert$ that is not consistent with reproducible oscillations
of $R_{\rm xy}$ due to chiral spin rotation. Because these traces are averaged
over several pulses, they do not provide information on stochastic rotations.
To investigate the occurrence of chiral spin rotation during individual
current pulses, we have thus measured single-shot time traces of $V_{\rm H}$.
Representative examples of such traces are shown in Fig. 5 (e,f) for a series
of 20-ns-long current pulses. Our analysis does not reveal evidence of
periodic oscillations of $V_{\rm H}$ consistent with chiral spin rotation
during single-shot pulses.

Figure 5: (a) Current-induced switching loops for different pulse lengths,
$\tau=0.3$ ns and $B_{\rm x}=-250$ mT. (b) Schematic of the time-resolved AHE
measurements. (c) Differential switching time traces averaged over 20
consecutive +21 V pulses with $B_{\rm x}=\pm 250$ mT. The pulses are 75 ns
long starting at $t=0$. (d) Differential switching time traces averaged over
100 consecutive 20-ns-long voltage pulses of amplitude +21 V vs $B_{\rm x}$.
The gray trace at the top shows the pulse shape. (e) Single shot differential
switching traces for 20-ns-long voltage pulses at $B_{\rm x}=-180$ mT and (f)
+180 mT. The black lines are moving averages over $1.5$ ns.

The absence of oscillations can be ascribed to different factors. First,
chiral spin rotation requires an injected spin current with polarization
parallel to the $c$-axis [43]. Given the polycrystalline nature of our
samples, we estimate to have a measurable amount of such grains in our Hall
crosses [53, 43, 50]. On the other hand, chiral spin rotation may take place
in different grains with different phase factors, averaging to zero in the
total Hall signal. Acording to simulations, however, these coherent effects
should result in visible oscillations also in polycrystalline samples [50].
Another possibility is that the rotation is too fast to be resolved by our
measurements, which have a temporal resolution of about 50 ps [54]. The
current density in the time-resolved measurements is $1.3\times 10^{7}$ A/cm2
when averaged over the entire thickness of Mn3Sn/Pt and about $6.2\times
10^{7}$ A/cm2 in Pt, as estimated using a parallel resistor model. The
rotation frequency corresponding to this current is 1.7 GHz [43], which is
within our time resolution. The continuous decrease of the AHE signal thus
indicates that any oscillation, if present, is strongly damped and that heat-
induced demagnetization dominates over coherent effects.

##  IV Conclusions

In summary, our work shows that the switching of chiral antiferromagnetic
order in Mn3Sn/Pt is incoherent and determined by the timed interplay of heat
and spin-orbit torques. Both effects are current-induced but heating up to
$T_{\rm N}$ occurs on a timescale of tens of ns whereas the injection of a
spin current from Pt closely follows the temporal profile of the current
pulses. Switching proceeds via a two-step demagnetization-remagnetization
process, whereby the final orientation of the g-vector is deterministic
between $\pm z$ states only if the sample cools down in the presence of a spin
current larger than a critical value. Our results provide insight into the
switching timescale and dynamics of topological antiferromagnets, showing that
it is different from both ferromagnets and collinear antiferromagnets and
limited by the sample heating rate. Additionally, this work shows that time-
resolved Hall effect measurements provide a viable method to investigate the
current-induced dynamics of antiferromagnetic order in topological materials.

_Acknowledgements_. This research was partially supported by the Swiss
National Science Foundation (Grants No. 200020-200465 and PZ00P2-179944).
During the resubmission of this manuscript we became aware of related work
reporting the multistate switching of Mn3Sn [59].

##  V References

## References

  * Wadley  _et al._ [2016] P. Wadley, B. Howells, J. Železný, C. Andrews, V. Hills, R. P. Campion, V. Novák, K. Olejník, F. Maccherozzi, S. S. Dhesi, S. Y. Martin, T. Wagner, J. Wunderlich, F. Freimuth, Y. Mokrousov, J. Kuneš, J. S. Chauhan, M. J. Grzybowski, A. W. Rushforth, K. Edmond, B. L. Gallagher, and T. Jungwirth, Spintronics: Electrical switching of an antiferromagnet, Science 351, 587 (2016).
  * Olejník  _et al._ [2017] K. Olejník, V. Schuler, X. Marti, V. Novák, Z. Kašpar, P. Wadley, R. P. Campion, K. W. Edmonds, B. L. Gallagher, J. Garces, M. Baumgartner, P. Gambardella, and T. Jungwirth, Antiferromagnetic CuMnAs multi-level memory cell with microelectronic compatibility, Nature Communications 8, 15434 (2017).
  * Meinert  _et al._ [2018] M. Meinert, D. Graulich, and T. Matalla-Wagner, Electrical Switching of Antiferromagnetic Mn2Au and the Role of Thermal Activation, Physical Review Applied 9, 064040 (2018).
  * DuttaGupta  _et al._ [2020] S. DuttaGupta, A. Kurenkov, O. A. Tretiakov, G. Krishnaswamy, G. Sala, V. Krizakova, F. Maccherozzi, S. S. Dhesi, P. Gambardella, S. Fukami, and H. Ohno, Spin-orbit torque switching of an antiferromagnetic metallic heterostructure, Nature Communications 11, 5715 (2020).
  * Siddiqui  _et al._ [2020] S. A. Siddiqui, J. Sklenar, K. Kang, M. J. Gilbert, A. Schleife, N. Mason, and A. Hoffmann, Metallic antiferromagnets, Journal of Applied Physics 128, 040904 (2020).
  * Arpaci  _et al._ [2021] S. Arpaci, V. Lopez-Dominguez, J. Shi, L. Sánchez-Tejerina, F. Garesci, C. Wang, X. Yan, V. K. Sangwan, M. A. Grayson, M. C. Hersam, G. Finocchio, and P. Khalili Amiri, Observation of current-induced switching in non-collinear antiferromagnetic IrMn3 by differential voltage measurements, Nature Communications 12, 3828 (2021), arXiv:2105.02277 .
  * Manchon  _et al._ [2019] A. Manchon, J. Železný, I. M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello, and P. Gambardella, Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems, Reviews of Modern Physics 91, 035004 (2019).
  * Marti  _et al._ [2014] X. Marti, I. Fina, C. Frontera, J. Liu, P. Wadley, Q. He, R. J. Paull, J. D. Clarkson, J. Kudrnovský, I. Turek, J. Kuneš, D. Yi, J.-H. Chu, C. T. Nelson, L. You, E. Arenholz, S. Salahuddin, J. Fontcuberta, T. Jungwirth, and R. Ramesh, Room-temperature antiferromagnetic memory resistor, Nature Materials 13, 367 (2014).
  * Chiang  _et al._ [2019] C. C. Chiang, S. Y. Huang, D. Qu, P. H. Wu, and C. L. Chien, Absence of Evidence of Electrical Switching of the Antiferromagnetic Néel Vector, Physical Review Letters 123, 227203 (2019).
  * Jacot  _et al._ [2020] B. J. Jacot, G. Krishnaswamy, G. Sala, C. O. Avci, S. Vélez, P. Gambardella, and C.-H. Lambert, Systematic study of nonmagnetic resistance changes due to electrical pulsing in single metal layers and metal/antiferromagnet bilayers, Journal of Applied Physics 128, 173902 (2020).
  * Matalla-Wagner  _et al._ [2020] T. Matalla-Wagner, J.-M. Schmalhorst, G. Reiss, N. Tamura, and M. Meinert, Resistive contribution in electrical-switching experiments with antiferromagnets, Physical Review Research 2, 033077 (2020).
  * Nakatsuji  _et al._ [2015] S. Nakatsuji, N. Kiyohara, and T. Higo, Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature, Nature 527, 212 (2015).
  * Nayak  _et al._ [2016] A. K. Nayak, J. E. Fischer, Y. Sun, B. Yan, J. Karel, A. C. Komarek, C. Shekhar, N. Kumar, W. Schnelle, J. Kübler, C. Felser, and S. S. P. Parkin, Large anomalous Hall effect driven by a nonvanishing Berry curvature in the noncolinear antiferromagnet Mn 3 Ge, Science Advances 2, e1501870 (2016), arXiv:1511.03128 .
  * Higo  _et al._ [2018a] T. Higo, D. Qu, Y. Li, C. L. Chien, Y. Otani, and S. Nakatsuji, Anomalous Hall effect in thin films of the Weyl antiferromagnet Mn3Sn, Applied Physics Letters 113, 1 (2018a), arXiv:1810.11599 .
  * Balk  _et al._ [2019] A. L. Balk, N. H. Sung, S. M. Thomas, P. F. Rosa, R. D. McDonald, J. D. Thompson, E. D. Bauer, F. Ronning, and S. A. Crooker, Comparing the anomalous Hall effect and the magneto-optical Kerr effect through antiferromagnetic phase transitions in Mn3Sn, Applied Physics Letters 114, 032401 (2019), arXiv:1901.07642 .
  * Zhao  _et al._ [2021] H. C. Zhao, H. Xia, S. Hu, Y. Y. Lv, Z. R. Zhao, J. He, E. Liang, G. Ni, L. Y. Chen, X. P. Qiu, S. M. Zhou, and H. B. Zhao, Large ultrafast-modulated Voigt effect in noncollinear antiferromagnet Mn3Sn, Nature Communications 12, 5266 (2021).
  * Uchimura  _et al._ [2022] T. Uchimura, J.-Y. Yoon, Y. Sato, Y. Takeuchi, S. Kanai, R. Takechi, K. Kishi, Y. Yamane, S. DuttaGupta, J. Ieda, H. Ohno, and S. Fukami, Observation of domain structure in non-collinear antiferromagnetic Mn3Sn thin films by magneto-optical Kerr effect, Applied Physics Letters 120, 172405 (2022).
  * Dong  _et al._ [2021] J. Dong, X. Li, G. Gurung, M. Zhu, P. Zhang, F. Zheng, E. Y. Tsymbal, and J. Zhang, Tunneling Magnetoresistance in Noncollinear Antiferromagnetic Tunnel Junctions, . (2021), arXiv:2112.06568 .
  * Kuroda  _et al._ [2017] K. Kuroda, T. Tomita, M.-T. Suzuki, C. Bareille, A. A. Nugroho, P. Goswami, M. Ochi, M. Ikhlas, M. Nakayama, S. Akebi, R. Noguchi, R. Ishii, N. Inami, K. Ono, H. Kumigashira, A. Varykhalov, T. Muro, T. Koretsune, R. Arita, S. Shin, T. Kondo, and S. Nakatsuji, Evidence for magnetic Weyl fermions in a correlated metal, Nature Materials 16, 1090 (2017), arXiv:1710.06167 .
  * Kimata  _et al._ [2019] M. Kimata, H. Chen, K. Kondou, S. Sugimoto, P. K. Muduli, M. Ikhlas, Y. Omori, T. Tomita, A. H. MacDonald, S. Nakatsuji, and Y. Otani, Magnetic and magnetic inverse spin Hall effects in a non-collinear antiferromagnet, Nature 565, 627 (2019).
  * Kondou  _et al._ [2021] K. Kondou, H. Chen, T. Tomita, M. Ikhlas, T. Higo, A. H. MacDonald, S. Nakatsuji, and Y. Otani, Giant field-like torque by the out-of-plane magnetic spin Hall effect in a topological antiferromagnet, Nature Communications 12, 6491 (2021).
  * Hu  _et al._ [2021] S. Hu, D.-F. Shao, H. Yang, M. Tang, Y. Yang, W. Fan, S. Zhou, E. Y. Tsymbal, and X. Qiu, Efficient field-free perpendicular magnetization switching by a magnetic spin Hall effect, , (2021), arXiv:2103.09011 .
  * Ghosh  _et al._ [2022] S. Ghosh, A. Manchon, and J. Železný, Unconventional Robust Spin-Transfer Torque in Noncollinear Antiferromagnetic Junctions, Physical Review Letters 128, 097702 (2022).
  * Gomonay and Loktev [2014] E. V. Gomonay and V. M. Loktev, Spintronics of antiferromagnetic systems, Low Temperature Physics 40, 17 (2014).
  * Baltz  _et al._ [2018] V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, Antiferromagnetic spintronics, Reviews of Modern Physics 90, 015005 (2018), arXiv:1606.04284 .
  * Šmejkal  _et al._ [2018] L. Šmejkal, Y. Mokrousov, B. Yan, and A. H. MacDonald, Topological antiferromagnetic spintronics, Nature Physics 14, 242 (2018), arXiv:1706.00670 .
  * Tomiyoshi and Yamaguchi [1982] S. Tomiyoshi and Y. Yamaguchi, Magnetic Structure and Weak Ferromagnetism of Mn3Sn Studied by Polarized Neutron Diffraction, Journal of the Physical Society of Japan 51, 2478 (1982).
  * Ohmori  _et al._ [1987] H. Ohmori, S. Tomiyoshi, H. Yamauchi, and H. Yamamoto, Spin structure and weak ferromagnetism of Mn3Sn, Journal of Magnetism and Magnetic Materials 70, 249 (1987).
  * Duan  _et al._ [2015] T. F. Duan, W. J. Ren, W. L. Liu, S. J. Li, W. Liu, and Z. D. Zhang, Magnetic anisotropy of single-crystalline Mn3Sn in triangular and helix-phase states, Applied Physics Letters 107, 10.1063/1.4929447 (2015).
  * Song  _et al._ [2020] Y. Song, Y. Hao, S. Wang, J. Zhang, Q. Huang, X. Xing, and J. Chen, Complicated magnetic structure and its strong correlation with the anomalous Hall effect in Mn3Sn, Physical Review B 101, 144422 (2020).
  * Ikhlas  _et al._ [2017] M. Ikhlas, T. Tomita, T. Koretsune, M. T. Suzuki, D. Nishio-Hamane, R. Arita, Y. Otani, and S. Nakatsuji, Large anomalous Nernst effect at room temperature in a chiral antiferromagnet, Nature Physics 13, 1085 (2017), arXiv:1710.00062 .
  * Li  _et al._ [2017] X. Li, L. Xu, L. Ding, J. Wang, M. Shen, X. Lu, Z. Zhu, and K. Behnia, Anomalous Nernst and Righi-Leduc Effects in Mn3Sn: Berry Curvature and Entropy Flow, Physical Review Letters 119, 056601 (2017), arXiv:1612.06128 .
  * Ikeda  _et al._ [2020] T. Ikeda, M. Tsunoda, M. Oogane, S. Oh, T. Morita, and Y. Ando, Fabrication and evaluation of highly c-plane oriented Mn3Sn thin films, AIP Advances 10, 015310 (2020).
  * Nakano  _et al._ [2021] T. Nakano, T. Higo, A. Kobayashi, S. Miwa, S. Nakatsuji, and K. Yakushiji, Fabrication of polycrystalline Weyl antiferromagnetic Mn3Sn thin films on various seed layers, Physical Review Materials 5, 054402 (2021).
  * Higo  _et al._ [2018b] T. Higo, H. Man, D. B. Gopman, L. Wu, T. Koretsune, O. M. J. V. Erve, Y. P. Kabanov, D. Rees, Y. Li, M.-t. Suzuki, S. Patankar, M. Ikhlas, C. L. Chien, R. Arita, R. D. Shull, J. Orenstein, and S. Nakatsuji, Large magneto-optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metal, Nature Photonics 12, 73 (2018b).
  * Ikeda  _et al._ [2019] T. Ikeda, M. Tsunoda, M. Oogane, S. Oh, T. Morita, and Y. Ando, Improvement of Large Anomalous Hall Effect in Polycrystalline Antiferromagnetic Mn3+xSn Thin Films, IEEE Transactions on Magnetics 55, 1 (2019).
  * You  _et al._ [2019] Y. You, X. Chen, X. Zhou, Y. Gu, R. Zhang, F. Pan, and C. Song, Anomalous Hall Effect–Like Behavior with In-Plane Magnetic Field in Noncollinear Antiferromagnetic Mn3Sn Films, Advanced Electronic Materials 5, 1800818 (2019).
  * Yoon  _et al._ [2020] J. Yoon, Y. Takeuchi, R. Itoh, S. Kanai, S. Fukami, and H. Ohno, Crystal orientation and anomalous Hall effect of sputter-deposited non-collinear antiferromagnetic Mn3Sn thin films, Applied Physics Express 13, 013001 (2020).
  * Yoon  _et al._ [2021] J.-Y. Yoon, Y. Takeuchi, S. DuttaGupta, Y. Yamane, S. Kanai, J. Ieda, H. Ohno, and S. Fukami, Correlation of anomalous Hall effect with structural parameters and magnetic ordering in Mn3+xSn1-x thin films, AIP Advances 11, 065318 (2021).
  * Khadka  _et al._ [2020] D. Khadka, T. R. Thapaliya, S. Hurtado Parra, X. Han, J. Wen, R. F. Need, P. Khanal, W. Wang, J. Zang, J. M. Kikkawa, L. Wu, and S. X. Huang, Kondo physics in antiferromagnetic Weyl semimetal Mn3+xSn1-x films, Science Advances 6, 10.1126/sciadv.abc1977 (2020).
  * Tsai  _et al._ [2020] H. Tsai, T. Higo, K. Kondou, T. Nomoto, A. Sakai, A. Kobayashi, T. Nakano, K. Yakushiji, R. Arita, S. Miwa, Y. Otani, and S. Nakatsuji, Electrical manipulation of a topological antiferromagnetic state, Nature 580, 608 (2020).
  * Tsai  _et al._ [2021a] H. Tsai, T. Higo, K. Kondou, A. Kobayashi, T. Nakano, K. Yakushiji, S. Miwa, Y. Otani, and S. Nakatsuji, Spin–orbit torque switching of the antiferromagnetic state in polycrystalline Mn3Sn/Cu/heavy metal heterostructures, AIP Advances 11, 045110 (2021a).
  * Takeuchi  _et al._ [2021] Y. Takeuchi, Y. Yamane, J. Y. Yoon, R. Itoh, B. Jinnai, S. Kanai, J. Ieda, S. Fukami, and H. Ohno, Chiral-spin rotation of non-collinear antiferromagnet by spin–orbit torque, Nature Materials 20, 1364 (2021).
  * Deng  _et al._ [2021] Y. Deng, R. Li, and X. Liu, Thickness dependent anomalous Hall effect in noncollinear antiferromagnetic Mn3Sn polycrystalline thin films, Journal of Alloys and Compounds 874, 159910 (2021).
  * Tsai  _et al._ [2021b] H. Tsai, T. Higo, K. Kondou, S. Sakamoto, A. Kobayashi, T. Matsuo, S. Miwa, Y. Otani, and S. Nakatsuji, Large Hall Signal due to Electrical Switching of an Antiferromagnetic Weyl Semimetal State, Small Science 1, 2000025 (2021b).
  * Miron  _et al._ [2011] I. M. Miron, K. Garello, G. Gaudin, P.-J. Zermatten, M. V. Costache, S. Auffret, S. Bandiera, B. Rodmacq, A. Schuhl, and P. Gambardella, Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection, Nature 476, 189 (2011).
  * Baumgartner  _et al._ [2017] M. Baumgartner, K. Garello, J. Mendil, C. O. Avci, E. Grimaldi, C. Murer, J. Feng, M. Gabureac, C. Stamm, Y. Acremann, S. Finizio, S. Wintz, J. Raabe, and P. Gambardella, Spatially and time-resolved magnetization dynamics driven by spin–orbit torques, Nature Nanotechnology 12, 980 (2017).
  * Fujita [2017] H. Fujita, Field‐free, spin‐current control of magnetization in non‐collinear chiral antiferromagnets, physica status solidi (RRL) – Rapid Research Letters 11, 1600360 (2017).
  * Yamane  _et al._ [2019] Y. Yamane, O. Gomonay, and J. Sinova, Dynamics of noncollinear antiferromagnetic textures driven by spin current injection, Physical Review B 100, 054415 (2019).
  * Yan  _et al._ [2022] G. Q. Yan, S. Li, H. Lu, M. Huang, Y. Xiao, L. Wernert, J. A. Brock, E. E. Fullerton, H. Chen, H. Wang, and C. R. Du, Quantum Sensing and Imaging of Spin–Orbit‐Torque‐Driven Spin Dynamics in the Non‐Collinear Antiferromagnet Mn3Sn, Advanced Materials , 2200327 (2022).
  * Nogués and Schuller [1999] J. Nogués and I. K. Schuller, Exchange bias, Journal of Magnetism and Magnetic Materials 192, 203 (1999).
  * Grimaldi  _et al._ [2020] E. Grimaldi, V. Krizakova, G. Sala, F. Yasin, S. Couet, G. Sankar Kar, K. Garello, and P. Gambardella, Single-shot dynamics of spin–orbit torque and spin transfer torque switching in three-terminal magnetic tunnel junctions, Nature Nanotechnology 15, 111 (2020).
  * [53] See Supplemental Material at [URL] for details on the sample fabrication, crystal structure, time-resolved measurements, switching of Mn3Sn/W and W/Mn3Sn/Pt, temperature calibration, orientation of domains probed by the ANE and dependence of the switching amplitude on applied field.
  * Sala  _et al._ [2021] G. Sala, V. Krizakova, E. Grimaldi, C. H. Lambert, T. Devolder, and P. Gambardella, Real-time Hall-effect detection of current-induced magnetization dynamics in ferrimagnets, Nature Communications 12, 656 (2021), arXiv:2102.00716 .
  * Avci  _et al._ [2014] C. O. Avci, K. Garello, M. Gabureac, A. Ghosh, A. Fuhrer, S. F. Alvarado, and P. Gambardella, Interplay of spin-orbit torque and thermoelectric effects in ferromagnet/normal-metal bilayers, Physical Review B 90, 224427 (2014).
  * Krizakova  _et al._ [2021] V. Krizakova, E. Grimaldi, K. Garello, G. Sala, S. Couet, G. S. Kar, and P. Gambardella, Interplay of Voltage Control of Magnetic Anisotropy, Spin-Transfer Torque, and Heat in the Spin-Orbit-Torque Switching of Three-Terminal Magnetic Tunnel Junctions, Physical Review Applied 15, 054055 (2021).
  * Wörnle  _et al._ [2019] M. S. Wörnle, P. Welter, Z. Kašpar, K. Olejník, V. Novák, R. P. Campion, P. Wadley, T. Jungwirth, C. L. Degen, and P. Gambardella, Current-induced fragmentation of antiferromagnetic domains, arXiv (2019), arXiv:1912.05287 .
  * Kašpar  _et al._ [2021] Z. Kašpar, M. Surýnek, J. Zubáč, F. Krizek, V. Novák, R. P. Campion, M. S. Wörnle, P. Gambardella, X. Marti, P. Němec, K. W. Edmonds, S. Reimers, O. J. Amin, F. Maccherozzi, S. S. Dhesi, P. Wadley, J. Wunderlich, K. Olejník, and T. Jungwirth, Quenching of an antiferromagnet into high resistivity states using electrical or ultrashort optical pulses, Nature Electronics 4, 30 (2021).
  * Pal  _et al._ [2022] B. Pal, B. K. Hazra, B. Göbel, J.-C. Jeon, A. K. Pandeya, A. Chakraborty, O. Busch, A. K. Srivastava, H. Deniz, J. M. Taylor, H. Meyerheim, I. Mertig, S.-H. Yang, and S. S. P. Parkin, Setting of the magnetic structure of chiral kagome antiferromagnets by a seeded spin-orbit torque, Science Advances 8, 10.1126/sciadv.abo5930 (2022).