High-temperature non-centrosymmetric magnets for skyrmionics

Topological spin textures have recently attracted growing attention in many fields of research as a source of a variety of emergent electromagnetic phenomena and functionalities.^1–3 Magnetic skyrmions are nanometric vortex-like spin textures characterized by an integer topological charge [Figs. 1(a) and 1(b)]. They behave as topologically stable particles that can be manipulated with an ultra-low current density (∼10⁶ Am⁻²) that is five to six orders of magnitude smaller than that required to drive ferromagnetic domain walls.^4–9 More recently, their antiparticles—“antiskyrmions,” which have a topological charge with the opposite sign [Fig. 1(c)]—have also been examined as a new topological spin texture. These nanometric topological spin textures are expected to be used in high-density multi-functional magnetic devices with low power consumption, such as racetrack memory¹⁰ and neuromorphic computing devices.^11,12

A variety of microscopic interactions are considered to stabilize skyrmions and antiskyrmions. One representative origin is the competition between ferromagnetic exchange interaction and the Dzyaloshinskii–Moriya interaction (DMI), the latter of which arises from the relativistic spin–orbit interaction in the presence of broken inversion symmetry either at the interfaces of heterostructures or in bulk materials with non-centrosymmetric crystal structures. The DMI gradually twists ferromagnetically coupled magnetizations to form a helical (Bloch-type) or cycloidal (Néel-type) spin modulation described by a magnetic propagation vector (q vector). The magnitude of q is given by q ∝ D/J, where the latter term is the ratio of the DMI constant to the exchange interaction. The corresponding magnetic periodicity λ = 2π/q is typically 10–100 nm. The superposition of triple q vectors perpendicular to the external field leads to the formation of a triangular lattice of the skyrmion crystal (SkX).

In 2009, Mühlbauer et al. first observed the SkX in a chiral magnet by using small-angle neutron scattering (SANS).¹³ In 2010, Yu et al. directly observed individual skyrmions by using Lorentz transmission electron microscopy (LTEM).¹⁴ Such topological spin textures have thus far been observed in a wide variety of magnetic systems.³ They are classified into three types depending on their crystallographic symmetry (Fig. 1 and Table I).^15,16 A Bloch-type skyrmion [Fig. 1(a)], constructed by helical propagations, has been observed in cubic chiral magnets with T or O symmetry, e.g., MnSi (T),¹³ (Fe,Co)Si (T),¹⁴ FeGe (T),¹⁷ Cu₂OSeO₃ (T),¹⁸ Co–Zn–Mn (O),¹⁹ and (Fe,Co,Rh)₂Mo₃N (O).²⁰ Cycloidal propagations form a Néel-type skyrmion [Fig. 1(b)], which has been stabilized in various heterostructures with interfacial DMI^21–26 and in bulk polar magnets with C_nv symmetry, e.g., GaV₄(S,Se)₈ (C_3v)^27–29 and VOSe₂O₅ (C_4v).³⁰ An antiskyrmion [Fig. 1(c)] is composed of both Bloch and Néel walls and has recently been observed in a few non-centrosymmetric magnets with D_2d or S₄ symmetry, i.e., Mn_1.4(Pt,Pd)Sn (D_2d),^31,32 Mn₂(Rh,Ir)Sn (D_2d),³³ and (Fe,Ni,Pd)₃P (S₄).³⁴ 

The stabilization and control of these topological spin textures above room temperature, both at hetero-interfaces and in bulk materials, are indispensable for their application to devices with the aim of realizing “skyrmionics.” An increasing number of studies have recently been published on the observation and manipulation of Néel-type skyrmions in multiple layers with interfacial DMI at room temperature.^23–26 However, only the following three compounds are known to host topological spin textures at and above room temperature among non-centrosymmetric magnets with bulk DMI: Co–Zn–Mn alloys (Bloch-type skyrmions), Mn_1.4(Pt,Pd)Sn (antiskyrmions), and (Fe,Ni,Pd)₃P (antiskyrmions). Their characteristic physical properties are summarized in Table II.

Against the above background, we review recent progress in research on the three non-centrosymmetric magnets mentioned above. First, we provide an overview of studies on skyrmions in Co–Zn–Mn alloys, including their basic physical properties (Sec. II A), robust metastable skyrmions, their lattice structural transformations, and various forms of topological textures (Sec. II B) and skyrmion dynamics (Sec. II C). Second, we review the results of recent research on room-temperature antiskyrmions in Mn_1.4(Pt,Pd)Sn (Sec. III A) and (Fe,Ni,Pd)₃P (Sec. III B) and focus on antiskyrmion-to-skyrmion topological transformations and the mechanism of stabilization of antiskyrmions.

Co–Zn–Mn alloys crystallize in a β-Mn-type chiral cubic structure with the space group P4₁32 or P4₃32, where 20 atoms per unit cell are distributed over 8c and 12d Wyckoff sites, as illustrated in Fig. 2(a). The network of 12d sites forms a hyperkagome structure composed of corner-sharing triangles. The 8c sites are mainly occupied by Co while the 12d sites are mainly occupied by Zn and Mn.^35–38 Therefore, Co–Zn–Mn alloys exhibit substantial structural and magnetic disorders owing to random site occupancies.^37–40 

In 2015, Tokunaga et al. discovered that skyrmions form in Co–Zn–Mn alloys above room temperature.¹⁹ These magnets were considered to be ferromagnetic,^35,36 but actually exhibit a helimagnetic ground state at zero field owing to ferromagnetic coupling of Co spins and bulk DMI inherent to the chiral structure, and host skyrmions when a magnetic field is applied. Skyrmions have been observed both in bulk single crystals by SANS and in thin plates (fabricated by ion milling or focused ion beams from bulk samples) by LTEM. In addition, by using differential phase contrast–scanning transmission electron microscopy (DPC-STEM), Matsumoto et al. observed a stable, single skyrmion confined to an artificial nanostructure fabricated by a focused electron beam.⁴¹ 

The magnetic phase diagram on the plane of temperature and Mn concentration (x) of (Co_0.5Zn_0.5)_20−xMn_x is shown for 0 ≤ x ≤ 10 in Fig. 2(b).^42,43 Both the magnetic transition temperature T_c and the helical period λ decrease with the partial substitution of Mn from Co₁₀Zn₁₀ (T_c ∼ 460 K, λ ∼ 185 nm) to Co₇Zn₇Mn₆ (T_c ∼ 150 K, λ ∼ 115 nm), and the helimagnetic phase is suppressed for x ≥ 7. The other end-member β-Mn [Mn₂₀, not shown in Fig. 2(b)] is known as a spin liquid owing to geometrical frustration among antiferromagnetically coupled Mn spins on the hyperkagome network of the 12d sites.^44,45 The frustrated Mn spins and random site occupancies in Co–Zn–Mn alloys give rise to a spin glass phase over a wide range of Mn concentrations (7 ≤ x ≤ 19). For 3 ≤ x ≤ 7, the spin-glass phase invades the helical phase to exhibit reentrant spin-glass behavior.

While the phase diagram has been explored in research, such details of the magnetic interactions as those of J and D have not been fully clarified throughout the phase diagram. The magnitudes of the DMI have been obtained as D ∼ 1.2 mJ m⁻² and 0.53 mJ m⁻² only for Co₉Zn₉Mn₂ and Co₈Zn₈Mn₄, respectively, by spin–wave spectroscopy.⁴⁶ In addition, systematic changes in the DMI have been investigated for Fe-doped, band-filling-controlled Co_8−yFe_yZn₈Mn₄ and have shown that a change of sign in the DMI, i.e., a reversal of magnetic helicity under fixed crystal chirality, occurs around y ∼ 0.27 due to a reduction in 3d electron filling.⁴⁷ These results demonstrate that DMI depends critically on the band structure and electron filling in metallic systems, in accord with the relevant theories.^48,49

Figure 3 summarizes the equilibrium and metastable SkX states on the plane of temperature and magnetic field in Co₁₀Zn₁₀, Co₉Zn₉Mn₂, Co₈Zn₈Mn₄, and Co₇Zn₇Mn₆ and the corresponding results of SANS and LTEM.^{42,43,50–52} In general, the field-induced first-order phase transition from a helical/conical state (single-q) to an SkX sate (triple q) is assisted by thermal fluctuations, and hence, a thermodynamically equilibrium SkX phase is confined to the region of a narrow temperature and magnetic field just below T_c. However, in 2016, Oike et al. demonstrated that the skyrmion phase in MnSi (T_c ∼ 29 K) can be quenched to lower temperatures and survive as a metastable state.⁵³ Subsequently, Karube et al. applied this method to Co₈Zn₈Mn₄ (T_c ∼ 300 K) and demonstrated that a once-created SkX at room temperature under a magnetic field can persist over the entire temperature region below room temperature and a wide magnetic field region including the zero field as a long-lasting metastable state [Fig. 3(d)].⁵⁰ In contrast to MnSi, for which ultra-rapid cooling (∼100 K/s) is necessary to quench the skyrmion phase,⁵³ conventional and slow field cooling at a rate of 1–10 K/min is sufficient to realize the metastable skyrmion state in Co₈Zn₈Mn₄.

This robust metastable SkX state is extended to an even wider region of the field temperature, including the zero field and above room temperature in Co₉Zn₉Mn₂ [Figs. 3(c), 3(h), and 3(i)],⁵¹ with an equilibrium triangular skyrmion lattice phase as high as 390 K [Figs. 3(c) and 3(g)], and in Co₁₀Zn₁₀ [Fig. 3(b)]⁴³ with T_c above 400 K. The lifetime of the metastable SkX is extremely long and virtually infinite below ∼0.9T_c (∼360 K in Co₉Zn₉Mn₂).^43,51 The metastability of the robust skyrmion is attributed to its topological protection, with a large number of spins involved in a single skyrmion, and to magnetic disorders that prevent topological defects (emergent magnetic monopole and antimonopole) from propagating and completely destroying the skyrmion strings. The latter seem to be more important in this system.

Furthermore, the lattice structure of the metastable SkX in Co₉Zn₉Mn₂, Co₈Zn₈Mn₄, and Co₇Zn₇Mn₆ changes from the conventional triangular lattice (triple q) to a square lattice [double q || 〈100〉, Fig. 3(k)] at low temperatures [pink regions in Figs. 3(c)–3(e)].^43,50 For Co₁₀Zn₁₀, the triangular lattice of the metastable SkX is slightly distorted to form a rhombic lattice (double q || 〈111〉) [purple region in Fig. 3(b)],⁴³ where this is caused by enhanced magnetocrystalline anisotropy along the 〈111〉 direction.⁵⁴ In Mn-doped compounds, the preferred orientation of magnetization and the q vector switches to the 〈100〉 direction,⁵⁴ and the triangular–square SkX transformation is accompanied by a significantly large increase in q (large decrease in the SkX period) by a factor of ∼1.5, similar to the large increase in the helical q upon zero-field cooling [red region in Fig. 2(b)]. As the total number of skyrmions should be conserved during the thermally reversible skyrmion–lattice transformation, the initially formed perfectly triangular SkX changes into a form featuring (i) the coexistence of a square SkX and a helical phase or (ii) elongated skyrmions on a square lattice, as illustrated in Fig. 3(j). The latter elongated skyrmions have been observed in a thin plate by LTEM [Figs. 3(l) and 3(m)].⁵² The large increase in q is attributed to the antiferromagnetic correlations of Mn spins, which act as a magnetic disorder for the helimagnetic Co spins and reduce the ratio of ferromagnetic exchange interaction to DMI.^43,55 The transformation of the SkX to the square lattice is, therefore, governed by the magnetic anisotropy of the cubic crystal as well as the contraction of the SkX period induced by magnetic disorder.

With a further increase in the magnetic disorder in Co₇Zn₇Mn₆, a novel equilibrium phase of three-dimensionally disordered skyrmions [Figs. 3(n)–3(q)] emerges near the low-temperature reentrant spin glass phase [orange region in Fig. 3(e)]. This is thermodynamically disconnected from the conventional SkX phase just below T_c.⁴² The low-temperature disordered skyrmion phase is stabilized by the magnetic disorder owing to the antiferromagnetic short-range correlations of Mn spins with a possibly non-coplanar spin arrangement.⁵⁶ 

In Co–Zn–Mn alloys, the interplay of magnetic anisotropy and DMI leads to the formation of various exotic skyrmion-related textures. In 2018, Yu et al. observed a meron–antimeron square lattice in a Co₈Zn₉Mn₃ (001) thin plate by LTEM.⁵⁷ The square lattice of merons and antimerons with fractional topological charges of ±1/2 can be described by the superposition of orthogonal double-q vectors but is topologically distinct from the square lattice of metastable skyrmions with an integer topological charge. In 2019, Nagase et al. observed a smectic liquid–crystalline structure of skyrmions in a Co_8.5Zn_7.5Mn₄ (110) plate by using LTEM,⁵⁸ where elongated skyrmions were oriented and periodically arranged only in the [110] direction while exhibiting a short-range order in the [001] direction. This smectic skyrmion structure was observed only at high temperatures and in thin regions of the lamella, where the aforementioned magnetic disorder due to Mn spins was less important. The structure can, thus, be attributed to magnetic anisotropy and chiral surface twist (non-collinear spin modulations near the surface of chiral magnets).^59,60 In 2021, the same group reported LTEM observations of domain wall bimerons, i.e., chains of skyrmion-like structures along the boundaries between conventional in-plane ferromagnetic domains.⁶¹ These bimerons were stabilized by a combination of magnetic anisotropy, dipolar interactions, and DMI.

As described above, Co–Zn–Mn alloys are unique materials that host skyrmions above room temperature, and chemical and magnetic disorders inherent to β-Mn-type alloys significantly enhance the stability and metastability of skyrmions over a wide range of temperatures and magnetic fields. Due to these properties, skyrmions are driven by current at room temperature, and hence, their dynamics can be investigated. In 2017, Yu et al. observed the DC current-induced nucleation and annihilation of SkX in Co₈Zn₉Mn₃ by using LTEM at room temperature.⁶² In 2021, Peng et al. created a metastable single skyrmion in Co₉Zn₉Mn₂ and succeeded in driving it by using nanosecond current pulses at room temperature.⁶³ As shown in Figs. 4(a)–4(e), the current-induced skyrmion Hall motion was directly observed by using LTEM. The observed Hall angles and velocities of the skyrmion as a function of the current density indicated the transitions of skyrmion dynamics from a pinned state to flow motion via a creep event that was in good accord with the theory.⁷ This demonstrated a significant role of spin-transfer torque (STT) and the pinning effect in skyrmion dynamics. In 2022, Wang et al. demonstrated the STT-induced creation, annihilation, and Hall motion of a single skyrmion and a skyrmion cluster by using nanosecond current pulses in Co₈Zn₁₀Mn₂ microdevices at room temperature.⁶⁴ 

In 2021, Shimojima et al. observed the one-cycle dynamics of metastable skyrmions in Co₉Zn₉Mn₂ above room temperature by using a time-resolved pump–probe LTEM technique.⁶⁵ As shown in Figs. 4(f) and 4(g), following photothermal excitation by a nanosecond pulse, the metastable skyrmions exhibited splitting, contraction, ordering, relaxation, and coalescence at nanosecond to microsecond time scales. The observed repeatable skyrmion dynamics arose from the variable, but still persistent, topological protection and demonstrated that skyrmions can be manipulated with high-frequency light pulses above room temperature.

Among non-centrosymmetric magnets, tetragonal compounds belonging to the D_2d or S₄ point groups with a fourfold roto-inversion (⁠$4̄$⁠) axis exhibit a unique feature of DMI whereby they have opposite signs along the x and y directions. This anisotropic DMI leads to the formation of an antiskyrmion [Fig. 1(c)] that is composed of both Bloch and Néel walls with opposite helicities along the orthogonal directions.

In 2017, Nayak et al. were the first to observe antiskyrmions in inverse tetragonal Heusler compounds with D_2d symmetry, Mn_1.4PtSn and Mn_1.4Pt_0.9Pd_0.1Sn, by using LTEM.³¹ The tetragonal crystal structure with the space group I$4̄$2m of Mn_1.4(Pt,Pd)Sn is shown in Fig. 5(a). The Mn vacancies in Mn₂PtSn stabilize the bulk single phase of the tetragonal structure (Vir et al. reported that the ordering of the Mn vacancies forms a superstructure with the space group I$4̄$2d⁶⁶), and the substitution of a small amount of Pd enhances tetragonality.³¹ Mn_1.4(Pt,Pd)Sn exhibits a ferromagnetic (or ferrimagnetic) transition at T_c ∼ 400 K with easy-axis magnetic anisotropy, while spin reorientation occurs below T_SR ∼ 170 K.^31,66 Figure 5(b) shows the LTEM image of a thin plate of Mn_1.4Pt_0.9Pd_0.1Sn with a triangular lattice of antiskyrmions.³¹ Antiskyrmions were observed over a wide range of temperatures from 400 to 100 K, including the zero field as a metastable state [Fig. 5(c)].³¹ 

In 2020, Peng et al. observed a square lattice of antiskyrmions in Mn_1.4Pt_0.9Pd_0.1Sn by using LTEM [Fig. 5(d)]³² and revealed that anisotropic DMI, as well as magnetic dipolar interactions (demagnetization energy), plays an important role in this compound. As shown in Fig. 5(e), the antiskyrmion has a square shape with four long Bloch walls along the [100] and [010] directions and four narrow Néel walls (Bloch lines) in between. The square deformation of antiskyrmions is attributed to dipolar interactions that prefer Bloch walls to Néel walls to minimize the magnetic volumetric charges.^32,67 Moreover, when a small in-plane field is applied by tilting the sample plate, the square antiskyrmion transforms into a bullet-shaped “non-topological (NT-) bubble” that consists of a half-antiskyrmion and a half-skyrmion [Fig. 5(f)].³² When the in-plane field is reduced to zero, the NT-bubble transforms into an elliptically deformed Bloch-type skyrmion [Fig. 5(g)]. The elliptic deformation of skyrmions is also ascribed to the combination of dipolar interactions and anisotropic DMI.^32,68 The square antiskyrmion lattice stabilizes above 265 K via the formation of NT-bubbles with in-plane fields, whereas the elliptic skyrmion lattice is more stable at lower temperatures.^32,68

Jena et al. subsequently created single chains of antiskyrmions and skyrmions at room temperature in nanostripes of Mn_1.4Pt_0.9Pd_0.1Sn, which were narrower than 0.5 μm, thus showing that this material is promising for use in applications, such as in racetrack memory devices.⁶⁹ 

In 2021, Karube et al. reported Pd-doped schreibersite, (Fe_0.63Ni_0.30Pd_0.07)₃P (or equivalently, Fe_1.9Ni_0.9Pd_0.2P), as a new room-temperature antiskyrmion material with S₄ symmetry.³⁴ The non-centrosymmetric tetragonal structure of M₃P (M: transition metal) with the space group I$4̄$ (symmetry class: S₄) is shown in Fig. 6(a). The end-member Fe₃P is a ferromagnet (T_c ∼ 680 K) with strong easy-plane magnetic anisotropy^70–72 that is rapidly suppressed by the partial substitution of Ni (30%–40%), and additionally, doping it with a small amount of Pd (at least 4%) induces easy-axis anisotropy.⁷² (Fe_0.63Ni_0.30Pd_0.07)₃P exhibits a ferromagnetic transition at T_c ∼ 400 K as well as large saturation magnetization (M_s ∼ 474 kA m⁻¹ ~2.4 μ_B/f.u. at 300 K) with a relatively weak easy-axis anisotropy (K_u ∼ 28 kJ m⁻³ at 300 K).⁷² The quality factor Q (= 2K_u/μ₀M_s²), the ratio of uniaxial anisotropy energy to the demagnetization energy, was then calculated to be Q ∼ 0.2 at 300 K.

As shown in Figs. 6(b) and 6(c), antiskyrmions are observed by using LTEM at room temperature under a magnetic field after the initial creation of NT-bubbles by tilting a thin plate.³⁴ The antiskyrmion consists of long Bloch walls along the [110] and [$1̄$10] directions to form a square shape with four Bloch lines at the corners. As the magnetic field is further increased, the square antiskyrmions transform into elliptic skyrmions with mixed helicities, where clockwise and anticlockwise skyrmions are elongated along the orthogonal [$1̄$10] and [110] directions, respectively [Figs. 6(d)–6(f)]. The square antiskyrmions and elliptic skyrmions are similar to those in Heusler compounds and are attributed to the cooperative interplay between anisotropic DMI and dipolar interactions. As shown in the phase diagram in Fig. 6(g), the phase of the antiskyrmions exists over a range of wide temperatures from T_c ∼ 400 K down to 100 K, and they are transformed into skyrmions at high fields just below the polarized ferromagnetic phase. Moreover, the antiskyrmions are stabilized in plates thicker than t ∼ 100 nm, whereas skyrmions preferentially form in thinner plates.³⁴ 

The thickness-dependent results of LTEM for (Fe_0.63Ni_0.30Pd_0.07)₃P and similar LTEM measurements for (Fe_0.63Ni_0.33Pd_0.04)₃P and (Fe_0.60Ni_0.32Rh_0.08)₃P are summarized into a single magnetic phase diagram on the plane of the uniaxial magnetic anisotropy energy and demagnetization energy, as shown in Fig. 6(h).⁷² This phase diagram indicates that stable antiskyrmions form when the uniaxial anisotropy is sufficiently large and comparable to the demagnetization energy. On the contrary, elliptic skyrmions are more dominant when the demagnetization energy is much larger than the uniaxial anisotropy, as in thin samples or in the case of Rh doping. Therefore, the stability of antiskyrmions is governed by an appropriate balance between easy-axis magnetic anisotropy and the demagnetization energy, in addition to anisotropic DMI.⁷² 

As described in Secs. II and III, significant progress has been made in research on non-centrosymmetric magnets with bulk DMI, particularly regarding the stabilization and control of skyrmions and antiskyrmions above room temperature as well as an understanding of their underlying physics.

Research has shown that Co–Zn–Mn alloys with the β-Mn-type chiral structure form Bloch-type skyrmions above room temperature. Once created, these skyrmions persist as long-living metastable states over a range of wide temperatures and magnetic field, including room temperature and a zero field, owing to the topological protection assisted by their chemical/magnetic randomness. The metastable skyrmions exhibit a triangular-to-square lattice structural transformation that is governed by magnetic disorders and anisotropy while maintaining their number. The robust metastable skyrmions and their lattice transformations demonstrate their particle nature and, thus, the key role of topology in them. Moreover, exotic topological textures, such as a meron–antimeron square lattice, smectic liquid–crystalline skyrmions, and domain wall bimerons, have been observed for thin-plate specimens in real space. Furthermore, the metastable skyrmions in Co–Zn–Mn alloys can be manipulated with nanosecond pulsed current or laser light at room temperature, where this is a significant step forward for skyrmionics.

The non-centrosymmetric tetragonal magnets Mn_1.4(Pt,Pd)Sn and (Fe,Ni,Pd)₃P, with D_2d and S₄ symmetries, respectively, have recently been found to host antiskyrmions over a wide range of temperature, including room temperature. The cooperative interplay among anisotropic DMI, uniaxial magnetic anisotropy, and magnetic dipolar interactions stabilizes square antiskyrmions and elliptic skyrmions. Remarkably, antiskyrmions and skyrmions with topological charges of opposite signs can be easily inter-converted by changing various parameters. This highlights their versatile tunability in the context of multi-functional skyrmionics devices.

Although all three non-centrosymmetric magnets considered here, with high magnetic transition temperatures well above room temperature (Table II), are promising for applications, their magnetic period, i.e., (anti)skyrmion size, is of the order of 100 nm (Table II). Reducing the (anti)skyrmion size down to the order of 10 nm or even smaller is a challenge for realizing high-density skyrmionics devices. One potential solution to this problem is to increase the spin–orbit interaction or to exploit the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction^73–76 by further optimizing the material composition.

This Perspective has underscored the significant potential of non-centrosymmetric magnets to realize skyrmionics and is expected to stimulate further research on both the fundamental physics and device applications of high-temperature topological spin textures.

The authors thank D. Morikawa, L. C. Peng, and T. Shimojima for fruitful discussion and are grateful to M. Ishida for technical assistance.

This work was supported by a JSPS Grant-in-Aid for Scientific Research (Grant No. 20K15164) and JST CREST (Grant No. JPMJCR20T1).

The authors have no conflicts to disclose.

Kosuke Karube: Writing – original draft (lead). Yasujiro Taguchi: Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are available within the article and from the corresponding author upon reasonable request.