1 Introduction

Skyrmions are topologically protected quasi-particles, which were proposed in nuclear physics by Skyrme in 1962 [1] and theoretically predicted to be stable in magnets by Bongdnov and Yablonskii [2] in 1989. The first experimental observation of skyrmions was carried out in MnSi, using the neutron scattering method by Pfleiderer’s group at Technische Universität München from Germany [3]. These exotic spin structures were then successfully observed in real space using Lorentz image, in other B20-type materials, including Fe0.5Co0.5Si [4, 5], MnGe [6] and FeGe [7] etc. Later, room-temperature skyrmions were found to exist stably in thin films [8,9,10,11,12,13] and multilayers [14,15,16,17,18,19] composed of alternating heavy metals and magnetic layers, which can be driven by the spin current readily.

Recently, robust skyrmions have been found in synthetic antiferromagnets [20,21,22], where the skyrmion Hall effect (SkHE) can be offset and hence skyrmions can be used in racetrack memory without the danger of losing the signal. Various types of skyrmions are also observed in ferrimagnets [23], ferroelectrics [24,25,26], antiferromagnets [27], semiconductors [28], superconductors [29] and two-dimensional (2D) materials [30,31,32]. In the meantime, other topological spin structures, such as antiskyrmions [33,34,35,36], bimerons [37], skyrmioniums [38], vortices [39, 40], half skyrmions [41], hopfions [42] and skyrmion bundles [43], have been investigated extensively in various materials. Skyrmions-related literatures have increased exponentially in recent years, and more than 400 papers were published in 2020, as given by Web of Science and shown in Fig. 1.

Fig. 1
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Number of papers related to skyrmion in the year of 2004–2020 from Web of Science

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Up to now, there are more than 60 skyrmions-related review articles have been published, most of which review one aspect of the skyrmions classified according to the physics, the materials or the applications [44,45,46,47,48,49,50,51,52,53,54,55]. However, few review articles focus on the role of rare metals so far, which play important roles in nucleating and controlling skyrmions as well as other topological spin structures. In this paper, we will systematically summarize the role of rare metals in generating and manipulating skyrmions and other topological spins, including rare-dispersed metals Ga, Ge, etc., and the noble metals Pt and rare-earth (RE) metals Nd etc.

2 Role of rare metals in generating skyrmions in B20 and other non-centrosymmetric materials

Magnetic skyrmions were first reported in 2009 by Mühlbauer et al. [3], which were found via the small-angle neutron scattering (SANS) method in a B20-type material, MnSi. As shown in Fig. 2a, the skyrmion in MnSi can only occur at very low temperatures (below 30 K), which, however, aroused great interests immediately due to its potential application in spintronics. Yu et al. [4] observed real-space skyrmions in Fe1-xCoxSi, another B20 material, based on Lorentz transmission electron microscopy (LTEM), as shown in Fig. 3a [5], which can only appear in a narrow temperature region from 7 to 36 K.

Fig. 2
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Reproduced with permission from Ref. [5]. Copyright 2018, Institute of Physics Publishing. b Change of skL period in MnGe with temperature at different applied fields, indicating that skyrmions can be stable in a wide temperature range of 10–150 K. Reproduced with permission from Ref. [6]. Copyright 2015, American Chemical Society

Comparison of phase diagrams of MnSi and MnGe, indicating role of rare metal Ge in stabilizing skyrmions. a B-T phase diagram of MnSi, where skyrmions (A-phase) can only exist in a narrow temperature range of 28–30 K.

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Fig. 3
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Reproduced with permission from Ref. [5]. Copyright 2018, Institute of Physics Publishing

Comparison of phase diagrams of Fe0.5Co0.5Si and FeGe, indicating role of rare metal Ge in stabilizing skyrmions. a Phase diagrams of spin textures observed in a thin film of Fe0.5Co0.5Si using Lorentz TEM, where skyrmions can only occur below 30 K; b phase diagrams for FeGe thin films with various values of thickness, demonstrating that skyrmions are stable from 50 K to room temperature.

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High-temperature skyrmions are found later in MnGe [6], FeGe [7] and other B20 materials with rare metals, which can exist at the zero magnetic field and are stable in a wider temperature range. Spontaneous ground-state skyrmions in MnGe can be stabilized up to 150 K, which is near its Curie temperature (TC = 170 K), as shown in Fig. 2b [5]. In the meantime, stable skyrmions are found in the FeGe thin-film from 50 K to the room temperature, as shown in Fig. 3b [5], due to its high Curie temperature (TC = 280 K). Recently, the so-called three-dimensional (3D) skyrmion, i.e., the skyrmion bundle, containing the skyrmion bag and ending with the chiral vortex, has also been obtained in the FeGe thin film [45]. Other B20 materials, such as Mn1-xFexSi [56] and Mn1-xFexGe [57], can host skyrmions as well, with skyrmions in Mn1-xFexGe being stable at a much higher temperature than those in Mn1-xFexSi.

As demonstrated above, the existence of Ge, a typical rare-dispersed metal, in various B20 chiral magnetic materials can help to stabilize skyrmions in a wider temperature range. Ge can induce strong spin–orbit coupling (SOC) to enhance DMI, which competes with the ferromagnetic exchange interaction to induce the peculiar twists of the spins and hence the formation of the skyrmions [6, 7, 57]. Later, it is found that other rare metal elements, including Se, Mo and Rh, can also increase the critical temperature and enhance the stability of the hosted skyrmions [58,59,60].

Skyrmions can occur in GaV4S8, a typical semiconductor material, in a narrow temperature range of 9–13 K [28], while they can be observed from 0 to 18 K in GaV4Se8 [58, 61]. Similarly, the transition temperature in the ferroelectric material GaMo4S8 is only 17.5 K, which can be raised to 27.5 K in GaMo4Se8 [59]. These results demonstrate that the rare metal Se can also improve SOC, enhance the DMI and help to stabilize skyrmions. Later, it is found that the incorporation of rare metal Rh into the strong ferromagnetic material Fe2Mo3N can produce significant DMI and stabilize skyrmions [60].

As summarized in Table 1, B20 materials with rare metals Ge, MnGe, FeGe and Mn1-xFexGe [5,6,7, 57, 62] have much higher TC than their counterparts without rare metals, indicating the important role of rare metal Ge in stabilizing skyrmions in these materials. At the same time, the substitution of Se in GaV4S8 and GaMo4S8 and incorporation of Rh into Fe2Mo3N can increase TC and produce large DMI as well [22, 28, 58,59,60, 63].

Table 1 Comparison of properties for typical non-centrosymmetric magnetic materials to demonstrate roles of rare metals in generating and stabilizing skyrmions
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3 Role of rare metals in layered systems with interfacial DMI

As demonstrated above, the DMI plays a key role in the generation of skyrmions, which occurs not only in systems with broken central symmetry, but also at the interface between ferromagnetic and heavy metals. As early as 1990, Fert [64] predicted the possibility of interfacial DMI in such thin film structures. The presence of skyrmion is stabilized by DMI provided by strong SOC at the interface of the heavy metal layer and perpendicular magnetic anisotropy (PMA) in the ferromagnetic layer [64,65,66], as shown in Fig. 4a for Co/Pt thin films [8].

Fig. 4
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Reproduced with permission from Ref. [5]. Copyright 2018, Institute of Physics Publishing

DMI in Co/Pt layered system, which helps to produce Néel-type skyrmions. a Sketch of a DMI at interface between a ferromagnetic metal (grey) and a rare metal (heavy metal) with a strong SOC (blue), where DMI vector D12 related to triangle composed of two magnetic sites and an atom with a large SOC is perpendicular to plane of triangle. Because a large SOC exists only in the bottom metal layer, this DMI is not compensated by a DMI coming from a symmetric triangle. b Néel-type skyrmion induced by DMI illustrated in a, where in-plane spins orient in radius direction; c in contrast, Bloch-type skyrmion usually occurring in B20 crystals is vortex like, where in-plane spins are circling around center.

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At the Co/Pt interface, due to the strong SOC in the rare metal (Pt) and the broken mirror symmetry of the magnetic material thin film (Co), an indirect exchange interaction conducted by the rare metal atoms will occur between two nearby magnetic atoms in the system [8, 9, 16,17,18, 67]. The symmetry of DMI at the interface in the magnetic film systems containing heavy metals is different from that in the B20 structure system. As shown in Fig. 4b, the interfacial DMI in the magnetic film system yields Néel-type skyrmions [28], whereas skyrmions induced by DMI in the B20 system are usually Bloch-type, as shown in Fig. 4c [5]. The rare metal Pt in the Co/Pt layered system provides both strong SOC and large PMA, which are both necessary for the formation of skyrmions in thin-film systems.

Néel-type skyrmion was also found in monolayer Fe/Ir [68], where the heavy metal Ir offers strong SOC and hence the large interfacial DMI. In addition to the interfacial DMI, the four-spin interaction in the system competes with the Heisenberg exchange interaction to form a Néel-type skyrmion with a diameter of only 1 nm, as shown in Fig. 4, which is the smallest skyrmion found in experiments up to now [69,70,71,72]. In this case, the rare metal Ir provides both the large SOC and the nontrivial four-spin interaction, which are responsible for the occurrence of the atomic level skyrmions.

The above thin-film systems, offering strong SOC and DMI, have been extended to multilayer structures composed of magnetic and heavy metals alternatively. The control of interfacial DMI and PMA in such materials can be achieved by changing the thickness, material combination and other parameters of magnetic film and rare metal film [14, 19, 73,74,75,76,77,78], which gives the material system a great degree of freedom, reduces skyrmion size and optimizes the stability and dynamic properties of skyrmions [79]. Two typical multilayers, [Ir/Co/Pt]10 [14] and [Pt/Co/Ta]15 [15], have been used in experiments to generate skyrmions. First-principles calculations show that the chiral direction of DMI provided by the two rare metals is opposite in the separate Ir/Co (Ta/Co) and Pt/Co structures, which, interestingly, can enhance the strength of DMI and facilitate the nucleation of the skyrmions [79, 80].

Quite a few experiments [81, 82] and calculations [18, 83, 84] show that the magnetic chirality at the Ir/Co interface is opposite to the Pt/Co interface, where large DMI has been observed in some Pt/Co/Ir multilayers. However, experiments using magnetic domain walls indicated that the magnetic chirality of the Ir/Co interface is the same as that of the Pt/Co interface [85, 86]. Further experiments confirm that the effective spin Hall angle of Ir has the same sign as Pt, suggesting that the sign of the DM exchange constant for Pt/Co and Ir/Co interfaces is the same, leading to a reduced DMI in some Pt/Co/Ir multilayers [87]. The DMI at the Ir/Co interface thus seems to depend on factors that are yet to be determined.

Recently, 3D spin configurations have been observed in [Ir/Co/Pt]N multilayers shaped into nanoscale disks where the skyrmion tube or the Hopfion is created [42]. With substantial DMI and PMA induced by the rare metals Ir and Pt into Co, these spin textures have a robust 3D structure [42].

Skyrmions are also found in layered metal/oxide heterostructures [19, 75], where the typical material is Ta/CoFeB/TaOx multilayers. First-principles calculations indicate that the interfacial DMI can originate not only from the interface between rare metal Ta and the ferromagnetic layer but also from the interface between rare metal oxide TaOx and the ferromagnetic layer [75]. First-principles calculations also demonstrate that the interfacial DMI between the ferromagnetic layer and rare metal oxide is related to charge transfer and electric polarization at the interface [75]. In this situation, rare metal oxides can increase the strength of DMI, thereby reducing the skyrmion size and improving the stability of skyrmions.

Another layered system proposed to generate skyrmions is the synthetic AFM multilayer structure based on rare metals, which has the advantage of inhibiting the SkHE and hence avoiding signal loss [20]. As shown in Fig. 5, there is strong AFM exchange coupling between two skyrmions with opposite polarity so that the net Magnus force is 0 and the SkHE is completely suppressed. Skyrmions have been successfully generated in various synthetic AFM multilayers, including [Co/Pd]/Ru/[Co/Pd] and [Co/Pt]N/NiO/[Co/Pt]N multilayers [21, 22]. The rare metals Pd and Pt here are to provide strong DMI, which is necessary for the formation of Néel-type skyrmions. On the other hand, the rare metal Ru is to enable the AFM exchange coupling between the upper and the lower Co/Pd layers and hence to suppress the SkHE, similar to the role of NiO in [Co/Pt]N/NiO/[Co/Pt]N.

Fig. 5
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Copyright 2016, Springer Nature. c Schematic diagram of force analysis in synthetic AFM multilayers, where Magnus forces in top and bottom layers cancel each other so that skyrmion moves in the direction of the driving current without drift

Skyrmions in synthetic antiferromagnetic (AFM) multilayer, where Magnus force is 0. a AFM-coupled bilayer nanotrack for study of motion of a bilayer-skyrmion driven by current perpendicular to plane, where charge current flows through heavy-metal substrate along x-direction, which gives rise to a spin current (p =  + y) perpendicularly injected to bottom ferrimagnetic layer because of spin Hall effect; skyrmion in bottom ferrimagnetic layer is driven by spin current, whereas skyrmion in top ferrimagnetic layer moves accordingly due to interlayer AFM exchange coupling. b Side view of bilayer-skyrmion. Reproduced with permission Ref. [20].

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4 Role of rare metals in manipulating skyrmions and other spin textures in layered systems

As mentioned in the last section, the synthetic AFM multilayer has been proposed as an ideal structure to overcome skyrmion Hall effect, where a pair of skyrmions with opposite polarity driven by the electric current can move along the racetrack without any transverse drift. Such spin-polarized electric current can be applied in various layered systems, with spin orbit torques [11, 88] or spin transfer torques [89] induced in the magnetic layers to direct the motion of skyrmions. In particular, there have been many researches on control of skyrmions by SOT at room temperature, with rare metals as an important host for the electric current. For example, Néel-type skyrmions have been created in Ta/Co20Fe60B20 (CoFeB)/MgO system by inserting an ultrathin Ta layer between the CoFeB and MgO [11], where skyrmions can be driven along racetracks by the SOT. The interfacial DMI due to the adjacent Ta rare metal layer with a large spin–orbit coupling facilitates the formation of the Néel-type skyrmions.

Further, SOT in various kinds of AFM/FM exchange bias has been used to generate and manipulate skyrmions [13]. Skyrmions can be created at the zero-field due to the exchange bias at the IrMn/CoFeB interface in Ta/Ir22Mn78/Co20Fe60B20/MgO/Ta system [13], where spins in antiferromagnetic IrMn have a sizable spin Hall angle, allowing SOT to control skyrmions. The rare metal Ir is responsible for the antiferromagnetic order in IrMn and hence for the formation of exchange bias in the system, in addition to the large interfacial DMI of the system.

Compared to the normal FM/HM system [10], the IrMn/CoFeB heterostructure has displayed some unique advantages in generating and tuning skyrmions. First, the exchange bias at the IrMn/CoFeB interface can eliminate the need for an external magnetic field, leading to zero-field skyrmion formation. Second, the antiferromagnetic order and PMA can be tuned by the IrMn and CoFeB film thicknesses, lending additional flexibility in interfacial control. Third, a sizable SOT in the IrMn permits energy-efficient current control of skyrmions. The rare metals Ta and Ir work together to provide exchange bias, adjust PMA and enhance DMI, so that a single skyrmion can be generated and tuned at the room-temperature and the zero field.

For a dynamic skyrmion in the racetrack, the local exchange-bias field (LEBF) [90,91,92] generated by the IrMn/CoFeB interface can be used to suppress SkHE effectively. The pinning effect by LEBF can make the skyrmion move along the current direction when it is driven by the pulsed current. Here, the rare metal Ir can enhance DMI and stabilize skyrmions in the racetrack. Most importantly, Ir helps to provide the LEBF in IrMn/CoFeB system, which supply an energy barrier and prevent the skyrmion from annihilating at the racetrack edge [12].

Besides synthetic AFM and exchanging bias, there are other methods to overcome SkHE, which can cause the disastrous loss of skyrmion signal. Rare-earth permanent magnets can provide additional energy barrier, similar to the LEBF, which will be discussed in Sect. 6. On the other hand, the Magnus force in the AFM materials is cancelled due to two sets of antiferromagnetic coupled sublattice, which is similar to the case in synthetic AFM and will be elaborated in Sect. 7. In addition, various other potential barriers have been proposed to confine skyrmions in the center region of the racetrack so that the annihilation at the racetrack edge is avoided [93,94,95,96,97,98]. Generally, the rare metals can offer tunnelable PMA as well as DMI and hence the necessary energy barriers, in addition to large SOT under the aid of the electric current.

As displayed above, the spin-polarized current provides an electric method to manipulate skyrmions, which has been used extensively in both experiments and simulations. This method, however, results in undesired Joule heating effects, so that other methods have been proposed to control skyrmions, including magnetic field [89, 99], magnetic field gradient [100], spin wave [101,102,103] and thermal gradient [104]. It should be noted that these methods together with the spin-polarized current can manipulate other exotic topological spin textures, e.g., skyrmionium [103], bimeron [99], bimeronium [95] and antiskyrmion [89]. In any case, rare metals can provide large DMI and PMA to realize the ideal motion of skyrmions and other spin textures.

Recently, various simulations [105] have shown that the electrical field can help to reverse the magnetic moments and hence to manipulate skyrmions in Cu2OSeO3 single crystal sample [106, 107] and CoFeB-MgO nanodisks [108], where the role of rare metals is not identified clearly. Generally, the rare metal can provide large enough DMI and facilitate the formation of skyrmions.

Later in 2019, Ma et al. [109] successfully generated and guided skyrmion bubbles in a [Pt(0.5 nm)/CoNi(0.5 nm)/Pt(0.5 nm)/CoNi(0.5 nm)/Pt(1 nm)] multilayer racetrack at room temperature, where the PMA could be finely tuned by the electric field in both the experiment and the simulation. The rare metal Pt helps to provide adjustable DMI and PMA through the change of the layer thickness, leading to the electric-field induced creation and directional motion of topological spin textures. In the experiment, the multilayer is sandwiched between the indium tin oxide/dielectric bilayer and the glass substrate, resulting in rare metal (Pt)/dielectric (SiO2) interfaces. Importantly, the large anisotropy change can be produced in the interfaces with electric quadrupole induction, which is different from the normal ferromagnet/dielectric interface. The mechanism of generating and manipulating skyrmions and other spin textures in some special materials (frustrated material and so on) will be discussed in next sections.

5 Role of rare metals in generating skyrmions in other materials

5.1 Role of rare metals in frustrated materials

Skyrmions have also been found in materials without DMI, particularly in frustrated materials, where competing exchange interactions or generalized RKKY interactions are responsible for the appearance of chiral spin structures. Skyrmion lattices (skLs) have been identified at low temperatures in gadolinium compounds GdRu2Si2 [110], Gd2PdSi3 [111] and Gd3Ru4Al12 [112], with the corresponding phase diagrams shown in Fig. 6. The formation of skLs is mainly due to the RKKY interactions in these materials, i.e., the coupling between the itinerant electrons and the local magnetic moments. Most itinerant electrons come from the 4d orbit of Ru, while the local magnetic moments result from the 4f orbit of Gd. Here, the rare metals, Gd and Ru, play important roles in providing the frustration and hence the formation of skLs. Chiral spin structures have also been found in other frustrated materials. Notably, Hou et al. [113,114,115,116] found high-temperature skyrmion bubbles in Fe3Sn2 and conducted a series of studies on their generation and manipulation.

Fig. 6
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Reproduced with permission from Ref. [110]. Copyright 2020, Springer Nature. b Contour plot of measured magnetoresistance (MR) of Gd2PdSi3, indicating that skL can exist only below 20 K in addition to a magnetic field (0–1.5 T). Reproduced with permission from Ref. [111]. Copyright 2020, IOP Publishing. c Contour plot of magnetic susceptibility χDC = ∂M/∂H (where M is bulk magnetization, and H is externally applied magnetic field) of Gd3Ru4Al12, demonstrating that skyrmions can only survive at low temperatures (below 15 K) and a strong applied field (1.0–1.7 T). Reproduced with permission from Ref. [112]. Copyright 2019, Springer Nature

Phase diagrams of GdRu2Si2, Gd2PdSi3 and Gd3Ru4Al12 in sequence. a Magnetic phase diagram of GdRu2Si2, where skyrmions can appear below 20 K with a large applied field (> 2 T).

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Zhang et al. systematically studied the static and dynamic properties of skyrmions and other topological spin structures in the frustrated material, including bimerons [37], bimeronium [117] and skyrmionium [38]. Using micromagnetic modeling, they found that Pb2VO(PO4)2 could be a suitable frustrated material for hosting skyrmions, where the frustration comes from the competition between the small nearest neighbor ferrimagnetic interaction and the large next-nearest neighbor AFM interaction. The AFM interaction originates from the rare metal V through the bridge of two oxygen atoms [118].

5.2 Role of rare metals in other centrosymmetric materials

It is noted that skyrmions and other topological spin structures have also been reported in other centrosymmetric materials. Biskyrmions have been identified in La2-2xSr1+2xMn2O7 [119] and MnNiGa [120,121,122], while skyrmion bubbles and skyrmions have also been found in La1-xSrxMnO3 [123] and BaFe12-x-0.05ScxMg0.05O19 (BFSO) [124], respectively. Here, the RE metals La and Ga are to provide and adjust the magnetic moments of the materials, while the doping of the rare metal Sc in BFSO film is mainly to tune the magnetic crystalline anisotropy [124].

5.3 Role of rare metals in 2D van der Waals and ferroelectric materials

Recently, 2D van der Waals (vdW) materials are also reported to be a suitable material for hosting topological spin structures. Particularly, Bloch-type skyrmion bubbles and Néel-type skyrmions have been found in single crystals of 2D vdW material Fe3GeTe2 [30] and 2D vdW heterostructure WTe2/Fe3GeTe2 [31], respectively. Both layers in the heterostructure have rare metal Te atoms, whose coupling enhances the DMI of the system and helps to form skyrmions [31]. Furthermore, the dynamics of the bimerons generated in the 2D vdW multiferroic heterostructure LaCl/In2Se3 has been investigated using micromagnetic simulation. Here, the ferroelectric polarization of In2Se3 destroyes the center inversion symmetry of LaCl, while the DMI comes from the strong SOC of the 5d orbit of the rare metal La, which promotes the generation of bimerons [32].

Ferroelectric materials are another branch of materials that can host skyrmions and related spin structures, including so-called 3D skyrmions in the PbTiO3 layer [25], skyrmion-like states in PbTiO3 nanodisks [125] and skyrmionic states in nanocomposites Ba0.15Sr0.85TiO3 [26].

5.4 Antiskyrmions in Heusler materials

In addition to the above-mentioned topological spin structures, antiskyrmions have also been found recently, which are identified in tetragonal Heusler materials Mn1.4Pt0.9Pd0.1Sn [33], low magnetization ferrimagnet Mn2Rh0.95Ir0.05Sn [34], Fe/Gd-based multilayers [35] and Co/Pt multilayers [36]. The specific structure of the antiskyrmion generated in Mn2Rh0.95Ir0.05Sn material is shown in Fig. 7a [34], where the transmitted electron beam converges vertically toward the center of the antiskyrmion and then diverges horizontally. Therefore, in the LTEM image of antiskyrmion, two bright and two dark lobes will form, as shown in Fig. 7a, b. Magnetic phase diagram of Mn2Rh0.95Ir0.05Sn is shown in Fig. 7c. The rare metal Rh in Mn2Rh0.95Ir0.05Sn material plays important roles in providing a small DMI, which can stabilize the antiskyrmion at nearly room temperature. Similar LTEM image of antiskyrmions has been observed in the Mn1.4Pt0.9Pd0.1Sn material [33].

Fig. 7
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Reproduced with permission from Ref. [34]. Copyright 2020, American Chemical Society

Schematic diagram of antiskyrmion in Mn2Rh0.95Ir0.05Sn. a Distribution of magnetic moment of an antiskyrmion; b LTEM image of a single antiskyrmion at 150 K in presence of a magnetic field of 83 mT, where insets being intensity profiles of contrast along [010] (blue color) and [100] (orange color) directions; c magnetic phase diagram of Mn2Rh0.95Ir0.05Sn, which shows that antiskyrmions are stable over a wide temperature range of 100–250 K at a suitable magnetic field, where H, aSk and FP stand for helical, antiskyrmion and field-polarized states, respectively.

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6 Generating and manipulating topological spin structures using RE permanent magnets

6.1 Spin-reorientation-related skyrmions in RE permanent magnets

The RE metals can offer strong SOC due to their 4f orbits with underfilling electrons and hence the huge crystalline anisotropy field. This giant crystalline anisotropy in turn provides the large coercivity and thus the great energy products necessary for the permanent magnets [126, 127, 128]. RE permanent magnets normally do not display topological spin structures because of the lack of the DMI. However, on certain special occasions, RE permanent magnets can display skyrmions or vortices states. The first case is associated with the spin reorientation, typically occurring at low temperatures for NdFeB. Xiao et al. [129] observed topologically stable skyrmions in Nd2Fe14B by LTEM around the spin reorientation temperature (TSR), whereas magnetic bubbles were observed at temperatures higher than TSR. Skyrmions appear because of the tunable anisotropy and saturation magnetization at TSR, which results mainly from the RE metal Nd. The fall in temperature leads to a significant change in the anisotropy constants from positive to negative, which triggers the spin-reorientation, thereby forming the stable skyrmions.

Similar trigger of topological spin structures by spin reorientation in RE-based magnets have been investigated by Hou et al. [130], where REMn2Ge2 (RE = Ce, Pr, and Nd) can host skyrmionic bubbles in a wide temperature range due to the change of the easy axis. Generally, the topological spin structures are more stable in materials with easy-plane anisotropy than in materials with easy-axis one, leading to the formation of the skyrmions [129] and skyrmionic bubbles [130] near the TSR. Owing to the same reason, skyrmions in GaV4Se8 with an easy-plane anisotropy are more stable than those in GaV4Se8 with an easy-axis anisotropy [28].

6.2 Generating vortices in hard/soft multilayers

On the other hand, RE permanent magnets can help soft magnetic metals to maintain the vortex state in the demagnetization process, as theoretically demonstrated in NdFeB/FeCo [39], exchange coupled NdFeB/Fe [40] and Sm-Co/Fe multilayers [131] with a perpendicular crystalline anisotropy. However, it should be noted that there is no vortex state reported in the hard/soft multilayers with an in-plane crystalline anisotropy [132,133,134].

Vortices states can normally occur in the thin films of very soft magnetic materials like permalloy to reduce the demagnetization energy. However, these vortices ultimately disappear, resulting in a full magnetic reversal under a small applied magnetic field due to the limited coercivity originating from very weak crystalline anisotropy. In exchange coupled multilayers, the large perpendicular crystalline anisotropies provided by the RE permanent magnets will pin the vortex in the soft phase so that it will survive in a larger applied field range, as shown in Fig. 8. Similar vortex states have been found in Ref. [40]. These vortices states produced in the soft phase within hard/soft multilayers have not been observed in experiments yet due to the experimental difficulty in separating the signals in hard and soft layers, which becomes more difficult because the soft phase is normally sandwiched between two hard phases. Technically, a hard/soft bilayer can produce the vortex state similar to a multilayer, where the vortex state in the soft phase can be detected relatively easier.

Fig. 8
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2D evolution of magnetic moments at hard-soft interface calculated by Mumax3 for a Nd2Fe14B(15 nm)/α-Fe(5 nm) bilayer with a perpendicular anisotropy, which demonstrates nucleation, evolution and annihilation of vortices state. a H = −0.35 T, formation of vortex magnetic state after nucleation; b H = −0.65 T, where vortex core begins to rotate away; c H = −1.53 T, right at coercive point where component of magnetic moment in film plane is the largest; and d H = −1.54 T, annihilation of vortex state after magnetic reversal

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6.3 Setting RE permanent magnets to prevent annihilation of skyrmions in racetracks and nano-oscillators

Another important role played by the RE permanent magnets is to pin the skyrmions in the racetrack center and hence to avoid the annihilation of the skyrmion signal [135]. Driven by the applied current, the skyrmions will be drifted to the CoPt racetrack edge due to the Magnus force. Setting the NdFeB and other RE permanent magnets with huge crystalline anisotropy at the edge provides an additional energy barrier that pushes the skyrmion back to the center of the racetrack. As a result, skyrmions will move along the racetrack stably and avoid the skyrmion signals loss. Interestingly, the skyrmion speed along the racetrack will be increased by 30% in comparison with the case of a normal CoPt racetrack without a setting. An in-depth analysis shows that the settings of the high crystalline anisotropy material at the edge push the transverse speed back to the longitudinal direction, thereby increasing the speed of the skyrmions along the racetrack. Similar idea has been used by Juge et al. [136] and Ohara et al. [137] in experiments to hold skyrmions in Pt/Co/MgO racetracks and [Pt/CoNi/FeCo]N multilayers, respectively, where the PMA and DMI have been modified by He+ irradiation [136] or fabricating square and stripe patterns [137]. The PMA and DMI at the edges are enhanced or reduced, hence forming an energy barrier (or trap) to prevent the annihilation of skyrmions at the edges.

Similar enhancement can be applied to a spin-torque nano-oscillator, where RE permanent magnets can be set at the edge of a CoPt disk to avoid the annihilation of the skyrmion signals at the edge. The inlay of the NdFeB at the edge provides an additional energy barrier, pushes back the skyrmion toward the disk center [138], avoids the annihilation of the skyrmion signals and increases the skyrmion frequency by 75%. The noble metal Pt provides the huge SOC and hence the large DMI values necessary for generating skyrmions. On the other hand, the RE metals Nd and Sm provide strong crystalline fields and hence the large PMA, which offer a necessary energy barrier to support skyrmion stability in the CoPt racetrack or the oscillator.

7 Manipulating and generating topological states in antiferromagnets and ferrimagnets

Using the AFM disk, the skyrmion frequency and the related speed in a spin-torque nano-oscillator can be raised by an order. As shown in Fig. 9 [139], the SkHE in an AFM disk disappears naturally so that the skyrmion can rotate steadily around the disk at an ultra-fast speed. Interestingly, the direction of the skyrmion motion is reversed when the current direction switches. In contrast, the skyrmion drifts toward the edge with a negative current while it drifts toward the center with a positive one. For spin-torque nano-oscillators based on ferrimagnetic and AFM skyrmions, the physical mechanisms of their steady motion are different.

Fig. 9
figure 9

Reproduced with permission from Ref. [139]. Copyright 2019, AIP Publishing

Motion of AFM and ferrimagnetic skyrmions driven by different currents in nanodisk, where solid lines and dash lines stand for trajectory of skyrmions and nanodisk edges, respectively. An AFM skyrmion driven by a current of a j = 20 MA·cm−2 and b j = −20 MA·cm−2; a ferrimagnetic skyrmion driven by a current of c j = 20 MA·cm−2 and d j = −20 MA·cm−2.

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AFM materials can also be used in a rectangular racetrack [140], where the AFM skyrmions can be driven efficiently by an anisotropy gradient. Similar to the spin-torque nano-oscillator, the AFM skyrmion speed can be enhanced by one order in comparison with a ferromagnetic skyrmion with the same anisotropy gradient.

AFM skyrmions combine the topology aspect of skyrmions with the fascinating AFM spintronics [141]. The latter has a lot of advantages over the fast-developed ferromagnetic spintronics, namely, much faster dynamics, eliminating the crosstalk between neighboring memory cells due to the disappearance of the net magnetization and multiple stable values via two sets of exchange coupled sublattices [141]. It is also noted that the defects [142] in AFM materials play a more important role in pinning the skyrmions than in ferromagnetic materials. In the latter case, skyrmions can circle around the defects so that the pinning effect around the defects is alleviated. AFM skyrmion-based logic gates have been designed, inspired by the pinning of defects in AFM materials [142].

Most works on AFM skyrmions are theoretical, which do not specify the material. In any case, the nontrivial DMI is necessary for the generation of skyrmions, which is usually related to rare metals. Morvan et al. [143] found that skyrmions can form in the ferromagnetic-AFM bilayer based on the micromagnetic calculation. The AFM material adopted is BiFeO3, which is also a multiferroic material. The rare metal Bi here is responsible for regulating both DMI and ferroelectronic behavior of the system.

Besides skyrmions, other topological spin structures can exist stably in AFM materials, including bimerons and half skyrmions [41]. Shen et al. [27] theoretically investigated the dynamics and chaos of AFM bimerons and found that the bimerons can be stable in AFM materials, which is confirmed by the experiment. Based on α-Fe2O3 capped with a Pt layer, AFM merons, antimerons and bimerons can emerge from the interface between α-Fe2O3 and Pt at room temperature [41], where these spin textures can be tuned by the anisotropy contributed by the rare noble metal Pt. Moreover, the doping of rare metal Rh in a basal α-Fe2O3 composite raises the temperature of the Morin transition, above which the complex spin textures are observed. By tuning the additional anisotropy induced by the rare metal overlayer Pt, which changes with the temperature, the authors show that they can control the (anti)meron core size.

Although antiferromagnets demonstrate ultrafast magnetization dynamics, their spin textures are difficult to be detected by electronic methods due to the zero net magnetization. On the other hand, ferrimagnets combine the advantages of both antiferromagnets and ferromagnets, namely, the high mobility and easy detection of skyrmions respectively. Caretta et al. [144] observed 10 nm skyrmions and fast-moving (1.3 km·s−1) domain walls in the ferrimagnetic Pt/Gd44Co56/TaOx, where the rare metals Pt and Gd can help to offer SOT and PMA, separately. Woo et al. [145] found the ferrimagnetic skyrmion with the reduced skyrmion Hall angle and provided a way of the writing and deleting of a single skyrmion in ferrimagnetic GdFeCo films [23]. Particularly, such ferrimagnetic films of amorphous alloys, consisting of 4f RE and 3d transition-metal elements (RE-TM alloys), can exhibit large PMA and host skyrmion states. Besides the single skyrmion mentioned above, the compact ferrimagnetic skyrmions, with a characteristic core radius about 40 nm, have been observed in the other RE-TM alloy, DyCo3 film [146]. In addition, two distinct skyrmion phases are realized in the hybrid ferro/ferri/ferromagnetic multilayer system at room temperature, containing two [Ir/Fe/Co/Pt]5 multilayers separated by the ferrimagnetic [TbGd/Co]6 layer [147]. The ferrimagnetic layer permits an independent adjustment of anisotropy and magnetization by the RE element ratio (Tb:Gd) and RE:TM thickness ratio (TbGd to Co), respectively.

8 Summary and outlook

The important roles of rare metals in generating and manipulating skyrmions and other topological spin structures are reviewed. In general, rare metals can raise the SOC and hence DMI and other related interactions, thereby enhancing the stability of the skyrmions and other topological spin structures. In B20 crystals, rare metal Ge is responsible for the increase of the TC and expansion of the temperature range in which Bloch-type skyrmions can occur. In thin films and multilayers composed of magnetic and heavy metals, rare metals help to provide considerable PMA or four spin interactions, in addition to strong DMI necessary for the emergence of Néel-type skyrmions. In frustrated materials, rare metals can offer the RKKY interaction or the competing ferrimagnetic and AFM exchange interactions to stabilize skyrmions. Moreover, rare metals can provide additional magnetocrystalline anisotropy and magnetic moments in various materials and trigger the formation of skyrmions and other topological spin structures. In particular, the appearance of skyrmions in Nd2Fe14B and GaV4Se near TSR is due to the abrupt change in the magnetocrystalline anisotropy and magnetic moments. This offers a new approach to search for novel materials generating skyrmions, i.e., the materials with spin reorientation where the crystalline anisotropy changes from the uniaxial to an easy plane.

Rare metals can also help to provide additional energy barrier or RKKY interaction to curb or cancel the SkHE and avoid the annihilation of signals in a skyrmion-based racetrack [20,21,22, 134]. Similar designs can be extended to skyrmion-based logic gates [148], nano-oscillators [149], diodes [150], transistors [151] and neuromorphic computing [152]. In addition, compared with the method driven by the current, the manipulation of exotic topological spin structures by the electric field is getting more and more attention and possess a strong potential to realize next-generation low-consumption spintronics [153, 154]. Therefore, rare metals can play more important roles in manipulating the dynamics of skyrmions in the future.