*Editorial* **Hawai'i in Focus: Navigating Pathways in Global Biocultural Leadership**

**Kevin Chang 1, Kawika B. Winter 2,3,4,\* and Noa Kekuewa Lincoln 5**

Received: 2 January 2019; Accepted: 4 January 2019; Published: 8 January 2019

**Abstract:** As an introduction to the special issue on "Biocultural Restoration in Hawai'i," this manuscript provides background for term 'biocultural restoration,' and contextualizes it within the realms of scholarship and conservation. It explores two key themes related to the topic. First, "Earth as Island, Island as Earth," scales up an island-borne concept of sustainability into a global context. Second, "Hawai'i as a Biocultural Leader," examines the reasons behind the global trend of looking to the most isolated landmass on the planet for solutions to global sustainability issues. We conclude by summarizing the content of the special issue and pointing out the historic nature of its publication. It is the largest collection to date of scientific papers authored by Native Hawaiians and *kama'aina ¯* (Hawai'i-grown) scholars, and more than 50% of both lead and total authorship are women. This Special Issue, therefore, represents a big step forward for under-represented demographics in science. It also solidifies, as embodied in many of the papers in this Special Issue, indigenous methodologies that prioritize working relationships and practical applications by directly involving those on the front lines of biocultural conservation and restoration.

**Keywords:** Native Hawaiian; social-ecological system; agro-ecology; *'aina momona ¯*


**6. Conclusions**

Covering rough set models are important research topics, which investigate data mining in a more general manner. Huang et al. [33] presented an IF rough set model and an optimistic multi-granulation IF rough set model. By investigation, we have found that no one has applied multi-granulation IF rough set models to MCGDM problems. In this paper, by showing some new notions and properties of IF *β*-covering approximation spaces, we mainly study Huang et al.'s models and propose a novel approach to MCGDM problems. The main conclusions in this paper and the further work are listed as follows.

**Author Contributions:** All authors have contributed equally to this paper. The individual responsibilities and contribution of all authors can be described as follows: the idea of this whole thesis was put forward by X.Z.; he also completed the preparatory work of the paper; J.W. analyzed the existing work of rough sets and IF sets, and wrote the paper.

**Funding:** This work is supported by the National Natural Science Foundation of China under Grant Nos. 61573240 and 61473239.

**Conflicts of Interest:** The authors declare no conflict of interest.


**3.8 Crash of Convair 580**

As many as 10 recent air crashes, including the American Airlines disaster in New York in November 2001, could have been linked to a newly uncovered scam by which old and faulty aircraft parts were sold as new [19]. Parts illegally salvaged from crashes, counterfeit parts, and other substandard components regularly find their way into the world's air fleets, sold at bargain prices, often with falsified documents about their origin or composition. The worst confirmed accident occurred on Sept. 8, 1989, when at 22,000 feet over the North Sea, the tail section of a Convair 580 turboprop plane began vibrating violently and tore loose [20]. The charter aircraft, carrying 55 people from Oslo to Hamburg, splattered over 3 1/2 miles of sea. Everyone onboard died. Norwegian investigators painstakingly dredged up 90% of the 36-yearold plane and found the cause: bogus bolts, bushings, and brackets.

## **3.9 Twin accidents involving Boeing 737 max**

A Boeing 737-Max airplane (Lion Air Flight 610) took off from Jakarta, Indonesia, on October 28th, 2018 and crashed into the Java Sea soon after takeoff, killing all 189 passengers and crew. Five months down the line, another Boeing 737-Max airplane (Ethiopian Airlines Flight 302) took off from Addis Ababa, Ethiopia, on March 10th, 2019 and crashed near the town of Bishoftu in Ethiopia, killing all 157 people in the aircraft. The aircraft contained a new feature called the Maneuvering Characteristics Augmentation System (MCAS) in its flight control computer [21]. Crash of these two Boeing 737max airplanes raised eyebrows about the technical design flaws, faulty assumptions about pilot responses, and management failures by both Boeing and the FAA.


*2.2. Anti-Inflammatory Response*

An inflammatory response to autocrine or paracrine stimulation prompts HSC activation and proliferation. HSC activation consists of two stages: initiation and perpetuation [25,27]. Early changes in gene expression and phenotype represent the initiation stage. Initiation is mainly induced by cytokines, or other stimuli from cells around HSCs and act as paracrine pathways [27]. Reactive oxygen species (ROS) released from Kupffer cells can directly stimulate and activate HSCs [45]. By cascade amplification of inflammatory response, a large number of inflammatory cells infiltrate the damaged sites, and secrete inflammatory cytokines, leading to HSC activation and proliferation [46]. Continuous stimulation can induce HSCs into myofibroblast cells, inducing the perpetuation stage. The activated HSCs subsequently release chemokines, further aggravating the inflammatory response. In this stage, HSC promotes inflammation, fibrosis, and cell proliferation in the autocrine and/or paracrine pathway. Therefore, the inflammation response plays an important role in liver fibrosis. Anti-inflammatory drugs such as corticosteroids [47], colchicine [48], and ursodeoxycholic acid [49] have been used to treat liver fibrosis. Another anti-inflammatory strategy involves the application of specific receptor antagonists to

neutralize inflammatory cytokines. In one study, the antifibrotic and anti-inflammatory effects of IL-10 were observed in patients infected with hepatitis C [50]. Moreover, hepatic macrophages participate in the pathogenesis of liver fibrosis by the secretion of inflammatory factors. Targeting hepatic macrophages is also an effective anti-inflammatory technique for the treatment of liver fibrosis [51].


**The Minipig — A New Tool in Stem Cell Research**

Hideyuki Kobayashi, Toshihiro Tai, Koichi Nagao and Koichi Nakajima

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/57603

**1. Introduction**

[58] West PR, Weir AM, Smith AM, Donley EL, Cezar GG. Predicting human develop‐ mental toxicity of pharmaceuticals using human embryonic stem cells and metabolo‐

[59] Kleinstreuer NC, Smith AM, West PR, Conard KR, Fontaine BR, Weir-Hauptman AM, et al. Identifying developmental toxicity pathways for a subset of ToxCast chemicals using human embryonic stem cells and metabolomics. Toxicology and ap‐

[60] Howes CG, Foster LJ. PrestOMIC, an open source application for dissemination of proteomic datasets by individual laboratories. Proteome science. 2007;5:8.

[61] Xirasagar S, Gustafson S, Merrick BA, Tomer KB, Stasiewicz S, Chan DD, et al. CEBS object model for systems biology data, SysBio-OM. Bioinformatics. 2004;20(13):

[62] Xirasagar S, Gustafson SF, Huang CC, Pan Q, Fostel J, Boyer P, et al. Chemical effects in biological systems (CEBS) object model for toxicology data, SysTox-OM: design

mics. Toxicology and applied pharmacology. 2010;247(1):18-27.

plied pharmacology. 2011;257(1):111-21.

196 Pluripotent Stem Cell Biology - Advances in Mechanisms, Methods and Models

and application. Bioinformatics. 2006;22(7):874-82.

2004-15.

The establishment of pluripotent mouse embryonic stem cells (ESCs), which have the capacity to differentiate into all cell types in the mammalian body, was first described by Evans and Kaufman in 1981. Seventeen years later, in 1998, the first report of human ESCs, with similar differentiation characteristics was published by James Thompson. In 2006, Takahashi and Yamanaka discovered that the genome of a differentiated somatic cell could be epigenetically reprogrammed to pluripotency by inducing the expression of pluripotency transcription factors, resulting in the production of pluripotent stem cells (iPSCs). This research has accelerated the study of regenerative medicine.

In 2009, the US Food and Drug Administration approved the first Phase I clinical trials of human ESC-derived cells for the treatment of spinal cord injuries. However, previous reports had revealed that stem cell-based therapies increase the risk of tumor development. Therefore, further basic research is needed before stem cell-based therapies can be applied in the clinic. The development of stem cell tools can be critically evaluated using animal models that express human disease genes.

Research on the stem cell biology of the minipig is developing rapidly. Although research on mouse and human stem cells currently predominates over that in other species, data from these well-studied species have provided a good foundation for current and future porcine stem cell research. In addition, the increasing popularity of alternative-species models for the study of human diseases and disease mechanisms has further spurred porcine stem cell research. As a model system for pluripotent embryonic stem cell research, however, the pig presents several challenges as compared with mice and humans. Nonetheless, porcine minipig embryonic germ cells have recently been produced, and may prove particularly useful for *in vitro* and *in vivo* differentiation studies, gene targeting, and the creation of transgenic animals. In addition,

© 2014 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

studies involving the transplantation of somatic mesenchymal stem cells into porcine heart, cartilage, and bone have yielded very promising results. Lastly, minipig induced pluripotent stem cells have been established by using Sendai viruses to introduce pluripotency transcrip‐ tion factors into the cells.

by somatic cell nuclear transfer, using minipig fetal or neonatal fibroblasts as the donor and prepubertal gilt oocytes, followed by culture *in vitro* to the blastocyst stage of development. Two cells lines could be cultured for more than 48 passages, and expressed alkaline phospha‐ tase (AP), SSEA1 and SSEA3, OCT4, TRA-1-60, and TRA-1-81. The only method used to characterize their differentiation ability was the observation of spontaneous differentiation into embryoid bodies (EBs), which are spheres of cells that contain cell types of all three germ layers. These EBs were assessed solely by gene analysis, thus further characterization would

The Minipig — A New Tool in Stem Cell Research

http://dx.doi.org/10.5772/57603

199

Only two reports to date describe the production of chimeras from porcine ESC-like cells: one in 1999, from Chen and colleagues [12], and a more recent publication in 2010 [13]. The first report claimed that somatic chimeric piglets could be produced, although clear analyses of these chimeric animals was lacking. The second report indicated that porcine ESC-like cells from an early passage could form chimeric piglets. The chimeric contribution was low, however; only 4 chimeric piglets were born after the transfer of hundreds of embryos. Only 2 of the 4 chimeric piglets showed coat chimerism, and this contribution was low and restricted to a single spot near the tail. Such a chimeric contribution is much lower than what would be expected from mouse ESCs, indicating that improvements to the cell culture conditions may

There are several possible reasons for the difficulty in producing porcine ESCs. The lack of defined culture conditions may be one reason. Pluripotency appears to be controlled by more than one cell-signaling pathway, and these pathways are different in mouse and human ESC lines. The origin of the cells, that is, the inner cell mass (mouse) versus the epiblasts (human) may contribute to this diversity of regulatory pathways. This idea is supported by a recent publication showing that even mouse EpiSCs regulate pluripotency slightly differently from human ESCs [14]. The cell signaling that governs pluripotency in the pig remains largely unknown, although the details are beginning to be investigated [15]. For example, it was reported that fibroblast growth factor (FGF) signaling may be active in porcine epiblasts, and that the JAK/STAT pathway is inactive. The Activin/Nodal pathway also appears to be active in porcine epiblasts [8]. Culturing porcine epiblasts in medium containing basic FGF (bFGF) cannot prevent their differentiation, indicating that other factors are apparently necessary to

Differences occurring during early embryonic development in the domestic pig, as compared with mouse and human, could also account for the observed difficulties in producing porcine ESCs. The early development of the porcine embryo prior to implantation takes longer and is less advanced than in the other species. The inner cell mass differentiates into the hypoblast and epiblast at a later time point than in the mouse and human, and the porcine epiblast expands and develops over a period of several days. The cell signaling controlling this development in the pig could differ markedly from that in the mouse or human, and should be investigated to ascertain which stage of development is optional for isolating the pluripotent cells. It is possible that the later epiblast is already predetermined at the cell-signaling level to undergo gastrulation, or that the inner cell mass cells have not yet acquired the necessary cell

be necessary before they could be verified as true ESCs.

be required to improve the plasticity of these cells.

help maintain cellular pluripotency.

signaling machinery to support proliferation.

Thus, despite the challenges of developing porcine pluripotent stem cells, recent successes in the fields of both induced pluripotent stem cells and somatic stem cells suggest that the future of research using minipig stem cells is quite promising.


**5.2.2 Analysis of jitter**

26 Mobile Networks

As shown in the (figure 35), in the time that the AMN is in the AHA zone (between t = 1.2s and t = 10s), the traffic experiences a delay below 250ms, this is due mainly to the fact that

Fig. 33. Scenario with 20 nodes

Fig. 34. Scenario with 30 nodes

**5.2.1 Analysis of delay**

The (figure36) illustrates the jitter behavior as time in the simulation.

As it can be seen in figure 36, the jitter has a similar behavior to the delay during the first 10s of simulation, in the sense that both present the lowest values throughout the simulation in this range, but after the AMN moves towards the PAR/LER1 a huge peak of about 650ms is registered, this corresponds with the packet that experiences more than 700ms in delay in figure 80. After this, the jitter is stabilized below 50ms when the AMN is in the ANAR/LER2 zone (after t = 20s) and below 100ms when the AMN is in the APAR/LER1 zone (between the 11s and 18s or so). Additionally it is noted that the transfer that takes place near the instant t = 16s has no significant effects on the experienced fluctuation. Finally the average jitter during the simulation was 15.84ms.

Mechamisms to Provide Quality of Service on 4G New Generation Networks 29

During the simulation 1610 packets were sent from the AMN to the ACN, out of which 1586 reached their destination, leading to the loss of 24 packets, which corresponds to 1.49% of

The table 11 presents various facts to highlight: first, both the delay and the fluctuation do not exhibit increasing tendency as the number of nodes increases, this is important because

Fig. 37. Illustrate throughput vs. time

Fig. 38. TCP congestion window vs. time

**5.2.5 Analysis of lost packets**

the total packets.

**5.2.6 Analysis of results**

Fig. 36. Jitter vs. time


Stabilizing Zero-Field Skyrmions at Room-Temperature in Perpendicularly Magnetized Multilayers

*Jeovani Brandão, Marcos Vinicius Puydinger dos Santos and Fanny Béron*

## **Abstract**

Magnetic skyrmions are twirling spin structures observed in bulk, thin films, and multilayers with several features for both fundamental physics understanding and spintronic applications, i.e., nanoscale size, efficient transport under electrical current, and topological protection against defects. However, most magnetic skyrmions have been observed under the assistance of an out-of-plane magnetic field, which may limit their use in magnetic memory technologies. In this chapter, we review and present two recent mechanisms to create zero-field skyrmions at room-temperature in ferromagnetic multilayers. First, by tuning the perpendicular magnetic anisotropy (PMA) and remnant magnetization (near magnetization saturation) in unpatterned symmetric multilayer systems, it was achieved a transition from worm-like domains to isolated skyrmions. Besides, we present how to find stable zero-field skyrmions in arrays of ferrimagnetic discs by tailoring their diameter. Both methods demonstrate a robust route to stabilize zero-field skyrmions at room temperature, thus providing an important contribution to possible applications of these textures in the next generation of skyrmionics devices.

**Keywords:** multilayers, room-temperature, stability, skyrmions, zero-field

## **1. Introduction**

Chiral magnets [1–8] have been investigated intensively in the last years due to their fascinating physical concepts and potential use in applications including sensors [9–11], logic [12–14], and magnetic memory devices [15, 16]. Among different magnetic structures, domain walls [17], vortices [18], and skyrmions [19] have been investigated both theoretically and experimentally. They exhibit remarkable static and dynamic behaviors under external stimulation such as magnetic [20] and electrical fields [21], thermal effects [22], and electrical currents [23]. More specifically, magnetic skyrmions, i.e., small-sized non-collinear chiral spin textures [24], have been attracted much attention as the favorable candidates for information storage in different technological devices, as examples, racetrack memories designed as nanowires [25] and nano-oscillators [26] based on confined nano-discs [27]. This

huge interest in manipulating skyrmions lies in their special properties including topological protection [28], efficient transport under low electric current density [29], and reduced (below 100 nm) size [30].

Experimentally, these non-collinear spin structures were firstly observed a little more than one decade ago in bulk systems [31], but at low temperatures (around 30 K) and under magnetic fields (around 0.2 T) [32, 33]. To achieve skyrmions at ambient conditions, perpendicularly magnetized multilayers made of nano-thick magnetic and non-magnetic materials have been used as a platform with suitable parameters to host skyrmions at room-temperature [20]. One important parameter is the Dzyaloshinskii-Moriya interaction (DMI) induced by spin orbit-coupling [34]. In the case of multilayers, it arises due to the interfacial nature between the atoms of the heavy metal (HM)\ferromagnetic (FM) layers [20]. The DMI is responsible for the chirality of the magnetic structure, i.e., the direction in which the spins rotate in the texture, giving rise to the topological skyrmion stability [6].

For multilayers made of thin films, such as Pt/Co/Ta, Pt/Co/Ir, Pt/Co/W, and other combinations, skyrmions have been observed in most cases under applied external magnetic fields [20, 35, 36], while at zero magnetic field the magnetic ground state favors the formation of spin spirals or labyrinthine magnetic configurations [37]. Under the assistance of a moderate magnetic field, the magnetic stripes shrink into small circular structures [20, 35], leading to the creation of magnetic skyrmions. This is possible thanks to the DMI that acts to protect the skyrmion against collapsing into a uniform magnetic state [20]. Moreover, the skyrmion size depends on the magnetic field strength, usually being inversely proportional to the applied field [20, 38].

This mechanism for creating skyrmions in multilayers under the aid of a magnetic field opened an avenue for controlling their fundamental physical properties such as size and density. On the other hand, the usage of skyrmions in the next generation of magnetic memory devices will depend on the achievement of skyrmions without the support of external stimuli. In this sense, the research for efficient methods to establish zero-field skyrmions at room-temperature yields interesting findings. For instance, zero-field skyrmions have been observed at roomtemperature in lithographically shaped squares [39], through an exchange bias-field created at the interface of antiferromagnetic/ferromagnetic-based structures [40], and by their direct writing using magnetic force microscopy (MFM) tips [41], X-rays [42], and electron beam [43].

In this chapter, we report on two current processes for stabilizing zero-field magnetic skyrmions in ferro- and ferrimagnetic multilayers at ambient conditions. The different approaches driving the formation of zero-field skyrmions consist of tuning the magnetic properties such as perpendicular magnetic anisotropy (PMA) and DMI in unpatterned symmetric multilayers, as well as by tailoring the geometric size of circular discs. The zero-field skyrmions were imaged by magnetic force microscopy at room-temperature. Both mechanisms establish efficient strategies to create zero-field skyrmions at ambient conditions, which is an important advance in the development of skyrmionics devices.

## **2. Zero-field Skyrmions in Unpatterned symmetric multilayers**

Skyrmions at room-temperature are created in perpendicularly magnetized multilayers made of a magnetic material sandwiched by two different heavy metal layers, HM1 and HM2, which yield sizeable DMI values to topologically protect and stabilize skyrmions under the assistance of a magnetic field [20]. Therefore,

**51**

**Figure 1.**

*Stabilizing Zero-Field Skyrmions at Room-Temperature in Perpendicularly Magnetized…*

most previous works have focused on asymmetric multilayers, which, at zero field and under the competition of different energies (exchange, anisotropy, dipolar, DMI), can lead to the labyrinthine domain structures. These domain structures turn into skyrmions in the presence of a magnetic field below the saturation

Alternatively, symmetric multilayers made of the same heavy metal layers, for instance Pt/Co/Pt and Pd/Co/Pd, can also be used to create skyrmions [44]. It has been demonstrated that for polycrystalline symmetric Pt/Co/Pt tri-layers deposited by magnetron sputtering, a low but non-negligible DMI is measurable in the system [45]. More recently, a strong DMI has been observed in symmetric Pd/Co superlattices grown by molecular beam epitaxial (MBE) technique [46]. This is due to the differences in the crystalline structures and inhomogeneities at the interfaces of the HM/FM and FM/HM layers, which yield to the formation of asymmetric interfaces. Therefore, a DMI emerges in these irregular interfaces and opens the possibility for

In this sense, in order to find zero-field skyrmions at room-temperature, multilayers of (Pd/Co/Pd)x15 were fabricated by magnetron sputtering technique, where the Pd thickness was fixed at 2 nm and the Co layer varied from 0.2 to 0.8 nm. **Figure 1** shows the schematic representation of the multilayer Pd/Co/Pd grown on

Hysteresis loops acquired under out-of-plane magnetic field for different Co thicknesses show that the reversal magnetization behavior depends on the Co thickness (**Figure 2**). At 0.8 nm-thick Co (down blue triangles), the hysteresis loop exhibits a very low remnant magnetization, while its saturation occurs beyond 150 mT, which is a larger magnetic field compared to the ones obtained for thicknesses below 0.8 nm. It essentially means that for this specific thickness, the in-plane anisotropy plays an important role in the magnetization reversal. It has already been demonstrated that above this thickness (0.8 nm thick Co), the magnetization of a

Moreover, by reducing the Co layer thickness to 0.6 nm, the hysteresis loop turns into a tail-like shape with reduced saturation magnetic field (up green triangles), but no significant change is observed for the remnant magnetization. This tendency is altered significantly when the Co thickness is reduced to 0.4 (red circles) and 0.2 nm (black squares). The square format of the magnetization curve is characterized by a reduction of the saturation magnetic field, as well as a notable enhancement of the remnant magnetization (near to the saturation magnetization),

*Stack of the symmetric multilayer produced by magnetron sputtering. Figure adapted from reference [47].*

exploring chiral magnetic textures in symmetric systems [47].

similar multilayered system lies in the sample plane [48].

*DOI: http://dx.doi.org/10.5772/intechopen.97179*

magnetization [20, 35, 36].

Si/SiO2 substrate.

**2.1 Magnetic properties**

*Stabilizing Zero-Field Skyrmions at Room-Temperature in Perpendicularly Magnetized… DOI: http://dx.doi.org/10.5772/intechopen.97179*

most previous works have focused on asymmetric multilayers, which, at zero field and under the competition of different energies (exchange, anisotropy, dipolar, DMI), can lead to the labyrinthine domain structures. These domain structures turn into skyrmions in the presence of a magnetic field below the saturation magnetization [20, 35, 36].

Alternatively, symmetric multilayers made of the same heavy metal layers, for instance Pt/Co/Pt and Pd/Co/Pd, can also be used to create skyrmions [44]. It has been demonstrated that for polycrystalline symmetric Pt/Co/Pt tri-layers deposited by magnetron sputtering, a low but non-negligible DMI is measurable in the system [45]. More recently, a strong DMI has been observed in symmetric Pd/Co superlattices grown by molecular beam epitaxial (MBE) technique [46]. This is due to the differences in the crystalline structures and inhomogeneities at the interfaces of the HM/FM and FM/HM layers, which yield to the formation of asymmetric interfaces. Therefore, a DMI emerges in these irregular interfaces and opens the possibility for exploring chiral magnetic textures in symmetric systems [47].

In this sense, in order to find zero-field skyrmions at room-temperature, multilayers of (Pd/Co/Pd)x15 were fabricated by magnetron sputtering technique, where the Pd thickness was fixed at 2 nm and the Co layer varied from 0.2 to 0.8 nm. **Figure 1** shows the schematic representation of the multilayer Pd/Co/Pd grown on Si/SiO2 substrate.

#### **2.1 Magnetic properties**

*Magnetic Skyrmions*

skyrmion stability [6].

applied field [20, 38].

[42], and electron beam [43].

in the development of skyrmionics devices.

[29], and reduced (below 100 nm) size [30].

huge interest in manipulating skyrmions lies in their special properties including topological protection [28], efficient transport under low electric current density

Experimentally, these non-collinear spin structures were firstly observed a little more than one decade ago in bulk systems [31], but at low temperatures (around 30 K) and under magnetic fields (around 0.2 T) [32, 33]. To achieve skyrmions at ambient conditions, perpendicularly magnetized multilayers made of nano-thick magnetic and non-magnetic materials have been used as a platform with suitable parameters to host skyrmions at room-temperature [20]. One important parameter is the Dzyaloshinskii-Moriya interaction (DMI) induced by spin orbit-coupling [34]. In the case of multilayers, it arises due to the interfacial nature between the atoms of the heavy metal (HM)\ferromagnetic (FM) layers [20]. The DMI is responsible for the chirality of the magnetic structure, i.e., the direction in which the spins rotate in the texture, giving rise to the topological

For multilayers made of thin films, such as Pt/Co/Ta, Pt/Co/Ir, Pt/Co/W, and other combinations, skyrmions have been observed in most cases under applied external magnetic fields [20, 35, 36], while at zero magnetic field the magnetic ground state favors the formation of spin spirals or labyrinthine magnetic configurations [37]. Under the assistance of a moderate magnetic field, the magnetic stripes shrink into small circular structures [20, 35], leading to the creation of magnetic skyrmions. This is possible thanks to the DMI that acts to protect the skyrmion against collapsing into a uniform magnetic state [20]. Moreover, the skyrmion size depends on the magnetic field strength, usually being inversely proportional to the

This mechanism for creating skyrmions in multilayers under the aid of a magnetic field opened an avenue for controlling their fundamental physical properties such as size and density. On the other hand, the usage of skyrmions in the next generation of magnetic memory devices will depend on the achievement of skyrmions without the support of external stimuli. In this sense, the research for efficient methods to establish zero-field skyrmions at room-temperature yields interesting findings. For instance, zero-field skyrmions have been observed at roomtemperature in lithographically shaped squares [39], through an exchange bias-field created at the interface of antiferromagnetic/ferromagnetic-based structures [40], and by their direct writing using magnetic force microscopy (MFM) tips [41], X-rays

In this chapter, we report on two current processes for stabilizing zero-field magnetic skyrmions in ferro- and ferrimagnetic multilayers at ambient conditions. The different approaches driving the formation of zero-field skyrmions consist of tuning the magnetic properties such as perpendicular magnetic anisotropy (PMA) and DMI in unpatterned symmetric multilayers, as well as by tailoring the geometric size of circular discs. The zero-field skyrmions were imaged by magnetic force microscopy at room-temperature. Both mechanisms establish efficient strategies to create zero-field skyrmions at ambient conditions, which is an important advance

**2. Zero-field Skyrmions in Unpatterned symmetric multilayers**

Skyrmions at room-temperature are created in perpendicularly magnetized multilayers made of a magnetic material sandwiched by two different heavy metal layers, HM1 and HM2, which yield sizeable DMI values to topologically protect and stabilize skyrmions under the assistance of a magnetic field [20]. Therefore,

**50**

Hysteresis loops acquired under out-of-plane magnetic field for different Co thicknesses show that the reversal magnetization behavior depends on the Co thickness (**Figure 2**). At 0.8 nm-thick Co (down blue triangles), the hysteresis loop exhibits a very low remnant magnetization, while its saturation occurs beyond 150 mT, which is a larger magnetic field compared to the ones obtained for thicknesses below 0.8 nm. It essentially means that for this specific thickness, the in-plane anisotropy plays an important role in the magnetization reversal. It has already been demonstrated that above this thickness (0.8 nm thick Co), the magnetization of a similar multilayered system lies in the sample plane [48].

Moreover, by reducing the Co layer thickness to 0.6 nm, the hysteresis loop turns into a tail-like shape with reduced saturation magnetic field (up green triangles), but no significant change is observed for the remnant magnetization. This tendency is altered significantly when the Co thickness is reduced to 0.4 (red circles) and 0.2 nm (black squares). The square format of the magnetization curve is characterized by a reduction of the saturation magnetic field, as well as a notable enhancement of the remnant magnetization (near to the saturation magnetization),

**Figure 2.** *Out-of-plane hysteresis curves for different Co thicknesses. Figure adapted from reference [47].*

indicating that the (PMA) is higher in this thickness range. It yields a thicknessdependency modulation of the remnant magnetization.

Consequently, both the tunable remnant magnetization and the PMA as a function of the thickness play an important role in the resulting magnetic domain patterns at zero magnetic field and room-temperature, as shown in **Figure 3**. The blue frame (0.8 nm) exhibits the formation of small periodic out-of-plane magnetic domains, while the green frame (0.6 nm), of the well-known worm-like domain pattern in such perpendicularly magnetized systems. The domain pattern transition occurs at Co-thick 0.4 nm (red frame), where the MFM image shows long separated magnetic stripes with a few circular domains in between. This is a preliminary indication of the magnetic skyrmion formation in the symmetric multilayer.

The formation of these round structures in symmetric multilayers is further confirmed for the 0.2 nm-thick Co film (black frame), in which the magnetic domain pattern is given by isolated skyrmions at room-temperature and zero magnetic field. This result shows that by carefully tuning the remnant magnetization and PMA of the multilayer, isolated skyrmions can be observed without the need of applying a magnetic field. In other words, increasing the PMA and the remnant magnetization can yield the formation of field-free skyrmions at ambient conditions. Notably, these skyrmions are created only by tuning the multilayer thickness, rather than through any geometric confinement or writing methodologies. This represents a straightforward and feasible alternative to stabilize zero-field skyrmions at room-temperature.

## **2.2 Skyrmion formation reproducibility**

The homogeneity of the magnetic skyrmions along the sample surface was also tracked by taking MFM images over different areas of the 0.2 nm-thick Cofilm, as shown in **Figure 4**. The skyrmions are isolated with randomly distributed positions. This result confirms that the skyrmions at zero-field are reproducible on the entire surface of the multilayer rather than from any topographic influence on the different sample regions. Besides, the skyrmion sizes observed in each image are slightly different, which arises from minor inhomogeneities in the sample and different local variations of the multilayer properties such as saturation magnetization (*M*s), PMA, and DMI [49].

To explore the features of the stabilized zero-field skyrmions, their size (diameter) and density (number of skyrmions per area) were extracted from the MFM

**53**

**Figure 3.**

**Figure 4.**

*adapted from [47].*

*reference [47].*

were ~ 165 nm ± 32 nm and 0.25/μm2

usually reduces these values [37].

*Stabilizing Zero-Field Skyrmions at Room-Temperature in Perpendicularly Magnetized…*

images. The skyrmion size was evaluated by performing line scans on the magnetic structures and using the full width at half maximum (FWHM), as shown in **Figure 5(a)** and compiled in a histogram in **Figure 5(b)**, along with the skyrmion density statistics (**Figure 5(c)**). The average size and density of the skyrmions

*Magnetic skyrmions observed in different areas of the 0.2 nm-thick Co film at the remnant state. Figure*

*Magnetic force microscopy (MFM) images of the zero-field domain evolution. Figure adapted from*

where skyrmions were stabilized under applied magnetic field [20, 35], which

. These values agree with previous works

*DOI: http://dx.doi.org/10.5772/intechopen.97179*

*Stabilizing Zero-Field Skyrmions at Room-Temperature in Perpendicularly Magnetized… DOI: http://dx.doi.org/10.5772/intechopen.97179*

**Figure 3.**

*Magnetic Skyrmions*

**Figure 2.**

indicating that the (PMA) is higher in this thickness range. It yields a thickness-

*Out-of-plane hysteresis curves for different Co thicknesses. Figure adapted from reference [47].*

Consequently, both the tunable remnant magnetization and the PMA as a function of the thickness play an important role in the resulting magnetic domain patterns at zero magnetic field and room-temperature, as shown in **Figure 3**. The blue frame (0.8 nm) exhibits the formation of small periodic out-of-plane magnetic domains, while the green frame (0.6 nm), of the well-known worm-like domain pattern in such perpendicularly magnetized systems. The domain pattern transition occurs at Co-thick 0.4 nm (red frame), where the MFM image shows long separated magnetic stripes with a few circular domains in between. This is a preliminary indication of the magnetic skyrmion formation in the symmetric multilayer. The formation of these round structures in symmetric multilayers is further confirmed for the 0.2 nm-thick Co film (black frame), in which the magnetic domain pattern is given by isolated skyrmions at room-temperature and zero magnetic field. This result shows that by carefully tuning the remnant magnetization and PMA of the multilayer, isolated skyrmions can be observed without the need of applying a magnetic field. In other words, increasing the PMA and the remnant magnetization can yield the formation of field-free skyrmions at ambient conditions. Notably, these skyrmions are created only by tuning the multilayer thickness, rather than through any geometric confinement or writing methodologies. This represents a straightforward and feasible alternative to stabilize zero-field

The homogeneity of the magnetic skyrmions along the sample surface was also tracked by taking MFM images over different areas of the 0.2 nm-thick Cofilm, as shown in **Figure 4**. The skyrmions are isolated with randomly distributed positions. This result confirms that the skyrmions at zero-field are reproducible on the entire surface of the multilayer rather than from any topographic influence on the different sample regions. Besides, the skyrmion sizes observed in each image are slightly different, which arises from minor inhomogeneities in the sample and different local variations of the multilayer properties such as saturation magnetization (*M*s),

To explore the features of the stabilized zero-field skyrmions, their size (diameter) and density (number of skyrmions per area) were extracted from the MFM

dependency modulation of the remnant magnetization.

skyrmions at room-temperature.

**2.2 Skyrmion formation reproducibility**

**52**

PMA, and DMI [49].

*Magnetic force microscopy (MFM) images of the zero-field domain evolution. Figure adapted from reference [47].*

**Figure 4.**

*Magnetic skyrmions observed in different areas of the 0.2 nm-thick Co film at the remnant state. Figure adapted from [47].*

images. The skyrmion size was evaluated by performing line scans on the magnetic structures and using the full width at half maximum (FWHM), as shown in **Figure 5(a)** and compiled in a histogram in **Figure 5(b)**, along with the skyrmion density statistics (**Figure 5(c)**). The average size and density of the skyrmions were ~ 165 nm ± 32 nm and 0.25/μm2 . These values agree with previous works where skyrmions were stabilized under applied magnetic field [20, 35], which usually reduces these values [37].

#### **Figure 5.**

*(a) Line scans performed on skyrmions of different sizes. Histograms of the skyrmion size (b) and number (c) distributions obtained in each MFM image. Figure adapted from [47].*

#### **Figure 6.**

*(a-c) Micromagnetic results of isolated skyrmions stabilized at zero magnetic field. (d) Skyrmion size obtained as a function of Ms for different values of PMA and DMI. Figure taken from [47].*

#### **2.3 Micromagnetic simulations**

The formation of zero-field skyrmions in unpatterned symmetric multilayers is described better with the assistance of micromagnetic simulations. Mumax3 was the chosen code to carry out the simulations, and the used methods and parameters can be found in [47]. The results are summarized in **Figure 6.**

**55**

**Figure 7.**

*from reference [47].*

*Stabilizing Zero-Field Skyrmions at Room-Temperature in Perpendicularly Magnetized…*

In **Figure 6(a-c)**, the micromagnetic simulations are representative for an anisotropy *K* = 0.06 MJm−3 and a Dzyaloshinskii-Moriya interaction *D* = 0.04 mJm−2, while the saturation magnetization *M*s was varied. It shows that skyrmions are stabilized at zero-field with a random distribution of their positions, corroborating our experimental findings. Furthermore, by varying *D* in the micromagnetic simulations and comparing with the size of zero-field skyrmions obtained experimentally, the DMI was estimated to range between 0.4–0.8 mJm−2. More details can

More remarkable, the skyrmion size increases for larger values of *M*s as clearly shown in **Figure 6(a-c)**, indicating that this parameter plays an important role on the skyrmion diameter due to the impact of the magnetization stray field upon the magnetic structure size. In addition to the saturation magnetization, the influence of both *K* and *D* parameters was evaluated to understand their effects on the skyrmion stability and size. Figure 6 (d) shows that the skyrmion size monotonically increases as a function of *M*s for any value of *K* and *D*. However, smaller *K* and *D* values lead to larger skyrmion size (black squares) compared to higher values (red circles and blue triangles). This important conclusion suggests that the sample saturation magnetization *M*s must be reduced, while the PMA and DMI must be increased slightly to reduce the skyrmion average size at zero-field. This can be accomplished by engineering the multilayer structure varying, for instance, the

A phase diagram was constructed using the micromagnetic simulations to explore and indicate the achievable magnetic ground states as a function of the

Three different magnetic ground states were acquired at zero magnetic field, as shown in **Figure 7(a)**: uniform magnetization (dark cyan frame), isolated skyrmions (cyan frame), and mixed phase (purple frame), in which the latter

*(a) Possible magnetic ground states. (b) DMI vs. Ms phase diagram for selected values of K. Figure adapted*

multilayer magnetic parameters, as can be seen in **Figure 7**.

*DOI: http://dx.doi.org/10.5772/intechopen.97179*

magnetic layer thickness.

**2.4 Magnetic domain phase diagrams**

be seen in the phase diagrams shown in the next section.

*Stabilizing Zero-Field Skyrmions at Room-Temperature in Perpendicularly Magnetized… DOI: http://dx.doi.org/10.5772/intechopen.97179*

In **Figure 6(a-c)**, the micromagnetic simulations are representative for an anisotropy *K* = 0.06 MJm−3 and a Dzyaloshinskii-Moriya interaction *D* = 0.04 mJm−2, while the saturation magnetization *M*s was varied. It shows that skyrmions are stabilized at zero-field with a random distribution of their positions, corroborating our experimental findings. Furthermore, by varying *D* in the micromagnetic simulations and comparing with the size of zero-field skyrmions obtained experimentally, the DMI was estimated to range between 0.4–0.8 mJm−2. More details can be seen in the phase diagrams shown in the next section.

More remarkable, the skyrmion size increases for larger values of *M*s as clearly shown in **Figure 6(a-c)**, indicating that this parameter plays an important role on the skyrmion diameter due to the impact of the magnetization stray field upon the magnetic structure size. In addition to the saturation magnetization, the influence of both *K* and *D* parameters was evaluated to understand their effects on the skyrmion stability and size. Figure 6 (d) shows that the skyrmion size monotonically increases as a function of *M*s for any value of *K* and *D*. However, smaller *K* and *D* values lead to larger skyrmion size (black squares) compared to higher values (red circles and blue triangles). This important conclusion suggests that the sample saturation magnetization *M*s must be reduced, while the PMA and DMI must be increased slightly to reduce the skyrmion average size at zero-field. This can be accomplished by engineering the multilayer structure varying, for instance, the magnetic layer thickness.

#### **2.4 Magnetic domain phase diagrams**

A phase diagram was constructed using the micromagnetic simulations to explore and indicate the achievable magnetic ground states as a function of the multilayer magnetic parameters, as can be seen in **Figure 7**.

Three different magnetic ground states were acquired at zero magnetic field, as shown in **Figure 7(a)**: uniform magnetization (dark cyan frame), isolated skyrmions (cyan frame), and mixed phase (purple frame), in which the latter

#### **Figure 7.**

*Magnetic Skyrmions*

**Figure 5.**

**54**

**Figure 6.**

**2.3 Micromagnetic simulations**

The formation of zero-field skyrmions in unpatterned symmetric multilayers is described better with the assistance of micromagnetic simulations. Mumax3 was the chosen code to carry out the simulations, and the used methods and parameters

*(a-c) Micromagnetic results of isolated skyrmions stabilized at zero magnetic field. (d) Skyrmion size obtained*

*(a) Line scans performed on skyrmions of different sizes. Histograms of the skyrmion size (b) and number*

*(c) distributions obtained in each MFM image. Figure adapted from [47].*

can be found in [47]. The results are summarized in **Figure 6.**

*as a function of Ms for different values of PMA and DMI. Figure taken from [47].*

*(a) Possible magnetic ground states. (b) DMI vs. Ms phase diagram for selected values of K. Figure adapted from reference [47].*

means that both skyrmions and magnetic stripes can coexist. The phase diagrams show that for low DMI values a uniform magnetization is the preferable ground state along the entire range of saturation magnetization *M*s (**Figure 7(b)**). For DMI values above 0.4 mJm−2, isolated skyrmions take place, while the area that covers this magnetic state in the phase diagram expands as the saturation magnetization *M*s and *K* values increase. On the other hand, the mixed phase exhibits an opposite behavior with a reduced area in the phase diagram when *M*s and *K* enhances. It demonstrates that at zero magnetic field, the stability of isolated skyrmions will strongly depend on the system magnetic parameters, mainly *M*s and *K*. Moreover, a DMI non-null value is required to stabilize isolated zero-field skyrmions, which has been achieved for both symmetric multilayers grown by MBE and magnetron sputtering techniques. Therefore, symmetric multilayers that present moderate values of DMI below 1 mJm−2, with high remnant magnetization and PMA, can be strategically used to stabilize skyrmions in the absence of external magnetic field.

## **3. Zero-field Skyrmions in Ferrimagnetic multilayers**

Ferromagnetic skyrmions have been shown remarkable phenomena under external excitation, which have helped to understand their fascinating properties. For instance, when driven by electrical current, ferromagnetic skyrmions experience a transverse motion with respect to the current direction, known as skyrmion Hall effect, which can lead to limiting their use in magnetic memory applications [50]. To overcome this issue, skyrmions have been researched in systems with antiferromagnetic coupling. It has been realized that skyrmions coupled with antiparallel magnetic moments, or, in other words, with opposite topological charges, may be used to suppress the undesirable skyrmion Hall effect when driven by electrical currents [51, 52].

In this context, materials with ferrimagnetic ordering are attractive candidates to host coupled skyrmions with opposite topological charges since they can reduce the skyrmion Hall effect due to the balance of the Magnus force acting on each skyrmion [53, 54]. In this section, we show how to observe skyrmions in lithographically shaped discs made of ferrimagnetic CoGd/Pt-based multilayer by tailoring the size of the disc diameter. For this purpose, unpatterned and patterned multilayers were grown by magnetron sputtering to image the evolution of the magnetic domain structures. **Figure 8** shows the schematic representation of the multilayer in the unpatterned and patterned (discs) geometries. The CoGd alloy was grown by using two independent Co and Gd targets in a co-sputtering deposition. The Pt/CoGd/Pt tri-layer was repeated 15 times and 2 nm Pt under and over layers were deposited as the buffer and protective oxidation, respectively. The CoGd thickness was fixed to 1.8 nm, and both unpatterned and patterned discs were deposited during the same

#### **Figure 8.**

*Representative geometries of the unpatterned (a) and patterned (b) multilayer (shaped as discs) of the CoGd/Pt multilayer. Figure adapted from [27].*

**57**

**Figure 9.**

*from [27].*

*Stabilizing Zero-Field Skyrmions at Room-Temperature in Perpendicularly Magnetized…*

sputtering batch. Electron beam lithography (EBL) was firstly performed on the Si/SiO2 substrate to fabricate the patterned discs. More details about the methods

As a first step, the magnetic properties of CoGd/Pt-based multilayer unpatterned sample were characterized. We used a vibrating sample magnetometer (VSM) and a SQUID to measure the hysteresis loops at ambient conditions and the

Hysteresis loops acquired by VSM at room-temperature exhibit the magnetization

temperature-dependent magnetization, respectively, as shown in **Figure 9**.

reversal for in-plane (IP) and out-of-plane (OOP) magnetic fields (**Figure 9(a)**). One may observe that the unpatterned CoGd multilayer presents a perpendicular magnetic anisotropy (PMA). On the other side, the out-of-plane magnetization has a tail-like structure with low remnant magnetization (blue curve) that reflects on the magnetic domain pattern observed at zero-field as it will be shown later. In **Figure 9(b)**, the temperature-dependent magnetization under zero magnetic field shows a behavior previously observed in ferrimagnetic alloys made of 3d transition metals and 4f rare earth elements. Depending on the composition between the alloy elements, the Co and Gd magnetic moments may align along the same or opposite direction, being ordered ferro- or ferrimagnetically. If the magnetic moments are arranged in an anti-parallel alignment, the compensation temperature corresponds to the magnetic moments of the Co and Gd sublattices compensating each other, leading to a minimization of the resultant magnetization [55]. This behavior is an important signature of the sample ferrimagnetic order. Starting from 2 K and without magnetic field, the sample magnetization decreases slowly as the temperature is increased, reaching a magnetization minimum at 154 K. By further increasing the temperature, the magnetization raises until reaching room-temperature (300 K), before gradually reducing around 350–400 K. This peculiar temperature-dependent behavior indicates that the CoGd/Pt based multilayer has a ferrimagnetic order of the

*DOI: http://dx.doi.org/10.5772/intechopen.97179*

**3.1 CoGd layer magnetic orientation**

*3.1.1 Magnetization behavior*

Co and Gd magnetic moments.

*3.1.2 X-ray spectroscopy and X-ray magnetic circular dichroism*

X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) were performed to extract the magnetic orientation of each Co and Gd

*(a) Hysteresis loops obtained with magnetic field applied in-plane (IP) (red curve) and out-of-plane (OOP) (blue curve). (b) Temperature-dependent magnetization in the absence of magnetic field. Figure adapted*

used in the sample fabrication can be found in Ref. [27].

sputtering batch. Electron beam lithography (EBL) was firstly performed on the Si/SiO2 substrate to fabricate the patterned discs. More details about the methods used in the sample fabrication can be found in Ref. [27].

## **3.1 CoGd layer magnetic orientation**

## *3.1.1 Magnetization behavior*

*Magnetic Skyrmions*

means that both skyrmions and magnetic stripes can coexist. The phase diagrams show that for low DMI values a uniform magnetization is the preferable ground state along the entire range of saturation magnetization *M*s (**Figure 7(b)**). For DMI values above 0.4 mJm−2, isolated skyrmions take place, while the area that covers this magnetic state in the phase diagram expands as the saturation magnetization *M*s and *K* values increase. On the other hand, the mixed phase exhibits an opposite behavior with a reduced area in the phase diagram when *M*s and *K* enhances. It demonstrates that at zero magnetic field, the stability of isolated skyrmions will strongly depend on the system magnetic parameters, mainly *M*s and *K*. Moreover, a DMI non-null value is required to stabilize isolated zero-field skyrmions, which has been achieved for both symmetric multilayers grown by MBE and magnetron sputtering techniques. Therefore, symmetric multilayers that present moderate values of DMI below 1 mJm−2, with high remnant magnetization and PMA, can be strategically used to stabilize skyrmions in the absence of external magnetic field.

**3. Zero-field Skyrmions in Ferrimagnetic multilayers**

Ferromagnetic skyrmions have been shown remarkable phenomena under external excitation, which have helped to understand their fascinating properties. For instance, when driven by electrical current, ferromagnetic skyrmions experience a transverse motion with respect to the current direction, known as skyrmion Hall effect, which can lead to limiting their use in magnetic memory applications [50]. To overcome this issue, skyrmions have been researched in systems with antiferromagnetic coupling. It has been realized that skyrmions coupled with antiparallel magnetic moments, or, in other words, with opposite topological charges, may be used to suppress the undesirable skyrmion Hall effect when driven by electrical currents [51, 52]. In this context, materials with ferrimagnetic ordering are attractive candidates to host coupled skyrmions with opposite topological charges since they can reduce the skyrmion Hall effect due to the balance of the Magnus force acting on each skyrmion [53, 54]. In this section, we show how to observe skyrmions in lithographically shaped discs made of ferrimagnetic CoGd/Pt-based multilayer by tailoring the size of the disc diameter. For this purpose, unpatterned and patterned multilayers were grown by magnetron sputtering to image the evolution of the magnetic domain structures. **Figure 8** shows the schematic representation of the multilayer in the unpatterned and patterned (discs) geometries. The CoGd alloy was grown by using two independent Co and Gd targets in a co-sputtering deposition. The Pt/CoGd/Pt tri-layer was repeated 15 times and 2 nm Pt under and over layers were deposited as the buffer and protective oxidation, respectively. The CoGd thickness was fixed to 1.8 nm, and both unpatterned and patterned discs were deposited during the same

*Representative geometries of the unpatterned (a) and patterned (b) multilayer (shaped as discs) of the*

**56**

**Figure 8.**

*CoGd/Pt multilayer. Figure adapted from [27].*

As a first step, the magnetic properties of CoGd/Pt-based multilayer unpatterned sample were characterized. We used a vibrating sample magnetometer (VSM) and a SQUID to measure the hysteresis loops at ambient conditions and the temperature-dependent magnetization, respectively, as shown in **Figure 9**.

Hysteresis loops acquired by VSM at room-temperature exhibit the magnetization reversal for in-plane (IP) and out-of-plane (OOP) magnetic fields (**Figure 9(a)**). One may observe that the unpatterned CoGd multilayer presents a perpendicular magnetic anisotropy (PMA). On the other side, the out-of-plane magnetization has a tail-like structure with low remnant magnetization (blue curve) that reflects on the magnetic domain pattern observed at zero-field as it will be shown later. In **Figure 9(b)**, the temperature-dependent magnetization under zero magnetic field shows a behavior previously observed in ferrimagnetic alloys made of 3d transition metals and 4f rare earth elements. Depending on the composition between the alloy elements, the Co and Gd magnetic moments may align along the same or opposite direction, being ordered ferro- or ferrimagnetically. If the magnetic moments are arranged in an anti-parallel alignment, the compensation temperature corresponds to the magnetic moments of the Co and Gd sublattices compensating each other, leading to a minimization of the resultant magnetization [55]. This behavior is an important signature of the sample ferrimagnetic order. Starting from 2 K and without magnetic field, the sample magnetization decreases slowly as the temperature is increased, reaching a magnetization minimum at 154 K. By further increasing the temperature, the magnetization raises until reaching room-temperature (300 K), before gradually reducing around 350–400 K. This peculiar temperature-dependent behavior indicates that the CoGd/Pt based multilayer has a ferrimagnetic order of the Co and Gd magnetic moments.

## *3.1.2 X-ray spectroscopy and X-ray magnetic circular dichroism*

X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) were performed to extract the magnetic orientation of each Co and Gd

#### **Figure 9.**

*(a) Hysteresis loops obtained with magnetic field applied in-plane (IP) (red curve) and out-of-plane (OOP) (blue curve). (b) Temperature-dependent magnetization in the absence of magnetic field. Figure adapted from [27].*

sublattice by taking advantage of the technique chemical selectivity. It allows us to further confirm the magnetic order of the CoGd alloy at room-temperature. The XAS was obtained under an out-of-plane magnetic field relative to the sample surface and parallel to the incoming X-rays by using a superconducting magnet [56]. Right and left circularly polarized X-rays were used to separate the dependent magnetic orientation of the Co and Gd elements.

**Figure 10(a)** shows the XAS acquired for Co around the L2,3 absorption edges. At the first and more intense peak around 779 eV (L3 edge), there are two distinct amplitudes: higher (dashed blue line), for left circularly polarized X-rays, and lower (solid red line), for right circularly polarized X-rays. This difference in amplitude is due to the X-ray magnetic circular dichroism that relates the dependence of the element magnetic orientation with the incoming X-ray polarization. Likewise, for Gd, a difference in amplitude is also observed at the most intense peak around 1552 eV at the Gd M5 edge. However, contrary to the Co case, higher amplitude occurs for right circularly polarized X-rays, while lower absorption for left circularly polarized X-rays (**Figure 10(c)**). These results reflect on the XMCD (difference between the right and left circularly polarized X-ray spectra), as demonstrated in **Figure 10(b, d)**.

Looking at the L3 and M5 edges where the XAS maximum occurs, one can see that the XMCD is negative for Co, while it is positive for Gd. This confirms that the magnetic orientation of the Co and Gd are arranged in an antiparallel direction, thus forming a ferrimagnetic CoGd alloy at room-temperature. This result helped us to conduct the magnetic force microscopy images of the CoGd/Pt

**Figure 10.**

*(a), (c) XAS acquired around the Co L2,3 and Gd M4,5 edges, respectively. (b), (d) XMCD acquired for Co and Gd. Figure adapted from [27].*

**59**

**Figure 11.**

*from [27].*

*Stabilizing Zero-Field Skyrmions at Room-Temperature in Perpendicularly Magnetized…*

multilayer and confirms the magnetic textures observed at ambient conditions as

Magnetic force microscopy was carried out to image the magnetic domains of the unpatterned sample and observe its features. **Figure 11(a)** shows the image acquired at remanence with alternating red and blue stripes in a typical worm-like configuration. By recalling that the out-of-plane magnetization of the unpatterned sample exhibits low remnant magnetization (see **Figure 9(a)**), it is expected to observe this type of magnetic texture in such CoGd/Pt-based multilayer.

The magnetic domain pattern is characterized by a spatial periodicity of the stripes obtained by using a linear profile on the MFM (dashed line) (**Figure 11(a)**). **Figure 11(b)** exhibits the oscillations along a 1 μm length of the spatial domain distribution of the up and down magnetic stripes, resulting in a wavelength of ~150 nm and domain width Δ of ~90 nm. The MFM image undertaken in the unpatterned multilayer will be used as a guide to evaluate the evolution of the magnetic domains in the confined structures, as will be discussed in the next section.

Here we present the magnetic domain textures of the CoGd/Pt multilayer influenced by the confinement induced by the geometric disc. We produced disc arrays by electron beam lithography and lift-off techniques with different diameters of 1 μm, 650 nm, and 250 nm. **Figure 12** (top) shows the scanning electron micros-

To visualize better the magnetic domain formation in the nanostructures, individual MFM images of the discs for each diameter are displayed at the bottom of **Figure 12**. **Figure 12** (a, bottom) displays the magnetic domain for the larger disc (1 μm). One may see that the disc supports a magnetic domain pattern like the one observed in the unpatterned multilayer (see **Figure 11(a)**), with alternating up and down magnetic stripes. Therefore, there is no significant influence of the geometric confinement at this specific diameter on the magnetic domain type formation. On the other hand, the geometric confinement leads to a modification of the magnetic stripe periodicity in the disc compared to the unpatterned sample

*(a) MFM image of the unpatterned sample exhibiting magnetic stripes (blue and red) with out-of-plane orientation. (b) Domain periodicity extracted by performing line scan on the MFM image. Figure adapted*

*DOI: http://dx.doi.org/10.5772/intechopen.97179*

ferrimagnetic domains.

**3.2 Magnetic textures**

*3.2.1 Unpatterned multilayer*

*3.2.2 Confined nanostructures*

copy images (SEM) of the arrays.

multilayer and confirms the magnetic textures observed at ambient conditions as ferrimagnetic domains.

## **3.2 Magnetic textures**

*Magnetic Skyrmions*

sublattice by taking advantage of the technique chemical selectivity. It allows us to further confirm the magnetic order of the CoGd alloy at room-temperature. The XAS was obtained under an out-of-plane magnetic field relative to the sample surface and parallel to the incoming X-rays by using a superconducting magnet [56]. Right and left circularly polarized X-rays were used to separate the dependent

**Figure 10(a)** shows the XAS acquired for Co around the L2,3 absorption edges. At the first and more intense peak around 779 eV (L3 edge), there are two distinct amplitudes: higher (dashed blue line), for left circularly polarized X-rays, and lower (solid red line), for right circularly polarized X-rays. This difference in amplitude is due to the X-ray magnetic circular dichroism that relates the dependence of the element magnetic orientation with the incoming X-ray polarization. Likewise, for Gd, a difference in amplitude is also observed at the most intense peak around 1552 eV at the Gd M5 edge. However, contrary to the Co case, higher amplitude occurs for right circularly polarized X-rays, while lower absorption for left circularly polarized X-rays (**Figure 10(c)**). These results reflect on the XMCD (difference between the right and left circularly polarized X-ray spectra), as

Looking at the L3 and M5 edges where the XAS maximum occurs, one can see that the XMCD is negative for Co, while it is positive for Gd. This confirms that the magnetic orientation of the Co and Gd are arranged in an antiparallel direction, thus forming a ferrimagnetic CoGd alloy at room-temperature. This result helped us to conduct the magnetic force microscopy images of the CoGd/Pt

*(a), (c) XAS acquired around the Co L2,3 and Gd M4,5 edges, respectively. (b), (d) XMCD acquired for Co and*

magnetic orientation of the Co and Gd elements.

demonstrated in **Figure 10(b, d)**.

**58**

**Figure 10.**

*Gd. Figure adapted from [27].*

## *3.2.1 Unpatterned multilayer*

Magnetic force microscopy was carried out to image the magnetic domains of the unpatterned sample and observe its features. **Figure 11(a)** shows the image acquired at remanence with alternating red and blue stripes in a typical worm-like configuration. By recalling that the out-of-plane magnetization of the unpatterned sample exhibits low remnant magnetization (see **Figure 9(a)**), it is expected to observe this type of magnetic texture in such CoGd/Pt-based multilayer.

The magnetic domain pattern is characterized by a spatial periodicity of the stripes obtained by using a linear profile on the MFM (dashed line) (**Figure 11(a)**). **Figure 11(b)** exhibits the oscillations along a 1 μm length of the spatial domain distribution of the up and down magnetic stripes, resulting in a wavelength of ~150 nm and domain width Δ of ~90 nm. The MFM image undertaken in the unpatterned multilayer will be used as a guide to evaluate the evolution of the magnetic domains in the confined structures, as will be discussed in the next section.

### *3.2.2 Confined nanostructures*

Here we present the magnetic domain textures of the CoGd/Pt multilayer influenced by the confinement induced by the geometric disc. We produced disc arrays by electron beam lithography and lift-off techniques with different diameters of 1 μm, 650 nm, and 250 nm. **Figure 12** (top) shows the scanning electron microscopy images (SEM) of the arrays.

To visualize better the magnetic domain formation in the nanostructures, individual MFM images of the discs for each diameter are displayed at the bottom of **Figure 12**. **Figure 12** (a, bottom) displays the magnetic domain for the larger disc (1 μm). One may see that the disc supports a magnetic domain pattern like the one observed in the unpatterned multilayer (see **Figure 11(a)**), with alternating up and down magnetic stripes. Therefore, there is no significant influence of the geometric confinement at this specific diameter on the magnetic domain type formation. On the other hand, the geometric confinement leads to a modification of the magnetic stripe periodicity in the disc compared to the unpatterned sample

#### **Figure 11.**

*(a) MFM image of the unpatterned sample exhibiting magnetic stripes (blue and red) with out-of-plane orientation. (b) Domain periodicity extracted by performing line scan on the MFM image. Figure adapted from [27].*

#### **Figure 12.**

*(Top) Scanning electron microscopy (SEM) images of the disc arrays. (Bottom) Respective MFM images of magnetic domain textures in individual discs. (a) 1* μ*m, (b) 650 nm, (c) 250 nm. Figure adapted from [27].*

**Figure 13.**

*Profile as a function of the length acquired by using line scan on the multiple skyrmions (a) and single skyrmions (b). Adapted from the supplementary material of reference [27].*

(~ 190 nm vs. ~150 nm, respectively). This indicates that the confinement given by the 1 μm diameter increases the distance between up and down magnetic stripes.

The impact of the disc size is more evidenced for the 650 nm diameter disc, where the confinement strongly modifies the magnetic domain pattern. The disc does not support a magnetic stripe domain, but rather the formation of small skyrmions, with a size of ~120 nm (**Figure 13(a)**). It is worth noting that this disc size supports three ferrimagnetic skyrmions at room-temperature and zero magnetic field. By further reducing the disc size to 250 nm, a stable single ferrimagnetic skyrmion is observed in the nanostructure. The single ferrimagnetic skyrmion exhibits a size of ~70 nm (**Figure 13(b)**), which is a very desirable feature for the use of this magnetic structure in future applications [57]. Therefore, by tailoring the disc diameter, we could stabilize magnetic domain textures at room-temperature and zero-field from magnetic stripe configurations, in larger discs, to multiple or single skyrmions in smaller discs. Furthermore, the reduction of the disc size and hence increased confinement modifies not only the magnetic domain type but also allows the existence of multiple or single ferrimagnetic skyrmions. This control can be used in new applications based on the dynamic mode of coupled skyrmions such as neuromorphic computing [58].

**61**

*Stabilizing Zero-Field Skyrmions at Room-Temperature in Perpendicularly Magnetized…*

To summarize, in this chapter we presented two recent approaches to stabilize skyrmions at zero magnetic field and room-temperature. First, ferromagnetic skyrmions were observed in unpatterned symmetric Pd/Co/Pd multilayer by tuning both the remnant magnetization and perpendicular magnetic anisotropy. The PMA enhancement in combination with high remnant magnetization found for the thinnest Co layer (0.2 nm) yields the formation of ferromagnetic skyrmions at ambient conditions without the assistance of a magnetic field. By comparing the experimental 165 nm and simulated skyrmion sizes, we are able to estimate the non-vanishing DMI around 0.4–0.8 mJm−2, as an additional sample parameter required to stabilize skyrmions even in nominally symmetric multilayers. The DMI obtained in the micromagnetic modeling emerges mainly owing to the imperfections (roughness, intermixing) at the Co/Pd interfaces, allowing the formation of zero-field magnetic

Second, ferrimagnetic skyrmions were stabilized in confined geometric discs made of Pt/CoGd-based multilayers. The ferrimagnetic order of the multilayer is confirmed by dependent-temperature SQUID measurement and room-temperature XMCD. By adjusting the disc diameter, magnetic stripes in larger discs evolve to multiple and single ferrimagnetic skyrmions in smaller discs. The single skyrmion observed in the 250 nm diameter exhibits a size of ~70 nm. This sub-100 nm size and quasi antiferromagnetic arrangement of the skyrmions are very desirable both for fundamental physics understanding regarding the skyrmion Hall effect and technological applications based on antiparallel coupled skyrmions. These mechanisms are robust to find skyrmions at ambient conditions and zero-field by

engineering symmetric multilayers made of ferro- or ferrimagnetic layers.

This work was supported by the Brazilian funding agencies *Fundação de Amparo à Pesquisa do Estado de São Paulo* (FAPESP) (Projects No. 2012/51198-2, 2017/10581-1; 2020/07397-7) and *Conselho Nacional de Desenvolvimento Científico e Tecnológico* (CNPq) (Projects 436573/2018-0 and 436573/2018-0). We thank the Microfabrication Laboratory of the Brazilian Nanotechnology National Laboratory (LNNano, CNPEM) for support in growing sample facilities and Laboratory of Materials and Low Temperatures of the University of Campinas (UNICAMP), for the use of VSM and SQUID techniques. We also thank the Planar Grating Monochromator (PGM) beamline at the Brazilian Synchrotron Light Laboratory

(LNLS, CNPEM) for XAS and XMCD measurements.

The authors declare no conflict of interest.

*DOI: http://dx.doi.org/10.5772/intechopen.97179*

domains and isolated skyrmions.

**Acknowledgements**

**Conflict of interest**

**4. Conclusion**

*Stabilizing Zero-Field Skyrmions at Room-Temperature in Perpendicularly Magnetized… DOI: http://dx.doi.org/10.5772/intechopen.97179*

## **4. Conclusion**

*Magnetic Skyrmions*

**Figure 12.**

**Figure 13.**

**60**

neuromorphic computing [58].

(~ 190 nm vs. ~150 nm, respectively). This indicates that the confinement given by the 1 μm diameter increases the distance between up and down magnetic stripes. The impact of the disc size is more evidenced for the 650 nm diameter disc, where the confinement strongly modifies the magnetic domain pattern. The disc does not support a magnetic stripe domain, but rather the formation of small skyrmions, with a size of ~120 nm (**Figure 13(a)**). It is worth noting that this disc size supports three ferrimagnetic skyrmions at room-temperature and zero magnetic field. By further reducing the disc size to 250 nm, a stable single ferrimagnetic skyrmion is observed in the nanostructure. The single ferrimagnetic skyrmion exhibits a size of ~70 nm (**Figure 13(b)**), which is a very desirable feature for the use of this magnetic structure in future applications [57]. Therefore, by tailoring the disc diameter, we could stabilize magnetic domain textures at room-temperature and zero-field from magnetic stripe configurations, in larger discs, to multiple or single skyrmions in smaller discs. Furthermore, the reduction of the disc size and hence increased confinement modifies not only the magnetic domain type but also allows the existence of multiple or single ferrimagnetic skyrmions. This control can be used in new applications based on the dynamic mode of coupled skyrmions such as

*Profile as a function of the length acquired by using line scan on the multiple skyrmions (a) and single*

*skyrmions (b). Adapted from the supplementary material of reference [27].*

*(Top) Scanning electron microscopy (SEM) images of the disc arrays. (Bottom) Respective MFM images of magnetic domain textures in individual discs. (a) 1* μ*m, (b) 650 nm, (c) 250 nm. Figure adapted from [27].*

To summarize, in this chapter we presented two recent approaches to stabilize skyrmions at zero magnetic field and room-temperature. First, ferromagnetic skyrmions were observed in unpatterned symmetric Pd/Co/Pd multilayer by tuning both the remnant magnetization and perpendicular magnetic anisotropy. The PMA enhancement in combination with high remnant magnetization found for the thinnest Co layer (0.2 nm) yields the formation of ferromagnetic skyrmions at ambient conditions without the assistance of a magnetic field. By comparing the experimental 165 nm and simulated skyrmion sizes, we are able to estimate the non-vanishing DMI around 0.4–0.8 mJm−2, as an additional sample parameter required to stabilize skyrmions even in nominally symmetric multilayers. The DMI obtained in the micromagnetic modeling emerges mainly owing to the imperfections (roughness, intermixing) at the Co/Pd interfaces, allowing the formation of zero-field magnetic domains and isolated skyrmions.

Second, ferrimagnetic skyrmions were stabilized in confined geometric discs made of Pt/CoGd-based multilayers. The ferrimagnetic order of the multilayer is confirmed by dependent-temperature SQUID measurement and room-temperature XMCD. By adjusting the disc diameter, magnetic stripes in larger discs evolve to multiple and single ferrimagnetic skyrmions in smaller discs. The single skyrmion observed in the 250 nm diameter exhibits a size of ~70 nm. This sub-100 nm size and quasi antiferromagnetic arrangement of the skyrmions are very desirable both for fundamental physics understanding regarding the skyrmion Hall effect and technological applications based on antiparallel coupled skyrmions. These mechanisms are robust to find skyrmions at ambient conditions and zero-field by engineering symmetric multilayers made of ferro- or ferrimagnetic layers.

## **Acknowledgements**

This work was supported by the Brazilian funding agencies *Fundação de Amparo à Pesquisa do Estado de São Paulo* (FAPESP) (Projects No. 2012/51198-2, 2017/10581-1; 2020/07397-7) and *Conselho Nacional de Desenvolvimento Científico e Tecnológico* (CNPq) (Projects 436573/2018-0 and 436573/2018-0). We thank the Microfabrication Laboratory of the Brazilian Nanotechnology National Laboratory (LNNano, CNPEM) for support in growing sample facilities and Laboratory of Materials and Low Temperatures of the University of Campinas (UNICAMP), for the use of VSM and SQUID techniques. We also thank the Planar Grating Monochromator (PGM) beamline at the Brazilian Synchrotron Light Laboratory (LNLS, CNPEM) for XAS and XMCD measurements.

## **Conflict of interest**

The authors declare no conflict of interest.

*Magnetic Skyrmions*

## **Author details**

Jeovani Brandão1 , Marcos Vinicius Puydinger dos Santos2 and Fanny Béron2 \*

1 Brazilian Synchrotron Light Laboratory (LNLS), Brazilian Center for Research in Energy and Materials (CNPEM), Campinas, SP, Brazil

2 Gleb Wataghin Institute of Physics, University of Campinas (UNICAMP), Campinas, SP, Brazil

\*Address all correspondence to: f<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**63**

*Stabilizing Zero-Field Skyrmions at Room-Temperature in Perpendicularly Magnetized…*

nanowires with an asymmetric branch. J. Appl. Phys., 121, 093905 (2017).

[11] B. Borie*,* J. Wahrhusen*,* H. Grimm*,* M. Kläui. Geometrically enhanced closed-loop multi-turn sensor devices that enable reliable magnetic domain wall motion. Appl. Phys. Lett. 111,

[12] Allwood, D. A. *et al.* Magnetic domain wall logic. Science 309,

[13] Currivan-Incorvia, J. A. *et al.* Logic circuit prototypes for three-terminal magnetic tunnel junctions with mobile domain walls. Nat. Commun. 7,

[14] Luo, Z., Hrabec, A., Dao, T.P. *et al.* Current-driven magnetic domain-wall

logic. Nature 579, 214 (2020).

[15] Parkin, S. S. P., Hayashi, M. & Thomas, L. Magnetic domain-wall racetrack memory. Science 320,

[16] Tomasello, R., Martinez, E., Zivieri, R. *et al.* A strategy for the design of skyrmion racetrack memories. Sci Rep

[17] R. D. McMichael, M. J. Donahue. Head to head domain walls structures in thin magnetic stripes. IEEE Trans.

[18] T. Shinjo *et al.*, Magnetic vortex observation in circular dots. Science

[19] U. K. Rößler, A. N. Bogdanov, C. Pfleiderer, Spontaneous skyrmion ground states in magnetic metals.Nature

[20] Moreau-Luchaire, C. *et al.* Additive

interfacial chiral interaction in multilayers for stabilization of small

242402 (2017).

1688 (2005).

10275 (2016).

190 (2008).

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*DOI: http://dx.doi.org/10.5772/intechopen.97179*

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Jeovani Brandão1

Campinas, SP, Brazil

, Marcos Vinicius Puydinger dos Santos2

2 Gleb Wataghin Institute of Physics, University of Campinas (UNICAMP),

Energy and Materials (CNPEM), Campinas, SP, Brazil

\*Address all correspondence to: f<EMAIL_ADDRESS>
provided the original work is properly cited.

1 Brazilian Synchrotron Light Laboratory (LNLS), Brazilian Center for Research in

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

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Thermodynamic theory of "weak" ferromagnetism in antiferromagnetic

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substances. Sov. Phys. JETP 5,

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**64**

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**Chapter 4**

**Abstract**

**1. Introduction**

**67**

Modeling the Bulk and

of Au and Ag

*Chi-Te Liang and Jamal Hemine*

Nanometric Dielectric Functions

In this work, we model the dielectric functions of gold (Au) and silver (Ag) which are typically used in photonics and plasmonics. The modeling has been performed on Au and Ag in bulk and in nanometric states. The dielectric function is presented as a complex number with a real part and an imaginary part. First, we will model the experimental measurements of the dielectric constant as a function of the pulsation ω by appropriate mathematical functions in an explicit way. In the second part we will highlight the contributions to the dielectric constant value due to intraband and interband electronic transitions. In the last part of this work we model the dielectric constant of these metals in the nanometric state using several complex theoretical models such as the Drude Lorentz theory, the Drude two-point critical model, and the Drude three-point critical model. We shall comment on which model fits the experimental dielectric function best over a range of pulsation.

**Keywords:** Modeling bulk and nanometric dielectric function, noble metals Au and

All the intrinsic effects corresponding to the process of light-matter interaction are contained in the dielectric function *ε ω*ð Þ**.** In the case of an isotropic material, the

where *ε ω*ð Þis generally a complex scalar value which depends upon the pulsation ω of the field. If the medium has an anisotropy, this magnitude is in the form of a tensor. It is often convenient to describe the optical response in an equivalent way from the complex refractive index *n*~ ¼ *n* þ *iκ* as *n* denotes the refractive index describing the phase speed of the wave and *κ* denotes the extinction index describing the absorption of the wave during propagation in the material. These two indices are directly related to the dielectric constant of the material. In fact, the real and imaginary parts of the dielectric function are deduced from the relation:

*ε ω*ð Þ¼ *ε*1ð Þþ *ω iε*2ð Þ *ω* (1)

Ag, interband transitions, intraband transitions, UV and IR pulsations

optical response is described by following equation

*Brahim Ait Hammou, Abdelhamid El Kaaouachi,*

*Abdellatif El Oujdi, Adil Echchelh, Said Dlimi,*

[58] Torrejon, J.; Riou, M.; Araujo, F. A.; Tsunegi, S.; Khalsa, G.; Querlioz, D.; Bortolotti, P.; Cros, V.; Yakushiji, K.; Fukushima, A.; Kubota, H.; Yuasa, S.; Stiles, M. D.; Grollier, J. Neuromorphic computing with nanoscale spintronic oscillators. Nature, 547, 428 (2017).

**Chapter 4**

*Magnetic Skyrmions*

184104 (2016).

racetracks and nanooscillators. Phys. Rev. B: Condens. Matter Mater. Phys. 94,

[58] Torrejon, J.; Riou, M.; Araujo, F. A.; Tsunegi, S.; Khalsa, G.; Querlioz, D.; Bortolotti, P.; Cros, V.; Yakushiji, K.; Fukushima, A.; Kubota, H.; Yuasa, S.; Stiles, M. D.; Grollier, J. Neuromorphic computing with nanoscale spintronic oscillators. Nature, 547, 428 (2017).

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