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Theoretical study on ordered spin states in amorphous and chiral magnets

Hirobe Mai 東北大学

2022.03.25

概要

The ordered states of magnetic materials, such as ferromagnets, ferrimagnets, and anti-ferromagnets, have long been investigated. Spintronics aims to propose low-power-consumption magnetic devices by utilizing magnons, accompanied by such ordered spin states as collective excitation. In this doctoral thesis, we describe the results of theoretical studies on magnetically ordered states in amorphous and chiral magnetic materials, where recent experimental and theoretical studies have pointed out their potential applications to the low-power magnetic devices.

As for the amorphous magnets, with the renewed interest in heat and spin transport, we re-visit the magnetic spectrum of amorphous ferromagnet using modern simulation methods. We find two parabolas in the spectrum, the magnons at wavenumber 0Å−1 and another magnons at wavenumber 3Å−1, which is similar to that observed in experiments. The physical interpretation of the second dip has long been unclear. We suggest it is due to the amorphous Umklapp scattering. The methods can easily be extended to study the spin transport properties in amorphous magnets and may pave the way to the spintronics applications.

In terms of spin transport via magnons, collective precession of magnetizations, crystalline magnetic materials have been utilized in the field of spintronics [1]. Recently, experimental attempts to utilize amorphous magnets as well have been made. However, their conclusions are controversial; The first observation has shown that amorphous magnetic materials can transport spins further than the corresponding crystal [2, 3]. Whereas following experiments cast doubt about the result [4, 5]. As a long-term goal, we aim to theoretically find if the amorphous magnets are capable of transporting spins. In the master course study, as a first step, we built a model to calculate magnon spectra in amorphous magnets. In the doctoral course study, we aim to understand the magnon spectra of first target material, amorphous ferromagnet Co4P, by applying the model. The amorphous ferromagnet Co4P has been extensively studied in the past [6, 7, 8], since its magnetic excitation has unique feature; The inelastic neutron scattering experiment shows a ‘roton-like’ excitation at wavenumber 3Å−1 [9]. Despite many efforts, the physical picture has been unclear. By utilizing numerical techniques we have developed so far [10] and recently developed [11], we have simulated thermal equilibrium spin states and magnetic spectra. The application of this method to Co4P suggests the existence of magnons at wavenumber 0Å−1, which follows the Bloch’s law, and at wavenumber 3Å−1. Our results, shown in Figs. 1.1(a)-(b), suggest its physical interpretation as amorphous Umklapp scattering [12]. The method used in the study can easily be extended to spin transport study for amorphous magnets, paving the way for theoretical studies on spintronics applications of amorphous magnets.

As for the chiral magnets, with the controlling magnetic skyrmions in mind, we theoretically study the mechanism and effects of the inter-skyrmion interactions in a two-dimensional model. We find that a deformation of a skyrmion shape makes the interaction weakly attractive. When the magneto-crystalline anisotropy is sufficiently large, the interaction becomes strongly attractive by forming a magnetic domain between two skyrmions. The creation of the magnetic domain, and thus the strength of the attraction, can be tuned in a wide range by changing the direction of an external field. The anisotropic inter-skyrmion attraction also affects the lattice structure of the skyrmion crystal phase. This model can easily be extended to the 3D systems and may pave the way for improving controlabilities of skyrmion magnetic memories.

Magnetic skyrmions, topologically stable nanometer-sized vortices, are potentially applicable as information carriers of a magnetic memory [13]. To improve the controllability of such devices, it is essential to control the trajectory of the skyrmions, i.e., by manipulating interactions between them. However, the control has been limited by the fact that only repulsive force acts between the typical isotropic skyrmions [14]. On the other hand, recent theoretical and experimental studies have revealed an attraction between skyrmions in some specific systems [15, 16, 17, 18]. Understanding the mechanism of the attractive interaction is important for academic and application purposes.

In this study, we find two mechanisms of attractive interaction, skyrmion distortion and magnetic domain formation, using a two-dimensional model [21]. We derive the analytical expression for the interaction between two skyrmions excited in the ferromagnetic (FM) phase. From the expression, we find that the distortion of skyrmions can change the sign of the interaction; The distorted skyrmions favor to be connected in the direction of elongation, to reduce the exchange interaction energy. When the easy-axes tilt from the direction of external magnetic field, i.e., due to the large magneto-crystalline anisotropy, magnetic domains are formed between two skyrmions. The energy profit from the exchange and anisotropic potential terms, from the domain area give rise to the strong attractive interaction [see Figs. 1.2(a)-(d)].

In terms of controlling the skyrmion trajectory, manipulating the strength of the attraction may be crucial. Since the skyrmion-skyrmion interactions are only visibly affect in the vicinity of the FM—skyrmion crystal (SkX) phase boundary, the strength of external magnetic field is automatically fixed at that of the critical field. Thus, it is hard to modify the attraction only via the strength of the magnetic field. We have found that, by changing the direction of the external magnetic field, the strength of the attraction can be tuned as much as two orders of magnitude. This is because the tilted magnetic field makes the domain unstable [see Figs. 1.3(a)-(d)]. The 2D model can be easily extended to the three-dimensional systems. This work lays a theoretical foundation for improving the controllability of skyrmion magnetic memory and qubits.

We have found that the interaction between two elongated skyrmions is anisotropic; In the direction of domain formation, it is attractive. Given that the large anisotropic attraction appears, we expect that the interaction may also affect the SkX structures. Indeed, distorted triangular lattice appears, in the vicinity of the SkX-FM phase boundary where the attractive interaction and skyrmion excitation energy may be comparable. In the resulting distorted triangular lattice, the interval of skyrmions along the direction of attraction is smaller than that of along the repulsion. Interestingly, the magnetic domain formed between the two skyrmions are expanded and connected to form domain wall skyrmion. This phase is qualitatively the same as that recently found experimentally [22]. We succeeded to find the qualitative mechanism of the domain wall skyrmions [see Figs. 1.4(a)-(c), and (e)]. In addition, we have found that the attraction expands the SkX phase in the 1D phase diagram of external magnetic field [see Fig. 1.4(d)]. In other words, the attraction expands the upper critical field of the elongated SkX phase. This new phase boundary corresponds to the field at which the energy loss of the skyrmion excitation balances with the energy profit of the attraction.

This thesis consists of 6 Chapters: In Chap. 2, we introduce the background and of the study. In Chap. 3, we explain numerical methods. Magnetically ordered states in amorphous ferromagnet Co4P is discussed in Chap. 4, and that of the chiral magnet is shown in Chap. 5. Finally, we conclude in Chap. 6.

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