Response of the Skyrmion Lattice in MnSi to Cubic Magnetocrystalline Anisotropies

Adams, Terry R.; Garst, Markus; Bauer, Andreas; Georgii, R.; Pfleiderer, C.

doi:10.1103/physrevlett.121.187205

Cited by 21 publications

(14 citation statements)

References 45 publications

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“…As shown in Figs. 1(f)-1(h), the same qualitative and quantitative behavior is also observed for field along 110 , 211 , and 111 , where the differences of the field range of the skyrmion lattice phase reflect the well-understood weak magnetocrystalline anisotropies that are fourth-order in spin-orbit coupling [44,86,93]. This suggests, in turn, the presence of skyrmionic fluctuations in the FD regime under small applied magnetic fields (roughly between ∼ 0.1 T and ∼ 0.3 T), regardless of the crystallographic direction in which the magnetic field is applied.…”

Section: A Magnetic Susceptibilitysupporting

confidence: 55%

Weak Crystallization of Fluctuating Skyrmion Textures in MnSi

et al. 2019

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We report an experimental study of the emergence of non-trivial topological winding and longrange order across the paramagnetic to skyrmion lattice transition in the transition metal helimagnet MnSi. Combining measurements of the susceptibility with small angle neutron scattering, neutron resonance spin echo spectroscopy and all-electrical microwave spectroscopy, we find evidence of skyrmion textures in the paramagnetic state exceeding 10 3Å with lifetimes above several 10 −9 s. Our experimental findings establish that the paramagnetic to skyrmion lattice transition in MnSi is well-described by the Landau soft-mode mechanism of weak crystallization, originally proposed in the context of the liquid to crystal transition. As a key aspect of this theoretical model, the modulation-vectors of periodic small amplitude components of the magnetization form triangles that add to zero. In excellent agreement with our experimental findings, these triangles of the modulation-vectors entail the presence of the non-trivial topological winding of skyrmions already in the paramagnetic state of MnSi when approaching the skyrmion lattice transition. I. MOTIVATIONA pre-requisite for the definition of topological magnetic textures is the presence of a continuous magnetization field with a finite amplitude in space and time. An example par excellence of such textures are magnetic skyrmions, representing topologically nontrivial whirls of this magnetization field [1]. The notions of topological winding and topological stability of such skyrmions are only meaningful when the magnetization is sufficiently smooth on local scales. This condition may be readily satisfied in systems exhibiting long-range magnetic order for temperatures far below the transition temperature T c . In contrast, changes of the topological properties require that the magnetization is capable of vanishing on short length and time scales. The associated microscopic mechanisms underlying the transition of skyrmions into different types of conventional long-range magnetic order have been explored in a large number of theoretical and experimental studies [2][3][4][5][6][7][8].A major unresolved question concerns, in contrast, the formation of skyrmion lattice order when starting from a state that is essentially paramagnetic and dominated by an abundance of fluctuations such that the local magnetization, on a coarse-grained level, practically vanishes on average [9][10][11][12][13][14][15]. This alludes to the question whether topologically non-trivial characteristics exist already in * a paramagnetic state, and how they may be accounted for in the framework of the present-day classification of phase transitions [16][17][18]. It connects also with the relevance of non-trivial topological properties in the search for novel electronic properties of solids, e.g., at quantum phase transitions [19,20].Magnetic skyrmions are ideally suited to address this question. However, they are typically portrayed from either one of two seemingly contrary points of view. On the one hand...

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Section: A Magnetic Susceptibilitysupporting

confidence: 55%

Weak Crystallization of Fluctuating Skyrmion Textures in MnSi

et al. 2019

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“…High-precision SANS measurements in pure MnSi establish that the precise orientation of the skyrmion lattice with respect to the applied field and crystal lattice originates in MCAs [33]. Contributions that are fourth order in SOC control tiny tilts of the skyrmion lattice plane against the field direction, whereas terms that are sixth order in SOC define the orientation within the skyrmion lattice plane.…”

Section: Skyrmion Lattice In Mn 1−x Fe X Simentioning

confidence: 93%

“…Instead, the in-plane orientation of the skyrmion lattice as reported here provides direct information on the sixth-order terms in SOC. However, it is important to note that highprecision measurements of the skyrmion lattice alignment require great efforts to avoid signal contamination by demagnetizing fields as observed in early work on MnSi [31,33,124]. They are therefore beyond the scope of the work reported here.…”

Section: B Broader Implicationsmentioning

confidence: 94%

“…In the bulk properties of MnSi, the effects of MCAs result in changes of the temperature range of the skyrmion lattice phase by a factor of two, extending over roughly 1 K for the 111 easy axes and roughly 2 K for the 100 hard axes. When the field is not aligned along a crystallographic high-symmetry direction, the MCAs induce also a slight tilting of the skyrmion lattice plane with respect to the field direction as well as the in-plane orientation of the skyrmion lattice with respect to the crystal lattice [11,29,[32][33][34][35].…”

Section: B Terminology and Outlinementioning

confidence: 99%

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Evolution of magnetocrystalline anisotropies in Mn1−xFexSi and Mn1−x
Kindervater
¹
,
Adams
²
,
Bauer
³

et al. 2020
Phys. Rev. B
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We report a comprehensive small-angle neutron scattering (SANS) study of magnetic correlations in Mn 1−x Fe x Si at zero magnetic field. To delineate changes of magnetocrystalline anisotropies (MCAs) from effects due to defects and disorder, we recorded complementary susceptibility and high-resolution specific heat data and investigated selected compositions of Mn 1−x Co x Si. For all systems studied, the helimagnetic transition temperature and magnetic phase diagrams evolve monotonically with composition consistent with literature. The SANS intensity patterns of the spontaneous magnetic order recorded under zero-field cooling, which were systematically tracked over forty angular positions, display strong changes of the directions of the intensity maxima and smeared out intensity distributions as a function of composition. We show that cubic MCAs account for the complex evolution of the SANS patterns, where for increasing x the character of the MCAs shifts from terms that are fourth order to terms that are sixth order in spin-orbit coupling. The magnetic field dependence of the susceptibility and SANS establishes that the helix reorientation as a function of magnetic field for Fe-or Co-doped MnSi is dominated by pinning due to defects and disorder. The presence of well-defined thermodynamic anomalies of the specific heat at the phase boundaries of the skyrmion lattice phase in the doped samples and properties observed in Mn 1−x Co x Si establishes that the pinning due to defects and disorder remains, however, weak and comparable to the field scale of the helix reorientation. The observation that MCAs, which are sixth order in spin-orbit coupling, play an important role for the spontaneous order in Mn 1−x Fe x Si and Mn 1−x Co x Si offers a fresh perspective for a wide range of topics in cubic chiral magnets such as the generic magnetic phase diagram, the morphology of topological spin textures, the paramagnetic-to-helical transition, and quantum phase transitions.

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“…Further high-resolution SANS experiments showed an exceptionally long-range ordered SkL and were able to prove the existence of weak, higher-order reflections (i) indicative of the particlelike character of the SkL (Adams et al, 2011) and (ii) the fixed phase relation of the triple-k state. The pinning of the SkL to the crystal lattice in the plane perpendicular to the field is given by weak higher-order anisotropy terms, which have been examined in a series of SANS experiments (Adams, 2015;Adams et al, 2018) including the use of uniaxial pressure (Chacon et al, 2015). As for the helix state, the SkL state in MnSi is only weakly affected by crystal anisotropies, which reflects in an essentially isotropic temperature-field phase diagram and the particular coupling of the SkL spin structure to the magnetic field.…”

Section: B Magnetic Skyrmions 1 the Concept Of Skyrmionsmentioning

confidence: 99%

Magnetic Small-Angle Neutron Scattering

Michels

2021

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This book provides the first extensive treatment of magnetic small-angle neutron scattering (SANS). The theoretical background required to compute magnetic SANS cross sections and correlation functions related to long-wavelength magnetization structures is laid out; and these concepts are scrutinized based on the discussion of experimental neutron data. Regarding prior background knowledge, some familiarity with the basic magnetic interactions and phenomena, as well as scattering theory, is desired. The target audience comprises Ph.D. students and researchers working in the field of magnetism and magnetic materials who wish to make efficient use of the magnetic SANS method. Besides revealing the origins of magnetic SANS (Chapter 1), and furnishing the basics of the magnetic SANS technique (Chapter 2), much of the book is devoted to a comprehensive treatment of the continuum theory of micromagnetics (Chapter 3), as it is relevant for the study of the elastic magnetic SANS cross section. Analytical expressions for the magnetization Fourier components allow one to highlight the essential features of magnetic SANS and to analyze experimental data both in reciprocal (Chapter 4) and real space (Chapter 6). Chapter 5 provides an overview of the magnetic SANS of nanoparticles and so-called complex systems (e.g., ferrofluids, magnetic steels, spin glasses, and amorphous magnets). It is this subfield where major progress is expected to be made in the coming years, mainly via the increased use of numerical micromagnetic simulations (Chapter 7), which is a very promising approach for the understanding of the magnetic SANS from systems exhibiting nanoscale spin inhomogeneity.

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Response of the Skyrmion Lattice in MnSi to Cubic Magnetocrystalline Anisotropies

Cited by 21 publications

References 45 publications

Weak Crystallization of Fluctuating Skyrmion Textures in MnSi

Weak Crystallization of Fluctuating Skyrmion Textures in MnSi

Evolution of magnetocrystalline anisotropies in Mn1−xFexSi and Mn1−x
Kindervater
¹
,
Adams
²
,
Bauer
³

et al. 2020
Phys. Rev. B
Self Cite
22
4
17
0
View full text Add to dashboard Cite

Magnetic Small-Angle Neutron Scattering

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Response of the Skyrmion Lattice in MnSi to Cubic Magnetocrystalline Anisotropies

Cited by 21 publications

References 45 publications

Weak Crystallization of Fluctuating Skyrmion Textures in MnSi

Weak Crystallization of Fluctuating Skyrmion Textures in MnSi

Evolution of magnetocrystalline anisotropies in Mn1−xFexSi and Mn1−xKindervater1, Adams2, Bauer3 et al. 2020Phys. Rev. BSelf Cite224170View full textAdd to dashboardCite

Magnetic Small-Angle Neutron Scattering

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Evolution of magnetocrystalline anisotropies in Mn1−xFexSi and Mn1−x
Kindervater
¹
,
Adams
²
,
Bauer
³

et al. 2020
Phys. Rev. B
Self Cite
22
4
17
0
View full text Add to dashboard Cite