Conical Spin-Spiral State in an Ultrathin Film Driven by Higher-Order Spin Interactions

Yoshida, Yasuo; Schröder, S.; Ferriani, P.; Serrate, David; Kubetzka, André; Bergmann, Kirsten; Heinze, Stefan; Wiesendanger, R.

doi:10.1103/physrevlett.108.087205

Cited by 76 publications

(76 citation statements)

References 16 publications

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“…One of the candidates is a two-dimensional monolayer system showing a noncoplanar magnetic structure [42][43][44][45]. It is also interesting to clarify the origin of multiple-Q magnetic orderings in three-dimensional compounds by our spin model: a scandium thiospinel MnSc 2 S 4 showing a triple-Q vortex crystal under an external magnetic field [46], a rare-earth borocarbide GdNi 2 B 2 C showing a double-Q ordering in the wide range of field-temperature phase diagram [47], and a strontium iron perovskite oxide SrFeO 3 , exhibiting several phases depending on magnetic field and temperature [48].…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets

2017

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Noncollinear and noncoplanar magnetic textures including Skyrmions and vortices act as emergent electromagnetic fields and give rise to novel electronic and transport properties. We here report a unified understanding of noncoplanar magnetic orderings emergent from the spin-charge coupling in itinerant magnets. The mechanism has its roots in effective multiple spin interactions beyond the conventional Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism, which are ubiquitously generated in itinerant electron systems with local magnetic moments. By carefully examining the higher-order perturbations in terms of the spin-charge coupling, we construct a minimal effective spin model composed of the bilinear and biquadratic interactions with particular wave numbers dictated by the Fermi surface. Taking two-dimensional systems as examples, we find that our effective model captures the underlying physics of the instability toward noncoplanar multiple-Q states discovered recently: a single-Q helical state expected from the RKKY theory is replaced by a double-Q vortex crystal with chirality density waves even for an infinitely small spin-charge coupling on generic lattices [R. Ozawa et al., J. Phys. Soc. Jpn. 85, 103703 (2016)], and a triple-Q Skyrmion crystal with a high topological number of two appears while increasing the spin-charge coupling on a triangular lattice [R. Ozawa, S. Hayami, and Y. Motome, Phys. Rev. Lett. 118, 147205 (2017)]. We find that by introducing an external magnetic field, our effective model exhibits a plethora of multiple-Q states. Our effective model will serve as a guide for exploring further exotic magnetic orderings in itinerant magnets, not only in two dimensions but also in three dimensions.

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Section: Summary and Concluding Remarksmentioning

confidence: 99%

Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets

2017

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“…Not only the sign of the asymmetry is preserved, but also the monotonous variation as a function of θ Co . The physical concept reported here can be of general application in a large variety of magnetic substrates with noncollinear ground states: 2 AL Fe/Cu(111) [26], 2 AL Mn/W(110) [22], 1 AL Mn/W(100) [27], 1 AL Mn/Ag(111) [21], 2 AL Fe/W(110) [28], 1 AL Fe/Ir(111) [29], and NiMn(001) [30]. This work opens a way to study not only the coupling of adatoms to those substrates, but also the possible magnetic interactions among atoms in artificial structures built by atomic manipulation.…”

Section: (D) and 2(e) Provided That P T = 0 And Aφ/w < 90mentioning

confidence: 99%

“…(1) becomes an approximation of the experimental magnetic height contrast. The interpretation of height contrast as magnetoconductance is particularly well suited when looking at magnetic periodic patterns [7,18,21,22] or bimodal contrast between states with opposite spin moment [1,23]. However, we are dealing with the shape of the atom's LDOS in a quantitative manner, and the use of Eq.…”

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confidence: 99%

Spin-sensitive shape asymmetry of adatoms on noncollinear magnetic substrates

et al. 2016

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The spin-resolved density of states of Co atoms on a noncollinear magnetic support displays a distinct shape contrast, which is superimposed on the regular height contrast in spin-polarized scanning tunneling microscopy. The apparent atom height follows the well-known cosine dependence on the angle formed by the tip and adatom local magnetization directions, whereas the shape contrast exhibits a sine dependence. We explain this effect in terms of a noncollinear spin density induced by the substrate, which in our case is the spin spiral of the Mn monolayer on W(110). The two independent contrast channels, apparent height and shape, are identified with the Co magnetization projections onto two orthogonal axes. As a result, all components of the overall atom magnetic moment vector can be determined with a single spin-sensitive tip in the absence of an external magnetic field. This result should be general for any atom deposited on noncollinear magnetic layers. DOI: 10.1103/PhysRevB.93.125424The control of the spin degree of freedom down to the single-atom limit is nowadays a central research issue [1][2][3][4][5][6][7], fostered by the increasing need for miniaturization and lowering power consumption in communication technologies. The most suitable technique to address the problem is spinpolarized scanning tunneling microscopy (SP-STM) [8], which has proven to be an excellent tool to perform single-atom magnetometry [1,6]. The design of magnetic structures with a given functionality calls for atomic-scale engineering by means of atomic manipulation or self-assembly of lowdimensional structures. Both of them can be combined with SP-STM [6,7,9,10]. For that reason, getting insight into the underlying physics of SP-STM and extending its range of applications is of crucial relevance. The SP-STM principle is the magneto-conductance effect in magnetic tunnel junctions [8,[11][12][13][14], and relies on probing the imbalance between majority and minority spins in the local density of states (LDOS) with respect to a particular magnetic quantization axis. Following the same notation as in Ref. [15], the spinpolarized tunneling current at sample bias V readswhere ρ T and P T are the tip's density of states and spin polarization,ρ s andm s the integrated sample total density of states and magnetization at r (tip position), and θ the angle formed between the tip and local sample magnetization. As a consequence, a SP-STM tip is only sensitive to the projection onto its magnetization direction, m s cos θ , and not to all other components ofm s . Here we show that the situation is radically different if the substrate's magnetic ground state is noncollinear within the spatial extent of an atomic wave function. Owing to the breaking of translational symmetry in spin space associated with the noncollinearity, the atoms' apparent shapes become distorted in spin-resolved STM images. We find that the strength of such distortion provides a quantitative measurement of the total spin component orthogonal to the default sensitivity direct...

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“…The competition between the DMI and the symmetric anisotropic exchange was recently found to explain the magnetic stability of decorated Fe trimers on the Pt(111) surface [34]. The intricate interplay of higher-order and anisotropic bilinear magnetic interactions generates various magnetic states: conical spin spirals [35] and more complex magnetic structures [31,36,37], such as an intricate nanoskyrmion lattice for a monolayer of Fe on the Ir(111) surface [38].…”

Section: Introductionmentioning

confidence: 96%

The chiral biquadratic pair interaction

2019

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Magnetic interactions underpin a plethora of magnetic states of matter, hence playing a central role both in fundamental physics and for future spintronic and quantum computation devices. The Dzyaloshinskii-Moriya interaction, D S S ij i j · ( ), being chiral and driven by relativistic effects, leads to the stabilization of highly-noncollinear spin textures such as skyrmions, which thanks to their topological nature are promising building blocks for magnetic data storage and processing elements.Here, we reveal and study a new chiral pair interaction, C S S S S ij i j i j · ( )( · ), which is the biquadratic equivalent of the DMI. First, we derive this interaction and its guiding principles from a microscopic model, and we connect the atomistic form to the micromagnetic one. Second, we study its properties in the simplest prototypical systems, magnetic 3d transition metal dimers deposited on the Pt(111), Pt(100), Ir(111), and Re(0001) surfaces, resorting to systematic first-principles calculations. Lastly, we discuss its importance and implications not only for magnetic dimers but also for extended systems, namely one-dimensional spin spirals and complex two-dimensional magnetic structures, such as a nanoskyrmion lattice found in an Fe monolayer on Ir(111).

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Conical Spin-Spiral State in an Ultrathin Film Driven by Higher-Order Spin Interactions

Cited by 76 publications

References 16 publications

Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets

Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets

Spin-sensitive shape asymmetry of adatoms on noncollinear magnetic substrates

The chiral biquadratic pair interaction

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