Squeezing N\'eel-type Magnetic Modulations by Enhanced Dzyaloshinskii-Moriya interaction of $4d$ Electrons
Ádám ButykaiK. GeirhosD. SzallerL. F. KissLászló BaloghMaria AzharMarkus GarstLisa DeBeer‐SchmittTakeshi WakiYoshikazu TabataHiroyuki NakamuraI. KézsmárkiS. Bordács
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In polar magnets, such as GaV$_4$S$_8$, GaV$_4$Se$_8$ and VOSe$_2$O$_5$, modulated magnetic phases namely the cycloidal and the N\'eel-type skyrmion lattice states were identified over extended temperature ranges, even down to zero Kelvin. Our combined small-angle neutron scattering and magnetization study shows the robustness of the N\'eel-type magnetic modulations also against magnetic fields up to 2 T in the polar GaMo$_4$S$_8$. In addition to the large upper critical field, enhanced spin-orbit coupling produces a variety of modulated phases with sub-10 nm periodicity and a peculiar distribution of the magnetic modulation vectors. Thus, our work demonstrates that non-centrosymmetric magnets with $4d$ and $5d$ electron systems are ideal candidates to host highly compressed magnetic spirals and skyrmions.Keywords:
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The spin wave spectra of antiferromagnetic BiFeO3-type multiferronics are analyzed theoretically. The presence of a spatially modulated cycloidal antiferromagnetic structure leads to a countable number of frequency branches of two oscillatory modes (Goldstone and activation) for spin waves propagating along a cycloid. When there is no magnetic field and anisotropy, the magnon spectrum is characterized by the absence of frequency gaps. The spectral features of the spin oscillations with changing anisotropy and application of a magnetic field are identified and the limits on the existence of an antiferromagnetic cycloid are established up to its transformation into a conical structure. In the transverse direction the spin oscillations have a mixed character which indicates that the cycloid is stable with respect to bending throughout its domain of existence.
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Low-dimensional spin systems reveal new and unexpected physical phenomena such as distinct plateaus in the magnetization as a function of magnetic field. In this paper we present ultrasonic measurements for the quasi-two-dimensional spin system SrCu 2 (BO 3 ) 2 in magnetic fields up to 50 T. From this technique we obtained detailed information about the spin state, the magnetic excitations and their interaction with phonons. The dimerized quantum-spin system SrCu 2 (BO 3 ) 2 exhibits plateaus in the magnetization and shows surprisingly strong magneto-elastic effects as a function of temperature and magnetic field. The pronounced elastic anomalies indicate a resonant interaction between the sound wave and the magnetic excitations.
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Magnetic excitations in a cycloidal magnet ${\text{LiCu}}_{2}{\text{O}}_{2}$ are explored using terahertz absorption spectroscopy in magnetic fields up to 12 T. Below the spin ordering temperature, eight optically active transitions are observed in the spin system of ${\text{LiCu}}_{2}{\text{O}}_{2}$ in the range from 4 to $30\text{ }{\text{cm}}^{\ensuremath{-}1}$. In magnetic field the number of modes increases and the electric polarization flop is seen as a change in magnetic field dependence of mode energies. The polarization dependence of two of the modes in zero magnetic field fits the selection rules for the cycloid tilted by $\ensuremath{\theta}=(41\ifmmode\pm\else\textpm\fi{}1)\ifmmode^\circ\else\textdegree\fi{}$ from the $bc$ plane. For the remaining six modes electric and magnetic dipole approximations cannot explain the observed polarization dependence. The electromagnon is not seen in the explored energy range although there is evidence that it could exist below $4\text{ }{\text{cm}}^{\ensuremath{-}1}$.
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Recent discovery of Skyrmion crystal phase in insulating multiferroic compound Cu$_2$OSeO$_3$ calls for new ways and ideas to manipulate the Skyrmions in the absence of spin transfer torque from the conduction electrons. It is shown here that the position-dependent electric field, pointed along the direction of the average induced dipole moment of the Skyrmion, can induce the Hall motion of Skyrmion with its velocity orthogonal to the field gradient. Finite Gilbert damping produces longitudinal motion. We find a rich variety of resonance modes excited by a.c. electric field.
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The two-dimensional metallic interface between lanthanum manganite and strontium iridate is a prototypical platform for the realization of a triangular crystal of Neel-type skyrmions at low temperatures in the presence of an external magnetic field, applied perpendicular to the interface. The skyrmion crystal is stabilized by the Dzyaloshinskii-Moriya -type anti-symmetric spin-exchange interaction located at the interface due to the broken structural inversion symmetry and strong spin-orbit coupling in the iridate. We investigate spin-wave excitations emerging from the skyrmion crystal by employing the Monte Carlo simulations and Landau-Lifshitz spin-dynamics calculations. The computed dynamical spin structure factor $S(\mathbf{q},\omega)$ reveals that six modes of spin-wave excitations appear in the skyrmion crystal at low temperatures and are supplemented by the spin-wave mode coming from the zero-momentum magnetic ordering of the ferromagnetic background. Above the critical temperature $T_s$ for the skyrmion crystallization, we find a diffusive regime of temperatures that confirms previous experimental findings that skyrmionic correlation starts to develop above $T_s$ as the precursor of the long-range skyrmion crystal order. We also explore the spin-wave excitations originating from the spin spiral phase that is stabilized spontaneously at zero magnetic field. We discuss the challenges and opportunities for the experimental detection of these spin-wave excitations of the skyrmion crystal in inelastic neutron-scattering experiments based on multi-layer superlattices of the manganite-iridate heterostructure.
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We study azimuthal spin-wave (SW) excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically nontrivial magnetization states, specifically, vortex, Bloch-type skyrmion, and N\'eel-type skyrmion states. A continuous transition between these states is realized by gradually changing the out-of-plane magnetic anisotropy and the Dzyaloshinskii-Moriya exchange interaction (DMI), and the corresponding SW spectra are calculated for each state. We observe the lifting of degeneracy of SW mode frequencies and a change in the systematics of frequency levels. The latter effect is induced by the geometric Berry phase, which occurs in SWs localized at the edge of the dot in the vortex state, and vanishes in the skyrmion states. Furthermore, channeling of edge-localized azimuthal SWs and a related large frequency splitting are observed in the skyrmion states. This is attributed to DMI-induced nonreciprocity, while the coupling of the breathing and gyrotropic modes is related to the skyrmion motion. Finally, we demonstrate efficient coupling of the dynamic magnetization to a uniform magnetic field in nanodots of noncircular symmetry in the skyrmion states.
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We study the dynamical interplay between ferroelectricity and magnetism in a multiferroic with a helical magnetic order. We show that the dynamical exchange-striction induces a biquadratic interaction between the spins and transverse phonons resulting in quantum fluctuations of the spontaneous ferroelectric polarization P in the ferroelectric phase. The hybridization between the spin wave and the fluctuation of the electric polarization leads to low-lying transverse phonon modes. Those are perpendicular to P and to the helical spins at small wave vector but then turn parallel to P at a wave vector close to the magnetic modulation vector. For helical magnetic structure, the spin chirality which determines the direction of P, also possesses a long-range order. Due to the dynamical Dzyaloshiskii-Moriya interaction, the spin chirality is strongly coupled to the spin fluctuation which implies an on-site inversion of the spin chirality in the ordered spin-(1/2) system and results in a finite scattering intensity of polarized neutrons from a cycloidal helimagnet.
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Effects associated with the interference of electron waves around a magnetic point defect in two-dimensional electron gas with combined Rashba-Dresselhaus spin-orbit interaction in the presence of a parallel magnetic field are theoretically investigated. The effect of a magnetic field on the anisotropic spatial distribution of the local density of states and the local density of magnetization is analyzed. The existence of oscillations of the density of magnetization with scattering by a non-magnetic defect and the contribution of magnetic scattering (accompanied by spin-flip) in the local density of electron states are predicted.
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We investigate the spin rotational structure of magnetic skyrmions in a tetragonal polar magnet VOSe2O5 via polarized small-angle neutron scattering (SANS). Spin polarization analysis of the scattered neutrons provides consistent evidence for the cycloidal spin modulation in all the incommensurate phases at zero and non-zero magnetic field along the c axis, including the triangular skyrmion-lattice phase. In the vicinity of the skyrmion phase, we performed extensive SANS measurements to unravel a field-induced incommensurate phase (IC-2 state). We discuss the possibility of anisotropic double-q state as an alternative spin structure to provisional square skyrmion-lattice state.
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