Multiply periodic states appear in a wide variety of physical contexts, such as the Rayleigh–Benard convection, Faraday waves, liquid crystals and skyrmion crystals recently observed in chiral magnets. Here we study the phase diagram of an anisotropic frustrated magnet which contains five different multiply periodic states including the skyrmion crystal. We clarify the mechanism for stabilization of these states and discuss how they can be observed in magnetic resonance and electric polarization measurements. We also find stable isolated skyrmions with topological charge 1 and 2. Their spin structure, interactions and dynamics are more complex than those in chiral magnets. In particular, magnetic resonance in the skyrmion crystal should be accompanied by oscillations of the electric polarization with a frequency depending on the amplitude of the a.c. magnetic field. These results show that skyrmion materials with rich physical properties can be found among frustrated magnets. We formulate rules to help the search.

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Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet

The helicity-orbital coupling is an intriguing feature of magnetic skyrmions in frustrated magnets. Here we explore the skyrmion dynamics in a frustrated magnet based on the J
 1-J
 2-J
 3 classical Heisenberg model explicitly by including the dipole-dipole interaction. The skyrmion energy acquires a helicity dependence due to the dipole-dipole interaction, resulting in the current-induced translational motion with a fixed helicity. The lowest-energy states are the degenerate Bloch-type states, which can be used for building the binary memory. By increasing the driving current, the helicity locking-unlocking transition occurs, where the translational motion changes to the rotational motion. Furthermore, we demonstrate that two skyrmions can spontaneously form a bound state. The separation of the bound state forced by a driving current is also studied. In addition, we show the annihilation of a pair of skyrmion and antiskyrmion. Our results reveal the distinctive frustrated skyrmions may enable viable applications in topological magnetism. Exploring the helicity-orbital coupling induced skyrmion properties is essential for the spintronic applications. Here the authors report the current controlled skyrmions and antiskyrmions dynamics with locking-unlocking helicity in frustrated magnets by including the dipole-dipole interaction in their model.

/pdf/skyrmion-dynamics-in-a-frustrated-ferromagnetic-film-and-6h9bda1jqt.pdf

Skyrmion dynamics in a frustrated ferromagnetic film and current-induced helicity locking-unlocking transition.

The term frustration refers to lattice systems whose ground state cannot simultaneously satisfy all the interactions. Frustration is an important property of correlated electron systems, which stems from the sign of loop products (similar to Wilson products) of interactions on a lattice. It was early recognized that geometric frustration can produce rather exotic physical behaviors, such as macroscopic ground state degeneracy and helimagnetism. The interest in frustrated systems was renewed two decades later in the context of spin glasses and the emergence of magnetic superstructures. In particular, Phil Anderson's proposal of a quantum spin liquid ground state for a two-dimensional lattice S  =  1/2 Heisenberg magnet generated a very active line of research that still continues. As a result of these early discoveries and conjectures, the study of frustrated models and materials exploded over the last two decades. Besides the large efforts triggered by the search of quantum spin liquids, it was also recognized that frustration plays a crucial role in a vast spectrum of physical phenomena arising from correlated electron materials. Here we review some of these phenomena with particular emphasis on the stabilization of chiral liquids and non-coplanar magnetic orderings. In particular, we focus on the ubiquitous interplay between magnetic and charge degrees of freedom in frustrated correlated electron systems and on the role of anisotropy. We demonstrate that these basic ingredients lead to exotic phenomena, such as, charge effects in Mott insulators, the stabilization of single magnetic vortices, as well as vortex and skyrmion crystals, and the emergence of different types of chiral liquids. In particular, these orderings appear more naturally in itinerant magnets with the potential of inducing a very large anomalous Hall effect.

https://iopscience.iop.org/article/10.1088/0034-4885/79/8/084504/pdf

Frustration and chiral orderings in correlated electron systems.

Recent experimental and theoretical investigations of frustrated triangular-lattice antiferromagnets are reviewed. An analysis is made of phases with different structures: partly disordered and double incommensurate states, helical configurations, triangular superstructures, etc. These phases appear because of an instability of the conical high-symmetry point in the Brillouin zone as a result of the dipole interaction, or they may be due to other factors. An analysis is made of magnetic transitions belonging to new universal classes as well as Berezinskiĭ–Kosterlitz–Thouless transitions with an exponential decay of correlations in the low-temperature phase. The chiral symmetry and the associated problem of transition accompanied by simultaneous ordering of discrete and continuous components of the order parameter space are considered for triangular antiferromagnets with different spins. The spectrum of collective modes of some incommensurate structures is analyzed.

https://iopscience.iop.org/article/10.1070/PU1989v032n10ABEH002765/pdf

Magnetic states and phase transitions in frustrated triangular-lattice antiferromagnets

The triangular and hexagonal classical Heisenberg model with suitable competing intraplane interactions have infinitely many ground states having inequivalent helical order of different pitch Q. The spin wave energy vanishes along a line in k space, the locus of the Q vectors. Helimagnetic long-range order is destroyed at finite temperature also in three dimensions. The existence of a new phase is suggested: an isotropic helimagnet that leads to a characteristic ring scattering. The effect of quantum corrections and of easy plane anisotropy is also considered.

Degenerate helimagnetic states, lines of soft modes and absence of long-range order in three dimensions

The magnetic structure of Ni0.92Zn0.08Br2 has been studied by single-crystal neutron diffraction as a function of temperature down to 4.2K and in magnetic fields along (110) up to 3 T. From TN=48.0+or-0.5K to TIC=21.0+or-0.5K the magnetic structure is a collinear easy-plane metamagnetic one like NiCl2. Below TIC it transforms to an incommensurate structure with a propagation length within the basal plane which decreases continuously with decreasing temperature, reaching 71+or-5 AA at 4.2K. Exploration of the scattering in the a*b* plane around (003/2) and (101/2) shows satellite structure best fitted to a ring, i.e. to a completely disordered propagation direction. The magnetic phase diagram has also been determined.

https://iopscience.iop.org/article/10.1088/0022-3719/14/23/018/pdf

Neutron diffraction study of the incommensurate magnetic phase of Ni0.92Zn0.08Br2

Inelastic neutron scattering study of magnetic excitations in the helimagnetic and antiferromagnetic phases of NiBr2

Magnetic phase diagrams and helical magnetic phases inMxNi1−xBr2 (M =Fe, Mn): A neutron diffraction and magneto-optical study

The variations of the 6000 A band system with temperature from 4.2 to 30 K and magnetic fields up to 3 T applied parallel to the basal plane have been used to map the magnetic phase diagram of NiBr2 and Ni1–xZnxBr2(x= 0.05, 0.08). For NiBr2 precise measurements are also reported of the temperature dependence of the wavelength of the two sharp exciton–magnon lines near 6080 A, and of their behaviour in magnetic fields up to 16 T applied parallel to the c-axis and their polarisation.

M.W. Moore

Papers

Neutron diffraction study of the incommensurate magnetic phase of Ni0.92Zn0.08Br2

Inelastic neutron scattering study of magnetic excitations in the helimagnetic and antiferromagnetic phases of NiBr2

Magnetic phase diagrams and helical magnetic phases inMxNi1−xBr2 (M =Fe, Mn): A neutron diffraction and magneto-optical study

Optical and magneto-optical study of the magnetic phase diagram and incommensurate magnetic phase of NiBr2 and Ni1–xZnxBr2

The effect of iodide doping on the incommensurate helical magnetic structure of NiBr2