Easy-axis Anisotropy Research Articles

Double frustration and magnetoelectroelastic excitations in collinear multiferroic materials

We discuss a model scenario for multiferroic systems of type II (collinear spins) where the electric dipolar order competes with a frustrated magnetic order in determining the elastic distortions of the lattice ion positions. High magnetic frustration due to second-neighbors exchange and small spin easy-axis anisotropy lead to the appearance of the so-called quantum magnetic plateau states. Increasing the magnetic field above the plateau border produces composite excitations, where fractionalized spin tertions arise together with spontaneous dipolar flips (in the form of domain walls) and enhanced localized elastic distortions. This peculiar magnetoelectric effect may be described by magneto-electric-elastic quasiparticles that could be detected by x-ray and neutron diffraction techniques. Our results are supported by extensive DMRG computations on the spin sector and self-consistent equations for the lattice distortions.

Ferromagnetic resonance of a magnetic particle using the Landau–Lifshitz–Bloch equation

In this work, we employ the Landau–Lifshitz–Bloch equation to study the ferromagnetic resonance of a magnetic nanoparticle assumed in a mono-domain with uniaxial anisotropy. We consider a constant magnetic field applied perpendicularly to the easy axis of anisotropy. We investigated the temperature effect on the resonance spectrum through the complex magnetic susceptibility tensor. We found a decrease in the resonance frequency as the temperature is incremented and a decrement in the resonance field range when the driven frequency increases.

Multimagnon dynamics and thermalization in the S=1 easy-axis ferromagnetic chain

Quasiparticles are physically motivated mathematical constructs for simplifying the seemingly complicated many-body description of solids. A complete understanding of their dynamics and the nature of the effective interactions between them provides rich information on real material properties at the microscopic level. In this work, we explore the dynamics and interactions of magnon quasiparticles in a ferromagnetic spin-1 Heisenberg chain with easy-axis onsite anisotropy, a model relevant for the explanation of recent terahertz optics experiments on NiNb$_2$O$_6$ [P. Chauhan et al., Phys. Rev. Lett. 124, 037203 (2020)],and nonequilibrium dynamics in ultracold atomic settings [W.C. Chung et al., Phys. Rev. Lett. 126, 163203 (2021)]. We build a picture for the properties of clouds of a few magnons with the help of exact diagonalization and density matrix renormalization group calculations supported by physically motivated Jastrow wavefunctions. We show how the binding energy of magnons effectively reduces with their number and explain how this energy scale is of direct relevance for dynamical magnetic susceptibility measurements. This understanding is used to make predictions for ultracold-atomic platforms which are ideally suited to study the thermalization of multimagnon states. We simulate the nonequilibrium dynamics of these chains using the matrix product state based time-evolution block decimation algorithm and explore the dependence of revivals and thermalization on magnon density and easy-axis onsite anisotropy (which controls the strength of effective magnon interactions). We observe behaviors akin to those reported for many-body quantum scars which we explain with an analytic approximation that is accurate in the limit of small anisotropy.

Thermodynamics of an Ising-like XXZ chain in a longitudinal magnetic field in the framework of the quantum transfer matrix approach

Taking the Ising chain as a reference model we have derived a perturbative expression for the free energy density of the Heisenberg–Ising chain with strong easy-axis anisotropy. All calculations are performed on the ground of the quantum transfer matrix approach. The obtained result agrees with the direct high-temperature expansion. It also agrees with the low-temperature cluster expansion in the special subregime when quantum fluctuations are weak against thermodynamical ones.

Spin-current instability at a magnetic domain wall in a ferromagnetic superfluid: A generation mechanism of eccentric fractional skyrmions

Spinful superfluids of ultracold atoms are ideal for investigating the intrinsic properties of spin current and texture because they are realized in an isolated, nondissipative system free from impurities, dislocations, and thermal fluctuations. This study theoretically reveals the impact of spin current on a magnetic domain wall in spinful superfluids. An exact wall solution is obtained in the ferromagnetic phase of a spin-1 Bose-Einstein condensate with easy-axis anisotropy at zero temperature. The bosonic-quasiparticle mechanics analytically show that the spin current along the wall becomes unstable if the velocity exceeds the critical spin-current velocities, leading to complicated situations because of the competition between transverse magnons and ripplons. Our direct numerical simulation reveals that this system has a mechanism to generate an eccentric fractional skyrmion, which has a fractional topological charge, but its texture is not similar to that of a meron. This mechanism is in contrast to the generation of conventional skyrmions in easy-axis magnets. The theoretical findings can be examined in the same situation as in a recent experiment on ultracold atoms. In terms of the universality of spontaneous symmetry breaking, unexplored similar phenomena are expected in different physical systems with the same broken symmetry.

Crystal field effects in the zig-zag chain compound SrTm2O[formula omitted

The single ion properties of the zig-zag chain compound SrTm2O4 have been investigated using heat capacity, magnetic susceptibility, magnetization, inelastic neutron scattering, and polarized muon spectroscopy. Two crystal field models are employed to estimate the single ion properties; a Density Function Theory based model and an effective charge model based on the Hutchings point charge model. The latter describes our experimental results well. This model estimates an easy-axis anisotropy for one of the Tm3+ sites and an easy-plane anisotropy for the second site. It also predicts a mixed ground state with dominating J=0 characteristics for both sites. Additionally, muon spin rotation/relaxation (μ+SR) spectra reveal oscillations, typically a sign of long-range magnetic order. However, the temperature dependence of the precession frequency and the relaxation rates indicate that the system is in an extended critical regime and the observed relaxation is actually dynamic.

Crystal structures and magnetic properties of Fe1.93-xCoxP1-ySiy compounds

In view of the interest that (Fe,Co)2(P,Si) compounds have as potential permanent magnets, their structural and magnetic phase diagrams are explored focusing on establishing the range where the hexagonal Fe2P-type structure is observed. In Fe1.93-xCoxP1-ySiy, the highest Si content prior entering a mixed phase domain is y ≈ 0.5. At high Si content but low Co for Fe substitutions, a structural distortion leading to a body-centered orthorhombic structure occurs. At high Co contents, when the Fe2P unit cell reaches a critical volume of about 102.4 Å3, the samples crystallize in a Co2P-type orthorhombic structure. Within the Fe2P-type structural range, the evolution of the unit-cell volume appears to follow the Vegard’s law, but this hides strongly anisotropic changes. Simultaneous Co for Fe and Si for P substitutions increase the range where the hexagonal structure is observed in comparison to ternary Fe2(P,Si) and (Fe,Co)2P. The samples are ferromagnetic, but with Curie temperatures showing an unusual evolution, uncorrelated to the c/a ratio of the lattice parameters. At low Si content, TC increases with Co for Fe substitutions. For y = 0.2, the evolution is not significant, while at high Si content TC systematically decreases with the increase in Co. Large Si and Co substitutions lead to a swift weakening of the magnetocrystalline anisotropy until the easy axis anisotropy turns from the c axis toward the a-b plane. This study guides future investigations by restricting the range where desirable properties for permanent magnetic applications can be expected to 0.1 ≲x≲ 0.3 and 0.1 ≲y≲ 0.3.

Large easy-axis magnetic anisotropy in a series of trigonal prismatic mononuclear cobalt(ii) complexes with zero-field hidden single-molecule magnet behaviour: the important role of the distortion of the coordination sphere and intermolecular interactions in the slow relaxation

A N6-tripodal ligand allows the preparation of a family of prismatic mononuclear cationic CoIIcomplexes with SMM behavior. Their axial anisotropy, magnetic relaxation and hysteresis width are modulated by the anion effects on the crystal structure.

Исследование неравновесного критического поведения сильно неупорядоченной трехмерной анизотропной модели Гейзенберга

The results of a Monte Carlo study of strongly structural disorder influence on nonequilibrium critical behavior of three-dimensional anisotropic Heisenberg models with spin concentration p = 0.5 are presented with its evolution from high and low temperature initial state. It is shown that presence of strongly disorder changes characteristics of nonequilibrium critical behavior of anisotropic model with easy axis anisotropy type in comparison with both pure anisotropic and isotropic Heisenberg models.

Неравновесное критическое поведение слабо неупорядоченной трехмерной анизотропной модели Гейзенберга

The results of a Monte Carlo study of weakly structural disorder influence onnonequilibrium critical behavior of three-dimensional anisotropic Heisenberg models with spin concentration p = 0.9 are presented with its evolution from high temperature initial state. It is shown that presence of even weakly disorder changes characteristics of nonequilibrium critical behavior of anisotropic model with easy axis anisotropy type in comparison with both pure anisotropic and isotropic Heisenberg models.

Asymmetric Interfaces in Epitaxial Off-Stoichiometric Fe3+xSi1−x/Ge/Fe3+xSi1−x Hybrid Structures: Effect on Magnetic and Electric Transport Properties

Three-layer iron-rich Fe3+xSi1−x/Ge/Fe3+xSi1−x (0.2 < x < 0.64) heterostructures on a Si(111) surface with Ge thicknesses of 4 nm and 7 nm were grown by molecular beam epitaxy. Systematic studies of the structural and morphological properties of the synthesized samples have shown that an increase in the Ge thickness causes a prolonged atomic diffusion through the interfaces, which significantly increases the lattice misfits in the Ge/Fe3+xSi1−x heterosystem due to the incorporation of Ge atoms into the Fe3+xSi1−x bottom layer. The resultant lowering of the total free energy caused by the development of the surface roughness results in a transition from an epitaxial to a polycrystalline growth of the upper Fe3+xSi1−x. The average lattice distortion and residual stress of the upper Fe3+xSi1−x were determined by electron diffraction and theoretical calculations to be equivalent to 0.2 GPa for the upper epitaxial layer with a volume misfit of −0.63% compared with a undistorted counterpart. The volume misfit follows the resultant interatomic misfit of |0.42|% with the bottom Ge layer, independently determined by atomic force microscopy. The variation in structural order and morphology significantly changes the magnetic properties of the upper Fe3+xSi1−x layer and leads to a subtle effect on the transport properties of the Ge layer. Both hysteresis loops and FMR spectra differ for the structures with 4 nm and 7 nm Ge layers. The FMR spectra exhibit two distinct absorption lines corresponding to two layers of ferromagnetic Fe3+xSi1−x films. At the same time, a third FMR line appears in the sample with the thicker Ge. The angular dependences of the resonance field of the FMR spectra measured in the plane of the film have a pronounced easy-axis type anisotropy, as well as an anisotropy corresponding to the cubic crystal symmetry of Fe3+xSi1−x, which implies the epitaxial orientation relationship of Fe3+xSi1−x (111)[0−11] || Ge(111)[1−10] || Fe3+xSi1−x (111)[0−11] || Si(111)[1−10]. Calculated from ferromagnetic resonance (FMR) data saturation magnetization exceeds 1000 kA/m. The temperature dependence of the electrical resistivity of a Ge layer with thicknesses of 4 nm and 7 nm is of semiconducting type, which is, however, determined by different transport mechanisms.

Multi- k spin ordering in CaFe3Ti4O12 stabilized by spin-orbit coupling and further-neighbor exchange

Orthogonal spin ordering is rarely observed in magnetic oxides because nearest-neighbor symmetric Heisenberg superexchange interactions usually dominate. We have discovered that in the quadruple perovskite $\mathrm{Ca}{\mathrm{Fe}}_{3}{\mathrm{Ti}}_{4}{\mathrm{O}}_{12}$, where only the $S=2$ ${\mathrm{Fe}}^{2+}$ ion is magnetic, long-range magnetic order consisting of an unusual arrangement of three interpenetrating orthogonal sublattices is stabilized. Each magnetic sublattice corresponds to a set of $\mathrm{Fe}{\mathrm{O}}_{4}$ square planes sharing a common orientation. This multi-$k$ magnetic spin ordering is the result of fourth-neighbor spin couplings with a strong easy-axis anisotropy. In an applied magnetic field, each sublattice tends towards ferromagnetic alignment, but remains polarized by internal magnetic fields generated by the others, thus stabilizing in a noncollinear canted ferromagnetic structure. $\mathrm{Ca}{\mathrm{Fe}}_{3}{\mathrm{Ti}}_{4}{\mathrm{O}}_{12}$ provides a rare example of how nontrivial long-range spin order can arise when near-neighbor Heisenberg superexchange is quenched.

Locking of skyrmion cores on a centrosymmetric discrete lattice: Onsite versus offsite

A magnetic skyrmion crystal (SkX) with a swirling spin configuration, which is one of topological spin crystals as a consequence of an interference between multiple spin density waves, shows a variety of noncoplanar spin patterns depending on a way of superposing the waves. By focusing on a phase degree of freedom among the constituent waves in the SkX, we theoretically investigate a position of the skyrmion core on a discrete lattice, which is relevant with the symmetry of the SkX. The results are obtained for the double exchange (classical Kondo lattice) model on a discrete triangular lattice by the variational calculations. We find that the skyrmion cores in both two SkXs with the skyrmion number of one and two are locked at the interstitial site on the triangular lattice, while it is located at the onsite by introducing a relatively large easy-axis single-ion anisotropy. The variational parameters and the resultant Fermi surfaces in each SkX spin texture are also discussed. The different symmetry of the Fermi surfaces depending on the core position is obtained when the skyrmion crystal is commensurate with the lattice. The different Fermi-surface topology is directly distinguished by an electric probe of angle-resolved photoemission spectroscopy. Furthermore, we show that the SkXs obtained by the variational calculations are also confirmed by numerical simulations on the basis of the kernel polynomial method and the Langevin dynamics for the double exchange model and the simulated annealing for an effective spin model.

Stability of skyrmion crystal phase in antiferromagnetic triangular lattice with DMI and single-ion anisotropy

We study a frustrated antiferromagnetic Heisenberg model on a triangular lattice with the Dzyaloshinskii–Moriya interaction (DMI) in the presence of an external magnetic field and focus on the effects of the single-ion anisotropy on the overall phase diagram topology and the skyrmion lattice (SkX) phase stability. Phase diagrams in the temperature-field plane for both easy-axis and easy-plane anisotropy of a varying strength are constructed in the regimes of a moderate and strong DMI by parallel tempering Monte Carlo simulations. For the considered range of parameters the phase diagrams featuring up to four ordered phases are identified. The SkX phase is found to be stabilized within some temperature and field window for sufficiently large DMI and not too strong anisotropy. We demonstrate that both types of the anisotropy can have beneficial effects on the SkX phase stabilization. Namely, in the systems with moderate DMI a small easy-plane anisotropy extends the field window of the SkX phase appearance by shifting its lower bound to smaller values and in the systems with larger DMI a small easy-axis anisotropy shifts the entire field range of the SkX phase stabilization towards smaller values. The Metropolis dynamics is employed to probe the persistence of the SkX phase upon quenching the field to zero or small finite values. It is confirmed that low temperatures, small DMI and small easy-plane anisotropy values support the skyrmions persistence, i.e., increase their lifetime.

Scalable computational measures for entropic detection of latent relations and their applications to magnetic imaging

Detection of material inhomogeneities is an important task in magnetic imaging and plays a significant role in understanding physical processes. For example, in spintronics, the sample heterogeneity determines the onset of current-driven magnetization motion. While often a significant effort is made in enhancing the resolution of an experimental technique to obtain a deeper insight into the physical properties, here we want to emphasize that an advantageous data analysis has the potential to provide a lot more insight into given data set, in particular when being close to the resolution limit where the noise becomes at least of the same order as the signal. In this work, we introduce two tools - the average latent dimension and average latent entropy - which allow for the detection of very subtle material inhomogeneity patterns in the data. For example, for the Ising model, we show that these tools are able to resolve exchange differences down to $1\%$. For a micromagnetic model, we demonstrate that the latent entropy can be used to detect changes in the easy axis anisotropy from magnetization data. We show that the latent entropy remains robust when imposing noise on the data, changing less than $0.3\%$ after adding Gaussian noise of the same amplitude as the signal. Furthermore, we demonstrate that these data-driven tools can be used to visualize inhomogeneities based on MOKE data of magnetic whirls and thereby can help to explicitly resolve impurities and pinning centers. To evaluate the performance of the average latent dimension and entropy, we show that they outperform common instruments ranging from standard statistics measures to state-of-the-art data analysis techniques such as Gaussian mixture models not only in recognition quality but also in the required computational cost.

Identification and manipulation of spin wave polarizations in perpendicularly magnetized synthetic antiferromagnets

Interlayer exchange-coupled synthetic antiferromagnets (SAFs) have the combined advantages of both high frequency of antiferromagnets and easy detection of ferromagnets. Here, magnetic excitations are investigated by theoretical analysis and micromagnetic simulations in SAFs that consist of two identical ferromagnetic layers with perpendicular magnetic anisotropy. Different from the common in-phase acoustic mode and out-of-phase optic mode, linearly or circularly polarized spin wave modes can be excited at zero bias field by using different types of microwave magnetic fields. Once a bias magnetic field is applied along the easy-axis, left-handed (LH) and right-handed (RH) polarization modes are observed, and the resonance frequency of RH (LH) mode of the SAFs increases (decreases) linearly with the increase of bias magnetic fields until a critical spin-flop field is reached, which is in accordance with collinear antiferromagnets with easy-axis anisotropy. These simulation results agree with the theoretical derivation and provide fundamental insight into the nature of dynamic properties of the perpendicularly magnetized SAFs, which may provide new prospects for spintronic applications.

Temperature-driven transition from skyrmion to bubble crystals in centrosymmetric itinerant magnets

Interplay between itinerant electrons and localized spins in itinerant magnets gives rise to a variety of noncoplanar multiple-Q spin textures, such as the skyrmion, hedgehog, meron, and vortex. We elucidate that another type of multiple-Q state consisting of collinear sinusoidal waves, a magnetic bubble crystal, appears at finite temperatures in a centrosymmetric itinerant electron system. The results are obtained for the classical Kondo lattice model with easy-axis single-ion anisotropy on a triangular lattice by a large-scale numerical simulation. We find that a finite-temperature topological phase transition between the skyrmion crystal and the bubble crystal occurs by changing the temperature. We obtain the minimal key ingredients for inducing the finite-temperature transition by analyzing an effective spin model where it is shown that the synergy between the multiple-spin interaction and magnetic anisotropy plays a significant role.

Magnetic properties of the quasi two-dimensional centered honeycomb antiferromagnet GdInO3

The crystal structure and magnetic property of the single crystalline hexagonal rare-earth indium oxides ${\mathrm{GdInO}}_{3}$ have been studied by combing experiments and model calculations. The two inequivalent ${\mathrm{Gd}}^{3+}$ ions form the centered honeycomb lattice, which consists of honeycomb and triangular sublattices. The dc magnetic susceptibility and specific heat measurements suggest two antiferromagnetic phase transitions at ${T}_{\text{N1}}=2.3\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and ${T}_{\text{N2}}=1.02\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. An inflection point is observed in the isothermal magnetization curve, which can be an indication of an up-up-down phase with a 1/3 magnetization plateau, further supported by our theoretical calculation. We also observe a large magnetic entropy change originated from the magnetic frustration in ${\mathrm{GdInO}}_{3}$. By considering a classical spin Hamiltonian, we establish the ground state phase diagram, which suggests that ${\mathrm{GdInO}}_{3}$ has a weak easy-axis anisotropy and is close to the equilateral triangular-lattice system. The theoretical ground-state phase diagram may be used as a reference in NMR, ESR, or $\ensuremath{\mu}\mathrm{SR}$ experiments in future.

Hierarchical single-ion anisotropies in spin-1 Heisenberg antiferromagnets on the honeycomb lattice

We examine the thermal properties of the spin-1 Heisenberg antiferromagnet on the honeycomb lattice in the presence of an easy-plane single-ion anisotropy as well as the effects of an additional weak in-plane easy-axis anisotropy. In particular, using large-scale quantum Monte Carlo simulations, we analyze the scaling of the correlation length near the thermal phase transition into the ordered phase. This allows us to quantify the temperature regime above the critical point in which -- in spite of the additional in-plane easy-axis anisotropy -- characteristic easy-plane physics, such as near a Berezinskii-Kosterlitz-Thouless transition, can still be accessed. Our theoretical analysis is motivated by recent neutron scattering studies of the spin-1 compound BaNi${}_2$V${}_2$O${}_8$ in particular, and it addresses basic quantum spin models for generic spin-1 systems with weak anisotropies, which we probe over the full range of experimentally relevant correlation length scales.

Spin transport on the ferromagnetic checkerboard lattice

I study spin transport on the anisotropic ferromagnetic checkerboard lattice with a Dzyaloshinskii -Moriya interaction and an easy-axis anisotropy term. I show that by fine-tuning the parameters, we can get a flat band. The transverse and longitudinal dynamical spin conductivities are calculated using a Kubo formula. The Drude weight was also calculated as a function of temperature. The Drude weight vanishes at T = 0 but is finite for T > 0. A finite Drude weight indicates an ideal conductor, which we refer to as ballistic transport.