Single-ion Anisotropy Research Articles

Mean Field Study of a Cylindrical Ferrimagnetic Nanotube with Different Anisotropies

In this paper, the ferrimagnetic mixed spins (1, 5/2) Blume-Capel model is proposed to investigate the phase diagrams and hysteresis behaviors of a magnetic cylindrical nanotube with a core-shell structure using the mean-field approximation based on the Bogoliubov inequality for the Gibbs free energy. The core sites are occupied by σ= ±1, 0 spins, whereas the shell sites are filled by S= ±5/2, ±3/2, ±1/2 spins. The effects of exchange couplings (Jin, JS) and single-ion anisotropies (DC, DS) on core, shell, and total magnetizations are investigated, as well as hysteresis behaviors. The entropy, free energy, and specific heat are analyzed to establish the stability of the solutions. The presentation and discussion of phase diagrams is detailed. The system shows a first-order and second-order phase transitions, as well as tricritical and critical end- points. In addition, the system shows compensation and reentrant behaviors. Various multiple hysteresis loop behaviors are seen according on the Hamiltonian parameters, such as the presence of triple, quintuple, and septuple hysteresis loops.

Delving into the anisotropic interlayer exchange in bilayer CrI3

Bilayer CrI3 attracted much attention due to stacking-induced switching between the layered ferromagnetic and antiferromagnetic order. This discovery brought under the spotlight the interlayer Cr–Cr exchange interaction, which despite being much weaker than the intralayer exchange, plays an important role in shaping the magnetic properties of bilayer CrI3. In this work we delve into the anisotropic part of the interlayer exchange with the aim to separate the contributions from the Dzyaloshinskii–Moriya (DMI) and the Kitaev interactions (KI). We leverage the density functional theory calculations with spin Hamiltonian modeling and develop an energy mapping procedure to assess these anisotropic interactions with accuracy. After inspecting the rhombohedral and monoclinic stacking sequences of bilayer CrI3, we reveal a considerable DMI and a weak interlayer KI between the sublattices of a monoclinic bilayer. We explain the dependence of DMI and KI on the interlayer distance, stacking sequence, and the spin–orbit coupling strength, and we suggest the dominant superexchange processes at play. In addition, we demonstrate that the single-ion anisotropy in bilayer CrI3 is highly stacking-dependent, increasing by 50% from monoclinic to rhombohedral bilayer. Remarkably, our findings prove that iodines are highly efficient in mediating the DMI across the van der Waals gap, much owing to spatially extended 5p orbitals which feature strong spin–orbit coupling. Our study gives promise that the interlayer chiral control of spin textures, demonstrated in thin metallic films where the DMI is with a much longer range, can be achieved with similar efficiency in semiconducting two-dimensional van der Waals magnets.

Natural pinning field effecting on one surface of C60-like-nanostructure antiferromagnetic mixed-spin (1/2, 1) Ising spin system

Based on magnetic phenomena at the interface in metal-C60 bilayer or multilayer film, we construct a natural pinning field effecting on one surface of C60-like-nanostructure antiferromagnetic mixed-spin (1/2, 1) Ising spin system. By use of the decoration transformation and the transfer matrix method, we found that the ground states, magnetic susceptibility, magnetization behavior and specific heat of the system display various unique properties. Eight ground state phases with different values of magnetization are shown in the parameter space of single-ion anisotropy and pinning field, and at some certain boundary between two phases, the magnetic susceptibility multiplied by temperature is a non-zero finite value at the zero-temperature limit. The specific heat curve appears double-peak phenomena, a sharp peak and a round peak respectively. The entropy of the system exactly shows considerable serried excited states adjacent to the ground state of the system with temperature increasing from zero, explaining why there is a sharp peak of specific heat at ultra-low temperature. This study can offer a reasonable theoretical explanation for unique magnetic phenomena at interface in metal-C60 bilayer or multilayer.

Magnetic properties and hysteresis loops of mixed spin - (3/2, 1) in core-shell hexagonal nanotube: comparative study of mean-field theory and Monte Carlo simulation

Based on the Ising model, Monte Carlo simulation (MCS) and the Mean- field approximation (MFA) were used to examine the magnetic properties and the phase diagram of a ferrimagnetic mixed-spin (2,3/2) hexagonal Ising nanotube with core-shell structure. The effects of exchange interactions ( ) and the single-ion anisotropies ( ) on the magnetization of the total system, the two sublattices and the hysteresis loops have been discussed in detail. The phase diagrams under the effect of different parameters have been provided. The results demonstrate the emergence of compensation phenomena as well as the second-order phase transitions. Multiple behaviors of hysteresis loop, including single and triple hysteresis loops, were identified as a result of competitions between various parameters.

Machine learning assisted derivation of minimal low-energy models for metallic magnets

We consider the problem of extracting a low-energy spin Hamiltonian from a triangular Kondo Lattice Model (KLM). The non-analytic dependence of the effective spin-spin interactions on the Kondo exchange excludes the use of perturbation theory beyond the second order. We then introduce a Machine Learning (ML) assisted protocol to extract effective two- and four-spin interactions. The resulting spin model reproduces the phase diagram of the original KLM as a function of magnetic field and single-ion anisotropy and reveals the effective four-spin interactions that stabilize the field-induced skyrmion crystal phase. Moreover, this model enables the computation of static and dynamical properties with a much lower numerical cost relative to the original KLM. A comparison of the dynamical spin structure factor in the fully polarized phase computed with both models reveals a good agreement for the magnon dispersion even though this information was not included in the training data set.

Magnetic properties of twisted bilayer magnetic thin films with interlayer dipolar interaction

In this paper, a model of bilayer film with single-ion anisotropy in z-direction and ferromagnetic exchange interaction in the layer and dipolar interaction between layers is established. The influence of dipolar interaction intensity on the magnetic properties of the system at different interlayer twisted angles θ was studied by using Landau Lifshitz Gilbert (LLG) equation. At zero temperature it is found that the system will be in the z-direction ferromagnetic state when the interlayer dipolar interaction intensity is small, but the state will become the z-direction magnetic domain structure when the interlayer dipolar interaction intensity is greater than a certain value. When θ = 0°, the Curie temperature and coercivity of the system decrease with the increase of dipolar interaction intensity, while the resonant frequency increases with the increase of dipolar interaction intensity. When θ ≠ 0°, if the interlayer dipolar interaction intensity is small, the change of θ has little effect on the magnetic properties, but the Curie temperature, coercivity and resonance frequency are slightly lower than that at θ = 0° when the interlayer dipolar interaction is big. When θ is larger than a certain angle, the change of θ has almost no effect on coercivity and resonance frequency, which is similar to the change of the total energy of the system.

Element-Specific Study of Magnetic Anisotropy and Hardening in SmCo5-xCux Thin Films.

This work investigates the effect of copper substitution on the magnetic properties of SmCo5 thin films synthesized by molecular beam epitaxy. A series of thin films with varying concentrations of Cu were grown under otherwise identical conditions to disentangle structural and compositional effects on the magnetic behavior. The combined experimental and theoretical studies show that Cu substitution at the Co3g sites not only stabilizes the formation of the SmCo5 structure but also enhances magnetic anisotropy and coercivity. Density functional theory calculations indicate that Sm(Co4Cu3g)5 possesses a higher single-ion anisotropy as compared to pure SmCo5. In addition, X-ray magnetic circular dichroism reveals that Cu substitution causes an increasing decoupling of the Sm 4f and Co 3d moments. Scanning transmission electron microscopy confirms predominantly SmCo5 phase formation and reveals nanoscale inhomogeneities in the Cu and Co distribution. Our study based on thin film model systems and advanced characterization as well as modeling reveals novel aspects of the complex interplay of intrinsic and extrinsic contributions to magnetic hysteresis in rare-earth-based magnets, i.e., the combination of increased intrinsic anisotropy due to Cu substitution and the extrinsic effect of inhomogeneous elemental distribution of Cu and Co.

Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy

Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy

Tilted Magnetic Anisotropy with In‐Plane Broken Symmetry in Ru‐Substituted Manganite Films

AbstractControlling the magnetic anisotropy of materials is important in a variety of applications including magnetic memories, spintronic sensors, and skyrmion‐based devices. Ru‐substituted La0.7Sr0.3MnO3 (Ru‐LSMO) is an emerging material, showing tilted magnetic anisotropy (TMA) and possible nontrivial magnetic topologies. Here anisotropic in‐plane magnetization is reported in moderately compressed Ru‐LSMO films, coexisting with TMA. This combination is attractive for technological applications, such as spin‐orbit torque (SOT) based devices and other spintronic applications. A microstructural analysis of films of this material is presented, and Ru single ion anisotropy and strain‐induced structural mechanisms are found to be responsible for both the in‐plane anisotropy and the TMA. The manifestation of these properties in a correlated oxide with Curie temperature near room temperature highlights an attractive platform for technological realization of SOT and other spintronic devices. Illustrating the mechanisms behind these properties provides the necessary engineering space for harnessing these phenomena for practical devices.

Electric polarization due to Yafet–Kittel ordering in spinels

We show that the triangular Yafet–Kittel magnetic ordering in AB2X4 spinels, in which the sublattice A spins are split into two noncollinear sublattices, leads to the appearance of electric polarization, and thus the crystal becomes multiferroic. Calculation of the magnetic and magnetoelectric properties of MnCr2S4 considering single-ion anisotropy illustrates the proposed mechanism.

Realistic Spin Model for Multiferroic NiI_{2}.

A realistic first-principle-based spin Hamiltonian is constructed for the type-II multiferroic NiI_{2}, using a symmetry-adapted cluster expansion method. Besides single ion anisotropy and isotropic Heisenberg terms, this model further includes the Kitaev interaction and a biquadratic term, and can well reproduce striking features of the experimental helical ground state, that are, e.g., a proper screw state, canting of rotation plane, propagation direction, and period. Using this model to build a phase diagram, it is demonstrated that, (i)the in-plane propagation direction of ⟨11[over ¯]0⟩ is determined by the Kitaev interaction, instead of the long-believed exchange frustrations and (ii)the canting of rotation plane is also dominantly determined by Kitaev interaction, rather than interlayer couplings. Furthermore, additional MonteCarlo simulations reveal three equivalent domains and different topological defects. Since the ferroelectricity is induced by spins in type-II multiferroics, our work also implies that Kitaev interaction is closely related to the multiferroicity of NiI_{2}.

Magnon Hall effect in antiferromagnetic lattices

Topology applied to condensed matter is an important area of research and technology, and topological magnetic excitations have recently become an active field of study. This paper presents a general discussion of magnon Hall transport in two-dimensional antiferromagnets. Although the Chern number is zero for a collinear antiferromagnet, we offer a general discussion that can be used in the more general case. First, we study the Union Jack lattice, where an effective time-reversal symmetry is broken, making the system display the magnon Hall effect. Then, we investigate the brick-wall lattice where such symmetry is present. Consequently, we have a phenomenon similar to the quantum spin Hall effect in electronic systems. Both lattices have not yet been studied from the topological point of view. The coexistence of opposite spin polarization in an antiferromagnet resembles the electron spin in various transport phenomena. We study magnon transport in the lattices mentioned above with Dzyaloshinskii-Moriya interaction and easy-axis single-ion anisotropy. We calculate the Berry curvature from the eigenvalues of the Hamiltonian. From that, we plot the spin Hall and thermal Hall conductivities, as well as the spin Nernst coefficient, as functions of the temperature. In the Union Jack lattice, we treat the effect of anharmonic interactions using a mean-field spin wave theory where the Hamiltonian becomes implicitly temperature-dependent. We determine self-consistently the renormalized dispersion and the staggered magnetization as a function of temperature. Our calculations can be applied to other antiferromagnetic lattices.

Spin-wave analysis of the ferromagnetic-ferromagnetic Heisenberg spin bilayer with intralayer single-ion anisotropy and interlayer antiferromagnetic interaction

In this paper, the spin wave theory is applied to the Heisenberg spin bilayer with intralayer ferromagnetic interaction [Formula: see text], intralayer single-ion anisotropy D and interlayer antiferromagnetic interaction [Formula: see text]. It is found that the effects of both D and [Formula: see text] on the thermodynamic quantities give rise to the two different low-temperature asymptotic behaviors with and without exponential law. For [Formula: see text], the interlayer antiferromagnetic interaction can induce the appearance of the maximum of the layer magnetization at finite temperatures. At the location of the layer magnetization maximum, the approximate behaviors (such as the power, linear, rational, exponential and logarithmic laws) which are driven by the temperature or the anisotropy, are obtained for the low-temperature thermodynamic properties. It is shown that the presence of antiferromagnetic interlayer interaction [Formula: see text] clearly induces more quantum fluctuations than the case where the interlayer interaction [Formula: see text] is ferromagnetic. Our results of the layer magnetization agree with the experimental data of the layered van der Waals crystal FeCl2 at low temperatures. In the monolayer case of [Formula: see text], our results are in agreement with the findings obtained by the existing theories and the quantum Monte Carlo data.

End-point singularity of the XY-paramagnetic phase boundary for the $$(2+1)$$D $$S=1$$ square-lattice $$J_1$$–$$J_2$$ XY model with the single-ion anisotropy

End-point singularity of the XY-paramagnetic phase boundary for the $$(2+1)$$D $$S=1$$ square-lattice $$J_1$$–$$J_2$$ XY model with the single-ion anisotropy

Transverse Magnetization in Spin-Orbit Coupled Antiferromagnets.

Some antiferromagnets under a magnetic field develop magnetization perpendicular to the field as well as more conventional ones parallel to the field. So far, the transverse magnetization (TM) has been attributed to either the spin canting effect or the presence of cluster magnetic multipolar ordering. However, a general theory of TM based on microscopic understanding is still missing. Here, we construct a general microscopic theory of TM in antiferromagnets with cluster magnetic multipolar ordering by considering classical spin Hamiltonians with spin anisotropy that arises from the spin-orbit coupling. First, from general symmetry analysis, we show that TM can appear only when all crystalline symmetries are broken other than the antiunitary mirror, antiunitary twofold rotation, and inversion symmetries. Moreover, by analyzing spin Hamiltonians, we show that TM always appears when the degenerate ground state manifold of the spin Hamiltonian is discrete, as long as it is not prohibited by symmetry. On the other hand, when the degenerate ground state manifold is continuous, TM generally does not appear except when the magnetic field direction and the spin configuration satisfy specific geometric conditions under single-ion anisotropy. Finally, we show that TM can induce the anomalous planar Hall effect, a unique transport phenomenon that can be used to probe multipolar antiferromagnetic structures. We believe that our theory provides a useful guideline for understanding the anomalous magnetic responses of the antiferromagnets with complex magnetic structures.

Spontaneous dimerization, spin-nematic order, and deconfined quantum critical point in a spin-1 Kitaev chain with tunable single-ion anisotropy

Kitaev-type spin chains have been demonstrated to be fertile playgrounds in which exotic phases and unconventional phase transitions are ready to appear. In this work, we use the density-matrix renormalization-group method to study the quantum phase diagram of a spin-1 Kitaev chain with a tunable negative single-ion anisotropy (SIA). When the strength of the SIA is small, the ground state is revealed to be a spin-nematic phase, which escapes conventional magnetic order but is characterized by a finite spin-nematic correlation because of the breaking spin-rotational symmetry. As the SIA increases, the spin-nematic phase is taken over by either a dimerized phase or an antiferromagnetic phase through an Ising-type phase transition, depending on the direction of the easy axis. For large enough SIA, the dimerized phase and the antiferromagnetic phase undergo a ``Landau-forbidden'' continuous phase transition, suggesting new platform of deconfined quantum critical point in spin-1 Kitaev chain.

Magnetic ground state and perturbations of the distorted kagome Ising metal TmAgGe

Magnetic order and excitations of the distorted kagome intermetallic magnet TmAgGe are explored using a variety of methods, including single-crystal neutron diffraction, inelastic neutron scattering, Monte Carlo simulations, and the random phase approximation. The magnetic properties are governed by strong, local single-ion anisotropy and geometrically frustrated magnetic exchanges. The authors establish multi-k structures at several different magnetic field configurations and model effective exchange parameters using field-dependencies of the magnetic neutron diffraction reflections and the weakly dispersive crystal electric field mode.

Static universality of the Ising and Blume–Capel models on two-dimensional Penrose tiles

We study the phase transitions and the critical behavior of the Ising and Blume–Capel models on two kinds of two-dimensional Penrose tiles employing Monte Carlo methods and detailed finite-size scaling analysis. The Wolff algorithm is used for the Ising model whereas the Wang–Landau and Metropolis algorithms are used for the Blume–Capel model to obtain critical temperatures and exponents. The phase diagram of the Blume–Capel model reveals the presence of the double transition, the reentrant behavior, and the tricriticality in the vicinity of the critical single-ion anisotropy. Our results indicate that continuous phase transitions of the Ising and Blume–Capel models on the Penrose tiles belong to the two-dimensional Ising universality class. However, the scaling functions depend on the spin magnitude, anisotropy, and graph shape. Lastly, we verify that the critical Binder cumulant is also universal but depends on the shape of the graph.

Tuning magnetoelectricity in a mixed-anisotropy antiferromagnet

Control of magnetization and electric polarization is attractive in relation to tailoring materials for data storage and devices such as sensors or antennae. In magnetoelectric materials, these degrees of freedom are closely coupled, allowing polarization to be controlled by a magnetic field, and magnetization by an electric field, but the magnitude of the effect remains a challenge in the case of single-phase magnetoelectrics for applications. We demonstrate that the magnetoelectric properties of the mixed-anisotropy antiferromagnet LiNi1−xFexPO4 are profoundly affected by partial substitution of Ni2+ ions with Fe2+ on the transition metal site. This introduces random site-dependent single-ion anisotropy energies and causes a lowering of the magnetic symmetry of the system. In turn, magnetoelectric couplings that are symmetry-forbidden in the parent compounds, LiNiPO4 and LiFePO4, are unlocked and the dominant coupling is enhanced by almost two orders of magnitude. Our results demonstrate the potential of mixed-anisotropy magnets for tuning magnetoelectric properties.

High field magnetism of the triangular lattice antiferromagnet CsFeCl$_3$ under high pressure

Magnetization measurements of the triangular lattice antiferromagnet CsFeCl_{3}3 at 1.4 K for H \parallel cH∥c were performed in pulsed high magnetic fields of up to 51 T under high pressures of up to 0.80 GPa. At ambient pressure, the magnetization below H_{c1}Hc1 = 4 T is small, and then it changes steeply between H_{c1}Hc1 and H_{c2}Hc2 = 12 T, followed by a gradual increase in magnetization up to H_{m}Hm = 33 T where a two-step metamagnetic transition occurs. With increasing pressure, the H_{c1}Hc1 and H_{m}Hm shifted to the low-field side, while the H_{c2}Hc2 shifted to the opposite side. The change in H_{m}Hm may depend on the difference in the single-ion anisotropies on pressure in the lowest JJ = 1 and the excited J=2J=2 states.