Easy-axis Single-ion Anisotropy Research Articles

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.

Rectangular and square skyrmion crystals on a centrosymmetric square lattice with easy-axis anisotropy

We report our theoretical results on the emergence of rectangular- and square-shaped magnetic skyrmion crystals on a centrosymmetric square lattice with magnetic anisotropy. By performing the simulated annealing for a frustrated spin model with an easy-axis single-ion anisotropy on a square lattice, we find that a competition of the interactions in momentum space gives rise to the formation of two skyrmion crystals, where the skyrmion cores are aligned in a rectangle- or square-lattice way. Especially, the interactions at the higher harmonic wave vectors play an important role in stabilizing the square/rectangular skyrmion crystals. Our results provide a reference to explore further skyrmion-hosting materials in centrosymmetric tetragonal systems.

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.

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-Field-Orientation Dependent Thermal Entanglement of a Spin-1 Heisenberg Dimer: The Case Study of Dinuclear Nickel Complex with an Uniaxial Single-Ion Anisotropy.

The bipartite entanglement in pure and mixed states of a quantum spin-1 Heisenberg dimer with exchange and uniaxial single-ion anisotropies is quantified through the negativity in a presence of the external magnetic field. At zero temperature the negativity shows a marked stepwise dependence on a magnetic field with two abrupt jumps and plateaus, which can be attributed to the quantum antiferromagnetic and quantum ferrimagnetic ground states. The magnetic-field-driven phase transition between the quantum antiferromagnetic and quantum ferrimagnetic ground states manifests itself at nonzero temperatures by a local minimum of the negativity, which is followed by a peculiar field-induced rise of the negativity observable in a range of moderately strong magnetic fields. The rising temperature generally smears out abrupt jumps and plateaus of the negativity, which cannot be distinguished in the relevant dependencies above a certain temperature. It is shown that the thermal entanglement is most persistent against rising temperature at the magnetic field, for which an energy gap between a ground state and a first excited state is highest. Besides, temperature variations of the negativity of the spin-1 Heisenberg dimer with an easy-axis single-ion anisotropy may exhibit a singular point-kink, at which the negativity has discontinuity in its first derivative. The homodinuclear nickel complex [Ni(Medpt)(-ox)(HO)](ClO)·2HO provides a suitable experimental platform of the antiferromagnetic spin-1 Heisenberg dimer, which allowed us to estimate a strength of the bipartite entanglement between two exchange-coupled Ni magnetic ions on the grounds of the interaction constants reported previously from the fitting procedure of the magnetization data. It is verified that the negativity of this dinuclear compound is highly magnetic-field-orientation dependent due to presence of a relatively strong uniaxial single-ion anisotropy.

Dynamic and static properties of two-sublattice anisotropic non-Heisenberg magnet

The influence of different types of single-ion anisotropy (easy-axis and easy-plane) on the phase states and on the dynamic properties of non-Heisenberg spin-1 magnet was investigated in the mean-field approximation. It was shown that account of the easy-axis single-ion anisotropy almost does not result in deviation of system’s properties from the isotropic case; while account of the easy-plane single-ion anisotropy changes the type of the phase transitions between the dipolar and the nematic phases and results in disappearance of SU(3) point. The phase diagrams of the system were drawn for both types of anisotropy.

Devlin-like approach to a spin-1 transverse XY model with biquadratic exchange and single-ion anisotropy

The effect of the biquadratic exchange interaction on the phase diagram of a d-dimensional spin-1 transverse XY model with easy-axis single-ion anisotropy is studied by employing the Devlin-like two-time Green functions framework. The chain of equations of motion is closed adopting the random phase approximation for the exchange higher order Green functions and treating exactly the crystal-field anisotropy terms. For short-range interactions and d > 2, analytical estimates and numerical calculations predict a reentrant behavior of the critical lines close to the magnetic-field-induced quantum critical point for appropriate values of the single-ion anisotropy parameter and suitable combinations of the bilinear and biquadratic exchange couplings. Remarkably, increasing the biquadratic exchange reduces or destroies the reentrant character of the quantum critical lines, in qualitative agreement with the findings of the Anderson-Callen-like strategy. In our formalism, the easy-plane anisotropy case can be studied similarly but the phase diagram and the quantum critical scenario do not present any reentrant phenomena.

Effect of biquadratic exchange on the phase diagram of a spin-1 transverse XY model with single-ion anisotropy

The two-time Green function method is employed to explore the effect of the biquadratic exchange interaction on the phase diagram of a $d$-dimensional spin-1 transverse XY model with single-ion anisotropy close to the magnetic-field-induced quantum critical point. We work at level of the Anderson-Callen-decoupling-like framework for both easy-plane and easy-axis single-ion anisotropy. The structure of the phase diagram is analyzed with analytical estimates and numerical calculations by adopting Tyablikov-like decouplings for the exchange higher order Green functions in the equation of motion. For dominant bilinear short-range exchange interaction the structure of the phase diagram close to the quantum critical point remains qualitatively the same of that in absence of biquadratic interaction including reentrant critical lines. When the biquadratic exchange becomes increasingly dominant its role appears more effective and tends to reduce or destroy the reentrant character of the critical lines.

Magnetic compensation and critical properties of a mixed spin-(2, 3/2) Heisenberg single-walled nanotube superlattice

In recent years, some theoretical interests have been focused on the binary alloy nanotubes and nanowires with mixed spins. Compared with ferrimagnetic nanowires, few studies have been done on ferrimagnetic nanotubes. In this paper, the magnetic properties of a mixed spin-(2, 3/2) Heisenberg single-walled nanotube superlattice are calculated by use of the double-time Green’s function method within the random phase approximation and the Anderson and Callen’s decoupling. Magnetic compensation and critical properties are obtained for a wide range of parameters in the Hamiltonian, and magnetic phase diagrams are plotted in the related planes. For Heisenberg single-walled nanotube superlattice model with Néel-type magnetic structure, anisotropy must be taken into account, and the easy-axis single-ion anisotropy is considered in this paper. The next nearest neighbor exchange interactions Jbb and/or single-ion anisotropy strength Db of the smaller spin sublattice were necessary in order to obtain a compensation point. The influence of the wall diameter number of the tubes, m, an important parameter of the system, on the compensation behavior is considered. Calculation shows that as Jbb and Db are fixed, only when m is beyond a certain minimum value, mmin, can compensation temperature Tcom appears, where the next nearest neighbor exchange interactions Jaa and single-ion anisotropy strength Da of the larger spin sublattice are absent. The compensation temperature and critical temperature increase with m rising, which indicates that the longitudinal correlation effect is enhanced and the fluctuation effect is weakened with the increase of m.

Reentrant behaviors in the phase diagram of spin-1 planar ferromagnet with single-ion anisotropy

We used the two-time Green function framework to investigate the role played by the easy-axis single-ion anisotropy on the phase diagram of (d>2)-dimensional spin-1planar ferromagnets, which exhibit a magnetic field induced quantum phase transition. We tackled the problem using two different kind of approximations: the Anderson-Callen decoupling scheme and the Devlin approach. In the latter scheme, the exchange anisotropy terms in the equations of motion are treated at the Tyablikov decoupling level while the crystal field anisotropy contribution is handled exactly. The emerging key result is a reentrant structure of the phase diagram close to the quantum critical point, for certain values of the single-ion anisotropy parameter. We compare the results obtained within the two approximation schemes. In particular, we recover the same qualitative behavior. We show the phase diagram, close to the field-induced quantum critical point and the behavior of the susceptibility for different values of the single-ion anisotropy parameter, enhancing the differences between the two different scenarios (i.e. with and without reentrant behavior).

Time-of-Flight Elastic and Inelastic Neutron Scattering Studies on the Localized 4d Electron Layered Perovskite La5Mo4O16

The magnetic structure and spin-wave excitations in the quasi-square-lattice layered perovskite compound La$_5$Mo$_4$O$_{16}$ were studied by a combination of neutron diffraction and inelastic neutron scattering techniques using polycrystalline sample. Neutron powder diffraction refinement revealed that the magnetic structure is ferrimagnetic in the $ab$ plane with antiferromagnetic stacking along the $c$ axis where the magnetic propagation vector is $\mathbf{k}=\left(0,0,\frac{1}{2}\right)$. The ordered magnetic moments are estimated to be $0.54(2)\mu_\text{B}$ for Mo$^{5+}$ ($4d^1$) ions and $1.07(3)\mu_\text{B}$ for Mo$^{4+}$ ($4d^2$) ions at 4 K, which are about half of the expected values. The inelastic neutron scattering results display strong easy-axis magnetic anisotropy along the $c$ axis due to the spin-orbit interaction in Mo ions evidenced by the spin gap at the magnetic zone center. The model Hamiltonian consisting of in-plane anisotropic exchange interactions, the interlayer exchange interaction, and easy-axis single-ion anisotropy can explain our inelastic neutron scattering data well. Strong Ising-like anisotropy and weak interlayer coupling compared with the intralayer exchange interaction can explain both the high-temperature magnetoresistance and long-time magnetization decay recently observed in La$_5$Mo$_4$O$_{16}$.

Reentrant behaviors in the phase diagram of spin-1 planar ferromagnets with easy-axis single-ion anisotropy via the Devlin two-time Green function framework

The Devlin two-time Green function framework is used to investigate the role played by the easy-axis single-ion anisotropy on the phase diagram of (d>2)-dimensional spin-1 planar ferromagnets which exhibit a magnetic-field-induced quantum phase transition (QPT). In this scheme, the exchange anisotropy terms in the equations of motion are treated at the Tyablikov decoupling level while the crystal field anisotropy contribution is handled exactly. The emerging key result is a reentrant structure of the phase diagram close to the quantum critical point for a well defined window of values of the single-ion anisotropy parameter. This experimentally interesting feature was recently recovered by employing the Anderson-Callen decoupling (ACD) which is considered to provide meaningful results only for small values of the single-ion anisotropy parameter. In this context, our findings suggest that the simplest ACD treatment offers the possibility to have, at least qualitatively, a correct physical scenario of quantum criticality close to a field-induced QPT avoiding the limiting mathematical difficulties involved in the Devlin scheme.

Commensurate and incommensurate magnetic order in spin-1 chains stacked on the triangular lattice inLi2NiW2O8

We report thermodynamic properties, magnetic ground state, and microscopic magnetic model of the spin-1 frustrated antiferromaget Li$_{2}$NiW$_{2}$O$_{8}$ showing successive transitions at $T_{\rm N1}\simeq 18$ K and $T_{\rm N2}\simeq 12.5$ K in zero field. Nuclear magnetic resonance and neutron diffraction reveal collinear and commensurate magnetic order with the propagation vector $\mathbf k=(\frac12,0,\frac12)$ below $T_{\rm N2}$. The ordered moment of 1.8 $\mu_B$ at 1.5 K is directed along $[0.89(9),-0.10(5),-0.49(6)]$ and matches the magnetic easy axis of spin-1 Ni$^{2+}$ ions, which is determined by the scissor-like distortion of the NiO$_6$ octahedra. Incommensurate magnetic order, presumably of spin-density-wave type, is observed in the region between $T_{\rm N2}$ and $T_{\rm N1}$. Density-functional band-structure calculations put forward a three-dimensional spin lattice with spin-1 chains running along the $[01\bar 1]$ direction and stacked on a spatially anisotropic triangular lattice in the $ab$ plane. We show that the collinear magnetic order in Li$_2$NiW$_2$O$_8$ is incompatible with the triangular lattice geometry and thus driven by a pronounced easy-axis single-ion anisotropy of Ni$^{2+}$.

Classical Heisenberg antiferromagnet on a triangular lattice in the presence of single-ion anisotropy

The Heisenberg antiferromagnet on a triangular lattice is one of the prototype examples of frustrated systems and has been studied for several decades. In the presence of magnetic fields, the system exhibits a phase diagram consisting of exotic phases. At low temperatures successive magnetic phase transitions occur as the magnetic field is increased. We analyze the ground states of the system to obtain the critical fields at zero temperature. It is also shown through Monte Carlo simulations that the easy-axis single-ion anisotropy in classical Heisenberg antiferromagnet results in the expansion of the uud-phase region.

Reentrant phenomena in a three-dimensional spin-1 planar ferromagnet with easy-axis single-ion anisotropy

The two-time Green function method is employed to explore the phase diagram and the magnetic-field-induced quantum criticality of a three-dimensional spin-one planar ferromagnet with easy-axis single-ion anisotropy. We adopt the Tyablikov and Anderson-Callen decouplings for higher order exchange and single-ion anisotropy Green functions, respectively. The central finding is that, within a characteristic range of the anisotropy parameter values, reentrant phenomena occur in the phase diagram close to the quantum critical point producing a sensible change of the conventional quantum critical scenario.

The magnetic properties of a quasi-two-dimensional spin 1 easy axis Heisenberg antiferromagnet with competing interactions

The Neel and collinear ordered phases of the two-dimensional S=1 antiferromagnet with next and next near neighbor exchange interactions and easy axis single ion anisotropy, on the square lattice, are studied at low temperature using a Modified Spin Wave Theory. We calculate the low-temperature quantities as a function of the temperature, frustration and anisotropy. We calculate also the phase diagram at T=0. We found a disordered phase separating the Neel and collinear phases.

Crystal-field, exchange interactions and magnetism in pyrochlore ferromagnet R2V2O7 (R3+=Y, Lu)

The temperature dependence of the observed bulk magnetic susceptibility, magnetization, paramagnetic Curie temperature θCW, magnetic specific heat of ferromagnetic semi-conducting pyrochlore-based vanadate compounds Y2V2O7 and Lu2V2O7, which are the simplest of R2M2O7 pyrochlore series of oxides, are simulated and analyzed, simultaneously and consistently, within the frame work of the appropriate crystal-field (CF) theory and a mean-field approximation by introducing effective anisotropic molecular-field tensors and also taking account of appreciable spin–orbit coupling. The electronic and magnetic properties are correlated to the structural parameters. Ten-fold degenerate 2D term of 3d1 V4+-ions is split into five Kramers doublets with overall CF splitting Δ1≈2eV and the total splitting of the 2T2g state Δ0≈0.4eV under combined actions of octahedral CF, trigonal (D3d) distortion at V-site and spin–orbit coupling. The ground doublet is a well-isolated effectively spin s=1/2 state, characterized by the anisotropic g-tensors and directional magnetic moments. The degeneracy of the ground state is lifted by the spin–spin correlations among V4-tetrahedra at T∼170K, which causes the formation of ferromagnetic clusters in these pyrochlores. The temperature dependence of the calculated directional site-susceptibilities shows that the V4+ ions have a substantial easy-axis single-ion anisotropy along local 〈111〉 axis of a given V4-tetrahedron in the magnetic phase where ferromagnetic clusters coexist with paramagnetic phase.

Magnetic phase transition in Heisenberg antiferromagnetic films with easy-axis single-ion anisotropy

The staggered susceptibility of spin-1 and spin-3/2 Heisenberg antiferromagnet with easy-axis single-ion anisotropy on the cubic lattice films consisting of n=2, 3, 4, 5 and 6 interacting square lattice layers is studied by high-temperature series expansions. Sixth order series in J/kBT have been obtained for free-surface boundary conditions. The dependence of the Néel temperature on film thickness n and easy-axis anisotropy D has been investigated. The shifts of the Néel temperature from the bulk value can be described by a power law n−λ with a shift exponent λ, where λ is the inverse of the bulk correlation length exponent. The effect of easy-axis single-ion anisotropy on shift exponent of antiferromagnetic films has been studied. A comparison is made with related works. The results obtained are qualitatively consistent with the predictions of finite-size scaling theory.

Single-ion anisotropy, Dzyaloshinskii-Moriya interaction, and negative magnetoresistance of the spin-12pyrochloreR2V2O7

The electronic and magnetic properties of spin-1/2 pyrochlores R2V2O7 were investigated on the basis of density-functional calculations. Contrary to the common belief, the spin-1/2 V4+ ions are found to have a substantial easy-axis single-ion anisotropy. The |D/J| ratio deduced from the magnon quantum Hall effect of Lu2V2O7, where J is the nearest-neighbor spin exchange and D is the Dzyaloshinskii-Moriya parameter, is much greater than the value estimated from our calculations (i.e., 0.32 vs. 0.05). We show that this discrepancy is due to the neglect of the single-ion anisotropy of the V4+ ions, and the negative magnetoresistance observed for R2V2O7 arises from a new mechanism.

The magnetic properties of three-dimensional spin-1 easy-axis single-ion anisotropic antiferromagnets

Abstract The ordered and disordered phases of spin-1 Heisenberg and Ising antiferromagnets with easy-axis single-ion anisotropy on a three-dimensional lattice are studied. By using of the double-time Green’s function method within the Tyablikov decoupling for the exchange anisotropy and Callen’s approximation for the single-ion anisotropy, the Neel temperature, magnetization and susceptibility are investigated. Their relations with the temperature and anisotropic parameter are analyzed over the entire range of temperature. It is found that our results agree well with spin wave theory results at low temperature, agree with the high temperature series results at high temperature, and compare reasonably well with the linked-cluster series approach and ratio method results at intermediate temperature.