Easy-plane Single-ion Anisotropy Research Articles

Cs2Fe2(MoO4)3-A Strongly Frustrated Magnet with Orbital Degrees of Freedom and Magnetocaloric Properties.

We report an in-depth study of the thermodynamic and magnetocaloric properties of a strongly frustrated magnet, Cs2Fe2(MoO4)3. The underlying structure belongs to the double trillium lattice, which consists of two FeII (S = 2) sites with easy-axis and easy-plane single-ion anisotropy. Detailed 57Fe Mössbauer spectroscopic investigations along with ligand-field calculations support the existence of disparate ground states. The antiferromagnetic ordered structure is presented by the propagation vector k = (0,0,0) with noncollinear magnetic moments of 2.97 μB (Fe1) and 0.17 μB (Fe2), respectively. Strong and disordered magnetic correlations exist in the temperature regime between T N ≈ 1.0 K and |θCW| ≈ 22 K. The large degeneracy of the ground state is investigated in terms of its magnetocaloric response. Magnetization and specific heat measurements indicate a significant magnetocaloric cooling efficiency, making this rare-earth-free compound a promising candidate for cryogenic magnetic refrigeration applications, with refrigeration capacity of 79 J kg-1 for Δ(μ0 H) = 8 T.

Dark discrete breather modes in a monoaxial chiral helimagnet with easy-plane anisotropy

Nonlinearity and discreteness are two pivotal factors for an emergence of discrete breather excitations in various media. We argue that these requirements are met in the forced ferromagnetic phase of the monoaxial chiral helimagnet $\mathrm{Cr}{\mathrm{Nb}}_{3}\mathrm{S}{}_{6}$ due to the specific domain structure of the compound. The stationary, time-periodic breather modes appear as the discrete breather lattice solutions whose period mismatches with a system size. Thanks to easy-plane single-ion anisotropy intrinsic to $\mathrm{Cr}{\mathrm{Nb}}_{3}\mathrm{S}{}_{6}$, these modes are of the dark type with frequencies lying within the linear spin-wave band, close to its bottom edge. They represent cnoidal states of magnetization, similar to the well-known soliton lattice ground state, with differing but limited number of embedded $2\ensuremath{\pi}$ kinks. The linear stability of these dark breather modes is verified by means of Floquet analysis. Their energy, which is controlled by two parameters, namely, the breather lattice period and amplitude, falls off linearly with a growth of the kink number. These results may pave a path to design spintronic resonators on the base of chiral helimagnets.

Effect of an uniaxial single-ion anisotropy on the quantum and thermal entanglement of a mixed spin-(1/2, [formula omitted]) Heisenberg dimer

Exact analytical diagonalization is used to study the bipartite entanglement of the antiferromagnetic mixed spin-(1/2, S) Heisenberg dimer (MSHD) with the help of negativity. Under the assumption of uniaxial single-ion anisotropy affecting higher spin-S (S>1/2) entities only, the ground-state degeneracy 2S is partially lifted and the ground state is two-fold degenerate with the total magnetization per dimer ±(S−1/2). It is shown that the largest quantum entanglement is reached for the antiferromagnetic ground state of MSHD with arbitrary half-odd-integer spins S regardless of the exchange and single-ion anisotropies. Contrary to this, the degree of a quantum entanglement in MSHD with an integer spin S exhibits an increasing tendency with an obvious spin-S driven crossing point, when assuming the easy-plane single-ion anisotropy. It is shown that the increasing spin magnitude is a crucial driving mechanism for an enhancement of a threshold temperature above which the thermal entanglement vanishes. The easy-plane single-ion anisotropy together with an enlargement of the spin-S magnitude is other significant driving mechanism for an enhancement of the thermal entanglement in MSHD.

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.

MoP3SiO11 : A 4d3 honeycomb antiferromagnet with disconnected octahedra

We report the crystal structure and magnetic behavior of the $4d^3$ spin-$\frac32$ silicophosphate MoP$_3$SiO$_{11}$ studied by high-resolution synchrotron x-ray diffraction, neutron diffraction, thermodynamic measurements, and ab initio band-structure calculations. Our data revise the crystallographic symmetry of this compound and establish its rhombohedral space group ($R\bar 3c$) along with the geometrically perfect honeycomb lattice of the Mo$^{3+}$ ions residing in disconnected MoO$_6$ octahedra. Long-range antiferromagnetic order with the propagation vector $\mathbf k=0$ observed below $T_N=6.8$ K is a combined effect of the nearest-neighbor in-plane exchange coupling $J\simeq 2.6$ K, easy-plane single-ion anisotropy $D\simeq 2.2 $ K, and a weak interlayer coupling $J_c\simeq 0.8$ K. The 12% reduction in the ordered magnetic moment of the Mo$^{3+}$ ions and the magnon gap of $\Delta\simeq 7$ K induced by the single-ion anisotropy further illustrate the impact of spin-orbit coupling on the magnetism. Our analysis puts forward single-ion anisotropy as an important ingredient of $4d^3$ honeycomb antiferromagnets despite their nominally quenched orbital moment.

In-plane magnetic field-induced skyrmion crystal in frustrated magnets with easy-plane anisotropy

We theoretically investigate the instability toward a skyrmion crystal (SkX) in frustrated triangular magnets. By performing simulated annealing and Monte Carlo simulations, we show that a frustrated spin model with easy-plane single-ion anisotropy exhibits a SkX in an in-plane external magnetic field. The emergent SkX is a counterpart of that induced by easy-axis anisotropy in an out-of-plane magnetic field, both of which show the topological Hall effect. We also find that a variety of multiple-$Q$ states distinct from the SkX are stabilized in the presence of easy-plane anisotropy. Our results provide a possibility to realize a SkX in easy-plane frustrated magnets by applying an in-plane magnetic field to in-plane cycloidal spiral magnets.

Magnetization and Magnetocaloric Effect in Antiferromagnets with Competing Ising Exchange and Single-Ion Anisotropies

The magnetization of a two-sublattice Ising antiferromagnet with easy-plane single-ion anisotropy, which is accompanied by two phase transitions, has been studied. The both phase transitions are induced by the magnetic field. One of them is isostructural, i.e., the system symmetry remains unchanged and a transition between two antiferromagnetic states with different sublattice magnetizations takes place. The other phase transition occurs when the antiferromagnetic state transforms into the ferromagnetic one. At both phase transitions, the field dependence of the system entropy has two successive positive jumps, which is not typical of ordinary antiferromagnets. On the other hand, if the temperature of the system is higher than the tricritical temperature of the isostructural phase transition, there appears a continuous maximum in the field dependence of the entropy.

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.

Effect of interchain coupling in the frustrated spin one heisenberg model with easy plane single ion anisotropy

We study the quantum disordered phase of the anisotropic Heisenberg spin one model with ferromagnetic nearest-neighbor interactions, frustrating antiferromagnetic next-nearest-neighbor interactions along the chain and antiferromagnetic interchain couplings along the axes perpendicular to the chain. We use the SU(3) Schwinger boson technique and calculate the phase diagram at zero temperature. The gap as a function of temperature is also presented.

Specific Features of the Magnetocaloric Effect in a Uniaxial Paramagnet with Kramers Ions

The changes in magnetic entropy upon isothermal magnetization of a uniaxial paramagnet with Kramers ions (spin S = 3/2) and single-ion easy-plane anisotropy were studied at low temperatures. It was demonstrated that the magnetocaloric effect upon magnetization in the easy direction is considerably stronger than the one corresponding to magnetization in the hard direction (perpendicular to the easy plane). It was found that magnetization in the hard direction is accompanied by an anomalous increase in magnetic entropy in a finite interval of magnetic fields. A nonmonotonic dependence of entropy on the final magnetization field is produced as a result.

Frustrated bilayer spin one XY model on the honeycomb lattice

The spin-one honeycomb bilayer XY antiferromagnet has been studied taking into account the effect of the next-near neighbor J2 exchange interactions and single-ion easy plane anisotropy, using a flavor wave theory. We found that, at a critical point αC=13.8, where α=J⊥/J1 is the ratio between the interlayer J⊥ to the intralayer near neighbor J1 exchange interaction, the system shows a quantum phase transition from an Néel ordered phase to a paramagnetic phase. The phase diagram at zero temperature is presented.

Effect of the Higgs mode in the spin transport of a Heisenberg antiferromagnet on a square lattice

We study spin transport at zero temperature in the two-dimensional spin-one Heisenberg antiferromagnet on a square lattice with easy-plane single-ion anisotropy in the Néel phase. The regular part of the spin conductivity is calculated at zero temperature using the SU(3) Schwinger boson formalism and the Kubo theory. Three magnon processes provide the dominant contribution to the spin conductivity. We find evidence of the Higgs mode contribution to the spin conductivity.

Chiral liquid phase of simple quantum magnets

We study a $T=0$ quantum phase transition between a quantum paramagnetic state and a magnetically ordered state for a spin $S=1$ XXZ Heisenberg antiferromagnet on a two-dimensional triangular lattice. The transition is induced by an easy plane single-ion anisotropy $D$. At the mean-field level, the system undergoes a direct transition at a critical $D = D_c$ between a paramagnetic state at $D > D_c$ and an ordered state with broken U(1) symmetry at $D < D_c$. We show that beyond mean field the phase diagram is very different and includes an intermediate, partially ordered chiral liquid phase. Specifically, we find that inside the paramagnetic phase the Ising ($J_z$) component of the Heisenberg exchange binds magnons into a two-particle bound state with zero total momentum and spin. This bound state condenses at $D > D_c$, before single-particle excitations become unstable, and gives rise to a chiral liquid phase, which spontaneously breaks spatial inversion symmetry, but leaves the spin-rotational U(1) and time-reversal symmetries intact. This chiral liquid phase is characterized by a finite vector chirality without long range dipolar magnetic order. In our analytical treatment, the chiral phase appears for arbitrarily small $J_z$ because the magnon-magnon attraction becomes singular near the single-magnon condensation transition. This phase exists in a finite range of $D$ and transforms into the magnetically ordered state at some $D<D_c$. We corroborate our analytic treatment with numerical density matrix renormalization group calculations.

Universality of magnetic-field-induced Bose-Einstein condensation of magnons

CsFeBr$_3$ is an $S\,{=}\,1$ hexagonal antiferromagnet that has a singlet ground state owing to its large easy-plane single-ion anisotropy. The critical behavior of the magnetic-field-induced phase transition for a magnetic field parallel to the $c$ axis, which can be described by the Bose-Einstein condensation (BEC) of magnons under the $U(1)$ symmetry, was investigated via magnetization and specific heat measurements down to 0.1$\,$K. For the specific heat measurement, we have developed a method of effectively suppressing the torque acting on a sample with strong anisotropy that uses the spin dimer compound Ba$_2$CoSi$_2$O$_6$Cl$_2$ with large and anisotropic Van Vleck paramagnetism. The temperature dependence of the transition field $H_{\rm c}(T)$ was found to follow the power-law $H_{\rm c}(T)\,{-}\,H_{\rm c}\,{\propto}\,T^{\phi}$ with a critical exponent of ${\phi}\,{=}\,1.50\,{\pm}\,0.02$ and critical field of $H_{\rm c}\,{=}\,2.60$ T. This result verifies the universality of the three-dimensional BEC of magnons described by ${\phi}_{\rm BEC}\,{=}\,3/2$.

Union Jack and checkerboard lattices with easy plane single ion anisotropy

The zero-temperature phase diagrams of the antiferromagnetic Union Jack and checkerboard lattices, with spin one and an easy-plane single anisotropy term, are studied using the SU(3) Schwinger boson formalism (also known as flavor wave theory). We find that the Union Jack lattice has a quantum phase transition (QPT) at J2/J1=0.707 between a Néel and a collinear phase, while the checkerboard lattice has a QPT at J2/J1=0.785, from the Néel to a magnetically disordered phase. The ground state phase diagrams of the two models are different, both from each other and from that of the square lattice antiferromagnet with all the next nearest neighbors. For the checkerboard lattice, we calculate the spin gap and the ground state energy in the disordered phase. This phase is a candidate for a spin liquid state.

J1x-J1y-J2 square-lattice anisotropic Heisenberg model

The spin one Heisenberg model with an easy-plane single-ion anisotropy and spatially anisotropic nearest-neighbor coupling, frustrated by a next-nearest neighbor interaction, is studied at zero temperature using a SU(3) Schwinger boson formalism (sometimes also referred to as flavor wave theory) in a mean field approximation. The local constraint is enforced by introducing a Lagrange multiplier. The enlarged Hilbert space of S=1 spins lead to a nematic phase that is ubiquitous to S=1 spins with single ion anisotropy. The phase diagram shows two magnetically ordered phase, separated by a quantum paramagnetic (nematic) phase.

Giant effect of Sm atoms on time stability of (NdDy)(FeCo)B magnet

Small amount of Sm additives (∼ 1 -3 at.%) slow down two times relaxation of magnetization of (NdDy)(FeCo)B alloys. Effective freezing of spontaneous relaxation of magnetization is caused by the enhancement of potential barriers of the domain walls. Easy plane single-ion anisotropy of Sm strongly disturbs the potential relief of the domain walls. The experimental results can be used to stabilize hard magnets.

Octanuclear Heterobimetallic {Ni4Ln4} Assemblies Possessing Ln4 Square Grid [2 × 2] Motifs: Synthesis, Structure, and Magnetism.

Octanuclear heterobimetallic complexes, [Ln4Ni4(H3L)4(μ3-OH)4(μ2-OH)4]4Cl·xH2O·yCHCl3 (Dy(3+), x = 30.6, y = 2 (1); Tb(3+), x = 28, y = 0 (2) ; Gd(3+), x = 25.3, y = 0 (3); Ho(3+), x = 30.6, y = 3 (4)) (H5L = N1,N3-bis(6-formyl-2-(hydroxymethyl)-4-methylphenol)diethylenetriamine) are reported. These are assembled by the cumulative coordination action of four doubly deprotonated compartmental ligands, [H3L](2-), along with eight exogenous -OH ligands. Within the core of these complexes, four Ln(3+)'s are distributed to the four corners of a perfect square grid while four Ni(2+)'s are projected away from the plane of the Ln4 unit. Each of the four Ni(2+)'s possesses distorted octahedral geometry while all of the Ln(3+)'s are crystallographically equivalent and are present in an elongated square antiprism geometry. The magnetic properties of compound 3 are dominated by an easy-plane single-ion anisotropy of the Ni(2+) ions [DNi = 6.7(7) K] and dipolar interactions between Gd(3+) centers. Detailed ac magnetometry reveals the presence of distinct temperature-dependent out-of-phase signals for compounds 1 and 2, indicative of slow magnetic relaxation. Magnetochemical analysis of complex 1 implies the 3d and the 4f metal ions are engaged in ferromagnetic interactions with SMM behavior, while dc magnetometry of compound 2 is suggestive of an antiferromagnetic Ni-Tb spin-exchange with slow magnetic relaxation due to a field-induced level crossing. Compound 4 exhibits an easy-plane single-ion anisotropy for the Ho(3+) ions and weak interactions between spin centers.

Quantum breathers in XXZ ferromagnetic chains with on-site easy-plane anisotropy

The existence and properties of quantum breathers in a one-dimensional XXZ ferromagnetic Heisenberg spin chain with single-ion easy-plane anisotropy are investigated analytically in the Hartree approximation. We show that the system can support the appearance of quantum breathers, and discuss their existence conditions and properties. In addition, our results show that, for quantum breathers in this system, both the corresponding energy and magnetic moment are quantized.

Magnetic quantum phase transitions and entropy in Van Vleck magnet

Field-induced magnetic quantum phase transitions in the Van Vleck paramagnet with easy-plane single-ion anisotropy and competing Ising exchange between ions with the spin S=1 have been studied theoretically. The description was made by minimizing the Lagrange function at zero temperature (Т=0) and the free energy at T≠0. Stable and unstable solutions of equations corresponding to the case ψ0=|0〉 asymptotically transform into those following from the Lagrange function at Т=0. First-order phase transitions from the Van Vleck paramagnet state into the ferromagnet one were found to take place at a sufficiently high single-ion anisotropy. The entropy of such a magnet was shown to grow with its magnetization, as it occurs for antiferromagnets. At the point of quantum phase transition, the entropy has a jump, which magnitude depends on the ratio between the Ising exchange and anisotropy constants, as well as on the temperature. The described magnetic phase transition was supposed to be accompanied by the magnetocaloric effect. In the case when the Ising exchange dominates over the single-ion anisotropy, the magnetization reversal of ferromagnetic state by an external field was shown to be a phase transition of the first kind, which does not belong to orientational ones and which should be regarded as a quantum order-order phase transition.