Small Single-ion Anisotropy Research Articles

Spin dynamics of the spin-chain antiferromagnet RbFeS2

We report transport and inelastic neutron scattering studies on electronic properties and spin dynamics of the quasi-one-dimensional spin-chain antiferromagnet ${\mathrm{RbFeS}}_{2}$. An antiferromagnetic phase transition at ${T}_{N}\ensuremath{\approx}195$ K and dispersive spin waves with a spin gap of 5 meV are observed. By modeling the spin excitation spectra using linear spin wave theory, intra and interchain exchange interactions are found to be $S{J}_{1}=100(5)$ meV and $S{J}_{3}=0.9(3)$ meV, respectively, together with a small single-ion anisotropy of $S{D}_{zz}=0.04(1)$ meV. Comparison with previous results for other materials in the same class of ${\mathrm{Fe}}^{3+}$ spin-chain systems reveals that although the magnetic order sizes show significant variation from 1.8 to $3.0\phantom{\rule{4pt}{0ex}}{\ensuremath{\mu}}_{B}$ within the family of materials, the exchange interactions $SJ$ are nevertheless quite similar, analogous to the iron pnictide superconductors where both localized and delocalized electrons contribute to the spin dynamics.

Evidence for two spin-glass transitions with magnetoelastic and magnetoelectric couplings in the multiferroic (Bi1−xBax)(Fe1−xTix)O3 system

For disordered Heisenberg systems with small single ion anisotropy, two spin glass transitions below the long range ordered phase transition temperature has been predicted theoretically for compositions close to the percolation threshold. Experimental verification of these predictions is still controversial for conventional spin glasses. We show that multiferroic spin glass systems can provide a unique platform for verifying these theoretical predictions via a study of change in magnetoelastic and magnetoelectric couplings, obtained from an analysis of diffraction data, at the spin glass transition temperatures. Results of macroscopic and microscopic (x-ray and neutron scattering) measurements are presented on disordered BiFeO3, a canonical Heisenberg system with small single ion anisotropy, which reveal appearance of two spin glass phases SG1 and SG2 in coexistence with the LRO phase below the A-T and G-T lines. It is shown that the temperature dependence of the integrated intensity of the antiferromagnetic peak shows dips with respect to the Brillouin function behaviour around the SG1 and SG2 transition temperatures. The ferroelectric polarisation changes significantly at the two spin glass transition temperatures. These results, obtained using microscopic techniques, clearly demonstrate that the SG1 and SG2 transitions occur on the same magnetic sublattice and are intrinsic to the system. We also construct a phase diagram showing all the magnetic phases in BF-xBT system. While our results on the two spin glass transitions support the theoretical predictions, it also raises several open questions which need to be addressed by revisiting the existing theories of spin glass transitions by taking into account the effect of magnetoelastic and magnetoelectric couplings as well as electromagnons.

On the origin of magnetic anisotropy in two dimensional CrI3

The observation of ferromagnetic order in a monolayer of CrI3 has been recently reported, with a Curie temperature of 45 K and off-plane easy axis. Here we study the origin of magnetic anisotropy, a necessary ingredient to have magnetic order in two dimensions, combining two levels of modeling, density functional calculations and spin model Hamiltonians. We find two different contributions to the magnetic anisotropy of the material, favoring off-plane magnetization and opening a gap in the spin wave spectrum. First, ferromagnetic super-exchange across the ≃90 degree Cr–I–Cr bonds, are anisotropic, due to the spin–orbit interaction of the ligand I atoms. Second, a much smaller contribution that comes from the single ion anisotropy of the S = 3/2 Cr atom. Our results permit to establish the XXZ Hamiltonian, with a very small single ion anisotropy, as the adequate spin model for this system. Using spin wave theory we estimate the Curie temperature and we highlight the essential role played by the gap that magnetic anisotropy induces on the magnon spectrum.

Magnetic correlations in the quasi-two-dimensional semiconducting ferromagnetCrSiTe3

Intrinsic, two-dimensional ferromagnetic semiconductors are an important class of materials for overcoming the limitations of dilute magnetic semiconductors for spintronics applications. CrSiTe$_3$ is a particularly interesting member of this class, since it can likely be exfoliated down to single layers, where T$_C$ is predicted to increase dramatically. Establishing the nature of the magnetism in the bulk is a necessary precursor to understanding the magnetic behavior in thin film samples and the possible applications of this material. In this work, we use elastic and inelastic neutron scattering to measure the magnetic properties of single crystalline CrSiTe$_3$. We find that there is a very small single ion anisotropy favoring magnetic ordering along the $c$-axis and that the measured spin waves fit well to a model where the moments are only weakly coupled along that direction. Finally, we find that both static and dynamic correlations persist within the $ab$-plane up to at least 300 K, strong evidence of this material's two-dimensional characteristics that are relevant for future studies on thin film and monolayer samples.

Temperature-Dependent Interplay of Dzyaloshinskii-Moriya Interaction and Single-Ion Anisotropy in MultiferroicBiFeO3

Low-energy magnon excitations in multiferroic BiFeO3 were measured in detail as a function of temperature around several Brillouin zone centers by inelastic neutron scattering experiments on single crystals. Unique features around 1 meV are directly associated with the interplay of the Dzyaloshinskii-Moriya interaction and a small single-ion anisotropy. The temperature dependence of these and the exchange interactions were determined by fitting the measured magnon dispersion with spin-wave calculations. The spectra best fit an easy-axis type magnetic anisotropy and the deduced exchange and anisotropy parameters enable us to determine the anharmonicity of the magnetic cycloid. We then draw a direct connection between the changes in the parameters of spin Hamiltonian with temperature and the physical properties and structural deformations of BiFeO3.

The magnetic and thermodynamic properties of a spin-2 Heisenberg ferromagnetic system

The magnetic and thermodynamic properties such as the magnetization, internal energy, specific heat and susceptibility of spin-2 Heisenberg ferromagnetic system on a square lattice are studied by using Green׳s function technique. Without including the next nearest neighbor interaction, one doesn׳t observe the second-order phase transitions. We found that only when the next nearest neighbor interaction is greater than the nearest neighbor interaction, the second-order phase transitions exist for the small single-ion anisotropy values. Indeed, in the case of negative anisotropy which corresponds to first-order phase transitions, the energies have discontinuities. At the same time, the specific heat shows two peaks.

Quantized antiferromagnetic spin waves in the molecular Heisenberg ringCsFe8

We report on inelastic neutron scattering (INS) measurements on the molecular spin ring CsFe$_8$, in which eight spin-5/2 Fe(III) ions are coupled by nearest-neighbor antiferromagnetic Heisenberg interaction. We have recorded INS data on a non-deuterated powder sample up to high energies at the time-of-flight spectrometers FOCUS at PSI and MARI at ISIS, which clearly show the excitation of spin waves in the ring. Due to the small number of spin sites, the spin-wave dispersion relation is not continuous but quantized. Furthermore, the system exhibits a gap between the ground state and the first excited state. We have modeled our data using exact diagonalization of a Heisenberg-exchange Hamiltonian together with a small single-ion anisotropy term. Due to the molecule's symmetry, only two parameters $J$ and $D$ are needed to obtain excellent agreement with the data. The results can be well described within the framework of the rotational-band model as well as antiferromagnetic spin-wave theories.

Thermodynamic Properties of Random Transverse Field Mixed Spin System in the Presence of Single-Ion Anisotropy**The project supported partly by Natural Science Foundation of Jiangsu Province under Grant No. 00SJB140003 and partly by Open Foundation of the Thin Film Materials Key Laboratory of Jiangsu Province under Grant No. K2022

We study the thermodynamic properties of random transverse field mixed spin system in the presence of single-ion anisotropy on a square lattice. By making use of the effective field theory and a cutting approximation, the detailed phase diagrams are described and some interesting results are found under trimodal random transverse field distribution. A small single-ion anisotropy can magnify magnetic ordering region at low temperatures and existence of a large transverse field can assist the occurrence of reentrant phenomena. With increasing disorder, second-order phase transitions are shown to change into first-order phase transitions. The trajectory of the tricritical point in the phase space as a function of disorder is presented. These indicate a strong correlation with the corresponding to trimodal transverse field distribution.

Spin configurations in VBr2 supported by uniaxal anistropy and quantum fluctuations (abstract)

Small single ion anisotropy is believed to play an important role in selecting the plane where the spins lie in hexagonal anitferromagnets on the basis of the classical approximation. For instance, in VBr2 a small easy-axis single ion anisotropy is expected to force the spins in a plane containing the c axis and the classical approximation suggests that the spin configuration should be an ‘‘umbrella’’ configuration with axis along the external magnetic field perpendicular to the c axis. However, the classical expectation is questionable because the zero point motion energy supports spin configurations with the spins lying in a plane containing the magnetic field. We find that the ‘‘planar’’ configuration with the spins in the plane containing the c-axis and the external magnetic field is stable for interplane coupling and anisotropy sufficiently small. Since this is the case of VBr2, our results rise some doubts about the interpretation of experimental data in VBr2 when an external magnetic field is applied.

The effect of quantum fluctuations on the ferromagnet-helix transition

The authors study the effect of quantum zero-point motion on the zero-temperature phase diagram of a Heisenberg system with competing interactions on a hexagonal lattice. Within the basal plane, first-neighbour interactions J1 are ferromagnetic while second- and third-neighbour interactions J2 and J3 can have either sign. The inter-plane interaction J' is taken to be small. They find that quantum fluctuations enhance the tendency towards a first-order transition from ferromagnetic to helical order. Even a very small single-ion anisotropy suffices to explain the small first-order jump observed in NiBr2.

Nuclear spin lattice relaxation in the linear antiferromagnet CsNiCl 3

Anisotropic effects have been found in the low temperature (< 10 K) nuclear spin lattice relaxation rates in the linear paramagnet CsNiCl 3 in a strong magnetic field (∼ 60 kOe). The existence of a small single ion anisotropy term may be the cause of these effects.

Spin fluctuations in random magnetic-nonmagnetic two-dimensional antiferromagnets. I. Dynamics

The magnetic excitations in the system ${\mathrm{Rb}}_{2}{\mathrm{Mn}}_{c}{\mathrm{Mg}}_{1\ensuremath{-}c}{\mathrm{F}}_{4}$ with $c=1, 0.57, \mathrm{and} 0.54$ have been measured using neutron-inelastic-scattering techniques. In pure ${\mathrm{Rb}}_{2}$Mn${\mathrm{F}}_{4}$ the magnon dispersion relation is accurately described by simple spin-wave theory with dominant Heisenberg antiferromagnetic nearest-neighbor exchange, a much weaker antiferromagnetic next-nearest-neighbor interaction, and a small single-ion anisotropy field. In the specimens with $c=0.57 \mathrm{and} 0.54$ the scattering shows a broad response but with substructure which may be associated with the different Ising energies of Mn ions in different environments. The measurements are in excellent accord with the results of computer simulations but theories based on the coherent-potential approximation do not give a satisfactory description of the measured spectra.