Large Single-ion Anisotropy Research Articles

Effect of large single-ion anisotropy on the dynamic and static properties of a non-heisenberg ferrimagnet

The influence of a large single-ion anisotropy of the "easy plane" type on the phase states and spectra of elementary excitations of a ferrimagnet with sublattices S = 1 and sigma=1/2 and non-Heisenberg exchange interaction for a sublattice with S = 1 is studied. It is shown that for different ratios of the material parameters of the system, only one phase state is possible, characterized by both vector and tensor order parameters (quadrupole-ferrimagnetic). The condition for sublattice spin compensation is determined, as well as the behavior of the spectra of elementary excitations near the spin compensation line. In the vicinity of the spin compensation line, the magnon spectra are "antiferromagnetically similar". Keywords: large single-ion anisotropy, biquadratic exchange interaction, ferrimagnet.

Влияние большой одноионной анизотропии на динамические и статические свойства негейзенберговского ферримагнетика

The influence of a large single-ion anisotropy of the “easy plane” type on the phase states and spectra of elementary excitations of a ferrimagnet with sublattices S=1 and σ=1/2 and non-Heisenberg exchange interaction for a sublattice with S=1 is studied. It is shown that for different ratios of the material parameters of the system, only one phase state is possible, characterized by both vector and tensor order parameters (quadrupole-ferrimagnetic). The condition for sublattice spin compensation is determined, as well as the behavior of the spectra of elementary excitations near the spin compensation line. In the vicinity of the spin compensation line, the magnon spectra are "antiferromagnetically similar".

Spin-orbit excitons and electronic configuration of the 5d4 insulator Sr3Ir2O7F2

Here, we report on the low-energy excitations within the paramagnetic spin-orbit insulator ${\mathrm{Sr}}_{3}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}{\mathrm{F}}_{2}$ studied via resonant inelastic x-ray scattering, ab initio quantum chemical calculations, and model Hamiltonian simulations. This material is a unique ${d}^{4} {\mathrm{Ir}}^{5+}$ analog of ${\mathrm{Sr}}_{3}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ that forms when F ions are intercalated within the SrO layers spacing the square lattice ${\mathrm{IrO}}_{6}$ bilayers of ${\mathrm{Sr}}_{3}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$. Due to the large distortions about the ${\mathrm{Ir}}^{5+}$ ions, our computations demonstrate that a large single-ion anisotropy yields an $S=1$ ($L\ensuremath{\approx}1, J\ensuremath{\approx}0$) ground-state wave function. Weakly coupled, excitonic modes out of the ${S}_{z}=0$ ground state are observed and are well described by a phenomenological spin-orbit exciton model previously developed for $3d$ and $4d$ transition metal ions. The implications of our results regarding the interpretation of previous studies of hole-doped iridates close to ${d}^{4}$ fillings are discussed.

Physical properties of the quasi-two-dimensional square lattice antiferromagnet Ba2FeSi2O7

We report magnetization (\ensuremath{\chi}, $M$), magnetic specific heat (${C}_{\mathrm{M}}$), and neutron powder diffraction results on a quasi-two-dimensional (2D) $S=2$ square lattice antiferromagnet ${\mathrm{Ba}}_{2}{\mathrm{FeSi}}_{2}{\mathrm{O}}_{7}$ consisting of ${\mathrm{FeO}}_{4}$ tetrahedrons with highly compressive tetragonal distortion (27%). Despite of the quasi-2D lattice structure, both \ensuremath{\chi} and ${C}_{\mathrm{M}}$ present three-dimensional magnetic long-range ordering below the N\'eel temperature ${T}_{\mathrm{N}}=5.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Neutron diffraction data show a collinear ${\mathbit{Q}}_{\mathbit{m}}=$(1,0,1/2) antiferromagnetic (AFM) structure below ${T}_{\mathrm{N}}$ but the ordered moment aligned in the $ab$ plane is suppressed by 26% from the ionic spin $S=2$ value ($4{\ensuremath{\mu}}_{\mathrm{B}}$). Both the AFM structure and the suppressed moments are well explained by using Monte Carlo simulations with a large single-ion in-plane anisotropy $D=1$.4 meV and a rather small Heisenberg exchange ${J}_{\mathrm{intra}}=0$.15 meV in the plane. The characteristic 2D spin fluctuations are recognized in the magnetic entropy release and diffuse scattering above ${T}_{\mathrm{N}}$. This new quasi-2D magnetic system also displays unusual nonmonotonic dependence of ${T}_{\mathrm{N}}$ as a function of magnetic field $H$.

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.

Lateral Modulation of Magnetic Anisotropy in Tricolor 3d–5d Oxide Superlattices

Manipulating magnetic anisotropy (MA) purposefully in transition metal oxides (TMOs) enables the development of oxide-based spintronic devices with practical applications. Here, we report a pathway to reversibly switch the lateral magnetic easy-axis via interfacial oxygen octahedral coupling (OOC) effects in 3d-5d tricolor superlattices, i.e. [SrIrO3,mRTiO3,SrIrO3,2La0.67Sr0.33MnO3]10 (RTiO3: SrTiO3 and CaTiO3). In the heterostructures, the anisotropy energy (MAE) is enhanced over one magnitude to ~106 erg/cm3 compared to La0.67Sr0.33MnO3 films. Moreover, the magnetic easy-axis is reversibly reoriented between (100)- and (110)-directions by changing the RTiO3. Using first-principles density functional theory calculations, we find that the SrIrO3 owns a large single-ion anisotropy due to its strong spin-orbit interaction. This anisotropy can be reversibly controlled by the OOC, then reorient the easy-axis of the superlattices. Additionally, it enlarges the MAE of the films via the cooperation with a robust orbital hybridization between the Ir and Mn atoms. Our results indicate that the tricolor superlattices consisting of 3d and 5d oxides provide a powerful platform to study the MA and develop oxide-based spintronic devices.

Classical spin dynamics based on SU(N) coherent states

We introduce a classical limit of the dynamics of quantum spin systems based on coherent states of $\mathrm{SU}(N)$, where $N$ is the dimension of the local Hilbert space. This approach, which generalizes the well-known Landau-Lifshitz dynamics from SU(2) to $\mathrm{SU}(N)$, provides a better approximation to the exact quantum dynamics for a large class of realistic spin Hamiltonians, including $S\ensuremath{\ge}1$ systems with large single-ion anisotropy and weakly coupled multispin units, such as dimers or trimers. We illustrate this idea by comparing the spin structure factors of a single-ion $S=1$ model that are obtained with the SU(2) and SU(3) classical spin dynamics against the exact solution.

Successive spin reorientations and rare earth ordering in Nd0.5Dy0.5FeO3 : Experimental and ab initio investigations

In present study, the magnetic structure and spin reorientation of mixed doped orthoferrite Nd$_{0.5}$Dy$_{0.5}$FeO$_3$ have been investigated. Similar to both parent compounds (NdFeO$_3$ and DyFeO$_3$), the magnetic structure of Fe$^{3+}$ belongs to ${\Gamma}_{4}$ irreducible representation (G$_{x}$, F$_{z}$) at room temperature. The experimental measurements confirmed the spin reorientation where magnetic structure of Fe$^{3+}$ changes from ${\Gamma}_{4}$ to ${\Gamma}_{2}$(F$_{x}$, G$_{z}$) between 75 and 20 \,K while maintaining G-type configuration. Such a gradual spin reorientation is unusual since the large single ion anisotropy of Dy$^{3+}$ ions causes an abrupt ${\Gamma}_{4}$${\rightarrow}$ ${\Gamma}_{1}$(G$_{y}$) spin reorientation in DyFeO$_3$. Between 20 and 10 \,K, the Fe$^{3+}$ magnetic structure is represented by ${\Gamma}_{2}$ (F$_{x}$, G$_{z}$). Unexpectedly, magnetic structure of Fe$^{3+}$ with ${\Gamma}_{4}$ representation re-emerges below 10\,K which also coincides with the development of rare-earth (Nd$^{3+}$/Dy$^{3+}$) magnetic ordering having C$_{y}$ configuration with magnetic moment of 1.8 ${\mu}_{B}$. The absence of any signature of second order phase transition in the specific heat confirms the role of $R$(Nd$^{3+}$/Dy$^{3+}$)-Fe$^{3+}$ exchange interaction in the observed "rare-earth ordering" unlike DyFeO$_3$ where Dy$^{3+}$ ordering takes place independently to the magnetic ordering of Fe$^{3+}$ magnetic structure. Our (DFT+U+SO) calculations show that the C-type arrangement of rare-earth ions (Nd$^{3+}$/Dy$^{3+}$) with ${\Gamma}_{2}$ configuration for Fe$^{3+}$ moments is the ground state whereas ${\Gamma}_{4}$ phase is energetically very close. Nd-Fe and Nd-Dy exchange interactions, estimated from DFT, are observed to have significant roles in the rare earth ordering and Fe spin reorientation corroborating our experimental results.

Magnon spectrum and electron spin resonance in antiferromagnet with large single-ion easy plane anisotropy

Motivated by recent experiments on quantum magnet NiCl2-4SC(NH2)2 (DTN) and its Br-doped counterpart DTNX we propose a theoretical description of optical magnon branch in the antiferromagnet with large single-ion anisotropy in the magnetically ordered phase. In the framework of the 1/S expansion we derive analytical expressions for optical magnon with k=0 energy magnetic field dependence Δ(h). It is shown that in the linear spin wave approximation Δ(h) is monotonic without extrema whereas first order in 1/S corrections makes it drastically different function with a minimum near the center of magnetically ordered phase. The latter behaviour was observed in ESR experiments. Moreover, we show that Δ(h) has nontrivial dependence on the system parameters. It solves the discrepancy between inelastic neutron scattering data where the growth of interaction constants in DTNX with small Br concentration was observed and ESR experiments showing almost unchanged Δ(h) in comparison with pure DTN.

Electrically tunable high Curie temperature two-dimensional ferromagnetism in van der Waals layered crystals

Identifying intrinsic low-dimensional ferromagnets with high magnetic transition temperature and electrically tunable magnetism is crucial for the development of miniaturized spintronics and magnetoelectrics. Recently, long-range 2D ferromagnetism was observed in van der Waals crystals CrI3 and Cr2Ge2Te6, however, their Curie temperature is significantly lowered when reducing down to monolayer/few layers. Herein, using renormalized spin-wave theory and first-principles electronic structure theory, we present a theoretical study of electrically tunable 2D ferromagnetism in van der Waals layered CrSBr and CrSeBr semiconductors with a high Curie temperature of ∼150 K and a sizable bandgap. The high transition temperature is attributed to the strong anion-mediated superexchange interaction and a sizable spin-wave excitation gap due to large exchange and single-ion anisotropy. Remarkably, hole and electron doping can switch the magnetization easy axis from the in-plane to the out-of-plane direction. These unique characteristics establish monolayer CrSBr and CrSeBr as a promising platform for realizing 2D spintronics and magnetoelectrics such as 2D spin valves and spin field effect transistors.

Study of short range correlations and two-fold spin reorientation in NdFe0.5Mn0.5O3

Detailed powder neutron diffraction studies as a function of temperature is performed on NdFe0.5Mn0.5O3 in the temperature range 400–1.5 K. Diffused magnetic scattering is observed due to three dimensional short range ordering (SRO), between Fe3+/Mn3+ spins, over the whole temperature range 400–1.5 K. The presence of SRO is independent of long range ordering (LRO) in this compound which has never been observed in any Fe3+/Mn3+ based compounds. Further, in this compound two-fold spin reorientation is discussed in the temperature range 300–1.5 K. Development of long range ordering at 300 K is due to the mixture of Γ4 and Γ1 magnetic structure, not like other orthoferrites which have Γ4 structure at 300 K. This occurs due to the presence of large single ion anisotropy of Mn3+ ions. Volume fraction of Γ4 decreases with temperature leading to pure Γ1 magnetic structure in the temperature range 150–90 K. Another spin reorientation of Fe3+/Mn3+ spins occurs from Γ1 to Γ2 in the temperature range 70–25 K.

Ferromagnetic ordering of linearly coordinated Co ions in LiSr2[CoN2]

LiSr$_2$[CoN$_2$] single crystals were successfully grown out of Li-rich flux. Temperature- and field-dependent measurements of the magnetization in the range of $T = 2 - 300$ K and up to $\mu_{0}\textit{H} = 7$ T as well as measurements of the heat capacity are presented. Ferromagnetic ordering emerges below $T_C = 44$ K and comparatively large coercivity fields of $\mu_0H = 0.3$ T as well as pronounced anisotropy are observed upon cooling. Polycrystalline samples of the Ca analog LiCa$_2$[CoN$_2$] were obtained and investigated in a similar way. In both compounds Co manifests orbital contributions to the magnetic moment and large single-ion anisotropy that is caused by second-order Spin-orbit coupling. Quantum chemistry calculations reveal a magnetic anisotropy energy of 7 meV, twice as large as the values reported for similar Co $d^{8}$ systems.

Role of the orbital moment in a series of isostructural weak ferromagnets

The orbital contribution to the magnetic moment of the transition metal ion in the isostructural weak ferromagnets ACO$_3$ (A=Mn,Co,Ni) and FeBO$_3$ was investigated by a combination of first-principles calculations, non-resonant x-ray magnetic scattering and x-ray magnetic circular dichroism. A non-trivial evolution of the orbital moment as a function of the $3d$ orbitals filling is revealed, with an anomalously large value found in the Co member of the family. Here, the coupling between magnetic and lattice degrees of freedom produced by the spin-orbit interaction results in a large single-ion anisotropy and a peculiar magnetic-moment-induced electron cloud distortion, evidenced by the appearance of a subtle scattering amplitude at space group-forbidden reflections and significant magnetostrictive effects. Our results, which complement a previous investigation on the sign of the Dzyaloshinskii$-$Moriya interaction across the series, highlight the importance of spin-orbit coupling in the physics of weak ferromagnets and prove the ability of modern first-principles calculations to predict the properties of materials where the Dzyaloshinskii$-$Moriya interaction is a fundamental ingredient of the magnetic Hamiltonian.

Role of square planar coordination in the magnetic properties of Na4IrO4

Iridates supply fertile grounds for unconventional phenomena and exotic electronic phases. With respect to well-studied octahedrally-coordinated iridates, we pay our attention to a rather unexplored iridate, Na4IrO4, showing an unusual square-planar coordination. The latter is key to rationalize the electronic structure and magnetic property of Na4IrO4, which is here explored by first-principles density functional theory and Monte Carlo simulations. Due to the uncommon square-planar crystal field, Ir 5d states adopt intermediate-spin state with double occupation of dz2 orbital, leading to a sizable local spin moment, at variance with many other iridates. The square-planar crystal field splitting is also crucial in opening a robust insulating gap in Na4IrO4, irrespective of the specific magnetic ordering or treatment of electronic correlations. Spin-orbit coupling plays a minor role in shaping the electronic structure, but leads to a strong magnetocrystalline anisotropy. The easy axis perpendicular to the IrO4 plaquette, well explained using perturbation theory, is again closely related to the square-planar coordination. Finally, the large single-ion anisotropy suppresses the spin frustration and stabilizes a collinear antiferromagnetic long-range magnetic ordering, as confirmed by Monte Carlo simulations predicting a quite low N\'eel temperature, expected from almost isolated IrO4 square-planar units as crystalline building blocks.

First-principles study of the giant magnetic anisotropy energy in bulk Na4IrO4

In 5d transition metal oxides, novel properties arise from the interplay of electron correlations and spin--orbit interactions. Na4IrO4, where 5d transition-metal Ir atom occupies the center of the square-planar coordination environment, is synthesized. Based on density functional theory, we calculate its electronic and magnetic properties. Our numerical results show that the Ir-5d bands are quite narrow, and the bands around the Fermi level are mainly contributed by d_{xy},d_{yz} and d_{zx} orbitals. The magnetic easy-axis is perpendicular to the IrO4 plane, and the magnetic anisotropy energy (MAE) of Na4IrO4 is found to be very giant. We estimate the magnetic parameters by mapping the calculated total energy for different spin configurations onto a spin model. The next nearest neighbor exchange interaction J2 is much larger than other intersite exchange interactions and results in the magnetic ground state configuration. Our study clearly demonstrates that the huge MAE comes from the single-ion anisotropy rather than the anisotropic interatomic spin exchange. This compound has a large spin gap but very narrow spin-wave dispersion, due to the large single-ion anisotropy and relatively small exchange couplings. Noticing this remarkable magnetic feature originated from its highly isolated IrO4 moiety, we also explore the possiblity to further enhance the MAE.

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 ${\phi}_{\rm BEC}\,{=}\,3/2$.

Two-magnon scattering in the 5d all-in-all-out pyrochlore magnet Cd2Os2O7

5d pyrochlore oxides with all-in-all-out magnetic order are prime candidates for realizing strongly correlated, topological phases of matter. Despite significant effort, a full understanding of all-in-all-out magnetism remains elusive as the associated magnetic excitations have proven difficult to access with conventional techniques. Here we report a Raman spectroscopy study of spin dynamics in the all-in-all-out magnetic state of the 5d pyrochlore Cd2Os2O7. Through a comparison between the two-magnon scattering and spin-wave theory, we confirm the large single ion anisotropy in this material and show that the Dzyaloshinskii–Moriya and exchange interactions play a significant role in the spin-wave dispersions. The Raman data also reveal complex spin–charge–lattice coupling and indicate that the metal–insulator transition in Cd2Os2O7 is Lifshitz-type. Our work establishes Raman scattering as a simple and powerful method for exploring the spin dynamics in 5d pyrochlore magnets.

Effective realization of random magnetic fields in compounds with large single-ion anisotropy

We show that spin $S=1$ system with large and random single--ion anisotropy can be at low energies mapped to a $S=1/2$ system with random magnetic fields. This is for example realized in \mbox{Ni(Cl$_{1-x}$Br$_{x}$)$_2$-4SC(NH$_2$)$_2$} compound (DTNX) and therefore it represents a long sought realization of random local (on-site) magnetic fields in antiferromagnetic systems. We support the mapping by numerical study of $S=1$ and effective $S=1/2$ anisotropic Heisenberg chains and find excellent agreement for static quantities and also for the spin conductivity. Such systems can therefore be used to study the effects of local random magnetic fields on transport properties.

Localized and propagating excitations in gapped phases of spin systems with bond disorder

Using the conventional $T$-matrix approach, we discuss gapped phases in one-, two-, and three-dimensional (3D) spin systems (both with and without a long-range magnetic order) with bond disorder and with weakly interacting bosonic elementary excitations. This work is motivated by recent experimental and theoretical activity in spin-liquid-like systems with disorder and in the disordered interacting boson problem. In particular, we apply our theory to both paramagnetic low-field and fully polarized high-field phases in dimerized spin-$\frac{1}{2}$ systems and in integer-spin magnets with large single-ion easy-plane anisotropy $\mathcal{D}$ with disorder in exchange coupling constants (and/or $\mathcal{D}$). The elementary excitation spectrum and the density of states are calculated in the first order in defects concentration $c\ensuremath{\ll}1$. In 2D and 3D systems, the scattering on defects leads to a finite damping of all propagating excitations in the band except for states lying near its edges. We demonstrate that the analytical approach is inapplicable for states near the band edges and our numerical calculations reveal their localized nature. We find that the damping of propagating excitations can be much more pronounced in considered systems than in magnetically ordered gapless magnets with impurities. In 1D systems, the disorder leads to localization of all states in the band, while those lying far from the band edges (short-wavelength excitations) can look like conventional wave packets.

Magnetic neutron spectroscopy of a spin-transitionMn3+molecular complex

We have investigated by inelastic neutron scattering (INS), neutron diffraction, andmagnetometry the magnetic properties of the mononuclear complex [Mn3+(pyrol)3(tren)] in both high-spin (5E, HS, S = 2) and low-spin (3T1, LS, S = 1) states. The system presents a spin transition (ST) around 47 K with a small hysteresis width (TST,↑ = 47.5 K and TST,↓ = 46 K) characteristic of an efficient collective transition process. In the HS state, the INS spectrum at 56 K and zero magnetic field is accounted for by a zero-field splitting with D = −5.73(3) cm−1 and |E| = +0.47(2) cm−1 which may be the result of a dynamic Jahn-Teller effect reported in the literature.In the LS state, a single magnetic peak at 4.87 meV is observed, still at zero field. Despite the existence of an unquenched orbital moment (L = 1) in the ground 3T1 state, we argue that it may be described by a genuine S = 1 spin Hamiltonian owing to the existence of a strong trigonal distortion of the Mn3+ coordination octahedron. The observed peak corresponds to a transition M = +1 within the S = 1 ground state split by a large single-ion anisotropy term D = +39.3 cm−1. A full spin-Hamiltonian model is proposed based on these first INS results obtained in a thermal ST molecular magnetic system.