Single-ion Anisotropy Research Articles

Crystal growth and magnetic properties of the coupled alternating S=1 spin chain Sr2Ni(SeO3)3

The structural, magnetic, and thermodynamic properties of a quasi-one-dimensional (1D) $S=1$ alternating spin chain compound ${\mathrm{Sr}}_{2}\mathrm{Ni}{(\mathrm{Se}{\mathrm{O}}_{3})}_{3}$ are investigated by using synchrotron x-ray powder diffraction, magnetic susceptibility $\ensuremath{\chi}(H,T)$, and heat capacity ${C}_{\mathrm{P}}(H,T)$ measurements together with density functional theory (DFT) calculations. The $\ensuremath{\chi}(H,T)$ and ${C}_{\mathrm{P}}(H,T)$ data reveal long-range antiferromagnetic order at ${T}_{\mathrm{N}}=3.4(3)$ K and short-range order at ${T}_{\mathrm{m}}\ensuremath{\approx}7.8\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The short-range magnetic order together with 95% of spin entropy release above ${T}_{\mathrm{N}}$ signifies the importance of 1D spin correlations persisting to $\ensuremath{\sim}8{T}_{\mathrm{N}}$. Theoretical DFT calculations with generalized gradient approximation determine leading exchange interactions, suggesting that interchain interactions are responsible for the observed long-range magnetic ordering. In addition, the temperature-field phase diagram of ${\mathrm{Sr}}_{2}\mathrm{Ni}{(\mathrm{Se}{\mathrm{O}}_{3})}_{3}$ is determined based on the $\ensuremath{\chi}(T,H)$ and ${C}_{\mathrm{P}}(T,H)$ data. Interestingly, a nonmonotonic phase boundary of ${T}_{\mathrm{m}}$ is found for an external field applied along a hard axis. Our results suggest that the ground state and magnetic behavior of ${\mathrm{Sr}}_{2}\mathrm{Ni}{(\mathrm{Se}{\mathrm{O}}_{3})}_{3}$ rely on the interplay of single-ion anisotropy, bond alternation, and interchain interactions.

Probing the influence of Ho3+ doping on structural and magnetic properties of (Gd1−yHoy)2Ti2O7 pyrochlore

Antiferromagnetically (AFM) linked Heisenberg spins are found to be extremely frustrating in the Gd2Ti2O7 pyrochlore lattice because of the minimization exchange energy. The influence of the Ho3+substitution at Gd3+ site on the structural and magnetic of (Gd1−yHoy)2Ti2O7 (y = 0.0, 0.2, 0.4 and 0.6) single phasic cubic pyrochlore oxides have been investigated. Structural evaluation has proven that cubic pyrochlore (impurity-free) crystals with a cell parameter that continuously shrinkage and justifies Vegard rule. Raman spectroscopy studies exhibit that Ho3+ was completely absorbed in the Gd2Ti2O7 host matrix without substantially affecting its structural integrity. Reduction in the crystallite size and shifts in position of Raman active modes with magnetic Ho substitution is validated by the deterioration in structural ordering of the produced specimens. Observation on the increase in Curie Weiss temperature (θCW = –9.13 to +0.14 K) and effective magnetic moment (μeff/f.u. = 3.64–4.56 μB) on Ho doping leads to enhancement of ferromagnetic feature of the materials. But, spin glassy pattern has not been detected in all compositions. Thus, magnetic studies demonstrate that the system becomes less AFM character due to generation of ferromagnetic interaction among Gd–Ho (Ho–Ho) spins and disrupted network of Gd3+ ions by increase in chemical pressure in Gd2Ti2O7. Moreover, measured values of Msat are found to lower with rise in chemical pressure of the (Gd1−yHoy)2Ti2O7 system owing to the effects of particle angular averaging and single ion anisotropy.

Inelastic neutron scattering in the weakly coupled triangular spin tube candidate CsCrF4

We performed inelastic neutron scattering (INS) experiments to measure spin dynamics on a polycrystalline sample of a spin tube candidate CsCrF$_{4}$. The compound exhibits a successive phase transition from a paramagnetic phase through an intermediate temperature (IT) phase of a 120$^{\circ}$ structure to a low temperature (LT) phase of another 120$^{\circ}$ structure. Elaborate comparison between observed and calculated neutron spectra in LT phase reveals that the spin Hamiltonian is identified as antiferromagnetic spin tubes including perturbative terms of intertube interaction, Dzyaloshinskii-Moriya interaction, and single ion anisotropy. A phase diagram for the ground state is classically calculated. A set of parameters in the spin Hamiltonian obtained from the INS spectra measured in LT phase is quite close to a boundary to the phase of the 120$^{\circ}$ structure of IT phase. The INS spectra measured in IT phase is, surprisingly, the same as those in LT phase in the level of powder averaged spectra, even though the magnetic structures in IT and LT phases are different. Identical dynamical structures compatible with two different static structures are observed. No difference in the observed spectra indicates no change of the spin Hamiltonian with the temperature, suggesting that the origin of the successive phase transition being order-by-disorder mechanism.

Three-Dimensional H–φ–θ Phase Diagram of ErB12 Antiferromagnet with Dynamic Charge Stripes

A three-dimensional (H, φ, θ, T = 2 K) magnetic phase diagram has been constructed for the first time for the antiferromagnetic metal Er11B12 with an amplitude-modulated magnetic structure exhibiting an electronic instability (dynamic charge stripes). The boundaries determining the shape of the main magnetic phases in the H–φ–θ space are reconstructed from measurements of the magnetoresistance. The role of dynamic charge stripes, which suppress the indirect Ruderman–Kittel–Kasuya–Yoshida exchange between the magnetic moments of the nearest Er3+ ions, and of the single-ion anisotropy in the formation of a complicated multicomponent phase diagram of Er11B12 is discussed.

Phase diagram of the spin Blume–Capel model in random single-ion anisotropy and magnetic field revisited

We used the Curie–Weiss mean-field approximation to study the effects of random single-ion anisotropy and random magnetic field in the phase diagram as well as in the thermodynamic properties of the spin-7/2 Blume–Capel model. The phase diagrams are presented in the planes temperature versus single-ion anisotropy and temperature versus magnetic field, temperature versus random parameters. The dependencies of magnetization are studied as a function of temperature and single-ion anisotropy.

Magnetic Anisotropy of Single-Ion Magnet (PPh4)2 [ReF6]·2H2O

Studying of single-molecule magnets has sprung many surprises such as, e.g., quantum tunneling of the magnetization, which is strongly related to the presence of a magnetic anisotropy. Electron spin resonance and inelastic neutron scattering measurements of (PPh4)2[ReF6]⋅2H2O complex evidence an unprecedented large single-site magnetic anisotropy of D sim 35 K in this material. Using state-of-the-art ab initio calculations we found that the single-ion anisotropy is indeed very large (but does not exceed 12 K) and revealed the physical mechanism lying behind this phenomenon.

Magnetic Behavior of Ising Nanowire with Mixed Integer Spins: A Monte Carlo Study

The magnetic and thermal properties of a ferrimagnetic mixed spin-1 and spin-2 cubic Ising nanowire are studied by using the Monte Carlo simulation. The influences of the nearest (JAB) and next-nearest neighbor (JA and JB) exchange interactions and the single-ion anisotropies (DA and DB) on the critical and compensation temperatures are illustrated. Moreover, the phase diagrams on the (temperature, anisotropy) plane are plotted for several values of JA/|JAB|. The system shows very rich and interesting behaviors, namely first and second order phase transitions, tricritical points and compensation phenomenon. Finally, the dependence of hysteresis loops on the anisotropies, the exchange interactions and the temperature is also investigated.

Exploring Spin-Phonon Coupling in Magnetic 2D Metal-Organic Frameworks

Layered magnetic metal-organic frameworks (MOFs) are an emerging class of materials that can combine the advantages of both MOFs and 2D magnetic crystals. The recent discovery of large coercivity and long-range magnetic ordering up to 515 K in a layered MOF of general formula MCl2(pyz)2 (M = transition metal, pyz = pyrazine) offers an exciting versatile platform to achieve high-TC magnetism at the 2D limit. In this work, we investigate the exfoliation feasibility down to the monolayer of VCl2(pyz)2 and CrCl2(pyz)2 by means of first-principles calculations. We explore their structural, electronic, magnetic and vibrational properties, as well as the effect of halide substitution. Then, we provide a full analysis of the spin-phonon coupling (SPC) in both 2D derivatives. Our calculations reveal a low SPC and thermal evolution of the magnetic exchange interactions and single-ion anisotropy mainly governed by low-frequency phonon modes. Finally, we provide chemical insights to improve the performance of these magnetic 2D MOFs based on the effective manipulation of the phonon modes that can present a major impact on their magnetic properties.

Studies of decoherence in strongly anisotropic spin triangles with toroidal or general noncollinear easy axes

Magnetic molecules are investigated with respect to their usability as units in future quantum devices. In view of quantum computing, a necessary prerequisite is a long coherence time of superpositions of low-lying levels. In this article, we investigate by means of numerical simulations whether a toroidal structure of single-ion easy anisotropy axes is advantageous as often conjectured. Our results demonstrate that there is no general advantage of toroidal magnetic molecules, but that arrangements of tilted anisotropy axes perform best in many cases.

Spin Wave Spectra in Pseudoperovskite Manganites with Superexchange Interaction Competition

In compounds La1/3Ca2/3MnO3 and BiMnO3, a calculation of spin-wave dispersion dependences along pseudoperovskite directions of reciprocal space is made. The model includes orbitally dependent superexchange interaction and single-ion anisotropy. Considered compounds present competing exchange interactions within magnetic unit cell because of orbital or charge-orbital ordering. The nearest neighbor superexchange interaction is taken into account. The magnetic structure and dispersion dependences of spin waves frequencies are calculated within the framework of regular multi-sublattice model. The peculiarities of frustrated magnetic spin-wave spectra are found. It is shown, that crossing and splitting of spin-waves branches in non-symmetric points of magnetic Brillouin zone is a common feature of the spectra due to exchange competition. The band structure of Г-point spectra for both compounds are predicted.

Zero-Field Miniature Skyrmion Crystal and Chiral Domain State in Breathing-Kagome Antiferromagnets

The stability of a miniature skyrmion crystal (SkX) with only a small number of spins in the magnetic unit cell has been theoretically investigated in $J_1$-$J_3$ antiferromagnets on the breathing kagome lattice with a single-ion anisotropy $D$ at zero field. It is found by means of Monte Carlo simulations that due to the breathing bond-alternation, a zero-field triple-${\bf Q}$ miniature SkX can be stabilized not only in the specific case of $D=0$ [K. Aoyama and H. Kawamura, Phys. Rev. B 105, L100407 (2022)] but also in more general situations with easy-axis ($D<0$) and easy-plane ($D>0$) anisotropies which favor triple-${\bf Q}$ collinear and noncoplanar states, respectively. Since the SkX and anti-SkX each having positive or negative chirality are energetically degenerate, the topological Hall effect of alternative sign is possible at zero field. It is also found that reflecting the chiral degeneracy, the collinear and coplanar phases preempting the SkX phase possess random domain structures consisting of positive- and negative-chirality clusters.

Microscopic parameters of the van der Waals CrSBr antiferromagnet from microwave absorption experiments

Microwave absorption experiments employing a phase-sensitive external resistive detection are performed for a topical van der Waals antiferromagnet CrSBr. The field dependence of two resonance modes is measured in an applied field parallel to the three principal crystallographic directions, revealing anisotropies and magnetic transitions in this material. To account for the observed results, we formulate a microscopic spin model with a bi-axial single-ion anisotropy and inter-plane exchange. Theoretical calculations give an excellent description of full magnon spectra enabling us to precisely determine microscopic interaction parameters for CrSBr.

The exact solution of the edge-modified graphene nanoribbon-like structure Ising-Heisenberg spin (1,1/2) system

A two-fold rotational symmetry ferromagnetic Ising-Heisenberg model modified by edge spin ( S = 1 / 2 ) with antiferromagnetic Heisenberg exchange interaction, whose shape is graphene nanoribbon-like has been constructed, and the host Ising spin ( S = 1 ). By use of the star-triangle transformation and the transfer matrix method, the edge states, thermodynamics and magnetization behavior of the system display various properties. The results perform that the unique edge-spin states and the host-spin states of the system are influenced with each other. And there are eleven different ground state phases, which are presented as the values of magnetic susceptibility multiplied by temperature at ultra-low temperature in the parameter space of single-ion anisotropy and antiferromagnetic Heisenberg interaction. Because of a large number of excited states close to the ground state, the specific heat curve shows multi-peak phenomena, which are analyzed by corresponding to the entropy of the system. The magnetization process of the system is complex, due to the direct correlation of the edge-spin states and the host-spin states of system, in which many different magnetization plateaus appear. The rigorous results of the number and width of magnetization plateaus and the saturation of the magnetization are written. This study offers unique opportunities for future technological applications such as proposed designs of graphene-based quantum spintronic devices as well as magnetic ordering.

Spin wave spectra of single crystal CoPS3

The spin waves in single crystals of the layered van der Waals antiferromagnet CoPS$_3$ have been measured using inelastic neutron scattering. The data show four distinct spin wave branches with large ($\gtrsim 14$ meV) energy gaps at the Brillouin zone center indicating significant anisotropy. The data were modelled using linear spin wave theory derived from a Heisenberg Hamiltonian. Exchange interactions up to the third nearest-neighbour in the layered planes were required to fit the data with ferromagnetic $J_1 = -1.37$ meV between first neighbours, antiferromagnetic $J_3 = 3.0$ meV between third neighbours, and a very small $J_2 = 0.09$ meV between second neighbours. A biaxial single-ion anisotropy was required, with a collinear term $D^x = -0.77$ meV for the axis parallel to the aligned moment direction and a coplanar term $D^z=6.07$ meV for an axis approximately normal to the layered crystal planes.

Frustrated magnetic cycloidal structure and emergent Potts nematicity in CaMn2P2

We report neutron-diffraction results on single-crystal CaMn$_2$P$_2$ containing corrugated Mn honeycomb layers and determine its ground-state magnetic structure. The diffraction patterns consist of prominent (1/6, 1/6, $L$) reciprocal lattice unit (r.l.u.; $L$ = integer) magnetic Bragg reflections, whose temperature-dependent intensities are consistent with a first-order antiferromagnetic phase transition at the N\'eel temperature $T_{\rm N} = 70(1)$ K. Our analysis of the diffraction patterns reveals an in-plane $6\times6$ magnetic unit cell with ordered spins that in the principal-axis directions rotate by 60-degree steps between nearest neighbors on each sublattice that forms the honeycomb structure, consistent with the $P_Ac$ magnetic space group. We find that a few other magnetic subgroup symmetries ($P_A2/c$, $P_C2/m$, $P_S\bar{1}, P_C2, P_Cm, P_S1$) of the paramagnetic $P\bar{3}m11^\prime$ crystal symmetry are consistent with the observed diffraction pattern. We relate our findings to frustrated $J_1$-$J_2$-$J_3$ Heisenberg honeycomb antiferromagnets with single-ion anisotropy and the emergence of Potts nematicity

A Trinuclear High-Spin Iron(III) Complex with a Geometrically Frustrated Spin Ground State Featuring Negligible Magnetic Anisotropy and Antisymmetric Exchange.

The trinuclear high-spin iron(III) complex [Fe3Cl3(saltagBr)(py)6]ClO4 {H5saltagBr = 1,2,3-tris[(5-bromo-salicylidene)amino]guanidine} was synthesized and characterized by several experimental and theoretical methods. The iron(III) complex exhibits molecular 3-fold symmetry imposed by the rigid ligand backbone and crystallizes in trigonal space group P3̅ with the complex cation lying on a crystallographic C3 axis. The high-spin states (S = 5/2) of the individual iron(III) ions were determined by Mößbauer spectroscopy and confirmed by CASSCF/CASPT2 ab initio calculations. Magnetic measurements show an antiferromagnetic exchange between the iron(III) ions leading to a geometrically spin-frustrated ground state. This was complemented by high-field magnetization experiments up to 60 T, which confirm the isotropic nature of the magnetic exchange and negligible single-ion anisotropy for the iron(III) ions. Muon-spin relaxation experiments were performed and further prove the isotropic nature of the coupled spin ground state and the presence of isolated paramagnetic molecular systems with negligible intermolecular interactions down to 20 mK. Broken-symmetry density functional theory calculations are consistent with the antiferromagnetic exchange between the iron(III) ions within the presented trinuclear high-spin iron(III) complex. Ab initio calculations further support the absence of appreciable magnetic anisotropy (D = 0.086, and E = 0.010 cm-1) and the absence of significant contributions from antisymmetric exchange, as the two Kramers doublets are virtually degenerate (ΔE = 0.005 cm-1). Therefore, this trinuclear high-spin iron(III) complex should be an ideal candidate for further investigations of spin-electric effects arising exclusively from the spin chirality of a geometrically frustrated S = 1/2 spin ground state of the molecular system.

Orbital structure and magnetic phase diagram of the four-sublattice ferromagnet PbMnBO4

A role of quadric and quartic single-ion anisotropy (SIA) of Mn3+-ions, dipole–dipole and Dzyaloshinsky–Moriya (DM) interactions for the magnetic ordering of the four-sublattice ferromagnet PbMnBO4 is investigated. A phase diagram of low-lying magnetic phases on the plane of the DM exchange components is obtained for different values of the SIA parameters. An effect of the isotropic interchain exchange on the spin orientation and, as a result, on the SIA energy in different magnetic phases is considered at the comparable values of the interactions. The determinative role of DM exchange for the magnetic anisotropy of PbMnBO4 is discussed.

Multiple-[formula omitted] instability under fourth-order inplane single-ion anisotropy

Multiple-Q instability under tetragonal single-ion anisotropy is theoretically investigated. By performing the simulated annealing for a spin model with the momentum-resolved interaction and fourth-order inplane single-ion anisotropy on a square lattice, we find that the interplay between the competing exchange interactions in momentum space and single-ion anisotropy leads to various field-induced double-Q states in the ground state. In particular, we show that a double-Q vortex crystal emerges when the interactions at high-harmonic wave vectors are comparable to those at wave vectors that give the dominant contributions. Our results underscore the importance of magnetic anisotropy, which brings about the multiple-Q instability in centrosymmetric magnets.

Interplay of Anisotropic Exchange Interactions and Single-Ion Anisotropy in Single-Chain Magnets Built from Ru/Os Cyanidometallates(III) and Mn(III) Complex.

Two novel 1D heterobimetallic compounds {[MnIII(SB2+)MIII(CN)6]·4H2O}n (SB2+ = N,N'-ethylenebis(5-trimethylammoniomethylsalicylideneiminate) based on orbitally degenerate cyanidometallates [OsIII(CN)6]3- (1) and [RuIII(CN)6]3- (2) and MnIII Schiff base complex were synthesized and characterized structurally and magnetically. Their crystal structures consist of electrically neutral, well-isolated chains composed of alternating [MIII(CN)6]3- anions and square planar [MnIII(SB2+)]3+ cations bridged by cyanide groups. These -ion magnetic anisotropy of MnIII centers. These results indicate that the presence of compounds exhibit single-chain magnet (SCM) behavior with the energy barriers of Δτ1/kB = 73 K, Δτ2/kB = 41.5 K (1) and Δτ1/kB = 51 K, Δτ2 = 27 K (2). Blocking temperatures of TB = 2.8, 2.1 K and magnetic hysteresis with coercive fields (at 1.8 K) of 8000, 1600 Oe were found for 1 and 2, respectively. Theoretical analysis of the magnetic data reveals that their single-chain magnet behavior is a product of a complicated interplay of extremely anisotropic triaxial exchange interactions in MIII(4d/5d)-CN-MnIII fragments: -JxSMxSMnx-JySMySMny-JzSMzSMnz, with opposite sign of exchange parameters Jx = -22, Jy = +28, Jz = -26 cm-1 and Jx = -18, Jy = +20, Jz = -18 cm-1 in 1 and 2, respectively) and single orbitally degenerate [OsIII(CN)6]3- and [RuIII(CN)6]3- spin units with unquenched orbital angular momentum in the chain compounds 1 and 2 leads to a peculiar regime of slow magnetic relaxation, which is beyond the scope of the conventional Glaubers's 1D Ising model and anisotropic Heisenberg model.

Triple-meron crystal in high-spin Kitaev magnets

Skyrmions hold great promise in future spintronics applications since they are robust against local deformations. The meron, due to its topological equivalence to a half skyrmion, has been widely found to appear in pairs. Motivated by recent progresses in high-spin Kitaev magnets, here we investigate numerically a classical Kitaev-Γ model with a single-ion anisotropy. An exotic spin texture consisting of three merons is discovered. Such a state features a peculiar property with an odd number of merons in one magnetic unit cell. Therefore, these merons cannot be dissociated from skyrmions as reported in the literature and their origin is briefly discussed. Moreover, we find that these three merons contribute a finite topological number and thus it can induce the topological Hall effect (THE). Experimentally this spin texture can be observed by the Lorentz transmission electron microscopy and the THE can be used to identify the finite topological number. Our work demonstrates that high-spin Kitaev magnets can host robust unconventional spin textures and thus they offer a versatile platform for exploring exotic spin textures as well as their applications in spintronics.