Ising Anisotropy Research Articles

Transforming from Kitaev to Disguised Ising Chain: Application to CoNb_{2}O_{6}.

For many years, CoNb_{2}O_{6} has served as an exemplar of the one-dimensional Ising model. However, recent experimental and theoretical analyses challenge its applicability to this material. Prior to that, a tailored spin model for 3d^{7} systems such as Co^{2+}, known as the JKΓ model, has emerged, featuring Heisenberg (J), Kitaev (K), and Gamma (Γ) interactions. While these interactions are permitted by the symmetry of the system, their role in CoNb_{2}O_{6} remains enigmatic. We present a microscopic theory based on spin-orbit entangled J_{eff}=1/2 states, aimed at elucidating the roles of Kitaev and Gamma interactions in shaping Ising anisotropy. Leveraging strong coupling theory, we identify a dominant ferromagnetic Kitaev interaction. Furthermore, by comparing dynamical structure factors obtained via exact diagonalization with those from inelastic neutron scattering experiments, we find an antiferromagnetic Γ interaction, which dictates the Ising axis and explains the mechanism behind moment pinning. Our theory provides a microscopic origin for Ising behavior in spin-orbit coupled one-dimensional chains and posits CoNb_{2}O_{6} as a rare Kitaev chain.

Synthesis, disorder and Ising anisotropy in a new spin liquid candidate PrMgAl11O19

Here we report the successful synthesis of large single crystals of triangular frustrated PrMgAl11O19 using the optical floating zone technique. Single crystal x-ray diffraction (XRD) measurements unveiled the presence of quenched disorder within the mirror plane, specifically ~7% of Pr ions deviating from the ideal 2d site towards the 6h site. Magnetic susceptibility measurements revealed an Ising anisotropy with the c-axis being the easy axis. Despite a large spin–spin interaction that develops below ~10 K and considerable site disorder, the spins do not order or freeze down to at least 50 mK. The availability of large single crystals offers a distinct opportunity to investigate the exotic magnetic state on a triangular lattice with an easy axis out of the plane.

Theory for magnetic impurity modes in two-dimensional van der Waals ferromagnetic films

A spin-wave analysis is developed to calculate the energies of the localized excitations occurring in two-dimensional ferromagnetic van der Waals monolayers when a substitutional magnetic impurity is introduced. The magnetic ions lie on a bipartite honeycomb lattice (similar to that for graphene) and the theory includes the effects of both Ising anisotropy and single-ion anisotropy to stabilize the magnetic ordering perpendicular to the atomic plane at low temperatures. A Dyson-equation formalism, together with the spin-dependent Green’s functions derived for van der Waals monolayers, is employed to evaluate the existence conditions and energies for the impurity modes, which lie above the band of spin-wave states of the pure host material. For realistic parameter values it is found that typically two impurity modes may exist, depending on the spin quantum number for the magnetic impurity atom. Numerical applications are made to CrI3 and Cr2Ge2Te6 as the host materials.

Stacking-induced magnetic frustration and spiral spin liquid

Like the twisting control in magic-angle twisted bilayer graphene, the stacking control is another mechanical approach to manipulate the fundamental properties of solids, especially the van der Waals materials. We explore the stacking-induced magnetic frustration and the spiral spin liquid on a multilayer triangular lattice antiferromagnet where the system is built from ABC stacking with competing intralayer and interlayers couplings. By combining the nematic bond theory and the self-consistent Gaussian approximation, we establish the phase diagram for this ABC-stacked multilayer magnet. It is shown that the system supports a wide regime of spiral spin liquid with multiple degenerate spiral lines in the reciprocal space, separating the low-temperature spiral order and the high-temperature featureless paramagnet. The transition to the spiral order from the spiral spin liquid regime is first order. We further show that the spiral-spin-liquid behavior persists even with small perturbations such as further neighbor intralayer exchanges. The connection to the ABC-stacked magnets, the effects of Ising or planar spin anisotropy, and the outlook on the stacking-engineered quantum magnets are discussed.

Quasi-Two-Dimensional Anomalous Hall Mott Insulator of Topologically Engineered Jeff=1/2 Electrons

We investigate an experimental toy-model system of a pseudospin-half square-lattice Hubbard Hamiltonian in [(SrIrO3)1/(CaTiO3)1] to include both nontrivial complex hopping and moderate electronic correlation. While the former induces electronic Berry phases as anticipated from the weak-coupling limit, the later stabilizes an antiferromagnetic (AFM) Mott insulator ground state in analogous to the strong-coupling limit. Their combined results in the real system are found to be an anomalous Hall effect with a non-monotonic temperature dependence due to the self-competition of the electron-hole pairing in the Mott state, and an exceptionally large Ising anisotropy that is captured as a giant magnon gap beyond the superexchange approach. The unusual phenomena highlight the rich interplay of electronic topology and electronic correlation in the intermediate-coupling regime that is largely unexplored and challenging in theoretical modelling.

Magnetic transitions induced by pressure and magnetic field in a two-orbital [formula omitted]-electron model in cubic and tetragonal lattices

We investigate the onset and evolution of under the simultaneous application of pressure and magnetic field of distinct itinerant Néel states using the underscreened Anderson Lattice Model (UALM) which has been proposed to describe 5f-electron systems. The model is composed by two narrow f-bands (of either α or β character) that hybridize with a wide d-band and local 5f-electron interactions. We consider both cubic and tetragonal lattices. The Néel order parameters ϕβ and ϕα are assumed to be fixed by an Ising anisotropy. The applied magnetic field hz is parallel to the anisotropy axis. It has been assumed that the variation of the band width W is sensitive to pressure. In the absence of a magnetic field, the increase of W takes the system from the phase AF1 to another phase AF2. The phase AF1 occurs when ϕβ>ϕα>0 while in the AF2 phase the gaps satisfy ϕα>ϕβ>0. In the presence of a magnetic field hz, the phase AF2 is quickly suppressed and reappears again at intermediate values of the magnetic field while it is predominant at higher magnetic fields. The analysis of the partial density of states close to the phase transition between the phases AF1 and AF2, allows a better understanding the mechanism responsible whereby the transition is induced by an increase in the magnetic field. As an important general result, we found that the magnetic field hz favours the phase AF2 while the phase AF1 is suppressed. For the tetragonal lattice, the phase AF2 is even more favored when hz and c/a increases concomitantly, where c and a are the lattice parameters.

Reaching the equilibrium state of the frustrated triangular Ising magnet Ca3Co2O6

Ca3Co2O6 is a frustrated magnet consisting of a triangular arrangement of chains of Ising spins. It shows regular magnetization steps vs magnetic field every 1.2 T that are metastable with very slow dynamics. This has puzzled the community for many years and given rise to numerous potential theories. Here we approach the problem by seeking the elusive magnetic equilibrium state at T = 2 K. To this end, we explore two approaches: (1) bypassing the slow dynamics produced by changing fields by instead field-cooling directly to the target temperature, and (2) quantum annealing in transverse magnetic fields. While we observe no measurable effect of the quantum annealing in fields up to 7 T, which is likely due to the large Ising anisotropy of Co spins in this material, we find that for the field cooling in longitudinal fields we achieve the predicted equilibrium 1/3 magnetization. We perform Monte Carlo simulations of the ground state phase diagram and we also simulate the quantum annealing process and find good agreement between experiment and theory. Thus we present an investigation of the elusive ground state properties of the canonical frustrated triangular system Ca3Co2O6.

Magnetic properties of the layered heavy-fermion antiferromagnet CePdGa6

We report the magnetic properties of the layered heavy fermion antiferromagnet CePdGa$_{6}$, and their evolution upon tuning with the application of magnetic field and pressure. CePdGa$_{6}$ orders antiferromagnetically below $T\rm_{N}$ = 5.2 K, where there is evidence for heavy fermion behavior from an enhanced Sommerfeld coefficient. Our results are best explained by a magnetic ground state of ferromagnetically coupled layers of Ce $4f$-moments orientated along the $c$-axis, with antiferromagnetic coupling between layers. At low temperatures we observe two metamagnetic transitions for fields applied along the $c$-axis corresponding to spin-flip transitions, where the lower transition is to a different magnetic phase with a magnetization one-third of the saturated value. From our analysis of the magnetic susceptibility, we propose a CEF level scheme which accounts for the Ising anisotropy at low temperatures, and we find that the evolution of the magnetic ground state can be explained considering both antiferromagnetic exchange between nearest neighbor and next nearest neighbor layers, indicating the influence of long-range interactions. Meanwhile we find little change of $T\rm_{N}$ upon applying hydrostatic pressures up to 2.2 GPa, suggesting that significantly higher pressures are required to examine for possible quantum critical behaviors.

Chemical tuning of magnetic anisotropy and correlations in Ni1−xFexPS3

We report the temperature and composition dependence of static magnetic susceptibility and Raman spectroscopic measurements on van der Waals antiferromagnets ${\mathrm{Ni}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{PS}}_{3}$. The end members ${\mathrm{NiPS}}_{3}$ and ${\mathrm{FePS}}_{3}$ feature $XY$- and Ising-like magnetism, respectively, enabling chemical tuning of magnetic anisotropy and spin correlations. ${\mathrm{Ni}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{PS}}_{3}$ shows a turnover from the $XY$ to Ising anisotropy through $x\ensuremath{\approx}0.1$. Although the $XY$ anisotropy is rapidly suppressed on introducing Fe content, two-magnon scattering evidences the slow repression of short-range magnetic correlations deep inside the Fe-rich side. Counterintuitively, the two-magnon signal undergoes less renormalization of its energy with increasing $x$ despite the larger spin number and enhanced classical magnetism. The disparate static and dynamic magnetic behaviors indicate the emergence of an exotic spin state in alloy van der Waals magnets.

Crystal growth and anisotropic magnetic properties of quasi-two-dimensional(Fe1−xNix)2P2S6

We report the crystal growth by chemical vapor transport together with a thorough structural and magnetic characterization of the quasi-2D magnets ${({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x})}_{2}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ with ${x}_{\text{Ni}}=\text{0,}\phantom{\rule{4.pt}{0ex}}\text{0.3,}\phantom{\rule{4.pt}{0ex}}\text{0.5,}\phantom{\rule{4.pt}{0ex}}\text{0.7,}\phantom{\rule{4.pt}{0ex}}\text{0.9}$, and 1. As-grown crystals exhibit a layered morphology with weak van der Waals interactions between layers parallel to the crystallographic $ab$ plane of the monoclinic structure in the space group $C2/m$ (No. 12). Magnetization measurements reveal an antiferromagnetic ground state for all grown crystals. In the ordered state, the magnetization along different crystallographic directions is in agreement with an Ising anisotropy for $0\ensuremath{\le}x\ensuremath{\le}0.9$ and only for ${\mathrm{Ni}}_{2}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ a different behavior is observed which is in line with an anisotropic Heisenberg or $XXZ$ model description. This striking abrupt change of anisotropy at a critical Ni concentration is coupled to a change in the width of the maximum in the magnetization around ${T}_{\text{max}}$. Furthermore, all intermediate compounds $0<x\ensuremath{\le}0.9$ exhibit an anisotropic magnetization already in the paramagnetic state similar to the parent compound ${\mathrm{Fe}}_{2}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$.

Phase diagram of the two-dimensional dipolar Heisenberg model with Dzyaloshinskii-Moriya interaction and Ising anisotropy

We study phase transitions in the two-dimensional Heisenberg model with Dzyaloshinskii-Moriya interaction, Ising anisotropy $\ensuremath{\eta}$, and dipolar interaction under zero and finite magnetic fields $H$. For three typical strengths (zero, weak, and strong) of the dipolar interaction, we present the $H\text{\ensuremath{-}}\ensuremath{\eta}$ phase diagrams by estimating order parameters for skyrmion-lattice and helical phases and in-plane magnetization using a Monte Carlo method with an $O(N)$ algorithm. We find in the phase diagrams three types of skyrmion-lattice phases, i.e., two square lattices and a triangular lattice, helical phases with diagonal and vertical (or horizontal) stripes, a canted ferromagnetic phase, and a polarized ferromagnetic phase. The effect of the dipolar interaction varies the types of the skyrmion and helical phases in a complex manner. The dipolar interaction also expands the regions of the ordered phases accompanying shifts of the phase boundaries to the positive $H$ and $\ensuremath{\eta}$ directions and causes an increase of the density of skyrmions and shortening of the pitch length (stripe width) of helical structures. We discuss the details of the features of the phase transitions.

Skyrmions in twisted van der Waals magnets

Magnetic skyrmions in 2D chiral magnets are in general stabilized by a combination of Dzyaloshinskii-Moriya interaction and external magnetic field. Here, we show that skyrmions can also be stabilized in twisted moir\'e superlattices in the absence of an external magnetic field. Our setup consists of a 2D ferromagnetic layer twisted on top of an antiferromagnetic substrate. The coupling between the ferromagnetic layer and the substrate generates an effective alternating exchange field. We find a large region of skyrmion crystal phase when the length scales of the moir\'e periodicity and skyrmions are compatible. Unlike chiral magnets under magnetic field, skyrmions in moir\'e superlattices show enhanced stability for the easy-axis (Ising) anisotropy which can be essential to realize skyrmions since most van der Waals magnets possess easy-axis anisotropy.

Pressure-induced phase transition in the J1−J2 square lattice antiferromagnet RbMoOPO4Cl

We report results of magnetization and $^{31}$P NMR measurements under high pressure up to 6.4~GPa on RbMoOPO$_4$Cl, which is a frustrated square-lattice antiferromagnet with competing nearest-neighbor and next-nearest-neighbor interactions. Anomalies in the pressure dependences of the NMR shift and the transferred hyperfine coupling constants indicate a structural phase transition at 2.6~GPa, which is likely to break mirror symmetry and triggers significant change of the exchange interactions. In fact, the NMR spectra in magnetically ordered states reveal a change from the columnar antiferromagnetic (CAF) order below 3.3~GPa to the N\'{e}el antiferromagnetic (NAF) order above 3.9~GPa. The spin lattice relaxation rate $1/T_1$ also indicates a change of dominant magnetic fluctuations from CAF-type to NAF-type with pressure. Although the NMR spectra in the intermediate pressure region between 3.3 and 3.9 GPa show coexistence of the CAF and NAF phases, a certain component of $1/T_1$ shows paramagnetic behavior with persistent spin fluctuations, leaving possibility for a quantum disordered phase. The easy-plane anisotropy of spin fluctuations with unusual nonmonotonic temperature dependence at ambient pressure gets reversed to the Ising anisotropy at high pressures. This unexpected anisotropic behavior for a spin 1/2 system may be ascribed to the strong spin-orbit coupling of Mo-4$d$ electrons.

The construction of dynamic dysprosium-carboxylate ribbons by utilizing the hybrid-ligand conception.

By utilizing the hybrid-ligand conception, three novel dysprosium complexes Dy(2-py-4-pmc)(L)(H2O) (H2-py-4-pmc = 2-(2-pyridyl)pyrimidine-4-carboxylic acid; L = fumarate (fum, 1), succinate (suc, 2), or pimelate (pim, 3)) have been successfully synthesized. Structural analysis reveals that the dicarboxylate ligands connect 2-py-4-pmc--protected Dy3+ to form one-dimensional molecular ribbons. Magnetic measurements indicate that the three complexes exhibit typical slow magnetic relaxation under a zero dc field with effective reversal barriers Ueff of 180 K, 145 K and 137 K for 1-3, respectively, which is mainly attributed to the strong Ising anisotropy of dysprosium ions induced by the appropriate arrangement of carboxylate groups. Ab initio calculations demonstrate that the charge distribution around dysprosium ions and the magnetic interactions between them are key contributions to their different dynamic behaviour.

Large magnetic anisotropy in a quasi-1D ferromagnetic complex Co(sba)(H2O)2·H2O (sba = 4-sulfobenzoate)

We have determined the crystal structures of new Co(II) polynuclear complex Co(sba)(H2O)2·H2O (sba ​= ​4-sulfobenzoate) (1) by X-ray crystallography. The crystal structure of 1 shows Co(II) uniform chains in which octahedral Co(II) centers are connected through double μ-OH2 single syn-syn μ-carboxylato bridging ligands, and these uniform chains are well separated by the sba ligands. Magnetization and magnetic susceptibility data of a single crystal of 1 taken along the different crystallographic axes suggest a large uniaxial magnetic anisotropy, the so-called Ising anisotropy, possessing large c∗-axis magnetic moments. Magnetic susceptibility data of 1 is explained by an 1D Ising ferromagnet with intra-chain exchange interaction of Jz/kB ​= ​39.6 ​K.

Approaching the quantum critical point in a highly correlated all-in–all-out antiferromagnet

Continuous quantum phase transitions involving all-in-all-out (AIAO) antiferromagnetic order in strongly spin-orbit-coupled 5d compounds could give rise to various exotic electronic phases and strongly-coupled quantum critical phenomena. Here we experimentally trace the AIAO spin order in Sm2Ir2O7 using direct resonant x-ray magnetic diffraction techniques under high pressure. The magnetic order is suppressed at a critical pressure Pc=6.30 GPa, while the lattice symmetry remains in the cubic Fd-3m space group across the quantum critical point. Comparing pressure tuning and the chemical series R2Ir2O7 reveals that the suppression of the AIAO order and the approach to the spin-disordered state is characterized by contrasting evolutions of both the pyrochlore lattice constant a and the trigonal distortion x. The former affects the 5d bandwidth, the latter the Ising anisotropy, and as such we posit that the opposite effects of pressure and chemical tuning lead to spin fluctuations with different Ising and Heisenberg character in the quantum critical region. Finally, the observed low-pressure scale of the AIAO quantum phase transition in Sm2Ir2O7 identifies a circumscribed region of P-T space for investigating the putative magnetic Weyl-semimetal state.

Effect of perturbations on the kagome S=12 antiferromagnet at all temperatures

The ground state of the $S=\frac{1}{2}$ kagome Heisenberg antiferromagnet is now recognized as a spin liquid, but its precise nature remains unsettled, even if more and more clues point towards a gapless spin liquid. We use high-temperature series expansions (HTSEs) to extrapolate the specific heat ${c}_{V}(T)$ and the magnetic susceptibility $\ensuremath{\chi}(T)$ over the full temperature range, using an improved entropy method with a self-determination of the ground-state energy per site ${e}_{0}$. Optimized algorithms give HTSE coefficients up to unprecedented orders (20 in $1/T$) and as exact functions of the magnetic field. Three extrapolations are presented for different low-$T$ behaviors of ${c}_{V}$: exponential (for a gapped system), and linear or quadratic (for two different types of gapless spin liquids). We study the effects of various perturbations to the Heisenberg Hamiltonian: Ising anisotropy, Dzyaloshinskii-Moriya interactions, second- and third-neighbor interactions, and randomly distributed magnetic vacancies. We propose an experimental determination of $\ensuremath{\chi}(T=0)$, which could be nonzero, from ${c}_{V}$ measurements under different magnetic fields.

Role of the spin anisotropy of the interchain interaction in weakly coupled antiferromagnetic Heisenberg chains**Project supported by the National Natural Science Foundation of China (Grant No. 11674392), the Ministry of Science and Technology of China, National Program on Key Research Project (Grant No. 2016YFA0300504), and the Research Funds of Remnin University of China (Grant No. 18XNLG24). R.Y. acknowledges the hospitality

In quasi-one-dimensional (q1D) quantum antiferromagnets, the complicated interplay of intrachain and interchain exchange couplings may give rise to rich phenomena. Motivated by recent progress on field-induced phase transitions in the q1D antiferromagnetic (AFM) compound YbAlO3, we study the phase diagram of spin-1/2 Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations, and investigate the role of the spin anisotropy of the interchain coupling on the ground state of the system. We find that the Ising anisotropy of the interchain coupling can significantly enhance the longitudinal spin correlations and drive the system to an incommensurate AFM phase at intermediate magnetic fields, which is understood as a longitudinal spin density wave (LSDW). With increasing field, the ground state changes to a canted AFM order with transverse spin correlations. We further provide a global phase diagram showing how the competition between the LSDW and the canted AFM states is tuned by the Ising anisotropy of the interchain coupling.

Butterfly-shaped magnetoresistance in triangular-lattice antiferromagnet Ag2CrO2

Spintronic devices using antiferromagnets (AFMs) are promising candidates for future applications. Recently, many interesting physical properties have been reported with AFM-based devices. Here we report a butterfly-shaped magnetoresistance (MR) in a micrometer-sized triangular-lattice antiferromagnet Ag2CrO2. The material consists of two-dimensional triangular-lattice CrO2 layers with antiferromagnetically coupled S = 3/2 spins and Ag2 layers with high electrical conductivity. The butterfly-shaped MR appears only when the magnetic field is applied perpendicularly to the CrO2 plane with the maximum MR ratio (≈15%) at the magnetic ordering temperature. These features are distinct from those observed in conventional magnetic materials. We propose a theoretical model where fluctuations of partially disordered spins with the Ising anisotropy play an essential role in the butterfly-shaped MR in Ag2CrO2.

Unfolding of antiferromagnetic phases and multicritical points in a two-orbital model for uranium compounds under pressure and magnetic field

We investigate the occurrence of multicritical points under pressure and magnetic field in a model that describes two $5f$ bands (of either $\ensuremath{\alpha}$ or $\ensuremath{\beta}$ characters), which hybridize with a single itinerant conduction band. The $5f$ electrons interact through Coulomb and exchange terms. The antiferromagnetic (AF) order parameter is a N\'eel vector, which is assumed to be fixed by an Ising anisotropy. The applied magnetic field is transverse to the anisotropy axis. Without field, our results for the temperature-pressure phase diagram show that at low temperatures a first-order phase transition occurs between two distinct antiferromagnetic phases, ${\mathrm{AF}}_{1}$ and ${\mathrm{AF}}_{2}$, as the pressure is increased. The two phases are characterized by the gaps of bands $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ given by ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\alpha}}$ and ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\beta}}$, respectively. The ${\mathrm{AF}}_{1}$ phase occurs when ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\beta}}>{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\alpha}}>0$, while in the ${\mathrm{AF}}_{2}$ phase the gaps satisfy ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\alpha}}>{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\beta}}>0$. The application of a magnetic field produces a drastic change in the phase diagram. The ${\mathrm{AF}}_{1}$ and ${\mathrm{AF}}_{2}$ phases separate, with the latter acquiring a dome shape that is eventually suppressed for large values of the applied field. The evolution of the phase diagram under pressure, without and with magnetic field, shows the presence of multicritical points. Our results show that the evolution of these multicritical points by the simultaneous application of pressure and magnetic field is also drastic, with the suppression of some multicritical points and the emergence of others. We believe that these results may have relevance for the growing field of multicritical points (classical and quantum) in the physics of uranium compounds.