Spin Frustration Research Articles

Influence of isothermal structural transition on the magnetic properties of Cr doped Bi0.86Nd0.14FeO3 multiferroics

In this work, we have studied the crystal structure, microstructure, magnetic properties, and the effect of isothermal structural transition on the magnetic properties of Bi0.86Nd0.14Fe1-xCrxO3 (0.02 ≤ x ≤ 0.1) ceramic compounds. The analysis of X-ray diffraction patterns reveals a mixture of the R3c rhombohedral and PbZrO3-type orthorhombic phases. With increasing Cr concentration, the PbZrO3-type phase percentage is gradually increased from 33% for x = 0.02–63% for x = 0.1 at the expense of the R3c phase. The magnetic properties of compounds are mainly attributed to the destruction of the long-range incommensurate cycloidal spin structure in the orthorhombic symmetry. The isothermal structural transition (IST) is observed at room temperature when samples are stored in laboratory conditions. A remarkable change of magnetic properties is observed, which is believed originated from the IST and spin frustration at the phase boundary.

Spin dynamics and magnetic ordering in the quasi-one-dimensional S=12 antiferromagnet Na2CuSO4Cl2

The $S=\frac{1}{2}$ quasi-one-dimensional antiferromagnet ${\mathrm{K}}_{2}{\mathrm{CuSO}}_{4}{X}_{2}\phantom{\rule{4pt}{0ex}}(X=\mathrm{Cl}$, Br) exhibits peculiar Dzyaloshinskii-Moriya (DM) interactions that are uniform along its spin chains and antiparallel with respect to neighboring chains. This feature has received much attention recently because it leads to spin frustration, however, the spin dynamics around ${T}_{\mathrm{N}}$ and magnetic structure have not been reported. Here we report magnetic behaviors of ${\mathrm{Na}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Cl}}_{2}$. The orthorhombic crystal structure of ${\mathrm{Na}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Cl}}_{2}$, which is identical to $\mathrm{K}{\phantom{\rule{0.16em}{0ex}}}_{2}{\mathrm{CuSO}}_{4}{X}_{2}$, was verified. The results of the thermodynamic measurements suggest that this compound has moderately strong intra- and interchain interaction for investigation of the spin state around ${T}_{\mathrm{N}}$. The inelastic neutron scattering and muon spin relaxation and rotation measurements reveal the presence of a two-spinon continuum, and below ${T}_{\mathrm{N}}$, the long-range order develops. However, the obtained critical exponent is $\ensuremath{\beta}=0.18$, which is not indicative of a three-dimensional magnetic system; instead, one-dimensional (1D) spin correlation likely affects the formation of magnetic ordering in ${\mathrm{Na}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Cl}}_{2}$. There is a possibility that ${\mathrm{Na}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Cl}}_{2}$ is a model compound for investigation of DM-induced frustration effects in a 1D quantum spin system.

Magnetocaloric effect in molecular spin clusters and their assemblies: Exact and Monte Carlo studies using exact cluster eigenstates

Frustrated magnetic molecules are promising alternatives to refrigerant materials for low temperature magnetic refrigeration. We investigate the magnetocaloric effect (MCE) in un-frustrated and frustrated spin clusters formed from spin chains of six sites, with site spins s=1,3/2 and 2 possessing site diagonal anisotropies and anisotropic exchange interactions, using exact diagonalization method. We also study MCE in spin clusters, on a chain, a 2-D square lattice and a 3-D cubic lattice with spin-dipolar interactions by a Monte Carlo method in spin-1 systems which uses exact eigenstates of a cluster. The magnetocaloric effect is closely related to the magnetic Grüneisen parameter ΓH. In this paper, we compute the magnetic Grüneisen parameter ΓH, and study its dependence on exchange anisotropy and spin-dipolar interaction. With increase of exchange anisotropy, the maxima in ΓH shifts to higher magnetic fields and becomes a sharp singularity. The singularities in ΓH correlate with cusps in the entropy as a function of magnetic field strength, and with crossover in the magnetization in the ground state in isolated clusters. The first maximum in ΓH shifts to lower fields as we increase spin-dipolar interaction. The first maximum in ΓH also shifts to lower magnetic field strength as the magnitude of the site spin increases. We show the dependence of ΓH on the dimensionality of the lattice for a fixed lattice constant.

Mapping of Solvent-Mediated Molecular Self-Assembly of Iron(III) Discrete Compounds: Exploring Their Magnetic Behavior and Phosphatase-Like Activity

Two newly synthesized Fe(III) based complexes, [Fe4L2(μ3-O)2(Cl)2(MeOH)4(H2O)4](ClO4)2.4H2O.MeOH (1) and [Fe2L3].4DMF (2) were isolated as solid crystalline form using the reaction of iron(III) perchlorate with the ligand H2L (H2L = 6,6’-((1E,1’E)-hydrazine-1,2-diylidenebis(methanylylidene))bis(2-methoxyphenol). (DMF= N,N-dimethylformamide, MeOH = methanol). Compound 1 was self-assembled in MeOH but when solvent was changed to DMF, compound 2 was harvested. Further, compound 1 was converted to compound 2 just by dissolving compound 1 in DMF. Sequential self-assembly and conversion of compound 1 to 2 were monitored by UV-Vis spectroscopy and ESI-Mass spectroscopy in solution phase. Single crystal X-ray analysis showed that compound 1 has μ3-oxo bridged tetranuclear structure whereas compound 2 has puckered di-nuclear structure. Magnetic studies indeed revealed frustrated magnetic spin for compound 1 whereas antiferromagnetic interaction was observed for compound 2. The spectrophotometrical investigation on...

Structural transition and magnetic properties of Mn doped Bi0.88Sm0.12FeO3 ceramics.

We investigated the effects of Mn doping on the crystal structure, phonon vibration, and magnetic properties of Bi0.88Sm0.12FeO3 ceramics. Mn doping effectively modified the rhombohedral symmetry and induced a structural transition from an R3c rhombohedral to Pnam orthorhombic structure. Magnetic measurements revealed a weak ferromagnetic behavior, which was related to the canted antiferromagnetic order of the Pnam structure. The cycloidal spin structure of the R3c phase could not be suppressed by substitution of Mn at the Fe site. Studies on the self-phase transition and electric field-induced structural transition revealed many changes in coercivity and remanent magnetization, which are believed to originate from the R3c/Pnam phase switching along with spin frustration. Observations of the field step-dependent hysteresis loop and the ferromagnetic-like hysteresis loop after poling in an electric field provided direct evidence of phase boundary (PB) ferromagnetism and magnetic coupling at the PB.

Launching a new dimension with 3D magnetic nanostructures

The scientific and technological exploration of three-dimensional magnetic nanostructures is an emerging research field that opens the path to exciting novel physical phenomena, originating from the increased complexity in spin textures, topology, and frustration in three dimensions. One can also anticipate a tremendous potential for novel applications with those systems in a magnetic sensor and information processing technologies in terms of improved energy efficiency, processing speed, functionalities, and miniaturization of future spintronic devices. These three-dimensional structures are distinct from traditional bulk systems as they harness the scientific achievements of nanomagnetism, which aimed at lowering the dimensions down to the atomic scale, but expand those now in a tailored and designed way into the third dimension. This research update provides an overview of the scientific challenges and recent progress with regard to advances in synthesis approaches and state-of-the-art nanoscale characterization techniques that are prerequisite to understand, realize, and control the properties, behavior, and functionalities of three-dimensional magnetic nanostructures.

Spin nematics in frustrated spin-dimer systems with bilayer structure

We study frustrated spin-1/2 dimer systems in two dimensions with a bilayer structure, where spins are ferromagnetically coupled in dimers. Our model includes frustrated two-spin exchange interactions as well as four-spin interaction. We pay particular attention to the spin nematic phase, which does not exhibit any magnetic (spin-dipole) order but has a spin-quadrupolar long-range order. Employing a perturbation calculation, a mean-field approximation, and a numerical many-variable variational Monte Carlo method, we determine ground-state phase diagrams on various two-dimensional lattices. It is found that the model exhibits the spin nematic phase with ferro-quadrupolar order in a wide parameter region, in addition to conventional magnetically-ordered phases. In particular, it is shown that even when the four-spin interactions are absent, frustrated two-spin exchange interactions can realize the spin nematic phase as a result of strong interdimer correlations. It is also found that the phase transitions between the spin nematic phase and antiferromagnetic phases can be continuous. Furthermore, we present some exact arguments that various phases including the spin nematic phase and the vector chiral (p-type nematic) phase emerge from an SU(4) symmetric point in the model by the addition of appropriate perturbative interactions. The spin nematic phase generated from the SU(4) point is connected with the spin nematic phase found numerically in the system with only two-spin interactions.

Bis(ethylenedithio)tetrathiafulvalene Cation Radical Salts Composed of Nonuniform Silver(I) Complex Polyanions.

Rational control of the molecular arrangement in solids has been the subject of intense research for many years. In particular, the structural control of bis(ethylenedithio)tetrathiafulvalene (ET) radical cations has attracted special interest because of the primary effect on the electronic properties of the salts. In this study, we obtained the first ET cation radical salts formed with nonuniform silver(I) complex polyanions, which involve multiple kinds of openings in the anionic layer, by an electrocrystallization method. θ-(ET)2Ag2(CN)[N(CN)2]2 (1) with a θ-type ET packing motif contains double helical chains composed of AgN(CN)2, whereas α″-(ET)2Ag2(CN)(SCN)2 (2) with an α″-type ET packing motif contains zigzag ladders composed of AgSCN. Both silver(I)-based tube-like assemblies are connected to each other by a cyano group, affording nonuniform polyanionic structures. Although both salts show semiconducting behavior, there is a distinct difference in their spin geometry, with an S = 1/2 Heisenberg antiferromagnetic square lattice in 1, which is associated with charge disproportionation or dynamical charge fluctuation in the ET layers, and an S = 1/2 Heisenberg anisotropic triangular lattice in 2, which results in spin frustration in the ET layers. The ability of the nonuniform polymeric structures in the anionic layers to act as templates for various arrangements of ET radical cations is demonstrated.

Substitution Effects on Magnetic Ground States with Geometrical Spin Frustration in Triangular Spin Tubes Formed in CsCrF4 and α-KCrF4

A chemical-impurity substitution in a geometrical spin-frustrated antiferromagnet often produces an unconventional antiferromagnetic state, because the ground states of the pure systems maintain a ...

Identification of emergent constraints and hidden order in frustrated magnets using tensorial kernel methods of machine learning

Machine-learning techniques have proved successful in identifying ordered phases of matter. However, it remains an open question how far they can contribute to the understanding of phases without broken symmetry, such as spin liquids. Here we demonstrate how a machine learning approach can automatically learn the intricate phase diagram of a classical frustrated spin model. The method we employ is a support vector machine equipped with a tensorial kernel and a spectral graph analysis which admits its applicability in an effectively unsupervised context. Thanks to the interpretability of the machine we are able to infer, in closed form, both order parameter tensors of phases with broken symmetry, and the local constraints which signal an emergent gauge structure, and so characterize classical spin liquids. The method is applied to the classical XXZ model on the pyrochlore lattice where it distinguishes---among others---between a hidden biaxial spin nematic phase and several different classical spin liquids. The results are in full agreement with a previous analysis by Taillefumier \emph{et al.} [Phys. Rev. X 7, 041057 (2017)], but go further by providing a systematic hierarchy between disordered regimes, and establishing the physical relevance of the susceptibilities associated with the local constraints. Our work paves the way for the search of new orders and spin liquids in generic frustrated magnets.

Molecular spin frustration in mixed-chelate Fe5 and Fe6 oxo clusters with high ground state spin values

The synthesis, structures, and magnetic properties are reported of three new polynuclear FeIII complexes containing the anions of picolinic acid (picH) and triethanolamine (teaH3) as chelates. The complexes [Fe6O2(OH)2(O2CR)4(pic)4(teaH)2] (R = Me (1), Ph (2)) and [Fe5O2(O2CBut)4(pic)3(teaH)2] (3) were obtained from the reaction of [Fe3O(O2CR)6(H2O)3](NO3) (R = Me, Ph, But) with picH and teaH3 in a 1:2:1 ratio in MeCN. The core of 1 and 2 consists of an [Fe4(µ3-O)2]8+ ‘planar-butterfly’ unit to which is attached an Fe atom on either side by bridging O atoms. The core of 3 consists of an [Fe5(µ3-O)2]11+ unit comprising two near-perpendicular vertex-sharing [Fe3(µ3-O)]7+ triangular units. Variable-temperature (T) and -field (H) solid-state dc and ac magnetization (M) studies in the 5.0–300 K temperature range revealed that 1 and 2 have an S = 5 ground state spin whereas 3 has an S = 5/2 ground state. Jij exchange couplings were calculated by DFT and a magnetostructural correlation (MSC) for polynuclear FeIII/O complexes. This allowed rationalization of the observed ground states from the analysis of the spin frustration effects operative, and provided good input values for fits of the experimental χMT vs T data to obtain the Jij values.

Complex magnetic structure and related thermodynamic properties of Mn2SnS4

Magnetic chalcogenide compounds have a great potential in the field of spintronics and biomedical applications. Unlike magnetic transition metal oxides, the study on magnetic chalcogenides is sparse. Here we investigate the magnetic, thermodynamic and electronic properties of a ternary chalcogenide, Mn2SnS4. Contrary to most of the 214-chalcogenide compounds which crystallize in well-known olivine structure with space group Pnma, the title compound, Mn2SnS4, crystallizes in the orthorhombic space group, Cmmm. Magnetic measurements reveal two distinct magnetic transitions: (i) an antiferromagnetic ordering below 152 K, (ii) a weak ferromagnetic ordering, possibly due to spin canting and frustration below 53 K. Neutron diffraction study at 100 K suggest that the magnetic moments (spins) within {1 1 1} planes are ordered ferromagnetically and the adjacent {1 1 1} planes are coupled antiferromagnetically, however, the magnetic spins are not collinear rather canted. LMTO-ASA calculation on an antiferromagnetic model indicates that the compound is poorly metallic in nature and the manganese spins are completely spin polarized.

Dipolar Cairo lattice: Geometrical frustration and short-range correlations

We have studied low-energy configurations in two-dimensional arrays consisting of Ising-type dipolar coupled nanomagnets lithographically defined onto a two-dimensional Cairo lattice, thus dubbed the dipolar Cairo lattice. Employing synchrotron-based photoemission electron microscopy (PEEM), we perform real-space imaging of moment configurations achieved after thermal annealing. These states are then characterized in terms of vertex populations, spin- and emergent magnetic charge correlations, and a topology-enforced emergent ice rule. The results reveal a strong dominance of short-range correlations and the absence of long-range order, reflecting the high degree of geometrical spin frustration present in this example of an artificial frustrated spin system.

Specific Heat Study of 1D and 2D Excitations in the Layered Frustrated Quantum Antiferromagnets Cs_{2}CuCl_{4-x}Br_{x}.

We report an experimental and theoretical study of the low-temperature specific heat C and magnetic susceptibility χ of the layered anisotropic triangular-lattice spin-1/2 Heisenberg antiferromagnets Cs_{2}CuCl_{4-x}Br_{x} with x=0, 1, 2, and 4. We find that the ratio J^{'}/J of the exchange couplings ranges from 0.32 to ≈0.78, implying a change (crossover or quantum phase transition) in the materials' magnetic properties from one-dimensional (1D) behavior for J^{'}/J<0.6 to two-dimensional (2D) behavior for J^{'}/J≈0.78. For J^{'}/J<0.6, realized for x=0, 1, and 4, we find a magnetic contribution to the low-temperature specific heat, C_{m}∝T, consistent with spinon excitations in 1D spin-1/2 Heisenberg antiferromagnets. Remarkably, for x=2, where J^{'}/J≈0.78 implies a 2D magnetic character, we also observe C_{m}∝T. This finding, which contrasts the prediction of C_{m}∝T^{2} made by standard spin-wave theories, shows that Fermi-like statistics also plays a significant role for the magnetic excitations in spin-1/2 frustrated 2D antiferromagnets.

Magnetic ground state of the frustrated spin- 12 chain compound β–TeVO4 at high magnetic fields

Frustrated spin-1/2 chains, despite the apparent simplicity, exhibit remarkably rich phase diagram comprising vector-chiral (VC), spin-density-wave (SDW) and multipolar/spin-nematic phases as a function of the magnetic field. Here we report a study of $\beta$-TeVO$_4$, an archetype of such compounds, based on magnetization and neutron diffraction measurements up to 25 T. We find the transition from the helical VC ground state to the SDW state at $\sim$3 T for the magnetic field along the $a$ and $c$ crystal axes, and at $\sim$9 T for the field along the $b$ axis. The high-field (HF) state, existing above $\sim$18 T, i.e., above $\sim$1/2 of the saturated magnetization, is an incommensurate magnetically ordered state and not the spin-nematic state, as theoretically predicted for the isotropic frustrated spin-1/2 chain. The HF state is likely driven by sizable interchain interactions and symmetric intrachain anisotropies uncovered in previous studies. Consequently, the potential existence of the spin nematic phase in $\beta$-TeVO$_4$ is limited to a narrow field range, i.e., a few tenths of a tesla bellow the saturation of the magnetization, as also found in other frustrated spin-1/2 chain compounds.

Geometrically frustrated anisotropic four-leg spin-1/2 nanotube

We develop a real space quantum renormalization group (QRG) to explore a frustrated anisotropic four-leg spin-1/2 nanotube in the thermodynamic limit. We obtain the phase diagram, fixed points, critical points, the scaling of coupling constants and magnetization curves. Our investigation points out that, in the case of strong leg coupling, the diagonal frustrating interaction is marginal under QRG transformations and does not affect the universality class of the model. Remarkably, the renormalization equations express that the spin nanotube prepared in the strong leg coupling case goes to the strong plaquette coupling limit (weakly interacting plaquettes). Subsequently, in the limit of weakly interacting plaquettes, the model is mapped onto a 1D spin-1/2 XXZ chain in a longitudinal magnetic field under QRG transformation. Furthermore, the effective Hamiltonian of the spin nanotube inspires both first and second order phase transitions accompanied by the fractional magnetization plateaus. Our results show that the anisotropy changes the magnetization curve and the phase transition points, significantly. Finally, we report the numerical exact diagonalization results to compare the ground state phase diagram with our analytical visions.

Magnon Pairs and Spin-Nematic Correlation in the Spin Seebeck Effect.

Investigating exotic magnetic materials with spintronic techniques is effective at advancing magnetism as well as spintronics. In this work, we report unusual field-induced suppression of the spin Seebeck effect (SSE) in a quasi-one-dimensional frustrated spin-1/2 magnet LiCuVO_{4}, known to exhibit spin-nematic correlation in a wide range of external magnetic field B. The suppression takes place above |B|≳2 T in spite of the B-linear isothermal magnetization curves in the same B range. The result can be attributed to the growth of the spin-nematic correlation while increasing B. The correlation stabilizes magnon pairs carrying spin 2, thereby suppressing the interfacial spin injection of SSE by preventing the spin-1 exchange between single magnons and conduction electrons at the interface. This interpretation is supported by integrating thermodynamic measurements and theoretical analysis on the SSE.

Universal lowest energy configurations in a classical Heisenberg model describing frustrated systems with wheel geometry

We minimize the energy function of the classical Heisenberg model describing the frustrated wheel shape systems consisting of an odd number of spin vectors, where a single vector is located at the center and the remaining vectors occupy $n$ sites on a ring. Using the Lagrange manifold method developed recently, we find the exact geometrical configurations of the spin vectors corresponding to the global energy minima. We reveal two subsets of collinear $n/2$ spin vectors which are tilted by an angle $\ensuremath{\psi}$ in the opposite direction with respect to that fixed by the central vector. We prove that $\ensuremath{\psi}$ does not depend on $n$ and all the spin vectors are collinear, if the system is nonfrustrated or it is subject to weak frustration, otherwise the sublattices start to rotate. In this frustration region, the configurations are double degenerate and differ by chirality. Our findings confirm that the classification of spin frustration holds in the classical limit and allows us to discriminate different regions by the proper configurations. We demonstrate the correspondence between the total spin in the ground state of the quantum model and a component of the net total spin vector which can be exploited in analysis of the quantum models and physical complexes.

Frustration phenomenon in the spin-1/2 Ising–Heisenberg planar model of inter-connected trigonal bipyramid structures

Ground-state and finite-temperature properties of the exactly solvable mixed spin-1/2 Ising–Heisenberg planar model composed of identical trigonal bipyramids that are arranged into a regular archimedean lattice are examined with the aim to clarify the frustration phenomenon at zero and finite temperatures. It is shown that the ground-state spin frustration persists even far above the second-order phase transition. If the interaction ratio between the Heisenberg and Ising exchange interactions is close enough to the ground-state boundaries between the neighboring phases, a remarkable re-entrance of the (non-)frustrated spin arrangement of the Heisenberg spins can be observed around the critical temperature of the model. It is also evidenced that entropy and specific heat show pronounced temperature variations not only around the critical temperature, but also in low-temperature regime if values of the interaction parameters are taken from neighborhood of the ground-state phase transitions, where energies of the neighboring phases are very close.

Partition function and energy spectrum for a three-ring Ising chain with even number of spins-

An even-site spins- linear chain of cyclic in the nearest-neighbour and next-nearest-neighbour interactions has necessarily a three-ring structure. In this study, the interactions are considered to be short-range through the coupling constants J and K, respectively. For an arbitrary even number of spins-, the exact classical solution of the partition function and the pair correlations between the nearest- and next-nearest-neighbours are calculated in terms of the constants J and K, without using the energy levels and their degeneracy factors. Then, this partition function is used to verify the validity of an ansatz on the allowed energies of the chain and their corresponding degeneracy factors. The influence of next-nearest-neighbour interactions K on the specific heat capacity per spin at the low-temperatures is analysed for the ferromagnetic and antiferromagnetic chains. We especially show that specific heat capacity exhibits the spin frustration when the ferromagnetic and antiferromagnetic orders are demanded via the coupling constants J and K, respectively. Also, the maximal frustration is obtained analytically by two distinct ground levels for even number of spins-.