Spin Frustration Research Articles

High-entropy structure design in layered transition metal dichalcogenides

Layered high-entropy compounds have been attracting a lot of attention in recent times due to their potential applications in energy storage and conversion. Generally, an intra-layer scheme is widely used to realize the high-entropy structure by introducing multi-principal elements into the metal-atom layers. Here, we propose an intercalation high-entropy scheme to realize the high-entropy structure in a series of layered transition metal dichalcogenides with a general chemical formula of MX2. Multi-principal metal elements are intercalated into the van-der-Waals gaps between MX2 slabs resulting in a series of (HEM)xMX2 compounds, in which HEM is high-entropy metals mainly composed of 3d transition metal elements such as Fe0.2Co0.2Cr0.2Ni0.2Mn0.2. Moreover, three kinds of 2D high-entropy magnetic lattices (a0×a0, 3a0×a0, 3a0×3a0) in the intercalated layers are found by tuning the intercalant content x. Significant differences in the effective moment and spin frustration among them are revealed. Furthermore, a multi-layered high-entropy structure is realized by a combination of intra-layer and intercalation schemes. The new intercalation high-entropy scheme and versatile 2D high-entropy structures reported in this work will reinforce the spirit on the exploration of new low-dimensional high-entropy systems for future applications.

Templated Growth of a Spin-Frustrated Cluster Fragment of MnBr2 in a Metal-Organic Framework.

The metal-organic framework Zr6O4(OH)4(bpydc)6 (bpydc2- = 2,2'-bipyridine-5,5'-dicarboxylate) is used to template the growth of a cluster fragment of the two-dimensional solid MnBr2, which was predicted to exhibit spin frustration. Single-crystal and powder X-ray diffraction analyses reveal a cluster with 19 metal ions arranged in a triangular lattice motif. Static magnetic susceptibility measurements indicate antiferromagnetic coupling between the high-spin (S = 5/2) MnII centers, and dynamic magnetic susceptibility data suggest population of low-lying excited states, consistent with magnetic frustration. Density functional theory calculations are used to determine the energies for a subset of thousands of magnetic configurations available to the cluster. The Yamaguchi generalized spin-projection method is then employed to construct a model for magnetic coupling interactions within the cluster, enabling facile determination of the energy for all possible magnetic configurations. The confined cluster is predicted to possess a doubly degenerate, highly geometrically frustrated ground state with a total spin of STotal = 5/2.

Non-chiral spin frustration versus highly degenerate ferromagnetic state with local chiral degrees of freedom of an exactly solvable spin-electron planar model of inter-connected trigonal bipyramids

The frustration phenomenon in an exactly solvable spin-electron planar model constituted by identical bipyramidal plaquettes is discussed within the Toulouse’s and dos Santos and Lyra’s frustration concepts. It is shown that the ground state of the model contains the unfrustrated spontaneously ordered quantum ferromagnetic phase with local chiral degrees of freedom in the electron sub-lattice and the disordered quantum one, where both the Ising and electron sub-lattices are frustrated. The frustration of the latter sub-lattice persists at finite temperatures, but only in the disordered region. It finally vanishes at a certain frustration temperature. The reentrant behaviour of the frustration in the electron sub-lattice with three consecutive frustration temperatures due to a competition with the unfrustrated ferromagnetic spin arrangement near the ground-state phase transition can also be observed.

Anomalous Hall effect in antiferromagnetic Cr thin films

Bulk chromium is the simplest antiferromagnet in our general material database, which has been firmly believed to exhibit a collinear spin structure and a consequent vanishing anomalous Hall effect (AHE). In this work, we report an unexpected weak AHE in polycrystalline thin films of chromium. We attribute this phenomenon to the noncollinear spin textures induced by the local spin frustration and rearrangement in certain areas with high residual strain and defect densities. Moreover, a dominant underlying mechanism of intrinsic Berry phase is speculated. This could be a general feature for all the collinear antiferromagnetic thin-film materials with moderately high defect concentrations, making them promising candidates for emergent antiferromagnetic spintronics.

Spin Frustration in Protonated Rutile Oxides

We report the topochemical protonation of rutile oxides Rh0.5V0.5O2 and Cr0.5V0.5O2 by low-temperature hydrogen gas treatment. After the treatment, nonmagnetic V5+ (d0) ions were selectively reduce...

A comparative investigation of B-site ordering and structure, magnetic, magnetocaloric effect, critical behavior in double perovskite Nd2BMnO6 (B = Co and Ni)

In the present work, we have investigated the crystal structure, magnetic, and magnetocaloric properties of the ordered monoclinic polycrystalline double perovskite Nd2BMnO6 (B = Co and Ni). A study of the magnetization dynamics employing temperature and magnetic field shows a powerful spin frustration state with freeing temperature of Tf ~154 K (for Nd2CoMnO6) and Tf ~ 194 K (for Nd2NiMnO6). The ac susceptibility measurements show exhibit frequency- and field-dependent behavior. Both the magnetic relaxation effects and related analysis indicate a typical spin-glass (SG) behavior in Nd2BMnO6. Furthermore, Nd2CoMnO6 (NCMO) and Nd2NiMnO6 (NNMO) show remarkable magnetocaloric effect (MCE) and relative cooling power (RCP) near the paramagnetic (PM) to ferromagnetic (FM) transition. Moreover, the critical behavior is investigated by different theoretical, such as modified Arrott plot (MAP) and Kouvel-Fisher (KF). The critical exponents (β, γ, and δ) of Nd2BMnO6 are obtained from the different methods, which are close to the mean-field model. The detailed analysis on the critical behavior in Nd2BMnO6, which suggests that the long-range FM interaction in the Nd2BMnO6.

Tension-free Dirac strings and steered magnetic charges in 3D artificial spin ice

3D nano-architectures presents a new paradigm in modern condensed matter physics with numerous applications in photonics, biomedicine, and spintronics. They are promising for the realization of 3D magnetic nano-networks for ultra-fast and low-energy data storage. Frustration in these systems can lead to magnetic charges or magnetic monopoles, which can function as mobile, binary information carriers. However, Dirac strings in 2D artificial spin ices bind magnetic charges, while 3D dipolar counterparts require cryogenic temperatures for their stability. Here, we present a micromagnetic study of a highly frustrated 3D artificial spin ice harboring tension-free Dirac strings with unbound magnetic charges at room temperature. We use micromagnetic simulations to demonstrate that the mobility threshold for magnetic charges is by 2 eV lower than their unbinding energy. By applying global magnetic fields, we steer magnetic charges in a given direction omitting unintended switchings. The introduced system paves the way toward 3D magnetic networks for data transport and storage.

Fracton excitations in classical frustrated kagome spin models

Fractons are topological quasiparticles with limited mobility. While there exist a variety of models hosting these excitations, typical fracton systems require rather complicated many-particle interactions. Here, we discuss fracton behavior in the more common physical setting of classical kagome spin models with frustrated two-body interactions only. We investigate systems with different types of elementary spin degrees of freedom (three-state Potts, XY, and Heisenberg spins) which all exhibit characteristic subsystem symmetries and fractonlike excitations. The mobility constraints of isolated fractons and bound fracton pairs in the three-state Potts model are, however, strikingly different compared to the known type-I or type-II fracton models. One may still explain these properties in terms of type-I fracton behavior and construct an effective low-energy tensor gauge theory when considering the system as a two-dimensional cut of a three-dimensional cubic lattice model. Our extensive classical Monte Carlo simulations further indicate a crossover into a low-temperature glassy phase where the system gets trapped in metastable fracton states. Moving on to XY spins, we find that in addition to fractons the system hosts fractional vortex excitations. As a result of the restricted mobility of both types of defects, our classical Monte Carlo simulations do not indicate a Kosterlitz-Thouless transition but again show a crossover into a glassy low-temperature regime. Finally, the energy barriers associated with fractons vanish in the case of Heisenberg spins, such that defect states may continuously decay into a ground state. These decays, however, exhibit a power-law relaxation behavior which leads to slow equilibration dynamics at low temperatures.

Energy levels and their degeneracies for two-ring Ising chains of spins-$$\frac{1}{2}$$ with NN and NNN couplings: spin frustration of ferromagnetic and antiferromagnetic orders

Energy levels and their degeneracies for two-ring Ising chains of spins-$$\frac{1}{2}$$ with NN and NNN couplings: spin frustration of ferromagnetic and antiferromagnetic orders

Quantum phases and spin liquid properties of 1T-TaS2

Quantum materials exhibiting magnetic frustration are connected to diverse phenomena, including high Tc superconductivity, topological order, and quantum spin liquids (QSLs). A QSL is a quantum phase (QP) related to a quantum-entangled fluid-like state of matter. Previous experiments on QSL candidate materials are usually interpreted in terms of a single QP, although theories indicate that many distinct QPs are closely competing in typical frustrated spin models. Here we report on combined temperature-dependent muon spin relaxation and specific heat measurements for the triangular-lattice QSL candidate material 1T-TaS2 that provide evidence for competing QPs. The measured properties are assigned to arrays of individual QSL layers within the layered charge density wave structure of 1T-TaS2 and their characteristic parameters can be interpreted as those of distinct Z2 QSL phases. The present results reveal that a QSL description can extend beyond the lowest temperatures, offering an additional perspective in the search for such materials.

Exchange Bias in a Layered Metal-Organic Topological Spin Glass.

The discovery of conductive and magnetic two-dimensional (2D) materials is critical for the development of next generation spintronics devices. Coordination chemistry in particular represents a highly versatile, though underutilized, route toward the synthesis of such materials with designer lattices. Here, we report the synthesis of a conductive, layered 2D metal–organic kagome lattice, Mn3(C6S6), using mild solution-phase chemistry. Strong geometric spin frustration in this system mediates spin freezing at low temperatures, which results in glassy magnetic dynamics consistent with a rare geometrically frustrated (topological) spin glass. Notably, we show that this geometric frustration engenders a large, tunable exchange bias of 1625 Oe in Mn3(C6S6), providing the first example of exchange bias in a coordination solid or a topological spin glass. Exchange bias is a critical component in a number of spintronics applications, but it is difficult to rationally tune, as it typically arises due to structural disorder. This work outlines a new strategy for engineering exchange bias systems using single-phase, crystalline lattices. More generally, these results demonstrate the potential utility of geometric frustration in the design of new nanoscale spintronic materials.

Structural evolution and magnetic properties of Bi0.86Nd0.14Fe1-xTixO3 ceramics

Ceramic Bi0.86Nd0.14Fe1-xTixO3 (0.02 ≤ x ≤ 0.1) compounds were prepared to study the structural evolution, microstructure, and magnetic properties. The structural analysis by X-ray diffraction and Rietveld refinement revealed a coexistence of the polar rhombohedral (R3c symmetry) and antipolar orthorhombic (Pbam symmetry) structures over the entire composition range, while Raman scattering spectroscopy detected not only the phonon vibrations of the R3c and Pbam but also the Pbnm symmetries. The microstructure investigation showed the small and large grain size regions corresponding to the R3c and Pbam/Pbnm phases, respectively. The dependence of magnetization on the Ti concentration suggested that the weak ferromagnetism observed in the compounds arised from the intrinsic collapse of cycloidal order rather than defect-induced magnetism. The magnetic aging observed at room temperature was explained on the basic of phase switching and spin frustration at the phase boundary. The influence of phase switching induced by an external electric field on the magnetic properties was also studied to reveal the contribution of phase boundary spins to the net magnetization.

Spin glass feature and exchange bias effect in metallic Pt/antiferromagnetic LaMnO3 heterostructure

Emergent phenomena at interfaces have been investigated intensely in pursuit of the next generation spintronics. In this work, we have integrated heterostructure consisting of paramagnetic (PM) metallic Pt and antiferromagnetic (AFM) insulator LaMnO3 (LMO). High-quality Pt (3 nm)/LMO (100 nm) heterostructure has been obtained by pulsed laser deposition. The structure, lattice strain and magnetic properties of epitaxial Pt/LMO heterostructure are fully studied. Due to the high sensitivity of synchrotron radiation and the high quality of epitaxial layer, the reflection intensity of the 3 nm-thick ultrathin Pt layer and LMO layer can be detected, and then lattice strain can be calculated. The LMO layer is under relative large tensile strain (2.13%), while the Pt layer is under relative small compressive strain (−0.46%). Magnetization measurements suggest that unexpected ferromagnetic behavior is observed clearly in the PM-Pt/AFM-LMO heterostructure. Moreover, spin glass (SG) state and exchange bias (EB) is also observed in this heterostructure. SG state is observed as a result of competing magnetic orders and spin frustration at the Pt/LMO interface. The heterostructure shows the EB effect below blocking temperature (T B), which is much lower than the Néel temperature (T N) of LMO, suggesting that the EB is strongly related to the SG state. The EB originates from the coupling between the SG and AFM phases.

Quantum phase transitions in frustrated 1D Heisenberg spin systems

A class of frustrated one-dimensional periodic Heisenberg spin systems formed either by triangular unit cells with spin 1/2 or by composite unit cells formed by two different structural units, triangles and small linear segments formed by an odd number of spin-1/2 is investigated. Based on perturbative processing and numerical calculations of the density matrix renormalization group method, the gapless character of the exact energy spectrum of excitation for these systems was found. Their instability with respect to regular (Peierls) oscillations of interactions between structural units is demonstrated. The corresponding critical exponents for the energies of the ground state are estimated numerically. For some frustrated systems, a quantum phase transition associated with the spin symmetry of the ground state, caused by frustration, has been discovered.

Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe(III)4S4] Cubanes.

Polynuclear transition-metal (PNTM) clusters owe their catalytic activity to numerous energetically low-lying spin states and stable oxidation states. The characterization of their electronic structure represents one of the greatest challenges of modern chemistry. We propose a theoretical framework that enables the resolution of targeted electronic states with ease and apply it to two [Fe(III)4S4] cubanes. Through direct access to their many-body wave functions, we identify important correlation mechanisms and their interplay with the geometrical distortions observed in these clusters, which are core properties in understanding their catalytic activity. The simulated magnetic coupling constants predicted by our strategy allow us to make qualitative connections between spin interactions and geometrical distortions, demonstrating its predictive power. Moreover, despite its simplicity, the strategy provides magnetic coupling constants in good agreement with the available experimental ones. The complexes are intrinsically frustrated anti-ferromagnets, and the obtained spin structures together with the geometrical distortions represent two possible ways to release spin frustration (spin-driven Jahn–Teller distortion). Our paradigm provides a simple, yet rigorous, route to uncover the electronic structure of PNTM clusters and may be applied to a wide variety of such clusters.

Emergence of metamagnetic transition, re-entrant cluster glass and spin phonon coupling in Tb2CoMnO6

The double perovskite compound Tb2CoMnO6 has been investigated using x-ray absorption spectroscopy (XAS), Raman spectroscopy, magnetic measurements and ab initio band structure calculations. It is observed that both anti-ferromagnetic (AFM) and ferromagnetic (FM) phase coexist in this material. The presence of anti-site disorder (ASD) has been established from the analysis of neutron diffraction data. Moreover, a prominent metamagnetic transition is observed in the M(H) behavior that has been explained with the drastic reorientation of the pinned domain which are aligned antiparallel by the antiphase boundaries (APBs) at zero field. The ASD further gives rise to spin frustration at low temperature which leads to the re-entrant cluster glass ∼33 K. The coupling between phononic degree of freedom and spin in the system has also been demonstrated. It is observed that the theoretical calculation is consistent with that of the experimentally observed behavior.

Complex changes in structural parameters hidden in the universal phase diagram of the quasi-one-dimensional organic conductors (TMTTF)2X ( X=NbF6, AsF6, PF6 , and Br)

Structural parameters in quasi-one-dimensional organic conductors ${(\mathrm{TMTTF})}_{2}X$ ($X=\mathrm{Nb}{\mathrm{F}}_{6}, \mathrm{As}{\mathrm{F}}_{6}, \mathrm{P}{\mathrm{F}}_{6}$, and Br) are investigated by synchrotron x-ray diffraction. The temperature dependences of the crystal structures differ significantly between octahedral and monatomic anion systems, corresponding to the presence or absence of a charge-ordering transition. Changes in temperature and chemical pressure control the dimensionality of the lattice and the degree of dimerization. Furthermore, the antiferromagnetic and spin-Peierls ground states in this system depend on the spin frustration due to transfer integral paths between the one-dimensional chain molecules.

Spin Frustration in Double Perovskite Oxides and Oxynitrides: Enhanced Frustration in La2MnTaO5N with a Large Octahedral Rotation.

The B-site sublattice in the double perovskite oxides A2BB'O6 (B: magnetic cation; B': nonmagnetic cation) causes spin frustration, but the relationship between the structure and spin frustration remains unclear although a number of compounds have been studied. The present study systematically investigated A2MnIIB'O6 (S = 5/2) and found that the frustration factor, defined by f = |θW|/TN (θW: Weiss temperature; TN: Néel temperature), scales linearly with the tolerance factor t, i.e., octahedral rotation. Unexpectedly, La2MnTaO5N (space group: P21/n) synthesized under high pressure is more frustrated (f = 6) than oxides with similar t values, despite the large octahedral rotation due to the small t value of 0.914. Structural analysis suggests that the enhanced frustration can be attributed to the site preference of nitride anions at the equatorial positions, which reduces the variance of neighboring Mn-Mn distances. Our findings provide a new guide to control and improve spin frustration in double perovskites with multiple anions.

Quantum phases and thermodynamics of a frustrated spin-1/2 ladder with alternate Ising–Heisenberg rung interactions

We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either isotropic S-type or discrete anisotropic σ-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both S and σ-type of spins are anti-ferromagnetically aligned with each other, two nearest S spins along the rung form an anisotropic singlet bond whereas two nearest σ spins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like specific heat C v (T), magnetic susceptibility χ(T) and thermal entropy S(T) are also calculated using the transfer matrix method for various phases. The magnetic gap in the SRFM and the SLFM can be noticed from χ(T) and C v (T) curves.

Study of the Structure, Magnetic, Thermal and Electrical Characterisation of ZnCr2Se4: Ta Single Crystals Obtained by Chemical Vapour Transport.

The new series of single-crystalline chromium selenides, Ta-doped ZnCr2Se4, was synthesised by a chemical vapour transport method to determine the impact of a dopant on the structural and thermodynamic properties of the parent compound. We present comprehensive investigations of structural, electrical transport, magnetic, and specific heat properties. It was expected that a partial replacement of Cr ions by a more significant Ta one would lead to a change in direct magnetic interactions between Cr magnetic moments and result in a change in the magnetic ground state and electric transport properties of the ZnCr2−xTaxSe4 (x = 0.05, 0.06, 0.07, 0.08, 0.1, 0.12) system. We found that all the elements of the cubic system had a cubic spinel structure; however, the doping gain linearly increased the ZnCr2−xTaxSe4 unit cell volume. Doping with tantalum did not significantly change the semiconductor and magnetic properties of ZnCr2Se4. For all studied samples (0 ≤ x ≤ 0.12), an antiferromagnetic order (AFM) below TN~22 K was observed. However, a small amount of Ta significantly reduced the second critical field (Hc2) from 65 kOe for x = 0.0 (ZnCr2Se4 matrix) up to 42.2 kOe for x = 0.12, above which the spin helical system changed to ferromagnetic (FM). The Hc2 reduction can lead to strong competition among AFM and FM interactions and spin frustration, as the specific heat under magnetic fields H < Hc2 shows a strong field decrease in TN.