Spin glasses: redux: an updated experimental/materials survey

Chemical Design of Spin Frustration to Realize Topological Spin Glasses

Patterning spins to generate collective behavior is at the core of condensed matter physics. Physicists develop techniques, including the fabrication of magnetic nanostructures and precision layering of materials specifically to engender frustrated lattices. As chemists, we can access such exotic materials through targeted chemical synthesis and create new lattice types by chemical design. Here, we introduce a new approach to induce magnetic frustration on a modified honeycomb lattice through a competition of alternating antiferromagnetic (AFM) and ferromagnetic (FM) nearest-neighbor interactions. By subtly modulating these two types of interactions through facile synthetic modifications, we created two systems: (1) a topological spin glass and (2) a frustrated spin-canted magnet with low-temperature exchange bias. To design this unconventional magnetic lattice, we used a metal-organic framework (MOF) platform, Ni3(pymca)3X3 (NipymcaX where pymca = pyrimidine-2-carboxylato and X = Cl, Br). We isolated two MOFs, NipymcaCl and NipymcaBr, featuring canted Ni2+-based moments. Despite this similarity, differences in the single-ion anisotropies of the Ni2+ spins result in distinct magnetic properties for each material. NipymcaCl is a topological spin glass, while NipymcaBr is a rare frustrated magnet with low-temperature exchange bias. Density functional theory calculations and Monte Carlo simulations on the NipymcaX lattice support the presence of magnetic frustration as a result of alternating AFM and FM interactions. Our calculations enabled us to determine the ground-state spin configuration and the distribution of spin-spin correlations relative to paradigmatic kagomé and triangular lattices. This modified honeycomb lattice is similar to the electronic Kekulé-O phase in graphene and provides a highly tunable platform to realize unconventional spin physics.

Freezing of short-range ordered antiferromagnetic clusters in the CrFeTi2O7system

We report on the CrFeTi2O7(CFTO) system using a combination of x-ray diffraction, dc magnetization, ac susceptibility, specific heat and neutron diffraction measurements. CFTO is seen to crystallize in a monoclinicP21/asymmetry. It shows a glassy freezing atTf∼22 K, characterized by the observation of bifurcation between ZFC and FCχ(T) curves, frequency dispersion acrossTfin ac susceptibility, and follows Vogel-Fulcher and power law type critical dynamics, very slow relaxation of iso-thermal remanent magnetization with time and a linear temperature dependence of magnetic contribution to specific heatCmbelowTf. The microscopic neutron diffraction analysis of CFTO not only confirms the absence of long-range antiferromagnetic (AFM) ordering but also exhibits diffuse scattering due to the presence of short-range ordered AFM correlated spin clusters.

Spin-Glass States Generated in a van der Waals Magnet by Alkali-Ion Intercalation

Tuning magnetic properties in layered van der Waals (vdW) materials has captured significant attention due to the efficient control of ground states by heterostructuring and external stimuli. Electron doping by electrostatic gating, interfacial charge transfer, and intercalation is particularly effective in manipulating the exchange and spin-orbit properties, resulting in a control of Curie temperature (TC) and magnetic anisotropy. Here, an uncharted role of intercalation is discovered to generate magnetic frustration. As a model study, Na atoms are intercalated into the vdW gaps of pristine Cr2Ge2Te6 (CGT) where generated magnetic frustration leads to emerging spin-glass states coexisting with a ferromagnetic order. A series of dynamic magnetic susceptibility measurements/analysis confirms the formation of magnetic clusters representing slow dynamics with a distribution of relaxation times. The intercalation also modifies other macroscopic physical parameters including the significant enhancement of TC from 66 to 240 K and the switching of magnetic easy-hard axis direction. This study identifies intercalation as a unique route to generate emerging frustrated spin states in simple vdW crystals.

Exchange Bias Induced by the Spin-Glass-Like State in a Te-Rich FeGeTe van der Waals Ferromagnet

We have experimentally investigated the mechanism of the exchange bias in 2D van der Waals (vdW) ferromagnets by means of the anomalous Hall effect (AHE) together with the dynamical magnetization property. The temperature dependence of the AC susceptibility with its frequency response indicates a glassy transition of the magnetic property for the Te-rich FeGeTe vdW ferromagnet. We also found that the irreversible temperature dependence in the anomalous Hall voltage follows the de Almeida-Thouless line. Moreover, the freezing temperature of the spin-glass-like phase is found to correlate with the disappearance temperature of the exchange bias. These important signatures suggest that the emergence of magnetic exchange bias in the 2D van der Waals ferromagnets is induced by the presence of the spin-glass-like state in FeGeTe. The unprecedented insights gained from these findings shed light on the underlying principles governing exchange bias in vdW ferromagnets, contributing to the advancement of our understanding.

Spin-Cluster Glassy and Long-Range Ordered Magnetic States in Honeycomb-Layered Compositionally Complex Oxides Na3-xLixT2SbO6 (T = Cu1/3Ni1/3Co1/3)

The concept of high-entropy oxides has triggered extensive research of this novel class of materials because their numerous functional properties are usually not mere linear combinations of those of the components. Here, we introduce the new series of compositionally complex honeycomb-layered magnets Na3-xLixT2SbO6 (T = Cu1/3Ni1/3Co1/3). An unusual feature of the system is its nonmonotonous dependences of the monoclinic lattice parameters b and β on x. Rietveld refinement of the crystal structures of the Na and Li end members reveals apparent Sb-T site inversion in the former and considerable Li-Cu site inversion in the latter. The materials are characterized by measurements of specific heat Cp, magnetization M, and ac and dc magnetic susceptibility χ. Na3T2SbO6 exhibits sharp long-range antiferromagnetic order (TN = 10.2 K) preceded by noticeable correlation effects at elevated temperatures. The magnetic phase diagram of Na3T2SbO6 is established. Introduction of Li, just at x = 0.8, destroys AFM order, resulting in spin-cluster glass behavior attributed to Li/Cu inversion, with TG growing with x to 10.4 K at x = 3.

Low-temperature cluster spin glass transition in the single-domain NiCr2O4nanoparticles

NiCr2O4nanoparticles with average particle size ∼15 nm, a single-domain size maintains the bulk canted antiferromagnetic ground state, were synthesized by a microwave combustion method. The magnetic behavior was carefully investigated by static and dynamic magnetic susceptibility measurements. In addition to a spin-glass-like behavior below paramagnetic-ferrimagnetic transition atTC, the NiCr2O4nanoparticles demonstrate a low-temperature cluster spin glass transition below the spin canting transitionTS, which manifests itself as a magnetic anomaly peak around ∼12 K (at 100 Oe) in the zero-field cooled magnetization with a relatively stronger field dependence in a 'de Almeida-Thouless' line for spin glasses. The AC susceptibility analyses in different approaches demonstrate a larger relative peak temperature variation per frequency decade and a longer characteristic relaxation time in the order of 0.04 and 10-7s, against 0.01 and 10-9s for the high-temperature blocking, indicating the slow spin dynamics for the low-temperature cluster glassy phase. A field-temperature magnetic phase diagram is proposed for the single-domain NiCr2O4nanoparticles.

Anharmonic theory of superconductivity and its applications to emerging quantum materials

The role of anharmonicity on superconductivity has often been disregarded in the past. Recently, it has been recognized that anharmonic decoherence could play a fundamental role in determining the superconducting properties (electron-phonon coupling, critical temperature, etc) of a large class of materials, including systems close to structural soft-mode instabilities, amorphous solids and metals under extreme high-pressure conditions. Here, we review recent theoretical progress on the role of anharmonic effects, and in particular certain universal properties of anharmonic damping, on superconductivity. Our focus regards the combination of microscopic-agnostic effective theories for bosonic mediators with the well-established BCS theory and Migdal-Eliashberg theory for superconductivity. We discuss in detail the theoretical frameworks, their possible implementation within first-principles methods, and the experimental probes for anharmonic decoherence. Finally, we present several concrete applications to emerging quantum materials, including hydrides, ferroelectrics and systems with charge density wave instabilities.

Ferrocenyl-substituted nitronyl nitroxide in the design of one-dimensional magnets

By the reaction of M(hfac)2 (M = Mn(II), Co(II), Cu(II), and Zn(II); hfac is the hexafluoroacetylacetonate anion) and ferrocenyl-substituted nitronyl nitroxide (L), we succeeded in the synthesis of stable heterospin complexes: mononuclear [Zn(hfac)2L], trinuclear {[Cu(hfac)2]3L2} and chain polymer [Mn(hfac)2L]n and [Co(hfac)2L]n. The specific steric bulkiness of the ferrocenyl substituent leads to the formation of trans-type coordination polyhedra in the [Mn(hfac)2L]n and [Co(hfac)2L]n chains. The introduction of the ferrocene substituent leads to an effective weakening of intermolecular or interchain magnetic exchange coupling. Ferrimagnetic ordering was observed for one-dimensional complexes [M(hfac)2L]n (M = Mn(II), Co(II)). [Co(hfac)2L]n exhibits features of single-chain magnet behaviour: slow relaxation of magnetization below 13 K is associated with a high coercive field (54 kOe at 2 K).

Critical Insight into Pretransitional Behavior and Dielectric Tunability of Relaxor Ceramics

This model discussion focuses on links between the unique properties of relaxor ceramics and the basics of Critical Phenomena Physics and Glass Transition Physics. It indicates the significance of uniaxiality for the appearance of mean-field type features near the paraelectric-to-ferroelectric phase transition. Pretransitional fluctuations, that are increasing up to the size of a grain and leading to inter-grain, random, local electric fields are responsible for relaxor ceramics characteristics. Their impact yields the pseudospinodal behavior associated with "weakly discontinuous" local phase transitions. The emerging model redefines the meaning of the Burns temperature and polar nanoregions (PNRs). It offers a coherent explanation of "dielectric constant" changes with the "diffused maximum" near the paraelectric-to-ferroelectric transition, the sensitivity to moderate electric fields (tunability), and the "glassy" dynamics. These considerations are challenged by the experimental results of complex dielectric permittivity studies in a Ba0.65Sr0.35TiO3 relaxor ceramic, covering ca. 250 K, from the paraelectric to the "deep" ferroelectric phase. The distortion-sensitive and derivative-based analysis in the paraelectric phase and the surrounding paraelectric-to-ferroelectric transition reveal a preference for the exponential scaling pattern for ε(T) changes. This may suggest that Griffith-phase behavior is associated with mean-field criticality disturbed by random local impacts. The preference for the universalistic "critical & activated" evolution of the primary relaxation time is shown for dynamics. The discussion is supplemented by a coupled energy loss analysis. The electric field-related tunability studies lead to scaling relationships describing their temperature changes.

Cluster-Spin-Glass Magnetic Behavior and Morphology in the Coordination Polymer Alloys FeyCo1-yBTT

We report the synthesis of a series of pseudo-1D coordination polymer (CP) materials with the formula FeyCo1-yBTT (BTT = 1,3,5-benzenetrithiolate). These materials were structurally characterized by PXRD Rietveld, EXAFS, and PDF analyses, revealing that the CP superstructure enables a continuous and isomorphous alloy between the two homometallic compounds. Lower Fe loadings exhibit emergent spin glass magnetic behavior, such as memory effects and composition-dependent spin glass response time constants ranging from 6.9 × 10-9 s to 1.8 × 10-6 s. These data are consistent with the formation of spin clusters within the lattice. The magnetic behavior in these materials was modeled via replica exchange Monte Carlo simulation, which provides a good match for the experimentally measured spin glassing and magnetic phase transitions. These findings underscore how the rigid superstructure of CP and MOF scaffolds can enable the systematic tuning of physical properties, such as the spin glass behavior described here.

Near Room-Temperature Intrinsic Exchange Bias in an Fe Intercalated ZrSe2 Spin Glass

Some magnetic systems display a shift in the center of their magnetic hysteresis loop away from zero field, a phenomenon termed exchange bias. Despite the extensive use of the exchange bias effect, particularly in magnetic multilayers, for the design of spin-based memory/electronics devices, a comprehensive mechanistic understanding of this effect remains a longstanding problem. Recent work has shown that disorder-induced spin frustration might play a key role in exchange bias, suggesting new materials design approaches for spin-based electronic devices that harness this effect. Here, we design a spin glass with strong spin frustration induced by magnetic disorder by exploiting the distinctive structure of Fe intercalated ZrSe2, where Fe(II) centers are shown to occupy both octahedral and tetrahedral interstitial sites and to distribute between ZrSe2 layers without long-range structural order. Notably, we observe behavior consistent with a magnetically frustrated and multidegenerate ground state in these Fe0.17ZrSe2 single crystals, which persists above room temperature. Moreover, this magnetic frustration leads to a robust and tunable exchange bias up to 250 K. These results not only offer important insights into the effects of magnetic disorder and frustration in magnetic materials generally, but also highlight as design strategy the idea that a large exchange bias can arise from an inhomogeneous microscopic environment without discernible long-range magnetic order. In addition, these results show that intercalated TMDs like Fe0.17ZrSe2 hold potential for spintronic technologies that can achieve room temperature applications.

Short-term memory capacity analysis of Lu3Fe4Co0.5Si0.5O12-based spin cluster glass towards reservoir computing

Reservoir computing is a brain heuristic computing paradigm that can complete training at a high speed. The learning performance of a reservoir computing system relies on its nonlinearity and short-term memory ability. As physical implementation, spintronic reservoir computing has attracted considerable attention because of its low power consumption and small size. However, few studies have focused on developing the short-term memory ability of the material itself in spintronics reservoir computing. Among various magnetic materials, spin glass is known to exhibit slow magnetic relaxation that has the potential to offer the short-term memory capability. In this research, we have quantitatively investigated the short-term memory capability of spin cluster glass based on the prevalent benchmark. The results reveal that the magnetization relaxation of Co, Si-substituted Lu3Fe5O12 with spin glass behavior can provide higher short-term memory capacity than ferrimagnetic material without substitution. Therefore, materials with spin glass behavior can be considered as potential candidates for constructing next-generation spintronic reservoir computing with better performance.

Ground-State Spin Dynamics in d1 Kagome-Lattice Titanium Fluorides

Many quantum magnetic materials suffer from structural imperfections. The effects of structural disorder on bulk properties are difficult to assess systematically from a chemical perspective due to the complexities of chemical synthesis. The recently reported S = 1/2 kagome lattice antiferromagnet, (CH₃NH₃)₂NaTi₃F₁₂, 1-Ti, with highly symmetric kagome layers and disordered interlayer methylammonium cations, shows no magnetic ordering down to 0.1 K. To study the impact of structural disorder in the titanium fluoride kagome compounds, (CH₃NH₃)₂KTi₃F₁₂, 2-Ti, was prepared. It presents no detectable structural disorder and only a small degree of distortion of the kagome lattice. The methylammonium disorder model of 1-Ti and order in 2-Ti were confirmed by atomic-resolution transmission electron microscopy. The antiferromagnetic interactions and band structures of both compounds were calculated based on spin-polarized density functional theory and support the magnetic structure analysis. Three spin-glass-like (SGL) transitions were observed in 2-Ti at 0.5, 1.4, and 2.3 K, while a single SGL transition can be observed in 1-Ti at 0.8 K. The absolute values of the Curie-Weiss temperatures of both 1-Ti (-139.5(7) K) and 2-Ti (-83.5(7) K) are larger than the SGL transition temperatures, which is indicative of geometrically frustrated spin glass (GFSG) states. All the SGL transitions are quenched with an applied field >0.1 T, which indicates novel magnetic phases emerge under small applied magnetic fields. The well-defined structure and the lack of structural disorder in 2-Ti suggest that 2-Ti is an ideal model compound for studying GFSG states and the potential transitions between spin liquid and GFSG states.

Nematic ordering in the Heisenberg spin-glass system in three dimensions

Nematic ordering, where the spins globally align along a spontaneously chosen axis irrespective of direction, occurs in spin-glass systems of classical Heisenberg spins in d=3. In this system where the nearest-neighbor interactions are quenched randomly ferromagnetic or antiferromagnetic, instead of the locally randomly ordered spin-glass phase, the system orders globally as a nematic phase. This nematic ordering of the Heisenberg spin-glass system is dramatically different from the spin-glass ordering of the Ising spin-glass system. The system is solved exactly on a hierarchical lattice and, equivalently, Migdal-Kadanoff approximately on a cubic lattice. The global phase diagram is calculated, exhibiting this nematic phase, and ferromagnetic, antiferromagnetic, disordered phases. The nematic phase of the classical Heisenberg spin-glass system is also found in other dimensions d>2: We calculate nematic transition temperatures in 24 different dimensions in 2<d≤4.

Non-collinear magnetic configuration mediated exchange coupling at the interface of antiferromagnet and rare-earth nanolayers

Mn[Formula: see text]Ir/CoFe bilayer is a prototypical exchange-coupled antiferromagnet (AF)-ferromagnet (FM) system. Nevertheless, a strong exchange coupling between FM and rare-earth(RE) interfaces of Fe/Dy and Fe/Tb has been established earlier. Strong coupling at the FM-RE interface originates from the number of irreversible spins owing to the imbalance in the non-collinear configuration in RE. However, exchange coupling between AF-RE could not be established due to the minimal number of irreversible spins in AF and RE. A frustrated inter-domain magnetic interaction leads to the coexistence of spin-freezing-like ordering around the temperature range of helical spin modulation at the exchange-coupled interfaces of RE-based specimens. To overcome the lack of coupling between the AF-RE interface, we use a sandwich structure of AF-FM-RE layers (Mn[Formula: see text]Ir/CoFe/Dy) as we demonstrate establishing considerable exchange bias in the system. Changing the bias direction during field cooling introduces possible differences in non-collinear directions (helicities), which affects the number of irreversible spins and consequent exchange coupling differently for opposite directions. The non-collinear structures in RE are topologically stable; thus, their directions of orientation can be regarded as an additional degree of freedom, which can be manipulated in all-spin-based technology.

Crossover From Individual to Collective Magnetism in Dense Nanoparticle Systems: Local Anisotropy Versus Dipolar Interactions

Dense systems of magnetic nanoparticles may exhibit dipolar collective behavior. However, two fundamental questions remain unsolved: i) whether the transition temperature may be affected by the particle anisotropy or it is essentially determined by the intensity of the interparticle dipolar interactions, and ii) what is the minimum ratio of dipole-dipole interaction (E_dd ) to nanoparticle anisotropy (K_ef V, anisotropy⋅volume) energies necessary to crossover from individual to collective behavior. A series of particle assemblies with similarly intense dipolar interactions but widely varying anisotropy is studied. The K_ef  is tuned through different degrees of cobalt-doping in maghemite nanoparticles, resulting in a variation of nearly an order of magnitude. All the bare particle compacts display collective behavior, except the one made with the highest anisotropy particles, which presents "marginal" features. Thus, a threshold of K_ef V/E_dd  ≈ 130 to suppress collective behavior is derived, in good agreement with Monte Carlo simulations. This translates into a crossover value of ≈1.7 for the easily accessible parameter T_MAX (interacting)/T_MAX (non-interacting) (ratio of the peak temperatures of the zero-field-cooled magnetization curves of interacting and dilute particle systems), which is successfully tested against the literature to predict the individual-like/collective behavior of any given interacting particle assembly comprising relatively uniform particles.

Magnetic order and disorder environments in superantiferromagnetic [Formula: see text] nanoparticles

Magnetic nanoparticles exhibit two different local symmetry environments, one ascribed to the core and one corresponding to the nanoparticle surface. This implies the existence of a dual spin dynamics, leading to the presence of two different magnetic arrangements governed by different correlation lengths. In this work, two ensembles of [Formula: see text] nanoparticles with mean sizes of 18 nm and 13 nm have been produced to unravel the magnetic couplings established among the magnetic moments located within the core and at the nanoparticle surface. To this end, we have combined neutron diffraction measurements, appropriate to investigate magnetically-ordered spin arrangements, with time-dependent macroscopic AC susceptibility measurements to reveal memory and aging effects. The observation of the latter phenomena are indicative of magnetically-frustrated states. The obtained results indicate that, while the [Formula: see text] magnetic moments located within the nanoparticle core keep the bulk antiferromagnetic commensurate structure in the whole magnetic state, the correlations among the surface spins give rise to a collective frustrated spin-glass phase. The interpretation of the magnetic structure of the nanoparticles is complemented by specific-heat measurements, which further support the lack of incommensurability in the nanoparticle state.

Site-Selective d10/d0 Substitution in an S = 1/2 Spin Ladder Ba2CuTe1-xWxO6 (0 ≤ x ≤ 0.3)

Isovalent nonmagnetic d10 and d0 B″ cations have proven to be a powerful tool for tuning the magnetic interactions between magnetic B' cations in A2B'B″O6 double perovskites. Tuning is facilitated by the changes in orbital hybridization that favor different superexchange pathways. This can produce alternative magnetic structures when B″ is d10 or d0. Furthermore, the competition generated by introducing mixtures of d10 and d0 cations can drive the material into the realms of exotic quantum magnetism. Here, Te6+ d10 was substituted by W6+ d0 in the hexagonal perovskite Ba2CuTeO6, which possesses a spin ladder geometry of Cu2+ cations, creating a Ba2CuTe1-xWxO6 solid solution (x = 0-0.3). We find W6+ is almost exclusively substituted for Te6+ on the corner-sharing site within the spin ladder, in preference to the face-sharing site between ladders. The site-selective doping directly tunes the intraladder, Jrung and Jleg, interactions. Modeling the magnetic susceptibility data shows the d0 orbitals modify the relative intraladder interaction strength (Jrung/Jleg) so the system changes from a spin ladder to isolated spin chains as W6+ increases. This further demonstrates the utility of d10 and d0 dopants as a tool for tuning magnetic interactions in a wide range of perovskites and perovskite-derived structures.

Creating a Ferromagnetic Ground State with Tc Above Room Temperature in a Paramagnetic Alloy through Non-Equilibrium Nanostructuring

Materials with strong magnetostructural coupling have complex energy landscapes featuring multiple local ground states, thus making it possible to switch among distinct magnetic-electronic properties. However, these energy minima are rarely accessible by a mere application of an external stimuli to the system in equilibrium state. A ferromagnetic ground state, with T_c above room temperature, can be created in an initially paramagnetic alloy by nonequilibrium nanostructuring. By a dealloying process, bulk chemically disordered FeRh alloys are transformed into a nanoporous structure with the topology of a few nanometer-sized ligaments and nodes. Magnetometry and Mössbauer spectroscopy reveal the coexistence of two magnetic ground states, a conventional low-temperature spin-glass and a hitherto-unknown robust ferromagnetic phase. The emergence of the ferromagnetic phase is validated by density functional theory calculations showing that local tetragonal distortion induced by surface stress favors ferromagnetic ordering. The study provides a means for reaching conventionally inaccessible magnetic states, resulting in a complete on/off ferromagnetic-paramagnetic switching over a broad temperature range.

Structure, magnetism and magnetocaloric effect in a new triangular lattice compound Gd3Cu9(OH)19Br8

A new triangular lattice compound Gd₃Cu₉(OH)₁₉Br₈ has been synthesized by the hydrothermal method. The structure, magnetism and magnetocaloric effect of Gd₃Cu₉(OH)₁₉Br₈ have been studied by X-ray diffraction, magnetic susceptibility, isothermal magnetization and specific heat measurements. In Gd₃Cu₉(OH)₁₉Br₈, the Cu²⁺ ions form a Kagome lattice along the ab plane, and Gd³⁺ ions are located in the center of hexagonal holes of the Kagome layer. The Cu-sublattice and Gd-sublattice overlap and constitute a magnetic triangular lattice. The temperature dependence of susceptibility and specific heat curves indicate no magnetic transition down to 2 K, suggesting a paramagnetic-like behavior at low temperature. The magnetocaloric effect (MCE) at low temperature has been calculated according to Maxwell's equations. The maximum value of magnetic entropy change −ΔS_M is 26.04 J kg⁻¹ K⁻¹ and adiabatic temperature change ΔT_ad is 13.79 K, for a field change of 0–7 T, indicating a potential application of this compound in the field of magnetic refrigeration at low temperature. The influence of 4f–3d interaction on magnetism and MCE is also discussed.

The two-dimensional magnetic lattice of Gd₃Cu₉(OH)₁₉Br₈, where Gd³⁺ ions are located in the center of hexagonal holes of the Cu-Kagome lattice.

Coupled electronic and magnetic relaxation in Fe1+yTe: direct evidence for the interaction between itinerant carriers and local moments

Iron chalcogenides are of particular interests among iron-based superconductors due to their distinct properties such as high-T_con FeSe monolayer and competing magnetic correlations in Fe_1+yTe. Here we report unusual transport properties observed near the critical composition of Fe_1+yTe (y∼ 0.09) where competing magnetic correlations exist. The resistivity exhibits surprising temperature-dependent relaxation behavior belowT_N, resulting in the increase of resistivity with time for 35 K <T<T_N, but the decrease of resistivity with time for 10 K <T< 35 K. Such resistivity relaxation is intimately coupled to the magnetization relaxation and can be attributed to the glassy magnetic states induced by the competing magnetic orders. These findings demonstrate strong coupling between itinerant carriers and local ordered moments in Fe_1+yTe.

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.

Spin glass behavior and magnetic boson peak in a structural glass of a magnetic ionic liquid

Glassy magnetic behavior has been observed in a wide range of crystalline magnetic materials called spin glass. Here, we report spin glass behavior in a structural glass of a magnetic ionic liquid, C4mimFeCl4. Magnetization measurements demonstrate that an antiferromagnetic ordering occurs at TN = 2.3 K in the crystalline state, while a spin glass transition occurs at TSG = 0.4 K in the structural glass state. In addition, localized magnetic excitations were found in the spin glass state by inelastic neutron scattering, in contrast to spin-wave excitations in the ordered phase of the crystalline sample. The localized excitation was scaled by the Bose population factor below TSG and gradually disappeared above TSG. This feature is highly reminiscent of boson peaks commonly observed in structural glasses. We suggest the "magnetic" boson peak to be one of the inherent dynamics of a spin glass state.

Memory and superposition in a superspin glass

The non-equilibrium dynamics of the superspin glass state of a dense assembly of ~ 2 nm MnFe₂O₄ nanoparticles was investigated by means of magnetization, ac susceptibility and Mössbauer spectroscopy measurements and compared to the results of Monte Carlo simulations for a mesoscopic model that includes particles morphology and interparticle interactions. The zero-field cooled (ZFC), thermoremanent (TRM), and isothermal remanent magnetization (IRM) were recorded after specific cooling protocols and compared to those of archetypal spin glasses and their dimensionality. The system is found to display glassy magnetic features. We illustrate in detail, by a number of experiments, the dynamical properties of the low-temperature superspin glass phase. We observe that these glassy features are quite similar to those of atomic spin glasses. Some differences are observed, and interestingly, the non-atomic nature of the superspin glass is also reflected by an observed superspin dimensionality crossover. Monte Carlo simulations—that explicitly take into account core and surface contributions to the magnetic properties of these ultrasmall nanoparticles in direct contact, as well as interparticle interactions—evidence effects of the interplay between (intraparticle) core/surface exchange coupling and (interparticle) dipolar and exchange interactions.

Ising spin glass in a random network with a Gaussian random field

We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable parameter in our theory, allowing us to answer what the differences are between this description and the mean-field theory i.e., the fully connected theory. We have considered the random network random field Ising model where the spin exchange interaction as well as the RF are random variables following a Gaussian distribution. The results were found within the replica symmetric (RS) approximation, whose stability is obtained using the two-replica method. This also puts our work in the context of a broader discussion, which is the RS stability as a function of the connectivity. In particular, our results show that for small connectivity there is a region at zero temperature where the RS solution remains stable above a given value of the magnetic field no matter the strength of RF. Consequently, our results show important differences with the crossover between the RF and SG regimes predicted by the fully connected theory.

Non-equilibrium magnetic response of canonical spin glass and magnetic glass

Time and history dependent magnetization has been observed in a wide variety of materials, which are collectively termed as the glassy magnetic systems. However, such systems showing similar non-equilibrium magnetic response can be microscopically very different and they can be distinguished by carefully looking into the details of the observed metastable magnetic behavior. Canonical spin glass (SG) is the most well studied member of this class and has been extensively investigated both experimentally and theoretically over the last five decades. In canonical SGs, the low temperature magnetic state obtained by cooling across the SG transition temperature in presence of an applied magnetic field is known as the field cooled (FC) state. This FC state in canonical SG is widely believed as an equilibrium state arising out of a thermodynamic second order phase transition. Here, we show that the FC state in canonical SG is not really an equilibrium state of the system. We report careful dc magnetization and ac susceptibility measurements on two canonical SG systems, AuMn (1.8%) and AgMn (1.1%). The dc magnetization in the FC state shows clear temperature dependence. In addition, the magnetization shows a distinct thermal hysteresis in the temperature regime below the SG transition temperature. On the other hand, the temperature dependence of ac susceptibility has clear frequency dispersion below SG transition in the FC state prepared by cooling the sample in the presence of a dc-bias field. We further distinguish the metastable response of the FC state of canonical SG from the metastable response of the FC state in an entirely different class of glassy magnetic system namely magnetic glass, where the non-equilibrium behavior is associated with the kinetic-arrest of a first order magnetic phase transition.

Conjecture on the Design of Helical Proteins

In an important advance in our understanding of protein folding, Wolynes and Onuchic found that the frustration ratio, T_f/T_s, for funneled energy landscapes is T_f/T_s ∼1.6. In our recent work on four heme proteins, we showed that when a protein unfolds from the native state to an early unfolded state, the degree of departure is characterized by a ratio f ∼1.6, where f is a measure of the elongation of n-residue segments of the polypeptide chain. Our analysis, which accounts for this apparent similarity in calculated signatures, is based on a logistic-map model of unfolding. We offer an important take home for the de novo protein synthesis community: in order to increase the probability of obtaining good quality crystals, nearest-neighbor repulsive interactions between adjacent residues (or sequences of residues) in the polypeptide chain must be propagated correctly.

Evidence for the coexistence of spin-glass and ferrimagnetic phases in BaFe12O19 due to basal plane freezing

We present here the results of low-temperature magnetization and X-ray magnetic circular dichroism studies on the single crystals of BaFe12O19 which reveal for the first time the emergence of a spin glass phase, in coexistence with a long-range ordered ferrimagnetic phase, due to the freezing of the basal plane spin component.

Spin Symmetry Breaking: Superparamagnetic and Spin Glass-Like Behavior Observed in Rod-Like Liquid Crystalline Organic Compounds Contacting Nitroxide Radical Spins

Liquid crystalline (LC) organic radicals were expected to show a novel non-linear magnetic response to external magnetic and electric fields due to their coherent collective molecular motion. We have found that a series of chiral and achiral all-organic LC radicals having one or two five-membered cyclic nitroxide radical (PROXYL) units in the core position and, thereby, with a negative dielectric anisotropy exhibit spin glass (SG)-like superparamagnetic features, such as a magnetic hysteresis (referred to as ‘positive magneto-LC effect’), and thermal and impurity effects during a heating and cooling cycle in weak magnetic fields. Furthermore, for the first time, a nonlinear magneto-electric (ME) effect has been detected with respect to one of the LC radicals showing a ferroelectric (chiral Smectic C) phase. The mechanism of the positive magneto-LC effect is proposed and discussed by comparison of our experimental results with the well-known magnetic properties of SG materials and on the basis of the experimental results of a nonlinear ME effect. A recent theoretical study by means of molecular dynamic simulation and density functional theory calculations suggesting the high possibility of conservation of the memory of spin-spin interactions between magnetic moments owing to the ceaseless molecular contacts in the LC and isotropic states is briefly mentioned as well.

Role of spin-glass behavior in the formation of exotic magnetic states in GdB6

Randomness and frustration are believed to be two crucial criteria for the formation of spin glass state. However, the spin freezing occurs in some well-ordered crystals below the related temperature T_f due to the instability of each spin state, which induces the variation of either magnetic moment value or exchange energy. Here we explore the new mechanism of the in-site originated disorder in antiferromagnets Gd_0.73La_0.27B₆ and GdB₆, which is caused by the random mutual shifts of Gd³⁺ spins from the centrally symmetrical positions in the regular cubic lattice. The universal scaling of ESR linewidth temperature dependencies to the power law ΔH(T) ~ ((T − T_D)/T_D)^α with α = − 1.1 ± 0.05 in the paramagnetic phase of both compounds demonstrates the identity of the origin of magnetic randomness. In Gd_0.73La_0.27B₆ the resulting random spin configurations freeze at T_f ≈ 10.5 K where the maximum of magnetization is observed. Below T_f the splitting of ZFC and FC magnetization curves takes place as well as the magnetic state depends on the antecedent sample history. In the case of GdB₆ the coherent displacement of Gd ions compete with these random shifts forming an antiferromagnetic (AFM) phase at T_N = 15.5 K, which prevails over the spin freezing at T_f ≈ 13 K, expected from the ESR data. The observation of the hysteresis of the ESR spectrum in the AFM phase suggests that its properties may be determined by the competition of two types of AFM orders, which results in formation of stable magnetic domains with nonequivalent positions of AFM Gd pairs at T < 10 K.

Iron-based superelastic alloys with near-constant critical stress temperature dependence

Shape memory alloys recover their original shape after deformation, making them useful for a variety of specialized applications. Superelastic behavior begins at the critical stress, which tends to increase with increasing temperature for metal shape memory alloys. Temperature dependence is a common feature that often restricts the use of metal shape memory alloys in applications. We discovered an iron-based superelastic alloy system in which the critical stress can be optimized. Our Fe-Mn-Al-Cr-Ni alloys have a controllable temperature dependence that goes from positive to negative, depending on the chromium content. This phenomenon includes a temperature-invariant stress dependence. This behavior is highly desirable for a range of outer space-based and other applications that involve large temperature fluctuations.

Disorder-driven non-Fermi liquid behavior in itinerant ferromagnet α-Co5Ge3

The physical properties of itinerant ferromagnet [Formula: see text]-Co₅Ge₃ with both strong disorder and spin fluctuations was studied. The dc and ac susceptibility show that both spin fluctuations and disorder dominate the physical properties. In the spin glass phase, with a coexisting ferromagnetic state ([Formula: see text]30 K), both non-Fermi liquid behavior and large exponent of scaling relation of [Formula: see text] are observed and attributed to the spin fluctuations and disorder induced by cobalt defects. Upon the increase of external field, Fermi liquid behavior restores due to the suppression of spin fluctuations and disorder. In addition, a large anomalous Hall coefficient R _s is observed. Our results suggest that [Formula: see text]-Co₅Ge₃ is a typical itinerant ferromagnet to explore the interplay of disorder and spin fluctuations.

Phase diagram of a three-dimensional dipolar Ising model with textured Ising axes

We study from tempered Monte Carlo simulations the magnetic phase diagram of a textured dipolar Ising model on a face centered cubic lattice. The Ising coupling of the model follow the dipole-dipole interaction. The Ising axes are distributed with a uniaxial symmetry along the [Formula: see text] direction with a Gaussian probability density of the polar angles. This distribution provides a quenched disorder realization of the dipolar Ising model making a continuous link between the parallel axes dipoles and the random axes dipole models. As expected the phase diagram presents three distinctive phases: paramagnetic, ferromagnetic and spin-glass. A quasi long range ferromagnetic and a reentrant spin-glass phases are obtained in the vicinity of the ferromagnetic spin-glass line. This model provides a way to predict the magnetic phases of magnetic nanoparticles supracrystals in terms of the texturation of the easy axes distribution in the strong anisotropy limit.

Theory of relaxor-ferroelectricity

Relaxor-ferroelectrics are fascinating and useful materials, but the mechanism of relaxor-ferroelectricity has been puzzling the scientific community for more than 65 years. Here, a theory of relaxor-ferroelectricity is presented based on 3-dimensional-extended-random-site-Ising-model along with Glauber-dynamics of pseudospins. We propose a new mean-field of pseudospin-strings to solve this kinetic model. The theoretical results show that, with decreasing pseudospin concentration, there are evolutions from normal-ferroelectrics to relaxor-ferroelectrics to paraelectrics, especially indicating by the crossovers from, (a) the sharp to diffuse change at the phase-transition temperature to disappearance in the whole temperature range of order-parameter, and (b) the power-law to Vogel-Fulcher-law to Arrhenius-relation of the average relaxation time. Particularly, the calculated local-order-parameter of the relaxor-ferroelectrics gives the polar-nano-regions appearing far above the diffuse-phase-transition and shows the quasi-fractal characteristic near and below the transition temperature. We also provide a new mechanism of Burns-transformation which stems from not only the polar-nano-regions but also the correlation-function between pseudospins, and put forward a definition of the canonical relaxor-ferroelectrics. The theory accounts for the main facts of relaxor-ferroelectricity, and in addition gives a good quantitative agreement with the experimental results of the order-parameter, specific-heat, high-frequency permittivity, and Burns-transformation of lead magnesium niobate, the canonical relaxor-ferroelectric.

LiZn2V3O8: a new geometrically frustrated cluster spin-glass

We have investigated the structural and magnetic properties of a new cubic spinel LiZn₂V₃O₈ (LZVO) through x-ray diffraction, dc and ac susceptibility, magnetic relaxation, aging, memory effect, heat capacity and ⁷Li nuclear magnetic resonance (NMR) measurements. A Curie-Weiss fit of the dc susceptibility [Formula: see text]([Formula: see text]) yields a Curie-Weiss temperature [Formula: see text] K. This suggests strong antiferromagnetic (AFM) interactions among the magnetic vanadium ions. The dc and ac susceptibility data indicate the spin-glass behavior below a freezing temperature T _f [Formula: see text] 3 K. The frequency dependence of the T _f is characterized by the Vogel-Fulcher law and critical dynamic scaling behavior or power law. From both fitting, we obtained the value of the characteristic angular frequency [Formula: see text] [Formula: see text] 3.56 [Formula: see text] 10⁶ Hz, the dynamic exponent [Formula: see text] [Formula: see text] 2.65, and the critical time constant [Formula: see text] [Formula: see text] 1.82 [Formula: see text] 10^-6 s, which falls in the conventional range for typical cluster spin-glass (CSG) systems. The value of relative shift in freezing temperature [Formula: see text] [Formula: see text] 0.039 supports a CSG ground states. We also found aging phenomena and memory effects in LZVO. The asymmetric response of the magnetic relaxation below T _f supports the hierarchical model. Heat capacity data show no long-range or short-range ordering down to 2 K. Only about 25% magnetic entropy change [Formula: see text] signifies the presence of strong frustration in the system. The ⁷Li NMR spectra show a shift and broadening with decreasing temperature. The spin-lattice and spin-spin relaxation rates show anomalies due to spin freezing around 3 K as the bulk magnetization.

Elevated effective dimension in tree-like nanomagnetic Cayley structures

Using state-of-the-art electron-beam lithography, Ising-type nanomagnets may be defined onto nearly any two-dimensional pattern imaginable. The ability to directly observe magnetic configurations achieved in such artificial spin systems makes them a perfect playground for the realization of artificial spin glasses. However, no experimental realization of a finite-temperature artificial spin glass has been achieved so far. Here, we aim to get a significant step closer in achieving that goal by introducing an artificial spin system with random interactions and increased effective dimension: dipolar Cayley tree. Through synchrotron-based photoemission electron microscopy, we show that an improved balance of ferro- and antiferromagnetic ordering can be achieved in this type of system. This combined with an effective dimension as high as d = 2.72 suggests that future systems generated out of these building blocks can host finite temperature spin glass phases, allowing for real-time observation of glassy dynamics.

Slow relaxation of magnetization for a Tb derivative in a biradical-based lanthanide chain

Four novel lanthanide-biradical chains have been obtained and the Tb derivative reveals field-induced slow magnetic relaxation behavior with an anisotropy barrier Δ/k_B = 22.08 K.

Tunable Magnetism of Organometallic Nanoclusters by Graphene Oxide On-Surface Chemistry

Assembly of interacting molecular spins is an attractive candidate for spintronic and quantum computing devices. Here, we report on-surface chemical assembly of aminoferrocene molecules on a graphene oxide (GO) sheet and their magnetic properties. On the GO surface, organometallic molecules having individual spins through charge transfer between the molecule and the sheet are arranged in nanoclusters having diameters of about 2 nm. The synthetic fine tuning of the reaction time enables to change the interspacing between the nanoclusters, keeping their size intact. Their magnetism changes from paramagnetic behavior to collective one gradually as the interspacing decreases. The creation of collective nature among weakly interacting molecular spins through their nanoscale arrangement on the GO surface opens a new avenue to molecular magnetism.

Pressure-tuned Frustration of Magnetic Coupling in Elemental Europium

Applying linear response and the magnetic force theorem in correlated density functional theory, the intersublattice exchange constants of antiferromagnetic Eu are calculated and found to vanish near the pressure of P_{c}=82  GPa, just where magnetic order is observed experimentally to be lost. The Eu 4f^{7} moment remains unchanged at high pressure, again in agreement with spectroscopic measurements, leaving the picture of perfect frustration of interatomic Ruderman-Kittel-Kasuya-Yoshida couplings in a broad metallic background, leaving a state of electrons strongly exchange coupled to arbitrarily oriented, possibly quasistatic local moments. This strongly frustrated state gives way to superconductivity at T_{c}=1.7  K, observed experimentally. These phenomena, and free energy considerations related to correlations, suggest an unusual phase of matter that is discussed within the scenarios of the Doniach Kondo lattice phase diagram, the metallic spin glass class, and itinerant spin liquid or spin gas systems.

Frustration and Glasslike Character in RIn1- xMn xO3 (R = Tb, Dy, Gd)

We bring together ac susceptibility and dc magnetization to uncover the rich magnetic field-temperature behavior of a series of rare earth indium oxides, RInO₃ (R = Tb, Dy, and Gd). The degree of frustration is much larger than expected, particularly in TbInO₃, and the ground states are glasslike with antiferromagnetic tendencies. The activation energy for spin reorientation is low. Chemical substitution with Mn³⁺ ions to form TbIn_{1- x}Mn _xO₃ ( x ≤ 0.01) relieves much of the frustration that characterizes the parent compound and slightly enhances the short-range antiferromagnetic order. The phase diagrams developed from this work reveal the rich competition between spin orders and provide an opportunity to compare the dynamics in the RInO₃ and Mn-substituted systems. These structure-property relations may be useful for understanding magnetism in other geometrically frustrated multiferroics.

Spin-glass polyamorphism induced by a magnetic field in LaMnO3 single crystal

We present experimental evidence of field-driven transition in spin-glass state, similar to pressure-induced transition between amorphous phases in structural and metallic glasses, attributed to the polyamorphism phenomena. Cusp in temperature dependences of ac magnetic susceptibility of weakly disordered LaMnO₃ single crystal is registered below the temperature of magnetic ordering. Frequency dependence of the cusp temperature proves its spin-glass origin. The transition induced by a magnetic field in spin-glass state, is manifested by peculiarity in dependence of cusp temperature on applied magnetic field. Field dependent maximum of heat capacity is observed in the same magnetic field and temperature range.

Spin-liquid-like state in a spin-1/2 square-lattice antiferromagnet perovskite induced by d10-d0 cation mixing

A quantum spin liquid state has long been predicted to arise in spin-1/2 Heisenberg square-lattice antiferromagnets at the boundary region between Néel (nearest-neighbor interaction dominates) and columnar (next-nearest-neighbor interaction dominates) antiferromagnetic order. However, there are no known compounds in this region. Here we use d¹⁰-d⁰ cation mixing to tune the magnetic interactions on the square lattice while simultaneously introducing disorder. We find spin-liquid-like behavior in the double perovskite Sr₂Cu(Te_0.5W_0.5)O₆, where the isostructural end phases Sr₂CuTeO₆ and Sr₂CuWO₆ are Néel and columnar type antiferromagnets, respectively. We show that magnetism in Sr₂Cu(Te_0.5W_0.5)O₆ is entirely dynamic down to 19 mK. Additionally, we observe at low temperatures for Sr₂Cu(Te_0.5W_0.5)O₆-similar to several spin liquid candidates-a plateau in muon spin relaxation rate and a strong T-linear dependence in specific heat. Our observations for Sr₂Cu(Te_0.5W_0.5)O₆ highlight the role of disorder in addition to magnetic frustration in spin liquid physics.

Low temperature thermoelectric and magnetoresistive properties of Tl2Cu3FeQ4 (Q = S, Se, Te)

Layered Tl₂Cu₃FeSe₄ and Tl₂Cu₃FeTe₄ possess low thermal conductivity, of which the selenide offers promising thermoelectric features and the presence of Fe in the weakly connected Cu square-net substructure results in intriguing ferromagnetic and magnetoresistance features.

Re-entrant spin glass transitions: new insights from acoustic absorption by domain walls

Re-entrant spin glass (RSG) transitions in Ni-Mn and Au-Fe have been reassessed by acoustic measurements of the magneto-mechanical damping by domain walls. Stress-induced non-thermally activated domain wall dynamics is progressively replaced by an intense thermally activated relaxational response when the temperature approaches the RSG freezing point. A “frozen” state with negligible motion of domain walls on atomic and mesoscopic scales occurs in the RSG. We propose that RSG freezing has its origin in intrinsic properties of domain walls.

Spin liquid and infinitesimal-disorder-driven cluster spin glass in the kagome lattice

The interplay between geometric frustration (GF) and bond disorder is studied in the Ising kagome lattice within a cluster approach. The model considers antiferromagnetic short-range couplings and long-range intercluster disordered interactions. The replica formalism is used to obtain an effective single cluster model from where the thermodynamics is analyzed by exact diagonalization. We found that the presence of GF can introduce cluster freezing at very low levels of disorder. The system exhibits an entropy plateau followed by a large entropy drop close to the freezing temperature. In this scenario, a spin-liquid (SL) behavior prevents conventional long-range order, but an infinitesimal disorder picks out uncompensated cluster states from the multi-degenerate SL regime, potentializing the intercluster-disordered coupling and bringing the cluster spin-glass state. To summarize, our results suggest that the SL state combined with low levels of disorder can activate small clusters, providing hypersensitivity to the freezing process in geometrically frustrated materials and playing a key role in the glassy stabilization. We propose that this physical mechanism could be present in several geometrically frustrated materials. In particular, we discuss our results in connection with the recent experimental investigations of the Ising kagome compound Co₃Mg(OH)₆Cl₂.