Dynamics in spin glasses

Double Helix of Icosahedra Structure and Spin Glass Magnetism of the δ-Co2.5Zn17.5-xMnx (x = 0.4-3.5) Pseudo-Binary Alloys

We have synthesized δ-Co2.5Zn17.5-xMnx (x = 0.4-3.5) pseudo-binary alloys of 10 different compositions by a high-temperature solid-state synthetic route, determined their crystal structures and the Mn substitution pattern, and estimated the existence range of the δ-phase. The alloys crystallize in two chiral enantiomorphic space groups P62 and P64, where the basic atomic polyhedron of the chiral structure is an icosahedron and the neighboring icosahedra share vertices to form an infinitely long double helix along the hexagonal axis (like in the δ-Co2.5Zn17.5 parent binary phase). The alloys are pure δ-phase up to the Mn content x ≈ 3.5. The Mn atoms partially substitute Zn atoms at particular crystallographic sites located on the icosahedra. The study of magnetism was performed on the Co2.5Zn17.1Mn0.4 alloy with the lowest Mn content. Contrary to the expectation that structural chirality may induce the formation of a nontrivial magnetic state, a spin glass state with no relation to the structural chirality was found. The magnetic sublattice contains all of the necessary ingredients (randomness and frustration) for the formation of a spin glass state. Typical out-of-equilibrium dynamic phenomena of a spin system with broken ergodicity were detected below the spin freezing temperature Tf ≈ 8 K.

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.

Complex magnetism of single-crystalline AlCoCrFeNi nanostructured high-entropy alloy

We have investigated magnetism of the Al₂₈Co₂₀Cr₁₁Fe₁₅Ni₂₆ single-crystalline high-entropy alloy. The material is nanostructured, composed of a B2 matrix with dispersed spherical-like A2 nanoparticles of average diameter 64 nm. The magnetism was studied from 2 to 400 K via direct-current magnetization, hysteresis curves, alternating-current magnetic susceptibility, and thermoremanent magnetization time decay, to determine the magnetic state that develops in this highly structurally and chemically inhomogeneous material. The results reveal that the Cr-free B2 matrix of composition Al₂₈Co₂₅Fe₁₅Ni₃₂ forms a disordered ferromagnetic (FM) state that undergoes an FM transition at TC≈ 390 K. The Al- and Ni-free A2 nanoparticles of average composition Co₁₉Cr₅₆Fe₂₅ adopt a core-shell structure, where the shells of about 2 nm thickness are CoFe enriched. While the shells are FM, the nanoparticle cores are asperomagnetic, classifying into the broad class of spin glasses. Asperomagnetism develops below 15 K and exhibits broken-ergodicity phenomena, typical of magnetically frustrated systems.

Waiting time dependence of aging

Aging phenomena have been observed in many non-equilibrium systems such as polymers and glasses, where physical properties depend on the waiting time between the starting time of observation and the time when the temperature is changed. The aging is classified into two types on the basis of the waiting time dependence of an instantaneous relaxation time: When the relaxation time is always an increasing function of the waiting time, the aging is called Type I and when it depends on the protocol of the temperature change, the aging is called Type II. Aging of a random walk in three dimensions is investigated when the free energy landscape controlling the jump rate responds to temperature change with a delay. It is shown that the intermediate scattering function of the random walk model exhibits Type II aging. It is also shown that the relaxation time of the free energy landscape can be deduced from the waiting time dependence of the instantaneous relaxation time.

Memory effect and phase transition in a hierarchical trap model for spin glasses

We introduce an efficient dynamical tree method that enables us to explicitly demonstrate the thermoremanent magnetization memory effect in a hierarchical energy landscape. Our simulation nicely reproduces the nontrivial waiting-time and waiting-temperature dependences in this nonequilibrium phenomenon. We further investigate the condensation effect, in which a small set of microstates dominates the thermodynamic behavior in the multilayer trap model. Importantly, a structural phase transition of the multilayer tree model is shown to coincide with the onset of the condensation phenomenon. Our results underscore the importance of hierarchical structure and demonstrate the intimate relation between the glassy behavior and structure of barrier trees.

Structure and Spin-Glass Magnetism of the MnxNi2Zn11-x Pseudobinary γ-Brasses at Low Mn Contents

The pseudobinary Mn_xNi₂Zn_11–x γ-brass-type phases at low Mn dopant levels (x = 0.1–0.5) were investigated. Crystal structures were determined for the two loading compositions of x = 0.3 and 0.5. The structures were solved in the cubic space group of I43m and are described in close analogy to the Ni₂Zn₁₁ parent γ-brass that is based on the 26-atom cluster, consisting of inner tetrahedron (IT), outer tetrahedron (OT), octahedron (OH), and cuboctahedron (CO). The refined site occupancies of the Mn_xNi₂Zn_11–x (x = 0.3, 0.5) reveal that the cluster center, which is empty in the Ni₂Zn₁₁, shows a partial occupation by Zn, with a partial depletion of Zn at the IT sites. The OH sites show a mixed Zn/Mn occupation. The OT and CO sites remain intact with respect to Ni₂Zn₁₁. Magnetic properties were studied for the Mn_0.3Ni₂Zn_10.7 composition. The temperature-dependent zero-field-cooled and field-cooled magnetization, the ac susceptibility, the M(H) hysteresis curves, the thermoremanent magnetization, and the memory effect demonstrate typical broken-ergodicity phenomena of a magnetically frustrated spin system below the spin freezing temperature T_f ≈ 16 K. The Mn_0.3Ni₂Zn_10.7 γ-brass phase classifies as a spin glass, originating predominantly from the random distribution of diluted Mn moments on the octahedral partial structure.

In a search for new pseudobinary/ternary γ-brass-type phases, we synthesized a series of Mn_xNi₂Zn_11−x compounds at low Mn doping levels (x = 0.1−0.5) and determined the structures for two compositions x = 0.3 and 0.5. Magnetic measurements show that the Mn_0.3Ni₂Zn_11.7 γ-brass is a spin glass.

Scaling of Memories and Crossover in Glassy Magnets

Glassiness is ubiquitous and diverse in characteristics in nature. Understanding their differences and classification remains a major scientific challenge. Here, we show that scaling of magnetic memories with time can be used to classify magnetic glassy materials into two distinct classes. The systems studied are high temperature superconductor-related materials, spin-orbit Mott insulators, frustrated magnets, and dilute magnetic alloys. Our bulk magnetization measurements reveal that most densely populated magnets exhibit similar memory behavior characterized by a relaxation exponent of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-n\approx 0.6(1)$$\end{document}1−n≈0.6(1). This exponent is different from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-{\boldsymbol{n}}\approx 1/3$$\end{document}1−n≈1/3 of dilute magnetic alloys that was ascribed to their hierarchical and fractal energy landscape, and is also different from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-{\boldsymbol{n}}=1$$\end{document}1−n=1 of the conventional Debye relaxation expected for a spin solid, a state with long range order. Furthermore, our systematic study on dilute magnetic alloys with varying magnetic concentration exhibits crossovers among the two glassy states and spin solid.

Aging, memory, and nonhierarchical energy landscape of spin jam

The notion of complex energy landscape underpins the intriguing dynamical behaviors in many complex systems ranging from polymers, to brain activity, to social networks and glass transitions. The spin glass state found in dilute magnetic alloys has been an exceptionally convenient laboratory frame for studying complex dynamics resulting from a hierarchical energy landscape with rugged funnels. Here, we show, by a bulk susceptibility and Monte Carlo simulation study, that densely populated frustrated magnets in a spin jam state exhibit much weaker memory effects than spin glasses, and the characteristic properties can be reproduced by a nonhierarchical landscape with a wide and nearly flat but rough bottom. Our results illustrate that the memory effects can be used to probe different slow dynamics of glassy materials, hence opening a window to explore their distinct energy landscapes.

Geometric origin of magnetic frustration in the μ-Al₄Mn giant-unit-cell complex intermetallic

The structurally ordered μ-Al(4)Mn complex intermetallic phase with 563 atoms in the giant unit cell shows the typical broken-ergodicity phenomena of a magnetically frustrated spin system. The low-field zero-field-cooled and field-cooled magnetic susceptibilities show splitting below the spin freezing temperature T(f) = 2.7 K. The ac susceptibility exhibits a frequency-dependent cusp, associated with a frequency-dependent freezing temperature T(f)(ν). The decay of the thermoremnant magnetization is logarithmically slow in time and shows a dependence on the aging time t(w) and the cooling field H(fc) typical of an ultraslow out-of-equilibrium dynamics of a nonergodic spin system that approaches thermal equilibrium, but can never reach it on the experimentally accessible time scale. The above features classify the μ-Al(4)Mn complex intermettalic among spin glasses. The origin of frustration of magnetic interactions was found to be geometrical due to the distribution of a significant fraction of Mn spins on triangles with antiferromagnetic coupling. The μ-Al(4)Mn phase is a geometrically frustrated spin glass.

Memory of multiple aging stages above the freezing temperature in the Relaxor ferroelectric PLZT

The dynamic dielectric susceptibility and the elastic compliance of the relaxor ferroelectric lanthanum lead zirconate titanate (PLZT) 9/65/35 have been measured under different cooling and heating protocols in order to study aging and memory. The memory of multiple aging stages at different temperatures has been found (several dips in the susceptibility curves on heating), as in spin glass systems below the glass transition. Remarkably, in PLZT the memory of several aging stages is retained also above the freezing temperature deduced from the dynamic susceptibilities. The results are discussed in light of the existing models of aging and memory in spin and dipolar glasses.

Aging in a relaxor ferroelectric: scaling and memory effects

A crossover as a function of temperature is found in the zero-field aging properties of the relaxor ferroelectric Pb(Mg(1/3)Nb(2/3))O3. Below a temperature near which nonlinear susceptibility has indicated a suspected phase transition, the time-frequency dependence shows simple scale-independent behavior resembling that for spin glasses. As in spin glasses, high temperature aging is stable as further aging occurs at lower temperature, but not vice versa, indicating hierarchical state arrangement. A more general interpretation of such effects is briefly discussed.

Aging effects in an anderson insulator

Aging, commonly observed in glasses, is a manifestation of breakdown of time-translational invariance. Here we demonstrate experimentally aging effects in the electronic system of an Anderson insulator. The aging phenomenon in the electron glass appears to be much less sensitive to temperature than in other systems. The differences in the behavior of the electron glass and a spin glass system are discussed in terms of some microscopic differences between the two systems.

Metastable states in spin glasses and disordered ferromagnets

We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical, and is based on the convergence of sigma(t), a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit sigma(infinity). The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations, and relations to thermodynamic states. For example, we show that their overlap distribution is a delta function at zero. We also define a dynamics for M=infinity, which provides a potential tool for investigating ground state structure.