Glassy metals not only exhibit technologically interesting properties, e.g. high fracture strength, excellent soft magnetic behaviour and good corrosion resistance, they also constitute ideal materials for the studies of low-temperature transport, critical behaviour and electrical properties of disordered metals. Considerable efforts at understanding their structure, atomic and electronic transport properties and low-temperature behaviour have been made. The author describes the nature of the glassy state, various quenching techniques and glass-forming alloys, and discusses structural models, experimental structural data and atomic transport properties including diffusivities and kinetics of structural relaxation, magnetic aging and crystallisation. The mechanical properties and magnetic behaviour are summarised, with emphasis laid on the influence of modification of these properties due to changes in structural and chemical disorder and states of magnetisation. Finally the electrical transport properties, spin wave excitations and critical behaviour, thermal and acoustic behaviour at very low temperatures, and chemical properties are presented.

REVIEW ARTICLE: Glassy metals

Static critical phenomena in ferromagnets with quenched disorder

A review is given of the collinear and random magnetic structures which may be found in magnetically‐concentrated amorphous solids General consequences of a non‐crystalline lattice on the atomic moments, exchange interactions and single‐ion anisotropy are presented Magnetic structures with one and two magnetic subnetworks are then described, taking examples from the literature of each type Some discussion is also given of the low energy excitations and the behavior at the spin freezing or ordering temperature What happens to the familiar forms of magnetic order—ferromagnetism, ferrimagnetism, antiferromagnetism—in the absence of a crystalline atomic lattice? This article sets out to give an overview of magnetic order in non‐crystalline solids in an attempt to answer the question The magnetism of two classes of disordered metals have received particular attention during the past five years; amorphous ferromagnets, notably the Metglas‐type alloys, and spin glasses, typically dilute solutions of transition‐metal impurities in a non‐magnetic crystalline matrix The subject‐matter here will be magnetically‐concentrated amorphous materials, with the accent on non‐collinear spin structures A coherent picture of amorphous magnetism will be presented, but it must be admitted that not all the magnetic structures discussed have been equally well established Some of them are directly analogous to those found in crystals Others are peculiar to amorphous (or disordered) solids, whereas one crystalline magnetic structure seems impossible in a noncrystalline lattice

Amorphous magnetic order

The critical behavior at the paramagnetic to ferromagnetic phase transition in ${\text{Pr}}_{0.5}{\text{Sr}}_{0.5}{\text{MnO}}_{3}$ is studied using techniques such as modified Arrott plot, Kouvel-Fisher plot, and critical isotherm analysis. Though the nature of this transition is found to be of second order, the estimated critical exponents $\ensuremath{\beta}$, $\ensuremath{\gamma}$, and $\ensuremath{\delta}$ are in between the theoretically predicted values for three-dimensional Heisenberg and mean-field interaction models. However, it is noteworthy that the scaling relations are obeyed indicating renormalization of interactions around the Curie temperature $({T}_{C})$. Temperature variation in effective exponents (${\ensuremath{\beta}}_{\text{eff}}$ and ${\ensuremath{\gamma}}_{\text{eff}}$) resemble with those for disordered ferromagnet. It is shown that fully localized-spin interaction models are not applicable for this compound, and ferromagnetic interaction has itinerant character. Moreover, the exponents determined in this study are close to those calculated from the results of renormalization group approach for a heuristic model of two-dimensional Heisenberg spins coupled with long-range interaction. These results suggest that critical phenomenon in ${\text{Pr}}_{0.5}{\text{Sr}}_{0.5}{\text{MnO}}_{3}$, which is found to be an inhomogeneous ferromagnet around ${T}_{C}$, could not be described within the framework of existing universality classes and probably belong to a separate class.

Critical behavior at paramagnetic to ferromagnetic phase transition in Pr 0.5 Sr 0.5 MnO 3 : A bulk magnetization study

Exhaustive magnetization measurements have been carried out on the amorphous ferromagnet ${\mathrm{Fe}}_{40}$${\mathrm{Ni}}_{40}$${\mathrm{P}}_{14}$${\mathrm{B}}_{6}$ in the temperature range 4.2 to 700 K in fields up to 16 kOe. Magnetization at low temperatures is found to decrease in accordance with the predictions of an isotropic nearest-neighbor Heisenberg model. It is observed that in this alloy the rms range of exchange interaction equals roughly the mean nearest-neighbor distance. A theoretical interpretation has been provided for the observation that the spin-wave stiffness constant $D$ is smaller in amorphous than in crystalline ferromagnets. Magnetization data taken in the critical region, besides yielding the values for the Curie temperature and critical exponents as ${T}_{C}=519.9\ifmmode\pm\else\textpm\fi{}0.2$ K, $\ensuremath{\beta}=0.38\ifmmode\pm\else\textpm\fi{}0.01$, $\ensuremath{\gamma}=1.31\ifmmode\pm\else\textpm\fi{}0.02$, and $\ensuremath{\delta}=4.46\ifmmode\pm\else\textpm\fi{}0.04$, satisfy the magnetic equation of state characteristic of a second-order phase transition. The observed exponent values not only obey the static scaling relation but also present a reasonable agreement with the theoretical values deduced from a three-dimensional Heisenberg model. They do, however, exhibit a slight but systematic shift towards the molecular-field values. This observation has been shown to imply an increased effective range of the exchange interaction in the critical region. Long-range forces are found to have a negligible influence on the critical fluctuations of magnetization. Critical amplitude values suggest that the elementary moments involved in the magnetic order-disorder transition are those forming a part of the giant superparamagnetic moments which are found to exist for temperatures well above ${T}_{C}$. Above 575 K, the susceptibility obeys the Curie-Weiss law. A careful analysis of the susceptibility data reveals that the spin polarization of conduction electrons gives a negligible contribution to the distribution of the magnetic moment and that the moments on Ni and Fe atoms remain localized even in the paramagnetic state. No evidence has been found for the indirect exchange between spins on magnetic atoms mediated by conduction-electron spin, as conjectured by Kaneyoshi in amorphous ferromagnets, in the present glassy alloy.

Detailed magnetization study of an amorphous ferromagnet

Results of x-ray diffraction, transmission-electron diffraction, and crystallization studies on amorphous (Mo1-xRux)80P20 alloys obtained by liquid quenching are presented and discussed. The alloys are all found to be superconducting with transition temperatures ranging from ∼ 3 to ∼ 9°K. The variation of Tc with alloy composition is compared to that obtained by Collver and Hammond for vapor-quenched transition-metal films. Results of magnetic-susceptibility measurements are used to estimate the variation of the electronic density of states at the Fermi level N(0) from the Pauli paramagnetic contribution. The relationship between the variation of Tc and N(0) is discussed in terms of the microscope theory of superconductivity. Finally, results of measurements of the upper critical field Hc2, and the normal-state electronic transport properties are presented and compared with recent theoretical models for amorphous superconductors.

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Superconductivity, magnetic susceptibility, and electronic properties of amorphous ( Mo 1 − x Ru x ) 80 P 20 alloys obtained by liquid quenching

Magnetization was measured between 4.2 and 290\ifmmode^\circ\else\textdegree\fi{}K in fields up to 70 kOe on liquid-quenched ${\mathrm{Gd}}_{80}$${\mathrm{Au}}_{20}$ amorphous alloys. The Curie temperature and critical exponents $\ensuremath{\beta}$, $\ensuremath{\gamma}$, and $\ensuremath{\delta}$ are found to be 149.45\ifmmode\pm\else\textpm\fi{}0.2\ifmmode^\circ\else\textdegree\fi{}K, 0.44\ifmmode\pm\else\textpm\fi{}0.02, 1.29\ifmmode\pm\else\textpm\fi{}0.05, and 3.96\ifmmode\pm\else\textpm\fi{}0.03, respectively. The data are fitted to an equation of state previously derived for a second-order phase transition in fluid systems. It is found that the magnetization exponent $\ensuremath{\beta}$ of amorphous ferromagnets studied so far has a value \ensuremath{\sim}0.4, slightly enhanced over those observed in corresponding crystalline elements, and the estimated specific-heat exponent $\ensuremath{\alpha}$ is negative. Both are in qualitative agreement with theories on the critical behavior of random systems. The effects of structural disorder on the magnetic properties studied are compared and discussed with recent theories on amorphous magnetism. A comparison of the magnetization data with Handrich's theory for amorphous ferromagnets suggests that in our amorphous alloys the average fluctuation in the exchange constant ($J$) can be an appreciable fraction of $J$ itself. The effective magnetic moment in the paramagnetic state has a value of $(8.9\ifmmode\pm\else\textpm\fi{}0.1){\ensuremath{\mu}}_{B}$ per gadolinium atom. The saturation moment extrapolated to 0\ifmmode^\circ\else\textdegree\fi{}K equals $(7.0\ifmmode\pm\else\textpm\fi{}0.25){\ensuremath{\mu}}_{B}$ per Gd atom. The low-temperature saturation magnetization follows the ${T}^{\frac{3}{2}}$ law from 0.13 ${T}_{c}$ to 0.80 ${T}_{c}$. The mean exchange integrals $J$ determined from the Rushbrooke-Wood formula and spinwave theory are found to be 2.28\ifmmode\pm\else\textpm\fi{}0.15\ifmmode^\circ\else\textdegree\fi{}K and 1.34\ifmmode\pm\else\textpm\fi{}0.08\ifmmode^\circ\else\textdegree\fi{}K, respectively. The exchange constant of the Ruderman-Kittel-Kasuya-Yosida interaction as estimated from the de Gennes model (${J}_{\mathrm{sf}}\ensuremath{\simeq}0.19$ eV) is not drastically reduced in this amorphous matrix. Finally, the Curie temperature of pure amorphous Gd is estimated and its value compared with those obtained from experimental extrapolation.

Critical phenomena and magnetic properties of an amorphous ferromagnet: Gadolinium-gold

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Superconductivity, magnetic susceptibility, and electronic properties of amorphous ( Mo 1 − x Ru x ) 80 P 20 alloys obtained by liquid quenching

Critical phenomena and magnetic properties of an amorphous ferromagnet: Gadolinium-gold