Critical Concentration For Ferromagnetism Research Articles

Magnetic order-disorder phase transition in Cr70Fe30 thin films

Dynamic magnetic response of Cr70Fe30 thin films with thickness in the range 11 nm ≤ t ≤ 978 nm and composition above the critical concentration for ferromagnetism was determined by measuring linear (χ1) and nonlinear (χ2 – χ5) ac-magnetic susceptibilities over three decades of frequency (101 – 104 Hz) in the temperature range 2–300 K. An elaborate analysis of χ1(T), measured in the absence or presence of a superposed dc magnetic field, Hdc, reveals that the asymptotic critical behavior of the films with t ≥ 21 nm is that of a three-dimensional (3D) isotropic dipolar ferromagnet. Interplay between long-range dipole–dipole and short-range exchange interactions causes a crossover to the 3D isotropic Heisenberg critical behavior when the temperature is increased above the Curie temperature, TC, outside the asymptotic critical region (ACR). By contrast, in the ACR, the film with t = 11 nm behaves as a 3D Ising ferromagnet. TC decreases with film thickness in accordance with the finite-size scaling with the value for the spin–spin correlation length exponent that corresponds to the 3D isotropic dipolar universality class. In the films with t ≤ 42 nm, besides the macroscopic length scale of the ferromagnetic order in the static limit, there exists a length scale that corresponds to finite spin clusters, whose dynamics is spin glass-like.

Magnetism ofPd1−xNixalloys near the critical concentration for ferromagnetism

We report results of a muon spin rotation and relaxation ($\mu$SR) study of dilute Pd$_{1-x}$Ni$_x$ alloys, with emphasis on Ni concentrations $x =$ 0.0243 and 0.025. These are close to the critical value $x_\mathrm{cr}$ for the onset of ferromagnetic long-range order (LRO), which is a candidate for a quantum critical point. The 2.43 and 2.5 at.% Ni alloys exhibit similar $\mu$SR properties. Both samples are fully magnetic, with average muon local fields $\langle B^\mathrm{loc}\rangle =$ 2.0 and 3.8 mT and Curie temperatures $T_C =$ 1.0 and 2.03 K for 2.43 and 2.5 at.% Ni, respectively, at $T = 0$. The temperature dependence of $\langle B^\mathrm{loc}\rangle$ suggests ordering of Ni spin clusters rather than isolated spins. Just above $T_C$ a two-phase region is found with separate volume fractions of quasistatic short-range order (SRO) and paramagnetism. The SRO fraction decreases to zero with increasing temperature a few kelvin above $T_C$. This mixture of SRO and paramagnetism is consistent with the notion of an inhomogeneous alloy with Ni clustering. The measured values of $T_C$ extrapolate to $x_\mathrm{cr}$ = 0.0236 $\pm$ 0.0027. The dynamic muon spin relaxation in the vicinity of $T_C$ differs for the two samples: a relaxation-rate maximum at $T_C$ is observed for $x$ = 0.0243, reminiscent of critical slowing down, whereas for $x =$ 0.025 no dynamic relaxation is observed within the $\mu$SR time window. The data suggest a mean-field-like transition in this alloy.

Ferromagnetic transition in dilute Pd-Fe alloys

We present low-field magnetization and specific-heat data for ${\mathrm{Pd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$ alloys, with x ranging from 0.08 to 0.6 at. % Fe. Both types of measurements were done on the same samples. The samples are more homogeneous than those used in previous investigations. We find that in contrast to previous suggestions, all samples undergo sharp ferromagnetic transitions with ${\mathit{T}}_{\mathit{C}}$ ranging from 0.4 K for the 0.08-at. % Fe alloy to 18.0 K for the 0.6-at. % Fe alloy. The specific-heat anomalies associated with the transitions have the form of a cusp very close to ${\mathit{T}}_{\mathit{C}}$ as determined from the magnetization. However, because of large fluctuations, these anomalies are very broad, extending to a region of temperatures well above ${\mathit{T}}_{\mathit{C}}$. Combining our results with earlier data, we argue that the critical concentration for ferromagnetism in Pd-Fe alloys is near 0.01 at. % Fe, lower by a factor of 10 than previously assumed.

Critical concentration for ferromagnetism in binary Fe alloys

A survey of data on the critical concentration xc for the onset of ferromagnetism in binary FexM1−x alloys, with M being a nonmagnetic component, is given. The xc values range from about 0.05 to over 0.7, with the bulk of the data for amorphous alloys centered at about 0.4. For random binary alloys a model which takes into account the effects of local environment, percolation, and frustration yields critical concentrations quite similar to those encountered in many amorphous systems.

Low Temperature Specific Heat of Nearly and Weakly Ferromagnetic Y(Co1-xAlx)2

The low temperature specific heat of nearly and weakly ferromagnetic Y(Co 1- x Al x ) 2 with 0≤ x ≤0.18 is studied between 1.4 K and 6.5 K. The results show an enhancement of the electronic specific heat coefficient, γ, around the critical concentration for ferromagnetism. A strong upturn in the C / T vs T 2 curve at low temperatures is observed for x ≥0.09. The origin of this upturn is discussed in terms of different models so far proposed.

Field-induced parameters of re-entrant magnets and concentrated spin glasses

We have used electron spin resonance measurements to derive the temperature and frequency dependences of the field-induced magnetization [ M( T, f)] and anisotropy field [ H an ( T)] in a number of amorphous alloys belonging to the series (Fe p Ni 1− p ) 75P 16B 6Al 3. In re-entrant ( p > p c, the critical concentration for ferromagnetism) alloys at hi gh frequencies ( f = 35 GHz, field ≈ 12 kOe) M reduces as T 3/2 at high T and as T below ≈ 40 K, the deviation from T 3/2 becoming more marked as p → p + c. For p close to p c, lowering the frequency first causes the T 3 2 term to increase and ultimately ( ≈ 4 GHz) changes the variation of M with T to that discovered previously for concentrated spin glasses, namely M is constant at low T and drops linearly at high temperatures. For the re-entrants, the results are interpreted on the basis of a model which invokes an energy gap in the spin-wave spectrum, introduces a non-zero density of states of the gap energy and takes into consideration a low- q cut-off in the spin-wave integral in thelow- T (≲ T) regime.In the concentrated spin glasses [ M (0) - M ( T)]/ M (0) is well represented by the function [exp (Δ / T) - 1] -1, where Δ has values close to the corresponding Curie-Weiss temperatures θ p but much larger than the respective spin glass transition temperatures T SG. The temperature dependence of H an is largely given by the function (1 - T/ T ∗), where T ∗ is equal to the zero-field freezing temperature for the re-entrants and T SG for the spin glasses, respectively.

Magnetic response near the critical concentration for ferromagnetism: Linear and nonlinear susceptibility in concentrated spin glasses

Low-field magnetization measurements are reported for a-Fe12Ni63G25 and a-Fe7Ni73G20. These are highly concentrated spin glasses since the critical Fe concentrations (xc) for onset of ferromagnetism are 12.4 and 7.7, respectively. Whereas the nonlinear susceptibility shows the expected rapid rise near Tg, it is remarkable that the close proximity to xc reveals itself via a similar sharp increase in the linear susceptibility. It turns out that all the data can be represented by a single empirical form: χ(t)=[χ(Tg)t−γ]/[Aχ(Tg)+t−γ].

Magnetic polarization clouds, percolation, and the critical concentration for ferromagnetism

The magnetic properties of many alloys are described in terms of magnetic polarization clouds. This is true in particular of dilute alloys of magnetic atoms in strongly exchange-enhanced hosts and of concentrated but magnetically dilute alloys of Ni in nonmagnetic hosts. In such alloys the locally averaged magnetization density is observed by diffuse neutron scattering to fall off as a Yukawa function away from the center of a polarization cloud. We present numerical calculations which confirm this Yukawa form and present an approximate theoretical derivation which gives a formula for the inverse range κ of a polarization cloud in an alloy in terms of the uniform exchange-enhancement factor α and the band susceptibility Γ(q) for the alloy. Assuming ferromagnetism in such alloys to arise from percolation amongst the polarization clouds, we also derive a relationship between the critical concentration c*cr, of polarization clouds for the onset of ferromagnetism and the average magnetization μ*cr and inverse range κcr of those clouds. This relationship is found to be in good agreement with experiment. Approximate calculated values of c*cr, μ*, and κ are presented for two cases. The effects of chemical ordering and clustering are considered briefly.

The extent of localisation of the Fe moment in Y(Fe1-xAlx)2and Zr(Fe1-xAlx)2-a comparison of the magnetic properties

Magnetisation, AC and DC susceptibility measurements of the pseudobinary systems Y(Fe1-xAlx)2 and Zr(Fe1-xAlx)2 are reported. On substituting Al for Fe the transition from ferromagnetism to paramagnetism in Y(Fe1-xAlx)2 is found to be dominated by freezing phenomena which are characteristic of a cluster-glass regime (0.1<x<0.35), while such freezing phenomena are not observed around the critical concentration for ferromagnetism (xc=0.55) in Zr(Fe1-xAlx)2. The analysis of the DC susceptibility data yields finite paramagnetic Curie temperatures and mu eff values up to about 90% Al for Y(Fe,Al)2, whereas for Zr(Fe,Al)2 both mu eff and theta exhibit the usual concentration dependence vanishing above xc. From these results the authors deduce that the Fe moment can be regarded as more delocalised in the Zr system than in the Y pseudobinaries which may be attributed to a larger degree of hybridisation of the d electrons in the Zr compounds when compared with those of Y.

Magnetization measurements of nearly ferromagnetic compounds TiBe 2-xMx (M = Cu, Ag, Au, Fe) in low and high fields

It is shown that the substitution of minute amounts of Cu for Be in TiBe 2 causes the susceptibility to increase monotonically. Magnetization data for TiBe2-xCux at 1.24 K and 4.17 K in fields up to 213 kOe are analysed in the Landau model of phase transitions. The critical concentration for ferromagnetism, xc, is about 0.2. Ag and Au as solutes decrease the susceptibility of TiBe2 (preliminary results). The magnetic moment of Fe in TiBe2-xFe x is estimated to be smaller than 0.01 μB.

Magnetic behaviour of Co-Cr alloys above the critical concentration for ferromagnetism

We have investigated Co-Cr alloys with chromium concentrations slightly larger than the critical concentration for long range magnetic order (25 %). Our results suggest a strong inhomogeneous magnetic state consisting of clusters with a large distribution of formation temperatures. At low temperatures one observes a superparamagnetic to ferromagnetic transition followed by a ferromagnetic to spin glass transition at lower temperature in the range of concentration 25 % to 29 %.

Effect of Local Environment on Formation of Local Moments in bcc Fe–Cr Alloys–Mössbauer Study

The Mössbauer spectra of Fe–Cr solid solutions in the concentration range of 60–96 at%Cr were obtained at 5 K. These spectra were analyzed to yield hyperfine field distribution curves which are characterized by two distinct peaks. It has been revealed that an isolated Fe atom has a very small hyperfine field indicating a nonmagnetic character. The profiles of the hyperfine field distribution curves as well as the magnetic properties of the alloys, particularly near the critical concentration for ferromagnetism, are discussed on the basis of the local environment model.

Magnetic-local-environment effect on the atomic magnetic moment in ferromagnetic transition-metal alloys

The magnetic structure of Ni-Cu alloys near the critical concentration for ferromagnetism is discussed as compared with Fe-V on the basis of several kinds of nonlocal susceptibility, and is shown to be directly related to the band structure.

Magnetic Form Factor of Ni-Pt Alloy System

Magnetic form factor of Ni-Pt alloy system with 8.5, 24, 32 and 46 at.% Pt was measured by means of the polarized neutron diffraction. The form factors were analyzed with the results that the atomic magnetic moment of Ni atom decreases with increasing Pt concentration and that of Pt atom has parallel magnetic moment. Experimental results were explained by a Coherent Potential Approximation. In the vicinity of the critical concentration for ferromagnetism, the partial state densities of Ni and Pt atom in the Ni-Pt alloy were calculated to be almost the same with each other, while the partial state densities of Ni and Pd atom in the Ni-Pd alloy turned out to be quite different.

Magnetic inhomogeneity of PtNi alloys

Low field (⩽2 Oe) d.c. susceptibility measurements have been made on two PtNi alloys below the critical concentration for ferromagnetism. The results have been interpreted as strongly indicating the magnetic inhomogeneity of the onset of ferromagnetism in PtNi, in conformity with the isoelectronic PdNi system.

Magnetic properties of ferromagnetic VFe alloys near the critical concentration for ferromagnetism

Magnetic measurements on a series of FeV alloys in the composition range 29–35 at .% Fe have been interpreted in terms of a local environment model. Values for the moment and density of magnetic clusters have been determined. Good agreement is obtained between values obtained from Curie constants, and those estimated from the critical coefficients. The results may be understood in terms of a random distribution of solute atoms.

Volume effects in itinerant ferromagnets

Magneto-volume experiments (including: pressure dependence of the magnetization, volume magnetostriction and magnetic contribution to the thermal expansion) on strongly paramagnetic and weakly ferromagnetic Ni 3Al and NiPt alloys can be described with one single magneto-volume parameter. Its value is discussed in the Stoner-Edwards-Wohlfarth model for very weak itinerant ferromagnetism. Alloys that follow this model have some characteristic magneto-volume properties. In view of these properties the transition from ferro- to paramagnetism at the critical concentration for ferromagnetism is studied for three pseudo binary alloy systems: Y 6(Fe, Mn) 23, Zr(Fe, Co) 2 and Ti(Fe, Co).

Itinerant magnetism in NiV alloys around the critical concentration for ferromagnetism

After subtraction of a contribution due to magnetic clusters, the magnetization of NiV alloys, as a function of the field, temperature and concentration, follows fairly well the itinerant model, on both sides of the critical concentration. In a critical alloy ( approximately 89 at% Ni) the percentage of Ni atoms in magnetic clusters probably does not exceed 10%. Special attention is focussed on the temperature dependence of the magnetization in high fields.

The absence of critical concentration for ferromagnetism in disordered PdNi-type alloys

The generalized Landau model is applied to disordered strongly 'paramagnetic' alloys. It is shown that there is a close analogy between the susceptibility of such magnetic alloys and the Green's function of ordinary (nonmagnetic) disordered binary alloys. The Green's function analogy is used to prove that within the generalized Landau theory, disordered alloys similar to PdNi do not exhibit a critical concentration for ferromagnetism. The magnetization of such alloys is estimated on the basis of a simple statistical model and it is proved quite rigorously that a spontaneous magnetization exists even in the so called 'paramagnetic' region (below 2.3% Ni for PdNi). These general conclusions are illustrated by a CPA calculation of the susceptibility of PdNi alloys. In contrast to previous CPA calculations, it is found that the CPA susceptibility never diverges, thus indicating the absence of a well-defined critical concentration.

Ferromagnetic and antiferromagnetic ordering in platinum-manganese alloys: Low-temperature specific heat

Measurements are reported of the specific heat of a number ofPtMn alloys. Interaction between the manganese impurities gives rise to antiferromagnetic or ferromagnetic ordering depending on the impurity concentration, the critical concentration for ferromagnetism being 0.8 at % Mn. Using the effect on the specific heat anomaly of the statistical fluctuations in the number of the impurities in a given volume, the interaction range of the impurities is estimated and found to agree with the band structure of platinum.