AuFe Alloys Research Articles

Magnetic field effects in the Anderson model of dilute magnetic alloys. III. Transport properties

An extension of previous studies is made on the magnetic field effects of the infinite-$U$ Anderson Hamiltonian. The magnetothermopower, the thermal magnetoresistivity, and the Lorenz number are calculated. We find that the thermopower decreases monotonically as a function of the applied field. In low fields, it varies linearly with the square of the impurity magnetization as well as with the negative electrical magnetoresistivity. In high fields, it follows a $\frac{1}{H}\ensuremath{-}\frac{1}{{H}_{0}}$ behavior. These features are in good qualitative agreement with the experiment of Berman and Kopp on Au-Fe alloys and with calculations based on the $s\ensuremath{-}d$ model. The field and temperature dependence of the negative thermal magnetoresistivity closely resemble those of the electrical one. A close parallelism is therefore established between the two quantities. The Lorenz number is found to be practically independent of the external magnetic field.

Crystal growth and precipitation in thin films of amorphous Fe–Au alloys

Abstract Metastable alloys of the Fe–Au system have been prepared by the vapour quenching technique. The films so obtained are studied by resistivity measurements and by transmission electron microscopy and diffraction. Alloys containing more than 60 at. % Fe are amorphous at low temperature and a transformation to a metastable b.c.c. solid solution occurs at a temperature ranging from 80 to 250 K when the concentration varies from 80 to 60 at. % Fe. A further annealing at higher temperature leads to the precipitation of a gold-rich f.c.c. phase which grows, in a platelet structure, from linear defects formerly observed in the metastable b.c.c. phase. Kinetic parameters of the crystallization and orientation relationship between the phases during the precipitation are determined.

Variation of RKKY interaction strength in dilute AuFe alloys

From measurements of the magnetic properties of some dilute AuFe alloys we find that V 0, the strength of the Ruderman-Kittel-Kasuya-Yosida interaction, V(r) = (V 0 cos 2k Fr)/r 3, decreases rapidly from V 0 = 11.9 × 10 -36 erg cm 3 at n = 42 ppm Fe to 1.03 × 10 -36 erg cm 3 at 6050 ppm Fe. We suggest that the observed decrease of V 0 is due to self-damping of the RKKY oscillations, and discuss the significance of this decrease for the interpretation of other experiments on AuFe.

Electrical resistivity ofAuFe alloys in the spin-glass, mictomagnetic, and ferromagnetic regimes

Measurements are presented of the electrical resistivity for a series of Au Fe alloys with concentrations between 0.5- and 22-at.% Fe, in the temperature range 0.5 - 300 K. We have called the concentration range between about 0.5- and 8-at.% Fe, the spin-glass regime. Here we find that the impurity resistivity $\ensuremath{\Delta}\ensuremath{\rho}$ has a ${T}^{\frac{3}{2}}$ dependence down to the lowest temperatures of measurement, the coefficient of this dependence decreasing very slowly with concentration. At higher temperatures, around the freezing temperature ${T}_{0}$ the impurity resistivity is increasing linearly with temperature, and this is followed, at much larger temperatures, by a very broad resistance maximum. We have called the concentration range above \ensuremath{\cong}10-at.% Fe, the mictomagnetic regime which is characterized by having large magnetic clusters and a sensitivity to thermal and magnetic history. Upon further increasing the concentration to the percolation limit $c\ensuremath{\gtrsim}15$ at.%, such that there is sufficient overlapping among these magnetic clusters, Au Fe gradually develops a long-range inhomogeneous ferromagnetic regime. Again we observe a ${T}^{\frac{3}{2}}$ temperature dependence throughout both of these regimes at low temperatures, but at higher temperatures the deviation away from this dependence is much more complicated than in the spin-glass regime. Further, the onset of magnetic ordering is clearly seen in $\ensuremath{\Delta}\ensuremath{\rho}$. We have also examined the temperature dependence of the derivative of the impurity resistivity $\frac{d(\ensuremath{\Delta}\ensuremath{\rho})}{\mathrm{dT}}$, and find that throughout our whole concentration range there is a well-defined maximum which correlates fairly well with ${T}_{0}$. The experimental and theoretical background of these measurements is fully discussed.

Ferromagnet or spin glass? Magnetic ordering in Au-Fe alloys

Bulk magnetization measurements on Au-Fe alloys are widely held as indicating the onset of long range ferromagnetism in alloys with Fe concentration above about 12 at.%. The 'ordering' temperatures deduced from these measurements appear to be in reasonable agreement with temperatures of the maxima of d rho /dT in the resistivity of the alloys but are considerably higher than the values obtained from Mossbauer effect measurements for alloys in the concentration range between 12 and 20 at% Fe. Magnetization measurements on a Au-15at% Fe alloys are presented which, contrary to the above, show a behaviour usually associated with spin glass alloys and indicate a spin freezing temperature close to the 'ordering' temperature expected from Mossbauer effect measurements. The results show that the apparent ferromagnetic behaviour and higher ordering temperatures obtained by previous workers in their magnetization measurements have a simple physical explanation based on the intrinsic properties of the alloys.

Effect of pressure on impurity-impurity interactions in a dilute Au(Fe) alloy

The electrical resistivity of the dilute magnetic alloy Au-0.13 at% Fe has been measured from 1.2 to 30 K in the pressure range 0-60 kbar. Application of pressure is found to shift the resistivity maximum from 3.5 J at zero pressure to lower temperatures at the rate of -5 mK kbar-1, indicating a possible decrease in the interaction between Fe spins as they are brought closer together. A close analogy is found to exist between the present measurements on Au(Fe) and the investigation of Star on the Au1-xCux(Fe) alloy series.

Magnetic-Moment Distribution in NiFe and AuFe Alloys

We have determined the magnetic form factors and the corresponding magnetic-moment distributions for ordered ${\mathrm{Ni}}_{3}$Fe and for disordered NiFe and AuFe alloys in an attempt to establish the variation of the individual atomic-moment distributions with composition. The results confirm the individual moments previously determined for NiFe alloys by neutron-diffuse-scattering methods and provide an upper limit of $0.03{\ensuremath{\mu}}_{B}$ for the Au moment in a 25-at.% Fe in Au alloy. A small negative moment density between atoms was found for all of the alloys studied. The symmetry of the moment distributions was determined at the Ni and Fe sites in ordered ${\mathrm{Ni}}_{3}$Fe and for Fe in ${\mathrm{Au}}_{0.75}$${\mathrm{Fe}}_{0.25}$. The Fe moment distribution is nearly spherical in both cases (54% ${T}_{2g}$ in ${\mathrm{Ni}}_{3}$Fe and 56% ${T}_{2g}$ in the AuFe alloy) while the Ni moment distribution is strongly distorted. There seems to be little difference between the individual moment distributions in ordered and disordered ${\mathrm{Ni}}_{3}$Fe. In both, the effective ${T}_{2g}$ character decreases relative to pure Ni. The $\mathrm{Ni} d$-function populations in ordered ${\mathrm{Ni}}_{3}$Fe suggest that this decreasing ${T}_{2g}$ character is associated with the larger size of, and the stronger $d\ensuremath{-}d$ overlap with, the Fe atoms. The $\mathrm{Ni} d(\mathrm{xz})$ and $d(\mathrm{yz})$ functions that are directed toward nearest-neighbor Ni atoms have essentially the same population as in pure Ni while the $d(\mathrm{xy})$ function directed toward nearest-neighbor Fe atoms loses population to $d({x}^{2}\ensuremath{-}{y}^{2})$. Thus, there is a repulsion of spin-up electrons away from the regions of strong overlap.

Thermopower of concentrated [formula omitted]Cr alloys

Measurements are presented of the thermopower of three concentrated Au Cr (0.9, 4.9 and 10.6 at.%Cr) alloys between 4 and 500°K. Considerable differences are observed in the thermopower compared with Au Fe alloys in a similar concentration range. Possible reasons for these differences are discussed in terms of current ideas on spin glasses and the pair model of Matho and Béal-Monod.

Magnetoelastic effects in dilute magnetic alloys

Ultrasonic studies of Cu Mn, Au Mn and Au Fe alloys where the concentrations of the transition metal ranges between 1 and 10% show that the longitudinal sound velocity has a marked field dependence at temperatures below the peak in the magnetic susceptibility and a negligible field dependence above it. This suggests that there may be an ordered magnetic state in these alloys.

Magnetization of gold-iron alloys

Magnetization measurements have been made on Au-Fe alloys containing from 0·05 to 12·5 at. % Fe at temperatures below the magnetic ordering temperature. In combination with Mössbauer spectroscopy a qualitative explanation is derived for the complex mictomagnetic behavior observed.

Internal friction behaviour of quenched Au–Fe alloys

The investigation shows that the torsion pendulum can be used to study the effect of quenched-in vacancies in gold–iron alloys. The ratio Em/Ef for the alloys is shown to be independent of concentration, and to be equal to the value obtained for pure gold. Damping changes associated with precipitation have been observed in a quenched and aged gold–57% iron alloy. The internal friction behaviour is explained by invoking two types of precipitate — a coherent one in the early stages of precipitation, which becomes semi-coherent or incoherent as the precipitation proceeds. Es wird gezeigt, das das Torsionspendel benutzt werden kann, um den Einflus von Leerstellen in Gold–Eisen-Legierungen zu untersuchen. Das Verhaltnis Em/Ef fur die Legierungen ist unabhangig von der Konzentration und gleich dem fur reines Gold erhaltenen Wert. Mit Ausfallung verbundene Dampfungsanderungen wurden in abgeschreckten und gealterten Gold–57% Eisen-Legierungen beobachtet. Das Verhalten der inneren Reibung wird mit zwei Ausfallungstypen erklart, einem koharenten in einem Fruhstadium der Ausfallung, der semikoharent oder inkoharent wird, wenn die Ausfallung fortschreitet.

Electrical resistivity of concentrated AuCr alloys

Preliminary data are presented of the electrical resistivity for two concentrated AuCr (3.3 and 10.6 at % Cr) alloys. The initial temperature dependence of the impurity resistivity of both alloys varies as T32/, in a similar manner to that observed in concentrated AuFe alloys. Both systems can be regarded as examples of a spin glass.

The magnetoresistance of gold-iron alloys in high fields

The resistance of Au-Fe alloys with Fe concentrations of 110, 300, 1100 and 1900 ppm has been measured in the temperature range 0.4-20 K in fields up to 77 kOe. Interaction effects are negligible for the two dilute alloys, but reduce the magnetoresistance of the others. The magnetoresistance of the dilute alloys is a universal function of H/T for temperatures above 2.5 K, but is reduced at lower temperatures. For high values of H/T the magnetoresistance increases roughly as lg H, as predicted by theory. However, the temperature dependence cannot be explained by simple theory. It appears that very large fields would be required to remove completely the anomalous magnetoresistance.

Magnetic-Moment Distribution in NiFe and AuFe Alloys

We have determined the magnetic form factors and the corresponding magnetic-moment distributions for ordered ${\mathrm{Ni}}_{3}$Fe and for disordered NiFe and AuFe alloys in an attempt to establish the variation of the individual atomic-moment distributions with composition. The results confirm the individual moments previously determined for NiFe alloys by neutron-diffuse-scattering methods and provide an upper limit of $0.03{\ensuremath{\mu}}_{B}$ for the Au moment in a 25-at.% Fe in Au alloy. A small negative moment density between atoms was found for all of the alloys studied. The symmetry of the moment distributions was determined at the Ni and Fe sites in ordered ${\mathrm{Ni}}_{3}$Fe and for Fe in ${\mathrm{Au}}_{0.75}$${\mathrm{Fe}}_{0.25}$. The Fe moment distribution is nearly spherical in both cases (54% ${T}_{2g}$ in ${\mathrm{Ni}}_{3}$Fe and 56% ${T}_{2g}$ in the AuFe alloy) while the Ni moment distribution is strongly distorted. There seems to be little difference between the individual moment distributions in ordered and disordered ${\mathrm{Ni}}_{3}$Fe. In both, the effective ${T}_{2g}$ character decreases relative to pure Ni. The $\mathrm{Ni} d$-function populations in ordered ${\mathrm{Ni}}_{3}$Fe suggest that this decreasing ${T}_{2g}$ character is associated with the larger size of, and the stronger $d\ensuremath{-}d$ overlap with, the Fe atoms. The $\mathrm{Ni} d(\mathrm{xz})$ and $d(\mathrm{yz})$ functions that are directed toward nearest-neighbor Ni atoms have essentially the same population as in pure Ni while the $d(\mathrm{xy})$ function directed toward nearest-neighbor Fe atoms loses population to $d({x}^{2}\ensuremath{-}{y}^{2})$. Thus, there is a repulsion of spin-up electrons away from the regions of strong overlap.

Low temperature thermocouples: KP, "normal" silver, and copper versus Au-0.02 at% Fe and Au-0.07 at% Fe

The Seebeck thermoelectric voltages of two dilute alloys of iron in gold, Au 0.02 at% Fe and Au-0.07 at% Fe, have been determined with respect to KP (a particular Ni-Cr alloy), "normal" silver, and copper in the temperature range from 4 to 280 K. The power series representation of these data, along with the calculated Seebeck coefficients and derivatives of the Seebeck coefficients, have been extrapolated to 0 K and are presented as a function of temperature. In addition to these reference data, seven different Au-0.07 at% Fe alloys were thermoelectrically intercompared in order to determine the variability in wires from different melts and from different manufacturers. The largest deviation found amounted to about 9 percent of the output of a KP versus Au-0.07 at% Fe thermocouple pair between 4 and 20 K. A more typical variation for this temperature range was 2 to 4 percent. Initial indications are that the reference data can be adjusted satisfactorily with data from spot calibrations on particular wires. The effect of heat treatment is illustrated by comparing our results to Rosenbaum's data for annealed and unannealed specimens of both Au-Fe alloys.

The thermoelectric power of dilute gold-iron alloys

We have measured the thermoelectric power of a number of Au-Fe alloys, with Fe concentrations between similar 10 and 1900 ppm. Measurements were made between 0.4 and 30 K in fields up to 70 kOe. The alloys exhibited the familar `giant' thermopower in zero field, the peak value observed being - 15 μ V K-1 at about 10 K. Both the order of magnitude and the temperature dependence of the zero-field thermopower agree fairly well with Kondo's theory of spin-flip scattering. The thermopower of all but the most dilute alloys shows an initial increase in a magnetic field, which we believe is caused by Fe-Fe interactions. The thermopower then decreases due to `freezing-out' of spin-flip scattering and a simple pair-interaction model accounts for most of this observed behaviour. For the most concentrated alloy the decrease is not observed, even for the maximum field applied. For still higher fields (and lower concentrations) the thermopower decreases approximately as 1/H, as is suggested by a recent perturbation calculation.

Magnetic Susceptibility of Au–Fe Alloys

Over the past years there has been considerable interest in the magnetic properties of the Au(Fe) system. Mössbauer measurements indicate that a complicated type of long-range ordering occurs below concentrations c of ∼12 at.% Fe and extends down to c<1%. Yet no definitive susceptibility study has been carried out over a complete range of temperatures and concentrations in order to characterize the magnetic ordering. We have measured the low-field magnetic susceptibility χ(T) for a series of eight Au–Fe alloys (1–22 at.% Fe), and we observe a definite peak in χ at those ordering temperatures determined from the Mössbauer data. The magnitude of χ greatly increases with c, while the shape of χ(T) in the region of the peak changes from a cusp-like behavior at low c to a behavior for c≳17% in which χ(T) gently rises, then sharply falls. These behaviors confirm the existence of a long-range order suggtesive of antiferromagnetism at low c (≤8%) with a more typical ferromagnetic ordering at high c. At intermediate c (≈12%), χ(T) seems to indicate the presence of a mixed type of long-range order.

Descriptive Model for the Magnetic Behavior of Au-Fe Alloys

Antiferromagnetic Au-Fe alloys acquire a ferromagnetic character, i.e., demonstrate remanence, possess a positive Curie $\ensuremath{\theta}$, etc., in the presence of an external field. A phenomenological model is presented which purports to describe the mixed magnetic behavior of these alloys. The model satisfactorily reconciles M\ossbauer and magnetization results and provides an insight into the nature of the magnetic order.

The magnetic field dependence of the specific heat of dilute PdCo alloys

A large difference between the response to a magnetic field of the specific heat of dilute PdCo alloys and a AuFe alloy has been found. Arguments are given which might explain this difference.

A study of dilute alloys of iron in gold using the M$ouml$ssbauer effect

A detailed analysis of Mossbauer absorption spectra of 57Fe in Au-Fe alloys has been carried through for the concentration range 05-128% at room temperature and for the 128% alloy from room temperature down to 04 °K. The results show that significantly different spectra are obtained for iron atoms with 0, 1, 2,... iron nearest neighbours. The concentration dependence of the mean isomer shift is consistent with the changes in charge density to be expected from the changes in atomic volume. As the temperature is reduced, measurable hyperfine fields appear first at iron sites with the largest number of iron nearest neighbours. The quadrupole splitting averaged over all iron sites tends to zero as the temperature is reduced, indicating that the angle between the spin direction and the electric field gradient has a mean value close to cos -1(1/radical3).