Muon hyperfine fields in iron and its dilute alloys

The temperature dependence (240 to 633 K) of the interstitial magnetic field, B_μ, as determined by the rotation of the spin of the μ⁺, has been measured for dilute polycrystalline iron alloys with Mo, Ti and Nb additions. In all cases the behaviours differ from one another and from the Fe(A1) alloys previously studied. B_μ, which is negative with respect to the magnetization, is increased in magnitude by A1 and Mo, and decreased greatly by Ti. The addition of Nb creates a two- phase alloy from which we can assess the role of heterogeneity and/or strain on B_μ in iron. If the temperature dependence of the hyperfine field B_hf extracted from B_μ for Fe(Mo) alloys is interpreted on the model previously used to discuss the Fe(A1) data, we would conclude that the muon is attracted to the Mo atom while repelled by the A1 atoms as the temperature decreases. Measurements giving room temperature values of B_μ for iron alloys with Mn, Cr, V and W taken after annealing above the recrystallization temperature are also reported.     

Self-consistent calculation of hyperfine fields and adiabatic potential of impurities in iron

Hyperfine fields of impurities of the atomic number Z=1–56 at the substitutional site and those of light impurities of Z=1–9 at the interstitial sites in ferromagnetic iron are calculated by the KKR method adapted to the system containing a single impurity atom. The potential of the impurity atom is determined self-consistently by use of the local spin density functional formalism. The results for nonmagnetic sp valence impurities agree with those of the previous nonself-consistent calculation by Katayama-Yoshida, Terakura and Kanamori except for a few cases, confirming their theory of the systematic variation of hyperfine fields. The calculation for magnetic impurities of transition elements is presented for the first time in this paper. The calculations mentioned so far assume that impurities are situated at the center of each site. For the purpose of discussing the stability of the impurity positions, the change of the adiabatic potential due to displacements from the center is calculated by carrying out similar self-consistent calculations for off-center impurity positions. It is concluded that positive muon and some light impurities including boron will be displaced from the center when trapped in a vacancy.     

Calculations of hyperfine fields

First principle methods for calculation of hyperfine fields in different systems are reviewed. The contributions from energy states close to the Fermi level are emphasized and are responsible for different observed systematic behaviours in the hyperfine field, not directly related to the host magnetic moment. Calculations on Fe, on Fe₂P, on surfaces, on impurity atoms in Fe and on the muon Knight shift in Sb are discussed.     

Size effects on the magnetic hyperfine fields at non-magnetic impurities in iron

An important contribution to the magnetic hyperfine fields at non-magnetic impurities in magnetic metals arises from the conduction-electron polarization (CEP). In the model of Stearns the CEP at the impurity site,Pce, arises from the exchange interaction of the conduction electrons at that site with the localized 3d host electrons. In this modelPce is a negative constant, independent of the impurity, so that an emperical volume-misfit correction has to be introduced to explain the observed positive hyperfine fields. The purpose of this paper is to show thatPce is not constant, but is strongly affected by the distortion of the lattice around the impurity. The correct form ofPce includes a volume term equivalent to that postulated by Stearns. The hyperfine fields for Cu, Zn, Sn, Sb and Au are calculated, taking the distortion effects into account. A fair agreement with the observed hyperfine fields is obtained. Furthermore, the effects of pressure on the CEP are discussed.Supported by the NSF Grant No. DMR 73-07665 AO 3     

Transient hyperfine magnetic fields

Fast ions traversing magnetized materials experience very large transient hyperfine magnetic fields. The processes responsible for these interactions are related to the interchange of electrons between the moving ion and the polarized medium. The dependence of the transient hyperfine fields on the atomic number and the velocity of the ion, and on the magnetization of the host has been mapped for a wide range of nuclei and magnetic hosts. The experimental evidence supporting specific models will be presented and applications to the measurement of magnetic moments of short-lived excited states will be described. Supported in part by the National Science Foundation     

Magnetic hyperfine fields of Zr in nickel and iron measured by the DPAD method

The magnetic hyperfine fields of Zr in nickel and iron were measured by the DPAD method. Using the 8⁺ isomeric states in⁹⁰Zr and⁸⁸Zr these fields were found to beH _hf(ZrNi)=–4.65(10) T andH _hf(ZrFe)=–27.4(4) T, respectively.     

Magnetic hyperfine fields in ferrigehlenites

Western Canadian cretaceous coal (WC5) and Appalachian carboniferous coal (AC4) are good coking coals, although their rheological properties predict a different behaviour with this respect. According to Mössbauer Spectroscopy, iron-based mineral matters of these coals are very different: WC5 spectrum exhibits chiefly Fe₃O₄ while AC4 contains mainly ferrous silicate and no ferric ion. However the spectra of the ashes exhibit a similarity: they characterize α-Fe₂O₃ with a distribution of particle sizes extended down to some tens of nanometers. Such a dispersion could favour catalytic processes during the low temperature stages of coking.     

Internal magnetic hyperfine fields at Hf nuclei in iron,cobalt and nickel hosts

Integral perturbed angular correlation technique has been used to measure the internal hyperfine magnetic fields at Hf nuclei in Fe, Co and Ni matrices. These represent a consistent set of measurements with diffused sources. The 9+/2 (208 keV) 9?/2 (113 keV) 7?/2 cascade in the decay of¹⁷⁷Lu→¹⁷⁷Hf was used for measurements. The results obtained are: $$\begin{gathered} H_{Fe}^{Hf} = - 266 \pm 47 kG, \hfill \\ H_{Co}^{Hf} = - 116 \pm 18 kG, \hfill \\ H_{Ni}^{Hf} = - 118 \pm 26 kG. \hfill \\ \end{gathered} $$ These measurements are compared with previous results and discussed in terms of methods of source preparation.     

Anomalous behaviour of hyperfine fields at iron in new magnetic systems RuxFey Si and RuFeB

A new class of magnetic system Ru_xFe_ySi, has been identified in which the hyperfine field at Fe, as sensed by⁵⁷Fe Mossbauer effect, is seen to evolve at a characteristic temperature far below the bulk magnetic ordering temperatures.     

Temperature dependence of the hyperfine fields for fluorine in ferromagnetic iron,nickel and gadolinium

The temperature dependence of the magnetic hyperfine fields at the sites of F nuclei implanted into ferromagnetic Fe, Ni and Gd has been studied in the temperature range from 77 K to 670 K. A pulsed proton beam was used to observe the time-differential precession of the 5/2⁺ state in¹⁹F. Deviations from the bulk magnetization were found for Fe and Ni. The damping of the two observed fields in Ni was interpreted in terms of a field distribution caused by an induced radiation damage. The occupation sites for F and possible mechanisms of the anomalous temperature dependence are discussed.     

Low temperature pressure dependence of the muon hyperfine fields in iron,cobalt and nickel

The pressure dependence of the μ⁺ local magnetic fields in polycrystalline Fe and Ni and a Co single crystal has been measured at 77 K, up to 0.7 GPa, using a He gas high pressure setup. The pressure derivatives dlnB_μ/dP in units of mT/GPa are +4.4±1.0 (Fe), -0.7±1.1 (Co) and +0.63±0.10 (Ni). From these values the hyperfine field volume derivatives are deduced. Using these values together with previously determined room temperature derivatives the thermal expansion part of the temperature dependence of the hyperfine field can be calculated. The remaining explicit temperature dependence below 300 K, which deviates markedly from the temperature dependence of the bulk magnetization, is discussed.     

The hyperfine field of sodium in iron

The hyperfine field of NaFe has been measured using Low Temperature Nuclear Orientation of cold implanted²⁴Na. The combination of both the γ-and β-anisotropies yields information on the implantation fraction of Na in Fe. Furthermore, an, upper limit for the relaxation time of Na in Fe could be deduced.     

The hyperfine field of krypton in iron

The hyperfine field of krypton nuclei at lattice sites in iron has been determined using nuclear orientation. From the anisotropy of the electrons emitted in the decay of⁸⁵Kr implanted in iron, a hyperfine field value of +31.2(8) T was deduced for a substitutional fraction of approximately 37%. Also, a relaxation time of the order of 900 see was observed at temperatures between 7 and 11 mK.     

The hyperfine field of oxygen in iron

From an on-line nuclear orientation measurement on¹⁵O implanted in iron, the hyperfine field of oxygen in iron was deduced as +12.2(16) T. This experiment, together with two measurements on¹⁷F, which was implanted in the same foil, also yielded information on the relaxation and implantation behaviour of light impurities when implanted at low dose and at low temperature.