F. Walz

A review of the magnetic relaxation and its application to the study of atomic defects in α-iron and its diuluted alloys

Abstract This review presents a comprehensive survey on intensive studies performed during the last decades on point defect reactions on α‐iron (α‐Fe) and its diluted alloys. Our intention is to give an actual account of the knowledge accumulated on this subject, as it has been obtained predominantly by means of the magnetic after‐effect (MAE) spectroscopy. After a concise introduction into the theoretical and experimental fundamentals of this technique, the main concern is focused on the presentation and detailed discussion of the MAE spectra arising — after low‐temperature electron (e–)‐ or neutron(n)‐irradiation and subsequent annealing — in: (i) high‐purity α‐Fe and α‐Fe doped with (ii) substitutional solutes (like Ni, V, Al, Cu, Ti, Be, Si, Mn, …) or (iii) interstitial solutes (like O, H, C, N). During the course of systematic annealing treatments, these respective spectra undergo dramatic variations at specific temperatures thereby revealing in great detail the underlying intrinsic reactions of the radiation‐induced defects, i.e., reorientation, migration, clustering, dissolution and finally annihilation. In alloyed Fe systems the corresponding reaction sequences are even multiplied due to additional interactions between defects and solute atoms. Most valuable information concerning formation‐, dissociation‐ and binding enthalpies of small, mixed clusters (of the type CiVk, NiVk; i, k ≥ 1) has been obtained in high‐purity α‐Fe base material which, after charging with C or N, had been e–‐irradiated. Concerning the basic recovery mechanisms in α‐Fe, two complementary results are obtained from the analysis of the various systems: (i) in high‐purity and substitutionally alloyed α‐Fe the recovery in Stage‐III (200 K) is governed by a three‐dimensionally migrating (H M I = 0.56 eV) stable interstitial (dumb‐bell); (ii) following the formation and dissociation kinetics of small clusters (C1Vk, N1Vk) in interstitially alloyed α‐Fe the migration enthalpy of the monovacancy must hold the following relation H M N (0.76 eV) < H M C (0.84 eV) < H M V1. These results are in clear agreement with the so‐called two‐interstitial model (2IM) in α‐Fe – a conclusion being further substantiated by a systematic comparison with the results obtained from nonrelaxational techniques, like i.e. positron annihilation (PA), which by their authors are preferentially interpreted in terms of the one‐interstitial model (1IM).

Analysis of Magnetic After-Effect Spectra in Titanium-Doped Magnetite

The magnetic after-effect (MAE) spectra of titanomagnetites, Fe 3-x-Δ Ti x O 4 , with constant vacancy content, Δ 10 -4 , and systematically varied Ti 4+ -substitutions, 0.01 ≤ x ≤ 0.4, are thoroughly analyzed in the temperature range 4 K < T< 460 K. These spectra are characteristically modified in the presence of already small Ti 4+ -substitutions (x ≥ 0.01): (i) the order-dependent, low-temperature (T < 125 K) electronic relaxations are severely affected; (ii) the ionic, vacancy mediated process III 1,2 (300 K) splits up into two satellites III * (260 K) and II 1,2 (around 400 K); (iii) near 200 K, additionally process IV 1,2 develops which is deduced to be of interstitial type. In terms of plausible models, the mechanisms and respective interrelations of these various processes are clearly revealed and their activation parameters numerically determined.

The influence of a finite bandwidth on the Verwey transition in magnetite

The role of the band structure in the Verwey transition in magnetite (Fe3O4) has been analysed within the framework of an exactly solvable two-band model based on an effective interionic Coulomb potential splitting the 3d band of the t2g electrons. The model predicts an instability of the Verwey order below a certain ratio β/W of the Coulomb interaction parameter β and the bandwidth W. This instability can be understood in terms of a clear physical picture showing the impossibility of constructing a self-consistent ordered charge distribution in this case. A resemblance to the Cullen-Callen criterion is evident. It is shown as well that the influence of the band structure on the Verwey temperature vanishes rapidly when β/W increase beyond its critical value. Band-structure effects do provide an explanation, however, for the discontinuity in the Verwey temperature as a function of the concentration of cation dopants or the oxygen stoichiometry, which marks the transition from a first- to a second-order Verwey transition. In this respect, the model reproduces the experimental data quantitatively. Fits obtained by application of the model yield values of 0.037-0.04 eV for the Coulomb gap and 0.012-0.014 eV for the bandwidth. The obtained values of the bandwidth are typical for a strongly localized electron system and support a polaronic band picture.

The role of volume effects in the Verwey transition in magnetite

Fe2+/Fe3+ ordering in magnetite is described in terms of a simple mean-field approach based on an effective interionic Coulomb potential. It is shown that first-order electronic order-disorder transformations, as reported in the literature, can only be reproduced when the dependence of the interionic potential on the unit-cell dimensions is taken into account. In this case the first-order transitions can then be viewed as the result of an interplay between the lattice-deformation energy and the free-energy contribution related to the electronic ordering of the octahedral Fe lattice. Furthermore, the effect of the lattice deformation by hydrostatic pressure on the Verwey transition can be successfully explained to some extent within the context of the same framework. In comparison to experimental data available from the literature, the mean-field approach developed in this paper yields very acceptable results with respect to both qualitative and quantitative aspects, thus opening an interesting new viewpoint on the mechanism of the Verwey transition.

Magnetic Aftereffects in Zinc Ferrites

Magnetic after-effect (MAE) spectra on differently sintered zinc ferrites, Zn x Fe 3-z-Δ O 4 with 0.1 < x < 0.5 containing orthogonal vacancies (10 -5 < Δ < 10 -3 ) are investigated in the temperature range 4 K < T < 450 K using an LC-oscillator technique. The low-temperature MAE processes due to electron tunnelling (4 K< T < 35 K) and hopping (50 K < T < 125 K) are severely affected and the Verwey transition is completely suppressed for the given range of Zn substitutions. Around 300 K, the vacancy-induced peak III appears, being accompanied by a Zn-induced high-temperature satellite (T ≥ 380 K), known as process II. The vacancy-mediated relaxation model of process III is modified so as to explain the role of substituted Zn 2+ on the observed MAE spectra.

Magnetic Aftereffects in Single and Polycrystalline Yttrium Iron Garnet

Magnetic aftereffect (MAE) measurements on single and polycrystalline yttrium iron garnet, Y 3 Fe 5 O 12 , have been carried out from 4.4 to 450 K by means of an LC-oscillator technique. In nonoriented and oriented single crystal samples three processes around 60, 130 and 250 K are observed. Similar peaks appear in polycrystalline samples which had been sintered in air or CO 2 atmospheres. Following CO 2 sintering, a negative MAE is observed at low temperatures (T < 100 K) which is affected by the conditions of sample demagnetization. The processes have been approximated using least squares fitting techniques and are discussed in terms of a model based on the presence of oxygen vacancies and Fe 2+ ions in tetrahedral and octahedral positions.

Timescale settling and nature of electron transport in magnetite - General considerations in view of new magnetic after-effect results on dilutely Ti4+-doped Fe3O4

The effect of dilute titanium (Ti4+)-doping on the magnetic after-effect (MAE) spectra of stoichiometric magnetite single crystals, Fe3?xTixO4???with 0.0001?x?0.008???is studied in the temperature range and analysed in terms of our revised relaxation model. The effects of these relatively low doping rates comprise: (i) strong impact on low-temperature (4?K TV). The recently accentuated discussion concerning the appropriate timescale of electron transport???deduced from modern x-ray resonant scattering to be about , over the whole temperature range (TTV), in contrast to up to thousands of seconds as determined from high-precision MAE experiments, in the low-temperature phase (T<TV)???gives us the chance to sharpen our arguments in favour of a clarification of the electronic conductivity mechanisms in magnetite.

The Verwey transition in magnetite as studied by means of definite impurity doping

Abstract The effect of low-dose cation doping (0.005 < x < 0.08) of magnetite single crystals, Fe3-xMxO4 (M = Ni, Mg, Co, Al, Ti, Ga), has been studied by means of the magnetic after-effect (MAE) s...

Influence of non-stoichiometry on magnetic relaxation in polycrystalline barium ferrites

Bao·nFe2O3 ferrites of various compositions, 5.7 < n < 23, were prepared by standard ceramic methods. Their chemical composition was verified by atomic absorption spectrometry and their crystalline structure was determined by X-ray diffraction. Magnetic aftereffects were measured in the temperature range 4.4 K < T < 450 K. In this paper we give a short survey on the influence of variant Ba-concentrations on the magnetic relaxation spectra of these ferrites.

Analysis of Magnetic After-Effects in Manganese Ferrites

The low-temperature (4 > T > 125), electron-induced magnetic after-effect (MAE) spectra of vacancy-doped manganese ferrites, Fe3—x—ΔMnxO4 (0.002 ≤ x ≤ 0.8 and δ ≈ × 10—3, are investigated in detail. The tunnelling-induced MAEs (4 K > T > 35 K are severely affected in the presence of even smallest Mn contents (x ≤ 0.002). The hopping regime, though strongly modified upon continued doping — i.e. by narrowing and low-temperature shifting (≤50 K) — persists over the whole concentration range. Its high-temperature collapse remains accompanied by a pronounced susceptibility jump, thus indicating preservation of a residual, second-order Verwey-like crystallographic phase transition. The vacancy-mediated process III (300 K) and its Mn-dependent satellite II (≈380 K) are quantitatively analyzed and the, also Mn-induced, process IV (200 K) interpreted in a novel way in terms of intrinsic interstitials. Die elektronischen, im Tieftemperaturgebiet (4 K > T > 125 K) auftretenden magnetischen Nachwirkungsspektren von Leerstellen (δ )-dotierten Manganferriten, Fe3—x—ΔMnxO4, der Zusammensetzung 0,002 ≤ x ≤ 0,8 und δ ≈ × 10—3, werden eingehend untersucht. Die typischen Tunnelprozesse, im Bereich 4 K > T > 35 K, werden bereits durch geringste Mn-Konzentrationen (x≤ 0,002) stark beeintrachtigt. Die Hupf-Prozesse dagegen — obwohl mit steigendem Mn-Gehalt ebenfalls deformiert und nach tiefen Temperaturen (≤50 K) verschoben — bleiben uber den ganzen Konzentrationsbereich erhalten. Dabei wird ihr Hochtemperatur-Abfall von einer sprunghaften Suszeptibilitatszunahme begleitet, die auf die Fortdauer einer Verwey-ahnlichen, kristallographischen Phasenumwandlung zweiter Ordnung hinweist. Der Leerstellen-unterstutzte Prozes III (300 K) und sein Mn-abhangiger Satellit II (≈380 K) werden quantitativ analysiert und der, ebenfalls Mn-abhangige, Prozes IV (200 K) auf neuartige Weise als Orientierungsnachwirkung intrinsischer Zwischengitteratome gedeutet.