Magnetic After-effect Spectra Research Articles

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) spectroscopy with respect to (i) the Verwey transition, (ii) the low-temperature (4 K < T < 125 K ≃ T V) charge transport mechanisms and (iii) the zero-crossing of the crystal anisotropy. The observed low-temperature shifting of the transition (T V) is in fair agreement with previous conductivity measurements. Variations of the MAE spectra clearly indicate the low-temperature tunnelling (4 K < T < 35 K) to be far more affected by smallest impurity doping than variable long-range hopping (50 K < T < 125 K) – this outstanding sensibility of the tunnelling processes against impurities or any other defects is also true when compared with the corresponding T V shifting. All samples undergo a doping-induced temperature splitting, ΔT VC, between the Verwey transition (spontaneous jump of the susceptibility at T V) and the zero-crossing of the crystal anisotropy (giving rise to a delayed susceptibility maximum) – in contrast to perfectly stoichiometric Fe3O4 single crystals where both effects are coincident. This range of temperature-splitting ΔT VC, found to be extremely large in the case of Co2+ doping, is characterized by destabilized magnetic domain structures due to locally disordered anisotropy distribution in the lattice.

Magnetic after-effect study of dislocation relaxation in Fe-based alloys

Dislocation-related relaxation processes are studied by measuring the magnetic after-effect spectra as a function of temperature in a variety of non-deformed and cold-worked iron alloys. In the α-Fe and Fe–1%Cu alloys the peak centred at about 320 K appears as a consequence of plastic deformation. On the basis of the behaviour of its parameters, such as the temperature position of the peak, the full width at half maximum and the integrated intensities, this feature is assigned to the relaxation process of thermally activated dislocation motion.

Point-defect interactions in electron-irradiated titanomagnetites—asanalysed by magnetic after-effect spectroscopy on annealing within80 K < Ta < 1200 K

During high-temperature growing of titanomagnetite single crystals (Fe2.8−ΔTi0.2O4,Δ < 0.005) in oxygen enrichedatmospheres, specific Ti4+- and vacancy-based defect configurations are induced, giving rise to magnetic after-effect(MAE) spectra with peaks near 450, 200 and 65 K. The atomistic mechanisms of theserelaxations are checked by exposing the crystals to low-temperature (80 K) electron (e−) irradiation and subsequent analysis of the interactions between radiation-induced andlattice-inherent defects on annealing over the range K.Within this interval, three characteristic temperature ranges are distinguished: (a) 80 K < Ta < 500 K, revealing vigorous interactions between radiation-induced and inherent defectconfigurations, thus demonstrating their common point-defect nature; (b) 500 K < Ta < 900 K wherein the MAE spectra re-assume, qualitatively, their initialstructure with, however, mutually modified amplitude ratios; (c) 900 K < Ta < 1200 K, being characterized by the complete annihilation of all MAEs but, interestingly, also thethermally induced re-appearance of vacancies and related defect configurations.The recovery kinetics of all prominent processes are numerically analysed and discussedwith respect to their underlying atomistic mechanisms.

Magnetic aftereffect spectroscopy of Fe- and Co-based amorphous alloys

Theoretical and experimental fundamentals of a computer-based spectroscopic method--magnetic aftereffect (MAE) spectroscopy---giving sets of elementary activation energy (AE) spectra of magnetic relaxation (MR) processes, are introduced. Structural MRs in two representative amorphous alloys, ${\mathrm{Fe}}_{75}{\mathrm{Si}}_{15}{\mathrm{B}}_{10}$ and ${\mathrm{Co}}_{70}{\mathrm{Fe}}_{5}{\mathrm{Si}}_{15}{\mathrm{B}}_{10}$, were investigated by MAE spectroscopy. The MAE measurements were performed on the as-cast and annealed samples in a temperature range of $77--620\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Activation parameters of the individual directional reordering processes were obtained. The B- and Si-type MRs were identified in the FeSiB and CoFeSiB alloys. The B-type MRs originate from the reorientation of Co-B or Fe-B atom pairs. The Si-type MRs come from the reorientation of Co-Si or Fe-Si pairs. Atom pairs Fe-B, Co-B, Fe-Si, and Co-Si are aligned by the increasing values of the most probable activation energies (AE) of the MR. For the B and Si types of the MR, the two most probable activation energies, ${Q}^{*}=1.33$ and $1.55\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, with the pre-exponential factors ${\ensuremath{\tau}}_{0}=2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ and $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$, respectively, were obtained in the as-cast FeSiB alloy. For the as-cast ${\mathrm{Co}}_{70}{\mathrm{Fe}}_{5}{\mathrm{Si}}_{15}{\mathrm{B}}_{10}$ alloy, the B and Si types of the MR are characterized by the activation energies ${Q}^{*}=1.38$ and $2.16\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and the pre-exponential factors ${\ensuremath{\tau}}_{0}=8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ and $9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$, respectively. Low temperature annealing causes lowering of the MAE peaks and shifts the peak temperatures and the AEs of MRs in both alloys to higher values. The MAE and AE spectra of the annealed CoFeSiB amorphous alloy exhibit one peak only.

Timescale settling and nature of electron transport in magnetite – Generalconsiderations in view of new magnetic after-effect results on dilutelyTi4+-dopedFe3O4

The effect of dilute titanium (Ti4+)-doping on the magnetic after-effect (MAE) spectra of stoichiometric magnetite single crystals,Fe3−xTixO4 – with0.0001≤x≤0.008 – is studied in the temperature range and analysed in terms of our revised relaxation model. The effects of theserelatively low doping rates comprise: (i) strong impact on low-temperature(4 K<T<35 K) incoherentelectron (e−)-tunnelling and combined intra-ionic thermal excitation; (ii) minor, thoughhighly instructive, modifications of thermally activated electron hopping(50 K<T<125 K), and (iii) low-temperature shifting of the Verwey transition(TV) relative to the temperature of zero-crossing of the crystal anisotropy(TK1). Due to the high oxygen stoichiometry of the crystals (absence ofB-site vacancies), no further MAEs appear in the high-temperature range(T>TV).The recently accentuated discussion concerning the appropriate timescale of electrontransport – deduced from modern x-ray resonant scattering to be about , over the whole temperature range(T≷TV), in contrast to up to thousands of seconds as determined fromhigh-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 electronicconductivity mechanisms in magnetite.

Structural magnetic relaxation of amorphous Co75B25 alloy

The structural magnetic relaxation of the amorphous Co75B25 alloy in the as-cast and annealed states has been investigated by means of the magnetic after-effect (MAE) spectroscopy. The relaxation process is realised by reorientations of atom pairs minimizing a free energy of the ferromagnetic system. The pre-exponential factor τ0=2×10−17 s and the most probable activation energy Q*=1.34 eV have been obtained from numerical analyses of MAE spectra and isotherms of the amorphous alloy in the as-cast state. A peak of the 180 s isochrone occurs at the temperature 383 K. Annealing at 653 K for 1800 s reduces relaxation intensity Δr/r from 38% to 9% and shifts the peak temperature to 473 K. Activation parameters of the magnetic relaxation of the annealed Co75B25 alloy were changed to τ0=9×10−16 s and Q**=1.53 eV. These effects are connected with reduction of the free volumes near to active atom pairs. Numeric analyses of the MAE isochrones and long time isotherms give very similar activation energy spectra.

Directional ordering in amorphous Co–Si–B alloys

Directional ordering in the amorphousCo75Si15B10 alloys by means of the magnetic after-effect (MAE) of the initial reluctivity andits influence on the Perminvar effect have been investigated. Two peak MAEspectra were obtained from isochronal measurements for as-cast as well asannealed samples. The spectrum of the as-cast sample has peak maxima at 383and 545 K. Comparing this MAE spectrum with the spectrum of amorphousCo75B25 alloy, we identified the first peak as a result of Co–B atom pair reorientation(B-type relaxation) and the second one at higher temperatures as a resultof Co–Si atom pair reorientation (Si-type relaxation). After annealing, thepeaks shift to 442 and 576 K, respectively. For the numerical analysis ofCo75Si15B10 MAE spectra we modified the micromagnetic model assuming the existence of morerelaxation processes, where each process is connected to the relaxation of onemetalloid element. The pre-exponential factor for B-type relaxation was found to beτ0,AC(B) = 7 × 10−17 s with the most probableactivation energy QAC*(B) = 1.31 eV. These values correlate very well with the magnetic relaxation (MR) activation parameters ofCo75B25 alloy,τ0,AC = 2 × 10−17 sand QAC* = 1.35 eV. Si-type relaxation has activation parametersτ0,AC(Si) = 6 × 10−18 sand QAC*(Si) = 1.96 eV. After annealing the sample at 683 K for 30 min they change to valuesτ0,AN(B) = 2 × 10−15 s,QAN*(B) = 1.38 eVand τ0,AN(Si) = 3 × 10−17 s, QAN*(Si) = 2.01 eV. The complicated shapes of the long-time isotherms reflect the superposition of tworelaxation processes. We have numerically split each isotherm into two sub-isothermsrepresenting the particular contributions of the two relaxation processes. The MAEspectrum of the critical field measured on the as-cast sample also has two peaks, like thereluctivity spectrum. The impact of Co–B and Co–Si atom pairs on the behaviour of thedomain wall stabilization potential is discussed for the explanation of the observed MRresults.

Influence of Cr on some structural and magnetic properties of amorphous Co-based alloys

Magnetic relaxation of the amorphous Co 80− x Cr x Si 6B 14, x=0, 2, 4, 6, 8 alloys have been investigated by the isothermal and isochronal magnetic after-effect (MAE) and the Perminvar effect. Addition of Cr influences all characteristic parameters of the MAE spectrum. It increases relaxation peak temperature T max, increases the width of the spectrum Δ T and suppresses relaxation intensity (Δ r/ r) max. Cr also significantly influences activation parameters of the magnetic relaxation. It increases the most probable activation energy Q * from 1.2 to 1.68 eV and decreases pre-exponential factor τ 0 from 5×10 −16 to 2×10 −19 s. The increase in T max and Q * is probably given by the formation of strong chemical bonds between Cr and metalloids, what decreases their mobility. The stabilisation effect induced by the presence of Cr atoms can be also visible in the change of T max, Δ T and (Δ r/ r) max after annealing the samples at 573 K for 60 min. These parameters do not change in the case of the samples with higher Cr content as intensively as in the case of Co 80Si 6B 14 sample. The stabilisation effect of Cr is also manifested by the long-time isothermal measurements as well as in the Perminvar effect measurements. Suppression of the magnetic relaxation by Cr was proven in concentration dependence of the domain wall (DW) critical field, too. It decreases with Cr content increase.

Irradiation-Induced Electron Tunnelling and Small-Polaron Hopping in Single-Crystalline YIG

In electron (e - )-irradiated (>10 23 e - m -2 ) single crystalline yttrium-ion Garnet (YIG), after moderate annealing, low-temperature (T < 125 K) magnetic after-effect (MAE) spectra are observed which are of striking similarity to the well investigated spectra occurring in magnetite (Fe 3 O 4 ) below the Verwey transition (T V 125 K). Our analysis shows that this similarity is the result of corresponding relaxation mechanisms in both systems, i.e. electron tunnelling and small-polaron hopping. Deeper insights into these mechanisms are obtained from a thorough inspection of these spectra and their physical preconditions in the two, a-priori, completely different ferrimagnetic systems: (i) semiconductor, transformed into a quasi-insulating state due to long-range ionic ordering at low-temperatures (Fe 3 O 4 ) and (ii) insulator, brought into a state of low resistivity due to radiation-induced perturbations of the charge equilibrium (YIG).

Magnetic aftereffect and electrical conductivity in double perovskite Ba2FeMoO6

In this work a study of the magnetic aftereffect and electrical conductivity in Ba2FeMoO6 is presented. Aftereffect measurements have been performed by recording the time evolution of magnetic permeability just after the sample demagnetization, while the electrical conductivity has been obtained by means of the four-probe technique working under ac excitation. The isochronal relaxation spectrum was constructed by evaluating at each temperature the relative variation of permeability between the end of demagnetization and a set of indexed time windows according to the fastness of the magnetic relaxation. The magnetic aftereffect spectra show two well-defined peaks related to the magnetic phase transition and the orientational processes that can be fitted by activation energies close to 0.65 eV. Electrical conductivity presents metallic behavior in the ferromagnetic region and semiconducting response in the paramagnetic zone with activation energy of 0.03 eV.

Magnetic after-effect and ferromagnetic resonance in LiZnTiMn-ferrites

Ferromagnetic resonance linewidths at room temperature for Li 0.79Zn 0.25Ti 0.83Fe (1.08− k) Mn 0.05O 4 polycrystalline ferrites sintered in oxygen atmosphere at 1050°C with k ranging from 0.00 to 0.10 are presented. The linewidths measured in these samples are comparable to most of commercial ferrites. Their values decrease with increasing k from 53 to 40 Oe. Magnetic after-effect spectra are also presented from 77 to 300 K. A relaxation process, whose amplitude decreases with increasing k, is observed at 250 K. A relationship between ferromagnetic resonance linewidth and magnetic after-effect spectra is presented.

A Review of the Magnetic Relaxation and Its Application to the Study of Atomic Defects in α-Iron and Its Diluted Alloys.

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).

Magnetic after-effect in FeNiZrCuB amorphous alloys

The magnetic after-effect (MAE) and AC susceptibility in the amorphous Fe 86 − x Ni x Zr 7Cu 1B 6 alloys with different contents of Ni ( x = 0–86 at%) were investigated. The Curie temperatures T c were estimated from the temperature dependences of the AC susceptibility measured in the temperature range 20–550°C. Additions of Ni up to x = 43 at% cause rapid increase of the Curie temperature from 71°C for Fe 86Zr 7Cu 1B 6 to 373°C for Fe 43Ni 43Zr 7Cu 1B 6 alloys. Higher concentrations of Ni cause decrease of T c down to paramagnetic state of Ni 86Zr 7Cu 1B 6 alloy at the room temperature. It was found that the additions of Ni drastically change shapes and amplitudes of MAE spectra. From the MAE spectra measured in the temperature ranges (− 197°C; T c) the activation energy spectra with the most probable value Q = 1.23 eV were obtained.

Magnetic after-effect spectra analysis by applying the lognormal distribution of relaxation times

An analysis of magnetic after-effect spectra made by applying the gaussian distribution in ln τ is presented and discussed in details. The procedure described allows to decompose very broad relaxation spectra into several relaxation processes with continuous distributions of relaxation times. This model is applied to the quantitative analysis of isochronal disaccommodation curves obtained for several amorphous and partially crystallized ribbons of Fe 73.5Cu 1Nb 3Si 13.5B 9 (after stress relieving at 673 K for 1 h and annealing at 823 K for 10 s), Fe 87Zr 7B 6 (in the as-quenched state and after annealing at 700 K for 1 h) and Co 66Fe 4Mo 2Si 16B 12 (annealed at 700 K for 30 s) alloys. From this analysis the mean activation enthalpy, pre-exponential factors, intensities and widths of the distributions in ln τ of individual processes are determined.

Time and thermal stability of magnetic properties of amorphous Fe80TM3B17 alloys

We have investigated the influence of the addition of different transition metals (Fe. Co. Cr. Mn. Mo. Ni. Os. Pt. Ru. Ta. Ti. V and W) on the time-temperature stability of amorphous Fe 80 TM 3 B 1- alloys. Time stability is represented by the Magnetic After - Effect (MAE). Each element influences near neighbourhood of other atoms by its characteristic way which results in a different chracteristics of the MAE spectra and its spectra of activation energies. It turned out from our measurements that samples can be divided into the three groups: The first one contains alloys with MAE similar to that of an FeB alloy, in the second there are alloys with different MAE, and in the third one there are alloys with almost no MAE. It was found that MAE can be successfuily descnbed on the basis of the micromagnetic model with activation parameters Q * = 1.3 - 1.7 eV and τ 0 = 10 -18 -10 -13 S. Small values of the preexponantial factor points out that MAE in Fe 80 TM 3 B 17 amorphous alloys is caused by the rearrangement of the mobile atom pairs within the domain walls.

Magnetic relaxation of hydrogen in La(Ni 0.7Fe 0.3) 5

The short-range hydrogen diffusion in the α-phase of the intermetallic compound La(Ni 0.7Fe 0.3) 5 has been studied by means of magnetic after-effect (MAE) measurements below the Curie temperature T c=250 K. At a hydrogen concentration of c H=4.7 at.% the MAE spectrum shows one broad relaxation maximum at 125 K, with an activation enthalpy of Q=(0.32±0.02) eV and a pre-exponential factor of τ 0=2×10 −12±0.5 s. With lower hydrogen content this maximum shifts to higher temperatures corresponding to an increase of the activating enthalpy. At a concentration of c H=0.4 at.% it splits up into a double maximum at 140 and 160 K. The corresponding enthalpy spectrum shows two peaks with activation enthalpies of (0.36±0.03) and (0.43±0.03) eV. The results are discussed taking into account the crystal structure of the AB 5 compound and hydrogen-induced internal stresses.

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

The magnetic after-effect (MAE) spectra of titanomagnetites, Fe3—x—ΔTixO4, with constant vacancy content, Δ ≈︂ 10—4, and systematically varied Ti4+-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 Ti4+-substitutions (x ≥ 0.01): (i) the order-dependent, low-temperature (T < 125 K) electronic relaxations are severely affected; (ii) the ionic, vacancy-mediated process III1, 2 (300 K) splits up into two satellites III* (260 K) and II1, 2 (around 400 K); (iii) near 200 K, additionally process IV1, 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. Die magnetischen Nachwirkungsspektren von Titanomagnetit, Fe3—x—ΔTixO4, werden im Temperaturbereich 4 K < T < 460 K eingehend untersucht in Abhängigkeit des Titangehalts, 0,01 ≤ x ≤ 0,4, bei konstantem Leerstellengehalt, Δ ≈︂ 10—4. Durch den Einbau bereits geringer Ti4+-Mengen (x ≥ 0,01) werden diese Spektren einschneidend verändert: (i) Die ordnungsabhängigen, elektronischen Tieftemperaturprozesse werden stark beeinträchtigt; (ii) die Leerstellen-induzierte Ionen-Nachwirkung III1, 2 spaltet auf in die beiden Satelliten III* (260 K) und II1, 2 (bei 400 K); (iii) nahe 200 K tritt Prozeß IV1, 2 auf, der als Relaxation anisotroper Zwischengitteratome gedeutet wird. Mit Hilfe plausibler Modelle gelingt es, Mechanismen und interne Zusammenhänge der verschiedenen Prozesse aufzuklären und deren Aktivierungsparameter numerisch zu bestimmen.

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.

Study of magnetic after-effects of complex permeability in amorphous CoFeCrSiB alloys

In our work we have investigated magnetic after-effect (MAE) of complex permeability (μ = μ 1 − jμ 2) in nearly non-magne-tostrictive ferromagnetic alloys CoFeCrSiB. MAE is represented by a relative change of both real ( r 1) and imaginary ( r 2) parts of the complex reluctivity Δ/( = 1/(#x003BC; − 1)) which may be expressed as follows: Δr 1(t)/r 1 = r 1(t) − r 1(t 1)/r 1(t 1), Δr 2(t)/r 2 = r 2(t) − r 2(t 1)/r 2(t 1) Time t 1 was 0.9 s for each measurement. Temperature dependences of both real (μ 1) and imaginary (μ 1) parts of complex permeability were measured in the temperature interval from − 175 to 100 °C. Computer analysis was made to evaluate the spectra of activation energies connected with MAEs. It was found that the MAE spectrum with a maximum at about 100 °C corresponds to the spectrum of activation energies with the most probable value 1.1 eV and τ 0 = 5.10 −15 s.

Analysis of Magnetite and related Ferrites by Means of Magnetic After-Effect-Spectra

The magnetic aftereffect (MAE) spectra of magnetite (Fe 3 O 4 ) and related spinel ferrites react most sensibly on smallest deviations of the crystal stoichiometry due to intrinsic or extrinsic lattice defects. Thus, the analysis of corresponding MAE spectra represents both an effective tool for quality control and classification of these materials and. moreover, a high-sensitive instrument for the detection and identification of respective lattice defects. The efficiency of this technique is demonstrated in the following on a series of instructive examples.