Abstract
The intrinsic magnetic relaxation properties of goethite are elucidated via a comparative study of the magnetism of a stoichiometric and a nonstoichiometric sample, \ensuremath{\alpha}-FeOOH and \ensuremath{\alpha}-Fe${}_{0.92}$\ensuremath{\square}${}_{0.08}$O${}_{0.76}$OH${}_{0.24}$, where \ensuremath{\square} denotes a vacancy site. It is proposed that both goethite samples exhibit ``mode superparamagnetism'' at low temperatures, wherein the iron moments undergo thermally induced fluctuations over an energy barrier separating two closely related geometrical arrangements for the sublattice spins. This is an intrinsic relaxation mechanism that was previously predicted from magnetic structure refinements, which we have identified here in ac susceptibility and thermal decay of remanence data. An additional magnetic relaxation mode occurs in the nonstoichiometric goethite. This mode is characterized by relatively slow fluctuations, observable on the microsecond timescale of muon spin relaxation experiments, but not on the fast timescale of M\ossbauer spectroscopy, and appearing in ac susceptibility and dc magnetization data as blocking transitions in the range 70 to 100 K. These data are best described as the result of ``cluster ordering'': the formation and relaxation of magnetic clusters in the disturbed environment of the nonstoichiometric lattice.
Highlights
Goethite (α-FeOOH) is a naturally occurring antiferromagnetic mineral of orthorhombic structure and the space group Pnma
This is in large part due to that fact that most naturally occurring goethite, and invariably all synthetic goethite, depart significantly from ideal stoichiometry, with vacancies and/or diamagnetic impurity atoms occupying Fe3+ sites in the lattice. This has led to the literature being dominated by the magnetism of nonstoichiometric goethite, in which the properties are determined by competing effects, including moment canting, magnetic relaxation, and spin clustering
In the experiments described above, evidence for magnetic relaxation was seen in thermal decay of remanence (TDR) magnetometry data, where the measurement timescale τm ≈ 100 s, and in ac susceptibility data, where τm was in the range 10 ms to 100 μs
Summary
Goethite (α-FeOOH) is a naturally occurring antiferromagnetic mineral of orthorhombic structure and the space group Pnma. Various explanations for this moment have been put forward over the years, including finite size effects, unequal iron sublattice occupancies, and uncompensated surface spins.17 It was not until 1995 that Coey et al performed a neutron diffraction study on a high-purity, natural, single-crystal goethite and by means of a detailed magnetic Rietveld refinement showed that the weak moment is the result of an intrinsically canted antiferromagnetic structure along the crystallographic b axis.. The cluster ordering model has not been universally accepted, and it has been argued that the superferromagnetism model is more physically reasonable.24,25 It should be stressed, and as a corollary to the neutron diffraction experiment commented above, that mode superparamagnetism (MSPM) is a consistent model in which the dynamic effects arise from thermally activated transverse spin fluctuations between two equal energy states in the canted moment structure. The present work is an attempt to move on from previous studies and to offer a conclusive contribution on the magnetism of goethite: (1) by making measurements on two representative samples, one a high-purity stoichiometric natural goethite, the other a well-characterized nonstoichiometric synthetic goethite; (2) by making measurements on timescales covering many orders of magnitude, from nanoseconds to tens of seconds, and unifying the understanding thereby gained; and (3) by making muon spin relaxation (μSR) measurements on goethite—a technique with an intermediate (ca. microsecond) timescale that transpires to be very helpful when it comes to distinguishing between the various models of relaxation behavior
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