Potbellies, wasp‐waists, and superparamagnetism in magnetic hysteresis

Abstract

Because the response of a magnetic substance to an applied field depends strongly on the physical properties of the material, much can be learned by monitoring that response through what is known as a “magnetic hysteresis loop”. The measurements are rapid and quickly becoming part of the standard set of tools supporting paleomagnetic research. Yet the interpretation of hysteresis loops is not simple. It has become apparent that although classic “single‐domain”, “pseudo‐single‐domain”, and “multidomain” loops described in textbooks occur in natural samples, loops are frequently distorted, having constricted middles (wasp‐waisted loops) or spreading middles and slouching shoulders (potbellies). Such complicated loops are often interpreted in oversimplified ways leading to erroneous conclusions. The physics of the problem have been understood for nearly half a century, yet numerical simulations appropriate to geological materials are almost unavailable. In this paper we discuss results of numerical simulations using the simplest of systems, the single‐domain/superparamagnetic (SD/SP) system. Examination of the synthetic hysteresis loops leads to the following observations: (1) Wasp‐waisting and potbellies can easily be generated from populations of SD and SP grains. (2) Wasp‐waisting requires an SP contribution that saturates quickly, resulting in a steep initial slope, and potbellies require low initial slopes (the SP contribution approaching saturation at higher fields). The approach to saturation is dependent on volume, hence the cube of grain diameter. Therefore there is a very strong dependence of hysteresis loop shape on the assumed threshold size. (3) We were unable to generate potbellies using an SP/SD threshold size as large as 30 nm, and wasp waists cannot be generated using a threshold size as small as 8 nm. The occurrence of both potbellies and wasp waists in natural samples is consistent with a room temperature threshold size of some 15 nm (±5). (4) Simulations using a threshold size of 15–20 nm with populations dominated by SP grain sizes, that is with a small number of SD grains, produce synthetic hysteresis loops consistent with measured hysteresis loops and transmission electron microscopic observations from submarine basaltic glass. (5) Simulations and measurements using two populations with distinct coercivity spectra can also generate wasp‐waisted loops. A relatively straightforward analysis of the resulting loops can distinguish the latter case from wasp‐waisting resulting from SP/SD behavior.

Geomagnetic intensity variations for the past 8 kyr: New archaeointensity results from Eastern China

“…Most of the specimens show similar hysteresis behavior (Figs. 3a, c) with slightly wasp-waisted or goosenecked shapes indicating either SP/SD mixtures or mixtures of different magnetic phases (Tauxe et al, 1996). Samples are generally saturated before 300 mT and the coercivity (B c ) ranges from ∼10 mT to ∼35 mT, which show the dominance of soft magnetic minerals.…”

IrSr2Sm1.15Ce0.85CuColman1, Mclaughlin2 2012Phys. Rev. B

“…At 2 K the loop takes an unconventional shape known as a wasp-waist that has previously been assigned to disorder in the magnetic exchange. 26 This complex type of magnetic behavior is commonly observed in reentrant spin-glasses (RSGs). 27 Upon cooling a reentrant spin-glass there is an initial onset of partial order at t 1 (>300 K in Ir 0.825 Sr 2 Sm 1.15 Ce 0.85 Cu 2.175 O 10 ), where ferromagnetic clusters are formed in the otherwise paramagnetic state.…”

Iron oxide minerals in dust-source sediments from the Bodélé Depression, Chad: Implications for radiative properties and Fe bioavailability of dust plumes from the Sahara

“…In all cases the loops have a positive high field slope ( hf ) due to the strong influence of paramagnetic or antiferromagnetic phases, and closure occurs by 500 mT characteristic of ferrimagnetic phases like magnetite. Some loops have shape factors, hys >0.2, producing a slight constriction near the origin and indicating a mixture of low-and high-coercivity phases representing either mixtures of different minerals (magnetite/maghemite and hematite/goethite) or mixtures of different particle sizes in a single mineral (microcrystalline and nanometric) (Tauxe et al, 1996;Roberts et al, 1995;Dunlop 2002a, b).…”