POTBELLIES, WASP-WAISTS, AND SUPERPARAMAGNETISM IN MAGNETIC HYSTERESIS

Because the response of a magnetic substance to an applied field depen ds strongly on the physical properties of the material, much can be le arned by monitoring that response through what is known as a ''magneti c hysteresis loop''. The measurements are rapid and quickly becoming p art of the standard set of tools supporting paleomagnetic research. Ye t the interpretation of hysteresis loops is not simple. It has become apparent that although classic ''single-domain'', ''pseudo-single-doma in'' 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 (potb ellies). Such complicated loops are often interpreted in oversimplifie d ways leading to erroneous conclusions. The physics of the problem ha ve been understood for nearly half a century, yet numerical simulation s appropriate to geological materials are almost unavailable. In this paper we discuss results of numerical simulations using the simplest o f systems, the single-damain/superparamagnetic (SD/SP) system. Examina tion of the synthetic hysteresis loops leads to the following observat ions: (1) Wasp-waisting and potbellies can easily be generated from po pulations of SD and SP grains. (2) Wasp-waisting requires an SP contri bution 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 s ize. (3) We were unable to generate potbellies using a SP/SD threshold size as large as 30 nm, and wasp waists cannot be generated using a t hreshold size as small as 8 nm. The occurrence of both potbellies and wasp waists in natural samples is consistent with a room temperature t hreshold size of some 15 nm (+/- 5). (4) Simulations using a threshold size of 15-20 nm with populations dominated by SP grain sizes, that i s with a small number of SD grains, produce synthetic hysteresis loops consistent with measured hysteresis loops and transmission electron m icroscopic observations from submarine basaltic glass. (5) Simulations and measurements using two populations with distinct coercivity spect ra can also generate wasp-waisted loops. A relatively straightforward analysis of the resulting loops can distinguish the latter case from w asp-waisting resulting from SP/SD behavior.