Probing The Origin of Alternating Field Induced Magnetic Heating with Lithographically Fabricated Collodial Solutions of Compensated Ferrimagnets

Magnetic nanoparticles (MNPs), used as alternating magnetic field (AMF) transducers, are currently actively being researched as a non-invasive way of manipulating biological systems. The nanomagnetic transducers turn the AMF into a force or field that can interact with biology. Most ubiquitous is the use of AMF transducers to generate heat. This heat can be used to ablate cancer cells, trigger ion channels, or open the blood brain barrier. Optimizing the heating from MNPs allows one to reduce the amount of MNPs used for medical treatment or to selectively heat on a cellular scale due to better local heating.<br/>Current theory says that the heating from a MNP in an AMF is proportional to the area of the hysteresis loop swept by the MNP. While this is an excellent approximation there have been some noticeable discrepancies observed in the current literature with this theory; it has been observed quite often that superparamagnetic nanoparticles have significant heating, but have no hysteresis loop area. Additionally, the Hamiltonian used when calculating energy loss in this theory lacks a term for ferromagnetic exchange.<br/>We instead turn to theory that describes accurately the switching of a MNP dynamically and includes ferromagnetic exchange. This theory predicts the heating induced in a magnet in an AMF is proportional to the sum of the speed of all the spins squared (|d<b>M</b>/dt|²). Intuitively one could think of this as a magnetic friction. This explains why superparamagnets have heating that is nearly the same as ferromagnetic nanoparticles but paramagnets do not. This also agrees with the previously put forward theory that larger anisotropy and larger hysteresis loops lead to larger heating.<br/>To confirm this theoretical framework we consider a system which, under the old theory should not heat but, with the accurate nanomagnetic heating theory, should heat: compensated ferrimagnets. Compensated ferrimagnets are ferrimagnets where the magnetization of the two sublattices are nearly the same, and therefore, below spin flip fields, have near zero net magnetization, have no hysteresis loop area, but still have two dynamically switching magnetic sub lattices.<br/>Turning films of magnetron sputtered amorphous near compensation GdCo (Gd = 25%) into colloidal solutions of lithographic microdisks we observe a net magnetization of 1.1emu/g (very small compared to 100emu/g for magnetite), and a near zero area hysteresis loop. However, we observe non-trivial AMF induced heating of 240 w/g (350w/g for magnetite in the same field conditions). These results demonstrate that magnetic heating is not purely proportional to hysteresis loop area but is a result of rapid, ferromagnetic exchange induced, magnetic motion.