Thermally assisted magnetic writing is an important technology utilizing temperature dependent magnetic properties to enable orientation of a magnetic data storage medium. Using an atomistic spin model we study non-equilibrium field cooled magnetization processes on sub-nanosecond timescales required for device applications. We encapsulate the essential physics of the process in a TRM-T curve and show that for fast timescales heating to the Curie temperature is necessary where the magnetic relaxation time is shortest. Furthermore we demonstrate the requirement for large magnetic fields to achieve a high thermoremanent magnetization necessary for fast recording or data rates. 75.60.Jk,75.10.Hk The increasing requirements for digital data storage over the past 30 years has led to an exponential growth in the storage capacity of magnetic recording media, with a typical hard drive today capable of storing around 900 Gigabits of data per square inch of recording medium. Magnetic recording has seen several significant enhancements over its lifetime, from the shift to giant magnetoresistive spin valve sensors 1 , longitudinal to perpendicular recording 2 and more recently to composite media designs such as exchange coupled composite media. 3 At the same time technologies such as magnetic random access memory (MRAM) promise the possibility of a universal memory 4 . However, current perpendicular magnetic recording technology is approaching its fundamental limit due to the magnetic recording trilemma 5 , which gives the three competing requirements for conventional magnetic recording: signal to noise ratio, thermal stability and writability. Current media designs are approaching the limits of the trilemma primarily due to the limited write field available in the inductive write head which is insufficient to reorient the high anisotropy media. One solution is a technology called Heat Assisted Magnetic Recording 6,7 (HAMR), which utilizes the temperature dependence of the magnetic properties using laser heating to enable writing of the media, while the data is stored at room temperature for thermal stability in excess of ten years.Unlike conventional recording, where the applied field initiates deterministic switching of the magnetic state, thermally assisted writing requires that at the writing temperature the applied field is strong enough to overcome the thermal writability to orient the magnetization m, defined by 8,9where µ 0 is the permeability of free space, µ is the magnetic moment, k B is the Boltzmann constant, H is the applied field and T wr is the writing temperature. In combination with the usual requirements for the trilemma, this leads to the magnetic recording quadrilemma, 9 which also places a fundamental limit on the ultimate achievable recording density 10 . For reasonably sized grains (with large µ), the thermal writability is close to one, meaning that given an infinite amount of time the writing process will achieve the thermal equilibrium value of the magnetization defined in Eq. 1. However, incre...