Temperature dependence of the energy barrier and switching field of sub-micron magnetic islands with perpendicular anisotropy

Abstract

Using the highly sensitive anomalous Hall effect we have been able to measure the reversal of a single magnetic island, of diameter 220 nm, in an array consisting of more than 80 of those islands. By repeatedly traversing the hysteresis loop, we measured the thermally induced fluctuation of the switching field of the islands at the lower and higher ends of the switching field distribution. Based on a novel easy-to-use model, we determined the switching field in the absence of thermal activation, and the energy barrier in the absence of an external field from these fluctuations. By measuring the reversal of individual dots in the array as a function of temperature, we extrapolated the switching field and energy barrier down to 0 K. The extrapolated values are not identical to those obtained from the fluctation of the switching field at room temperature, because the properties of the magnetic material are temperature dependent. As a result, extrapolating from temperature dependent measurements overestimates the energy barrier by more than a factor of two. To determine fundamental parameters of the energy barrier between magnetisation states, measuring the fluctuation of the reversal field at the temperature of application is therefore to be preferred. This is of primary importance to applications in data storagea and magnetic logic. For instance in fast switching, where the switching field in the absence of thermal activation plays a major role, or in long term data stability, which is determined by the energy barrier in the absence of an external field.

Thermal stability of magnetic states in submicron magnetic islands

“…These results show that a value of 10 9 Hz as was assumed in refs. [31,32] gives reasonable approximation.…”

“…For a permalloy island in a spin ice structure [17], K 1 > 0 and K 2 > 0 describe easy axis shape anisotropy and easy plane shape anisotropy, respectively. For CoPt islands [31,32], there is an intrinsic out of plane anisotropy and K 2 < 0 whereas K 1 ≈ 0 due to the round shape of the islands. The same system can be described by K 1 < 0 and K 2 ≈ 0 when the y-axis is chosen to be perpendicular to the island plane.…”

“…In the calculations shown in Fig. 3 the value of K 2 is different, 116 kJ/m 3 , to roughly correspond to CoPt islands [31,32]), and the magnetic field is chosen to have strength of H = 1.33 MA/m and direction given by θ H = π/10 and φ H = π/2. There are two local minima A and B on the energy surface corresponding to the stable magnetic states.…”

Calculations of switching field and energy barrier for magnetic islands with perpendicular anisotropy

“…A large difference was found in the maximum field needed to switch the magnetization of different islands, likely due to variations in the thickness and composition of the metallic layers from one island to another. "Weak" islands had, for example, a maximum in the SFD at a field of 84 kA/m while "strong" islands a maximum at 184 kA/m in measurements carried out at 10 K [15]. As the temperature was increased to 300 K, the peaks shifted to the lower field by ca.…”

“…In recent experiments, de Vries et al were able to measure the SFDs of individual magnetic islands and found a large variation in the properties of the islands even though the shape and size were the same [15]. In these experiments, the SFD is only a reflection of the stochastic nature of the thermal activation since the measurements are carried out for one island at a time but with repeated sweeps of the magnetic field.…”