Method of easy-axis determination of uniaxial magnetic films by vector vibrating sample magnetometer

Abstract In this article, we introduce a method, which can be used to find the direction of easy axis (EA) or hard axis (HA) of a uniaxial Permalloy film easily and accurately. The method is called the vector vibrating sample magnetometer (V-VSM) measurement. It means that besides measuring the typical M x -hysteresis (i.e. when the x -axis pick-up coils are parallel to external field H → E ), we also simultaneously measure the M y -hysteresis (i.e. when the y -axis pick-up coils are perpendicular H → E ). The uniaxial sample is so oriented that its HA is more or less parallel to H → E , while its EA is biased by the Earth field h → e . Due to this biasing effect, the symmetry of M y -hysteresis is very sensitive on how the sample orientation φ being turned away from H → E . When φ ≅0°, we can identify two peak amplitudes, M y (R) and M y (L), on the M y -hysteresis curve. By varying φ in fine steps, we find that only when φ =0° exactly (i.e. when HA is found), do we have the full symmetry of M y (R)= M y (L). Otherwise, M y (R)≠ M y (L). Hence, the accuracy in determining HA by this method can be down to 0.25°. Further, we can sort those M y -hysteresis curves into three groups belonging to different ranges of φ , respectively; i.e. the in-center zone, the intermediate zone, and the off-center zone groups. The critical angle φ c from the in-center to the intermediate zone can be either set experimentally or calculated theoretically. Both the coercive force H c and the demagnetization factor D are relevant to find the relation between φ c and the width to length ratio w / L , and to find the second relation between φ c and the film thickness t .