Origin of the Planar Hall Effect in NanocrystallineCo60Fe20B20

Abstract

An angle dependent analysis of the planar Hall effect (PHE) in nanocrystalline single-domain Co 60 Fe 20 B 20 thin films is reported. In a combined experimental and theoretical study we show that the transverse resistivity of the PHE is entirely driven by anisotropic magnetoresistance (AMR). Our results for Co 60 Fe 20 B 20 obtained from first principles theory in conjunction with a Boltzmann transport model take into account the nanocrystallinity and the presence of 20 at. % boron. The ab initio AMR ratio of 0.12% agrees well with the experimental value of 0.22%. Furthermore, we experimentally demonstrate that the anomalous Hall effect contributes negligibly in the present case. DOI: 10.1103/PhysRevLett.107.086603 PACS numbers: 72.25.Ba, 71.70.Ej, 72.15.Gd Electron transport effects employing the electronic spin degree of freedom lie at the heart of spintronics and its applications not only in information technology [1] but more increasingly also in sensorics for biomedical purposes, where the utmost sensitivity for detecting minute magnetic stray fields is needed. The planar Hall effect (PHE) and the anomalous Hall effect (AHE) as well as tunneling magnetoresistance are promising phenomena for realizing highly sensitive sensors. From a materials point of view, nanocrystalline Co 60 Fe 20 B 20 (CoFeB) attracts growing attention since it combines large saturation magnetization with low coercivity [2,3], both favoring high sensitivities.PHE and AHE are both observed as a voltage transverse to the applied current [4,5] in contrast to the anisotropic magnetoresistance (AMR), which is measured in the longitudinal geometry. For PHE the magnetization M lies in the plane spanned by the current density j ¼ je x and the direction e y of the transverse voltage measurement, and for AHE the component of M perpendicular to j and e y matters. Although AMR has been known since Thomson's-later known as Lord Kelvin-observations in 1856 [6], PHE was discovered only a century later in polycrystalline permalloy [7]. More recently, PHE has also been found in crystalline La 2=3 Fe 1=3 MnO 3 [8] and as a very large effect at low temperatures in the dilute magnetic semiconductor (Ga,Mn)As [9]. The transverse resistance xy characterizing the PHE and the longitudinal resistivity xx denoting the AMR are given by [10] xy ¼ ð k À ? Þ sinÈ cosÈwhere k ( ? ) is the resistivity along (perpendicular to) the direction of the in-plane component of M, and È is the angle enclosed by j and M. A transverse voltage arises whenever the current is neither perpendicular nor parallel to the magnetization. Even though the AMR is a subtle spin-orbit effect, quantitatively reliable predictions from first principles based on the density functional theory (DFT) can be made [11,12]. In this Letter, we elucidate the role of AMR in the PHE in nanocrystalline Co 60 Fe 20 B 20 thin films experimentally and by ab initio calculations. We measure AMR and PHE in longitudinal and transverse four-probe transport experiments. The single-domain behavior enforced by an ...

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“…(38)-Eq. (41). Figure 2 presents the results of the generalized Wannier interpolation of the band structure compared to the direct calculation.…”

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