The magnetoresistance of Ni 81 Fe 19 and Co 83 Gd 17 ferromagnetic thin films is measured in Corbino disk geometry, and compared to magnetoresistance of same films measured in Hall-bar geometry. The symmetry of magnetoresistance profiles is drastically modified by changing geometry of sample, i.e., by changing boundary conditions. These properties are explained in a simple model, showing that Corbino magnetoresistance is defined by potentiostatic boundary conditions while Hall-bar magnetoresistance is defined by galvanostatic boundary conditions. The Hall was first measured in 1879 by Hall [1] by applying a magnetic field to a conducting slab contacted to an electric generator at extremities. Later on, Corbino [2] found a similar by applying a magnetic field on a disk geometry with two concentric electrodes. Quickly question arose on whether measured by Corbino (the so-called Corbino effect) in a disk and by Hall in a bar have same origin. In 1914, Adams and Chapman measured Corbino in many different metals [3] by using an oscillating current flowing from center of disk to its outer. Adams concluded in 1915 that the Corbino is, essentially, same as Hall effect [4]. However, question remains about exact meaning of adverb essentially. In 1950's, Hall in Corbino geometry was studied for its practical applications. The magnetoresistance of InSb slabs was shown to depend strongly on shape of samples [5]. The reason is that near current injection edge, Hall electric field is shorted and a transverse electric current appears which causes an increase of resistance as in Corbino geometry [6-9]. Accordingly, one can see Corbino geometry as extreme scenario where Hall electric field is zero everywhere and a Hall current is flowing, or, in other terms, one can view Corbino disk as a Hall bar in which electrostatic charge accumulation is reduced to zero everywhere. The system cannot generate a voltage between edges so that a Hall current is flowing and Joule heating is higher than in Hall bar for an equivalent volume [10-12]. The mechanism responsible for both Hall and Corbino is indeed same, but Corbino disk is a device that is more constrained than Hall bar, due to change of boundary conditions. At turn of last century, emergence of spintronics has shown possibility of exploiting spin-polarized currents * jean-eric.wegrowe@polytechnique.edu and spin-dependent potentials, and has paved way to realization of new electronic devices. Recently, various developments about spin-Hall effects (anomalous Hall effect, spin-Hall effect, spin-pumping effect, spin-Seebeck effects, etc. [13,14]) tend to show that usual Hall-bar conditions with spin relaxation could be turned into Corbino-like boundary conditions, in sense that electric charge accumulation drops to zero at edges and a pure spin current can be generated instead of a Hall voltage [11]. In this context, goal of this Rapid Communication is to study NiFe and GdCo ferromagnetic Corbino disks and Hall bars, in order to understand behavior of magnetoresistance [13,15-17] when boundary conditions are switched (by changing geometry) from spin current to spin-dependent voltage. The alloys Ni 81 Fe 19 and Co 83 Gd 17 are chosen for their maximum contribution to anisotropic magnetoresistance and anomalous Hall magnetoresistance (that defines anomalous Hall angle), respectively. First, we will present our measures of Corbino magne-toresistance performed on NiFe and CoGd rings. The results are then analyzed in framework of generalized Ohm's law by defining Corbino magnetotransport coefficients C as a function of usual Hall-bar coefficients [see Eq. (12) below]. The consistency of proposed explanation is checked independently, by measuring magnetotransport coefficients of Hall bar. The samples studied are 20-nm-thick layers of Ni 81 Fe 19 and Co 83 Gd 17 sputtered on glass substrates. The magnetic layers are sandwiched between 5-nm-thick Ta buffers and 3-nm-thick Pt caps. The magnetic properties of thin layers have been previously studied [18] (see Supplemental Material [19]). The sample magnetization is uniform for quasistatic states, although nonuniform states could take place at low magnetic fields (this regime is, however, not considered in present study). The NiFe is textured with small uniaxial anisotropy lying in sample plane. The coercivity field in in-plane geometry is of order of 1 mT. The out-2469-9950/2018/98(22)/220405(5) 220405-1
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May 30, 2020
Syed Shaheen Shah + 4
Open Access