Modeling the Magnetoresistance versus Field Curves of GMR Multilayers with Antiferromagnetic and/or Orthogonal Coupling by Assuming Single-Domain State and Coherent Rotations

Abstract

─ In order to better understand the role of possible couplings in determining the giant magnetoresistance (GMR) behavior of multilayers, a knowledge of the dependence of the GMR on magnetic field H appears to be useful. Since a few specific cases have only been treated theoretically in the literature, it was decided to carry out a modeling of the GMR(H) curves of ferromagnetic/non-magnetic (FM/NM) multilayers with various interlayer couplings. For simplicity, we focused on a trilayer structure (FM 1 /NM/FM 2 ) corresponding fairly well to the case of a large number of FM/NM bilayers. To carry out the calculations, some fundamental assumptions were made: (i) each FM layer consists of a single domain and the magnetizations are in the layer planes; (ii) the magnetization of each layer is the same; (iii) the magnetization vectors rotate in the plane of the layers in an external magnetic field. In order to calculate the GMR(H) function, we need to know the magnetization process in the trilayer, i.e., the M(H) function. Therefore, first we calculate the equilibrium angle ϕ(H) between the two magnetization vectors as a function of the field by minimizing the total energy of the multilayer. According to most previous theoretical and experimental works, the angular dependence of the GMR is fairly well described by the relation GMR(ϕ) ∝ (1 -cos ϕ) and we used this relation to derive the GMR(H) function. Along this line, the M(H) and GMR(H) curves were calculated for the following cases: (i) pure AF coupling; (ii) pure orthogonal coupling; (iii) AF coupling and orthogonal coupling simultaneously present. As to the calculation of the GMR(H) curves, some of these configurations have not yet been treated formerly or for some specific parameter values only. For those cases for which calculations were reported in the literature for M(H) and GMR(H), our results agree with previous reports.

Influence of Ag Additive to the Spacer Layer on the Structure and Giant Magnetoresistance of Electrodeposited Co/Cu Multilayers

“…At the large spacer layer thickness of 7 nm, probably no antiferromagnetic coupling exists between the magnetic layers 8 and the observed GMR arises due to the random alignment of the magnetizations of adjacent layers. 8,61 In spite of the relatively large bilayer thickness ( = 10 nm), these Co/Cu(Ag) multilayers prepared from a perchlorate bath exhibited a GMR effect at least as large as commonly observed in ED Co/Cu multilayers obtained from sulfate-type baths with smaller bilayer repeats. [5][6][7][8][9]53,54,62,63 Thus, the SNMS, XRD and magnetoresistance results are all compatible with the conclusion that the present ED Co/Cu(Ag) multilayers below about 8 at.% Ag incorporated exhibit a multilayer structure even if this layered structure is far from perfect.…”

Magnetic and magnetoresistance studies of nanometric electrodeposited Co films and Co/Cu layered structures: Influence of magnetic layer thickness

“…The GMR effect originally discovered in FM/NM multilayer structures [1,2] is the highest when the adjacent layer magnetizations are antiparallel aligned [6][7][8]. In physically deposited multilayer structures, this can be achieved by choosing spacer layer thicknesses ensuring an AF coupling between adjacent layers which occurs at the so-called AF maxima [9][10][11].…”

Clusters of Spin Valve Sensors in 3D Magnetic Field of a Label

“…From the experimental side, the angular variation of the GMR effect was found to be very close to the relation R GMR (ϕ) = R 0 GMR (1 − cosϕ)/2 in the current-in-plane (CIP) geometry for various systems, where R 0 GMR is the amplitude of the GMR effect [ 27 , 29 ].…”