A typical H perpendicular to I magnetoresistance trace for an MBE-grown specimen is shown in Figure 1. At zero applied field, the moments of the two Fe films are antialigned due to the exchange coupling A12.[1] As has been explained previously,6 at the field indicated in Figure 1 as HJ, the magnetic moment of one of the two Fe layers jumps by about 90 degrees toward the applied field direction. Magnetic saturation is finally achieved at the field Hs. In the analysis of the data, HJ is defined as the applied field where |dr/dH|, the slope of the resistivity, has a maximum. Hs is determined by fitting the linear portion of the magnetoresistance data for HJ < H < Hs, and taking the field at which the linear fit reaches the saturation resistance. The fields HJ and Hs are shown in Figure 2 as a function of temperature for an Fe-Cr-Fe sandwich with a chromium thickness, tCr, of 16Å. Clearly the temperature variation of Hs is well- described by a straight line, but HJ shows no temperature dependence within experimental error. The temperature variation of Hs, though small, is significant since Hs is a function of the antiferromagnetic exchange. When H is along a hard axis, as in Figure 2, the relation is:
Hs = 4A12/tFeMs + 2K1/Ms (1)
where A12 is the interlayer exchange coupling per unit area, K1 is the fourth-order cubic magnetocrystalline anisotropy energy characteristic of Fe, tFe is the thickness of a single Fe layer, and Ms is the saturation magnetization.[2,6] There is at the moment no closed-form formula for HJ, but it is also a function of K1 and A12.
The saturation field Hs was determined for the evaporated samples in a similar fashion as for the MBE-grown samples. The slope and zero-intercepts of the linear fits to Hs(T) for both kinds of sandwiches are presented in Table I. Also included are parameters derived from a linear fit to Hs(T) data in Ref. 2. This data was taken on an MBE-grown Fe-Cr superlattice with twenty repeats of tFe = 16Å and tCr=12 Å.[2]
The magnetoresistance itself as a function of temperature was also determined from individual field sweeps like that shown in Figure 1. Figure 3(a) shows the temperature variation of the H perpendicular to I magnetoresistance for two MBE-grown samples, while Figure 3(b) displays the temperature dependence of both the H perpendicular to I and H||I magnetoresistance for a polycrystalline sandwich. The data for the other evaporated polycrystalline sandwich (not shown) are nearly identical to those in Figure 3(b). From these plots one can see that Dr/r(T) in all samples is nearly constant up to about 70 K, above which it decreases linearly with temperature.
The values of the exchange constant A12 in Table I were determined using Equation (1) along with (K1/Ms) = 0.25 kOe for the MBE-grown samples, a value determined by ferromagnetic resonance (FMR) measurements.[6] For the polycrystalline sandwiches, which have a small observed in-plane magnetic anisotropy, Hs = (4A12/tFeMs). The linearity of Hs(T) then implies that the antiferromagnetic exchange A12 is also approximately linear with temperature. In the Fe-Cr superlattices, where the exchange is very large,[2] the linearity of Hs(T) similarly requires a linear temperature dependence of the exchange. The linearity of A12(T) is a potentially useful clue about the fundamental nature of the interlayer exchange interaction.