Thickness dependence of spin Hall magnetoresistance in FeMn/Pt bilayers

We investigated spin Hall magnetoresistance in FeMn/Pt bilayers, which was found to be one order of magnitude larger than that of heavy metal and insulating ferromagnet or antiferromagnet bilayer systems, and comparable to that of NiFe/Pt bilayers. The spin Hall magnetoresistance shows a non-monotonic dependence on the thicknesses of both FeMn and Pt. The former can be accounted for by the thickness dependence of net magnetization in FeMn thin films, whereas the latter is mainly due to spin accumulation and diffusion in Pt. Through analysis of the Pt thickness dependence, the spin Hall angle, spin diffusion length of Pt and the real part of spin mixing conductance were determined to be 0.2, 1.1 nm, and $5.5 * 10^{14} {\Omega}^{-1} m^{-2}$, respectively. The results corroborate the spin orbit torque effect observed in this system recently.


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Recently unconventional magnetoresistance (MR) has been reported in a variety of ferromagnet (FM) / heavy metal (HM) bilayers, with the FMs including both ferromagnetic insulators such as yttrium iron garnet (YIG), [1][2][3][4][5][6][7][8][9][10][11][12] CoFe2O4, 13 NiFe2O4, 4 Fe3O4 4,14 and LaCoO3 15 and ferromagnetic metals, e.g., Co, 16,17 CoFeB, [18][19][20] and NiFe, 21 and the HMs including Pt, [4][5][6][7][8]10,[13][14][15] Pd, 9 Ta, 5,11 and Ru. 22 Despite its debatable origin, 2,3,23-25 the experimental data reported to date seem to support the spin Hall magnetoresistance (SMR) theory. [3][4][5][6][7][8][9][10][11][12][13][14][16][17][18][19][20]22 In the SMR scenario, the charge current passing a thin HM layer generates a transverse spin current in the thickness direction via the spin Hall effect (SHE). The spin current is partially reflected back to the HM layer when it reaches the FM/HM interface, with the reflection coefficient determined by the angle between the polarization of spin current ( ) and magnetization direction of the FM ( ). The reflected spin current in turn generates an additional charge current through the inverse spin Hall effect (ISHE), leading to the appearance of SMR: , where Rxx is the longitudinal resistance, R0 the isotropic longitudinal resistance, and ΔR the change in resistance induced by the SMR effect. In addition to FMs, the SMR has also been observed in SrMnO3/Pt 26 in which SrMnO3 is an antiferromagnetic (AFM) insulator. Compared to the FM/HM bilayers, the MR behavior of AFM/HM is more complex as the spin state of AFM is strongly dependent on its thickness. When viewed from a different perspective, however, this sensitivity to thickness provides a convenient way to study how the SMR is related to both the magnitude and direction of AFM magnetization through varying its thickness systematically. The results obtained shall shed light on spin orbit torque (SOT) in AFM/HM bilayers, a phenomenon that is closely related to the SMR.
In view of the above, we investigated both the Pt and FeMn thickness dependences of SMR in FeMn/Pt bilayers, a system where we have recently observed a large SOT effect due to the presence of small net magnetic moments in FeMn. 27 Through angle-dependent magnetoresistance (ADMR) 3 measurement, it was found that the MR observed in FeMn/Pt is dominantly from the SMR origin. The size of the MR is on the order of 10 -3 , one order of magnitude larger than that of SrMnO3/Pt bilayers, 26 and is comparable to that of NiFe/Pt bilayers. The results are in good agreement with the strong SOT effect observed in FeMn/Pt bilayers. A clear FeMn thickness dependence of SMR was observed, which can be understood by taking into account the spin transport in both FeMn and Pt layers, and thickness dependence of net magnetization in FeMn. It is found that the latter plays a more dominant role in determining the FeMn thickness dependence of SMR in FeMn/Pt bilayers, in a sharp contrast to NiFe/Pt bilayers wherein the NiFe thickness effect is mainly attributed to the spin transport in both NiFe and Pt layers above a certain NiFe thickness. In addition, through Pt thickness dependence analysis of SMR in FeMn/NiFe bilayers, 27 it was found that FeMn starts to show the onset of clear exchange bias only at a thickness around 4 -5 nm. At tFeMn = 0.5 nm, the FeMn can be considered as a superparaantiferromagnet at room temperature when it is standalone; however, when contacted with Pt, it behaves more like a FM due to interaction with Pt. When tFeMn increases to 3 nm, weak AFM order appears as reflected in the enhancement of coercivity in FeMn/NiFe bilayers. Therefore, in both the tFeMn = 0.5 nm and 3 nm samples, there is significant amount of uncompensated spins in the FeMn layer and their spin sub-lattices can be rotated easily by the external field. When tFeMn increases further to 15 nm, the AFM order becomes more rigid and difficult to be rotated by the external field. In this case, it is the uncompensated spins at the interface that are responsible for the MR observed. On the other hand, the MR behavior of FeMn/Pt is found to be insensitive to the change in Pt thickness at a fixed FeMn thickness. Based on these considerations and the strong dependence of both the magnitude and curve shape of MR on tFeMn, it is apparent that the MR observed in the FeMn/Pt samples is closely related to the spin configuration of FeMn. The same polarity of MR in x-and z-directions suggests that the MR observed is of SMR origin. Although the so-called Hanle effect MR induced in the Pt layer itself also has the same polarity, 24 its size on the order of 10 -6 , as verified by a Pt(3)/SiO2/Si control sample, is too small to account for the MR observed in FeMn/Pt bilayers.
In order to extract the SMR contribution from the overall MR, ADMR measurements were performed on these bilayers. As illustrated in Fig. 2(a), the longitudinal resistance of the sample was measured while rotating a constant field H in zy, zx, and xy planes, respectively. The SMR ratio is calculated from the relation ratio, on the order of 10 -3 , is one order of magnitude larger than that of the SrMnO3/Pt system. 26 Fig. 2(c) shows the ADMR results of a NiFe(3)/Pt(3) bilayer measured in the same configurations for comparison.
The main difference with FeMn(3)/Pt (3) is that the AMR (θzx-dependence of MR) is much larger in this case, which causes a clear separation between the θxyand θzy-dependence of MR curves. It is apparent that the sum of MR measured with the field rotating in the zx and zy plane is equal to that measured when the field rotates in the xy plane. It is also worth noting that the magnitudes of SMR in both systems are similar. 6 To have a more quantitative understanding of the SMR effect in FeMn/Pt bilayers, we investigated the thickness dependence of the effect for each layer. Fig. 3(a) shows the θzy-dependence of MR for the FeMn(3)/Pt(tPt) series of samples with tPt = 1 nm, 2 nm, 5 nm, 8 nm and 15 nm, respectively. As summarized in Fig. 3(b), the SMR ratio shows a non-monotonic dependence on the Pt thickness; it increases initially at small thicknesses, peaks at about 3 nm, and then decreases between 3 -15 nm. The tPt-dependence of SMR is similar to those observed in CoFeB-based FM/HM bilayers. [18][19][20] When dealing with metallic FM/HM bilayers, one has to take into account both the charge current shunting effect 18   PC approaches unity, the FM becomes a half-metal. In this case, the spin current cannot flow vertically in the FM layer due to lack of minority spin carriers and thus there will be no additional correction to 7 SMR except for the current shunting effect. The situation is more complex in FeMn/Pt bilayers, in particular when FeMn is thin. In this case, the FeMn is neither a good AFM nor an FM; its spin structure depends strongly on the thickness. Considering the much smaller spin Hall angle 29,30 and larger resistivity of FeMn as compared to Pt, the spin current generated in FeMn can be neglected. The SMR of FeMn/Pt bilayers is dominantly due to the spin current in Pt. Therefore, without losing generality, we may still use Eq.
(1) to model the SMR dependence on FeMn thickness, but we have to introduce a thickness-dependent polarization for FeMn. This is a reasonable approach because when tFeMn is large, a rigid AFM order will form which results in diminishing polarization. On the other hand, when tFeMn is small (e.g., tFeMn = 3 nm), the net magnetic moment induced by an external field shall lead to a non-zero PC value. Based on these considerations, we first analyze the tPt-dependence of SMR with a constant PC value and then discuss the tFeMn-dependence by taking into account the thickness dependence of polarization, which can be inferred from the magnetization data.
As shown in Fig. 3(b), the tPt-dependence of SMR can be fitted reasonably well using Eq. The results indicate that the drift-diffusion model can satisfactorily describe the spin current generation and transport in FeMn/Pt bilayers at a fixed FeMn thickness. 8 We now turn to the tFeMn-dependence of SMR in the bilayers. Fig. 4(a) shows the θzy-dependence of MR for FeMn(tFeMn)/Pt(3) bilayers with tFeMn = 0.5 nm, 2 nm, 5 nm, 8 nm, and 15 nm, respectively. For comparison, we also show in Fig. 4 Fig. 4(c) and Fig.   4(d), respectively. Similar to the Pt thickness dependence shown in Fig. 3 (b), a non-monotonic dependence on tFeMn or tNiFe is obtained. Despite the fact that the tPt-dependence of SMR can be explained reasonably well using Eq. (1), the same equation is unable to fit the tFeMn-dependence if we use a fixed PC value. As mentioned above, to account for tFeMn-dependence, it is necessary to use a tFeMndependent PC value for FeMn. It is noticed that in metallic FMs, the tunneling spin polarization (PT) is approximately linear to the magnetization, i.e., Ts PM  . 35,36 As a first approximation, we assume that the same relation also holds for current spin polarization (PC) used in Eq. (1) and net magnetization in thin AFM layers. This is supported by the fact that: i) PC determined by point-contact Andreev reflection spectroscopy is similar to PT determined by the superconductor tunneling spectroscopy for many transition metallic FMs; 37 ii) sizable net moment can be induced in FeMn by an external field (30 kOe in the SMR measurement). In this sense, we may correlate PC with the net magnetization Ms of FeMn obtained by magnetometry measurements. Fig. 4(e) shows the thickness dependence of Ms for FeMn at H = 30 kOe extracted from the M-H loops of coupon films with the same thickness combination as the Hall bar samples. 27 As can be seen, the non-monotonic tFeMn-dependence of Ms resembles that of SMR ( Fig. 4(c)) with a peak at round 2 nm, which suggests that the tFeMn-dependence of SMR is closely related to the spin structure of FeMn. More quantitatively, we introduce a phenomenological expression for the current spin polarization ( obtained from the fitting of Fig. 3(b) and () s FeMn Mt in Fig. 4(e), the tFeMn-dependence in Fig. 4(c) can be reproduced well (solid line) with a constant  value of 3.1×10 -3 emu -1 cm 3 , especially at tFeMn > 2 nm.
The deviation at small tFeMn below 2 nm may be caused by the roughness and surface effect. It is worth emphasizing again that the curve cannot be fitted at all if we use a constant PC value. This suggests that the tFeMn-dependence of SMR is mainly determined by the tFeMn-dependence of net magnetization in FeMn induced by an external field. Similar thickness dependence has also been observed in the investigation of spin orbit torque effective field in FeMn/Pt bilayers. 27 On the contrary, the tNiFedependence of SMR at large tNiFe can be well reproduced (solid line in Fig. 4 38,39 The deviation at tNiFe < 3 nm can also be attributed to the roughness and surface effect which has not been taken into account in Eq. (1). These results imply that the SMR is not just an interface effect. The presence of magnetic moment in the layer adjacent to the heavy metal is crucial to obtain a large SMR. It also explains why the SMR is closely related to the spin orbit torque effect in FM/HM and AFM/HM bilayers.
In conclusion, we observed a large SMR in FeMn/Pt bilayers, with a magnitude comparable to that of NiFe/Pt bilayers. A clear FeMn thickness dependence of SMR is observed, which is mainly attributed to the thickness dependence of the net magnetization in FeMn induced by an external field. This is different from the NiFe/Pt bilayers in which the NiFe thickness dependence of SMR is mainly caused by the spin transport in both layers. Our findings shed light on interactions of spin current with spin sublattices in AFMs and corroborate the spin orbit torque effect observed in this system recently.