Giant anisotropic magnetoresistance and nonvolatile memory in canted antiferromagnet Sr2IrO4

Antiferromagnets have been generating intense interest in the spintronics community, owing to their intrinsic appealing properties like zero stray field and ultrafast spin dynamics. While the control of antiferromagnetic (AFM) orders has been realized by various means, applicably appreciated functionalities on the readout side of AFM-based devices are urgently desired. Here, we report the remarkably enhanced anisotropic magnetoresistance (AMR) as giant as ~160% in a simple resistor structure made of AFM Sr2IrO4 without auxiliary reference layer. The underlying mechanism for the giant AMR is an indispensable combination of atomic scale giant-MR-like effect and magnetocrystalline anisotropy energy, which was not accessed earlier. Furthermore, we demonstrate the bistable nonvolatile memory states that can be switched in-situ without the inconvenient heat-assisted procedure, and robustly preserved even at zero magnetic field, due to the modified interlayer coupling by 1% Ga-doping in Sr2IrO4. These findings represent a straightforward step toward the AFM spintronic devices.


Supplementary Note 1: Anisotropic magnetotransport in J eff =1/2 antiferromgnet Sr 2 IrO 4
Sr 2 IrO 4 has a layered antiferromagnetic (AFM) ground state, which has been demonstrated by various techniques, including resonant x-ray scattering and neutron scattering [1][2][3]. As sketched in Supplementary Fig. 1, the J eff =1/2 moments (red arrows) are antiferromagnetically arranged in each IrO 2 layer, and show uniform canting angle relative to the c-axis. Because of canting, each IrO 2 layer has a net magnetic moment (green arrows) which is alternatively aligned along the c-axis. As a consequence, Sr 2 IrO 4 is fully compensated at the ground state without showing macroscopic magnetization. With applying H above a critical value H flop , a flop transition is triggered, and then the net moments of IrO 2 layers are ferromagnetically coupled along the c-axis, leading to a weak ferromagnetic phase. The flop transition has been demonstrated using resonant x-ray scattering previously [1].
Accompanying with the flop transition (also known as AFM to weak FM transition), the resistance (R) shows a sudden drop, causing evident magnetoresistance (MR) in the samples. As shown in Supplementary Fig. 1b and c, the observed R c (H) trace correlates very well with M(H), suggesting that the field induced variation in magnetic order determines the magnetotransport in Sr 2 IrO 4 . This is in agreement with the previous results [4,5]. If having a look at the arrangement of the net magnetic moments (green arrows), one would see that the flop transition highly resembles the operation in a giant-magnetoresistance (GMR) device. Therefore, the large MR related to the flop transition is called as an atomic scale GMR-like effect in our work.
Achieving a large MR effect in antiferromagnets has been a focused issue for a long time. This has been intensively discussed for AFM heterostructures/multilayers, i.e. AFM/ non-magnetic-spacer/AFM. The existence of AFM counterpart to the GMR, called AFM-GMR, was theoretically proposed in such AFM structures [6,7]. The AFM-GMR was found to be purely an interface effect, and a spin-polarized state at the interface is essential [8]. For instance, a lower resistance will be achieved when the facing layers of antiferromagnets have the same spin orientation.
However, an experimental realization of the proposed AFM-GMR has encountered great challenge, since a theoretically assumed perfect interface quality can be an issue for epitaxial growth for artificial AFM-multilayers or heterostructures. For the Sr 2 IrO 4 single crystal, it is a natural antiferromagnet without such interface problem, and more importantly it hosts a layered AFM structure akin to the AFM multilayers: the AFM IrO 2 layers separated by non-magnetic SrO layers, and each IrO 2 layer has net magnetic moment  net due to the J eff = 1/2 canting.
Indeed, a large MR related to the transition from AFM state to weak FM state is identified in Sr 2 IrO 4 . Very recently, the first principles calculations on the MR in Sr 2 IrO 4 confirmed the critical role of scattering effects at domain walls [9]. This scenario is consistent with the scenario proposed in AFM multilayers. The crystals were crashed thoroughly and then powder X-ray diffraction (XRD) measurements were performed at room temperature. As shown in Supplementary Fig. 2, the refinements are high quality with small difference between the measured and refined spectra. The reliability parameter R wp is 3.98% for Sr 2 IrO 4 and 6.68% for Sr 2  Energy dispersive x-ray spectroscopy (EDX) equipped with a scanning electron microscope was used to check the elements' distribution and molar ratio in Sr 2 IrO 4 and Sr 2 Ir 0.99 Ga 0.01 O 4 crystals.
All crystals are found to be homogeneous, according to our EDX results shown in Supplementary   Fig. 3. The moral ratio of elements was estimated to be Sr:Ir ~2:1 in Sr 2 IrO 4 crystals, and Recently, Lee et al. reported interesting AMR phenomenon in Sr 2 IrO 4 [9]. An in-plane experimental set-up was used in their work, and a domain wall resistance scenario was proposed to explain the AMR phenomenon.
According to their calculations, the flop transition shows negligible effect on the electronic band structure in Sr 2 IrO 4 . Therefore, the large MR related to the flop transition is dominated by magnetic scattering, which is the common point between Lee's work and ours. The key difference between Lee's work and ours is sketched in Supplementary Fig. 10, i.e. the currents are in-plane in Lee's work but along the c-axis in our experiment. Therefore, the magnetic scattering at in-plane (IP) Large IP-and OP-MR associated with the AFM -FM transition can be observed in Sr 2 IrO 4 , and the OP-MR effect (i.e. ~67% at T=90 K) is found to be much larger than the IP-MR (~40% at T=90 K), as show in Supplementary Figs 1 and 10. This is reminiscent of the observations in conventional GMR devices [16]. The IP-and OP-GMR effects have been studied for years, and the difference is ascribed to the different scaling lengths of the problem [16].
Here for Sr 2 IrO 4 , similar physics to the conventional GMR effects may be shared, while this topic definitely deserves for further investigations. We are not aware of any conclusive answer for this question, but three factors should be concerned. First, along the c-axis, the IrO 2 layers are separated by SrO layers, fundamentally different from the in-plane case. Therefore, the out-of-plane transport and magnetism is certainly different from the in-plane case. Second, the interlayer scattering takes place in every unit cell, which is much more popular than the domain wall In addition, Wang et al. performed similar out-of-plane AMR measurements in Sr 2 IrO 4 [5,17], while a unique point contact technique was used. Indeed, very different results were obtained in comparison with ours. First, Wang et al. found that both MR and AMR strongly depends on the contact size (i.e. the AMR ratio was found to be increased from ~1% to 14% as the contact size was decreased at T=77 K). Second, a crossover from fourfold to twofold rotational symmetry of the AMR was identified in response to an increasing magnetic field. In our experiments, a standard method was used for the transport measurements, and no appreciable electrode-size (~1 mm 2 ) dependence was seen. Importantly, a fourfold AMR symmetry was eventually stabilized upon increasing magnetic field in our experiments, which was also observed by Lee et al. [9]. Therefore, the much smaller AMR magnitude (ten times smaller than ours) and the essentially different AMR