Unraveling the Extraordinary Anisotropic Magnetoresistance in Antiferromagnetic Perovskite Heterostructures: A Case Study of CaMnO₃/CaIrO₃ Superlattice

Abstract

Antiferromagnetic (AFM) spintronics offers advantages over ferromagnetic (FM) spintronics, such as zero stray fields, closer packing, and imperviousness to disruptive fields. Anisotropic magnetoresistance (AMR) can be enhanced by materials with pronounced spin-orbit coupling (SOC) and magnetocrystalline anisotropies. AMR research aims to develop new materials and heterostructures with enhanced and tunable anisotropic transport properties for advanced electronic devices. The nonmagnetic ground state of iridium pseudospin moments in SrIrO3 and CaIrO3 is determined by SOC and electron correlations (U). This study shows that by coupling CaIrO3 with a severely distorted canted AFM manganite CaMnO3, the AMR can be increased by more than one order of magnitude, primarily due to interlayer coupling. Additionally, the spin-flop transition in a nearly Mott region contributes to an unprecedented AMR of 70%, two orders of magnitude larger than previously achieved. The study demonstrates that thin films of canted AFM phases of CaMnO3 and CaIrO3 exhibit dimensionality control, with a diminishing magnetic moment, and the valence state can be altered at interfaces in superlattices involving manganites.

1. Introduction

Antiferromagnetic (AFM) spintronics has emerged as a promising alternative to ferromagnetic (FM) spintronics due to several advantages. AFM spintronics offers a significant advantage over other technologies as its ordered microscopic moments alternate between individual atomic sites, resulting in zero stray fields and enabling closer packing of devices without interference. Thus, AFM materials possess a remarkable property of being externally invisible in magnetic fields, owing to their zero net magnetic moments, which implies that any information stored in their magnetic moments would be impervious to disruptive magnetic fields and beyond the detection capabilities of commonly used magnetic probes [1, 2, 3, 4, 5, 6]. Antiferromagnets have been discovered to have greater potential than just being used as passive elements in exchange bias applications. When a soft ferromagnet is placed next to a thin antiferromagnet, and a feeble external magnetic field is applied, the ferromagnet can reposition itself, causing its interfacial moments to pull the adjacent antiferromagnetic moments via the interfacial exchange spring. Metal antiferromagnets, such as the Ir-Mn alloys, are versatile materials with various applications, ranging from serving as advantageous passive exchange-bias components to functioning as active electrodes in Tunneling Anisotropic Magnetoresistance (TAMR) devices [7, 8, 9, 10, 11]. Additionally, AFM spintronics devices require lower operational power, which makes them more energy-efficient. AFM spintronics allows for ultrafast control of the staggered spins at terahertz frequencies, which can enable faster and more efficient data processing. Current-induced spin-orbit torque (SOT) and anisotropic magnetoresistance (AMR) are two important phenomena used in AFM spintronics devices and in this way, the spin of the AFM material can be accessed for data writing and reading operations. SOT is a process that utilizes electric current to generate torque on the magnetization of a material, primarily used in AFM spintronic devices. The electron’s spin polarization generates a spin current when a current is passed through a thin layer of heavy metal. The interaction of the spin current with the AFM moments at the interface generates a torque that can reorient the magnetic moments of the AFM layer, enabling precise data writing and reading operations by controlling the current’s direction and magnitude. Moreover, the SOT-based devices have the advantage of low power consumption and fast switching speeds making them promising candidates for future high-density data storage and processing applications [6, 10, 12]. AMR is a phenomenon that causes the resistance of a material to change as a function of the angle between the direction of current flow and the magnetization direction. Overall, AFM spintronics has the potential to revolutionize the field of spintronics and enable the development of faster, more efficient, and more compact devices [13, 14, 15].

Here, a detailed discussion of AMR will be given in 3d/5d perovskite heterostructures. The origin of AMR depends on whether the material is crystalline or noncrystalline. In both cases, the AMR response arises from the anisotropy of the electron scattering or transport properties. In crystalline materials, AMR arises from the anisotropy of the electron scattering rate, which is influenced by the orientation of the magnetic field with respect to the crystal lattice [14, 16, 17]. As an example, a high electronic band coupling to crystal sites can lead to a stronger AMR response and itinerant electrons from higher energy bands typically contribute to the magnetic effects in AMR, resulting in a greater change in electrical resistance in LaAlO₃/SrTiO₃ (111) heterostructure [18]. On the other hand, in noncrystalline materials such as amorphous alloys, the AMR originates from the anisotropy of the electron transport properties. Researchers working on AMR seek to design heterostructures with specific properties that can enhance the AMR effect. One approach is to use materials with pronounced SOC and magnetocrystalline anisotropies. This can cause the anisotropies to manifest as anisotropic transport. In some cases, the magnetic field and weak magnetic moments of the canted AFM phase can couple together, resulting in emergent magnetic and topological properties in oxide heterostructures. For example, 3d-5d oxide heterostructures such as epitaxial superlattices (SLs) of iridium oxides (Ca/SrIrO₃)/SrTiO₃ and manganite/iridate SLs, have been found to exhibit large atomic SOC and electron-correlation-dominated AMR [19]. Furthermore, current-dependent AMR and MR offer an opportunity to explore momentum-dependent scattering to elucidate the role of Rashba SOC. The Rashba SOC introduces spin splitting along the momentum axis, whereas atomic SOC does not [20]. However, a few research groups have proposed that besides the atomic SOC, the Rashba SOC also plays an important role in the AMR in transport. The primary focus of AMR research is to design and develop new materials and heterostructures that can exhibit enhanced and tunable anisotropic transport properties for use in advanced electronic devices.

The nonmagnetic ground state of iridium (Ir) pseudospin moments in SrIrO₃ and CaIrO₃ is determined by the interplay between SOC and electron correlations (U). The value of U, which represents the strength of the Coulomb interaction between electrons, affects the electronic and magnetic properties of the system. When U is large, the system tends to favor a Mott insulating state, which is characterized by the localization of electrons due to strong Coulomb repulsion. On the other hand, when U is small, the system can exhibit metallic behavior. In epitaxial thin films, the dimensionality of the system can be tuned by controlling the thickness of the film. It has been found that reducing the dimensionality in epitaxial thin films can increase U and induce pseudospin-based emergent magnetism in SrIrO₃ and CaIrO₃ [21, 22, 23, 24]. This emergent magnetism arises from the system’s delicate balance between SOC and U. In a low-bandwidth SL, i.e., CaIrO₃/SrTiO₃, the AMR effect is attributed to a combination of different factors including in-plane biaxial magnetic anisotropy, magneto-elastic coupling, and interlayer exchange coupling based on tilted oxygen octahedra with glazer notation (a⁻a⁻c⁺) across the constituent layers [19, 25, 26]. Despite the concerted efforts to enhance the AMR effect in 3d-5d heterostructures, the maximum amplitude of the fourfold AMR signal is still limited to 1%. This limitation highlights the need for the development of new strategies for enhancing the AMR effect, such as the careful selection of constituent materials and the optimization of heterostructure architecture to get a larger AMR effect. This study shows that by coupling the CaIrO₃ with a severely distorted canted AFM manganite CaMnO₃ and using the same sense of (a⁻a⁻c⁺) oxygen octahedra tilts, the AMR can be increased by more than one order of magnitude which is about 20%. This increase is mainly generated due to the interlayer coupling of the CaMnO₃/CaIrO₃ layer. Additionally, the spin-flop transition in a nearly Mott region triggers an additional two-order of AMR amplitude along with a four-fold symmetry component. By combining these two effects, an exceptional AMR of 70% has been achieved, surpassing the previous record by two orders of magnitude. The study also shows controls and other unique facets related to these effects. The study demonstrates that thin films of canted AFM phases of CaMnO₃ and CaIrO₃ exhibit dimensionality control, with a diminishing magnetic moment. The M-T curve shows a signature of a magnetic transition occurring around 70–100 K, representing an AFM phase transition in the CaMnO₃/CaIrO₃ SLs. The valence state can be altered at interfaces in SLs involving manganites, resulting in emergent magnetic phenomena through the transfer of charge. Research conducted on CaRuO₃/CaMnO₃ SLs has revealed that electron leakage into the CaMnO₃ layer decreases exponentially from the interface to the bulk of the layer [27]. From the exchange bias data of CaMnO₃/CaIrO₃ SLs, it is clear that a charge transfer from the CaIrO₃ to CaMnO₃ layer near the interface develops FM and AFM phases at the interface and bulk of CaMnO₃ layers, respectively.

2. Experimental section

2.1 Sample synthesis and structural characterizations

Pulsed laser deposition (PLD) is a valuable experimental technique in condensed matter physics for investigating interface properties [27, 28]. Creating a well-defined interface and high-quality thin film is essential, and PLD involves laser ablation of target material, plasma plume dynamics, and nucleation and growth of atoms on the substrate surface. Laser energy selection is critical based on the ablation threshold energy of bulk materials, and a KrF excimer laser with a wavelength of 240 nm is commonly used in lab experiments. The gas pressure is used to control plume dynamics and reduce its energy, resulting in a dense and unidirectional plume. The nucleation of atoms on the substrate is a crucial step in crystal formation, and the suitable combination of laser energy, gas pressure, and substrate temperature determines the mobility of surface atoms. Oxygen gas is supplied inside the PLD chamber from an external cylinder via an inlet to produce an oxide film, and different growth mechanisms, depending on the mobility of surface atoms and surface smoothness, occur on the surface (Figure 1).

Figure 1.

Pulsed laser interval deposition [29]. (a) How the oscillation intensity changes with the increasing number of laser shots and the formation of each layer represented by one complete oscillation. (b) RHEED specular spot intensity and its surface plot in X-Y coordinates.

Reflection high energy electron diffraction (RHEED) technology is used to study the growth mechanism, providing valuable information about the surface morphology and structure. RHEED enables the monitoring of various types of growth such as layer-by-layer (2D) growth and island (3D) growth. The process involves nucleation and growth of atoms on the substrate surface which can be visualized using the RHEED set-up. High-pressure RHEED has been developed to monitor surface structure during oxide deposition at higher pressures, opening up new possibilities for material synthesis. To obtain the atomically sharp TiO₂-terminated surface which is essential for layer-by-layer growth, the substrates were treated in deionized water and buffered NH₄F-HF (BHF) solution [30], followed by thermal annealing at 960°C for 1.5 hours. The SLs were grown on a substrate maintained at a temperature of 730°C and under an oxygen partial pressure of 6 Pa. Subsequently, the samples underwent a post-annealing process at identical temperature and pressure conditions for a duration of 30 minutes. The thickness of the SLs was precisely controlled and monitored by using in-situ RHEED. The high structural quality of the SLs was examined in detail by performing room temperature X-ray diffraction (XRD) scans using a PANalytical X’pert Pro diffractometer. Finally, the thickness of the SLs was confirmed by using X-ray reflectivity (XRR).

The samples are CaMnO₃/CaIrO₃ SLs with different configurations based on the periods of constituent layers. The SLs are coded as (MIxy)z, where M and I refer to CaMnO₃ and CaIrO₃ layers, respectively. The value of ‘x’ and ‘y’ represents the period or unit cell (u.c.) of the CaMnO₃ and CaIrO₃ layers, respectively, and ‘z’ represents the number of repetitions. The article discusses the structural properties and variations in AMR of CaMnO₃/CaIrO₃ SLs. The samples are categorized based on the period of constituent layers as (I) The first category involves the simultaneous variation of CaMnO₃ and CaIrO₃ u.c., with samples including (MIxy)z for x = y = 2–4, and (MI84)₅ with a larger CaMnO₃ period; (II) The second category involves the control of AMR by fixing CaIrO₃ period while varying the CaMnO₃ period, with samples (MIx2)₅ for x = 2,4,6,8 and (MIx4)₅ for x = 2,4,6; (III) The third category involves keeping the CaMnO₃ period fixed and varying the CaIrO₃ period, with samples (MI2y)z for y = 2,4,5 and (MI5y)z for y = 2,5,8. The SLs were formed by using a pulsed interval deposition technique and analyzed by using XRD and HAADF-STEM. In Figure 1(a), the synthesis of (MI82)5 SL is shown, where one complete oscillation represents the formation of one u.c. Additionally, the Gaussian pattern of the specular spot intensity after finishing the deposition confirms sharp, layer-by-layer growth, as shown in Figure 1(b). Figure 2(a) and (b) provide XRD and XRR data, respectively, for the primary series and higher periodic SL, i.e., (MI84)₅ SL. Also, Figure 2(c) shows HAADF-STEM data for (MI84)₅ SL. These data offer insights into the crystal structure, periodicity, and interface quality of the SLs.

Figure 2.

(a, b) Scan of θ-2θ and X-ray reflectivity for (MIxy)z with x = y = 2–4, (MI22)₁₀, (MI33)₅, (MI44)₅, and (MI84)₅ SLs. (c) Cross-sectional HAADF-STEM image that exhibits the atomic level resolution of CaMnO₃ and CaIrO₃ layers in the (MI84)₅ SLs is shown. (Reprinted from [14] © 2023 American Physical Society).

2.2 Investigating magnetic-properties of interface

2.2.1 Magnetization measurements, X-ray absorption study, and understanding charge transfer and spin canting mechanism across CaMnO₃/CaIrO₃ Heterointerface

The magnetization (M) versus temperature (T) and magnetic field (H) data of (MIxy)z SLs with x = y = 2–4 are plotted in Figure 3(a) and (b). As the number of periods increases, there is a noticeable decrease in both the magnetic transition temperature (Tc) and the saturation magnetic moment (Msat), as depicted in Figure 3. For example, the (MI22)₁₀ SL exhibits Tc of approximately 100 K, while the Tc decreases to approximately 60 K for (MI44)₅ SL and vanishes for the higher periodic (MI84)₅ SL. This trend suggests that the magnetic properties of the SLs are strongly influenced by the periodicity of the constituent layers, with larger periods leading to weaker magnetism. The M-H data in Figure 3(b) shows a saturation magnetic moment (Msat) of approximately 0.4 μB/f.u. for (MI22)₁₀ SL, which value is consistent with the reported canted AFM state in CaIrO₃/CaMnO₃ heterostructures [31]. To further investigate the magnetic properties of the SLs, the exchange-bias fields (H_EB) were measured by performing field-cooled M-H measurements, as shown in Figure 3(c).

Figure 3.

Displays (a) the temperature (T), (b) field (H) dependence of magnetization (M), and (c) the strength of the exchange bias field (H_EB) for (MIxy) SLs with varying stacking of CaMnO₃ and CaIrO₃ layers. X-ray absorption spectra around (d) the Mn L_2,3 edge (TEY modes) and (e) Ir L₃ edge (FY modes) are also presented for (MIxy)z SLs, where the insets show a comparison of the (MI25)₅ SL with the IrO₂ sample. (f) a schematic illustration is shown, demonstrating the spin canting in the CaIrO₃ and CaMnO₃ layers. CaIrO3 and CaMnO3 layers are organized into BO6 planes that are arranged in the ab plane and stacked along [001]. To simplify the explanation, a top-down view of the canted moments and net magnetic moment is shown along two in-plane directions, namely [010] and [100], with respect to the pseudocubic STO (100) substrate. The length of the arrows showing the net magnetic moment does not represent the relative size of the magnetic moment in CaIrO₃ or CaMnO₃ layers. (Reprinted from [14] © 2023 American Physical Society).

The interfacial charge transfer and electronic structure near the Fermi level were examined using x-ray absorption spectroscopy (XAS) at both the Mn and Ir L-edges. The spin-orbit coupled states are obtained in the spectra containing two features, the L₃(2p_3/2) and L₂(2p_1/2) edges, respectively, in Mn 2p core hole, as shown in Figure 3(d). A clear shift of the L₃ edge of the spectra towards lower energy with respect to the other samples was observed in the (MI25)₅ SL, indicating the presence of Mn³⁺ ions, which were likely formed by the transfer of charge from the Ir to the Mn at the interface. This shift was evident in both the surface-sensitive total electron yield (TEY) and bulk-sensitive fluorescence yield (FY) mode for Mn-edge and Ir-edge spectra, respectively, as shown in Figure 3(d, e) and 4. Thinner CaMnO₃ layers in SLs receive a larger fraction of electrons, causing a larger shift in the Mn edge for (MI25)₅ with 2 u.c. of CaMnO₃ period compared to SLs with thicker CaMnO₃ layers compared to CaIrO₃, as shown in Figure 3(d). Additionally, the larger thickness/volume of CaIrO₃ in (MI25)₅ SL will transfer a larger number of electrons to CaMnO₃. The observed minimal shift in the Ir edge, as shown in Figures 3(e) and 4, suggests that the Ir⁴⁺ state is highly stable, and only a small amount of charge transfer occurs across the interface. Therefore, the remaining change in the Mn valency is assumed to arise from vacancies in the manganese layer. Approximately, 0.1 hole/electrons per Ir/Mn ion are transferred at CaMnO₃/CaIrO₃ interfaces for the (MI82)₅ SL, while the remainder of the change in the Mn valence is due to vacancies in the manganese layer and, also, the charge transfer is sensitive to the constituent layer thickness, with a maximum of approximately 0.25 hole/electron per Ir/Mn ion transferred for the (MI25)₅ SL, as shown in the table-I. It is observed from the table that there is charge transfer from Ir to Mn assuming a valency range of ∼3.8–3.95 for the bare CaMnO₃ layer. As the CaIrO₃ layer thickness increases and becomes comparable with CaMnO₃ layer thickness, such as in MI25, MI44, and MI42 samples, the fraction of charge transfer increases, contributing to the larger conductivity and number of carriers available for charge-transfer in thicker CaIrO₃ layers. This is evident in the comparison between MI25 and MI62 samples (Table 1).

Figure 4.

XAS spectra around the Mn L_2,3 edges for [(CaMnO3)_x/(CaIrO3)_y)]_z measured in the (a) TEY and (b) TFY modes. XAS spectra of the Ir L_2,3-edges for [(CMOx/CIOy)]z measured in the fluorescence yield modes. Insets depict the comparison view of [(CaMnO₃)₂/(CaIrO₃)₅)]₅ with the reference IrO₂ sample. (Reprinted from [14] © 2023 American Physical Society).

Sample	MI82	MI62	MI42	MI44	MI25
Mn edge valency	3.68(4)	3.78(8)	3.79(2)	3.74(4)	3.59(4)
Ir edge valency	4.09(7)	4.05(7)	4.18(1)	4.17(4)	4.25(9)

Table 1.

Charge transfer across CaMnO₃/CaIrO₃ interface.

The charge transfer between CaIrO₃ and CaMnO₃ layers depends on the volume or the number of available carriers in CaIrO₃ and the number of CaMnO₃ layers. Due to the vacant ‘e_g’ orbital near the Fermi level, CaMnO₃ with a distorted lattice exhibits a significant attraction towards electrons. In another study on Ce⁴⁺ − doped CaMnO₃, even a small electron doping induced canting of the AFM lattice resulting in a significant increase in magnetic moments [32]. Leakage of electrons into CaMnO₃ decay exponentially from the interface to the bulk of the layer in CaRuO₃/CaMnO₃ SLs [27, 33]. The interface layer receives the maximum charge density, inducing a double-exchange governed FM phase or a largely canted AFM phase at the CaMnO₃ interface layer. The deeper CaMnO₃ layer tends to remain AFM. The formation of a magnetic gradient across the CaMnO₃ layer is well supported by both theory and experiments [33]. The H_EB is the signature of FM and AFM phases across the interface. As depicted in Figure 3(c), the (MI22)10, (MI33)5, (MI44)5, and (MI84)5 SLs display H_EB of 3, 15, 50, and 35 Oe, respectively. To achieve a higher H_EB, a virtual arrangement of the FM/AFM interface is necessary, which is absent in the first SL since its CaMnO₃ layers are only present at the interface. However, in the latter three SLs, the CaMnO₃ layer thickness increases along with the FM interface, resulting in the manifestation of H_EB which increases with the thickness of the CaMnO₃ layer. This result can be used to look for the formation of such magnetic gradients also where the AFM state apart from the interface remains unchanged for both CaIrO₃ and CaMnO₃.

2.3 Study on anisotropic magnetoresistance (AMR)

2.3.1 ϕ-AMR in (MIxy)z (x = y = 2: 4)

The AMR, also referred to as angular dependent magnetoresistance, was measured in three different senses of rotations of the SLs with respect to the magnetic field, as shown in Figure 5(a), and is calculated as

Figure 5.

(a) Three different rotational geometries schematically illustrating the measurements of AMR. (b) The impact of extended CaMnO₃ and CaIrO₃ periods on the sheet resistance was examined by plotting the temperature-dependent behavior of (MIxy)z (x = y = 2–4) SL and (MI84)5 SL. (c) Polar plots comparing the ϕ, θ, and γ AMRs are presented for (MI22)₁₀ and (d) (MI33)₅ SL. (e) The variation in ϕ-AMR at 30 K is demonstrated for both (MIxy)z (x = y = 2–4) and (MI84)₅ SL. (f) The variation in the ϕ-AMR amplitude as a function of temperature for H = 9 T is shown. (Reprinted from [14] © 2023 American Physical Society).

$$\mathrm{AMR}=\frac{\rho \left[B\left(\mathit{\text{angle}}\right)\right]-\rho \left[B\left(\mathit{\text{angle}}=90°\right)\right]}{\rho \left[B\left(\mathit{\text{angle}}=90°\right)\right]}$$E1

Where ‘angle’ represents the angle between the magnetic field and the current direction.

In Figure 5(a), H rotates in the xy, yz, and zx planes while three rotation angles, namely ϕ, θ, and γ, are depicted. Additionally, the current direction is along the (100) axis of the sample. Figure 5(b–f) depicts the magnetic and electrical behavior of (MIxy)z (x = y = 2–4), which can be explained by the enhancement of ‘U’ induced by dimensionality and the charge transfers. All SLs demonstrate diminishing AMR in the range of 70–100 K which is the same as the magnetic transition temperature (Tc) of the SLs. The sheet resistance was also measured, and it was found to increase with decreasing CaIrO₃ period, as shown in Figure 5(b). The Mott state is characterized by a sudden increase in resistivity below 50 K. As the CaIrO₃ period decreases, the sheet resistance increases and the resistance of a 10 nm CaIrO₃ film is clearly distinct from the other SLs. In particular, (MI22)₁₀ tends to exhibit a Mott-type state below 30 K. These SLs’ emergent magnetic and transport properties are related to their AMR, which will be discussed further below. Now, it is important to investigate AMR properties of several 3d-5d SLs including (MI22)₁₀, (MI33)₅, (MI44)₅, and (MI84)₅ as a function of temperature, magnetic field, and period of SLs. The AMR measurements reveal that the ϕ-AMR exhibits four-fold sinusoidal oscillations for both (MI22)₁₀ and (MI33)₅, with a subtle two-fold component superimposed on a dominant four-fold component, shown in Figure 5(e). In Figure 5(f), the ϕ-AMR in (MI22)₁₀ SL is particularly striking, exhibiting an astounding 70% amplitude at 10 K, which decreases to 23% at 20 K and gradually ceases to manifest at 100 K. This is the largest amplitude of four-fold ϕ-AMR reported not only for 3d-5d SLs but also for other oxide heterostructures. Furthermore, the ability to tune the ϕ-AMR by two orders of magnitude is demonstrated by varying the period of the SLs. The θ- and γ-AMRs, shown in Figure 5(c, d), also show a phenomenal amplitude of 15% for (MI22)₁₀, which is much larger than observed for any 3d-5d SL. The AMR decreases with increasing temperature and completely disappears around the transition temperature in the range of 70–100 K for all samples. The ϕ-AMR observed in (MI22)₁₀ SL, as shown in Figure 5(f), is exceptional because it is much larger than what has been reported in any 3d-5d heterostructures so far, and it is the largest among complex oxide heterostructures. Additionally, the ϕ-AMR reduces by one order of magnitude as the period (x = y) increases from 2 to 4. This sensitivity to the constituent layer thickness suggests the presence of a unique phenomenon that promotes interlayer coupling.

2.3.2 The origin of the AMR

One method for determining the origin of AMR is to compare the behavior of different types of AMRs and analyze their dependence with the magnetic field. In particular, the ϕ, θ, and γ AMRs have been studied extensively.

3. Non-quadratic dependence of ϕ-AMR with field

One observation that has been made is that none of the ϕ, θ, and γ AMRs follow a quadratic dependence on the magnetic field because ϕ-AMR does not vary linearly with B², as shown in Figure 6. These results rule out Lorentz scattering as the origin of the effect. Lorentz scattering is a mechanism in which the magnetic field causes the scattering of electrons, leading to a change in resistance [19]. Another observation that has been made is that the magnitude and phase of the θ and γ AMRs for the sample (MI22)₁₀ are coincident. This eliminates the possibility of spin Hall MR or s-d scattering as the underlying mechanisms. Spin Hall MR is a mechanism in which the spin Hall effect causes a change in resistance, while s-d scattering is a mechanism in which the scattering of electrons between the spin-polarized d-band and s-band causes a change in resistance [34, 35, 36, 37].

Figure 6.

At various temperatures, the (MI22)₁₀ and (MI33)₅ SL display non-quadratic dependence of B as seen in the polar plots of ϕ, θ, and γ - AMRs presented. (Reprinted from [14] © 2023 American Physical Society).

3.1 Intra and interlayer coupling in ϕ-AMR for varying periodicity: (MIx2)z for x = 2, 4,6 and 8 and (MI2y)z for y = 2,4 and 5 SLs

In the canted AFM phase of these SLs, interlayer coupling controls the domain scattering mechanism based on biaxial magnetic anisotropy, which is believed to be the underlying cause of the AMR. Domain scattering refers to the scattering of electrons as they pass through the domains (regions) with different magnetic orientations in a material. In this case, the domains are created by the canted AFM phase of the SLs, and the domain scattering is thought to be responsible for AMR observed in the material. The magnitude of interface coupling and the dimensions of the individual layers are determining factors in the strength of interlayer coupling. The magnetic interactions for intra- and interlayer bonds of neighboring iridium ions can be expressed in a common form [eq. (2)], with different coupling constants for inter- and intralayer bonds [38].

$${\mathrm{H}}_{\mathrm{ij}}={\mathrm{J}}_{\mathrm{ij}}{\overrightarrow{\mathrm{S}}}_{\mathrm{i}}.{\overrightarrow{\mathrm{S}}}_{\mathrm{j}}+{\mathrm{J}}_{\text{1c}}{\overrightarrow{\mathrm{S}}}_{\mathrm{i}}.{\overrightarrow{\mathrm{S}}}_{\mathrm{j}}+{\text{Γ}}_{\mathrm{ij}}{{\overrightarrow{\mathrm{S}}}_{\mathrm{i}}}^{\mathrm{z}}.{{\overrightarrow{\mathrm{S}}}_{\mathrm{j}}}^{\mathrm{z}}+{\overrightarrow{\mathrm{D}}}_{\mathrm{ij}}.\left[{\overrightarrow{\mathrm{S}}}_{\mathrm{i}}\times {\overrightarrow{\mathrm{S}}}_{\mathrm{j}}\right]$$E2

Where J_ij is the in-plane isotropic Heisenberg exchange among pseudospin ${\overrightarrow{S}}_i\mathit{\text{and}}{\overrightarrow{S}}_j$, and J_1c represents the first interlayer interaction. In the case of 5d material, pseudospin is an entangled state of spin and orbital moment denoted as J_eff [39]. Γ_ij represents symmetric exchange anisotropy that favors collinear c-axis spin order, and $\overrightarrow{D}$_ij whose direction is along the c-axis represents antisymmetric exchange anisotropy via Dzyaloshinskii-Moriya (DM) interaction that favors canting of in-plane spin order in the ab plane. Specifically, octahedral rotation and tetragonal distortion lead to symmetric and antisymmetric exchange anisotropy terms that are responsible for ϕ-AMR [38, 40]. This is due to the strong SOC that locks the staggered AFM pseudospins moments to the antiferrodistortive octahedral, and as a result, canted pseudospin as well as the net in-plane moment is obtained. To prevent the cancelation of canted moments, they must be aligned parallel to each other across the interlayer. The in-plane canted moments and their stability depend on the strength of interlayer AFM coupling as well. The Hamiltonian is originally proposed for layered Sr₂IrO₄ for explaining the strength of interlayer coupling between IrO₂ layers separated by nonmagnetic SrO layer. In a different study, the theory of interlayer coupling is used to describe the magnetic properties of artificially synthesized SLs, i.e., SrIrO₃/SrTiO₃ [41]. Increasing the insulating SrTiO₃ layer helps to reduce interlayer coupling and decrease magnetic transition temperature. The magnetic exchange interactions can be governed directly from one layer to another layer of the IrO₂ plane separated by the SrO layer in Sr₂IrO₄ or can be governed by electron hopping through the SrTiO₃ layer in SrIrO₃/SrTiO₃ SL. As the periodicity increases from (SrIrO₃)1/(SrTiO₃)1 (1/1-SL) to (SrIrO₃)1/(SrTiO₃)2 (1/2-SL), the transition temperature is significantly reduced due to the decrease in interlayer exchange coupling. The insertion of additional insulating SrTiO₃-blocking layers hinders the electronic hopping and exchange coupling along the c-axis, causing a decrease in interlayer coupling. Both Sr₂IrO₄ and 1/1-SL exhibit net magnetizations originating from the canting of the AFM moments within the IrO₂ plane [22]. The coupling of LaNiO₃ to the insulating FM LaMnO3 at the interface can lead to the stabilization of an induced AFM order in the [111] direction, which can generate interlayer AFM coupling between two LaMnO₃ layers separated by 7 u.c of LaNiO₃, as suggested by the authors in a separate study [21].

3.2 CaMnO₃ and CaIrO₃ periodicity dependent AMR study in CaMnO₃/CaIrO₃ SLs

In this section, we discuss a study conducted to understand further the role of individual layers in AMR. The study aims to determine the specific role of individual layers in achieving a large AMR in (CaIrO₃)x/(CaMnO₃)y SLs. The AMR of different sets of heterostructures is analyzed, and the results are presented in Figure 7(a–d).

1. (MIx2)₅ for x = 4, 6, and 8 as (MI42)₅, (MI62)₅, and (MI82)₅, with the CaIrO₃ period fixed to 2 u.c.: The ϕ-AMR values of this series of SLs are plotted in Figure 7(a). It is clear that, except for x = 2, the ϕ-AMR of all other SLs is in the range of 0.4–0.8%.

2. (MIx4)₅ for x = 2, 4, and 8 as (MI24)₅, (MI44)₅, and (MI84)₅, with the CaIrO₃ period fixed to 4 u.c.: In this case, the variation of the CaMnO₃ period for a fixed larger CaIrO₃ period (4 u.c.) shows a ϕ-AMR in the range of ∼0.02–1.5%; however, except for (MI24)₅, the AMR of the SLs is less than 0.2%. These data are plotted in Figure 7(b).

3. The SLs (MI2y)z for y = 4 and 5 are considered, with a fixed CaMnO₃ period of 2 u.c. The data shows that as the CaIrO₃ period increases from 2 to 4 and 5, the AMR decreases significantly. The plot of the AMR data is given in Figure 7(c).

4. The SLs (MI5y)z for y = 2, 5, and 8 are studied, with a fixed CaMnO₃ period of 5 u.c. It is observed that the decrease in AMR is pronounced as the CaIrO₃ period increases. For (MI58)₅, the AMR follows the behavior of a CaIrO₃ film of the same thickness. The plot of the AMR data is given in Figure 7(d).

5. It is found that the AMR of (MI58)₅, having a large CaIrO₃ period of 8 u.c., matches with that of a 10-nm-thick CaIrO₃ film in terms of phase and amplitude.

Figure 7.

Exhibits the ϕ-AMR for (a) (MIx2)₅ with x = 4, 6, and 8, and (b) (MIx4)₅ with x = 2, 4, and 8, recorded at various temperatures with a 5 T magnetic field. Figures (c) and (d) display the ϕ-AMR for (MI2y)z with y = 4 and 5 and (MI5y)z with y = 2, 5, and 8, respectively, measured at different temperatures with a magnetic field of 5 T. (Reprinted from [14] © 2023 American Physical Society).

The first three points suggest that a short CaMnO₃ period contributes to a high AMR value when the CaIrO₃ period is also small. However, when the maximum period of CaMnO₃ and CaIrO₃ in CaMnO₃/CaIrO₃ SLs is reached, the interlayer coupling necessary for biaxial anisotropy is lost, and the SL behaves like a single CaIrO₃ film, as stated in the fifth point. SLs with a higher periodic thickness of CaMnO₃ and CaIrO₃, such as the (MI33)5 and (MI24)5 SLs, exhibit reduced octahedral distortion. As a result, these SLs demonstrate a decrease in AMR response compared to the (MI22)10 SL. This reduction results in a lower possibility of obtaining a net canted moment from each IrO₂ plane, thereby reducing the AMR response of (MI33)₅ and (MI24)₅ SLs in comparison to the (MI22)₁₀ SL. The AMR value of ∼1% for (MI24)₅ and (MI52)₅ SL confirms that the CaMnO₃ and CaIrO₃ periods have an equal impact on interlayer coupling in CaMnO₃/CaIrO₃ SLs. Therefore, in CaIrO₃/CaMnO₃ SLs, the similarity of magnetic phase and structural distortion of (a⁻a⁻c⁺) type in low dimensions is a unique attribute and can be argued as a decisive factor for strong interlayer coupling. The structural distortion of both constituent layers in CaIrO₃/CaMnO₃ heterostructures contributes to a parallel interlayer alignment of moments, as shown in previous studies [19, 42]. This results in biaxial anisotropy and a large fourfold sinusoidal AMR in the heterostructures.

3.3 Dynamics of ϕ-AMR in (MI22)z: Biaxial anisotropy and spin-flop transition

The trough and crest of ϕ-AMR are assigned by the difference in scattering by soft (100) and hard (110) axes in (MI22)₁₀ SL, a biaxial anisotropic system, as shown in Figure 8(a, b). There appears a transition from uneven scattering from (110) family of axes at 25 K to (100) axes at 14 K, as emphasized in Figure 8(c).

Figure 8.

(a) The crystallographic in-plane directions for the (100) and (110) families are labeled as a, B, C, D, and A′, B′, C′, D′ respectively. (b) The ϕ-AMR for (MI22)₁₀ is shown at different temperatures between 25 K and 100 K with a magnetic field of 9 T. (c) The ϕ-AMR for (MI22)₁₀ is displayed for the temperature range between 10 K and 22 K, showing a fourfold symmetry, and indicating the onset of the spin-flop transition at 22 K. (d) The field dependence of ϕ-AMR for (MI22)₁₀ is presented at 15 K. (e) The spin arrangement in relation to the AMR is shown. The spins depicted in red and blue correspond to the two sublattices of the antiferromagnetic order. A subtle canting in AFM order at B = 0 is observed, which increases at a field of 9 T along the easy (100) axis (1 and 2), while the effect is less pronounced when B is applied along the (110) hard axis (panel 3). For B = 9 T along (010), the spin-flop arrangement at 10 K is depicted in the last panel (panel 4). (Reprinted from [14] © 2023 American Physical Society).

At 25 K, the stronger crest peaks at (110) and (−1–10) axes suggest larger scattering compared to that at (−110) and (1–10) peaks, despite the uniformity in scattering observed by the (100) family of axes, as shown in Figure 8(b, c). Similarly, at 14 K, crest peaks are uniform in magnitude whereas trough peaks are not uniform in magnitude. Hence, the ϕ-AMR in (MI22)₁₀ SL deviates from regular four-fold sinusoidal symmetry. As scrutinized in very close temperature intervals in the range of 10–25 K, as shown in Figure 8(c), as one moves from the (100) to the (110) crystal axes, a new superimposed feature in the form of a four-fold pattern of AMR kinks emerges alongside the underlying sinusoidal pattern. At 25 K, there is a clear and well-defined four-fold pattern of ϕ dependent AMR, but as the temperature decreases to 22 and 18 K, the pattern becomes more complex, with multiple kinks. Finally, at 15 K, the pattern reverts to a symmetric and sharp four-fold single kink configuration. The smooth pattern appears at 14 K which further transforms to a sharp step-like humungous amplitude of 70% at 10 K. The polarity of AMR peak amplitudes transforms for different fields, i.e., 9 and 5 T, as shown in Figure 9(a). This unprecedented ϕ-AMR is complex both in its pattern and amplitude. At 5 T, the smooth sinusoidal modulation of the ϕ-AMR displays a modest 10% increase, as shown in Figure 9(a). However, when the magnetic field is increased to 9 T, a remarkable metamagnetic transition occurs, which is responsible for generating a substantial 70% step-like AMR. This transition is identified as a spin-flop transition [43] since the trough of the ϕ-AMR at 5 T coincides with the crest at 9 T. By comparing the ϕ-AMR at these two fields, it is clear that there is an abrupt drop in resistance at 9 T when the sinusoidal ϕ-AMR peak starts appearing at 5 T, as shown in Figure 9(a). These observations establish that the spin-flop metamagnetic transition is responsible for the enormous ϕ-AMR at 9 T and 10 K. Magnetic-field dependence of ϕ-AMR was conducted at 15 and 25 K to investigate spin-flop-induced transition. Figure 9(b) and (c) shows a kink-like transition indicative of the spin-flop transition only at 9 T and 15 K, absent at 25 K. Two primary phenomena are responsible for the diverse characteristics of the ϕ-AMR. Firstly, a robust biaxial magneto-crystalline anisotropy contributes to the sinusoidal ϕ-AMR, which can reach up to 20%. Secondly, the spin-flop transition induces kink- and step-like metamagnetic AMR of up to 70% at a maximum field of 9 T. To explain the anomalous AMR of CaIrO₃/CaMnO₃ SLs, a competition between pseudospin–lattice (S-L) coupling and field-pseudospin coupling is proposed. The S-L coupling in iridates is represented by Eq. (3) with the Hamiltonian Hs-ι [19, 38].

Figure 9.

Comparison of ϕ-AMR at T = 10 K for (MI22)₁₀ reveals differences between measurements at 9 and 5 T. field dependence of ϕ-AMR for (MI22)₁₀ is measured at 15 and 25 K. (Reprinted from [14] © 2023 American Physical Society).

$$H_{s\text{-ι}}={\mathrm{\Gamma }}_{\left(x^2-y^2\right)}cos\left(\text{2α)(}{S_i}^x{S_j}^x-{S_i}^y{S_j}^y\right)+{\mathrm{\Gamma }}_{\left(\mathit{xy}\right)}sin\left(\text{2α)(}{S_i}^x{S_j}^y+{S_i}^y{S_j}^x\right)$$E3

The energy scales of S-L coupling to the distortions along (100) and (110) are denoted by ${\mathrm{\Gamma }}_{\left(x^2-y^2\right)}$ and ${\mathrm{\Gamma }}_{\left(\mathit{xy}\right)}$, respectively, while α represents the angle between the staggered moments and the (100) axis. As it is mentioned previously that AFM staggered pseudospins in ab plane are entangled to the antiferrodistortive octahedral via SOC, resulting canted pseudospin, hence, pseudospins have some special symmetric directions, i.e., $\mathit{xy}$ and $x^2-y^2$ quadruple symmetries. The competition between $\mathit{xy}$ and $x^2-y^2$ quadruple symmetries of pseudospins have two solutions: α=0 for ${\mathrm{\Gamma }}_{\left(x^2-y^2\right)}$<${\mathrm{\Gamma }}_{\left(\mathit{xy}\right)}$ and α=45° for ${\mathrm{\Gamma }}_{\left(x^2-y^2\right)}$>${\mathrm{\Gamma }}_{\left(\mathit{xy}\right)}$.${\mathrm{Sr}}_2$ IrO₄ and an engineered SL, SrIrO₃/SrTiO₃, both possess a similar magnetic structure and exhibit the former phenomenon, whereas the latter is observed in CaIrO₃/SrTiO₃ heterostructures. In both cases of SrIrO₃ and Sr₂IrO₄, the ϕ-AMR phase lags by 45° compared with CaIrO₃/CaMnO₃ SL [19, 44]. In the case of CaIrO₃/CaMnO₃ SLs, the optimal solution is achieved at α=0 since the minimum of AMR oscillation aligns with the (100) axes, which is analogous to that of CaIrO3/SrTiO3 SLs. The difference in the phase lag between SrIrO₃- and CaIrO₃-based 3d-5d SLs is due to the different sense of octahedral rotations in their low-dimensiona limits (Figure 10).

Figure 10.

Temperature dependence of the ϕ-AMR amplitude for (MIxy)z SLs at H = 5 T. (Reprinted from [14] © 2023 American Physical Society).

3.4 Temperature dependence of ϕ-AMR in the context of magneto-elastic coupling

The behavior of solid-state materials in the vicinity of a magnetic transition is a complex and fascinating area of research. At such points, the coupling between the spin and lattice degrees of freedom, known as S-L coupling, plays a critical role, and its strength changes as the temperature decreases [38, 45]. One of the most striking manifestations of S-L coupling is the appearance of a sinusoidal ϕ-AMR due to the continuous lattice deformation under the influence of an external magnetic field. There are two ways in which S-L coupling can occur in CaMnO₃/CaIrO₃ SLs, namely, the coupling of pseudospins with octahedral distortion and the response of pseudospins to lattice vibrations or phonons that vary with temperature. It is noteworthy that the structural transition responsible for octahedral deformations has not been reported yet in layered systems, i.e., SrIrO₃/SrTiO₃ or CaIrO₃/SrTiO₃ SL.

As the temperature changes, the strength of S-L coupling can be described in two regimes based on the magnetic moment of the layered system. (i) In lower magnetic moment-based SLs such as (MIx2)₅ (x = 4, 5, 8), the anisotropic scattering of electrons due to the orbital degree of freedom via lattice vibration is more prominent near the transition temperature, leading to strong pseudospin-lattice coupling. At lower temperatures, however, due to the stiffness of the lattice, the response of pseudospins with the lattice is low, and AMR is expected to be governed by field-pseudospin coupling only. (ii) In higher magnetic moment-based SL such as (MI22)₁₀, at a temperature of 10 K, the (MI22)₁₀ SL exhibits a sharp four-fold single kink separated by 90° with no sinusoidal variation observed in its ϕ-AMR. This suggests that the orbital degree of freedom of electrons contributed by lattice vibration is suppressed at this temperature, and the step-like AMR pattern in (MI22)₁₀ SL is a result of field-pseudospin coupling, facilitated by higher magnetic moment. In contrast, the absence of the kink pattern in (MIx2)₅ (x = 4, 5, 8) represents the absence of field-pseudospin coupling. Thus, the AMR mechanism in (MIx2)₅ (x = 4, 5, 8) SLs is mainly governed by orthorhombic distortion through S-L coupling restoring the sinusoidal resistance [22].

Furthermore, it is noteworthy that the sinusoidal ϕ-AMR pattern with a kink observed in the temperature range of 15 to 22 K in the (MI22)₁₀ SL indicates the coexistence of both S-L coupling and field pseudospin coupling. Additionally, in the cases of both (MI22)₁₀ and (MI33)₅ SLs, the amplitude of ϕ-AMR steadily increases with decreasing temperature. This suggests that the competition between these two couplings, which varies with temperature, ultimately determines the ϕ-AMR behavior in the (MI22)₁₀ SL. Specifically, at high temperatures, the S-L coupling is responsible for the reorientation of moments, whereas at lower temperatures when the lattice is rigid but the moments are larger, the direct coupling of field pseudospin dominates.

3.5 Metamagnetic transitions in perovskite manganites and iridates

Metamagnetic transitions are a fascinating phenomenon that has been observed in a variety of materials including manganites and iridates. Over the past few decades, much attention has been focused on the ABO₃ perovskite-type mixed valent manganites which have the general formula, i.e., R_1-xA_xMnO₃, where ‘R’ represents a trivalent rare-earth cation and ‘A’ represents a divalent cation [46]. These materials have been extensively studied due to their intriguing properties arising from the interplay between the charge-orbital coupling. One of the most interesting features of these compounds is the colossal magnetoresistance phase that emerges due to the interplay between charge and orbital ordering. The evolution of different magnetic ground states is also observed in these compounds as the value of ‘x’ varies from 0 to 1. For instance, in Nd_1-xSr_xMnO₃, the magnetic phase transitions from FM metallic state to a C-type insulating phase as ‘x’ increases from 0.3 to 0.8, via an A-type AFM metallic phase with a ferromagnetic plane featuring uniform ${\mathrm{d}}_{(x^2-y^2)}$-type orbital order. In another material, Pr_1-xCa_xMnO₃, a transition from a charge-orbital ordered AFM-CE type insulating state to FM metallic state is observed as the temperature decreases in the presence of an external magnetic field. Moreover, a larger field of 27 T is required to destabilize the charge-ordered insulating state via a metamagnetic transition at low temperatures in the half-doped Pr_1-xCa_xMnO₃ (x = 0.5) material [46, 47]. These results indicate that mixed valent manganites exhibit strong spin-charge-orbital-lattice coupling, resulting in the field-induced metamagnetic transition [48]. More recently, materials based on late transition metal ions with strong SOC have come into focus. These compounds no longer treat spin-orbital separation as a separate entity that requires magnetism to be reformulated using pseudospin. Spin-flop-based metamagnetic transitions, which are the result of spin-lattice coupling, have been observed in these materials [45, 49]. As an example, the theoretical basis for the spin-flop transition lies in the stronger interlayer coupling that varies from Sr₂IrO₄ to Sr₃Ir₂O₇. Overall, the occurrence of metamagnetic transitions in manganites and iridates, as well as the diverse phenomena associated with these transitions, highlight the complex interplay between charge, orbital, and spin degrees of freedom in these materials.

3.5.1 Metamagnetic transition in thin-film

Obtaining a spin-flop transition in thin films can pose a significant challenge due to the reduced thickness of the film. However, in a thin film, the magnetic moments are often constrained by the surface and interface effects as well as defects [48, 50, 51, 52, 53]. These effects can create a preferential orientation for the magnetic moments, hindering their ability to rotate easily in response to an external magnetic field. It is crucial to have a strong SOC effect to effectively leverage large magnetoresistance anisotropy. However, if the magnetic moments are aligned along an easy axis that is perpendicular to the film plane, it becomes quite challenging to rotate them away from this easy axis and towards the basal plane. As a result, utilizing TAMR effects may be impossible. On the other hand, in Mn₂Au, the magnetic moments are oriented in the basal plane of the structure. This makes it relatively easy to rotate them from one easy in-plane direction to another with the aid of a relatively small external excitation [54]. Defects and imperfections in thin films can also have a considerable impact on the spin-flop transition based on the rotation of spin [55]. These defects can act as pinning sites for the magnetic moments, impeding their motion. Thus, a sharp interface is essential for achieving a spin-flop transition. Careful consideration of the film thickness, interface effects, shape anisotropy, and defects, among other factors, is necessary to optimize the magnetic properties and achieve the desired behaviors. The resistance oscillations in the current CaIrO₃/CaMnO₃ SLs stem from a magnetic moment that oscillates with respect to the crystallographic axis embedded in a system with in-plane biaxial magnetic anisotropy. Along with these oscillations, there are sharp kink- and steplike transitions that induce an additional large component ϕ-AMR and originate from spin-flop metamagnetic transition. In Figure 8(e), there is a depiction of a pseudospin arrangement that corresponds to the crest and trough of the spin-flop-based AMR. When a field of 9 T is applied along the (100) easy axis, the canting angle and magnetic moment increase. The canting effect is less pronounced when the field is applied along the (110) hard axes, where the AFM spin arrangement is rotated along the direction of the field. When the magnetic moments are tilted at larger angles along the (100) and (010) directions, the material shows less resistance to the flow of electric current compared to when the magnetic moments are tilted along the (110) direction. Additionally, Figure 8(e) illustrates a spin-flop transition that occurs at 10 K in a field of 9 T.

4. Conclusion

Ultimately, it should be highlighted that the selection of a suitable 3d compound is crucial for achieving efficient interlayer coupling and distortion, which are necessary to adjust a significant ϕ-AMR. In the case of CaIrO₃/SrTiO₃ SLs, the CaIrO₃ layers with distorted (a^˗˗a^˗˗c⁺) octahedral as per Glazer notations convey this distortion between them via distortion of the mediating SrTiO₃ layer octahedra, only for one layer thickness of the latter [19]. In present CaIrO₃/CaMnO₃ SLs, in contrast, the presence of AMR in (MI82)5 SL, 8 u.c.s thick CaMnO3 mediating SL, suggests that CaMnO₃ is the most suitable candidate known so far to promote interlayer exchange coupling. Here, the coupling is such long-range that the CaIrO₃ layers separated by even eight u.c.s of CaMnO₃ in (MI82)₅ SL are capable of inducing a ϕ-AMR of 0.25% at 5 T and 50 K. The reason for this is that when few unit cells are considered, both CaMnO₃ and CaIrO₃ films exhibit orthorhombic distortion with the same octahedral rotation pattern (a^˗˗a^˗˗c⁺) according to Glazer’s notations. Moreover, they also share a similar in-plane DM-type canted AFM phase. This similarity of distortion of both the constituents is key for phenomenal CaIrO₃ interlayer coupling, and, hence, a large biaxial anisotropy is obtained. The presence of a stronger H_EB, as observed in (MI44)5 and (MI84)5, leads to the formation of a graded AFM/FM phase within the CaMnO₃ layer, which acts as a hindrance to a uniform interlayer coupling of CaIrO₃. The impact is evident in the comparison between (MI22)10, which has an AMR of 23% in the absence of H_EB, and (MI33)5, which has a moderate H_EB and a reduced AMR of just 3%.

The CaIrO₃/CaMnO₃ SLs prove to be the most potent 3d-5d heterostructures for achieving an unprecedented AMR of about 70%, utilizing two key factors of a strong biaxial anisotropy and a spin-flop metamagnetic transition. On the fundamental side, employing the tolerance factor to appropriately manage the structural and surface layer construction of a large bi-axial magnetic anisotropy, fine-tuning the interlayer coupling facilitated by an exceptionally thick layer, and showcasing the spin-flop transition to enhance the degree of anisotropic AMR are all significant advancements in the realm of 3d-5d SLs. These developments hold immense promise in the field of contemporary quantum materials and their application in technological advancements. This proof-of-concept study opens new avenues for designing highly sensitive AMR readout devices for emerging AFM spintronics.

Acknowledgments

The authors extend their gratitude to several organizations for their financial support and provision of research facilities. Specifically, D.S.R. expresses thanks to the Department of Science and Technology (DST) Nanomission and the Science and Engineering Research Board Technology, New Delhi for their financial support through Research Project No. SM/NM/NS-84/2016 and Project No. CRG/2020/002338, respectively. XAS measurements were performed at UC San Diego as part of a search for materials for spin-torque oscillators, which was supported by Quantum Materials for Energy Efficient Neuromorphic Computing, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences under Award No. DE-SC0019273. Also, Resources for this research were made available through the Advanced Photon Source, which is operated by Argonne National Laboratory for the DOE Office of Science under Contract No. DE-AC02-06CH11357, with supplementary support from the National Science Foundation under Grant No. DMR-0703406. The authors also acknowledge the DOE Office of Science for supporting extraordinary facility operations through the National Virtual Biotechnology Laboratory. The authors express their appreciation to various individuals for their assistance in performing magnetization, transport, and x-ray diffraction characterizations, as well as in the preparation of transmission electron microscopy specimens. Finally, the authors express their gratitude for the utilization of the HZDR Ion Beam Center TEM facilities and the financial support provided by the German Federal Ministry of Education and Research (Grant No. 03SF0451) through the Helmholtz Energy Materials Characterization Platform for the funding of TEM Talos.