Robust Biaxial Anisotropy and Switchable Néel Vectors in LaFeO₃ Epitaxial Films

Abstract

Antiferromagnets with highly stable but switchable Néel vectors are desired for antiferromagnetic spintronics with ultrafast speed and terahertz frequencies. Electrical switching of antiferromagnetic insulators has been demonstrated using binary antiferromagnets, while large families of complex antiferromagnets such as perovskites are largely unexplored. Here, we show that epitaxial LaFeO₃ thin films on SrTiO₃(001) exhibit clear, robust biaxial anisotropy with a spin-flop field of a few tesla. Angular-dependent spin-Hall magnetoresistance (SMR) characterizations of Pt/LaFeO₃ bilayers with the current channel along SrTiO₃ [100] and [110] reveal distinct, intriguing shapes and field dependence. Simulations using a macrospin model accurately describe the main behavior and fine features of the SMR data from which key antiferromagnetic parameters are extracted. Furthermore, remanent SMR measurement confirms the high fidelity of the Néel vector along either easy axis of the biaxial anisotropy, indicating that epitaxial films of LaFeO₃ and potentially other perovskite antiferromagnets offer an attractive platform for antiferromagnetic spintronics.

Antiferromagnetic (AFM) spintronics offer advantages over their ferromagnetic (FM) counterparts for memory devices and other technologies because of their faster dynamics and higher packing density.¹⁻⁴ The demonstrations of electrical switching of the Néel vector in AFM metals⁵⁻⁷ and insulators⁸⁻¹⁰ in recent years have generated significant excitement arising from the promise of electrical manipulation of AFM spins. For practical AFM-based applications, the AFMs should have high Néel temperatures (T_N) and well-defined bistable states (two easy axes of Néel vector representing “0” and “1”) separated by a robust energy barrier (e.g., AFM hard axis). The energy barrier should be high enough so that the AFM spin information can be stored for years but not too high for information writing by an electrical pulse or magnetic field.

To date, electrical switching of AFM insulators has been mostly focused on a few well-understood binary oxides such as α-Fe₂O₃, CoO, and NiO.⁸⁻¹⁵ Meanwhile, these simple AFMs have limitations that may hinder their applications. α-Fe₂O₃ has a weak triaxial anisotropy and is often considered an easy-plane AFM, which may not be robust enough against perturbations. CoO and NiO are essentially cubic with a biaxial anisotropy; however, CoO has a low T_N, while NiO has a high anisotropy barrier as evidenced by a rather large spin-flop (SF) field (H_SF). AFMs with a robust biaxial anisotropy, high T_N, and intermediate H_SF are desired for storage, electrical writing, and reading of AFM spin information. In this regard, the large family of complex oxide AFMs are attractive but much less explored candidates for AFM spintronics. In particular, AFM perovskites offer the benefits of high T_N’s and pseudocubic structures that can be epitaxially strained to various cubic substrates with biaxial anisotropy and high tunability.

In this work, we report the growth of fully strained LaFeO₃ (LFO) epitaxial thin films and the observation of a clear biaxial anisotropy and field-switchable AFM spins revealed by angular-dependent spin-Hall magnetoresistance (SMR) characterization and macrospin simulations. LaFeO₃ is a classic AFM perovskite¹⁶⁻²¹ with a T_N = 740 K. Bulk LaFeO₃ has an orthorhombic structure with octahedral tilting that leads to a canted moment of ∼0.01 μB/Fe and lattice constants of a = 5.557 Å, b = 5.565 Å, and c = 7.854 Å or a pseudocubic (pc) lattice constant a_pc = 3.930 Å, which has a small 0.6% mismatch with SrTiO₃ substrates.

Epitaxial LaFeO₃(t_LFO) films are grown on SrTiO₃ (001) substrates using off-axis magnetron sputtering,²² where t_LFO = 1, 2, 3, and 10 nm, followed by the deposition of a 3 nm Pt layer on LaFeO₃ at room temperature. The LaFeO₃ thin films are characterized by X-ray diffraction (XRD), as shown in Figure 1a, which exhibit Laue oscillations near the LaFeO₃ (002) peak down to t_LFO = 2 nm, indicating highly coherent crystalline ordering. Scanning transmission electron microscopy images of our LaFeO₃ films confirm the excellent atomic ordering without any detectable defects.²³ Atomic force microscopy imaging of a LaFeO₃ (10 nm) film (Figure 1b) reveals smooth surface terraces with a root-mean-square (RMS) roughness of 0.14 nm.

Figure 1.

Characterization of structural quality of LaFeO₃ epitaxial films. a, 2θ–ω XRD scans of LaFeO₃ films with thicknesses of 2, 3, and 10 nm grown on SrTiO₃(001) substrates. b, Atomic force microscopy image of a LaFeO₃(10 nm) film on SrTiO₃(001) with an RMS roughness of 0.14 nm. c, Schematic of a patterned Hall bar used in angular-dependent SMR measurements where α is the angle between the applied in-plane magnetic field and the current channel.

The Pt(3 nm)/LaFeO₃(t_LFO) bilayers are patterned into standard Hall bars with a channel width/length of 10/40 or 100/400 μm as shown in Figure 1c with the current channel oriented along either the SrTiO₃ [100] or [110] direction. V_xx and V_xy are measured in a Physical Property Measurement System (PPMS) in a magnetic field (H) applied at an in-plane angle α with respect to SrTiO₃ [100] at various temperatures (T), from which the longitudinal (ΔR_xx) and transverse (ΔR_xy) SMR are obtained.

We start with SMR results of a Pt(3 nm)/LaFeO₃(3 nm) bilayer with the current channel along SrTiO₃ [100]. Figures 2a and 2b show the angular dependencies of ΔR_xy and ΔR_xx, respectively, taken at T = 25 K in a magnetic field from 0 to 14 T, which exhibits several distinct features. First, ΔR_xy (Figure 2a) is flat at μ₀H = 0 and 1 T, suggesting that the AFM spins are essentially unperturbed by the applied field up to 1 T. In contrast, at μ₀H = 2 T, ΔR_xy becomes square-shaped with nearly 90°-wide plateaus, indicating a spin-flop transition^9,24,25 with H_SF between 1 and 2 T for the 3 nm LaFeO₃ film. Since the SF field is correlated with the strength of AFM anisotropy, this H_SF of 1–2 T is desirable for AFM-based devices, i.e., robust, and switchable.

Figure 2.

Angular dependencies of spin–Hall magnetoresistance. a, ΔR_xy and b, ΔR_xx for a Hall bar of a Pt(3 nm)/LaFeO₃(3 nm) bilayer taken at T = 25 K in the presence of an in-plane magnetic field of 0 to 14 T. The current channel of the Hall bar is along SrTiO₃ [100]. The solid curves are simulations of the experimental data (open symbols) at various magnetic fields using the same AFM anisotropy field of 10 Oe.

Second, the square shape of ΔR_xy in Figure 2a at μ₀H = 2 and 3 T is quite uncommon for SMR in AFMs such as α-Fe₂O₃ and CoO, which are mostly sinusoidal above the SF transition. The square ΔR_xy indicates that the Néel vector (n, |n| = 1) strongly prefers to align along two orthogonal orientations: n || 45°/225° (plateaus of α ≈ 90°–180° and 270°–360°) and n || −45°/135° (α ≈ 0°–90° and 180°–270°), which correspond to the two easy axes of a biaxial anisotropy along SrTiO₃ [110] and [110], respectively. These two preferred orientations can be detected by ΔR_xy with two discrete values (bistable states) following ΔR_xy ∝ n_xn_y in a monodomain state, where n_x and n_y are the x and y components, respectively, of the Néel vector.²⁶ As the field is rotated across α = 90°, 180°, 270°, and 360°, the Néel vector is switched sharply to the other easy axis by overcoming the hard axis along SrTiO₃ [100] or [010]. At higher fields, ΔR_xy gradually evolves from square to sinusoidal shape while the magnitude of ΔR_xy decreases with increasing field. We note that the square-shaped angular dependence of ΔR_xy resembles that of the planar Hall resistance reported in ferromagnetic semiconducting (Ga,Mn) As films, for which the mechanism is distinct from the SMR in our Pt/AFM-insulator bilayers.²⁷

Third, the ΔR_xx results in Figure 2b exhibit primarily a sawtooth (triangular) shape with fine features that evolve with magnetic field from 1 to 12 T. The clear contrast of the ΔR_xy and ΔR_xx shapes arises from their different dependencies on the Néel vector orientation: ΔR_xy ∝ n_xn_y and ΔR_xx ∝ n²_y in a monodomain.²⁶ The evolution of ΔR_xy and ΔR_xx can be accurately modeled by macrospin simulations, as shown below.

To further understand the SMR results and gain insights into the AFM fundamental properties of the LaFeO₃ films, we simulate the angular dependencies of ΔR_xy and ΔR_xx at various magnetic fields using a two-dimensional macrospin model for a monodomain considering the competition of the AFM exchange interaction, biaxial anisotropy, Dzyaloshinskii–Moriya (DM) interaction, and Zeeman energy. First, the free energy density E(m̂₁, m̂₂) for a two-sublattice AFM in the exchange limit is²⁸

1

where M is the AFM sublattice magnetization and H, H_ex, and D are the external magnetic field, exchange field, and DM field, respectively. m̂₁ and m̂₂ are the normalized AFM sublattice moments, which make an angle of ₁ and φ₂, respectively, relative to the SrTiO₃ [100] (x-axis), as illustrated in Figure 3a. E_an is the AFM anisotropy energy density. The Néel vector is related to m̂₁ and m̂₂ by φ.

Figure 3.

Contrast of SMR with the Hall bar channel along [100] and [110] orientations. a, Schematic of two Hall bars of a Pt/LaFeO₃ bilayer grown on a SrTiO₃ substrate, where the blue and red Hall bars have the current channel along the SrTiO₃ [100] (AFM hard axis) and [110] (AFM easy axis), respectively. Angular dependencies of b, ΔR_xy and c, ΔR_xx for the blue and red Hall bars of a Pt(3 nm)/LaFeO₃(3 nm) bilayer taken in a magnetic field of 3 and 10 T at T = 25 K with distinct square-like and triangular shapes. The simulations (solid curves) match well with the experimental data (open symbols) for both sample orientations at different magnetic fields using an AFM anisotropy field of 10 G.

Assuming that the sublattice moments lie in the xy plane, the free energy in eq 1 can be rewritten in terms of the in-plane sublattice moment angles, ₁ and φ₂ (see Figure 3a), with a biaxial AFM anisotropy:

2

where H_a is the biaxial anisotropy field. E(φ₁, φ₂) is then minimized to find equilibrium sublattice moment angles φ₁ and φ₂ for each field strength and angle, which are used to calculate the Néel vector orientation with φ_n = (φ₁ + φ₂)/2 + π/2. Finally, the SMR (ΔR_xy and ΔR_xx) with current along SrTiO₃ [100] can be calculated using φ_n (see Section 1 in the Supporting Information for more details)^24,26

3

where A is a material-dependent constant and φ is the length/width aspect ratio of the Hall bars. For each Pt/LaFeO₃ bilayer, a single value of A is used for simulations of ΔR_xx and ΔR_xy.

The calculated ΔR_xy and ΔR_xx using eqs 3 are shown in Figures S1a and S2a, respectively, in the Supporting Information. The simulations agree well with the SMR data at 2 and 3 T, but they deviate significantly at higher fields, especially the magnitude. This is because eq 3 yields a constant magnitude of SMR for all fields and cannot explain the decreasing magnitudes of ΔR_xx and ΔR_xy with increasing field.

To model the decreasing magnitude of SMR at higher fields, we introduce an additional (bH)sin(2α) term, where b is a constant, which has a linear dependence on the field strength and sinusoidal dependence on the field angle.^29,30 Then the final SMR equations become,

4a

4b

Since the Néel vector tends to align perpendicularly to the magnetic field above the SF transition, the first and second terms in eqs 4a and 4b have opposite signs, resulting in the reduction of SMR magnitudes with increasing field. In general, the first term in eq 4 associated with the Néel vector is called “negative SMR”, while the second term is called “positive SMR”, which is typically seen in FMs or systems with a net magnetic moment (see Section 2 in the Supporting Information for further discussion).

For our simulations, we use H_ex = 1,000 T and D = 2 T in eq 2(31−33) and obtain a biaxial anisotropy field of H_a = 10 Oe from fitting the SMR data at 2–3 T. Then scaling parameters A = 0.035 Ω and b = 0.073 T^–1 are determined by fitting the magnitudes of SMR at all fields. As can be seen in Figure 2, the fitting curves not only describe the shape and magnitude of ΔR_xx and ΔR_xy with excellent agreement but also reproduce the fine features and subtle curvatures (e.g., ΔR_xx at 5 and 12 T) of the SMR data, indicating that the model captures all the important mechanisms in Pt/LaFeO₃. To help visualize how ΔR_xx and ΔR_xy evolve with a rotating magnetic field, we include animation plots in the PowerPoint slide of the Supporting Information.

To gain further insights into the biaxial anisotropy in LaFeO₃ films, we pattern another Hall bar with the current channel along SrTiO₃ [110] (easy axis) near the Hall bar shown in Figure 2 with the current channel along SrTiO₃ [100] (hard axis) on the same bilayer, which are labeled Sample #[110] and #[100], respectively, as illustrated in Figure 3a. Figures 3b and 3c compare the SMR results of the two Hall bars at 3 and 10 T taken at 25 K. The most obvious contrast is that the shapes of ΔR_xy and ΔR_xx for the two samples are switched, i.e., Sample #[100] (blue) has square ΔR^#[100]_xy and sawtooth ΔR^#[100]_xx, while Sample #[110] (red) has sawtooth ΔR^#[110]_xy and square ΔR^#[110]_xx (see Section 4 in the Supporting Information for an explanation).

The SMR results for sample [110] can also be accurately simulated by the same model described above for sample [100] using the same parameters A and b. Since the current direction of Sample #[110] is at 45° with respect to that of Sample #[100], eqs 4 for Sample #[110] can be rewritten as,

5a

5b

which explains the shape switch of ΔR_xy and ΔR_xx for the two samples, including the sign flip of ΔR^#[110]_xy from ΔR^#[100]_xx. As shown in Figures 3b and 3c, the simulation curves agree very well with the experimental data for both samples at both fields.

The SMR results in Figures 2 and 3 are taken at T = 25 K due to the 3 nm thin LaFeO₃ films and their distinct SMR features at low temperatures. Figure S4 in the Supporting Information shows ΔR_xy and ΔR_xx of the Pt(3 nm)/LaFeO₃(3 nm) Hall bar with the current channel along SrTiO₃ [100] at various temperatures from 5 to 300 K in a magnetic field of 2 T. The square shape of ΔR_xy persists up to ∼150 K, after which ΔR_xy becomes more sinusoidal while maintaining negative SMR. This indicates that the LaFeO₃(3 nm) film remains antiferromagnetic but is a rather weak AFM at room temperature with reduced anisotropy.

For room-temperature applications, thicker LaFeO₃ epitaxial films are preferred. Figures S5 and S6 in the Supporting Information shows the SMR data for a Pt(3 nm)/LaFeO₃(10 nm) Hall bar taken at 25 and 300 K, respectively, which demonstrate robust biaxial anisotropy at room temperature for the 10 nm LaFeO₃ film. In addition, Figure S7 in the Supporting Information shows the angular dependencies of ΔR_xy for Pt(3 nm)/LaFeO₃(t_LFO) bilayers with t_LFO = 1, 2, and 3 nm taken at T = 25 K and μ₀H = 2 T. The 2 nm LaFeO₃ sample maintains an approximately square shape, evidence of a robust biaxial anisotropy, while the 1 nm LaFeO₃ sample exhibits a small but clear negative SMR, indicating AFM ordering persists down to 1 nm LaFeO₃ at 25 K.

The LaFeO₃ epitaxial films discussed above exhibit a robust biaxial anisotropy and an SF field of 1 to a few T, which are desired for AFM switching with two distinct and switchable states. As a preliminary test of the bistable states of the Néel vector in the absence of a magnetic field, we perform remnant SMR measurements on a Pt(3 nm)/LaFeO₃(10 nm) Hall bar. The experimental sequence is illustrated at the top of Figure 4: (1) at each angle α, a 3 T field (above H_SF) is first applied and ΔR_xy is measured; (2) the field is lowered to 0 T and remnant ΔR_xy is measured; (3) the same sequence for the next angle α. Figure 4 demonstrates that the AFM spins strongly prefer to stay along either of the two easy axes at zero field, which can be switched by an intermediate field.

Figure 4.

Control of the Néel vector by a magnetic field: further confirmation of a strong biaxial anisotropy. Angular dependencies of ΔR_xy for a Pt(3 nm)/LaFeO₃(10 nm) Hall bar along SrTiO₃ [100] for remnant Néel vector measurements. The flowchart at the top illustrates the measurement sequence. At each angle α, the magnetic field is ramped to 3 T (well above the spin-flop field) and ΔR_xy (orange) is measured. Next, the field is lowered to 0 T (remnant state), and ΔR_xy (green) is measured. Then, this sequence is repeated for every angle α between 0° and 360°. The clear bistable states with high remnant values at α = 45° (225°) and 135° (315°) indicate the biaxial anisotropy along these two orientations in the Pt(3 nm)/LaFeO₃(10 nm) bilayer.

In conclusion, we present an AFM platform in LaFeO₃ epitaxial films, which exhibit a robust biaxial anisotropy with two easy axes along the SrTiO₃ [110] and [110] directions as well as an intermediate spin-flop field. SMR measurements reveal distinct rich features arising from the underlying AFM and interfacial interactions in the Pt/LaFeO₃ bilayers. Our macrospin simulations accurately describe the primary features and fine details in the SMR data. Lastly, remnant SMR measurements indicate that the Néel vector exhibits a strong preference in staying along one of the easy axes in LaFeO₃. This suggests that it is plausible that the AFM spins in LaFeO₃ films can be switched by an electric current between the two orthogonal easy axes, which warrants further investigations.

Methods

Epitaxial Film Growth

LaFeO₃ epitaxial thin films are grown on SrTiO₃ by off-axis magnetron sputtering. SrTiO₃(001) substrates (from MTI corporation) are first treated by buffered HF, followed by annealing at 1050 °C for 2 h in air to form TiO₂-terminated terraces. The SrTiO₃ substrates are heated to 650 °C for LaFeO₃ epitaxial growth. A mixture of Ar and 3% O₂ with a total pressure of 12 mTorr and an RF power of 65 W is used for sputtering, which results in a deposition rate of 60 nm/h. Then, a 3 nm Pt layer is deposited at room temperature in the same off-axis geometry.

Angular-Dependent Spin–Hall Magnetoresistance Measurements

Angular-dependent spin–Hall magnetoresistance measurements are performed in a Quantum Design Dynacool PPMS with an angular rotation attachment using a Keithly 2182 nanovoltmeter and a Keithly 6221 current sourcemeter. An in-plane magnetic field of 0–14 T is applied, and the sample is rotated from 0 to 360° with a step size of 5°. Pulse-delta measurements are performed to limit the heating in samples with a 1 mA current pulse of 1 ms duration, while V_xy and V_xx are measured.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.4c04810.

• Details of macrospin simulations of the spin–Hall magnetoresistance results in the Pt/LaFeO₃ bilayer system, explanation of the square and sawtooth shapes in the spin-Hall MR data, and spin–Hall MR results at various temperatures and different LaFeO₃ film thicknesses (PDF)

• Animation plots of ΔR_xx and ΔR_xy(PPTX)

Author Contributions

J.L. performed the sample growth and patterning, film characterization, SMR measurements, and data analysis and led the writing of the manuscript. J.M. performed the simulations and some SMR measurements and analysis. J.F. performed the initial SMR measurements. F.Y. supervised the project. All authors contributed to the writing of the manuscript.

The authors declare no competing financial interest.