Strain-induced extrinsic high-temperature ferromagnetism in the Fe-doped hexagonal barium titanate

Abstract

Diluted magnetic semiconductors possessing intrinsic static magnetism at high temperatures represent a promising class of multifunctional materials with high application potential in spintronics and magneto-optics. In the hexagonal Fe-doped diluted magnetic oxide, 6H-BaTiO3-δ, room-temperature ferromagnetism has been previously reported. Ferromagnetism is broadly accepted as an intrinsic property of this material, despite its unusual dependence on doping concentration and processing conditions. However, the here reported combination of bulk magnetization and complementary in-depth local-probe electron spin resonance and muon spin relaxation measurements, challenges this conjecture. While a ferromagnetic transition occurs around 700 K, it does so only in additionally annealed samples and is accompanied by an extremely small average value of the ordered magnetic moment. Furthermore, several additional magnetic instabilities are detected at lower temperatures. These coincide with electronic instabilities of the Fe-doped 3C-BaTiO3-δ pseudocubic polymorph. Moreover, the distribution of iron dopants with frozen magnetic moments is found to be non-uniform. Our results demonstrate that the intricate static magnetism of the hexagonal phase is not intrinsic, but rather stems from sparse strain-induced pseudocubic regions. We point out the vital role of internal strain in establishing defect ferromagnetism in systems with competing structural phases.

Figure 1. Schematic interface of the two crystallographic phases in BaTiO_3-δ.

Pseudocubic (3C) and hexagonal (6H) crystallographic polymorph of BaTiO_3-δ. Fe³⁺ cations substitute for Ti⁴⁺ ions (spheres) within FeO₆ ochatedra (polyhedra). Two crystallographically different Ti sites are found in the 6H structure, while only one exists in the 3C structure. High-temperature ferromagnetism (FM) is ascribed to sparse regions of the 3C phase, while the majority 6H phase remains paramagnetic (PM).

Figure 2. Bulk magnetization measurements.

(a) The temperature dependence of zero-field cooled (full symbols) and field-cooled (open symbols) field-normalized bulk magnetization in the 20% Fe-doped 6H-BaTiO_3-δ. The solid line is the fit to the Curie-Weiss model M/μ₀H = N_Aμ²/3k_B(T − θ_CW) (see text for details), while the vertical dashed lines display the temperatures of the magnetic transitions in the annealed sample. (b) Magnetization curves of F20BTOa at different temperatures displaying the FM hysteresis. Inset shows the 2 K data (circles) and the fit with the modified Brillouin function M = f · μ · B_5/2(μB/k_BT_eff) (see text for details). (c) The time-dependent magnetization in the F20BTOa sample at 300 K after applying and removing the magnetic field of 1 T.

Figure 3. ESR characterization of 6H-BaTiO_3-δ.

(a) The temperature dependence of the ESR spectra in 20% Fe-doped 6H-BaTiO_3-δ displaying a single line in the non-annealed sample and a multi-feature line in the annealed sample. Spectra are displaced vertically for clarity. The g = 2 position is marked with the vertical line. (b) The increase of the ESR line width with doping concentration in the non-annealed samples at 300 K. The peak-to-peak line width ΔB of both spectra is indicated by the horizontal arrows. (c) Comparison of the 300-K spectra of F20BTOa at 9.4 GHz and at 24.3 GHz. Side-band shifts that are frequency independent are marked with vertical lines. (d) Resonance field of various resonance modes observed in the annealed Fe-doped 6H-BaTiO_3-δ samples below T_c3. The temperature independent position (horizontal mode) corresponds to the g = 2 mode. (e) Comparison of the ESR intensity decrease of the single-line FM mode observed above T_c3 in F20BTOa and the PM signal of the F20BTO sample with Curie-like dependence. Both ESR intensities are normalized at 450 K.

Figure 4. μSR characterization of 6H-BaTiO_3-δ.

The temperature dependence of muon polarization in (a) 10% and (b) 20% Fe-doped 6H-BaTiO_3-δ samples in zero applied field showing increased relaxation rates with increasing temperature. The upper panels correspond to non-annealed samples and the lower panels to annealed samples. The solid lines are fits to the stretched exponential (SE) model of equation (1). (c) The room-temperature muon polarization of the F20BTOa sample in ZF and in a weak longitudinal applied field. The dashed lines correspond to the static Kubo-Toyabe (KT) model of equation (2), while the solid lines are fits to the model encompassing both static KT and dynamical SE relaxation (see text for details). The error bars of muon polarization data are defined as a square root of the total number of detected positrons.