Evolution of spatial spin-modulated structure with La doping in Bi_1-yLa_yFeO₃ multiferroics

Highlights

• The presence of spatial spin-modulated structure (SSMS) in Bi_1-yLa_yFeO₃ is confirmed.

• The SSMS is characterised by a positive magnetic anisotropy constant Κ_u > 0 at 4.2 K.

• At 300 K Κ_u > 0 for y = 0 – 0.03 while Κ_u < 0 for higher La content.

• At 300 K for y = 0.03 – 0.05 the SSMS is close to harmonic.

• A high-frequency peak proportional to La content was observed in ⁵⁷Fe NMR spectra.

Abstract

In this paper we present study of the magnetic structure of multiferroic series Bi_1-yLa_yFeO₃ (y = 0, 0.015, 0.03, 0.05 and 0.10) using nuclear magnetic resonance (NMR) at 4.2 K and Mössbauer spectroscopy at room temperature on ⁵⁷Fe nuclei. We observed the presence of cycloid type spatial spin-modulated structure (SSMS) in the whole range of compositions. The study of the concentration dependence of the anharmonicity parameter m revealed that at the temperature of liquid helium in the composition region y = 0 – 0.10 as well as at room temperature for y = 0.03 the magnetic state of multiferroics is described by cycloid type SSMS with a positive effective uniaxial constant of magnetic anisotropy Κ_u > 0 (“easy axis” model). The study at room temperature in turn revealed that magnetic state of the multiferroics with y = 0 – 0.03 is described by cycloid type SSMS with a positive effective uniaxial constant of magnetic anisotropy Κ_u > 0 (“easy axis” model). In contrast, the magnetic state of multiferroics with y = 0.05 and 0.10 is described by a negative effective uniaxial constant of magnetic anisotropy Κ_u < 0 (“easy plane” model). Anharmonicity parameter m at room temperature for y = 0.03 – 0.05 is close to zero, which means that SSMS in this range of compositions is close to harmonic.

Introduction

Promising prospects of Ι type multiferroic BiFeO₃ (BFO) application in spintronics, data storage and various multifunctional devices generate keen interest in BFO-based compounds over the past 30 years [1], [2], [3], [4]. Pure undoped BiFeO₃ possesses rhombohedral distorted perovskite structure (sp. gr. R3c), high Curie temperature of 1100 K and Neel temperature of 670 K [5], [6]. In paper [7] the authors observed a complicated cycloid type spatial spin-modulated structure (SSMS) with relatively big period λ = 620 ± 20 Å incommensurate with the crystal lattice period by means of time-of-flight neutron diffractometry. Each magnetic moment of the trivalent iron ion Fe³⁺, surrounded by neighbouring Fe³⁺ ions with spins antiparallel to the spin of the central atom, rotates along the direction of the modulated wave in a plane perpendicular to the hexagonal basal plane. The presence of SSMS reduces to zero the total magnetization and linear magnetoelectric effect [8]. One can conclude that for practical applications of these ferrites SSMS must be suppressed. Various methods for suppressing SSMS are described in the literature, for example, replacing bismuth or iron with other elements [8], [9], [10], synthesizing samples in the form of nanocrystallites or thin films [2], [11], [12], [13], and also using an external magnetic field [14], [15].

The replacement of bismuth atoms by rare-earth atoms affects the physical properties (including magnetoelectric). This effect is due to the difference between ionic radii, valency and other parameters of Bi³⁺ ions and substitute ions [16]. It was shown in [17] that doping of BFO with lanthanum leads to a structural transition from the rhombohedral to the orthorhombic phase due to chemical compression. Evidence of a decrease in the concentration of charge defects, dielectric losses, and leakage current upon doping with La is given in [18], [19]. It was also found that certain concentrations of various elements replacing bismuth lead to the destruction of SSMS in compounds based on BFO [11], [20], [21].

In [22], a mathematical description of SSMS in BFO is given through the function of the anharmonic cycloid:

$$cos\theta \left(x\right)=sn\left(\pm \frac{4K\left(m\right)}{\lambda }x,m\right)\mathrm{a}\mathrm{t}{\mathrm{K}}_{\mathrm{u}}>0$$

$$sin\theta \left(x\right)=sn\left(\pm \frac{4K\left(m\right)}{\lambda }x,m\right)\mathrm{a}\mathrm{t}{\mathrm{K}}_{\mathrm{u}}<0$$

where θ is the angle of rotation of the antiferromagnetism vector relative to the c axis; x is the coordinate along the direction of propagation of the cycloid; sn(x, m) is the Jacobi elliptic function with the anharmonicity parameter m; K(m) is a complete elliptic integral of the first kind. The SSMS period λ is determined by the exchange stiffness A, the effective constant of the uniaxial magnetic anisotropy K_u, and the anharmonicity parameter m [22], [23].

As follows from Eqs. (1), (2), the SSMS anharmonicity leads to a non-uniform distribution of the magnetic moments of iron over the angle θ, leading to their higher concentration near the c axis or in the perpendicular direction, depending on the sign of the K_u magnetic anisotropy constant. Moreover, magnetic anisotropy also leads to a weak anisotropy of local hyperfine fields at the nuclei ⁵⁷Fe H_hf (θ) [22], [24]:

$$H_{\mathit{hf}}\left(\theta \right)=H_{is\mathrm{o}}+H_{\mathit{an}}\left(3{\mathit{cos}}^2\theta -1\right)/2$$

where H_iso is the isotropic contribution to the hyperfine magnetic field H_n, determined mainly by the Fermi contact interaction with s-electrons localized on the nucleus and polarized by the atomic spin. H_an is the anisotropic contribution due to the magnetic dipole–dipole interaction with localized magnetic moments of atoms and the anisotropy of the hyperfine magnetic interaction of the nucleus with the electrons of the ion core of its own atom. From Eq. (3) one can obtain a relation between the values of the hyperfine fields for the orientation of the magnetic moment of the iron atom parallel to (H_‖) and perpendicular (H_⊥) to the crystal symmetry axis the with isotropic and anisotropic contributions by simple relations [24]:

$$H_{\Vert }=H_{\mathit{iso}}+H_{\mathit{an}}\mathrm{a}\mathrm{n}\mathrm{d}{H}_{\perp }=H_{\mathit{iso}}-H_{\mathit{an}}/2$$

Experimental methods that can detect SSMS and observe its evolution caused, for example, by replacement of bismuth or iron by other ions or by distortions of the crystal structure are of significant importance for study perovskites based on BiFeO₃ ferrite. Such methods are neutron diffraction, nuclear magnetic resonance (NMR), and nuclear gamma resonance (Mössbauer effect).

The existence of SSMS in BiFeO₃ was revealed by the Mössbauer effect method on ⁵⁷Fe nuclei [24], [25]. In [25], when processing the Mössbauer spectra of BiFeO₃ taking into account the lattice ε_lat and magnetic ε_mag contributions to the quadrupole shift, the anharmonicity parameter was estimated as m = 0.5 at room temperature and m = 0.6 at 90 K, i.e. SSMS is highly anharmonic. In [24], an estimate of the additional contribution from the magnetic component ε_mag to the quadrupole shift showed that this contribution is small and can be neglected when processing the Mössbauer spectra, which leads to a decrease in the estimate of the anharmonicity parameter to m = 0.26 at 4.2 K.

One of the most obvious and direct methods for observing SSMS is NMR spectroscopy. The rotation of magnetic moments modifies the line shape in such a way that the spectrum becomes frequency distributed within 2 MHz and acquires a characteristic shape with two peaks at the edges of the spectrum of different (in the general case) intensities and a gap between them. In [26], NMR spectra were obtained for samples of the Bi_1-yLa_yFeO₃ series with y = (0, 0.1, 0.2, 0.9 and 1.0). In the first two samples with the lowest La content, the magnetic order of the SSMS type of the cycloid type was preserved.

Up to now, only a few papers report on the effect of replacement of bismuth by rare-earth atoms on SSMS studied by neutron diffraction, NMR, or Mössbauer spectroscopy.

This work aims to systematic study of effect of replacement of trivalent bismuth atoms by trivalent lanthanum atoms on SSMS, local magnetic and electrical states of Fe atoms in the rhombohedral phase R3c of the Bi_1-yLa_yFeO₃ system (y = 0, 0.015, 0.03, 0.05 and 0.10) by means of NMR at 4.2 K and the Mössbauer effect at room temperature on ⁵⁷Fe nuclei. In the present paper, we combined NMR spectroscopy at low temperature and Moessbauer spectroscopy to study the region of drastic changes in the magnetic structure of the Bi_{1 – y}La_yFeO₃: the destruction of SSMS and anisotropy type change at room temperature.