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Coexistence of spin glass and ferroelectricity in highly ordered Bi2FeMnO6 epitaxial thin film

Highly ordered Bi2FeMnO6 epitaxial thin films have been successfully grown on SrTiO3 substrate. Both synchrotron X-ray reciprocal space mapping and high resolution transmission electron microscopy confirmed the alternative alignment of Fe and Mn along [111] direction of Bi2FeMnO6 films. Magnetic and ferroelectric properties of Bi2FeMnO6 films are characterized and analyzed. The room-temperature ferroelectricity is well kept in Bi2FeMnO6 film as expected. However, it is very interesting that Bi2FeMnO6 film exhibits a typical spin-glass behavior and very weak magnetism rather than a ferri/ferromagnetism as generally believed. Our first-principles calculations suggest a spin frustration model for Bi2FeMnO6, which can well explain the intriguing magnetic property of Bi2FeMnO6 film.


INTRODUCTION
Multiferroic materials have attracted significant attention in recent years because of their intriguing physical phenomena and huge potential applications in multifunctional devices, such as sensors and memory devices for storage data [1][2][3]. Single-phase multiferroics are very rare because ferroelectricity generally requires empty d-orbitals whereas ferromagnetism needs partial filled d-orbitals, which is commonly incompatible [4]. As exceptions, bismuth based perovskite oxides BiFeO 3 (BFO) and BiMnO 3 (BMO) are well-known multiferroic materials. The coexistence of ferroelectricity and (anti)ferromagnetism in these compounds is thought to be realized by the combination of magnetic element (Fe or Mn) at B site and Bi 6s 2 lone-pair electrons at A site. However, BFO is a canted antiferromagnet (Néel temperature T N ∼ 640 K), which leads to very weak ferromagnetism, although it has a very high ferroelectric Curie temperature (T c ∼ 1103 K) [5]. As for BMO, its ferroelectric Curie temperature approaches to 450 K, whereas it has a low ferromagnetic (FM) Curie temperature (∼ 105 K) far below room-temperature (RT) [6]. Moreover, BMO is metastable, which makes its fabrication very difficult. Previous studies have pointed out that the bulk phases of BMO have to be synthesized by the high-pressure method [7] and the growth of pure phase BMO epitaxial films can only be achieved by strain engineering [6,8,9]. These drawbacks of BFO and BMO materials inevitably limit their practical applications on spintronic devices, especially in RT environment.
In BFMO, Fe and Mn ions were reported to energetically favor high spin state, i.e., Fe 3+ and Mn 3+ [10], and the coupling of dissimilar ions of Fe 3+ (d 5 )-O-Mn 3+ (d 4 ) were suggested to be antiferromagnetic (AFM) in previous studies [10,12,13]. This antiparallel coupling is believed to provide a net magnetization as Fe 3+ and Mn 3+ ions have unequal magnetic moments. Thus, we expect ferrimagnetism could be induced via the alternative periodic arrangement of Fe 3+ and Mn 3+ at B sites along [111] direction of BFMO. Similar idea has been proposed by Rabe et al. [14,15] to predict the coexistence of ferroelectricity and ferrimagnism in BFO-BMO checkerboard (i.e., the (110)-oriented BFO-BMO superlattice).
It should be emphasized that Fe and Mn have very similar scattering factor and it is quite difficult to detect very weak diffraction peak from Fe and Mn More interestingly, it can be observed that M -H loop at 5 K, which is entirely differ-ent from that of 300 K, does not exhibit the saturation in magnetic field up to 1 T. The out-of-plane zero-field-cooled (ZFC) and field-cooled (FC) temperature dependent magnetization (M -T ) curves for BFMO film were measured under 1000 Oe from 5 K to 300 K, which is shown in Fig 5b. The M -T curve of STO substrate was measured and subtracted from BFMO/STO data. The ZFC and FC magnetization values of BFMO increase with decreasing the measured temperature in the range of 50 K-300 K. Below 50 K, ZFC and FC magnetization curve begin to split and a peak appears at around 18 K in ZFC curve whereas FC curve continues to increase with decreasing the temperature up to 5 K. This phenomenon exhibits a signature of spin-glass behavior, since the evidences of spin-glass state in oxide include that there is a difference between ZFC and FC curves at low temperature, and a cusp (or peak) exists in ZFC curve [37]. Similar observation has been reported in LaFe 0.5 Mn 0.5 O 3 film and La doped BFMO ceramics with spin-glass state [38]. Thus, BFMO is likely to be a spin glass and the spin-freezing temperature (T f ) is about 18 K, corresponding to the peak temperature in ZFC curve. It can be understood that the M -H loop at 5 K reveals weak ferromagnetism in BFMO film due to spin freezing and it does not show the saturation even at 1 T field like other spin glass systems [39].
It should be pointed out that the deviation of ZFC and FC curves and the existence of peak in ZFC at low temperature region are not sufficient evidence for spin glass behavior. For example, this behavior can also appear in superparamagnetic and AFM materials. However, spin glass state is a metastable phase and the phenomenon of aging is one of important characteristics of spin glass. Both superparamagnetic and AFM systems have no aging behavior. To further confirm the spin glass behavior of BFMO film, we have measured the relaxation of magnetization at 5 K (< T f ) and 150 K (> T f ). The BFMO sample was cooled in 10000 Oe field from 300 K to 5 K or 150 K, waited for 30 s, and then decreased the field to 500 Oe and measured the time-dependent magnetization. An extended exponential decay can be applied to describe the magnetic relaxation of spin glass, which is as follows: where M 0 stands for the nonrelaxed magnetization under 500 Oe field, M r contributes to the observed relaxed effects, the time constant τ and exponent n reflect the relaxation rate of spin glass. If 0 < n < 1, it represents spin glass system [40][41][42]. Fig. 5c shows the time dependent remnant magnetization at 5 K for BFMO film and there is a typical relaxation behavior measured at 5 K for BFMO film. Red solid curve is the best fitting curve to the measured data with equation (1) and the fitting parameters are also listed in Fig. 5c. The fitting to experimental data is excellent. The n and τ parameter of BFMO is 0.69 and 821 s, respectively. These two parameters are close to those of BFO/BMO, which is a spin glass system [40]. In comparison, Fig. 5d gives the time dependent remnant magnetization at 150 K ( > freezing temperature T f ) for BFMO film. No relaxation is observed at 150 K and fitting to measured data also verifies it. Hence, the combination of M -T curve (Fig. 5b) and M -t relaxation (Fig. 5c,d) eventually identify that BFMO has a typical spin-glass behavior.
Why does BFMO exhibit a spin-glass-like behavior? Site disorder and spin frustration generally give rise to spin-glass state. Our BFMO samples, however, have been proved to be highly ordered single crystalline film. To further explore the magnetic structure of BFMO, X-ray magnetic circular dichroism (XMCD) measurement, a powerful element-specific technique to investigate the magnetic response of materials [43,44] was adopted. Magnetic moments of Fe and Mn elements can be characterized or estimated respectively by XMCD. Fig. 5e,f show X-ray absorption spectroscopy (XAS) at L-edges and XMCD of Fe and Mn element of BFMO film, respectively. XMCD is defined as the difference between the XAS with the polarization of the incident X-ray to be parallel and anti-parallel to the applied magnetic field (1 T in the measurements here). And its intensity represents the element-specific net magnetization. As shown in Fig. 5c Based on SQUID and XMCD experimental data, we argue that a spin frustration magnetic structure occurs in (111) Fe or Mn plane for BFMO. The presence of spin frustration will lead to no or very weak magnetism, which can be used to explain the magnetic behavior of BFMO.
Orbital model analysis and simulations of magnetic structures. As mentioned before, previous studies [10,12,13] suggested that Fe 3+ -Mn 3+ coupling should be AFM, consequently BFMO should produce sizable net magnetism and no frustration can be created.
Nevertheless, all magnetic measurements suggest that BFMO sample is a spin frustrated system featuring very weak or no magnetism. This pushes us to reconsider the coupling between Fe 3+ and Mn 3+ . In general, an octahedral crystal field in cubic lattice leads to double orbital degeneracy of e g , however, in our case with Jahn-Teller ions Mn 3+ , the orbital degeneracy of e g is lifted by reduction of symmetry of lattice where a pc ≈ 3.905Å and c pc ≈ 4.015Å, thus e g orbital splits into d x 2 −y 2 and d z 2 orbitals whose shapes are described in Fig. 6a. In paraelectric phase of BFMO, the regular octahedral crystal fields push up the d x 2 −y 2 level slightly higher than d z 2 level for magnetic ions, as shown in Fig. 6b,c,d,e.
In this case, the in-plane Fe 3+ and Mn 3+ are ferromagnetically coupled (see Fig. 6b) and the out-of-plane Fe 3+ and Mn 3+ are antiferromagnetically coupled (see Fig. 6c). Because the lattice parameter c pc is just slightly bigger than a pc , ferroelectric displacements of Fe 3+ and Mn 3+ may have a significant effect on the energy levels of respective d x 2 −y 2 and d z 2 orbitals. Especially in that case as illustrated in Fig. 6f,g,h where the d x 2 −y 2 and d z 2 levels of Mn 3+ are reversed, consequently the in-plane superexchange of Fe 3+ and Mn 3+ is switched from FM coupling (Fig. 6b) to AFM coupling (Fig. 6g), and meanwhile the out-of-plane superexchange of Fe 3+ and Mn 3+ is switched from AFM coupling (Fig. 6c) to FM coupling ( Fig. 6h). Besides, whatever the Fe 3+ -Mn 3+ exchange interaction is, Fe 3+ -Fe 3+ and Mn 3+ -Mn 3+ exchange interactions favor AFM coupling because of the virtual hoping between the half-filled orbitals as given in Fig. 6d, Fig. 7a-f) are adopted to perform total energy calculations and Heisenberg Hamiltonian is used to describe the exchange parameters, as shown in Fig. 7g. One can see that it is a very frustrated system where spin directions are arranged randomly.
In this system, random spins cancel each other, consequently the net magnetization is weak.
In simulations, we also find that the magnetic structure is extremely sensitive to perturbations, e.g. external magnetic field, which is one of the most notable features of glassy state.
These theoretical results agrees well with our experimental observations. Tesla external magnetic field were applied during the XMCD measurements. All measurements were done at room temperature.
First-principles calculations. Computational methods: Our calculations were performed by both full-electron calculations and projected augmented wave (PAW) method. Allelectron calculations use the full-potential linearised augmented-plane wave method, as implemented in the WIEN2k code [46], and PAW calculations use the plane wave basis set in Vienna ab-initio simulation package (VASP) [47]. Generalized gradient approximation (GGA) and GGA plus Hubbard U (GGA+U ) were treated for the exchange-correlation potential.
We employed effective Hubbard U of 4 eV and 5.2 eV [14,15] for Fe and Mn 3d orbitals, respectively. In VASP [47], the energy cutoff for the plane-wave basis was set to 520 eV in relaxations and 800 eV in total energy calculations, respectively.  nm-thick BFMO films grown on (001)-oriented STO substrates, K β symbol represents the Cu-K β signal from STO substrate.     of Mn 3+ , in-plane Fe 3+ -Mn 3+ superexchange becomes antiferromagnetically coupled between two half-filled d x 2 −y 2 orbitals(g), and the out-of-plane Fe 3+ -Mn 3+ becomes ferromagnetically coupled contributed by the virtual hopping from a half-filled d z 2 orbital to an empty d z 2 orbital(h).