First-principles simulations were carried out by employing generalized gradient approximation (GGA)/GGA + U with Perdew–Burke–Ernzerhof (PBE) formalism (Blöchl 1994; Perdew et al., 1996) on the basis of density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP) (Kresse and Hafner 1993). The supercell models of Co-Fe-B/Co-Fe-B-O system with a total of 200 atoms were adopted as initial structures. Automatic k-point mesh of 1 × 1 × 1 containing Gamma was used for geometry optimization. The convergence criterion used in the electronic self-consistent was set to 10^–5 eV and the magnitude of force on each atom fell below 0.005 eV Å⁻¹. For the Co-Fe-B/Co-Fe-B-O system, isothermal process was simulated at 300 K with 1,000 steps being collected for structural analysis. Electron spins were taken into account throughout the simulation.

The melt-and-quench approach (Kresse and Hafner 1994) has been used to theoretically obtain the structural model for amorphous transition metal oxides (ATMOs). Previously, it has been verified that such approach can successfully generate the structural models for amorphous semiconductors (Kresse and Hafner 1994) and MGs (Guan et al., 2012).

Thin films were deposited on different substrates such as quartz glass, single-crystal silicon and silica by radio frequency (RF) magnetron sputtering. The base pressure was lower than 6 × 10^–5 Pa while the working pressure was 0.3 Pa under a gas mixture of high purity argon and oxygen. The composition of thin film was measured by auger electron spectroscopy (AES). The structure of the thin film was investigated by using a high resolution transmission electron microscope (HRTEM). The magnetic properties were measured by a superconducting quantum interference device-vibrating sample magnetometer (SQUID-VSM). The electrical properties were examined by a physical property measurement system (PPMS-9T).

We select Co₄₀Fe₄₀B₂₀ and Co₂₃Fe₁₄B₁₀O₅₃ for first-principles calculations to study the effects of oxygen addition on both structure and properties of the Co-Fe-B system. Firstly, the difference in the atomic structures of the two systems are analyzed. The partial and total pair correlation functions (PCFs) for the Co-Fe-B and Co-Fe-B-O samples are plotted in the g(r) curves of Figure 1. The total PCFs of the two systems show broad peaks characteristic of their glass structures. Two obvious peaks arising from the first-nearest-neighbor shells are observed in the total PCF of the Co-Fe-B system as shown in Figure 1A. Compared with the partial PCFs of the elements involved in the Co-Fe-B system, one peak at around 2.1 Å mainly corresponds to the bonding pairs between the ferromagnetic (Co, Fe) atoms and metalloid (B) atom. The other peak at ∼2.55 Å is caused by the bonding pairs of transition metal (TM) elements Co-Co, Co-Fe and Fe-Fe. With the oxygen addition, the number and position of the first-nearest-neighbor peaks in the PCFs of the Co-Fe-B-O system differ from those of the Co-Fe-B system as shown in Figure 1B.

Three obvious first-nearest-neighbor peaks are observed in the total PCF of the Co-Fe-B-O system in Figure 1B. Compared with its partial PCFs, the first peak is mainly attributed to the first-nearest-neighbor pairs of oxygen and boron atoms with an average atomic distance of about 1.35 Å between them. The second peak at around 1.95 Å is mainly due to the contributions from the atomic pairs between the TM atoms and non-metallic (O) atom. Owing to the high affinity of both Co and Fe to oxygen, there exists strong interaction between the Co, Fe atoms and O atoms, resulting in their intense first-nearest-neighbor peaks in the g(r) curves. Therefore, unlike the first-nearest-neighbor binding of TM-B at 2.1 Å in the Co-Fe-B system, no B as first nearest neighbors around the TM atoms can be observed due to the addition of oxygen. But B exists as the second nearest neighbors at about 3 Å around the TM atoms. In comparison, the third peak stems primarily from the first-nearest-neighbor atomic pairs of Co-Co, Co-Fe and Fe-Fe. Besides, the second-nearest-neighbor atomic pair of B-B also contributes to the third peak. At the same time, due to the addition of oxygen, the first-nearest-neighbor distances of TM-TM pairs increase as a whole. And all the first peaks of the partial PCFs of Co-Co, Co-Fe and Fe-Fe split as shown in Figure 1B. Such splitting suggests that ferromagnetic Co and Fe atoms may exist in different environments and thus form atomic bonds with different bond lengths.

In order to further understand the local atomic structure of the Co-Fe-B MG and the Co-Fe-B-O OG, the bond pair index method of Honeycutt and Andersen (HA) is used. The type distributions of characteristic bond pairs with more than 1% in the amorphous Co-Fe-B and Co-Fe-B-O systems are shown in Figure 2. Among them, the 1,551 characteristic bond pairs representing the icosahedral clusters have the highest fraction, followed by 1,541 and 1,431 bond pairs representing the deformed icosahedra in the Co-Fe-B system (Figure 2A). These three bond pairs account for 72% of the total bond pairs, which is a typical feature for MGs. Figure 2B shows the statistical results of characteristic bond pairs in the Co-Fe-B-O system, which are very different from those of the Co-Fe-B system. The cluster structures characterized by 1,001, 1,102 and 1,202 bond pairs are the most popular, accounting for 88% of the total architecture. According to the definition of HA index, the 1,001 bond pair represents the B-O covalent bond, because its directivity and saturation determine the absence of its common first-nearest-neighbor atoms shared by B and O. And 1,102 and 1,202 bond pairs are more inclined to correspond to the mixture of ionic and metallic bonds. It shows that the number of atoms around the bond pair studied reduces.

The investigation of coordination number is based on the PCF analysis, taking the distance at the first trough as the cutoff value for the first nearest neighbors of the center atoms in the PCF curves. The average coordination numbers in M (Co, Fe, B, O)-centered clusters are listed in Table 1. Due to the oxygen addition, the average coordination numbers of Co and Fe elements become 7.6 and 6.9, respectively, which are much lower than 13.6 and 14.4 in the Co-Fe-B MG. The average coordination number around the B atom also decreases sharply from 9.0 to 3.1 after the oxygen addition. In the Co-Fe-B MG, these B-centered local structures with the coordination number of 9.0 are related to the tricapped trigonal prisms (TTP) at normal conditions, similar to the local configurations such as BFe₉ and B₂Fe₈ in Fe-B amorphous alloys (Tian et al., 2012). But the B-centered polyhedra have changed to the determined local BO₃ structural units in the Co-Fe-B-O OG as shown in Figure 3, similar to those in boron oxide. The average coordination number of O is 3.4, which further verifies the results of the HA index analysis. Therefore, the addition of oxygen causes dramatic structural changes, including the difference in the coordination environments of magnetic atoms and the emergence of oxide structural units, which may bring special magnetic and electrical properties.

In order to study the magnetic properties of the materials, the electrons’ spins were considered during the simulation. Firstly, according to the relationship between saturation magnetic induction (B _S) and magnetic moment (M _S) of B S   =   μ 0 ( M S / V S ) , where V _S is the involved supercell volume, μ ₀ is vacuum permeability (4π × 10^–7 TmA⁻¹), the calculated B _S value of the Co-Fe-B amorphous system is 1.62 T. Meanwhile, the partial and average magnetic moments of different electron orbits of M (Co, Fe, B) atoms are listed in Table 2, which are similar to the calculation results of conventional CoFe-based amorphous alloys (Li et al., 2019).

However, magnetic calculation of ATMOs is more complicated and less studied. This is because the magnetic super-exchange interactions mediated by oxygen atoms depend on their structures, whereas the amorphous short-range ordered structure is different from the unit cell structure of crystals. Therefore, it is difficult to determine the spin direction of each atom in the system. In this paper, we discuss the spin order of the Co-Fe-B-O system from its microstructure, and use a concise and effective theoretical method to determine the magnetic ground state of the involved ferromagnetic atoms combined with first-principles calculation.

From the structural analysis in the previous section, it is known that, unlike the atomic structure of the Co-Fe-B system, two different coordination environments exist for the magnetic Co and Fe within the Co-Fe-B-O system. According to the partial PCFs, the first peaks of Co-Co and Fe-Fe split into two sub-peaks (Figure 1B). The location of the first sub-peak is close to the first nearest-neighbor distance between the magnetic atoms in the Co-Fe-B system, while the second sub-peak locates at an average distance corresponding to the M-O-M groups connected by oxygen atoms. Therefore, the location of the splitting valley can be taken as a critical cutoff distance to distinguish the M-M and M-O-M groups, which experience the direct and indirect exchange interactions, respectively (Hu et al., 2014). According to the M-M bond lengths, the area consisting of magnetic atoms can be thus classified into two regions. One has short-range ordering clusters with direct exchange interaction via ferromagnetic coupling (D-region), while the other possesses local clusters with indirect exchange interaction via antiferromagnetic coupling (I-region). From the relative sizes of the two sub-peaks in the partial PCF diagrams (Figure 1B), almost all Co atoms are direct neighbors. Based on the Co-Fe-B-O atomic structure model in Figure 3, most of these directly neighbored Co atoms form tetrahedral structural units. In comparison, only a small number of Fe atoms are directly connected and experience direct exchange interaction, whereas most of Fe atoms form the oxygen-mediated Fe-O-Fe structural units with indirect exchange interaction (Figure 3). The bonding ability of the involved TMs of Co and Fe with oxygen depends on their affinities to oxygen. Fe has higher affinity to oxygen than Co, thus bonding with oxygen more easily. Hence, most local structural units of TM-O-TM are Fe-O-Fe, which may contribute to the decreased saturation magnetization.

In order to better understand the correlation between local cluster structure and magnetic exchange interaction, the average Fe coordination numbers of Fe atoms involved in the two regions are counted to be 1.5 for D-region and 0.6 for I-region, respectively. At the same time, the Voronoi polyhedron analysis is used to probe the local atomic configurations via short-range order of the simulated amorphous structure (Medvedev 1986). The major types of the Fe-centered clusters are differentiated with the corresponding Voronoi polyhedral indices as shown in Figure 4A (Co-Fe-B MG) and Figure 4B (Co-Fe-B-O OG), respectively. From the statistical histogram of Voronoi polyhedral indices in Figure 4A, the Fe-centered clusters in the Co-Fe-B system are mainly characterized by two types of polyhedra indexed as < 0, 2, 8, x > and <0, 1, 10, x >. These two types of polyhedra are generally grouped as icosahedral-like clusters, indicating that the short-range ordering mainly exists in terms of icosahedral-like clusters (Zhang et al., 2015). Compared with the Fe-centered clusters in the Co-Fe-B system, the atomic configurations are quite different in the Co-Fe-B-O system (Figure 4B). All the typical coordination polyhedra are almost completely different from those in the Co-Fe-B system. Meanwhile, the percentages of these polyhedron types generally decrease and the distribution is more uniform in the Co-Fe-B-O system. To correlate the local structure and the ferromagnetism of this Co-Fe-B-O system, the Voronoi index type distributions of Fe-contained clusters in the D-region and I-region are statistically analyzed, respectively. As shown in Figure 4C and Figure 4D, the Fe-contained Voronoi polyhedron types are different in these two regions. The distribution of the Voronoi polyhedron indices in the I-region is almost identical to that of the overall Fe-contained Voronoi polyhedron indices of the system (Figure 4B). This indicates that the Fe atoms are mainly distributed in the I-region. In addition, in the statistical analysis of the Fe-O-Fe structural units, it is found that the average bond lengths of the two Fe atoms in the indirect exchange interaction are in the first and the second half of the posterior sub-peak, respectively. Figure 5 shows the average bond length distribution of Fe atoms in the system. Therefore, considering the combining influence of the coordination environment of Fe atoms and oxygen atoms on their spin directions, the Fe atoms in the I-region can be divided into two zones. One includes Fe atoms with large bond lengths (I_L-region) and the other consists of Fe atoms with small bond lengths (I_S-region). Different spin directions can be assigned to Fe atoms in these two zones, respectively. Thus, based on this method, we set up four spin ground states comprising the non-ferromagnetic (NM) state, the ferromagnetic coupling in all regions (FM), the negative magnetic moments of magnetic atoms in the I_S-region (AFM-Ⅰ) and the negative magnetic moments of magnetic atoms in the I_L-region (AFM-Ⅱ). Then, the total energy for each type of spin ordering can be calculated using the first-principles calculations. The calculated results are summarized in Table 3.

From Table 3, the AFM-Ⅱ type spin ordering is the lowest in energy. Based on this magnetic moment setting of the ground state, the partial and average magnetic moments of different electron orbits of M (Co, Fe, B, O) atoms are calculated. Compared with the Co-Fe-B MG, the average magnetic moment of Co atoms does not decrease, but slightly increases as shown in Table 4. This can be explained from two aspects. First, the oxygen addition appropriately increases the bond lengths between Co atoms, which enhances the direct magnetic exchange effect and therefore strengthens the ferromagnetism. Second, although there are fewer Co atoms in the I-region, the charge transfer between oxygen and Co atoms also contributes to the improvement of atomic magnetic moment. In contrast, Fe has a higher affinity to oxygen than Co, thus bonding with oxygen more easily. Most of Fe form the oxygen-mediated Fe-O-Fe structural units with indirect exchange interaction, whereas most of Co are direct neighbors with direct magnetic interaction. The average magnetic moment of Fe atoms decreases from 2.364 µ _B in the Co-Fe-B system to 0.879 µ _B in the Co-Fe-B-O system, which is mainly due to the presence of negative magnetic moments induced by oxygen-mediated indirect exchange interaction. Eventually, the B _S value decreases from 1.62 T in the Co-Fe-B system to 0.44 T in the Co-Fe-B-O system. Meanwhile, the Co-Fe-B-O OG becomes ferrimagnetic because of the presence of the negative magnetic moments.

The DFT is an exact theory for reproducing and predicting ground state properties of an electronic system. Nevertheless, the usual LDA and GGA approximations cannot describe correctly the strongly correlated systems with partially filled d or f shells (Terakura et al., 1984). Therefore, the strong electronic correlations between 3d electrons in the transition metal atoms suggest the necessity to use a DFT + U approximation with correlation energy correction (Anisimov et al., 1991). We employed a GGA + U approach to characterize the electronic structure of the Co-Fe-B-O amorphous oxide, using a 3 × 3 × 3 Gamma centered k-point mesh and U _eff = 6.9 and 5.9 eV for d electrons of Co and Fe atoms, respectively (Anisimov et al., 1991).

In order to understand the difference in the electronic structures of the Co-Fe-B and Co-Fe-B-O systems, we calculated the charge density distribution and density of states (DOS) for the two systems. Their two-dimension (2d) charge density diagrams are shown in Figure 6. Compared with the Co-Fe-B-O system, the overall charge density of the Co-Fe-B MG is higher and more uniformly distributed, which conforms to the free-electron gas model of metals. The much more localized electron charge distribution of the Co-Fe-B-O OG indicates that this system tends to become insulating due to the oxygen addition.

Figure 7 shows the total and partial DOS of the Co-Fe-B MG, characterizing metallic conductivity. The Fermi level (E _F) located in the gap of the spin-down bands, indicating that the system presents strong ferromagnetism (Malozemoff et al., 1984; Wang et al., 2013). The bands near E _F are mainly attributed to Fe-3d states with a small contribution from the 2p states of B, manifesting evidently the hybridization between 2p and 3d orbitals.

The total and partial DOS of the Co-Fe-B-O OG are shown in Figure 8. According to the analysis of the total DOS, its E _F is in the band gap. The calculated band gap of the Co-Fe-B-O OG is about 1.7 eV, characterizing its semiconducting transport properties. At the same time, the asymmetry of the spin density of states demonstrates that the Co-Fe-B-O OG is still ferromagnetic. It is noted that there exist intermediate energy levels at around -1 eV in the spin-down band gap and near E _F in the spin-up band gap as enlarged in Figure 8B. Compared with the partial DOS diagrams, it is found that these intermediate energy levels are mainly attributed to the Co-3d, Fe-3d and O-2p states. This indicates that the TM (Co, Fe)-O bonding is dominated by the electron hybridization of the 2p states from O and the 3d states from TM. The density of states of Co atoms at the intermediate energy levels is higher than that of Fe atoms. But near the top of the valence band and the bottom of the conduction band, the Fe atoms contribute more electrons, indicating that the bonding of Fe-O may have an important role in the metal-semiconductor transition of the system. Therefore, Co-O and Fe-O jointly regulate the magnetic and semiconducting electrical properties of the system. There are also small amounts of s and p electrons of TM in the intermediate energy levels, suggesting the hybridization of non-local conductive s, p electrons and the 3d electrons of the TM atoms. Similar electron distribution also exists in the bands between −17.5 eV and −20.5 eV. Such hybridization-induced s-d exchange interaction between the carrier spins and the localized magnetic moments leads to the spin polarization of the s-like conduction electrons. The mutual interaction of the electrical conduction from spin-polarized s-like electrons and ferromagnetism from 3d electrons paves the way for controlling the intrinsic ferromagnetism externally by electrical means in MSs (Meng et al., 2007; Walsh et al., 2008; Dietl, 2010; Tian et al., 2010; Hu et al., 2014).

To verify our computer calculation results, we further conducted the corresponding experiments. The Co_22.6Fe_14.4B_9.9O_53.1 thin film was deposited by magnetron sputtering. The HRTEM image of the thin film shows maze-like atomic arrangements, characterizing disordered amorphous structure (Figure 9A). The corresponding selected area electron diffraction (SAED) pattern inserted in Figure 9A contains one obvious diffuse halo ring, further confirming the formation of single-phase OG in the Co-Fe-B-O thin film.

The magnetic properties of the Co-Fe-B-O OG are shown in Figure 9B. Its B _S at room temperature is 252 emu/cm³ (0.32 T), confirming its room-temperature ferromagnetism. The experimental B _S is lower than the calculated B _S value (0.44 T). In fact, thin film ferromagnets usually show lower B _S values than their bulk counterparts because both the free surfaces of the thin films and the interfaces between the substrate and the thin films could decrease B _S (Poulopoulos and Baberschke 1999). As shown in Figure 9C, the M-T curve of the sample indicates that the Co-Fe-B-O sample has a Curie temperature higher than 620 K. At first, the magnetization decreases with increasing temperature from 300 to 640 K, which is consistent with the temperature dependence of spontaneous magnetization for traditional magnetic metals. When the temperature is higher than 640 K, the magnetization of the sample begins to increase likely due to the crystallization of the thin film. Similar results were also reported for the Co-Fe-Ta-B-O thin films (Liu et al., 2016).

As shown in Figure 9D, the room-temperature resistivity of the Co-Fe-B-O film is of order of 1 Ω cm (in the range of 10⁻³–10¹² Ω cm for semiconductors). In addition, the Co-Fe-B-O sample shows a negative temperature dependence of resistivity in terms of l n ( ρ / ρ 0 )   ∝   T − 1 / 2 (inset of Figure 9D), typically observed for semiconductors. In the amorphous semiconductors, the presence of structural disorder induces the localization of electrons. Éfros suggested that the conduction mechanism underlying this correlation was electron hopping between the localized states, which occurred at low temperature by taking into account the Coulomb interaction in disordered systems (Anderson 1958; Éfros and Shklovskii 1975). In comparison with the non-magnetic semiconductors, the transport mechanism for ATMOs is supposed to be spin-dependent due to the presence of doped TM atoms (Yan et al., 2006). Our calculation results show that the 3d electrons of TM atoms in the Co-Fe-B-O MS are hybridized with those s electrons on the one hand and interact with 2p electrons of O on the other hand. These two interactions together could make our Co-Fe-B-O OG possess the intrinsic magnetoelectric coupling effects modulated by the spin-polarized carriers. Therefore, we anticipate that such Co-Fe-B-O MS could show intriguing magnetoelectrical transport properties, which is out of the scope of the present study and needs to be further investigated in our future work.