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Strain-engineered high-temperature ferromagnetic Oxygen-substituted NaMnF3 from first principles

Using first-principles calculations, we investigated the magnetic, electronic, and structural properties of oxygen-substituted NaMnF3 (NaMnF1.5O1.5) with in-plane biaxial strain. For simplicity, a structure containing an oxygen octahedron is used to explore the underlying physical mechanism. We found that the oxygen octahedron induces a transition from an insulating antiferromagnet to a high-temperature half-metallic ferromagnet. More importantly, the Curie temperature can be significantly enhanced and even might reach room temperature by applying tensile strain. The changing trends of exchange coupling constants with the increasing biaxial tensile strain can be attributed to the cooperative effects of Jahn-Teller distortion and rotation distortion. It is expected that these findings can enrich the versatility of NaMnF3 and make it a promising candidate for spintronic applications.

Using first-principles calculations, we investigated the magnetic, electronic, and structural properties of oxygen-substituted NaMnF 3 (NaMnF 1.5 O 1.5 ) with in-plane biaxial strain. For simplicity, a structure containing an oxygen octahedron is used to explore the underlying physical mechanism. We found that the oxygen octahedron induces a transition from an insulating antiferromagnet to a high-temperature half-metallic ferromagnet. More importantly, the Curie temperature can be significantly enhanced and even might reach room temperature by applying tensile strain. The changing trends of exchange coupling constants with the increasing biaxial tensile strain can be attributed to the cooperative effects of Jahn-Teller distortion and rotation distortion. It is expected that these findings can enrich the versatility of NaMnF 3 and make it a promising candidate for spintronic applications.
In contrast, although some specific properties are demonstrated in halide perovskites [14] such as photocatalytic behavior in KMgF 3 [15] and the phase transition from the perovskite to the postperovskite in NaCoF 3 and NaNiF 3 [16,17], the researches on the magnetic properties for the fluoroperovskite are still scarce and desiderative [18,19]. NaMnF 3 , an incipient multiferroic fluoroperovskite, having a coupling phenomenon of ferroelectricity and G-type antiferromagnetic (G-AFM) ordering with a transition temperature of 66 K from the antiferromagnetic to the paramagnetic state [6,20], has attracted significant interest theoretically [6,21] and experimentally [19,22,23].
Nevertheless, the antiferromagnetic ground state limits the applications of NaMnF 3 in information storage [24,25] and spintronics [26]. So far, the ferromagnetic property based on NaMnF 3 has never been investigated experimentally or theoretically, let alone the half-metallic ferromagnetism, which is one of the most demanded property for spintronics [27,28]. The previous studies have shown that, unlike oxides, in which the hybridization plays a dominant role, the effective ionic charges in fluoroperovskites are close to their nominal valence [6,21]. Furthermore, it is known that rotations and distortions of the oxygen octahedra affect the magnetic, electrical, and structural functionalities of perovskites [29][30][31]. Moreover, these properties can be conveniently tailored using external control parameters such as strain [32,33], electric field [34], and pressure [20]. For example, strain-induced magnetism in perovskite oxides was reported both theoretically [13,35] and experimentally [29,36].
Previous studies have also shown that the perovskite oxyfluorides, oxyhydrides, and oxynitrides have been synthesized by topochemical reactions, and novel effects of anion substitution on physical properties such as magnetic coupling [37,38] and dielectric properties [39] have been unveiled. For further exploring some novel property of the fluoroperovskite and establishing a link with perovskite oxides, here, by adopting the method of anion substitution, we theoretically predict a simple structure in which the oxygen octahedra are introduced into NaMnF 3 by replacing half fluorine atoms with oxygen atoms (NaMnF 1.5 O 1.5 ), and its novel magnetic and transport properties, especially manipulated by the in-plane biaxial strain. We speculate that the structure is reasonable in accordance with the previous theoretical result [40], which means that NaMnF 1.5 O 1.5 should exhibit well-ordered anion configuration due to the low-symmetry features inherited from precursor (NaMnF 3 ).
Except presenting the results of high-temperature ferromagnetism and electronic structures in NaMnF 1.5 O 1.5 by employing first-principles calculations, we demonstrate that oxygen octahedron induces a transition from an insulating antiferromagnet to a late-model half-metallic ferromagnet and the Curie temperature ( ) can be significantly increased by an in-plane biaxial tensile strain. Our results propose a new high-temperature half-metallic ferromagnet and illustrate the ability of strain engineering in tuning magnetism in NaMnF 1.5 O 1.5 .

Ⅱ COMPUTATIONAL METHOD
The first-principles calculations based on density functional theory (DFT) are performed by Vienna ab initio simulation package (VASP) [41,42]. The core and valence electrons are described by projected augmented wave (PAW) [43], with the electronic configuration as follows: 3s 1 (Na), 3d 6 4s 1 (Mn), 2s 2 2p 5 (F) and 2s 2 2p 6 (O). We apply the generalized gradient approximation (GGA) exchange-correlation interaction within the revised Perdew-Burke-Ernzerhof method for solids (PBEsol) [44]. The GGA+U method [45] is adopted to improve the description of on-site Coulomb interactions to the Mn d orbital with U eff = 4.0 eV (U eff = U-J, where the Hund exchange parameter J is set to 0 eV.) according to the previous studies [20,46]. Different U eff are also conducted for magnetic ground state (See Fig. S1 in Supplemental Material for details [47]). For structural optimization, the GGA+U is adopted within different magnetic states to perform a full relaxation, including FM, C-AFM, A-AFM, and G-AFM in both NaMnF 3 and The tilting of the purple MnF 6 octahedra of the ab + atype according to the Glazer's labeling [31], the deformation of octahedra, and the displacement of Na + cations result in the change of structural symmetry, indicating the coupling between tilting of MnF 6 and Na + displacement exists in the orthorhombic structure of NaMnF 3 [6]. We obtained the lattice parameters a = 5.72 Å, b = 7.96 Å, and c = 5.49 Å from our DFT calculations, the corresponding accuracy is 99.46%, 99.41%, and 99%, respectively, compared with the experimental data [50].   Table. S1 [47]. The density of states (DOSs) of four structures are basically the same, as shown in Fig. S4 [47]. Then, the formation energy of NaMnF 1.5 O 1.5 is calculated to study the thermodynamical stability [52,53], which can be evaluated by the following expression: where (NaMnF . O . ) and (NaMnF ) are the total energies of indicates the perovskite oxyfluoride is experimentally feasible [53][54][55][56].
Furthermore, the tolerance factor t is usually used as a descriptor for the stability of perovskite structure [57,58]. For the perovskite oxyfluorides NaMnF 1.5 O 1.5 , it is defined as where (1.02 Å), , and are the ionic radii of the Na + , the arithmetic average radii of coexisting Mn 3+ (0.65 Å) and Mn 2+ (0.67 Å), and the weighted average of two anion radii, respectively. Here, with x denoting the fraction of oxygen, =1.40 Å, and =1.33 Å.
We calculate the value for t = 0.83, implying the perovskite structure can be maintained.
To determine the relative stability between different magnetic states, The antiferromagnetic transition temperature can be estimated by mean-field approximation (MFA) [59,61]: where is the Boltzmann constant. From Eq. (5) and Eq. (6), the calculated results of are also listed in Table Ⅰ and similarly, the can be estimated by MFA [59,61]: The calculation results indicate that plays a crucial role in the high-temperature FM NaMnF 1.5 O 1.5 (see Table Ⅰ).
To reveal the mechanism of the magnetic transition from AFM Strain engineering, as a promising way in manipulating the magnetism of transition metal compounds [46,65], providing an effective avenue to discover the novel magnetism of the ferromagnetic NaMnF 1.5 O 1.5 . Here, we define the strain as = , where and correspond to the pristine and strained in-plane lattice constants, respectively. Thus, the positive value represents tensile strain and negative value represents compressive strain. Herein, large strains are taken into account based on previous experimental method [66]. Due to the lowering effect of compressive strain on (see Fig. S6 [47]), we only discuss the effect of tensile strain on the NaMnF 1.5 O 1.5 , within which structural stability can be kept (see Fig. S7 [47]). The calculations of noncollinear magnetism are performed to test whether the magnetic ordering orientations change under the tensile strain (see Fig. S8 [47]).
By applying different in-plane biaxial tensile strains to the NaMnF 1.5 O 1.5 , we predict the changing trend of exchange coupling constants , as shown in Fig. 3(a). The result clearly shows that the exchange coupling constants , , and increase with the increase in biaxial tensile strain from 0 to 6%. However, as the larger tensile strain than 6% is applied, and show an obvious decay, and even the sign of changes from positive to negative, which means the occurrence of the transition from FM interaction to AFM interaction. As can be seen from Fig. 3(a), plays a major role in the magnetic interactions. Fig. 3(b) shows that the can be strongly enhanced by the in-plane biaxial tensile strain from 613 K to 906 K in the strain range of 0 to 8%. As mentioned above, the MFA usually overestimates the transition temperature due to the neglected effect of spin fluctuation [62], and our calculated result (151 K) presented above is 2.3 times of data from the experimental measurement [50,63]. This kind of correlation coefficient between the theoretical and experimental values was also used by the previous researches [61,67,68]. Thus, it can be expected that a room temperature might be achieved with tensile strain less than 8%.
With larger tensile strain, the shows a slow uptrend, which is the same trend as the major . To study the effect of in-plane biaxial tensile strain on structural distortions, we mainly focus on the oxygen-dominated octahedra, as shown in Fig. 4(a). It is generally believed that structural distortion of orthorhombic LaMnO 3 -like perovskite consists of octahedral rotation distortion and Jahn-Teller (JT) distortion, which can be evaluated from the deviation of magnetic-ion-ligand-magnetic-ion bond angles from 180° and the relative size of Mn-O bonds in oxygen octahedra, respectively. [69]. To understand the effect of biaxial tensile strain on the changing trends of exchange interactions, we calculated the total density of states (TDOS) of NaMnF 1.5 O 1.5 at zero strain and biaxial tensile strain of 10%, as shown in Fig. 5(a) and Fig. 5(b), respectively. One notable feature is that the Fermi level only across the spin-up states without any strain, which means that the spin-up channel possesses metallic conductivity while the spin-down channel is semiconducting, indicating a half-metallic character, as shown in Fig. 5(a). Moreover, Fig. 5(a) shows that the spin-flip excitation energy (∆ ) is equal to the spin-down gap (∆ ↓ ) at zero strain. When a large tensile strain ( =10%) is applied, the ∆ and ∆ ↓ increase from 1.91 eV to 2.72 eV and 2.84 eV, respectively, as shown in Fig. 5(b). The enhanced spin polarization increases the spin transport distance, which indicates that the strain-tuned NaMnF 1.5 O 1.5 is a potential candidate for spintronic materials. As shown in Fig. 5(c), the schematic electronic structures restructuring illustrates the regulation mechanism more visually. We then investigated the PDOS on the Mn-3d orbitals in MnO 6 octahedra (Mn2) at various biaxial tensile strain, as shown in Figs.
6(a)-6(f). For comparison, Fig. S9 [47] shows that the orbitals change slightly with the increased biaxial tensile strain. According to the previous study [65,70], the ( / ) exchange interactions are FM and mainly determine the interplanar exchange. As mentioned above, the Q 3 -type JT distortion of the oxygen octahedra gradually promotes as the applied biaxial tensile strain increases (see Fig. 4(d)), which enhanced the crystal field splitting. Further results can be seen from Figs. 6(a)-6(f), the tensile strain increases the orbital overlap between and , implying the FM -exchange interaction is enhanced, which explains the increase of the interplanar exchange coupling constant with increasing biaxial tensile strain (see Fig. 3(a)). Furthermore, the bond-angle-related rotation distortion is considered. According to the Goodenough-Kanamori-Anderson rules, the super-exchange interaction favors AFM with 180° Mn-O-Mn bond angle [71][72][73]. The out-of-plane Mn-O-Mn bond angle θ 3 decreases monotonically with the increase of the biaxial tensile strains, as shown in Fig. 4(b), indicating the AFM interaction lessens, which also links the rotation distortion to the changing trend of the major exchange coupling constant (see Fig.   3(a)). However, previous study confirmed that the -FM exchange determine the changing trend of the intraplane exchange and is strongly affected by the in-plane Mn-O-Mn bond angle [65]. As shown in Figs.
6(a)-6(c), the intensity of the projected orbital changes slightly at the smaller biaxial tensile strain (0-4%). As the tensile strain increases, in-plane Mn-O-Mn bond angle θ 2 gradually decreases and the intensity of the projected orbital increases obviously, indicating that the bandwidth of the decreases and the in-plane orbital overlaps between the states reduce. These results further lead to the reduction of the in-plane FM exchange coupling constant (see Fig. 3(a)).

Ⅳ. CONCLUSIONS
In conclusion, we theoretically investigated the structural, magnetic, and electronic properties of oxygen-substituted NaMnF 3 under biaxial tensile strain by the first-principles approaches. We selected the simpler structure containing an oxygen octahedron to explore the underlying physical mechanism, which demonstrates that the introduced oxygen octahedra induce a transition from the intrinsic G-AFM NaMnF 3