Effect of transition metal (TM) doping on structural and magnetic properties in hexagonal YMn0.917TM0.083O3 systems

Suitable TM doping at the Mn site is an important access to manipulate magnetic properties of hexagonal YMnO3, however, it has not yet been systematically explored how the strength of antiferromagnetic interactions and the magnetic transition temperatures (TN) are modified in the doping YMn0.917TM0.083O3 systems. In the work, we have performed first-principles calculations to study the effect of TM doping on the structural and magnetic properties of hexagonal YMn0.917TM0.083O3 bulks; the results are combined with the available experimental results. The calculated results reveal that the planar TM-O bonds and O-TM-O angles of TMO5 bipyramid are both prominent structural features for the transformations of magnetic properties. We have also predicted the Ti, V, Cr and Fe doping effects on magnetic properties and further analyzed the TM electronic structures of TMO5 bipyramid in the YMn0.917TM0.083O3(001)/MgO(001) film configurations, which could provide more understanding towards the designing of new generation multifunctional devices.


Introduction
Multiferroic materials exhibit simultaneous ferroic responses with coupled electric, magnetic, and structural orders. They are very important because of their unique and strong coupling of electric and magnetic properties, giving rise to the simultaneous presence of more than one ferroic property. Hexagonal YMnO 3 is the most extensively studied multiferroic material among all hexagonal manganites [1], which possesses magnetism and ferroelectricity simultaneously with a high ferroelectric transition temperature (w900 K) and a low antiferromagnetic (AFM) transition temperature (w70 K). The crystal structure of YMnO 3 (P6 3 cm) can be described as stacks of corner-linked MnO 5 trigonal bipyramid (Mn atoms with two apical oxygen (O1 and O2) atoms and three planar oxygen (O3 and O4) atoms) layers separated by Y atom layers along the crystallographic c-axis. In the hexagonal structure there appears to be a small tilting (a cooperative tilting distortion which buckles the trigonal planes) of MnO 5 bipyramids, which consist of five MneO bonds: MneO1 and MneO2 oriented along the c direction while MneO3 and two pairs of MneO4 bonds lie within the ab plane. The noncollinear magnetic order is originating from the strong antiferromagnetic superexchange interaction of Mn spins in the ab plane of YMnO 3 structure below the N eel temperature T N of 70 K [2,3]. As the symmetry breaking distortion is driven by geometric but not electronic factors in hexagonal YMnO 3 , there is some freedom to tune the magnetic behavior of manganese atoms by electronic doping, without losing the acentric structure of host phase [4]. Doping atoms with different atomic radius will inevitably change the lattice constant and also the Mn-Mn bond distance. This change in the Mn-Mn bond distance, in particular on the ab plane, leads naturally to variations in the exchange integral, which is a critical parameter for the formation of magnetic ground state [5]. Therefore doping at the Mn site in the hexagonal YMnO 3 , one can manipulate the physical properties and change the magnetic ground state.
In recent years, a few studies have been reported on the influence of transition metal (TM) elements doping at Mn-site in hexagonal manganite bulks [5,6,7,8,9,10,11,12,13], in which most of doping concentrations were kept about 10% to preserve the phase isostructural. For examples, N. Sharma et al. [6] pointed out that doping with that Co, Ni and Cu doping at Mn-site in hexagonal YMnO 3 with a specific composition of 1/3 would improve the structural and magnetic properties. L. Jeuvrey et al. [12] proposed that the magnetic transition temperature T N of hexagonal YMn 1-x Cu x O 3 had decreased from 70 K down to 49 K when x went from 0 to 0.15. A. M. Zhang et al. [13] revealed that the polycrystalline YMn 1-x Zn x O 3 with low Zn doping concentration (x < 0.1) maintained single phase which demonstrated hexagonal structure with space group of P6 3 cm, and the T N temperatures were respectively 75 K, 65 K and 60 K with x ¼ 0, 0.04 and 0.08.
As mentioned above, a systematic understanding of doping effect on T N is still lacking although a number of experimental results were given in TM doping YMn 0.9 TM 0.1 O 3 (TM ¼ TiwZn) bulks. Besides, it remains to be elucidated how the antiferromagnetic interactions and N eel temperatures are modified by dopant incorporation in hexagonal manganite films [14]. In the work, we have firstly used the first-principles method to calculate a variety of TM elements from Ti to Zn atoms doping at the Mn site, and investigate how such doping affects the structural and magnetic properties of hexagonal YMn 0.917 TM 0.083 O 3 bulks (approximating to experimental YMn 0.9 TM 0.1 O 3 compositions [5,6,7,8,9,10,11,12,13]). Then we have also studied the effect of Ti, V, Cr and Fe doping on magnetic properties and discussed the varied electronic structures of TMO 5 in the YMn 0.917 TM 0.083 O 3 film configurations, which could provide more understanding towards the designing of new generation multifunctional devices.

Calculation
We have performed first-principles density-functional theory (DFT) calculations within the generalized gradient approximation (GGA) [15] using the Vienna ab initio Simulation Package (VASP) [16,17]. The eigenstates of electron wave functions were expanded on a plane-wave basis set using pseudopotentials to describe the electron-ion interactions within the projector augmented-wave approach [18] (PAW). The Monkhorst-Pack (MP) scheme [19] is used for the k-point sampling and the Brillouin zone integration is performed with the Gaussian smearing method.
The plane-wave basis energy cutoff is chosen as 500 eV. We respectively treated 11 valence electrons for Y (4s 2 4p 6 5s 2 4d 1 ), 15 for Mn (3s 2 3p 6 4s 2 3d 5 ), and 6 for oxygen (2s 2 2p 4 ). The atomic positions are fully relaxed until atomic forces are less than 10 meV/ A and the total energy is obtained when it converges to 0.1 meV in the electronic self-consistent loop. In the calculations, the Perdew-Burke-Ernzerhof (PBE) [15] form was chosen as the exchange-correlation potentials within the DFT þ U scheme. The DFTþU integrals, determined by the PAW on-site occupancies and the on-site electron-electron interaction, are normally specified in terms of the effective on site Coulomb and exchange parameters, U and J [20]. Here, the values of U ¼ 8.0 eV and J ¼ 0.88 eV are applied for the Mn 3d states [21]. U eff is generally expressed as the difference between two parameters (UÀJ), which determines an orbital-dependent correction to the DFT energy. According to the reported literatures [22,23,24,25,26,27,28,29], the proper Hubbard correlation item U eff values U eff (Ti) ¼ 3.2 eV, U eff (V) ¼ 2.64 eV, U eff (Cr) ¼ 3.0 eV, U eff (Fe) ¼ 4.0 eV, U eff (Co) ¼ 6.0 eV, U eff (Ni) ¼ 4.7 eV, U eff (Cu) ¼ 7.05 eV, U eff (Zn) ¼ 8.0 eV are adopted using the Dudarev implementation [30] in the following calculations. To be close to the doping concentration [5,6,7,8,9,10,11,12,13], we built the supercell of a theoretical formula YMn 0.917 TM 0.083 O 3 bulk with twelve formula units, in which one of 12 Mn atoms was substituted by a TM atom (shown in Fig. 1 Table 1 lists the calculated To study the doping effects on the magnetic properties of hexagonal YMn 0.917 TM 0.083 O 3 (TM ¼ TiwZn) bulks, the theoretical magnetic transition temperatures (T N ) have been calculated based on the different magnetic structures (such as collinear AFM state, non-collinear magnetic G1 state and FM state) and the nearest-neighbor spin-exchange interactions [36]. In all doping systems, the lowest energy state is the G1 state, whose lattice parameters are listed in Table 1. The calculated N eel temperatures are also listed. The formula to calculate N eel temperatures will be shown in Section 3.2. Fig. 2 shows that the calculated N eel temperatures var-  As is well known, the structural parameters can be varied by suitable substitution and hence one can tune the magnetic property in these types of materials [39]. In the   To further investigate the structural variations of TMO 5 bipyramids (shown in the inset of Fig. 3), Figs. 4 and 5 respectively demonstrate the bond lengths and bond angles dependence on doping elements (TM) from Ti to Zn. Table 2 lists the calculated main bond lengths and bond angles for TMO 5 (001) configurations. The nearest-neighbor spin-exchange coupling J nn in the hexagonal structure of YMnO 3 can be calculated as: [36] J nn ¼ where E AFM , E G 1 and E FM are respectively total energies for different magnetic configurations (three N eel spin states) as collinear AFM state, non-collinear magnetic G1 state and FM state. Then according to L. Capriotti et al. [37,38], the magnetic transition temperature can been estimated as T N ¼ À0:3J nn S þ 1  MgO(001) configuration. Nevertheless, the m eff values of Cr, Mn and Fe doping are comparable within the difference (2%). The value of parameter f ¼ jQ CW j T N is a magnetic frustration factor which can be used as a measure of the spin frustration strength. If the ratio f is larger than 10, the spin system should be classified as the one with strong geometrical frustration since the value cannot be explained by the simple mean-field theory [40]. For the hexagonal YMnO 3 bulk, the calculated Q CW is À468 K and T N is 73 K, then the frustration factor (f ¼ 6.41) can be obtained; which is very close to the experimental value (f ¼ 6.43) [9]. For the YMn 0.917 TM 0.083 O 3 (001)/MgO(001) configurations, it can be seen in Table 3  As we know, the crystal field of hexagonal YMnO 3 splits the Mn d orbitals into two doublets (e 1g and e 2g ) and a singlet (a 1g ). In the TMO 5 bipyramids (shown in the inset of Fig. 3

Conclusions
In

Declarations
Author contribution statement Dong Chen: Analyzed and interpreted the data, Wrote the paper.
Yu-Jia Wang: Conceived and designed the analysis.
Yin-Lian Zhu, Xiu-Liang Ma: Contributed analysis tools or data.

Funding statement
This work was supported by the National Natural Science Foundation of China(NSFC) (51371176, 51571197 and 51671194), and the Frontier Science Key