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Noncollinear magnetic ground state of PrFeAsO This article has been downloaded from IOPscience. Please scroll down to see the full text article.
2011 EPL 93 17003 Download details: IP Address: 128.130.131.2 The article was downloaded on 25/04/2012 at 12:30 Please note that EPL, 93 (2011) 17003 Noncollinear magnetic ground state of PrFeAsO J. Liu , B. Luo , R. Laskowski 1 School of Physics, Huazhong University of Science and Technology - Wuhan 430074, China 2 Technische Universit¨at Wien - Getreidemarkt 9/165TC, A-1060 Vienna, Austria, EU 3 International Center of Materials Physics, The Chinese Academy of Science - Shengyang 110015, China received 13 April 2010; accepted in final form 18 December 2010published online 28 January 2011 PACS 74.25.Jb – Electronic structure (photoemission, etc.)PACS 74.70.Dd – Ternary, quaternary, and multinary compounds (including Chevrel phases, borocarbides, etc.) Abstract – Noncollinear magnetic investigations of the ground state in PrFeAsO have beenperformed by the density-functional theory. We calculated the total energy and made structureoptimization, and the electronic density of states of PrFeAsO was analyzed. There are threedifferent magnetic structures in PrFeAsO defined by experiments. Based on these magneticstructures, we studied four collinear and four noncollinear cases. The ground state is found totake the ordering proposed by Zhao, in which the FeAs plane is of stripe antiferromagnetism andPr spins are perpendicular to Fe spins. The electronic density of states indicates that for PrFeAsOthe increase of the electron Coulomb interaction leads to a decrease in conductivity.
Antiferromagnetism is relevant to high-temperature Kimber et al. proposed the collinear magnetic model, superconductivity because copper oxide and iron arsenide where both Fe and Pr spin ordering are within the ab-plane superconductors arise from electron- or hole- doping in the two-left, one-right magnetic structure [5]. Accord- of their antiferromagnetic parent compounds [1,2]. If ing to Kimber's structure, we constructed two kinds of magnetism is important for the superconductivity of collinear solutions CM1 and CM2. Pr spins are aligned these materials, it is essential to get the correct magnetic antiferromagnetically along the b-axis in the CM1 solu- ground state of their parent compounds. The neutron tion (see fig. 1(a)) and are aligned ferromagnetically in the powder diffraction has defined the crystal structure and CM2 solution (fig. 1(b)). Simultaneously a rather compli- the magnetic ordering of the RFeAsO system, which cated noncollinear magnetic structure was shown by Zhao shows a structural phase transition from tetragonal et al. [6], where the Pr spins align along the c-axis, trios to orthorhombic with decreasing temperature [3–8].
of spins are coupled ferromagnetically, and adjacent trios However, it is found that at very low temperature there align antiferromagnetically. This noncollinear magnetic exits strong magnetic coupling between the rare-earth structure is called NCM1 in our work (fig. 1(c)). Finally, elements, and they form antiferromagnetic ordering in Maeter et al. reported a new noncollinear magnetic struc- the RO layer, meanwhile their spins are coupled with iron ture different to NCM1, which is called NCM2 [7]. In spins. The Fe spin structure is supposed to be the same NCM2 Pr spins order within the ab-plane and Fe spins as that arranged above the magnetic phase transition make an acute angle with the ab-plane (fig. 1(d)).
temperature when data fitting. Hence it needs more The two-dimensional electronic structure in the iron- investigations to help define the iron spins ordering and arsenide compound has been analyzed by many groups, the rare-earth element spin ordering in the ground state.
but there are few reports about the three-dimensional PrFeAsO is one parent compound of the iron arsenide electronic-structure calculations including the rare-earth family, and it has a transition temperature of up to 52 K magnetic-moment direction. With the unconstrained with oxygen partially replaced by fluorine. Three groups method, we defined the Pr spin ordering and Fe spin have worked on determining the magnetic structure of ordering in the ground state. The lattice parameters PrFeAsO and their results are totally different. First, were taken from refs. [6,9], and we made a All calculations were performed by the WIENNCM code [10,11], the Perdew-Burke-Ernzerh of 96 GGA J. Liu et al.
other [13–15]. The stripe antiferromagnetic ordering isobserved by experiments [16–18]. In order to comparewith experiments and other theoretical work, we alsoconsidered the checkboard antiferromagnetic ordering. Weused checkboard ordering instead of stripe ordering in theabove four solutions and got the corresponding solutionsof CM1-FeC, CM2-FeC, NCM1-FeC and NCM2-FeC.
(The magnetic structure of CM1-FeC is similar to CM1,but the FeAs plane takes a checkboard ordering, see fig. 1(e).) Only two kinds of antiferromagnetic orderingare discussed in the NCM structure, for the experimentsand previous theoretical calculations both indicate anti-ferromagnetic ordering is more stable than other orderings(ferromagnetic, nonmagnetic and paramagnetic) [19,20].
Table 1 gives the energy of each configuration. The energy value in the CM1 case is set to zero; the other casesare given as the energy differences relative to the CM1case (energy values reserve four decimal places). Fromtable 1, it can be seen that two kinds of noncollinearmagnetic models are more stable than the collinear magnetic models. When the Coulomb repulsion is consid-ered into Pr and Fe ions, NCM1 is the ground state andNCM2 is the metastable state. On three different on-siteCoulomb interactions, NCM1 keeps the lowest energy.
In NCM1 the Fe spin shows stripe antiferromagneticordering within the ab-plane and the Pr spin plane isperpendicular to the Fe spin plane. Both NCM1 andNCM2 structures. Moreover the energy results indicate that in noncollinear magnetic structure the stripe ordering is more stable than the checkboard ordering, because the NCM1 case and NCM2 case have lower energy than theNCM1-FeC case and NCM2-FeC case, respectively. If the Fig. 1: (a) (Colour on-line) The collinear magnetic structure of Coulomb repulsion is not considered, NCM2 takes the the CM1 case; (b) the CM2 case; (c) the noncollinear magneticstructure of NCM1 case; (d) the NCM2 case; (e) the CM1-FeC lowest energy. The X-ray absorption (XAS) and resonant case. The red arrows indicate the magnetic-moment directions inelastic X-ray scattering (RIXS) for 122 and 1111 Fe of the magnetic ions. Light-green balls indicate Fe ions, green pnictides show qualitative similarity to the Fe metal, balls indicate Pr ions, red balls indicate O ions and purple balls therefore the cases which included Coulomb interaction indicate As ions.
are in accord with the actual conditions [12,21].
Using the unconstrained approach, the magnetic struc- ture can be optimized according to the charge density.
exchange-correlation potential was used. Atomic sphere The orientation of the spins is described using spherical radii were set to 2.04, 2.39, 2.12 and 2.30 a.u. for O, Fe, As coordinates. Each magnetic moment is symbolized by a and Pr, respectively. We used a 4 × 4 × 4 k-point sampling vector R(ρ, θ, ϕ), so that θ corresponds to the angle in the of the Brillouin zone. The unconstrained approach was basal plane, and ϕ is the angle relative to the c-axis (z- adopted in order to lower the total energy and optimize direction). In the optimization of the magnetic structure, the magnetic structure. The RKmax value was set to Pr spins and Fe spins are found to make small changes in θ 7.0. Within GGA+U calculations, the effective Coulomb but give a relative large deflection in ϕ. The modification interaction value was set to 2 eV, 4 eV and 5 eV for Fe for θ is no more than ±0.5◦, this means that the magnetic ions and 4 eV, 6 eV and 7 eV for Pr ions, respectively [12].
ordering is quite stable within the ab-plane. Table 2 lists Energy convergence and charge convergence were attained the average ϕ deflection angles (between ρ- and c-axis) in CM1, NCM1 and NCM2. From table 2 we can see that The two interpenetrating square antiferromagnetic the NCM1 case almost keeps the original magnetic struc- orderings (checkboard ordering and stripe ordering) in ture after optimization: both in GGA and GGA+U, Pr the FeAs plane have been proposed by theoretical works, deflection is no more than ±2◦ and Fe deflection is no for the Fe-Fe effective nearest-neighbor and next-nearest- more than ±1◦. A larger alteration occurred to the NCM2 neighbor magnetic interactions are comparable to each case: within GGA, ϕ deflection of Pr spin up to ±11.5◦ Noncollinear magnetic ground state of PrFeAsO Table 1: Energies for each configuration of PrFeAsO. The unit of the energy is Ry.
Table 2: Optimization results of magnetic structure: the average ϕ deflection angles in the CM1 case, NCM1 case and NCM2case.
The average ϕ deflection angles (◦) and Fe deflection is ±3.4◦; within GGA+U, Pr deflection interaction the Fe moment is 2.59 µB and 2.99 µB foris between ±5.66◦ and ±5.13◦, Fe deflection is between 4.41 a.u. and 4.69 a.u. Fe-As bonds, respectively [27–29].
±0.4◦ and ±0.08◦. It tells us Pr spins are straying from However the Pr moment keeps 1.90 µB during the increase the ab-plane and approaching the c-axis, and the trend of volume and it is not sensitive to the Pr-O bonds.
is weakened with the increase of the electronic correla- Figure 2 illustrates the optimized results of energy and tions. The same tendency is also found in the CM1 case.
For this reason, the optimization results prove that the Finally, the electronic density of states (DOS) of the NCM1 magnetic model is more stable than others. Within NCM1 case is given (see fig. 3). In fig. 3, PrFeAsO the GGA+U method we get Fe and Pr moments of about indicates the metallic property within GGA; the Fe 3d 2.83 µB/Fe and 1.96 µB/Pr using the experimental lattice. band and Pr 4f band are continuous across the FermiThe calculated Fe moments do not reduced in noncollinear level. While within GGA+U, the Fe 3d band and Pr magnetic calculation or spin orbital coupling compared 4f band split and move away from the Fermi level, the with other people's work [22–26].
distance between the split bands and the Fermi level We also performed the volume optimization, this time depends on the effective Coulomb repulsion value. The the spin direction of Pr and Fe were constrained. There results of the DOS are in agreement with other theoret- are two cases: 1) without considering on-site Coulomb ical calculations [20,30,31], which perform the electronic- interaction, 2) with Ueff = 2 eV for the Fe ion and Ueff = structure calculation for PrFeAsO within LDA or GGA.
4 eV for the Pr ion. When the on-site Coulomb interac- If the electronic correlations are weak enough in Fe ions, tion is not included, the lowest total energy occurs at the FeAs plane will be metallic or easily conductive in about V /Vexp = 5%, the lattice parameters are obtained the excited state [21]. CM1, CM2, NCM2 and NCM1with a = 8.738 ˚ A. If the effec- have a similar DOS under one Coulomb interaction, that tive Coulomb interaction are set to 2 eV and 4 eV for is to say, the Pr spin direction does not much affect the Fe and Pr ions, respectively, the structure can be stabi- density of states at the Fermi level. In fig. 3(a), Fe has a lized in V /Vexp = 9% by the lattice parameters a = 8.848 ˚ few similar peaks with Pr between –2 eV and 2 eV, hence A. Additionally, the Fe magnetic there exits a magnetic coupling between the FeAs plane moment is sensitive to the Fe-As bonds, with Coulomb and the PrO plane. We believe that the magnetoelastic J. Liu et al.
Fig. 2: (Colour on-line) The energy and magnetic moment for volume optimization.
Fig. 3: (Colour on-line) Density of states of the NCM1 case. (a) The DOS without Coulomb interaction. (b) The DOS withCoulomb interaction (U − J = 2 eV for Fe and U − J = 4 eV for Pr).
volume effect reported in ref. [5] originates from both NCM1 in which the Pr spin is perpendicular to the Fe Pr spin density waves and Fe spin density waves. The spin and the FeAs plane takes stripe antiferromagnetic superconducting isotropy of PrFeAsO1−y suggests a ordering. Another noncollinear magnetic structure NCM2quasi–three-dimensional is considered for metastable states. We found that the Pr spin direction does not much affect the density of states tions confirm it also has a three-dimensional magnetic at the Fermi level. The Fe magnetic moment is sensitive structure [32].
to the Fe-As bonds but the Pr moment is not sensitive to In conclusion, this work has investigated four collinear the Pr-O bonds. The conductivity of PrFeAsO is mainly and four noncollinear magnetic structures in PrFeAsO.
depending on the electronic correlation interaction, if the Total energy calculation, magnetic structure optimization electronic correlations are weak enough, the PrFeAsO will and volume optimization define the magnetic ground state show metallic character or semi-metallic character.
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