First-principles study of the effect of iron doping on the electronic and magnetic properties of TbMn2O5

Journal of Physics and Chemistry of Solids 72 (2011) 940–944

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First-principles study of the effect of iron doping on the electronic and magnetic properties of TbMn2O5 X.F. Zhu , L.F. Chen Department of Physics, Nanjing Normal University, Nanjing 210097, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 September 2010 Received in revised form 16 March 2011 Accepted 28 April 2011 Available online 8 May 2011

We have studied the electronic and magnetic properties of TbFexMn2  xO5 (x ¼ 0, 0.125, 0.25) samples using first-principles density functional theory within the generalized gradient approximation (GGA) schemes. The crystal structure of TbMn2O5 is orthorhombic containing Mn4 þ O6 octahedra and Mn3 þ O5 pyramids. The structure changes to monoclinic symmetry for the Fe-doping at the Mn sites. Our spinpolarized calculations give an insulating ground state for TbMn2O5 and a metallic ground state for Fe-doped TbMn2O5. Based on the magnetic properties calculations, it is found that the magnetic moment enhances with increase in the Fe-content in TbMn2O5. Most interestingly, the enhanced magnetic moment is due to a substantial reduction of the magnetic moments at the Fe sites. & 2011 Elsevier Ltd. All rights reserved.

Keywords: D. Electronic structure

1. Introduction Multiferroics materials, which exhibit simultaneous magnetic and ferroelectric order, have attracted much attention recently because of the interesting physics of systems with coupled multiple order parameters and because of their potential for cross electric and magnetic functionality. Thus, electrically accessible magnetic memory and processing and vice versa are important possibilities. Fundamental interest in multiferrocity also derives from the strong interplay between magnetic frustration, ferroelectric order and fundamental symmetry issues in phase transformations that characterize these materials [1–4]. Multiferroics with magnetic and electric ordering united in a single phase were thought to be rare [5,6]. RMn2O5 (R¼Tb, Dy, Ho, Y, etc.) belongs to a very special class of multiferroics because the ferroelectricity is driven by the magnetic ordering [7–9]. The structure of RMn2O5 is orthorhombic and contains MnO6 and MnO5 units. From considerations relating to the Mn–O distances and the observed magnetic couplings, it can be assumed that octahedrally coordinated manganese cations are tetravalent, whereas MnO5 square-planar pyramids correspond to Mn3 þ cations. These compounds therefore possess strong magnetoelectric (ME) coupling, showing remarkable new physical effects, such as the colossal magnetodielectric [10], magneto-polarization flop effects [11–13], etc. The strong ME coupling effects are not only interesting in the view of fundamental physics, but also they have potential important applications in future multifunctional devices.

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E-mail address: [email protected] (X.F. Zhu). 0022-3697/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2011.04.016

However, the low operation temperature and the high operation field are the roadblocks for many practical applications. Current research is, therefore, focused on achieving large magneto-electric coupling at room temperature (RT). In the previous work by Shim et al. [14], the substitution of Fe for Mn seems a promising route to enhance the Curie temperature (TC) of YMn2O5. Recent X-ray diffraction experiment suggests that the magnetic moment enhances with increase in the Fe-content in TbMn2O5 and if a strong coupling between magnetic moment and electric polarization exists, the Fe-doped sample may have a higher polarization/ferroelectric effect, which should be a great advantage for the future application of the spintronics devices [15]. To our knowledge there is no report available on the evolution of the magnetic properties for the Fe-doped TbMn2O5 system. In this work, we aim to study the effect of Fe-doping on the electronic and magnetic properties of multiferroic TbMn2O5 and obtain a definitive understanding of magnetism in this class of compounds.

2. Computational details First-principles calculations of TbFex Mn2x O5 (x¼0, 0.125, 0.25) are performed in a plane-wave basis set using the projector augmented wave (PAW) method in the generalized gradient approximation (GGA) as it is implemented in the Vienna ab initio simulation program (VASP). A plane-wave basis and projector augmented-wave pseudopotentials are used, with Mn 3p3d4s, Fe 3pd7s1 and Tb 5p5d6s electrons treated self-consistently. A 500 eV plane-wave cutoff results in good convergence of the total energies. Forces on atoms were calculated, and atoms were allowed to relax using a conjugate gradient technique until their residual forces had

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˚ significantly shorter than the remaining four Mn–O bonds (1.934 A) which are not listed in Table 1. In the Fe-doped TbMn2O5, the orthorhombic structure changes to monoclinic symmetry and the cell volumes are slightly decreased except the Fe3 (x¼0.125) and Fe3Fe3 (x¼0.25) substitute forms. Comparing the radii of Fe3 þ ˚ Mn3 þ (0.72 A) ˚ and Mn4 þ (0.68 A), ˚ it implies that the Fe (0.69 A), cannot remain in the trivalent state in TbFex Mn2x O5 . The average bond distances are also given in Table 1. The average /MnO5 S bond distances are almost unchanged when we replace Mn4 þ with Fe, whereas the average /MnO5 S bond distances get larger when we replace Mn5 þ with Fe. The /FeO5 S bond distance increases with Fe-doping and is the largest in the Fe3Fe3 substitute forms while the /FeO6 S bond distance decreases with Fe-doping. We show the calculated total density of states (DOSs) and various partial densities of states for TbMn2O5 in Fig. 2. The DOSs of spin-up and spin-down electrons are identical as expected for an AFM state. From the results, the band gap is estimated to be 0.2 eV, confirming the experimental fact that TbMn2O5 is an insulator. However, it is well known that GGA greatly underestimates the band gap, especially for the 3d compounds. The real

˚ Experimentally, TbMn2O5 is found converged to less than 0.01 eV/A. to be incommensurate antiferromagnetic (AFM) below 24 K, with the propagation vector k  ð0:48, 0, 0:32Þ. To accommodate the magnetic structure, one needs a huge supercell, which is computationally prohibitive. Instead, we use a 2  1  1 supercell, equivalent to approximating the propagation vector k¼(0.5, 0, 0). The validity of this approximation has been justified in the previous work [16]. For the supercell we used, a 1  2  4 Monkhorst–Pack k-point mesh converges very well with the results. The most stable structure we found has the spin configuration identical to that proposed in Ref. [17]. In this spin configuration, Mn4 þ forms an AFM square lattice in the ab plane, whereas Mn3 þ couples to Mn4 þ either antiferromagnetically along the a-axis or with alternating sign along the b-axis. To study the effect of iron doping on the magnetic properties of TbMn2O5, we replace some of the Mn with Fe in the supercell. There are two valences of Mn (Mn3 þ and Mn4 þ ) in TbMn2O5, so we consider two substitute forms (in sign of Fe3 (0.5, 0.5, 0.2618) and Fe4 (0.044, 0.851, 0.5) replacing Mn3 þ and Mn4 þ , respectively) for x¼0.125 and three substitute forms (Fe3Fe3 (0.044, 0.851, 0.5; 0.206, 0.351, 0.5), Fe3Fe4 (0.044, 0.851, 0.5; 0.0, 0.5, 0.7382) and Fe4Fe4 (0.5, 0.5, 0.2618; 0.5, 0.5, 0.7382)) for x ¼0.25. It was demonstrated in Ref. [18] that the largest electric polarization is associated with a commensurate antiferromagnetic state and the spins are almost collinear. Therefore, in the calculations, we use the collinear spin approximation and ignore the spin–orbit coupling. Our results agree very well with the known experiments, indicating that these approximations capture the essential physics in TbMn2O5.

3. Results and discussion We start the structural relaxation from the experimental structural parameters [19]. The unit cell shape, lattice vectors and atomic coordinates were optimized simultaneously during optimizing. Here, we consider only the spins of Mn and Fe ions. The calculated lattice constants of the ground-state structure for different compositions are listed in Table 1 and are in very good agreement with the experiments. The errors of the lattice constants are about 1%, which are typical errors for GGA. The crystal structure of TbMn2O5 is orthorhombic containing Mn4 þ O6 octahedra and Mn3 þ O5 pyramids. MnO6 octahedra form infinite chains parallel to the c-axis, sharing edges via oxygens. The chains are interconnected by MnO5 pyramids, which in fact, form dimer units, Mn2O8, as shown in Fig. 1. The Tb cations are in the eightfold-oxygen-coordinated holes of the network. It is noteworthy ˚ that MnO6 octahedra are fairly flattened, with two bonds (1.873 A)

Fig. 1. Structure of TbMn2O5 unit cell, showing Mn4 þ O6 octahedra and Mn3 þ O5 pyramids.

Table 1 Calculated structural parameters and total magnetic moments for TbFexMn2  xO5. Experimental measurements are listed for comparison. Composition x

0.0

0.125

Substitute forms

–

Fe3

0.25 Fe4

Fe3Fe3

0.0 Fe3Fe4

Fe4Fe4

0.2

–

–

–

˚ a (A)

7.319

7.297

7.294

7.309

7.303

7.283

7.3251a

7.325b

7.325b

˚ b (A) ˚ c (A)

8.549

8.569

8.569

8.575

8.568

8.569

8.5168a

8.501b

8.511b

5.666

5.674

5.671

5.679

5.670

5.670

5.6750a

5.666b

5.672b

–

–

– –

Volume of cell (A˚ 3) ˚ d/MnO S (A)

354.52

354.75

354.47

355.92

354.79

353.87

1.922

1.923

1.921

1.925

1.922

1.921

1.931a

–

˚ d/MnO6 S (A) ˚ d/FeO S (A)

1.913

1.914

1.910

1.911

1.912

1.911

1.904a

–

–

–

1.903

–

1.947

1.929

–

–

–

–

˚ d/FeO6 S (A) mT ðmB Þ

–

–

1.911

–

1.909

1.907

–

–

–

0.0

0.254

0.631

1.462

 0.814

2.087

–

–

–

5

5

a b

Ref. [19]. Ref. [15].

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Fig. 2. Total (black line) densities of states and partial densities of states of Mn 3d (blue line) and O 2p (olive line) in TbMn2O5. The upper and lower panels show the DOS for spin-up and spin-down, respectively. The energy zero (dotted line) is taken at the Fermi level. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Total (black line) densities of states and partial densities of states of Mn 3d (blue line), Fe 3d (red line) and O 2p (olive line) in TbFexMn2  xO5 (x¼ 0.25, three substitute forms). The upper and lower panels show the DOS for spin-up and spindown, respectively. The energy zero (dotted line) is taken at the Fermi level. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 3. Total (black line) densities of states and partial densities of states of Mn 3d (blue line), Fe 3d (red line) and O 2p (olive line) in TbFexMn2x O5 (x ¼0.125, two substitute forms). The upper panel and lower panels show the DOS for spin-up and spin-down, respectively. The energy zero (dotted line) is taken at the Fermi level. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

band gap might be much larger. For our discussion of the density of states, which is limited to an energy window of  8 to about 4 eV, we shall be primarily concerned with the Fe-d, Mn-d and O-p states, since the Tb-derived states are quite small in the selected energy range. We see that the DOS near the Fermi level is mainly from Mn 3d and O 2p orbits. The generic features of the DOS for x ¼0 are consistent with the previous result [17]. Figs. 3 and 4 show the calculated total density of states and various partial densities of states for Fe-doped TbMn2O5 at x¼0.125 and 0.25, respectively. Our self-consistent calculations yield the ground state to be metallic for all the substitute forms at x¼0.125 and 0.25. In Fe3 substitute form, the spin-up conduction band crossing the Fermi level (EF) is dominated by the admixture of Fe 3d and Mn 3d states and the spin-down band crossing EF is mostly due to the Mn 3d state while the magnitude of the spindown DOS is very small; in Fe4 substitute form, both spin-up and spin-down conduction bands crossing EF have a contribution of O 2p state besides Fe 3d and Mn 3d states (see Fig. 3). In Fig. 4, the

densities of states of Fe3Fe3 and Fe4Fe4 forms around EF are in close similarity with the features of the DOS of Fe3 and Fe4 forms, respectively. We further calculated the site-projected partial density of states (PDOS) for Fe d electrons at x¼0.25 in the energy range of  3.5 to 3.5 eV around the Fermi level, as shown in Fig. 5. Compared with the PDOS of Mn in TbMn2O5, it is important to note that there is a weaker polarization of the states at and near EF at Fe site. The depolarization effects of Fe are strongly influenced by the number of O atoms in the nearest-neighbor shell and the Fe-content in TbMn2O5, which we will discuss later. The magnetic structures for x ¼0 are found to be the antiferromagnetic (AFM) state where the Mn4 þ spins form an AFM square lattice in the ab plane and are aligned ferromagnetically in the bc plane, whereas Mn3 þ couples to Mn4 þ either antiferromagnetically along the a-axis or with alternating sign along the b-axis. The magnetic structures for x ¼0.125 and 0.25 are the ferrimagnetic (FIM) states while the arrangement forms of the Fe/Mn spins are the same as that in TbMn2O5. The calculated total magnetic moments ðmT Þ for TbFexMn2  xO5 are also listed in Table 1. We notice that the total magnetic moments enhance with increase in the Fe-content in TbMn2O5 while are not the same in different substitute forms at x¼0.125 or 0.25. The local magnetic moments of Mn and Fe for each Fe-content are given in Table 2. The calculated local moment of Tb ions is negligibly small and the spin moments on the oxygen ions are also small due to the nearly closed 2p shells, which are not listed in Table 2. The magnetic moments are estimated for Mn3 þ to be 3:316mB and for Mn4 þ to be 2:583mB in TbMn2O5. The magnitudes are larger than the refined magnetic moments 2:40mB for Mn3 þ and 1:81mB for Mn4 þ , which may be due to a significant component of the moment that remains disordered in the real system [18]. In addition, the magnetic moments also relate to the ionic radii we use in the calculation. With increase in x, the absolute magnetic moments of Mn change slightly while the absolute magnetic moments of Fe change hugely in different substitute forms.

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Fig. 5. Site-projected partial density of states (PDOS) of Fe d electrons for TbFex Mn2x O5 (x ¼0.25). The upper and lower panels show the DOS for spin-up and spin-down, respectively. The energy zero (dotted line) is taken at the Fermi level.

Table 2 The signs Mn1 and Mn2 show the atoms with positive and negative magnetic moments. The fourth columns give the nearest oxygen number of Mn or Fe neighbor. The last column gives the magnetic moment at various sites. x

Substitute form

x¼0

x ¼ 0.125

Fe3

Fe4

x ¼ 0.25

Fe3Fe3

Fe3Fe4

Fe4Fe4

Sites

nn

Magnetic moment ðmB Þ

Mn1 Mn2 Mn1 Mn2

5O 5O 6O 6O

3.316  3.316 2.538  2.538

Fe Mn1 Mn2 Mn1 Mn2 Fe Mn1 Mn2 Mn1 Mn2

5O 5O 5O 6O 6O 6O 5O 5O 6O 6O

 2.648 3.294  3.308 2.538  2.522  1.199 3.257  3.284 2.530  2.513

Fe Mn1 Mn2 Mn1 Mn2 Fe3 Fe4 Mn1 Mn2 Mn1 Mn2 Fe Mn1 Mn2 Mn1 Mn2

5O 5O 5O 6O 6O 5O 6O 5O 5O 6O 6O 6O 5O 5O 6O 6O

 1.703 3.284  3.318 2.549  2.530  3.413 1.458 3.281  3.272 2.502  2.528  0.251 3.203  3.259 2.528  2.528

We can see that the mT increases with x primarily because of the change in the local moments at Fe site. For instance, in the Fe3 and Fe4 substitute forms at x ¼0.125, the absolute moment of Fe ð2:648mB and 1:199mB Þ is smaller than Mn ð3:316mB and 2:518mB Þ so the net magnetic moments are not zero any more. Surprisingly, the absolute magnetic moment of Fe decreases to 0:251mB in the Fe4Fe4 substitute form at x ¼0.25. In order to understand the microscopic origin of this reduction in the magnetic moment, we discuss our results in some detail. We notice that the magnetic moments at the Fe sites in TbFexMn2 xO5 are smaller than Mn in TbMn2O5. Magnetic interactions may be

weakened by a modulation of the Mn–O–Fe bond angles, a realization of the so-called magnetic Jahn–Teller effect. In the Fe4Fe4 substitute form, we replace two Mn4 þ (the nearest neighbors along the c-axis) atoms with Fe and our results clearly show that the Fe–O–Fe interaction is also ferromagnetic but with very small magnetic moment. We note that the local magnetic moment of an element is determined by two factors: the occupation of the corresponding spin-up and spin-down bands and the hybridization of the states with other occupied and unoccupied states. In Fig. 5(d), the spin-up and spin-down channels of Fe4 are both partly filled, resulting in a small negative magnetic moment. The reduction of the magnetic moment at the Fe sites may be explained by considering the fact that the charge transfer energy between Fe and Mn is substantial. As a result the presence of Fe neighbors increases the hopping probability from the Fe site, reducing the importance of electron correlation and the hopping to neighboring Fe sites enhances the bandwidth, making the central Fe site less correlated with a reduced magnetic moment.

4. Conclusions In conclusion, we have investigated a study of the structural, electronic and magnetic properties of TbFexMn2  xO5 (x ¼0, 0.125, 0.25) using first-principles density functional theory within the generalized gradient approximation (GGA) schemes. In the Fedoped TbMn2O5, the orthorhombic structure changes to monoclinic symmetry and the cell volumes are slightly decreased except the Fe3 (x¼0.125) and Fe3Fe3 (x ¼0.25) substitute forms. The Fe-doping is found to destroy the insulating nature in TbMn2O5; moreover, doping leads to a significant enhancement in the net magnetic moment. The increase in the magnetic moment is caused by the decrease in the individual magnetic moments of Fe sites due to the various distributions of the neighbors and consequent bandwidth/correlation effects.

Acknowledgments Project supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant no. 10KJB140005). Numerical calculation was carried out using the facilities of the Department of Physics in Nanjing Normal University.

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