Physics Letters A 374 (2010) 2972–2979

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Physics Letters A

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Magnetic and electronic structure studies of the perovskite oxide Nd2/3Sr1/3MnO3from the first principle calculation

Lin Zhu a, Lin Li a,∗, Taimin Cheng b, Guozhu Wei a

a Department of Physics, Northeastern University, Shenyang 110004, People’s Republic of Chinab Department of Mathematics and Physics, Shenyang Institute of Chemical Technology, Shenyang 110142, People’s Republic of China

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 September 2009Received in revised form 5 May 2010Accepted 7 May 2010Available online 11 May 2010Communicated by R. Wu

Generalized gradient approximation (GGA) and GGA + U (U denotes on-site Coulomb interactions)methods are applied to investigate the magnetic and electronic structures of the perovskite oxideNd2/3Sr1/3MnO3. Under GGA the compound prefers ferrimagnetic ordering in which Nd sublattice isspin-antiparallel to Mn sublattice. Nd 4f states cross over the Fermi level under GGA, leading theferrimagnetic Nd2/3Sr1/3MnO3 to a metallic character. The on-site Coulomb interactions should beincluded to emphasize the localized feature of Nd 4f states. Under GGA + U , the spins of Nd and Mnsublattices tend to be parallel in the ground state, and fully spin-polarized Mn 3d electrons yield a half-metallic band structure for the ferromagnetic Nd2/3Sr1/3MnO3. The ferromagnetic coupling between Ndand Mn sublattices is ascribed to the super-exchange interaction between Nd 4f and Mn 3d (t2g) electronsvia O 2p electrons.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

The mixed-valent manganites RE1−xAExMnO3 (where RE andAE are rare-earth and alkaline-earth elements) have been a pop-ular subject of contemporary research because of their abun-dant physical properties such as competing magnetic orderings,metal–insulator transition and colossal magnetoresistance. Lan-thanum manganites have been extensively studied in past years.Undoped LaMnO3 is an insulator with a strongly distorted or-thorhombic structure and A-type antiferromagnetic (AFM) order-ing [1]. In the region of 0.2 < x < 0.5, the AE-doped compoundsare ferromagnetic (FM) and metallic at low temperature [2,3]. Inparticular at the optimally doped composition (x ∼ 1/3), the com-pound shows very large magnetoresistance (up to 106%) aroundthe Curie temperature, and their electrons become fully spin-polarized at the Fermi level (EF), reach the so-called half-metallicstate [4].

At the constant optimal AE2+ doping level, substitution of La3+ions with smaller-sized rare-earth ions would decrease the tol-erance factor, and result in the suppression of double-exchangeinteraction and the increase of magnetoresistance ratio [5,6]. How-ever, the substitution would not only induce the lattice distortionbut also introduce extra magnetic coupling, due to the magneticmoments of rare-earth ions.

* Corresponding author. Tel.: +86 24 83687679; fax: +86 24 83687679.E-mail address: ririn@sohu.com (L. Li).

0375-9601/$ – see front matter © 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.physleta.2010.05.017

A characteristic dip was observed in the magnetization curveof Nd0.7Pb0.3MnO3 [7] and Nd0.7Ba0.3MnO3 [8] at low tempera-ture in low fields. Specific heat measurement of Nd2/3Sr1/3MnO3(NSMO) gives evidence of exchange interaction between Nd andMn spin systems [9]. The field-dependent magnetization curvesshow that such two-spin systems are difficult to achieve saturationmagnetization in the field of several Tesla [10–12]. Especially forLa0.7−yGd(Sm)ySr0.3MnO3 (y = 0.6 and 0.7) [11,12], the magneti-zation increases continuously with the increase of magnetic fieldand show less sign of saturation. Ghosh et al. [7,13] proposed thatNd and Mn sublattices may display spin-canted or ferrimagnetic(FiM) ordering, since the magnetic moments of Nd-based mangan-ites are considerably lower than the spin-only values of collinearspin arrangement of Nd and Mn sublattices. Snyder et al. [14]reported that a molecular field model with antiparallel spin ar-rangement of Gd and Mn sublattices can qualitatively explain themagnetic data of Gd0.67Ca0.33MnO3. However, neutron diffractionstudies [15,16] on Nd-based manganites show that the Nd andMn sublattices tend to order ferromagnetically below the order-ing temperature of Nd sublattice. The above-mentioned studiesindicate that the magnetic coupling between the rare-earth andMn sublattices of these rare-earth manganites is not fully under-stood.

First principle calculation is helpful to understand the anomalyphysical properties of these materials. Pandey et al. [17] performeda spin-unpolarized calculation on PrCoO3, and proved that theCoulomb interactions are important to 4f and 3d electrons. Anisi-

L. Zhu et al. / Physics Letters A 374 (2010) 2972–2979 2973

Fig. 1. Model of NSMO (Nd2Sr1Mn3O9) adopted in our calculations.

mov et al. [18] and Fujiwara and Korotin [19] focused their stud-ies on the spin, charge and orbital ordering in Mn sublatticesof Pr1−xCaxMnO3 and Nd1−xSrxMnO3. Pal et al. [20] predicted ahalf-metallic band structure for cubic FM Pr0.75Sr0.25MnO3. As faras we know, few reports focused on the magnetic coupling be-tween 4f and 3d electrons of the perovskite manganites. In thisLetter the magnetic and electronic structures of the perovskite ox-ide NSMO are explored in the frame work of density-functionaltheory. The composition x = 1/3 is chosen because the double-exchange interaction would be maximized at this composition [21].Our results are also compared with those of experimental stud-ies.

2. Computational details

The supercell Nd2SrMn3O9 is used to simulate NSMO in ourcalculation as seen in Fig. 1. Two distinct Mn sites occur in this su-percell: Mn1 site sandwiched between two Nd layers and Mn2 sitelying between Nd and Sr layers. Several possible magnetic order-ing structures in our study are exhibited in Fig. 2. For clarity onlyNd and Mn ions are depicted in that figure. Due to the stronger3d exchange interaction relative to that of 4f, we expect Mn–Mncoupling to be stronger than Nd–Mn, and Nd–Nd interaction tobe negligible. Hence the Nd sublattices are assumed to be FM inour calculations. Fig. 2(a) and (d) denote the antiparallel and par-allel spin alignment of Nd and Mn sublattices. It is also possible toobtain FiM configurations in which Mn1 and Mn2 align antiferro-magnetically (see Fig. 2(b) and (c)). These four magnetic orderingstructures are defined as FiM-1, FM, FiM-2 and FiM-3 respectively.The experimentally measured cubic perovskite structure with lat-tice constant 3.85 Å [22] is adopted.

Spin-polarized calculations are performed by means of the full-potential augmented plane waves plus local orbital (APW + lo)

(a)

(b)

(c)

(d)

Fig. 2. Several magnetic configurations of NSMO discussed in our calculations:(a) FiM-1; (b) FiM-2; (c) FiM-3; (d) FM. Only Nd and Mn are shown for clarity.

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Fig. 3. Partial density of states of Mn 3d, O 2p and Nd 4f states of FiM-1 NSMO. Spin-up (down) bands are depicted in the upper (lower) graph. The zero of the energy scaledenotes to the position of EF, the same as following figures.

Fig. 4. Total density of states of FiM-1, FiM-2, FiM-3 and FM NSMO under GGA.

L. Zhu et al. / Physics Letters A 374 (2010) 2972–2979 2975

Fig. 5. Total and partial density of states of FiM-1 NSMO under GGA + U : (a) U4f = 3 eV; (b) U4f = 9 eV. (c) Partial density of states of Nd 4f states as U4f = 3.5 eV and thephotoemission spectrum extracted from Ref. [29].

method, as implemented in WIEN2k code [23]. The exchange-correlation potential proposed by Perdew, Burke and Ernzerhof[24] is applied. In order to explore the influence of Coulomb in-teractions on the magnetic and electronic structures, GGA + U(SIC) [25] method is also applied for the calculation of Nd 4fand Mn 3d electrons. An effective parameter Ueff = U − J , whereU and J are the Coulomb and exchange parameters respectively,is adopted in the GGA + U calculation. For simplicity U is usedto denote the effective parameter in the following discussion, in-stead of Ueff. The value of U varies from 1 to 9 eV. Spin–orbitcoupling is incorporated in a second-variational way [26]. Further-more a relativistic p1/2 local orbital is employed for Nd element[27]. The basis sets are determined by a plane wave cutoff pa-rameter Rmt Kmax = 8.0, and 1000 k points is used in the wholeBrillouin zone. Self-consistency is achieved by demanding the con-vergence of total energy to be smaller than 10−5 Ry and charge tobe smaller than 10−4 e.

3. Results and discussion

The partial density of states (PDOS) of FiM-1 NSMO under GGAis depicted in Fig. 3. Strong hybridization between Mn 3d and O 2pstates is observed especially in spin-up channel. Two narrow peaksaround 1.5 and 1.0 eV below EF in Fig. 3(a) and (b) come from t2gstates of Mn1 and Mn2 respectively. That the t2g states are en-ergetically degenerate with O 2p states in valence-band indicatescovalent interaction between t2g and O 2p electrons. The remainingMn 3d bands broadly distributed due to the strong hybridizationcome from eg states. Nd 4f states exhibit a double-peak charac-ter around EF in spin-down channel, and lead to a metallic bandstructure (see Fig. 4). For FiM-2 (or FiM-3) phase, spin-antiparallelMn 3d states locate at EF in spin-up and spin-down channels re-spectively. Thus the total density of states (TDOS) of the FiM-2 (orFiM-3) phase also displays a metallic character. The TDOS of FM

phase, in which Nd and Mn sublattices are spin-parallel, shows atypical half-metallic band structure with a gap of about 1.4 eV inspin-down channel. It is reminiscent of the electronic structure oflanthanum manganites [28].

Usually local density approximation (LDA) and GGA methodsare not accurate for a proper description of f and d electrons. Asshown in Fig. 3, Nd 4f states under GGA cross over EF, conflictingwith those of photoemission spectrum [29]. Therefore the on-siteCoulomb interactions between Nd 4f electrons require being con-sidered in the calculation. Fig. 5 shows that the double peaks ofNd 4f states around EF split into lower and upper bands with theincrease of U4f. The lower component shifts towards lower energyregion and tends to localize in valence-band, while the upper com-ponent merges into conduction-band. The FiM-1 phase displays ahalf-metallic band structure with a gap of about 1.0 eV in spin-down channel as U4f = 2 eV (not depicted). The gap reaches amaximum value 1.4 eV and almost keeps constant as U4f � 3 eV(see Fig. 5(a)). The Coulomb interactions of Nd 4f electrons donot change the transport properties of the FiM-2, FiM-3 and FMphases. By a comparison with the photoemission spectrum [29] inFig. 5(c), we find that the parameter U4f = 3.5 eV is appropriateto describe the Coulomb interactions between Nd 4f electrons inNSMO.

The Coulomb interactions between Mn 3d electrons are ex-plored in Fig. 6, where the value of U3d varies from 1 to 9 eV whilethe value of U4f is fixed at 3.5 eV. With the increase of U3d, the oc-cupied t2g states move towards lower energy region. Moreover, thet2g characteristic peak close to EF is significantly suppressed butstrengthened around −6 (or −7) eV. This may be related to thestrong hybridization between Mn 3d and O 2p electrons, sincethe covalent bond peaks of eg electrons are also strengthened inthe same energy region. By a comparison with the photoemissionspectra [29–31], we adopt the parameter U3d = 5 eV to describethe electronic structure of Mn 3d states. In this case Nd 4f, Mn 3d

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Fig. 6. Mn 3d bands of FM NSMO: (a) U3d = 1 eV; (b) U3d = 3 eV; (c) U3d = 5 eV; (d) U3d = 9 eV. The value of U4f is fixed at 3.5 eV.

Table 1Calculated electronic states of NSMO under GGA and GGA + U (U4f = 3.5 eV, U3d = 0, 5 eV); total energy (meV) per formula unit relative to the ground state; spin andorbital moments in Nd, Mn1 and Mn2 spheres, total magnetic moment per formula unit (μB ) and experimental data.

State Energy Ndspin Ndorb Mn1spin Mn1orb Mn2spin Mn2orb Total

GGA FiM-1 0 −3.12 2.26 3.07 −0.01 2.97 −0.02 2.84FiM-2 18 3.16 −2.25 −2.94 0.01 2.97 −0.02 1.77FiM-3 23 3.15 −2.27 2.96 −0.01 −2.95 0.02 0.53FM 17 3.17 −2.33 3.14 −0.02 3.01 −0.02 4.06

GGA + U4f(U4f = 3.5 eV, U3d = 0 eV)

FiM-1 9 −3.06 2.69 3.12 −0.01 3.01 −0.02 3.24FiM-2 27 3.07 −2.69 −3.01 0.01 3.03 −0.02 1.42FiM-3 29 3.07 −2.69 3.00 −0.01 −3.03 0.02 0.91FM 0 3.07 −2.77 3.20 −0.01 3.07 −0.02 3.77

GGA + U4f(U4f = 3.5 eV, U3d = 5 eV)

FM 3.02 −2.89 3.63 −0.02 3.47 −0.02 3.71

GGA + U4f (pnma)(U4f = 3.5 eV, U3d = 5 eV)

FM 2.99 −1.41 3.55 −0.02 3.48 −0.02 4.70

Exp. Nd Mn Total

Nd0.7Ba0.1Sr0.2MnO3 (Ref. [32]) 0.37 3.47Nd0.7Sr0.3MnO3 (Ref. [16]) 0.78 3.42Nd0.7Pb0.3MnO3 (Ref. [7]) 3.8NdMnO3 (Ref. [36]) 1.2 3.22

and O 2p states are highly mixed in valence-band. The Coulombinteractions between 3d electrons do not qualitatively change theelectronic structure of NSMO as the value of U3d varies from 1 to9 eV.

The calculated total energy and electronic states of NSMO underGGA and GGA + U are summarized in Table 1. These results sug-gest that the value of U4f is important to obtain the energeticallyfavored magnetic ordering of such a two-spin system. Under GGAthe FiM-1 state is dominant over other three magnetic states. How-ever, the FiM-1 NSMO under GGA shows a metallic band structure,which conflicts with the typical half-metallic character of thesematerials, and Nd 4f electrons need the Coulomb interactions toemphasize the localized feature. As the parameter U4f = 3.5 eV,

the spins of Nd and Mn sublattices tend to be parallel in theground state. This is consistent with the neutron diffraction studieson Nd0.7Sr0.3MnO3 [15,16] and Nd0.7Ba0.7−ySryMnO3 (y � 0.05)[32], in which the FM contributions of Nd and Mn sublattices ap-pear below the Nd ordering temperature. Both GGA and GGA + Ucalculations demonstrate that the antiparallel spin arrangementbetween Mn ions is not energetically favored in these compounds[28].

The mechanism of the magnetic coupling between 4f and 3delectrons in rare-earth manganites is still not well understood. Inearlier studies on intermetallics of rare-earth and transition metals,the 4f–3d coupling was proposed as the RKKY-type exchange in-teraction via spin-polarized s-conduction electrons [33]. However,

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Fig. 7. Partial density of states of Nd 4f, Nd 5d, Mn 3d and O 2p states of FM (a) and FiM-1 (b) NSMO under GGA + U (U4f = 3.5 eV and U3d = 5 eV).

the applicability of this type exchange interaction is limited, sincethe sign of 4f–3d coupling in the intermetallics is invariable withdistance [34]. As for the rare-earth manganites, the outer shell selectrons of rare-earth elements are almost lost and unable to actas conduction electrons.

Recently the well accepted mechanism of 4f–3d magnetic cou-pling in the rare-earth-transition intermetallics is based on indirect4f–5d–3d exchange interaction [35], in which 5d electrons are po-larized by 4f moments via 4f–5d interaction, and 5d–3d interactionindirectly induces the 4f–3d coupling. It is considered that Nd 5dand Mn 3d electrons cannot interact directly in rare-earth man-ganites due to the lattice structure. If the 4f–5d–3d mechanismproposed for the intermetallics remains operative in rare-earthmanganites, O 2p electrons would mediate the 5d–3d interactionto form 4f–5d–2p–3d exchange interaction. Fig. 7 gives the PDOSof Nd 4f, Nd 5d, Mn 3d and O 2p of FM and FiM-1 NSMO ob-tained from GGA + U calculation with the optimal values of U4fand U3d. It can be seen that a few electrons occupy the empty 5d0

orbital and a spin splitting between the spin-up and spin-down 5dsubbands appears in valence-band. By a comparison of the DOSbetween the FiM-1 and FM phases (see Fig. 7(a) and (b)), it is

found that the spin splitting arises not from the 4f spins but fromthe hybridization of Nd 5d, Mn 3d and O 2p electrons. In addi-tion the spin splitting does not induce a net spin for 5d electrons.Both the spin-up and spin-down 5d electrons localize in valence-band and their occupancies in muffin-tin spheres are only 0.21 and0.18 respectively. Therefore, the mechanism of 4f–3d coupling inthe rare-earth manganites is different from that in the rare-earth-transition intermetallics.

Fig. 8 shows a U3d-dependent character of the energy differ-ence between the antiparallel and parallel spin arrangement of Ndand Mn sublattices (U4f = 3.5 eV). The energy difference increasessteeply with the increase of U3d (U3d < 5 eV), and increases grad-ually as U3d increases further. The PDOS of Mn 3d and Nd 4f ofFM NSMO are depicted in Fig. 9 to explore the relation betweenthe energy difference and the electronic structure. For clarity O2p states are not included. It is found that the energy differencebetween the FiM-1 and FM phases is closely related to the hy-bridization between Nd 4f and Mn t2g states via O 2p states. AsU3d = 1 eV, the main peaks of Nd 4f and Mn t2g states in Fig. 9(a)overlap slightly, and the hybridization is comparatively weak. Theweak hybridization leads to smaller energy difference. With the

2978 L. Zhu et al. / Physics Letters A 374 (2010) 2972–2979

increase of U3d (see Fig. 9(b) and (c)), Mn t2g peak shifts towardslower energy region, and overlaps with Nd 4f peak clearly. The sig-nificantly strengthened hybridization increases the energy differ-ence steeply. As U3d increases further (U3d > 5 eV), Nd 4f and Mnt2g states almost locate in the same energy region, the Mn t2g peakthat hybridizes with the Nd 4f peak is significantly suppressed, and

Fig. 8. U3d-dependent energy difference between FiM-1 and FM NSMO.

consequently the energy difference increases gradually. Therefore,we presume that the FM coupling between 4f and 3d electrons inNSMO arises from the 4f–2p–3d (t2g) super-exchange interactioninduced by strong hybridization of Nd 4f, Mn 3d and O 2p statesin valence-band.

The calculated magnetic moments including spin and orbitalcontributions are listed in Table 1. The orbital moment of Mnmostly coming from the 3d orbital polarization is estimated tobe no more than 0.02μB . The near-zero orbital moments maybe ascribed to the crystal-field that quenches orbital angular mo-mentum. The calculated moments of Mn basically agree with theexperimental data. Most of the orbital moment of Nd comes fromthe orbital polarization of 4f electrons. The opposite signs of thespin and orbital moments are consistent with Hund’s rule in caseof the rare-earth ions with less than half-filled f shells. The largeminus orbital moments of Nd 4f would lead to lower experimentalmagnetic moments [7,13] besides the possible spin-canted order-ing. It can be observed in Table 1 that the experimental magneticmoments of Nd exhibit a significant variation in homologous com-pounds. One of the possible origins of the variation is the existenceof spin-canted ordering. We consider that another possible originis the influence of crystal-field on the orbital moments. To val-idate this inference, an additional calculation of NSMO with anorthorhombic structure (pnma space group) given in Ref. [16] isperformed. The results are also listed in Table 1. The calculatedorbital moments of Nd 4f in the cubic and the orthorhombic struc-

Fig. 9. Partial density of states of Nd 4f and Mn 3d of FM NSMO under GGA + U : (a) U3d = 1 eV; (b) U3d = 3 eV; (c) U3d = 5 eV; (d) U3d = 9 eV. The value of U4f is selectedas 3.5 eV.

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tures are −2.89μB and −1.41μB respectively, while the spin mo-ments almost keep constant.

4. Conclusions

First principle calculations are performed on Nd2/3Sr1/3MnO3by using GGA and GGA + U methods. By a comparison betweencalculated results and available experimental data, it is found thatthe Coulomb interactions between 4f electrons are necessary todescribe the magnetic and electronic structures of these materi-als. Under GGA + U the moments of Nd and Mn sublattices tendto be parallel in the ground state. Due to the localized feature ofNd 4f states, the band structure around the Fermi level is dom-inated by Mn 3d and O 2p states, which produce a half-metalliccharacter for the ferromagnetic phase. Nd 4f, Mn 3d and O 2pstates strongly hybridize in valence-band, inducing the 4f–2p–3d(t2g) super-exchange interaction that favors ferromagnetic couplingbetween Nd 4f and Mn 3d electrons.

Acknowledgement

This work is supported by the Natural Science Foundation ofLiaoning Province (Grant No. 2006222002).

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