PDF Magnetism, conductivity, and orbital order in (LaMnO3)2nÕ(SrMnO3 ... - NJU

Magnetism, conductivity, and orbital order in (LaMnO

)

Õ (SrMnO

)

superlattices

Shuai Dong,^1,2,3Rong Yu,^1,2Seiji Yunoki,^4,5Gonzalo Alvarez,⁶J.-M. Liu,³and Elbio Dagotto^1,2

1Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA

2Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 32831, USA

3Nanjing National Laboratory of Microstructures, Nanjing University, Nanjing 210093, China

4Computational Condensed Matter Physics Laboratory, RIKEN, Wako, Saitama 351-0198, Japan

5CREST, Japan Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan

6Computer Science and Mathematics Division and Center for Nanophase Materials Science, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

共Received 8 October 2008; published 21 November 2008兲

The modulation of charge density and spin order in 共LaMnO₃兲2n/共SrMnO₃兲n 共n= 1 – 4兲 superlattices is studied via Monte Carlo simulations of the double-exchange model.G-type antiferromagnetic barriers in the SrMnO₃regions with low charge density are found to separate ferromagnetic LaMnO₃layers with high charge density. A metal-insulator transition with increasingnis observed in the direction perpendicular to the inter- faces. Our simulations provide insight into how disorder-induced localization may cause the metal-insulator transition occurring atn= 3 in experiments.

DOI:10.1103/PhysRevB.78.201102 PACS number共s兲: 71.30.⫹h, 73.21.Cd, 75.47.Lx

Transition-metal oxide heterostructures provide a new av- enue to utilize the complex properties of strongly correlated electronic materials to produce multifunctional devices. Sev- eral exotic phenomena emerge in these heterostructures due to the reconstruction at the interfaces, such as the existence of a conducting state between two insulators in LaAlO₃/SrTiO₃ 共STO兲and LaTiO₃/SrTiO₃.¹As one of the most representative families of strongly correlated oxide ma- terials, the manganites can also be prepared into heterostruc- tures with other oxides, such as cuprates, and they exhibit interesting behavior, such as orbital reconstruction.²

Even without involving other oxides, manganite hetero- structures can be prepared utilizing manganites with different doping, e.g., LaMnO₃共LMO兲and SrMnO₃共SMO兲.^3–8At low temperature 共T兲, bulk LaMnO₃ is an A-type antiferromag- netic共A-AFM兲insulator, while SrMnO₃ is aG-type antifer- romagnetic 共G-AFM兲 insulator.⁹ The alloy-mixed La_1−xSrxMnO₃共LSMO兲is a ferromagnetic共FM兲metal at low T and 0.17⬍x⬍0.5. However, the LMO-SMO superlattices can behave differently from bulk LSMO even with the same average charge density: 共i兲 the ordered A-site cations in the superlattices remove the A-site disorder, which is important in alloy manganites and 共ii兲the artificially modulatedA-site cations also modulate the physical properties, such as charge density, magnetism, and conductivity. In fact, recent experi- ments on共LMO兲2n/共SMO兲nsuperlattices highlighted the ex- istence of an exotic metal-insulator transition 共MIT兲 at n= 3.^5–8Moreover, LMO thin films on a STO substrate were found to be FM instead ofA-AFM.^7,8

Theoretically, in addition to ab initiocalculations,¹⁰most previous model Hamiltonian investigations on manganite heterostructures were based on the one-orbital model,¹¹miss- ing the important orbital degree of freedom. Although more realistic two-orbital models were used very recently,^12,13sev- eral properties of the共LMO兲2n/共SMO兲nsuperlattices are still not understood particularly the explanation for then= 3 MIT.

The two-orbital double-exchange共DE兲model is used here to study 共LMO兲_2n/共SMO兲n superlattices via Monte Carlo

共MC兲simulations. This model Hamiltonian has been exten- sively studied before and it is successful to reproduce the several complex phases in manganites.¹⁴ Details about the Hamiltonian and MC technique can be found in previous publications.¹⁵ Schematically, the Hamiltonian reads as

H=H_DE共t0兲+H_SE共JAF兲+H_EP共␭兲+

兺

whereH_DE,H_SE, andH_EPare the standard two-orbital large- Hund-coupling DE, superexchange 共SE兲, and electron- phonon 共EP兲 interactions, respectively.¹⁴ ni is the eg charge density at sitei.␮is the uniform chemical potential, and⑀iis the on-site effective potential generated by long-range Cou- lomb interactions that cannot be neglected in superlattices involving different electronic compositions. There are four main input parameters: the SE couplingJ_AF, the EP coupling

␭,␮^{, and}⑀i. All these parameters are in units oft₀, which is the DE hopping between nearest-neighbor共NN兲d_3z²_−r²orbit- als along thezdirection.^14,15The constant-density phase dia- gram is determined by J_AF and ␭. The expected e_g charge density is obtained by tuning ␮. Due to the valence differ- ence between La³⁺and Sr²⁺, the on-site Coulomb potential⑀i

is inhomogeneous for the Mn sites. In almost all previous model investigations, the Coulomb interaction is treated us- ing the Hartree-Fock共HF兲approximation.^11–13However, this HF approximation is rather difficult to converge for the three-dimensional 共3D兲 two-orbital model when both t_2g classical spins and lattice distortions are also MC-time evolving. For this reason, here we adopt another strategy.

Each ⑀i will be determined by its eight NN A-site cation neighbors.¹⁶ More specifically, in the LMO-SMO superlat- tices, ⑀i is 0 for those Mn between two LaO planes 共LMO region兲, it becomes V/2 for those between LaO and SrO planes, and finally it isV for those between two SrO planes 共SMO region兲 关Figs.1共a兲and1共b兲兴. Therefore, this共positive兲 constant V is the only parameter to regulate the Coulomb potential and it is related with the dielectric constant in the PHYSICAL REVIEW B78, 201102共R兲 共2008兲

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HF approach. Our approximation is expected to capture the main physics in the LMO-SMO superlattices since the effec- tive Coulomb potential is mainly caused by the modulation ofA-site cations, and we believe that our qualitatively simple results shown below do not depend on these assumptions.

The Coulomb screening by the eg electron redistribution is also taken into account in part by regulating the value ofV.

In our simulation, four sets of V: 0.3, 0.6, 0.9, and 1.2 are used, covering the realistic potential drop range between LMO and SMO. The important practical fact is that this ap- proximation enables the MC simulation on large enough lat- tices.

For our studies, we use 3D 共Lx⫻Ly⫻Lz兲 clusters with periodic boundary conditions共PBCs兲. BothLxandLyare set to 4, while Lz equals 3n 共1ⱕnⱕ4兲. Thus, the superlattices are grown along thezdirection共关001兴兲 关Figs.1共a兲and1共b兲兴. The MC simulation on the 4⫻4⫻12 lattice is already at the cutting edge of current computational resources. To charac- terize physical properties, the charge density, spin structure factors, and conductivity are calculated.^15,17

Before the simulation of superlattices, it is essential to understand why the LMO thin films on STO are experimen- tally found to be ferromagnetic, instead ofA-AFM. For most RMnO₃ 共R= La, Pr, Nd, Sm, and Eu兲, the A-AFM phase is the ground state.¹⁸ However, in the previously obtained the- oretical phase diagram for the two-orbital DE model, the A-AFM regime was found to be rather narrow in parameter space, while the FM orbital-ordered共OO兲phase was clearly more robust.¹⁹ Thus, to understand the FM nature of LMO thin films, we should consider lattice distortions in real man- ganites. In the bulk, the LMO lattice transits from a cubic perovskite to an orthorhombic one at T⬃800 K, below which the lattice constant along thecaxis shortens compared with those along the a and b axes.²⁰ For instance, at T

= 300 K, l_c is only ⬃0.964l_ab, where l_c 共l_ab兲 is the NN Mn-Mn distance along the c axis 共within the a-b plane兲.

Using an empirical formula by Zhou and Goodenough,²¹the AFM exchange intensity along c becomes about 1.3 times that on the a-b plane. Thus, this stronger AFM coupling alongcwill favor theA-AFM state. However, for LMO thin films on STO, the LMO lattice is compressed in the a-b plane but it is elongated along the caxis, leading to an al- most cubic crystal structure.⁴Therefore, the theoretical phase diagram,¹⁹ derived assuming lattice isotropy, should be ap- plicable to the LMO thin films that prefer the FM OO phase instead of theA-AFM one.

Following the theoretical phase diagram,¹⁹ here we choose a particular set of parameters共JAF= 0.09, ␭= 1.2兲for the simulation below. To justify this choice, first we perform a MC calculation on a 4⫻4⫻4 lattice 共PBCs兲 with all ⑀i

= 0 to examine whether the above parameters are suitable for LSMO. The eg charge density ni, NN spin correlation 共具Si·Sj典兲, and conductivity are calculated at lowT 共T= 0.01兲 共⬃60 K ift₀⬃0.5 eV兲, as shown in Fig.1共c兲. Forni⬃1, the phase is found to be FM but insulating, in agreement with the results found for experimental LMO thin films. The en- ergy gap at the Fermi level is 0.3 共⬃150 meV兲, which is compatible with the experimental excitation energy 共⬇125 meV兲.⁷The insulating character of the state is caused by orbital ordering driven by Jahn-Teller distortions.²²In the density range 0.5⬍ni⬍0.8, the system is FM and conduct- ing, also in agreement with the LSMO properties at the cor- responding dopings. For ni⬍0.5, the NN spin correlations turn out to be negative, suggesting an AFM phase. The con- ductivity becomes poor with decreasingniuntil it reaches an insulating state. This ni⬍0.5 behavior is also compatible with LSMO at the corresponding doping. Then, as a conclu- sion, the setJ_AF= 0.09 and␭= 1.2 should be a proper param- eter set to describe 共cubic兲LSMO. Below, we will use this set to study the共LMO兲2n/共SMO兲n superlattices.

FIG. 2.共Color online兲 共a兲Charge modulation in the superlattices with differentV’s共the case of L2S1 withV= 1.2 cannot be obtained due to phase separation兲. The two horizontal lines denote 0.5 and 2/3.共b兲In-plane spin structure factor forV= 0.9. In共a兲and共b兲, pink bars denote SrO layers in the共LMO兲2n/共SMO兲nsuperlattice, while LaO layers are not highlighted. The lattices are simply repeated along thezdirection if their periods are shorter than 12.

FIG. 1. 共Color online兲 共a兲 Superlattice unit studied here. 共b兲 On-site potential used in our simulation.共c兲Thee_gcharge density, NN spin correlation, and conductivity共see Ref.17for its units兲of a 4⫻4⫻4 lattice vs␮atT= 0.01. All ⑀iare set to zero to simulate bulk clean-limit LSMO.

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We will focus first on the low-T共=0.01兲MC results which can shed light on the ground-state properties. The local eg

charge densities of each layer vs layer index are shown in Fig.2共a兲. For共LMO兲2/共SMO兲1共L2S1兲, the charge distribu- tion is fairly uniform despite the use of substantial values for V 共0.3–0.9兲; namely, the local charge density fluctuates weakly around the average of 2/3. This is easy to understand since there is no SMO region in the L2S1 superlattice and, thus, the potential fall here is only V/2. For other superlat- tices, and usually共V⬎0.3兲, the densities in the SMO regions are lower than 0.5. TheV= 1.2 case already restricts most of the eg electrons to be in the LMO regions, whileV= 0.3 is low enough that it spreadsegelectrons to the SMO regions.

Therefore, it is reasonable to conclude that the potential am- plitude range used in our model is the proper one to cover the potential drop in real manganites. In the following, we will focus on the caseV= 0.9, for which the results are simi- lar to the experimental data.

Figure 2共b兲 shows thex-y plane spin structure factors vs layer index forV= 0.9 andT= 0.01. There are only two main components: FM and G-AFM. The latter exists only in the SMO regions, while FM dominates in the LMO regions, and at the LMO/SMO interfaces. This spin arrangement agrees with experiments.^6,7 Our calculated spin order supports the idea that the local phases in superlattices are mainly deter- mined by the local densities n_local.¹³ If n_local⬎0.5, the spin order is FM, and it is G-AFM when n_local⬇0. Therefore, other spin orders, e.g.,A-AFM orC-AFM, may emerge once the n_local is slightly lower than 0.5. In fact, we observed the coexistence of several complex spin orders at, e.g., the SMO region共nlocal⬇0.15兲for L8S4 withV= 0.9关Fig.2共b兲兴.

One of the most important experimental discoveries in the 共LMO兲2n/共SMO兲nsuperlattices is the MIT with increasingn.

To try to understand this phenomenon, here two conductivi- ties共only from the DE process兲 are calculated vsT: the in- plane one共along thexor ydirection兲and the perpendicular one共along thezdirection兲, as shown in Figs.3共a兲and3共b兲.

All in-plane conductivities are robust and increase with de- creasing T, suggesting metallicity. Our result agrees with previous studies showing that the charge transfer at inter- faces between Mott and band insulators can generate con- ducting interfaces.^1,11In contrast, the perpendicular conduc- tivities show metallic behavior when nⱕ2, but insulating behavior when nⱖ3. To understand this MIT, the spin ar- rangement at the FM/G-AFM interface should be considered.

The intralayer NN spin correlations 共not shown here兲 con- firm that spins at the FM/G-AFM interfaces are almost col- linear at lowT, namely, the NN spins are parallel or antipar- allel, as shown in Fig. 3共c兲. Therefore, when there is only one G-AFM layer in each superlattice unit 共n= 2兲, the spin-up channels of theG-AFM layer link the NN FM layers, allowing for a good conductance. However, once the SrO layers thickness is 3, the two G-AFM layers cut off the same-spin channels, giving rise to an insulating behavior along the zdirection. Therefore, it is natural to expect that n= 3 must be the MIT critical point in 共LMO兲2n/共SMO兲n

superlattices.

However, it should be noted that the experimental resis- tance measurements were performed using the four-point method 关Fig. 3共d兲兴.^6,7 Thus, to understand the experimental MIT, Anderson localization effects should also be consid- ered. When nⱖ3, as mentioned before, the DE conducting process becomes exclusively two-dimensional-like 共within the x-y plane兲. In this case, insulating behavior may be in- duced by interface disorder, such as roughness, and Ander- son localization, as discussed in the experimental literature.⁷ But a 3D metallicity in the nⱕ2 superlattices, avoiding the Anderson localization mechanism, can be achieved by the DE process perpendicular to the interfaces, as shown sche- matically in Fig.3共d兲. In short, although the in-plane conduc- tivity is metallic in our small lattices without disorder, the criticalnfor the real superlattices MIT may still correspond to the same value found in our simulations via studies of the perpendicular conductivity.

FIG. 3.共Color online兲 共a兲In-plane conductivity for the superlat- tices studied here.共b兲Perpendicular conductivity.共c兲Sketch of the spin order at interfaces for L4S2共left兲and L6S3共right兲.共d兲Sketch of experimental setup for resistance measurements. Pink bars are SMO regions. Typical conducting paths via the DE process共black curves兲 connect NN interfaces, but they will be broken when n ⱖ3.

FIG. 4. 共Color online兲 共a兲 Orbital occupation of the sixth to ninth layers for L6S3 whenV= 0.9 andT= 0.01. The sixth and ninth are interface layers between the LaO and SrO layers, while the seventh and eighth are within the SMO region. Here the circle’s area is proportional to the local e_g charge density. 共b兲 Sketch of orbital ordering at the interface forn= 2 and 3.

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The spin configuration in Fig.3共c兲can also induce orbital order near the interfaces. It should be pointed out that the strain or stress due to the lattice mismatch between substrates and LMO/SMO can induce orbital order, even without charge transfer.¹⁰However, here we propose that the parallel spin channels can provide another driving force for orbital order in manganite superlattices. Our simulations in the n

= 2, 3, and 4 cases show that the eg electrons have more tendency to occupy the d_3z²_−r² orbital than the dx²−y² one around the interfaces . One example is shown in Fig.4. This orbital order optimizes the DE process between the FM re- gions via the G-AFM layers. But in real superlattices the combined effect of this spin-driven tendency to orbital order and that induced by strain or stress may compete and more quantitative calculations will be needed to decide which or- bital order dominates.

We have studied the two-orbital double-exchange model for the 共LMO兲_2n/共SMO兲n superlattices. First, we have ex- plained why the LMO thin films on STO are FM instead of

A-AFM. Then, our simulations showed that the spin order in the SMO regions is G-AFM, while it is FM elsewhere. The spin arrangement between the FM andG-AFM layers causes a metal-insulator transition, with n= 3 as the critical value, which may explain the experimental results.

ACKNOWLEDGMENTS

We thank A. Bhattacharya, S. May, M. Daghofer, and S.

Okamoto for helpful discussions. This work was supported by the NSF under Grant No. DMR-0706020 and the Division of Materials Science and Engineering, U.S. DOE, under con- tract with UT-Battelle, LLC. S.Y. was supported by CREST- JST. G.A. was supported by the CNMS, sponsored by the Scientific User Facilities Division, BES-DOE. J.-M.L. was supported by the 973 Projects of China 共Grant No.

2006CB921802兲 and NSF of China 共Grant No. 50832002兲.

S. D. was supported by the China Scholarship Council.

1M. Huijben, G. Rijnders, D. H. A. Blank, S. Bals, S. V. Aert, J.

Verbeeck, G. V. Tendeloo, A. Brinkman, and H. Hilgenkamp, Nature Mater. 5, 556 共2006兲; A. Ohtomo and H. Y. Hwang, Nature共London兲 427, 423共2004兲; A. Ohtomo, D. A. Muller, J.

L. Grazul, and H. Y. Hwang,ibid., 419, 378共2002兲; S. Okamoto and A. J. Millis, ibid., 428, 630 共2004兲; E. Dagotto, Science

318, 1076共2007兲.

2J. Chakhalian, J. W. Freeland, H. -U. Habermeier, G. Cristiani, G. Khaliullin, M. V. Veenendaal, and B. Keimer, Science 318, 1114共2007兲.

3T. Koida, M. Lippmaa, T. Fukumura, K. Itaka, Y. Matsumoto, M.

Kawasaki, and H. Koinuma, Phys. Rev. B 66, 144418共2002兲.

4A. Bhattacharya, X. Zhai, M. Warusawithana, J. N. Eckstein, and S. D. Bader, Appl. Phys. Lett. 90, 222503共2007兲.

5Ş. Smadici, P. Abbamonte, A. Bhattacharya, X. Zhai, B. Jiang, A. Rusydi, J. N. Eckstein, S. D. Bader, and J. M. Zuo, Phys.

Rev. Lett. 99, 196404共2007兲.

6S. J. May, A. B. Shah, S. G. E. te Velthuis, M. R. Fitzsimmons, J. M. Zuo, X. Zhai, J. N. Eckstein, S. D. Bader, and A. Bhatta- charya, Phys. Rev. B 77, 174409共2008兲.

7A. Bhattacharya, S. J. May, S. G. E. te Velthuis, M. Waru- sawithana, X. Zhai, B. Jiang, J. M. Zuo, M. R. Fitzsimmons, S.

D. Bader, and J. N. Eckstein, Phys. Rev. Lett. 100, 257203 共2008兲.

8C. Adamo, X. Ke, P. Schiffer, A. Soukiassian, W. Waru- sawithana, L. Maritato, and D. G. Schlom, Appl. Phys. Lett. 92, 112508共2008兲.

9E. Wollan and W. Koehler, Phys. Rev. 100, 545 共1955兲; O.

Chmaissem, B. Dabrowski, S. Kolesnik, J. Mais, D. E. Brown, R. Kruk, P. Prior, B. Pyles, and J. D. Jorgensen, Phys. Rev. B

64, 134412共2001兲.

10B. R. K. Nanda and S. Satpathy, Phys. Rev. B 78, 054427 共2008兲.

11S. S. Kancharla and E. Dagotto, Phys. Rev. B 74, 195427 共2006兲; C. Lin, S. Okamoto, and A. J. Millis, ibid. 73, 041104共R兲 共2006兲; S. Yunoki, E. Dagotto, S. Costamagna, and J.

A. Riera,ibid. 78, 024405共2008兲; I. González, S. Okamoto, S.

Yunoki, A. Moreo, and E. Dagotto, J. Phys.: Condens. Matter 20, 264002共2008兲.

12L. Brey, Phys. Rev. B 75, 104423共2007兲; M. J. Calderón, J.

Salafranca, and L. Brey,ibid. 78, 024415共2008兲.

13C. Lin and A. J. Millis, Phys. Rev. B 78, 184405共2008兲.

14E. Dagotto, T. Hotta, and A. Moreo, Phys. Rep. 344, 1共2001兲.

15S. Dong, R. Yu, S. Yunoki, J. M. Liu, and E. Dagotto, Phys. Rev.

B 78, 064414共2008兲.

16G. Bouzerar and O. Cépas, Phys. Rev. B 76, 020401共R兲 共2007兲.

17J. A. Vergés, Comput. Phys. Commun. 118, 71共1999兲. The con- ductance via DE processes is calculated using the Kubo formula, in units ofe²/h.

18J. S. Zhou and J. B. Goodenough, Phys. Rev. Lett. 96, 247202 共2006兲.

19T. Hotta, M. Moraghebi, A. Feiguin, A. Moreo, S. Yunoki, and E. Dagotto, Phys. Rev. Lett. 90, 247203共2003兲.

20J. Rodríguez-Carvajal, M. Hennion, F. Moussa, A. H. Moudden, L. Pinsard, and A. Revcolevschi, Phys. Rev. B 57, R3189 共1998兲.

21J. S. Zhou and J. B. Goodenough, Phys. Rev. B 77, 132104 共2008兲.

22T. Hotta, S. Yunoki, M. Mayr, and E. Dagotto, Phys. Rev. B 60, R15009共1999兲. The orbital ordering in strained cubic LMO is slightly different from thed_3x2−r²/d_3y2−r²pattern in the bulk.

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