Letter to the Editor

Strongly reduced band gap in NiMn2O4 due to cation exchange

Jhih-Rong Huang a, Han Hsu b, Ching Cheng a,n

a Department of Physics, National Cheng Kung University, Tainan 70101, Taiwanb Department of Physics, National Central University, Jhongli City, Taoyuan 32001, Taiwan

a r t i c l e i n f o

Article history:Received 10 May 2013Received in revised form20 January 2014Available online 31 January 2014

Keywords:Nickel manganiteDensity functional calculation

a b s t r a c t

NiMn2O4 is extensively used as a basis material for temperature sensors due to its negative temperaturecoefficient of resistance (NTCR), which is commonly attributed to the hopping mechanism involvingcoexisting octahedral-site Mn4þ and Mn3þ . Using density-functional theory þ Hubbard U calculations,we identify a ferrimagnetic inverse spinel phase as the collinear ground state of NiMn2O4. By a 12.5%cation exchange, a mixed phase with slightly higher energy can be constructed, accompanied by theformation of an impurity-like band in the original 1 eV band gap. This impurity-like band reduces the gapto 0.35 eV, suggesting a possible source of NTCR.

& 2014 Elsevier B.V. All rights reserved.

Nickel manganite, NiMn2O4 (NMO), has long been broadly used asa basis material for temperature sensors due to the negativetemperature coefficient of resistance (NTCR) [1]. The NTCR exhibitsa uniform exponential decrease with increasing temperature which,however, is inferred as distinct from the transport property based onthe extended-state model for the tetrahedral-bonded semiconduc-tors [1]. NMO's electrical property is commonly accounted for by thehopping mechanism of the local charges originating from the Mn4þ

and Mn3þ cations on the octahedral sites of the structure, i.e. mixedvalency [2]. Recently NMO is also considered in the magnetic tunneljunction for future spintronic application [3] and as a catalyst forozone decomposition at room temperature [4].

In this letter, we performed spin density functional theory þHubbard U (DFTþU) [5,6] calculations to investigate the collinearphases of NMO through exploring various cation distributions andmagnetic orders in the material. We demonstrate that the cationexchange in the lowest-energy phase, i.e. a ferrimagnetic inversespinel structure, introduces an impurity-like band within the originalband gap which could contribute to the observed NTCR of thematerial.

NMO crystallizes in the cubic spinel structure which consists ofcations filling the tetrahedral and octahedral site (denoted as A and Bsite respectively hereafter) in the fcc sublattice of oxygen. Unlike thepure normal spinel materials such as ZnFe2O4 with all the A sitesbeing occupied by the Zn cation, or the inverse ones such as NiFe2O4

with all the Ni cations occupying the B sites (denoted with aninversion parameter δ of 100%), NMO generally crystallizes in a mixedphase, i.e. Ni occupying mainly, but not completely, the B sites.

Depending on the material preparation and thermal history, the δ inNMO usually scatters between 74% and 95% [7].

Throughout this study, a 56-atom supercell (8 formula units) isused in order to investigate the ionic and magnetic interactionsbetween cations. The cations (or spin configurations) at B sites areequally divided into two groups (denoted as B1 and B2 hereafter)and three different distributions (SC1–SC3) are generated for thepresent study [8]. Both the cation arrangements and magneticorders can be created according to the three distributions. Thestructures of NMO are denoted as, e.g. I3ppn (N3ppn), whichcorresponds to the inverse (normal) spinel structure with the SC3distribution of cations (spin configurations) at B site. The corre-sponding cation types and magnetic orders are listed in Table 1.The following notations, e.g. B1(Mn) and Mn(B1), will be usedhereafter for the particular site (B1 sites occupied by Mn cations)and cation (Mn cations occupying B1 sites) respectively. As boththe B1 and B2 sites are occupied by Mn ions in the normal spinelstructures, all the different B-site distributions for the magneticorders of pnn and ppp correspond to the same structure and aresimply denoted with Npnn and Nppp. In the inverse spinelstructures, the SC3 distribution is found to be more stable thanthe SC1 and SC2 ones by more than 100 meV/fu for the phaseswith the same magnetic order. Consequently the following dis-cussions for the inverse spinel phases will focus on the structureswith the SC3 distribution.

In this study, most of the calculations use the plane-wave-based Vienna ab initio simulation program [9] with the generalizedgradient approximation for the exchange-correlation energy func-tional [10]. The interaction between ions and valence electrons isdescribed by the projector augmented wave method [11] and thenumbers of valence electrons included for Ni, Mn and oxygen are10, 7 and 6 respectively. For the transition-metal elements, theDFTþU approach is employed to cover the strong correlation of

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Journal of Magnetism and Magnetic Materials

0304-8853/$ - see front matter & 2014 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jmmm.2014.01.048

n Corresponding author.E-mail address: ccheng@mail.ncku.edu.tw (C. Cheng).

Journal of Magnetism and Magnetic Materials 358-359 (2014) 149–152

the d-orbital electrons [6]. This scheme incorporates a spheri-cally averaged Hubbard parameter U for the on-site Coulombinteraction in the localized d orbitals and a parameter J for thescreened exchange energy into the standard DFT methods. The Jvalues were shown to be weakly dependent on the valenceconfiguration [12]. In this study, J¼0.7 eV is adopted for both Niand Mn. In contrast, a wide range of Hubbard U (4–7 eV) is appliedto Mn and Ni to examine its possible effect.

To further ensure the accuracy of our study, we also computethe Hubbard U from the first principle using a linear responseapproach [13] in a self-consistent manner [14,15], currently imple-mented in the Quantum ESPRESSO package [16]. Referred to asself-consistent U (USC), this method has successfully found theground state of various transition-metal compounds [15,17].To compute USC, as detailed in Ref. [15] and its SupplementalMaterial, we start with a DFTþU calculation with a trial U (Uin) tostabilize the desired state. By perturbing the local potential of theNi or Mn site with the Hubbard potential held fixed, a new U (Uout)can be extracted from the linear response of the local electronoccupation to the local perturbation and will be used as the newUin for the next iteration. The procedure is repeated until a self-consistency is achieved, namely, Uin ¼Uout . For the NMO system,the computed USC's are 5.0 and 5.3 eV for the Ni(A) and Mn(B) ionsin the Npnn phase and 4.4, 5.3 and 4.6 eV for the Mn(A), Mn(B1)and Ni(B2) ions in the I3ppn phase. The set of USC values aretherefore within the range of U values we included in this study.

All the self-consistent calculations are converged until the totalenergy difference between electronic iterations being smaller than10�4 eV per cubic cell (56 atoms). The energy cutoff that deter-mines the number of plane waves is 400 eV, and the k-pointsampling according to Monkhorst-Pack [18] is (4�4�4). Atomicrelaxation is implemented until the atomic forces are less than0.02 eV/Å and the cell volume is also relaxed while keeping theunit cell in cubic symmetry. Tests on higher energy cutoff (500 eV)and denser Mohkhorst-Pack mesh (6�6�6) show that the energydifference between the lowest-energy phases of the normal andinverse spinel NFO (498 meV/fu) are converged to within 3 meV/fuin the case using 4 and 5 eV for UNi and UMn. The lattice constantsfor all the studied phases, irrespective of the U values, are found tobe all within 1% deviation of the experimentally reported room-temperature value of 8.40 Å [19].

The most stable structure is identified as the I3ppn phase which islower in energy than the most stable normal spinel phase Npnn bymore than 400 meV/fu, regardless of the size of the U values used inthis study (Fig. 1). This result is consistent with the fact that thedominant contribution observed experimentally for NMO is theinverse spinel structure. The second lowest energy phase can be eitherI3ppp or I3pnn, depending on the U values. For the cases with UNioUMn as well as USC, I3ppp is the second lowest energy phase. Note that,the magnetic moments of these two phases are very different, i.e. 10and 0 μB=fu for I3ppp and I3pnn respectively. For the normal spinelstructures, the energies in order from lowest to highest are Npnn,N3pnp, N1pnp, N2pnp and Nppp, regardless of the U values.

The magnetic property of bulk NMO involves two magnetictransitions as temperature decreases, i.e. from the high-temperatureparamagnetic to the collinear ferrimagnetic phase at �145 K for singlecrystal NMO [20] followed by the second transition to the proposedcanted phase at �70 K [21]. The magnetic moment estimated fromthe magnetic susceptibility measurement at high temperature rangesfrom 6.27 to 6:9 μB=fu and the saturation moment at low temperatureis around 1 μB=fu [20–22]. The low saturation moment is usuallyattributed to either compensated moments between the normal andinverse phase or the canted order [20–22]. However, there has neverbeen any discussion about how the ferrimagnetic order of the Ni andMn cations can lead to a magnetic moment larger than 6 μB=fu.

The calculated total magnetic moments of all the studiedphases are independent of the U values and can be accountedfor by the proposed integer local moments as listed in Table 1.The different U values would modify the presented local momentsfor the cations listed in Table 1 by at most 70:2 μB. The proposedinteger local moments imply the valences of Mn2þ(A), Mn4þ(B1)and Ni2þ(B2) in the inverse spinel phases and Ni2þ(A) andMn3þ(B) in the normal spinel phases. Both the lowest-energyphases of the inverse and normal spinel structures, i.e. I3ppn andNpnn, have a moment of 6 μB=fu. The second-lowest energy phasein the case with USC is I3ppp which is 102 meV/fu higher in energythan the lowest-energy phase I3ppn and has a total moment of10 μB=fu. That the experimentally deduced magnetic moment ofNMO is higher than 6 μB=fu [20–22] could be due to the presenceof a slight portion of the I3ppp phase in the mixed NMO samples.

The exchange interactions between cations can be determinedby applying the Heisenberg model: H ¼ �∑i4 jJijSi � Sj to theevaluated total energies of the considered phases. Note that wehave taken the proposed integer local moments listed in Table 1 asone (Si¼1) in this analysis. That is, the exchange interactioncorresponds to half of the energy required to flip a local momentif only one neighbor is present.

Table 1The notations and the corresponding cations and magnetic orders of the normal and inverse spinel phases considered in the present study. Also included are the calculatedtotal moment mT (in unit of Bohr magneton per formula, i.e. μB=fu) of these phases and the calculated as well as the proposed integer (mI) local moments for the cations (inunit of μB).

Normal spinel Inverse spinel

site ion Npnn Nppp N1pnp N2pnp N3pnp mI site ion I3pnn I3ppp I3pnp I3ppn mI

A Ni þ1.7 þ1.8 þ1.8 þ1.8 þ1.8 2 A Mn þ4.6 þ4.5 þ4.6 þ4.5 5B1 Mn �3.9 þ3.9 �3.9 �3.9 �3.8 4 B1 Mn �3.0 þ3.4 �3.0 þ3.4 3B2 Mn �3.9 þ3.9 þ3.9 þ3.9 þ3.8 4 B2 Ni �1.7 þ1.7 þ1.7 �1.7 2

mT (μB=fu) 6 10 2 2 2 mT (μB=fu) 0 10 4 6

Fig. 1. The calculated energies of the studied normal and inverse spinel phases ofNMO at different U values. The energy of the lowest-energy phase, i.e. I3ppn,is taken as zero.

J.-R. Huang et al. / Journal of Magnetism and Magnetic Materials 358-359 (2014) 149–152150

With the total energies of the four magnetic orders consideredin this study for the inverse spinel phases, i.e. I3pnn, I3ppp, I3pnp,and I3ppn, three exchange interactions can be derived. They are allinteractions between nearest neighbors, i.e. JAB1 for A(Mn) and B1(Mn), JAB2 for A(Mn) and B2(Ni), and JB1B2 for B1(Mn) and B2(Ni).The JAB1 is found to be ferromagnetic (FM) while the JAB2 and JB1B2are both antiferromagnetic (AFM) (Fig. 2). In general, the magni-tudes of JB1B2 are slightly smaller than those of JAB1 and JAB2.Note that the signs of the JAB1, JAB2 and JB1B2 alone, regardless oftheir magnitudes, are able to determine the most stable magneticorder of the inverse spinel phases as the ppn one.

For the normal spinel phases, the nearest-neighbor interaction(JAB) between A(Ni) and B(Mn) can be obtained from the energiesof Nppp and Npnn alone while the interactions of the first threeneighboring interactions (J1BB, J2BB, J3BB) among the B(Mn) cationsrequire the energies of three more phases, i.e. N1pnp, N2pnp andN3pnp. The JAB in the normal spinel phases is AFM whosemagnitude is about the same as J1BB. The sizes of the furtherneighboring interactions between the B(Mn) cations, i.e. J2BB andJ3BB, are considerably smaller though J2BB is found FM.

That some of these exchange interactions are FM (positive) isthe distinguishing characteristic of NMO as none of the consideredexchange interactions for the similar spinel materials, i.e. MnFe2O4

(MFO) [23] and NiFe2O4 [24], was found to be FM interaction in theprevious studies. The transition temperature between the ferri-magnetic and paramagnetic phase is related to the exchangeinteractions. The magnitudes of the major exchange interactionsfor NMO are at least an order of magnitude smaller than those ofMFO. These results are closely linked to the fact that the Neeltemperature for NMO is around 145 K while that for MFO, which isalso a mixed-phase material, is about 600 K.

All the phases considered in this study are found to be insula-ting (Fig. 3). The size of band gaps depends on the magnetic orderas well as the cation distribution. The band gap for the lowest-energy phase, i.e. I3ppn, is around 1 eV. Although both theGGAþU and GGAþUSC methods lead to insulating NMO, theGGA method, i.e. U¼0 case, predicts conducting Npnn state.Besides, the GGA method also wrongly predicts the Npnn as theground state of NMO. These results all indicate the importance ofincluding the on-site U effect in studying this material. The effectof gap opening from the original calculated conducting state bythe LDA and GGA methods was also achieved by the self-interaction-correction method for other transition-metal-oxidematerials as studied previously [25].

The energy distribution of the normal and inverse spinelphases is well separated into two groups (Fig. 1). That the energiesof the normal and inverse spinel phases are divided into twogroups of more than 300 meV difference indicates the cationdistribution on the A and B sites predominantly determine the

relative stability. That is, the energy differences from the differentmagnetic orders are smaller than those between the normal andinverse spinel structures. The formation of the mixed phase istherefore not likely through the samples consisting of segregatedphases of the normal and inverse spinel structures.

We have generated a few structures of mixed phases byexchanging the Ni(B2) with Mn(A) cations in the lowest-energyI3ppn phase. That is, the mixed phases are generated throughsimple cation exchange in the I3ppn phase, but not through thesegregated phases of I3ppn and Npnn. These studies use 4 and5 eV for UNi and UMn respectively as the physical properties of theinverse spinel phases with this set of U values resemble mostthose of the case with USC. For the mixed phases with a single-cation exchange in the 8-formula cubic cell, i.e. δ¼87.5%, theenergy is around 100 meV/fu higher than that of the I3ppn phase,i.e. about the energy of the second lowest-energy phase of I3ppp.This is higher than the energy obtained from a simple linearinterpolation of the energies of Npnn (one eighth) and I3ppn(7 eighths) by �37 meV/fu. Note that different magnetic orders forthe exchanged cations have been investigated and the most stableone corresponds to the magnetic order of n and p for theexchanged Ni(A) and Mn(B2) cations respectively in the I3ppn-based mixed phase. That is, the exchanged cations in the mixedphase prefer retaining their original magnetic polarizations.

The cation exchange introduces an energy band within theoriginal 1.05 eV band gap of I3ppn which appears similar to theimpurity band in a doped semiconductor and reduces the bandgap to 0.35 eV (Fig. 4). The main contribution of this additionalband (two electrons per exchanged cation) is due to the eg orbitalsof the exchanged B2(Mn) cations (contributing one electron) andits surrounding six oxygen atoms (contributing the other electron).We notice that the local moment of the exchanged Mn(B2) cationresembles that of the Mn(A) in both sign and magnitude. Theformer implies the same polarization as the conduction band(majority spin polarization) and therefore the possible excitationof the impurity-band electrons from the exchanged B2(Mn) cationsto the conduction band without flipping the electrons' moment. Thelatter suggests the loosely bound electrons due to the cationexchange around the B2(Mn) sites which is similar to the looselybound electrons of donors in a doped semiconductor and thereforethe formation of an energy band closer to the conduction band.According to this picture, the electric conduction in the mixedphase of NMO could be due to the free carries originating fromexciting the eg electrons of the exchanged B2(Mn) cations to theconduction band whose main cation contribution is from the egband of the B1(Mn) cations. This small band gap in the mixed phasecould contribute to the observed NTCR property of NMO.

In conclusion, we have carried out DFTþUSC calculations tostudy the structural, magnetic, and electronic properties of

Fig. 2. The exchange interactions for the normal (JAB, J1BB , J2BB , J3BB) and inverse(JAB1, JAB2, JB1B2) spinel phases at different U values.

Fig. 3. The calculated band gaps of the studied normal and inverse spinel phases atdifferent U values.

J.-R. Huang et al. / Journal of Magnetism and Magnetic Materials 358-359 (2014) 149–152 151

NiMn2O4. The most stable phase is identified as the ferrimagneticI3ppn inverse spinel phase and the exchange interactions betweenthe cations are evaluated. Generation of mixed phases by exchan-ging the Mn(A) with the Ni(B2) cations in the I3ppn phaseintroduces an impurity-like band within the original band gapand reduces the band gap to 0.35 eV. The conduction mechanismsuggested by the mixed phase is through the excitation involvingthe electrons of the exchanged Mn(B2) to the conduction band(Mn(B1)), which could be a possible source of NTCR.

Acknowledgments

This work was supported by the National Science Council (NSC)of Taiwan for J.R.H. and C.C. and under Grant No. NSC 102-2112-M-008-001-MY3 for H.H. Part of the calculations were performed atthe National Center for High-Performance Computing Center(NCHC). We also thank National Center for Theoretical Sciences(NCTS) for the support through the Computational MaterialResearch (CMR) focus group.

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Fig. 4. The density of states (DOS) and partial DOS of the δ¼ 87:5% NMO mixedphase.

J.-R. Huang et al. / Journal of Magnetism and Magnetic Materials 358-359 (2014) 149–152152