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Electronic, magnetic and transport properties of rare-earth monopnictides

Chun-gang Duan, 1,2 R. F. Sabirianov, 2,3 W. N. Mei, 2,3 P. A. Dowben, 1,2 S. S. Jaswal, 1,2

and E. Y. Tsymbal 1,2 1 Department of Physics, University of Nebraska-Lincoln, Lincoln, Nebraska 685882 Nebraska Center for Materials and Nanoscience, University of Nebraska-Lincoln, Lincoln, Nebraska3 Department of Physics, University of Nebraska at Omaha, Omaha, Nebraska 68182

E-mail: wxbdcg@gmail.com

AbstractThe electronic structures and magnetic properties of many rare-earth monopnictidereviewed in this article. Possible candidate materials for spintronics devices from theearth monopnictide family, i.e. high polarization (nominally half-metallic) ferromagnantiferromagnet, are identified. We attempt to provide a unified picture of the electproperties of these strongly correlated systems. The relative merits of severalab initio theoretical methods, useful in the study of the rare-earth monopnictides, are discussepresent current understandings on the possible half-metallicity, semiconductor-mtransitions, and magnetic orderings in the rare-earth monopnictides. Finally, based onstudies, we propose some potential strategies to improve the magnetic and electproperties of these candidate materials for spintronics devices.

Contents

1 Introduction .........................................................................................................................2 Early experiments and theoretical studies.............................................................................3 Recent theoretical and experimental progresses....................................................................

3.1. SIC-LSD.....................................................................................................................3.2. LSDA+U ........................................................................................................................3.3. GW Approximation (GWA) ...........................................................................................3.4. Dynamical Mean-Field Theory (DMFT) ......................................................................3.5. Other theoretical approaches ........................................................................................3.6. Experimental Studies...................................................................................................

4 Electronic, magnetic and transport properties.......................................................................4.1. Gd monopnictides ........................................................................................................4.2. Eu monopnictides........................................................................................................4.3. Er monopnictides .........................................................................................................

5 Half-metallicity and other interesting phenomena ................................................................5.1. Origins of half-metallicity ............................................................................................5.2. Metal-insulator transitions............................................................................................5.3. Magnetic ordering........................................................................................................5.4. Spin-orbit coupling......................................................................................................

6 The Future Possibilities........................................................................................................

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6.1. Possible half-metallic antiferromagnets........................................................................6.2. Enhancement of the transition temperatures and potential device applications..............

7 Conclusions .........................................................................................................................Acknowledgments ...............................................................................................................References ...........................................................................................................................

1 Introduction

Half-metallic ferromagnets, which were first so named by de Grootet al. in 1983 [1], recently haveattracted growing interest from both experimentalists and theorists [2,3]. Currently, most nominally half-metallic ferromagnets found are compounds that involve transition metal elementCrO2, Fe3O4, Co2MnSi [3], and suffer from a number of deficiencies that limit their application aspolarization materials in spintronics. The electronic structures of nominally half-metallic systeof considerable interest as a mechanism for studying the interplay between high polarization anstructure. There attraction remains in spite of the growing recognition that true half metallic chis unlikely to be ever demonstrated at finite temperatures, due to magnons [4,5], as well atemperature interactions [6,7]. It is natural, therefore, to explore the rare-earth compounds, aearth elements generally have much larger magnetic moments and demonstrate some fascphenomena [8,9].

Rare-earth elements are chemically very similar due to an almost identical outer elearrangement [10]. It remains, however, difficult to obtain impurity free single crystals of thearths or rare-earth compounds, and this may be responsible for some of the long stacontroversies concerning their electronic structure, transport properties and magnetic properties

The rare-earths do, however, have different occupation numbers on the shallow inner 4 f shell,ranging from 0 to 14 through the series La to Lu. This changing 4 f occupation means that the rare-earth elements and their compounds have wide range of different magnetic properties and elestructures. Due to the unfilled 4 f shells of rare-earth atoms, it is a challenging problem to obtaaccurate theoretical description of the electronic structure of rare-earth compounds [11]. In spitfact that the 4 f energy levels often overlap with the non-4 f broad bands of the system, they generallyform very narrow resonances, and are often treated as core states in the theoretical efforts. Duehighly localized nature of the 4 f electrons, the direct f - f interactions between neighboring rare-earthatoms are generally considered to be nearly negligible. However, there is evidence that this belief has to be modified. For instance, in the cases of cerium (uranium) compounds [12,13,144 f (5 f ) level dispersions were observed experimentally, suggesting smaller f level localization in thesesystems. The unoccupied f states certainly will adopt all the trappings of band structure in the evconventional sense.

In addition, the f orbital moments generally cannot be quenched by the crystal field. Therefortotal magnetic moments have both orbital and spin components, and spin-orbital interactioparticularly strong for many of the rare-earth elements and compounds. These inner shell mmoments are largely aligned through intra-atomics(d )- f exchange interaction and weaker inter-atomics-s (d -d ) exchange interactions, thus their magnetic transition temperatures are generally much than those of 3d transitional metal elements or compounds. In spite of the increasingly compeevidence for band structure [12], the 4 f bands are generally very narrow, significantly different frothe bands dominated by s, p and d states. Therefore there exist strong on-site Coulomb repulsiobetween the highly localizedf electrons [17,18]. It makes the independent particle approximation

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longer valid and calculations based on local spin density approximation (LSDA) fail to descrrare-earth 4 f electrons correctly. Thus to explain the behaviors of rare-earth 4 f electrons, many-bodyeffects must be taken into account and more accurate approximations or calculations beyond are absolutely necessary.

With the availability of better quality single crystals and thin films, together with the treme

theoretical efforts in combining many-body theory and density functional theory (DFT) in ttwenty years, a better picture of electronic structure and magnetic properties of rare-earth elemetheir compounds has taken shape. It is the major objective of this review to provide a detailed aof the progress made in the field of rare-earth monopnictides, RX (X=N, P, As, Sb, Bi). This pafamily is chosen because there are more than fifty members that crystallize in the simple NaCstructure, making the rare-earth monopnictides excellent candidates for both experimenttheoretical analysis.

In what follows, we first review early experiments and theoretical studies on raremonopnictides, most of which were carried out between 1960s ~ 1990s. Then we report theoretical and experimental progress. In particular, several novel theoretical techniques are introduced for handling strongly correlated systems. Then we discuss several interesting phenom

rare-earth monopnictides. In providing an overview of the electronic, magnetic and traproperties of rare-earth monopnictides, we have given some preference to GdN and EuN. GEuN are considered to be the most promising nominally half-metallic ferromagnets in the RX Attracting our attention are the mechanisms for magnetic ordering, the pressure/strain and imeffects. Finally, we discuss the potential device applications and the possibilities for enhancitransition temperatures of rare-earth monopnictides.

2 Early experiments and theoretical studies

Studies of the rare-earth elements and their compounds can be traced back more than seventyThe agreement between experiment and calculations made by Van Vleck and Frank [19] effective magneton number of the rare-earth ions was regarded as one of the most succapplications of quantum mechanics to magnetism [20]. The surge in the study of rare-earth comin the 1960s was mainly motivated by a search for new ferromagnetic semicondu[21,22,23,24,25,26,27]. Researchers began realizing that it was too complicated to interpexperimental results if crystal distortions or impurities were considered. Thus, investigations oearth monopnictides gradually became one of the most important branches in rare-earth smostly because these binary compounds crystallize into the simple NaCl-type structure andsupposed to be more amenable to theoretical analyses [21].

Nevertheless, even for rare-earth compounds, with such simple structure, the full understanrare-earth monopnictides electronic structure and magnetic properties is still not complete. Rarmonopnictides demonstrate rich magnetic orderings and their electronic structures are sensiexternal pressure and impurities. Due to the poor computational power and limited theoretical mearlier theoretical studies were restricted to analytical model calculations, such as crystalline fieeffective-point-charge [28],d-f Coulomb interaction [29] and p-f mixing [30]. These calculationscould explain some phenomena for certain rare-earth monopnictides, but the overall agreemeexperiments for the whole RX family was not satisfactory.

The earliestab initio band structure calculation of the rare-earth monopnictides was carried ouHasegawa and Yanase in 1977 [31]. They adopted augmented planewave method with Slat X

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exchange potential [32] to calculate the energy bands of GdX (X=N, P, As, Sb), in a self-conway. To deal with the 4 f electrons, they used frozen-core approximation, i.e. the 4 f electrons aretreated as core electrons. They claimed that GdN is semiconductor with an adjusted band gap oand other Gd monopnictides are semimetallic, in their calculations. But they also realized thatpolarization is taken into account, then the 5d-4 f exchange splitting, which is estimated also to b

around 1 eV, could make GdN exhibits metallic character as well [31].In 1988, using a tight binding model with parameters chosen to fit the band structures calcby Hasegawa and Yanase [31], Narita studied the magnetic susceptibilities and spin structures o[33]. This was the first attempt to understand the magnetic properties of rare-earth monopnictidband structure calculations, though he otained wrong magnetic ground states for these comUsing similar method, Xiaet al . [34] studied the electronic structure of GdAs/GaAs supperlattice1991.

The first spin-polarizedab initio calculations on rare-earth monopnictides was provided bPetukhovet al. in 1994 [35]. Using the linear-muffin-tin-orbital (LMTO) method within LSDAtreating the Er 4 f states as localized corelike states with fixed spin occupancies, they calculatedelectronic structure of ErAs and ErxSc1-xAs alloys. Later in 1996, they studied extensively th

electronic structures, equilibrium lattice constants, cohesive energies, bulk moduli and mamoments of GdX and ErX (X=N, P, As) [36]. They found that the corelike treatment issatisfactory for most purposes not involving 4 f electrons directly. They also found that the electroexchange splittings of the nitrides are significantly stronger than those for the arsenidephosphides, rendering GdN to be metallic for one spin channel and semiconductive for the othethey were actually the first to claim that GdN could be half-metallic, within their calculation which did not involve the 4 f states explicitly. There were other theoretical studies on Gd compoune.g., Kasuya and Li tried f -d mixing and f -d exchange interactions to explain the strongferromagnetism in GdN In 1997 [37].

The early experimental reports on rare-earth monopnictides are widely scattered in the liteFor reviews on experimental studies before 1970s, one can refer to Refs. [25], [38] and [3focusing on the experimental studies on the electronic, transport and magnetic properties, in thefrom 1970s to 1990s, provides an insight into the parallel growth of materials science and espectroscopy. It should be pointed out that Gd monopnictides have been investigated most exteamong the rare-earth monopnictide family. This is because Gd is located in the middle of thearth group in the periodical table, and the Gd 4 f orbitals are exactly half occupied, hence the orbitaangular momentum is zero, as the ground state of Gd3+ is 8S7/2. Thus the spin-orbit, multipole, p-f andd-f mixing interactions are small [33], greatly simplifying the problems associated with elecstructure. In addition, the Gd monopnictides (and Gd metal) generally have much higher tratemperatures than those of their counterparts of other rare-earths, thus attracting much more pinterest [38].

Kaldis reported the first successful growth of large single crystals of GdP in 1974 [40]opened the door to a reliable determination of the electronic structure of GdP. Based on oinvestigation [41], Gntherodt, Kaldis and Wachter deduced that the crystal field splitting of thed states is about 1.8 eV and the positions of occupied Gd 4 f levels in GdP are about 7 eV below E F. Theyalso found that GdP exhibits metal-like conductivity. Later experiments on GdN were controvGdN was reported as semiconductor [42] and semimetal [43]. Studies on the magnetic exinteraction on Gd compounds clearly demonstrated that the free carriers contribute to a RudKittel-Kasuya-Yosida (RKKY) [44,45,46] indirect exchange interaction [47,48].

Urban et al. [49] observed a large variation of the thermal broadening of the electron

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resonance (ESR) linewidth of Gd across the pnictides in 1978. They then claimed that the conelectrons exhibit almostd character, thus the exchange interaction depends on the amount overlapping betweend wave functions. Palmstrmet al. [50] successfully grew single crystal ErAsfilms on GaAs in 1988. Later magnetotransport measurements showed that ErAs is a low-dsemimetal that magnetically orders at low temperature (4.5 ~ 4.8 K) [51].

In 1990, Degiorgi, Bacsa and Wachter reported on results obtained from large single crystals of cubic and stoichiometric YbN [52]. They claimed that YbN is a self-compensated semimetal woccupied f states about 6 eV below E F and the empty f states about 0.2 eV above E F. Their later studiesconfirmed the semimetallic nature of YbP and YbAs [53]. Chattopadhyayet al. carried out high-pressure magnetization and neutron-diffraction experiments on CeSb in 1994 [54]. They found magnetic ordering of CeSb is very sensitive to hydrostatic pressure. Waldfriedet al. used angle-resolved photoemission to study the electronic structure of dissociatively chemisorbed nitroGd(0001) in 1995 [55]. Xiao and Chien found that GdN films are insulating [56]. Liet al. reported thegrowth of large single crystal of GdX (X=P, As, Sb, Bi) in 1996 and found them all to becompensated semimetals and order antiferromagnetically [ 57 ,58]. The photoemission studYamadaet al. showed that the occupied 4 f states in GdP lie around 8.4 eV below E F, and are shifted

down from GdP to GdBi [59]. The experiments on polycrystal GdN confirmed that stoichioGdN is ferromagnetic with a transition temperature 58 K [60].

3 Recent theoretical and experimental progresses

Recent theoretical progresses on the rare-earth monopnictides studies follow the development of electronic structures calculation in solids. For strongly correlated systems, the accurate evalrequire going beyond the LSDA scheme. The following described methods have been develoovercome the deficiency of LSDA calculations.

3.1. SIC-LSD

Despite the impressive successes of the local spin density approximation (LSDA) in the past deso [61], LSDA calculations have an intrinsic deficiency, i.e. the self-interaction energy problemThe self-Coulomb and self-exchange interactions in LSDA do not cancel completely, as in the Hartree-Fock approximation. This means that LSDA will fail to correctly describe systems withelectron-electron interactions. Numerous efforts have been made to address this problem [62,63In the self-interaction-corrected local-spin density (SIC-LSD) approximation [65], the non-pelectron self-interactions, including both SIC Coulomb and corresponding SIC exchange-corrterms, are subtracted from the LSDA Hamiltonian, and the energy functional is written as

3 3 3( ) ( ') ' ( ) ( ( ),0)'

occ i iSIC LSDA i xc i

i

n n E E d rd r n n d r = + r r r rr r

, ( 1 )

where E LSDA is the energy functional in LSDA,n i(r ) is the charge density corresponding to theithsolution of the SIC-LSD equation, and ( , ) xc n n is exchange-correlation energy density of ahomogeneous systems with spin densitiesn and n . The SIC approach generates a orbital-dependenpotential which can be significant for localized states, yielding a much-improved description

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static Coulomb correlation effect compared to that provided by LSDA. The inclusion of SIC arquite successful [66,67,68,69].

Another advantage of the SIC-LSD method is that the minimization of total energy, with resthe number of localized electrons, leads to a determination of the nominalvalence defined as theinteger number of electrons available for band formation

v core SIC N Z N N = , ( 2 ) whereZ is the atomic number, N core and N SIC are the number of core and localized (SIC) electron statrespectively. This information is important to the analyses of chemical properties of rarecompounds [67].

Application of the SIC-LSD methodology to the rare-earth monopnictides has been carriedAertset al. [70], Horneet al. [71], Szoteket al. [72] in 2004. Together, these studies represent systematic study of the electronic structure of thirteen rare-earth nitrides, from CeN to YbNcalculations show that the rare-earths are trivalent in the mono-nitride ground state, with the exof Ce which is tetravalent in CeN. On the basis of the SIC-LSD calculations, the claim is tharare-earth nitrides display wide range of electronic properties, despite the same structure and

lattice constants. Specifically, TbN, DyN and HoN are found to be narrow gap insulators, CeNTmN and YbN are metallic in both spin channels, while PrN, NdN, PmN, SmN, EuN and Ghalf-metallic ferromagnets in these ground state calculations. They found that the f -band manifold wassplit by the SIC into localized and bandlike f electrons. Because of the different degree ohybridization between the rare-earth bandlike f and the nitrogen p states, in the vicinity of the Fermilevel, these compounds demonstrate different electronic properties. This is consistent wielectronic structures of SmX (X=N, P, As, Sb, Bi) which have been studied by Svaneet al. [73]. Svaneand coworkers found that the occupied f bands are formed in the vicinity of the Fermi level in all tSmX compounds.

3.2. LSDA+U

In the LSDA, the potential is treated as an averaged orbital-independent one-electron potentiamay be a reasonable approximation for weakly correlated system, which corresponds to an ecase of a Hubbard model [74] where the on-site Coulomb repulsion (HubbardU ) is approaching zero.For strongly correlated systems like Mott insulators, however, ignoring the effective CoparameterU results in totally wrong prediction of the energy gap. The LSDA+U [75,76,77,78] methodwas initially proposed to describe Mott insulators correctly. Following the Anderson modeelectrons are separated into two subsystems: localizedd or f electrons and delocalizeds or p electrons.

The d-d ( f-f ) interaction is described by Hubbard term12 i ji j

U n n , wheren i is the d ( f )-orbital

occupancy, instead of the LSDA averaged term (approximately) ( 1) / 2 E UN N = . Then an newenergy functional can be written as

1 1( 1)2 2

LSDA U LSDAi j

i j

E E UN N U n n+

= + , ( 3 ) and the orbital energies

i are given by

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1( )2

LSDA U LSDA U LSDA

ii ii

E U n

n +

+ = = + . ( 4 )

This new formula splits the orbital energies of occupied localized electrons (n i = 1) and unoccupiedlocalized electrons (n i = 0) byU , thus reproducing the qualitatively correct physics for Mott-Hubbinsulators [77]. The above analysis is, however, only the simplified overview. The realizatLSDA+U scheme in practice requires much more theoretical work [75] which is not addressed hepassing, it is worth noting that a rotationally invariant form of the LSDA+U functional is given by

[Tr Tr( )]2

LSDA U LSDA U J E E

+ = + , ( 5 ) in which is the spin,U and J are the (spherically averaged) screened Coulomb electron-electinteraction (Hubbard parameterU ) and Hunds rule exchange parameter (Stoner parameter I ),respectively [80].

In practice, parametersU and J can be taken as adjustable parameters (e.g., obtained throucomparison with photoemission and inverse photoemission experiments).U and J can also beevaluated from the LSDA through the supercell LSDA approach [81]. Specifically,U = F 0, J =(F 2+F 4)/14 ford electrons, J = (286F 2+ 195F 4+ 250F 6)/6435 for f electrons [78], whereF k (k = 0, 2, 4,6) are Slater integrals [82].

The first LSDA+U calculation on the rare-earth monopnictides was carried out by Liechtensteet al . [83] in 1994. They studied the electronic structure and magneto-optical effects in CeSb. Th f level is found to be 2 eV below the Fermi level and is hybridized with Sb p bands. Using LMTOmethod, in 2003 Komesuet al . [84] studied the electronic structure of ErAs and obtained badispersions qualitatively similar to experiments. In 2004, Duanet al. [85] considered the spin-orbitcoupling in the LSDA+U calculation of bulk ErAs, using the full-potential linear-augmented-plwave (FLAPW) method [86]. The theoretical 4 f multiplet structure agrees well with photoemissioexperiments. In addition, clear evidence of 4 f -5d hybridization was found [86]. Later, with the samtheoretical methodology, the electronic structure and magnetic ordering of ErN and ErAinvestigated [87].

In 2005, Duanet al. reported on the effect of strain on the electronic and magnetic propertieGdN [88]. The results of LSDA+U indicate that GdN is nominally a ground state half-metalliexperimental lattice constant, but may undergo phase transition to a semiconductor with expansion. Soon thereafter, these studies were extended to the electronic structure and maordering of the GdX monopnictides [89]. Duanet al. provided a quantitative analysis of the RKKYand superexchange interaction [90] of the GdX monopnictide systems.

As previously indicated, a number of rare earth pnitcides appear to resemble ground statmetallic ferromagnets. Johannes and Pickett studied the electronic structure and magnetic exinteractions in EuN and EuP also using FLAPW method [91]. They found EuN is a ground stametallic ferromagnet within conventional LSDA+U band theory. Ghoshet al. studied the electronic,magnetic and optical properties of GdX in 2005 [92], with LMTO in the LSDA+U scheme. They alsofound GdN is half-metallic if no further adjustment is implemented. Using LMTO withLSDA+U approach, Larson and Lambrecht [93] found that by putting the HubbardU also on thed orbital, GdN is found to be a semiconductor, otherwise it is half-metallic, as noted by others [70

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3.3. GW Approximation (GWA)

Eigenvalues of the Kohn-Sham equations [94] are often interpreted as single-particle energies compared with photoemission spectra. This is not really justified and in many cases leads to inpredictions. A proper way to interpret the photoemission spectra is to use quasiparticle concep

The quasiparticle energies E i can be obtained [96] from:2 31[ ( ) ( )] ( ) ( , ; ) ( ) ( )2 i i i i i

V d r E E + + = r r r r r r r , ( 6 )where the self energy addresses the effect of exchange and correlation and is intrinsically a nonloperator. The calculation of is, however, generally very difficult and requires some approximatioIn the so calledGW approximation (GWA) [97], is obtained by the Greens function method:

( , , ) ( , ; ) ( , ; )2i

E d G E W

= r r r r r r , ( 7 )hereG stands for the Greens function,W is the screened Coulomb interaction and can be evaluated the random phase approximation (RPA) [98], i.e. assuming the electrons are non-interacting whrespond to the external and induced field.

The application of GWA to realistic materials was first carried out by Hybertsen and Louie 1980s [99]. Godbyet al. [100] also obtained similar results using same approach. Due to complexity in calculating the self energy, the application of GWA to rare-earth compounds hbeen undertaken (for a recent review on GWA calculations, see Ref. [101]) until recentlySchilfgaardeet al. [102] have drawn attention to their quasiparticle self-consistentGW (QSGW)calculations on Gd, GdP and GdAs. The QSGW calculations overestimate the position of the mGd f shell by ~ 4 eV. The details of these calculations are not yet available.

In 2000, using the LMTO method and assuming the quasi-particle energy gap correctioninversely with the dielectric constant, Lambrecht [103] predicted that GdN is a narrow indirecgap insulator. He also claimed that by applying a magnetic field, the band gaps can be tunaligning the Gd 4 f magnetic moments.

3.4. Dynamical Mean-Field Theory (DMFT)

Dynamical mean-field theory (DMFT) is a more modern, non-perturbative method that has prbe successful in investigating strongly correlated systems with local Coulomb interactions [104theory was initially developed from thelocal impurity self-consistent approximation [105], which isthe natural generalization of quantum many-body problems of the Weiss mean-field theory [10believed to be a major step towards the reunion of two theoretical approaches, i.e. the DFT andbody model Hamiltonian of condensed matter physics.

The spirit of DMFT is to map a lattice problem with many degrees of freedom onto an efsingle-site (impurity) problem with less degrees of freedom. DMFT becomesexact in the limit of highlattice coordination numbers [105]. The underlying physical idea is that the dynamics, at a givmay be considered to be the interaction of the degrees of freedom at this site with an externcreated by all other degrees of freedom on other sites, adynamical mean-field approximation [106].This impurity problem has to be solved self-consistently together with thek -integrated Dyson equationconnecting the frequency dependent self energy ( ) and the on-site Green functionG at frequency :

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1 1( )( ) ( ) B LDA

d k V H

= + kG , ( 8 )where is the chemical potential,0 LDA H is the one-particle Hamiltonian without the local Coulominteraction,V B is the volume of the Brillouin zone.

Many techniques have been applied to solve the Anderson impurity model, such as quMonte Carlo, iterative perturbations, the fluctuation exchange approximation, the mean-fielboson approach and the numerical renormalization group [104]. With these efforts, it is now pto combine DMFT with modern electronic structure calculations to carry out LDA+DMFT [spectral DFT [108] calculation.

The DMFT method has been successfully used to explain the transition in cerium, the -phase of plutonium and several Mott insulators [104]. To our knowledge, however, there is noof using DMFT to study the rare-earth monopnictides; but as there is no substantive technical such calculations are only matter of time.

3.5. Other theoretical approaches

There are also several calculations of rare-earth monopnictides using other approaches. Kalvodet al. studied the cohesive properties of GdN clusters using a quantum chemical (Hartree-Fock) me1998 [109]. They obtained a reasonable lattice constant for GdN (1.3 ~ 2.0 % larger thexperiment values), but the details concerning the electronic structure were not presented.

Combining a many-body model (multi-band Kondo lattice model) and ab initio band structurecalculations (LMTO), Santos, Nolting and Eyert studied ferromagnetism and temperature-depelectronic structure of hcp Gd in 2004 [110]. Later, using the same approach, Sharma and Nstudied temperature dependant electronic correlation effects in GdN in 2006 [111]. Assuming be a semiconductor, they obtained its quasi-particle spectral densities and density of states andthat the correlation effects were strongly temperature dependant. Usings- f model, Bhattacharjee and

Jaya, in 2006 [112], studied correlation and temperature effects on the electronic structure of bthin film GdN. Bhattacharjee and Jaya also found a red shift of the GdN conduction bands withto the temperature. Without any special treatment of the 4 f states, Landrum calculated the electronicstructure of CeN in 1999 using LMTO method [113].

In summarizing the various theoretical approaches, discussed above, all have their advantagdrawbacks. For instance, because of the localized nature of the strongly correlated electrons, mthe theoretical methods, except for GWA, were first developed using the LMTO method, wbased on local orbital basis, as a starting point. For 4 f systems, SIC+LSD method sometimesoverestimates the separation between the occupied and unoccupiedf states [70]. The LSDA+U methodnow has been implemented into several band structure schemes, due to its relatively simple pand thus is much more widely accepted. The HF approximation treatment in the LSDA+U scheme to

the on-site Coulomb interactions is, however, too crude for strongly correlated systems [107approach is successful in describing the long-range ordered insulating states of correlated sywhile it fails to describe correctly the strongly correlated paramagnetic states. GWA and Dmethods are believed to be more accurate, than many other strategies, in describing the stcorrelated systems. But at this stage, the GWA and DMFT approaches are still too cumbersomused by the whole community.

Nevertheless, concepts like the HubbardU and the self energy are now being widely adopted[73,107]. In addition, the Wannier functions make it possible to set up localized orbital through

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wave basis [114,115]. Thus we expect that there will be many moreab initio studies on stronglycorrelated systems over the next few years.

3.6. Experimental Studies

A series of ESR measurements have been carried out on single crystals of GdAs [116], GdP [1GdBi [118] since 2000. The magnetic structure of these compounds were confirmed to be Atype. The Fermi surface and magnetic properties of TbSb have been investigated by Nakanishiet al. in2004 [119] using de Hass-van Alphen and high-field magnetization measurements.

In 2005 Leuenbergeret al. [120] reported electronic and magnetic properties of high-quality tfilms of GdN. They found that a 500 thick GdN film already shows very close physicmagnetic properties to that of bulk GdN. The element specific x-ray magnetic circular dich(XMCD) measurements clearly demonstrated that the N p states are magnetically polarized. Thisagrees with theoretical predictions, as will be shown later. Leuenberger and coworkers also fouthe electrical conductivity of GdN is thermally activated down to the ferromagneticT c, below whichGdN exhibits metallic character. They attribute the origin of this semiconductor-metal transiti

nonstoichiometric GdN film, similar to that found for EuO [121,122]. Later experiments demoa significant reduction of T c as a result of the influence of lattice expansion [123], as predictedtheory [88]. More recently, Granvilleet al. [124] claimed that GdN is semiconducting in botparamagnetic and ferromagnetic states (T c =68 K). They think that the N vacancies may be responsibfor the conductivity in GdN.

As a final note, although tangential to GdN, Leuenberger and coworkers [125] also found layers induce long range magnetic order in GdN layer at temperatures above theT c of GdN in GdN/Femultilayers.

4 Electronic, magnetic and transport properties

There are many similarities among the rare-earth monopnictide family, and some studifferences with regard to metallicity and magnetic ordering. This is summarized in Table 1 lists the experimental lattice constants of all the rare-earth monopnictides, together with their mordering, transition temperatures and metallicity, i.e., insulating (semiconducting) or (semi)mfor most of the more than sixty compounds in the rare-earth monopnictide family. Most of thearth monopnictide family have the NaCl-type structure (space group3Fm m ). EuAs, EuSb and EuBido not adopt the NaCl-type structure, and have been omitted in Table 1. There is no experireport on the Pm monopnictides, most probably due to the fact that Pm must be artificially prand we also unable to find any report on YbBi.

From Table 1, we can see that the lattice constants of rare-earth monopnictides, as a generalincrease from N to Bi but decrease from La to Lu: the lattice constant typically decreaseincreasing 4f occupancy, as indicated in Figure 1. This trend in the lattice constant can be explained by the increase of anion sizes and the decrease of cation sizes with the increase of number. Thus the smallest lattice constant belongs to LuN (4.766 ), while the largest to LaBi): a difference of about 38%. We note that there are exceptions to this general trend, e.g., CeNAs shown in the experiments of Olcese [126] and theoretical calculations by Aertset al. [70], the jumpin lattice constants from CeN to PrN is due to the fact that the ground state for Ce in CeN is tetr

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instead of trivalent.The bonding between the rare-earth atoms and pnictogen atoms cannot be simply descri

ionic or covalent, otherwise all rare-earth monopnictide family would be expected to be ins(semiconductors). However, from N to Bi, we can see the gradually increasing metallicity incompounds. The typical carrier concentrations in these compounds are around 1019 ~ 1021 cm-3 [103],

making them semimetals or highly dopedn-type semiconductors.In listing the known energy gaps for those rare-earth monopnictide compounds that are regasemiconductors, we note that the light pnictides, like nitride, tend to be larger energysemiconductors than the heavy pnictogen compounds. The changes of energy gaps from La torather scattered and it is hard to find a clear trend. We should point out that those data for energare not that reliable, since the electronic and transport properties are strongly affected by imdopants, thus a lot of controversies exist in the comparison of various experiments. For examplGdAs and GdSb were thought to be semiconductors [39], but later experiments on high-samples clearly showed that they are actually semimetals [47,57].

Figure 1. Lattice constants of rare-earth monopnictides: RN (squares), RP (cirlces), RAs (stars), RSb (down triangle(up triangles).

The magnetic ordering of rare-earth monopnictides is also quite complicated, rangingferromagnetic (FM), flip-flop FM [22], to different antiferromagnetic (AFM) configurationstypical AFM configurations (also see Ref. [127]) are depicted in Figure 2. As we can see from Tmost monopnictides have AFM ground states with exceptions among the nitrides and phosOverall, we can see that the magnetic interactions gradually increase from La to Gd (FM, 58 Kdecrease again from Gd to Lu. With the increase of anion sizes, the FM pnictides become AFthe Nel temperature increases. Apparently, HoP and DyP are in the intermediate region betweand AFM, as flip-flop FM can be regarded as combination of a FM and an AFM configuratioThis balance between AFM and FM ordering may also be the reason that CeN and TmN happarent net magnetic order.

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Figure 2. Three antiferromagnetic ordering configurations in rare-earth monopnictides: (a) AFM-I, (b) AFM-II, (c

III. Arrows indicate magnetic moment orientations on rare-earth atoms.The electronic structure calculations on three typical rare-earth pnictides, based on LSDU

scheme with FLAPW method [86], confirm some of these trends and also can illustrate someaffect of changing lattice constant, without changing the pnictide, which is not easily doexperiment. For the convenience, the Brillouin zone of the face-centered cubic (fcc) lattice is shFigure 3, together with definitions of some high-symmetryk -points andk -lines.

Figure 3 . The Brillouin zone of the face-centered cubic lattice.

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Table 1. Physical and magnetic properties of rare-earth monopnictides. Unless explicitly indicated, the data are from Ref. [39]. Numbers in the Metallicity are band gaps in eV derived from optical absorption of thin filmmaterial is insulator or semiconductor. SC means semiconductor, SM means semimetal.

N P As Sb Bia () 5.295a 6.035b 6.137c 6.490d 6.577e La

Metallicity SC, 0.82 SC, 0.7-0.8

a () 5.013a

5.90 6.06 6.40 6.49Ordering No order down to 1.5 K AFM-I AFM-I AFM(complicated) AFM(complicaT N(C)(K) 6~7, 8.5, 9 5~7.5, 7.5 16, 18 25, 25.5, 26

CeMetallicity SM f SC, 1.1 SC, 0.7 SM f

a () 5.135g 5.893 6.018 6.364 6.448OrderingT N(C)(K)

Pr

Metallicity SC, 1.03 SC, 1.0 SC, 0.66a () 5.123a 5.826 5.958 6.31 6.41

Ordering FM AFM-I AFM-I AFM-I AFM-IT N(C)(K) 27.6, 29, 32, 35 7, 11 10.6, 12.5, 13 15.5, 16 24, 25

Nd

Metallicity SC, 0.8 SC, 1.04a () 5.035 5.75 5.91 6.26 6.35

Ordering AFM AFM AFM AFM AFMT N(C)(K)

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4.1. Gd monopnictides

Though Gd monopnictides were studied most extensively in the RX family, there remains icontroversy regarding the electronic structure and transport properties, especially on [31,36,43,58,70,88,93,103,120,124]. Various calculations have been undertaken on different m

phases (FM and AFM) with different schemes (LSDA and LSDA+U ) of GdX (X=N, P, As, Sb, Bi).The electronic structures, typical for rare-earth monopnictides, are presented in the discussiofollows.

Figure 4 shows band structure of GdN in FM state with and without on site 4 f Coulombinteractions. Here we used an effective Hubbard4eff = = 9.2 f U U J eV for Gd compounds in theLSDA+U scheme. As we will show later, this value gives much better agreement of the 4 f energylevels found in experiment than those of the values used in previous studies on Gd metal compounds [140,141,142,88,89], i.e.U = 6.7 and J = 0.7 eV.

As can be seen from Figure 4(a), the LSDA+U strategy has no significant impact on the wholLSDA band structure of GdN, except upon the energy levels of the occupied and unoccupied 4 f states.In the pure LSDA scheme, the occupied 4 f states are placed about 3.2 eV below E F, stronglyhybridized with N 2 p states, while the unoccupied 4 f states locate about 2 eV above E F, mixed with Gd5d states. There is no direct photoemission data on GdN single crystal, but experiments on(As,Sb,Bi) show that the occupied and unoccupied 4 f levels are situated 8 ~ 10 and 5 ~ 6 eV belowand above E F, respectively [59]. Furthermore, the x-ray photoelectron spectroscopy (XPS) experion GdN films show that the Gd 4 f levels are 7.8 eV below E F [120]. Thus the LSDA calculation failsto give correct the 4 f energy level binding energies. This situation is much improved by the LSDU method [Figure 4(b)]. In fact, now the unoccupied 4 f states remain around 6.6 eV above E F, and theoccupied 4 f states are 7.8 eV below E F, in very good agreement with experiments.

Figure 4 . Electronic structure of ferromagnetic GdN on experimental lattice constants (a = 4.974 ) : (a) LSDA, (b)LSDA+U withU eff = 9.2 eV. Solid and dotted lines represent spin majority and spin minority states, respectively.

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Figure 4(b) actually shows the typical features of the band structure of most rare-monopnictides. The pnictogen p derived states (here N 2 p) dominate the top of the valence bands.Precisely speaking, these pnictogen p states are actually hybridized with rare-earth (here Gd) 5d (6s)states, which dominate the bottom of conduction band. This hybridization results in a hole poc point and an electron pocket at X point in metallic pnictides. The numbers of electrons and ho

the same [31]. Even if the pnictides are determined to be semiconductors, the close proximitlikely Fermi level crossing) of the unoccupied rare-earth 5d states near the X point would make theenergy gap to be indirect. A significant exchange splitting can be found in the band structure, ais indeed the origin of the nominal half-metallicity in rare-earth monopnictides, as we will disdetail later.

Figure 5. Thel-projected DOS of GdN. Spin-minority states are of negative values.

The l-projected density of states (DOS) plot (Figure 5) provides an even clearer picture electronic structure of GdN. As one can see, those top valence states right below the Fermi lepredominantly N 2 p states. The Gdd states, however, also make noticeable contribution. Note hereour calculation both 5d eg and 5d t 2g states participate in the hybridization with N 2 p states, though thecontributions to the bottom of the conduction band(s) are dominated by 5d t 2g states. Not only does thecalculated 4 f levels agree well with experiment, but the Gd 5 p states are located at the same binding

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energy position (about 21 eV below E F) found in experiment [120]. The 1.8 eV separation between Gd 5 p majority and minority states is caused by the exchange splitting. We would like to point othe Gd 5d -X 2 p hybridization is important in establishing the physical properties of GdX. hybridization results in magnetic moments on pnicogen sites and is responsible for the intmagnetic orderings and transport properties.

Band structures for other Gd monopnictides in the ferromagnetic state, using LSDA+U , are shownin Figure 6. Note that the magnetic ground states of these compounds are AFM-II type. Howecan consider these structures as the saturated limit of the paramagnetic states in a magnetic field

Figure 6. Electronic structure (LSDA+U withU eff = 9.2 eV) of (a) GdP (aexp= 5.709 ), (b) GdAs (aexp = 5.864 ), (c)GdSb (aexp= 6.219 ), (d) GdBi (aexp= 6.295 ) in ferromagnetic phase.

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The band structures seen for the rare earth pnictides from GdN to GdBi are quite similar, that for GdSb and GdBi there are no gaps between the Gd 5d states and pnicogen p states at the point. We find that, with a single universal4eff U , the f levels in these compounds, both occupied andunoccupied, are all in excellent agreement with experimental observations [59,120], vindicatapplication of the LSDA+U scheme. This is clearly shown in the XPS and X-ray bremsstrahlisochromat spectroscopy (X-BIS) spectra of GdX (Figure 7). There exists a monotonic energyshift from GdN to GdBi [59], which is clearly represented in LSDA+U band structures of GdX.

Figure 7 . The XPS and X-BIS spectra of GdX (X=P, As, Sb, Bi) (from [59]). Red lines are addeGdN according to Ref. [120], assuming same Uff for GdN.

From the LSDA+U calculations, all the Gd monopnictides are seen to be semi metallic excepGdN which is nominally half-metallic with a half-metallic gap about 0.5 ~ 0.6 eV. ExperimentaGdP (As, Sb, Bi) pnictides are found to be metallic [58]. For GdN, as noted previouslexperimental temperature dependent resistivity of GdN film [124] shows a picture (Figure 8) thatdiffers from other GdX compounds (Figure 9, Ref. [58]). The high temperature behavior resistivity of GdN is more like that of a semiconductor, apparently different from othemonopnictides. The peak around the transition temperature can be explained by the longmagnetic ordering which significantly decreases the spin-dependent scattering of charge carriebroad range of this peak may be attributed to the imperfect of periodicity or the Kondo-lattice[143,144]. Though the resistivity in the very low temperature is not huge (5cm), it is still more likea semiconductor.

If GdN is really a semiconductor, with an optical gap about 1.5 ~ 2 eV [124], then it mea

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there still is something important missing in the ab initio calculations. Lambrecht [103], Ghoshet al .[92], Larson and Lambrecht [93] used different approaches to shift Gd 5d bands and managed to makeGdN semiconducting. However, these empirical treatments of the theory do not give the cpositions of Gd 4 f levels. Apparently, more efforts is needed to fill the gap between theory experiment.

Figure 8. Temperature-dependent resistivity of a 200 nm thick GdN film. The pronounced peak at 68corresponds to the measured Curie temperature of the film. The inset shows the low temperature beof the resistivity (from [124]).

Figure 9. Temperature-dependent resistivity of stoichiometric GdX (X=P, As, Sb, Bi) single crystalsmeasured at zero field (from [58]).

Since the ground states of GdX (X=P, As, Sb, Bi) are all of AFM-II type [see Figure 2(b)interesting to compare the difference between the AFM and FM electronic structures. Figure 10both AFM and FM bands of GdP with the same rhombohedral cell (where the Brillouin zone isin Figure 11) and adopting the experimental lattice constants. As we can see, the AFM bands shaverage effect of the FM spin majority and minority bands and this leads to a small reduction energy. The essential feature of the electronic structure, however, remains the same.

From the above analysis, apparently GdN is on the border between semiconductor and semstates. Thus the GdN physical properties are very sensitive to nonstoichiometry, impurities, prtemperature, and magnetic field,etc . In addition, exotic phenomena, such as electron-hole liquid [14

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may occur in the region between semiconductor and semimetal states. Again, if it is true that Gsemiconductor and GdP is a semimetal, then most probably there would exist some GdN-GdPthat would be half-metallic.

Figure 10 . Electronic structure of GdP with rhombohedral cell (a) antiferromagnetic phase (AFM-Iferromagnetic phase. Note that in antiferromagnetic phase there is no difference between the spin mand minority states.

Figure 11. The Brillouin zone of the rhombohedral lattice.

4.2. Eu monopnictides

In the europium pnictide family only EuN and EuP crystallize with fcc structure. According to rules [146], the ground state of Eu3+ (4 f 6) is7F 0, i.e.S = 3, L = 3, J = 0. Thus isolated Eu3+ is supposed

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to be nonmagnetic. In the crystalline environment, however, the orbital moment generally wsuppressed by the crystal field, thus net magnetic moments may exist in EuX (X=N, P). In addin the case of Gd monopnictides, there could be induced magnetic moments on pnicogen Taking into account the spin-orbit coupling, bulk Eu3+ could exhibit significantly different magneticproperties from that of isolated Eu3+.

Experimental studies on the electronic structure of the EuX (X=N, P) compounds are verTheoretical calculations are also limited. So far there has only two published calculations on Eumonopnictides, to our knowledge. As previously noted, Horneet al. reported EuN to be half metallicbased on the SIC+LSD method [71] and was confirmed by Johannes and Pickett [91] usiLSDA+U scheme.

Following Johannes and Pickett [91], using the LSDA+U approach withU and J set as 8 and 1 eVrespectively, we have obtained similar band structures for EuN and EuP, as shown in Figure 12. Thespin-orbital effects are not considered in these calculations and will be discussed in next cJohannes and Picketts calculations showed that the ground state of EuN and EuP are FM and Arespectively. Here we only present results of FM states of two compounds for direct comparisodifference between the FM and AFM states of EuP is very similar to the case of GdP (Figure 10

Figure 12 . Electronic structure (LSDA+U withU eff = 7 eV) of (a) EuN (aexp= 5.017 ) and (b) EuP (aexp= 5.756 ) inferromagnetic phases.

As we can see from the above Figure, the band structures of Eu monopnictides are similar tof Gd monopnictides (Figure 4 and Figure 6). The major differences arise from the unoccup f majority states. In EuN, this state is about 1 eV above E F, whereas in EuP this state crosses the Ferm

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level. In both cases, the unoccupied 4 f states are strongly hybridized with Eu 5d and pnicogen p states.Figure 12(a) shows that, in this conventional LSDA+U band calculation, EuN is half-metallic with a0.5 eV gap in minority spin channel. Other Eu monopnictides are semimetallic, like EuP, as illuin Figure 12(b).

4.3. Er monopnictidesErbium monopnictides have been chosen for investigation because Er3+ represents another type of rare-earth ion, which has more than a half-filled 4 f electron shell. This provides a contrast with G(with a half-filled 4 f electron shell) and Eu (with a less than half-filled 4 f electron shell). The groundstate of isolated Er3+(4 f 11) is4 I 15/2, i.e.S = 3/2, L = 6, J = 15/2. Only ErAs has been studied extensivelyexperimentally [50,51,84], whereas theoretical studies of all of the Er monopnictides haveundertaken [35,36,70,84,85,87]. Except for ErN, all Er monopnictides have AFM ground stahave similar electronic structures and physical properties. Here we present our LSDA+U bandcalculations for ErN and ErP in the ferromagnetic state. Following Komesuet al . [84],U and J arechosen to be 8.6 and 0.75 eV, respectively.

Figure 13 . Electronic structure (LSDA+U withU eff = 7.85 eV) of (a) ErN (aexp= 4.835 ), (b) ErP (aexp= 5.595 ) inferromagnetic phases.

In Er monopnictides, all the 4 f majority states and four of the seven 4 f minority are occupied.Because of the Coulomb repulsion, the unoccupied 4 f states reside 3.2 ~ 3.6 eV above E F in ErN. Azero half-metallic gap is found for ErN in the LSDA+U band calculations, whereas EuP issemimetallic in both spin channels with the 4 f bands shifted down about 1 eV.

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Duanet al. [88] studied both volume and lattice strain effect on the electronic properties of using 4eff 6 f U = eV. The results are shown in Figure 14. It is evident that, at larger volumes, the ele(hole) pockets become substantially shallower, meaning that the bottom (top) of the band apprthe Fermi energy and the area of the Fermi surface decreases. Both carrier density and carrier mdecreases with an increase of the cell volume. Though it is hard to realize such dramatic vchange in practice, the trend should be correct in the regimes that prove to be experimeaccessible. This transition is close to resembling a Mott metal-insulator transition, and such m[153] may be used to explain the gap in GdN found experimentally.

We note that there is another mechanism of metal-semiconductor transition, i.e. throughd - f or s-f hybridization. In the famous Falicov-Kimball model [154], the single-electron states conextended Bloch functions and localized states centered at the metallic ions in the crystal. Thustemperatures, the quasiparticle excitations are either localized holes or itinerant electronselectron-hole interaction may be responsible for the semiconductor-metal phase transition. Thspirit is presented in the electron-hole liquid theory [145], which is used to explain the ground ScN. Using a novel many-body theory and Kondo lattice model (s- f model), Kreissl and Noltingpredicted that the decrasing magnetic order induces a transition from half-metallic to semiconbehavior in EuB6 [155]. If this can be confirmed experimentally, then similar examples shoulfound among the rare-earth monopnictides.

Figure 14 . The LSDA+U (U eff = 6.0 eV ) band structure of GdN in the vicinity of the Fermi energy for three volumeat the calculated equilibrium lattice parameter a = 4.92 , (b) at the lattice parameter increased by 5% (a = 5.16 the lattice parameter increased by 14% (a = 5.63 ). Solid and dotted lines represent spin majority and spin minorrespectively. The change of conducting properties are indicated by the change of energy difference between(bottom) of the hole (electron) pockets and the Fermi energy (from [88]).

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5.3. Magnetic ordering

The magnetic properties are closely related to the electronic and transport properties in rarmonopnictides. For instance, dramatic change of electric resistance has been found nearT c in GdN[120,124]. Despite their rather simple fcc structure, the magnetic orderings of the rare-earth pn

are very complicated [22,23,39,54]. Based on the experience with rare-earth metals [9,142generally believed that there exists an indirect RKKY exchange interactions in the rare-earth pnIn 1997, Liet al. estimated the exchange parameters of GdX from their several experimental dataThey attributed the sign change of exchange parameters to RKKY oscillations. Several groups that the super-exchange interaction should also exist, and may dominate these compounds [88,8

Duanet al. [88,89] proposed a systematic way to study the magnetic ordering in the rare-pnictides fcc structures. The basic strategy is to first deduce the exchange interaction parameGdX compounds by fitting the first-principles total energies of different magnetic configuratthose computed within the Heisenberg model,

th NN

1 2 3

n

n i jn i j

H J = , , >

= S S . ( 9 ) Here iS is the unit vector in the direction of the magnetic moment at thei-th lattice site, J n is theexchange parameter between then-th NN magnetic atoms, and we limit our consideration to third interactions. In this case the difference between the energy of the three AFM states( I, II, III)n E n = shown in Fig.1 and the energy of the FM state E FM are

I I 1 3

II II 1 2 3

III III 1 2 3

8 16 ,6 6 12 ,8 2 8 .

FM

FM

FM

E E E J J

E E E J J J

E E E J J J

= + = + + = + +

( 10 )

The so derived exchange parameters are then put into Monte Carlo simulations to calculatransition temperatures of the compound. Results on GdX are shown in Table 2.

Table 2. Calculated total energy differences per formula between ferromagnetic and three antiferromagnetic configfor Gd monopnictides n FM E E E = (n = I, II, III). Values inside the parentheses are calculated using the theoretical laconstants. Theoretical and experimental transition temperatures [14] are listed for comparison (from [89]).

a()Exp.(Theor.)

E I (meV)

E II (meV)

E III (meV)

J 1(meV)

J 2(meV)

J 3(meV)

T N(C)(K)MC Exp.

GdN 4.97 (4.92) 6.7(7.1) 4.2(5.1) 6.5(7.3) 0.86(0.95) -0.14(-0.04) -0.01(-0.03) 34(38) 5

GdP 5.71 (5.63) -2.8(-3.3) -6.5(-6.9) -3.5(-4.0) -0.17(-0.21) -0.74(-0.74) -0.09(-0.11) 12(13) 1

GdAs 5.86 (5.77) -3.9(-4.3) -8.4(-8.8) -4.7(-5.4) -0.22(-0.34) -0.91(-0.93) -0.13(-0.10) 14(16) 1

GdSb 6.22 (6.11) -5.7(-6.6) -11.1(-11.5) -7.2(-7.9) -0.51(-0.60) -1.13(-1.10) -0.10(-0.11) 20(19) 2

GdBi 6.30(6.24) -6.9(-7.3) -13.4(-13.8) -8.8(-9.3) -0.66(-0.71) -1.37(-1.38) -0.10(-0.10) 22(23) 2

The lattice constant dependence of the exchange parameters J 1 and J 2 are also obtained (Figure15). From the analysis of these data, Duanet al. [89] proposed an expression for the superexchanginteraction:

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4super2 3

pd d

t J n= , ( 11 )

where is the energy difference between the rare-earth 5d orbital and the outmost p state of pnicogenion,nd is the inducedd moment on rare-earth atom due to atomic 4 f -5d exchange interactions, and the

hopping parametert pd can be evaluated according to Harrison [156]. We should note here evaluation of Eq. (11) is quite empirical, since the accurate determinations of and other parametersare not available. Nevertheless, the estimated superexchange interactions in GdX are found to band have the same magnitude as the total effective magnetic interactions. These AFM superexinteractions are strengthened when the size of pnicogen atoms increases and eventually dominmagnetic interactions in rare-earth pnictides. This picture agrees well with experimental obser[60]. Using similar technique, Larson and Lambrecht [93] also obtained the exchange parameGdX in good agreement with experiment.

Figure 15. Calculated exchange parameters J 1 (a) and J 2 (b) for Gd pnictides as a function of the latticestrain: GdN (circles), GdP (stars), GdAs (diamonds), GdSb (squares), GdBi (triangles). The latticis defined by the relative deviation of the lattice constant from the theoretical equilibrium lattice c(from [89]).

Duan et al. [87] also investigated the magnetic dipole interactions and magnetic anisotrenergies to the magnetic properties in rare-earth monopnictides. They found that dipole-interactions could play an important role in the determining the magnetic behavior of the rar

compounds, and are especially instrumental in the magnetic anisotropy, but they cannot solely for stabilizing the magnetic ordering in a fcc structure [51].It should be pointed out that although the calculated Curie temperatures, using theor

exchange coupling parameters within the Heisenberg model, agree reasonably well with experiis still difficult to uniquely attribute the mechanism of exchange interactions in these compoundRKKY or super-exchange mechanisms. The relative contribution from RKKY interaction considerably due to the change in metallicity across the monopnictides. For example, if the syinsulating, the RKKY interactions should vanish. Therefore, in addition to the RKKY exchan

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superexchange contributions, other exchange coupling mechanisms are possible in the rarmonopnictides, such as higher order exchange interactions [37], direct exchange, and double exinteractions. Actually, there is experimental evidence that direct exchange coupling couresponsible for the higher Curie temperature found in insulating GdN films [124].

5.4. Spin-orbit couplingThe spin-orbit coupling is important for the band structure and many other properties, e.g. mcrystalline anisotropy, of compounds containing heavier elements like RE. For Gd ions, the spterm L (here s and L are spin and orbital angular momentum operators, respectively) mayignored since the 4 f shells are exactly half occupied. For other rare-earth ions with nonzero torbital angular momentum, the spin-orbit term may be significant. There are very fewab initio calculations on the rare-earth pnictides involving spin-orbit coupling. Duanet al. studied spin-orbiteffect in ErAs [85], and Johannes and Pickett also considerd this effect in their studies on EuEuP [91]. Leuenbergeret al. mentioned the presence of an important spin-orbit interaction in the fN p states of GdN [120].

Figure 16 presents the theoretical band structure of ErAs that takes into account both HubbU term and spin-orbit interaction. In this calculation, the inclusion of spin-orbit interaction is reala fully relativistic approach for the core electrons and a second variational method for the vstates [157]. In contrast to the LSDA+U result [84], the occupied 4 f bands are split further due to spin-orbit coupling, leading to better agreement with experiments [85].

Figure 16. The calculated LSDA+U +SO band structure of bulk ErAs. In the spin-orbit calculation, spup and spin down states are mixed (from [85]).

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Spin-orbit coupling is at the heart of magnetooptical effects such as Kerr and Faraday polarrotation. CeSb has been claimed to have a 90 degrees Kerr rotation [158]. While the intrinsic vthe Kerr rotation of CeSb is still debated, agreement exists that in any case CeSb has among theKerr rotation, possibly the largest. A series of calculations of the magnetooptical properties of tearth monopnictides reproduced experiment results with various success [83,92,159].

6 The Future Possibilities

While the rare-earth monopnictides have the simplest structure of the rare-earth composubstantive changes can be easily undertaken by altering the constituents. Actually, by mixinearth pnictides in different ratios, we can tune the physical properties, e.g. theT c, carrier density,resistance, of rare-earth pnictides to desired one [24,38,43,47,35,162]. Impurity dopingnonstoichiometry, also has significant influence on the properties on rare-earth pnictides. subjects are too complicated and are beyond the scope of our current review. We just want to mthat there are many choices for improving the physical, magnetic and transport properties of rapnictides.For binary rare earth pnictide compounds, there are various formulas with different structurexample, there are at least five structure types in the RX2 phases, i.e. LaP2, NdAs2, SmSb2, HoSb2,ZrSi2 [39]. Of particular interest we mention anti-Th3P4-type pnictides, which have attracted muchinterest recently [160,161]. As will show later, some of them demonstrate very largeT c. For ternarycompounds, the situation is much more complicated [39]. Active experimental studies arecarried out on these systems [162,163,164].

6.1. Possible half-metallic antiferromagnets

In 1995, Van Leuken and de Groot proposed another type of half-metallic material, i.e. themetallic antiferromagnet [165]. This material is calculated to be 100% spin polarized at thesurface but has zero net magnetization, thus could be used as a tip material in spin-polarized sctunneling microscopy. There are several theoretical predictions concerning the existence of thmetallic antiferromagnet [165,166,167,168], but none of them has been confirmed experimenta

Half-metallic antiferromagnets cannot be found with the simple pure rare-earth monopnictidFigure 10(a) shows, the symmetric arrangement of Gd ions forms exactly the same averaged pofor both spin-up and spin-down electrons, thus their DOS plots are the same. In considering G3+ andEu2+, which have the same electron configuration (8S7/2), and that both EuO and GdN are potentiahalf-magnetic materials, it may be very possible to make an EuO-GdN compound, in which E2+ andGd3+ are aligned antiparallel, yet two spin channels may show difference at Fermi level and resnominal half-metallicity. This idea needs further verifications, but if it is true, then this materialbe a half-metallic antiferromagnet with the simplest structure (double fcc).

6.2. Enhancement of the transition temperatures and potential device applications

The rare-earth monopnictides compounds have generally rather low transition temperatures. Gthe largestT c (58 ~ 68 K), but it is still far below the room temperature. How to improve theT c inthese compounds is of interest.

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In 1971, Kuznietz reported the effect of anion substitution in GdN and UN [169]. It was foucarbon substitution can significantly improve theT c, while O substitution works the other way. Anexample is GdN0.88C0.12(Gd4N3.5C0.5in Ref. [38]), whoseT c was reported to be as high as 190 K. Thiscan be explained by the reduction of Gd-Gd distance, which may lead to increase in 5d -5d overlap.Considering that Gd metal has somewhat higherT c = 293.2 K [170], efforts in this direction are ver

promising. Wachter and Kaldis also confirmed this kind of effect of Gd-Gd distance [43]. AcRef. [38] also reported that some other GdN derived alloys haveT c even higher than room temperature(340 K).

The other possibility for increasing theT c in the rare-earth pnictides is impurity doping. Magnetimpurities are helpful in assisting in the alignment of neighboring magnetic moments and strethe magnetic interactions or even change the RKKY interaction to a long-range ferromainteraction, thus dramatically enhancing theT c. Examples can be found in Ref. [171], which reportethat by adding few percent of magnetic ions such as Mn, theT c of GaN or ZnO well exceeds the roomtemperature. Again mentioning the experiments on GdN/Fe multilayers [125] in this contexworth noting that the Fe layers are found to be responsible for the long range magnetic order ilayer at temperatures largely aboveT c.

In addition, we noticed that some rare-earth pnictides of the Th3P4 type (or its anti-type) have veryhighT c values, even higher than that of Gd metal. For example, theT c of Gd4Bi3 is 340 K [172], forGd4Sb3 is 260 K [173], for Tb4Bi3 is 200 K. The origin of these highT cs needs further investigations.

Despite their low transition temperatures, applications for the rare earth pnictides do exisexample, ErAs has been used to study magnetotransport [51] and resonant tunneling [174]; Ebeen used in hybrid spin filter devices [175,176]. These materials are of special interest for ubarriers in magnetic tunnel junctions [177]. This is due to the exchange splitting of the conband which makes the barrier height spin-dependent. Thus, given the exponential dependencetunneling current on barrier height, a highly spin-polarized current is expected. In a series odependant tunneling experiments, Mooderaet al . found a tunneling spin polarization of approximate80% in Al/EuS/M junctions, where M was Ag, Au, or Al [178]. Using a related Eu chalcoEuSe, they were able to demonstrate essentially 100% spin polarization [179]. New hybrid dutilizing the spin filtering properties of rare-earth monopnictides are expected in the near future

7 Conclusions

After more than forty years efforts, stimulated first by the search for magnetic semiconductonow by spintronics materials, we now have a better understanding of the electronic, magnetransport properties of rare-earth monopnictides.

Rare-earth monopnictides are generally semiconductors or semimetals. Despite their simplsalt structure, they demonstrate various types of magnetic ordering generally with low tratemperatures. Their electronic structures and magnetic properties are sensitive to the tempepressure (strain) and impurity effects. The rare-earth 4 f -5d interactions and the hybridizations betweenthe rare-earth non-4 f and pnictogen p states are responsible for many fascinating phenomena that ocin rare-earth monopnictides. Different from the rare-earth metals, both super-exchange interactiindirect RKKY-type interaction coexist in rare-earth monopnictides, and the former is dominheavy rare-earth monopnictides. It is possible that other exchange coupling mechanisms, such aexchange and double exchange, also could be found in rare-earth monopnictides.

Based on the discussion in this paper, we conclude that the high polarization, nominally

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metallic, rare-earth monopnictides are most likely to be found in rare-earth nitrides or niinvolved rare-earth alloys. This is because those nitrides are on the border between semiconducmetal due to their anion sizes. Impurity doping, structural distortion, lattice constraint effectsignificant influence on the electronic, magnetic and transport properties of rare-earth nitridmight be helpful to modify these compounds into desired products.

During the past decades, various theoretical and experimental studies have been maunderstand the intriguing properties of these materials. Theoretically, much more powerful toobeen developed to solve the complicated yet fascinating many-body problem existing in these scorrelated systems, such as SIC, LSDA+U , GWA and DMFT. With the unbelievable increase of thcomputational power and the maturity of massively parallel computing technology, we nowenough confidence to deal with large scale calculation involved in these theoretical stExperimentally, state-of-the-art crystal and film growth techniques make it possible to determelectronic structures, e.g. the Fermi surfaces, and physical properties of these compounds. Mtechniques like low energy electron-diffractions, scanning tunneling microscopy, angle-re(inverse) photoemission, neutron-diffraction are helpful to make clear the geometric, electronmagnetic structures of the film and crystal. In addition, now element specific XMCD experim

study the properties of individual atoms in the system.There are still many unresolved issues related to the half-metallicity in rare-earth monopnand many blanks that need to be filled in Table 1. To address these issues or fill in the blanks, collaboration between experimentalists and theorists is absolutely necessary. Nevertheless, it jua little imagination to conclude that, in the future, we should expect further exciting results to from the study of electronic structure of rare-earth compounds.

Acknowledgments

The authors acknowledge insightful discussions with P.W. Anderson, D.S. Wang, A.G. PetukhNolting and A. Sharma. Special thanks to S. Granville, S. Suga, D.X. Li for giving permissionthe original figures in their publications. This work was supported by NSF (Grants DMR-02MRSEC-DMR-0213808, and EPS-9720643), the Nebraska Research Initiative and DepartmenArmy Grants DAAG 55-98-1-0273 and DAAG 55-99-1-0106 and the Office of Naval ResearchNo. N00014-06-1-0616). The computational part of this work was completed utilizing the RComputing Facility of the University of Nebraska-Lincoln.

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