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Journal of Magnetism and Magnetic Materials 321 (2009) 607–612

Contents lists available at ScienceDirect

Journal of Magnetism and Magnetic Materials

0304-88

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/jmmm

Theoretical investigation on structural, magnetic and electronic properties offerromagnetic GdN under pressure

Vipul Srivastava a,�, M. Rajagopalan b, Sankar P. Sanyal a

a Department of Physics, Barkatullah University, Hoshangabad Road, Bhopal, Madhya Pradesh 462026, Indiab Crystal Growth Centre, Anna University, Chennai 600 025, India

a r t i c l e i n f o

Article history:

Received 24 September 2008Available online 29 October 2008

PACS:

71.20.�b

31.15.aq

82.60.Fa

75.20.Hr

Keywords:

Band structure

Tight-binding calculations

Half-metallic

Phase transition

Magnetic properties

53/$ - see front matter & 2008 Elsevier B.V. A

016/j.jmmm.2008.10.019

esponding author. Tel.: +919827539398; fax

ail address: vips73@yahoo.com (V. Srivastava

a b s t r a c t

The tight-binding linear muffin tin orbital (TB-LMTO) method within the local density approximation is

used to calculate structural, electronic and magnetic properties of GdN under pressure. Both

nonmagnetic (NM) and magnetic calculations are performed. The structural and magnetic stabilities

are determined from the total energy calculations. The magnetic to ferromagnetic (FM) transition is not

calculated. Magnetically, GdN is stable in the FM state, while its ambient structure is found to be stable

in the NaCl-type (B1) structure. We predict NaCl-type to CsCl-type structure phase transition in GdN at a

pressure of 30.4 GPa. In a complete spin of FM GdN the electronic band picture of one spin shows

metallic, while the other spin shows its semiconducting behavior, resulting in half-metallic behavior at

both ambient and high pressures. We have, therefore, calculated electronic band structures, equilibrium

lattice constants, cohesive energies, bulk moduli and magnetic moments for GdN in the B1 and B2

phases. The magnetic moment, equilibrium lattice parameter and bulk modulus is calculated to be

6.99mB, 4.935 A and 192.13 GPa, respectively, which are in good agreement with the experimental

results.

& 2008 Elsevier B.V. All rights reserved.

1. Introduction

Gadolium nitride, GdN, has significant experimental andtheoretical importance due to intricate electronic and magneticproperties [1–6]. The ambient structure of GdN is NaCl-type(B1 phase) (Table 1) structure and the magnetic structure of GdNhas been the subject of notorious discussion in the literature [7,8].Nevertheless, modern studies elucidate that it is a ferromagnetwith Curie temperature �58–69 K [7,9–12]. The rare-earth (RE)nitrides lie on the boundary between metals and insulators, andas such present an exciting challenge to both experiment andtheory. Although most RE nitrides have been shown to besemimetallic, there is still ambiguity about GdN regardingwhether it is an insulator or a semiconductor or a metal [2–5].Such ambiguous behavior of GdN is discussed by Doll [13] in hisrecent study. From the theoretical point of view, several studiesare reported, where similar ambiguity is found however; the firsttheoretical study on GdN was an augmented plane wavecalculation using the Slater exchange potential [6], in which hereported its insulating nature with a very small gap. Most of thespin-dependent study shows GdN as half-metallic (HM). HMbehavior was found in many RE pnictides by Aerts et al. [14] using

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: +91755 2677723.

).

the ab-initio self-interaction corrected local spin density (SIC-LSD)calculations. According to Aerts et al., in one whole series(Ce–Yb–nitride) various nitrides show various properties likeHM, insulating and metallic. Starting from Ce–Gd–nitride, thesenitrides are found to be half-metallic, where GdN is on theboundary. After GdN, the series Tb–Ho–nitride shows insulatingbehavior, while the series Er–Yb–nitride belongs to the metalliccategory. In the HM behavior, one spin species is metallic and theother is semiconducting/insulating. This property has led to someinterest in GdN as a possible candidate for spin-dependenttransport devices, exploiting the spin filter, giant magnetoresis-tance or tunneling magnetoresistance effects. In a study of GdN byAerts et al., the calculated value of band gap is found to be0.082 Ry in one spin, while in another spin density of states (DOS)at the Fermi level is calculated to be 0.065 States/Ry/f.u., resultingin GdN as an HM candidate. A recent detailed review regardingthe electronic, magnetic and transport properties of RE mono-pnictides is presented by Duan et al. [15]. It can be clearlyreviewed from the study presented by Duan et al. that GdN underdifferent schemes, e.g. LSDA and LSDA+U, shows HM nature with agap of about 0.5–0.6 eV in ambient conditions.

An accurate description of the electronic structure of REcompounds is a very challenging problem because of theirpartially filled 4f shells [16]. These partially filled 4f shells areresponsible for many of the interesting properties in the pnictides.As far as the f-electron effect is concerned to GdN, in the first

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Table 1Structural properties of GdN for B1 and B2 phases.

Properties NaCl type CsCl type

P-I P-II

Lattice parameter (A)

Pre. 4.935 2.785

Expt. 4.99a Not observed

Bulk modulus (GPa)

Pre. 192.13 204.6

Expt. 192735b Not observed

Pressure derivative

Pre. 3.64 �

Expt. � �

m (mB/GdN)

Pre. 6.99 6.98

Others 7.0c

Structural transition pressure (GPa)

Pre. 30.4 (P-I-P-II)

Expt. Not observed

V/V0 at Pt

Pre. 0.845 0.696

Pre., Present; Expt., Experimental.a Ref. [31].b Ref. [32].c Ref. [20].

V. Srivastava et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 607–612608

study by Slater [6] the f-electrons were treated as core states inthe calculation. A further calculation with the f-electrons in core[1] using local density approximation (LDA) gave a similar bandstructure (BS), but without a gap. The spin-polarized solution wasfound to be metallic for majority spin, and insulating for minorityspin. Recently, several calculations explicitly treating thef-electrons were performed. When the pure LDA was used, ametal was obtained [17,18], with the occupied f-states beingbelow the Fermi level. Taking into account the strongly correlatednature of the f-electrons still resulted in a metallic solution[17–19]. A slightly different approach to take into account thestrongly correlated nature of this system is to apply a self-interaction correction. This led again to an HM ground state forGdN, with a gap in the minority channel [14].

So far as the pressure-induced studies on GdN are concerned,very less information is available [20]. The interest in the nitridesof RE and transition metal (TM) is increased with respect to theirstructural, electronic and magnetic properties, both experimen-tally and theoretically. Our interest in NaCl structure type ismotivated by the following five facts: (i) the NaCl type is thesimplest and most common AB-type structure, where A is the REion and B is pnictogen, (ii) ambiguious information about GdNwith respect to structural, electronic and magnetic propertiesunder ambient conditions, (iii) no information on pressure-induced structural changes in the literature, (iv) the variation inmagnetic moment (MM) under pressure and (v) role of f-electronin HM character under pressure. We have therefore performedboth spin- and non-spin-polarised electronic BS calculations usingthe first-principles tight-binding linear muffin tin orbital (TB-LMTO) method at ambient as well as at high pressure to check thestability in magnetic and nonmagnetic (NM) phases. We reportthat GdN crystallizes in NaCl-type structures and is stable in theferromagnetic (FM) phase. Under the application of pressure, GdNretains as HM FM but undergoes structural phase transition. Wepredict a B1 to B2 structural phase transition in GdN at a highpressure of 30.4 GPa. We further report the DOS, energy gap inrespective up- and down-spins, lattice parameters, bulk modulusand MM at different pressures.

The organization of the paper is as follows: Section 2 describesthe method of calculation of electronic BS and phase transitionpressure. In Section 3 potentially interesting results with somepredictions are discussed. Sections 3.1 and 3.2 deal with thestructural and electronic, magnetic properties of GdN at ambientand at high pressure, respectively. Finally in Section 4, we haverecapitulated the results.

2. Method of calculation

The total energy, BS and DOS for GdN are calculated in NM andFM states, similar to our earlier work [21–24] using the TB-LMTOmethod [25,26] within the LDA [27]. von-Barth and Hedin [28]parameterization scheme had been used for exchange corre-lation potential. GdN crystallizes in the NaCl-type structure(space group, P42/mnm, no. 225) and is magnetically stable inthe FM state. In the FM ground state, gadolium and nitrogenatoms are located at the following positions: Gd: (0, 0, 0) and N:(0.5, 0.5, 0.5). The structure of the high-pressure phase is CsCl-type (space group, Pm3m, no. 221) with positions at Gd: (0, 0, 0)and N: (0.5, 0.5, 0.5). As mentioned earlier [21–23], the TB-LMTOmethod works well for the close-packed structures and since GdNbelongs to the NaCl-type structure, which is not a close-packedstructure, two equivalent empty spheres are introduced atpositions (0.25, 0.25, 0.25) and (0.75, 0.75, 0.75). The emptyspheres are introduced in such a way that they do not break thecrystal symmetry [28]. However, the CsCl-type structure (high-pressure phase) is a close-packed structure and the TB-LMTOmethod does not include any empty spheres. The total energy(per formula unit) was calculated for GdN in these two structures.The Wigner–Seitz sphere was chosen in such a way that thesphere boundary potential is minimum and the charge flowbetween the atoms is in accordance with the electro-negativitycriteria [29]. The E and k convergence were also checked. Forboth B1 and B2 phases, the calculations were performed for 512kpoints (grid of 8�8�8) in the Brillouin zone. The tetrahedronmethod of Brillouin zone integration had been used to calculatethe total DOS. The total energy was computed by reducing thevolume from 1.05 to 0.70 V0, where V0 is the equilibrium cellvolume. The calculated total energy was fitted to the Birchequation of state [30] to obtain the pressure–volume (P–V)relation. The pressure is obtained by taking volume derivative ofthe total energy. The bulk modulus B ¼ �V0 dP/dV is calculatedfrom the P–V relation.

The structural phase transition is said to occur when changesin the structural details of the phase are caused by a variation ofthe free energy. The GdN transforms from their initial B1 to B2

structure under pressure. The stability of a particular structureis decided by the minima of the Gibbs energy (Enthalpy, atabsolute T). The phase transition pressure PT can be obtained bymatching enthalpies of both the structures. Therefore, at PT thedifference in enthalpy becomes DH ¼ HB2�HB1 ¼ 0.

3. Results and discussion

Most of the rare-earth pnictides crystallize in the common rocksalt (RS) structures. We have performed self-consistent TB-LMTOcalculations for RS-GdN to explore the structural, electronic andmagnetic properties under ambient and at high pressure.

3.1. Structural properties

This section describes the structural and magnetic stabilities ofGdN at high pressure. Both structural and magnetic stabilities are

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Fig. 2. Total (per formula unit) energy variation of GdN in different structures.

Fig. 3. Pressure–volume relation for NaCl-type GdN.

V. Srivastava et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 607–612 609

checked by obtaining the total energies. First, we have checkedthe magnetic stability of NaCl-type GdN. We have obtained totalenergies in NaCl-type structures by performing spin-polarized(FM) and non-spin-polarized calculations. In order to show themagnetic stability of GdN in NaCl-type structures, we have plottedthe variation of total energy under compression in Fig. 1. One cannotice from the figure that the stability of GdN is found to be inthe FM state. No FM to NM transition is seen in GdN undercompression and the FM state is stable at ambient pressure.A difference amount of total energy in FM and NM states iscalculated to 534.47 m Ry at V/V0 ¼ 1, which remains almostconstant for other compressions. The equilibrium cell volume inthe FM state at ambient pressure is estimated to be 4.93 A,which can be compared with the experimentally obtained value of4.99 A [31].

Similar calculations are also performed for CsCl-type struc-tures, which is taken as the high-pressure phase in the presentcalculations. The total energy is estimated in the B1 and B2

phases in the FM state. Fig. 2 shows the variation of total energywith relative volume for both B1 and B2 phases in the FM stateand it is found that the B1 phase is more stable than the B2

phase at ambient pressure. The minimum of the total energyin the B1 phase changes to the B2 phase as pressure reaches30.4 GPa. We predict a first-order structural phase transition inGdN at a pressure of 30.4 GPa. It may be mentioned here thatin the B1 phase, the calculated volume reduces from 202.79 to176.58 a.u3 with an increase in pressure from ambient to 30.4 GPa.The variation of lattice parameter a, at the phase transitionpoint, due to this change in volume is estimated to be from 4.93to 4.71 A. The calculated total energies are fitted to the Birchequation of state [30] in order to obtain the P–V relation-ship, which is shown in Fig. 3. The calculation of transitionpressure is completed by estimating enthalpy in both thestructures, as mentioned in Section 2. In Fig. 4, we have there-fore plotted the variation of enthalpy with pressure in the B1 andB2 phases. The matching of enthalpy at a pressure of 30.4 GPaindicates a structural phase transformation in GdN and isindicated by an arrow in Fig. 4. Fig. 3 further infers the volumecalculated just after transition 145.83 a.u3, which correspondsto an a value of 2.79 A. Nevertheless, we have calculated atotal volume collapse of 14.9% during phase transition. For wantof experimental results, we are unable to compare the presentprediction. Furthermore, the bulk modulus at ambient pressure

Fig. 1. Variation of total energy with relative volume in ferromagnetic and non-

magnetic states of NaCl-type.

is calculated to be 192.13 GPa and is compared with the avail-able experimental results of 192735 GPa in the literature [32]and with the other theoretical results [1,13,17]. Furthermore,from the present study the bulk modulus for the B2 phase isfound to be 204.6 GPa. The bulk modulus for the B2 phase hasnot been reported so far and hence comparison is not possible.The Muffin Tin radii (RMT) used in the present calculation forGd, N and E (empty sphere) are 3.152, 2.197 and 1.480 a.u,respectively.

As stated above that GdN is found to be FM and from thepresent study we find that the contributions to the MM comeentirely from the Gd atom rather than the N atom. At ambientpressure the net MM is calculated to be 6.99mB [for Gd, 6.99mB],which is in good agreement with others’ reported value of 7.0mB

[14]. We have also calculated MM under various compressions,which are shown in Table 2. It is clear from the table that the totalMM of GdN decreases as pressure increases, which is a commonphenomenon in such kind of compounds. The total MM in the B2

phase is also calculated and found to be 6.98mB [for Gd, 6.92mB].

3.2. Electronic properties

The spin-polarized electronic structure calculations (based onLDA) for GdN in the NaCl- and CsCl-type structures are performed.

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Fig. 4. Variation of enthalpies in NaCl- and CsCl-type structures.

Table 2Magnetic moments (mB) of GdN under compression in B1 and B2 phases (in Bohr

magneton, mB).

B1 Phase B2 Phase

V/V0 Gd N Total Gd N Total

1.00 6.994 �0.030 6.999 6.959 �0.040 6.999

0.95 6.987 �0.029 6.999 6.958 �0.042 6.999

0.90 6.988 �0.039 6.999 6.955 �0.045 7.000

0.85 6.979 �0.042 6.995 6.949 �0.049 6.998

0.80 6.958 �0.045 6.981 6.940 �0.054 6.994

0.75 6.920 �0.049 6.945 6.907 �0.070 6.977

0.70 6.858 �0.057 6.884 6.876 �0.078 6.955

0.65 6.771 �0.050 6.799 6.876 �0.078 6.955

Fig. 5. Band structure of ferromagnetic GdN at ambient pressure. Solid line

represents majority spins while dash lines represent minority spins.

Fig. 6. The partial density of state of GdN at high pressure in CsCl-type structure.

Spin minority states are of negative values with dot lines.

V. Srivastava et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 607–612610

The electron dispersion curves along the high-symmetry direc-tions in the Brillouin zone for FM GdN in the B1 phase are shownin Fig. 5. In Fig. 5, the solid line represents the BS of majority spins,while BS for minority spins in the B1 phase is shown by dottedlines. It is HM, because the bands for majority spin cross the Fermienergy, whereas the minority bands have a gap. The f-bands arepositioned at �–2.6 eV (occupied 4f states) below and �3.5 eV(unoccupied 4f states) above the Fermi energy. The Fermi level Ef

is shown by single horizontal dotted line and is set to 0. In Fig. 5the other bands at the lower energy side are due to the s-likestates of nitrogen, and mixing of Gd-d states and N-p states near Ef

indicates its metallic nature, while the gap between the nitrogenp-like and gadolium d-like states indicates its semiconducting

nature, overall indicating it as HM. Due to the FM decoupling, oneof the spin subbands (generally the majority-spin or up-spinsubband) is metallic, whereas the Fermi level falls into a gap of theother (down-spin) subband. Our results on the electronic proper-ties of GdN under ambient pressure are in good agreement withthe results reported by others [14,17,18] . Nevertheless, in a veryrecent study, Doll [13] also reported its HM nature in LDAtreatment and insulating behavior in Hartree Fock (HF) treatment.On the third hybrid functional B3LYP treatment, three solutionswere found by Doll. The lowest one had a gap for majority spin;however, for minority spin, the valence and conduction bandsonly touch at certain points of the Brillouin zone. The correspond-ing DOS was thus very small around the Fermi energy. The secondsolution was very close in energy (�0.1 eV higher), and themajority bands cross the Fermi energy. A third solution was foundto be insulating.

The DOS, projected on N-(s and p), Gd-d and Gd-f, is shown inFig. 6, which provides a clear picture of the elemental contributionto the electronic structure of GdN. The BS and the projected DOSdiagram shows that bands in the top of valence band region(or just below the Ef) are due to N-2p states (in the energy range of0–5 eV), which are actively participating in hybridization withGd-5d states in the majority spin. Such Gd-5d–2p hybridization(GX direction) is imperative in ascertaining many physicalproperties in Gd-pnictides. This hybridization results in MMs onthe pnictogen site and is responsible for the attractive magneticordering and transport properties [15]. One can notice from Fig. 6that there is no separation between the majority and minoritystates of N-s, N-p and Gd-d states and these states exist at thesame energy level except for Gd-f states. The separation betweenthe Gd-f majority and minority states is caused by the exchangesplitting. The exchange splitting is a necessary factor to causehalf-metallicity in the FM compound.

As predicted in the previous Section, under the application ofpressure HM GdN transforms (PT ¼ 30.4 GPa) from NaCl- to CsCl-type structure. In the CsCl-type structure, GdN is found to be FM,we have therefore plotted the BS along the high-symmetrydirections for majority (solid lines) and minority spin (dotted

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Fig. 7. Band structure of half-metallic GdN at Pt ¼ 3.4 GPa in CsCl-type structure.

Solid and dash lines represent majority and minority spins states, respectively.

Fig. 8. The partial density of state of GdN at high pressure in CsCl-type structures.

Spin minority states are of negative values with dot lines.

V. Srivastava et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 607–612 611

lines) channels in Fig. 7 at a pressure of phase transition pressure,i.e. 30.4 GPa. It is found from Fig. 7 that all the states seem verysimilar to the NaCl-type structure. As we increase the pressure,the hybridization of Gd-‘d’ and N-‘p’-like states increases and thelower energy bands are shifted to the higher energy side. In theminority spin channel the gap between the N-p and Gd-d statesreduces, while Gd-f states shift to the higher energy side andparticipate in the bonding with N-p states. On the other hand, incase of majority spin the metallic property increases, resulting inHM in CsCl-type structures.

Fig. 8 shows the partial DOS of GdN at transition pressure inCsCl-type structures. In the first diagram a sharp peak around�13 eV is of N-2s states, while N-2p states can be seen in theenergy range of 0 to �5 eV. The more broadened N-2p states nearthe Fermi level hybridized strongly with Gd-d and -f states.The number of f-states in the CsCl-type structure reduces fromnearly 30 to 15 states/eVcell. This decrease may be due to afractional change in the valence state of Gd during the pressure-induced structural transition. It may be mentioned here that

this fractional valence change involves a decrease in energyseparation (dEg) between the f-states and the conduction-bandedge with an increase in pressure. Critically the fractionaldelocalization of these f-states is possible due to the decrease indEg with pressure.

4. Conclusion

The scalar-relativistic electronic band-structure calculationsare obtained for both the B1 and B2 phases of GdN using the TB-LMTO method. The phase stability has been studied using thetotal energy calculations and our results show that GdN is stablein the magnetic state and there is no NM to magnetic or magneticto NM transition. At ambient pressure it also shows half-metallicity with a total MM of 6.99mB. From the energy–volumerelation we find that GdN is stable in the B1 phase as compared tothe B2 phase at ambient pressure and we predict a phasetransition from the B1 to the B2 phase at around 30.4 GPa. Thetotal MM in the B2 phase is also calculated and found to be 6.98mB

[6.92mB/Gd]. The calculated lattice parameters, transition pres-sure and volume collapse are compared with experimentallyobserved results. The bulk modulus and MMs are found to be inagreement with others’ results. State of affairs of the experimentis not fully apparent; high-pressure experimental studies areindeed needed to verify our structural and magnetic propertiesof GdN.

Acknowledgements

The present work is financially supported by the Departmentof Science and Technology (DST), New Delhi. One of the authors,VS, is thankful to DST for the award of Young Scientist under theFast Track scheme (DST Project no. SR/FTP/PS-30/2005). SPSgratefully acknowledges CSIR, New Delhi.

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