Chemical Physics Letters 568–569 (2013) 121–124

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Chemical Physics Letters

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Magnetoelectric effect in organometallic vanadium–benzene wires

0009-2614/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.cplett.2013.03.025

⇑ Corresponding author. Fax: +91 1905 237945.E-mail address: arti@iitmandi.ac.in (A. Kashyap).

Priyanka Manchanda a,b, Pankaj Kumar a,b, Ralph Skomski b, Arti Kashyap a,⇑a School of Basic Sciences, Indian Institute of Technology, Mandi 175001, Himachal Pradesh, Indiab Department of Physics and Astronomy and NCMN, University of Nebraska, Lincoln, NE 68588, United States

a r t i c l e i n f o

Article history:Received 22 October 2012In final form 7 March 2013Available online 20 March 2013

a b s t r a c t

The magnetism of organometallic vanadium–benzene [V(C6H6)]1 nanowires in an electric field has beeninvestigated by density functional calculations. In the absence of an applied external electric field,[V(C6H6)]1 is found to be ferromagnetic (quasi-half metallic), with a moment of 0.92 lB per unit cell,and an applied electric field enhances this value substantially, to 1.32 lB in a field of 1.8 eV/Å. The electricfield also changes the preferential magnetization direction (easy-axis direction), from perpendicular tothe wire to parallel to the wire. This transition occurs in an electric field of 1.0 eV/Å.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Molecular magnets have recently attracted much attention dueto their intriguing magnetic properties and because they have po-tential applications in quantum computing and spintronics [1–3].Among these molecular magnets, one dimensional organometallicsandwich molecular wires (SMWs) are of particular interest, be-cause they exhibit unique properties such as half metallic nature[4,5], negative differential resistance [6], and a pronounced spin-filter effect [7–9]. Experimentally, seven-decker Vn(C6H6)m

[5,10,11] and eighteen-decker Eun(C8H8)m [12] nanorods have beensynthesized by a laser vaporization technique. The magnetic mo-ment of Mn(C6H6)m (M = Al, Sc, Ti, and V) has been measured usingStern–Gerlach molecular-beam reflection experiments [5,11]. Themagnetic moments of Scn(C6H6)n+1 (n = 1–2) and Vn(C6H6)n+1

(n = 1–4) increase monotonically with n and Tin(C6H6)n+1(n = 2, 3)was also found to be magnetic, whereas Ti(C6H6)2 was predictedto be nonmagnetic.

In the absence of an electric field, the magnetism of thesemolecular wires is theoretically well understood, although somecontroversy persists about transitions from half-metallic ferromag-netism to ordinary ferromagnetism. In agreement with the above-mentioned moments of Vn(C6H6)n+1, Kandalam et al. predict thatthe magnetic moment of Vn(C6H6)n+1 increases linearly with n[13] and that the V atoms couple ferromagnetically. Xiang et al.make the following predictions: Mn[(C6H6)]1 is a half-metallicferromagnet, [V(C6H6)]1 is ferromagnetic (quasi half-metallic, thatis, close to half-metallicity), Sc[(C6H6)]1 is paramagnetic, andTi[(C6H6)]1 is antiferromagnetic [8]. By contrast, Maslyuk et al.and Rahman et al. both found that the ground state of[V(C6H6)]1 is half-metallic [4,14]. Shen et al. studied the onset of

magnetism in wires containing cyclopentadienyl (C5H5) and first-row transition metals (M = Sc, Ti, V, Cr, Mn and Fe) and foundlong-range magnetism due to the transfer of one valence electronof the transition metal to C5H5 to form alternating M+ andC5H5

� ionic structures [15]. Zhou et al. have used density-functional theory to predict that Fe[C5H5]1 is half-metallic andshows a strong spin-filter effect [6]. The electronic and magneticproperties of Mn[Fe(C5H5)]n+1 clusters and M[Fe(C5H5)]1 (M = Sc,Ti, V, Mn) SMWs have also been studied using density-functionaltheory and the results indicate that M[Fe(C5H5)]1 is a ferromag-netic semiconductor [16].

Tunability of magnetic and magneto-transport properties by anapplied electric field is attractive from the viewpoint of applica-tions and has been reported for various systems [17,18].

Da et al. reported that a transverse external electric field can beused to switch [(C5H5)Fe(C5H5)V]1 molecular wires between ferro-magnetic semiconducting and half-metallic states, thereby alsochanging the magnetization [19]. A change in magnetization direc-tion from in-plane to axial has been observed by charging and dis-charging Eu2(C8H8)3 molecules [20]. Wu and Zeng investigated theswitching from nonmagnetic semiconducting to half-metallicbehavior due to positive and negative charging of [Cr(C6H6)]1and Mn(C5H5)1 SMWs [9].

However, the investigation of magnetoelectric effects in orga-nometallic wires is still in its infancy. In this Letter, we performdensity functional theory (DFT) calculations to investigate the ef-fect of an external electric field on electronic and magnetic proper-ties of [V(C6H6)]1 single-molecule nanowires. We have chosen the[V(C6H6)]1 system, chosen because [V(C6H6)]1 is a potentiallyeffective spin-filter [4].

2. Calculations

Our calculations have been performed using the projectedaugmented wave (PAW) method, as implemented in the Vienna

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ab initio simulation package (VASP) [21]. The generalized gradientapproximation (GGA-PBE) is used for exchange and correlation[22], and the kinetic energy cut-off is taken as 450 eV. For the elec-tronic-structure calculations, a 1 � 1 � 45 Monkhorst–Pack grid fork-point sampling is used [23]. The full structure relaxation wasperformed until the force acting on each atom was less than10�2 eV/Å, and a convergence criterion of 10�6 eV has been usedfor the electronic-structure calculations.

Figure 1 shows the considered organometallic wire structure.Our optimized lattice constant, c = 3.37 Å, is consistent with previ-ous results [8,15]. The lattice constant in x and y directions are ta-ken to be 15 and 20 Å, to ensure that there is no interactionbetween neighboring wires. The external electric field (EEF) isintroduced by a dipole-layer method, where a dipole sheet isplaced in the middle of the vacuum [24].

3. Results

Figure 2 shows the total magnetic moment as a function of theapplied electric field E. In low fields, the initial behavior is nonlin-ear and nearly quadratic, whereas for E > 0.7 eV/Å the dependenceis approximately linear. Our calculations show that the magneticmoment changes significantly as the electric field is applied, fromV–C6H6 0.925 lB per unit cell for E = 0–1.32 lB per unit cell in afield of E = 1.8 eV/Å. The zero-field value agrees with previous

Figure 1. The organometallic structure investigated in this Letter: a sandwichmolecular wire (SMW) of [V(C6H6)]1 in an external electric field.

Figure 2. The calculated magnetic moment of [V(C6H6)]1 as a function of theexternal electric field.

measurements [8,15]. The field-induced magnetization change ofabout 25% in 1 eV/Å is large compared to previous predictions formetallic systems (about 4%) [17,25]. Note, in particular, that thislarge enhancement is obtained only in the organometallic struc-ture, not for pure vanadium.

In zero electric field, the magnetism of the [V(C6H6)]1 wires isunderstood from the total and projected density of states (DOS)shown in Figure 3. There is a gap above the Fermi level of themajority states, Figure 3a, showing that the state of the organome-tallic [V(C6H6)]1wires is quasi half-metallic. As shown in Figure 3b,the magnetic moment mainly originates from the 3d orbitals of theV, which is split in the ligand field of the benzene. This splitting isnecessary to achieve ferromagnetism in the wires. By contrast, themoment contribution of the benzene p-orbitals is rather small. Dueto the crystal field of benzene, the bands of V split into three sets,namely degenerate D1(dxy, dx2�y2 ) and D2(dyz, dxz) bands, and non-bonding dz2 bands. Due to symmetry, the six p-orbital of benzeneform one pr, two pp (below the Fermi level), two pd, and onep/ (above the Fermi level) orbitals. The hybridization of the pp-orbital of benzene with the D2 orbitals of V is very strong, but thisdoes not contribute to the magnetic or electric properties, becausethese subbands are completely empty. The dz2 band is localized,weakly coupled to the pr-orbital of benzene, and spin split. Dueto its high DOS at the Fermi level, it yields a strong contributionto the magnetic moment. The small negative moment on benzeneis due to hybridization between D1 and pd states.

The effect of the electric field on the magnetization is shown inFigure 4, which compares the spin-density distributions in zeroelectric field and 1.6 eV/Å. In zero electric field, the spin distribu-tion is symmetric, but in 1.6 eV/Å, it shifts towards the negativeside of the electric dipole which results in a change in magneticmoment. A more detailed explanation of the effect of the electricfield on the magnetization is provided by the density of states. Fig-ure 5 shows total and projected DOS in an electric field of 1.6 eV/Å.The corresponding change in magnetization is realized by both adownshift of majority states and an upshift of minority states.Since the spin moment is equal to the difference between majorityand minority electrons, this mechanism yields a magnetizationchange as a function of electric field.

The electric field redistributes k-dependent energy levels nearthe Fermi energy, especially the dz2 levels and also the dx2�y2 )and dxy levels, whereas no significant change is seen in dxz anddyz states. Figure 6 compares the orbital-projected vanadium dz2

densities of states in a field of 1.6 eV/Å (orange line) with thosein 0.7 eV/Å (dashed line) and zero electric field (black line). As indi-cated by the blue arrow, the changes in the DOS (and therefore inthe magnetization) depend on the strength of the electric field. Forthe dz2 band, the changes in the majority DOS predominantly occurbetween zero and 0.7 eV/Å, whereas most of the changes in theminority DOS (for example in the region indicated by the arrow)are realized above 0.7 eV/Å.

4. Discussion

Our zero-field moments are consistent with values published inthe literature [8,15]. The ferromagnetism is due to the double-ex-change mechanism which is direct exchange coupling betweenneighboring metal atoms [26,27]. The moments are slightly smal-ler than those reported by Maslyuk et al. [4], which is probablydue to the semilocal GGA functional, which underestimates themagnetic moment of SMWs as compared with the hybrid func-tional such as B3LYP some cases [28]. The change in magnetic mo-ment of [V(C6H6)]1 as a function of electric field is significant ascompared to metallic systems [17,29].

Figure 3. Densities of states (DOS) of [V(C6H6)]1 in zero electric field: (a) total DOS, d-state DOS of V, and p-state DOS of benzene, and (b) orbital-projected DOS for thed-orbitals of V and the p-orbitals of benzene. The top and bottom parts of the figures refer to majority and minority spin directions, respectively.

Figure 4. Spin-density distribution projected to the y–z plane: (a) in the absence of an electric field and (b) in a field of 1.6 eV/Å. The difference is seen most clearly bycomparing the centers of (a) and (b), where the wire axis pierces a benzene plane.

Figure 5. Densities of states (DOS) of [V(C6H6)]1: total DOS, d-state DOS of V, andp-state DOS of benzene in the presence of 1.6 eV/Å. Figure 6. Orbital-projected 3d vanadium densities of states (DOS) for the dz2 states.

The blue arrow points to a region of minority states where the DOS remainsvirtually unchanged between 0 eV/Å (black line at the bottom) and 0.7 eV/Å(dashed line) but undergoes a strong variation between 0.7 and 1.6 eV/Å (orangeline). Such changes lead to a complicated dependence of the magnetization on theelectric field. (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

P. Manchanda et al. / Chemical Physics Letters 568–569 (2013) 121–124 123

To further gauge the accuracy of our numerical method, wehave studied the effect of correlations on the magnetic propertiesof SMWs, using a GGA + U approach [30] and assuming thatU � J = 3 eV [4] for the V atoms. We find that the electric-fielddependence of the moment remains nearly unchanged after inclu-sion of GGA + U, indicating that correlations are ratherunimportant.

So long as the electric field E is a small perturbation, the mag-netic moment m can be expanded into a series of m = mo + c1E + c2E2.By symmetry, c1 = 0, so that only the quadratic term survives.

However, this perturbative regime breaks down in large electricfields. Figure 2 shows that m(E) undergoes a fairly sharp transitionfrom a quadratic to an more or less linear dependence at 0.7 eV/Å,with a discontinuous reduction in the slope dm/dE. If the seriesexpansion was extended to fourth order, such a slope reduction

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would could correspond to c4 < 0, but the description of disconti-nuities requires terms of arbitrary order. The reason is that thecharacter of the primarily involved 3d abruptly subbands changesas the electric field increases. For example, Figure 6 indicatesqualitative changes at 0.7 eV/Å, which are difficult or impossibleto describe by a series expansion.

As a side project, we have investigated the effect of the electricfield on the magnetocrystalline anisotropy energy (MAE). The MAEis calculated by taking the difference of energy in magnetizationdirection along the wire and perpendicular to the wire. The calcu-lated uniaxial anisotropy constant K1 [27] in zero electric field is0.02 meV per unit cell, and the easy magnetization direction is per-pendicular to the wire. Our MAE results quantitatively differ fromthose in Ref. [31]. This is not surprising, because magnetocrystal-line anisotropy exhibits a pronounced dependence on details ofthe electronic structure [32–34]. In the present case, the effect isprobably due to different lattice parameters, but this is difficultto judge, since no lattice parameters are provided in Ref. [31].The preferential magnetization direction (easy axis) changes fromperpendicular to along the wire with K1 = �0.04 meV at theE = 1.0 eV/Å, and at E = 1.5 eV/Å, K1 = �0.06 meV.

As the magnetization change, the change in magnetocrystallineanisotropy is explained by the d-electron shift explains. The reasonis that itinerant anisotropy is caused by spin–orbit-interactingpairs of occupied and unoccupied levels below and above the Fermilevel, respectively [33,34]. This result is important, because it indi-cates that an electric field can be used to switch the magnetizationdirection.

5. Conclusions

In summary, we have used first-principle calculations to ex-plore electronic and magnetic properties of organometallic wiresin an external electric field. For our calculations, we have usedvanadium–benzene sandwich wires, which are experimentallyand technologically relevant. We have found that the external elec-tric field yields a substantial change in magnetization of vana-dium–benzene wires, one to two orders of magnitude larger thanin typical metallic wires. Furthermore, the preferred magnetizationdirection, or easy axis, switches between perpendicular directionand along the wire. Both findings are important for the scientificunderstanding of organometallic nanostructures and may havefar-reaching implications in molecular electronics and spintronicapplications.

Acknowledgement

This research is supported by NSF-MRSEC (DMR-0820521) andDST.

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