Transport and magnetic properties of

Transport and magnetic properties of BaVSe3

Ana Akrap,1,* Vladan Stevanović,2 Mirta Herak,3 Marko Miljak,3 Neven Barišić,1,4 Helmuth Berger,1 and László Forró1

1Institut de Physique de la Matière Complexe, EPFL, CH-1015 Lausanne, Switzerland2Institut Romand de Recherche Numérique en Physique de Matériaux (IRRMA) and Institute of Theoretical Physics (ITP),

Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland3Institute of Physics, P.O. Box 304, HR-10000 Zagreb, Croatia

4Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany�Received 9 September 2008; revised manuscript received 22 October 2008; published 10 December 2008�

We report a comprehensive study of transport, magnetotransport, and magnetic properties of single crystalsof BaVSe3. The paramagnetic metal-ferromagnetic metal transition at 43 K was followed as a function ofpressure by measuring the electrical resistivity and the thermoelectric power. The exponent of the low-temperature power-law dependence of the resistivity increases with pressure. The effective magnetic momentobtained from magnetic susceptibility in the paramagnetic regime is �eff=1.40�B. The study was completed byband-structure calculations based on density-functional theory both at ambient and high pressures. Transportcoefficients of BaVSe3 resemble the high-pressure phase of BaVS3, which suggest that the replacement ofsulfur with selenium can be viewed as chemical pressure.

DOI: 10.1103/PhysRevB.78.235111 PACS number�s�: 74.25.Fy, 71.20.�b, 75.47.�m, 74.62.Fj

I. INTRODUCTION

The paramagnetic-ferromagnetic �PM-FM� transition in3d transition-metal compounds has received lot of attentionbecause of its importance in applications, for example, incolossal magnetoresistance compounds,1 or because of theexotic physics it can lead to, such as in the case of MnSi.2,3

Like this latter compound, BaVSe3, which has a structurallyone-dimensional character, shows a PM-metal to FM-metaltransition at 43 K.4,5 The in-depth investigation of this com-pound and its comparison to other 3d correlated systems hasbeen precluded until now due to the lack of sizable singlecrystals. A further importance in studying BaVSe3 is a recentinterest in its sister compound of BaVS3, which has a veryrich phase diagram6–8 and whose high-pressure magneticground state is poorly understood. Formally, because of thestronger interchain overlap due to the larger selenium atoms,BaVSe3 could be considered as the high-pressure counterpartof BaVS3.

The room-temperature structure of the selenide is thesame as that of the sulfide and is shown in Fig. 1. Slightlyabove room temperature, BaVSe3 crystallizes in the hexago-nal P63 /mmc symmetry.9 Vanadium chains directed along caxis form a triangular lattice in the ab plane. Each vanadiumatom is surrounded by a trigonally distorted octahedron ofchalcogen atoms. The unit cell contains two vanadium sitesalong the chain. Barium atoms lay between the chains in 12coordinated sites. Due to the difference in the chalcogensizes, the unit cell in BaVSe3 is slightly larger than in thesulfide. The V-V distance along the c direction is 2.93 Å andperpendicular to the chains is 7.0 Å. For comparison, thesevalues are 2.8 and 6.75 Å in the sulfide. A structural transi-tion from hexagonal to orthorhombic unit cell was reportedto take place between 290 and 310 K.9 This transition leadsto a zigzag distortion of the vanadium chains in the bc plane.

Because of the enhanced interchain orbital overlaps, incontrast to the insulating ground state of BaVS3, the selenidewas found to be metallic in the whole temperature range,4

just like BaVS3 at p�2.0 GPa. Furthermore, it undergoes aferromagnetic transition at Tc�43 K. In BaVS3 under am-bient pressure, magnetic order is established at TX�30 K�Ref. 6�: the vanadium spins order ferromagnetically alongthe chains, but overall the system is a helicoidalantiferromagnet.7 It is not entirely clear how TX evolves un-der pressure in BaVS3. The appearance of a hysteresis in theresistivity under high pressure, for 1.75� p�2.0 GPa, hintsthat there is possibly a crossing of the TX and the TMI in thepressure-temperature phase diagram.10 In that sense, the fer-romagnetic ground state of BaVSe3 corroborates with theidea that this system corresponds to the high-pressure metal-lic phase of BaVS3.10

Although a synthesis of single crystals was reported in theoriginal work of Kelber et al.,9 the properties of single crys-tal BaVSe3 have not been studied so far. All that we knowabout BaVSe3 comes from the measurements on ceramicsamples. The ferromagnetic transition could be clearly ob-served in such samples at ambient pressure. However, due tothe polycrystallinity, the absolute value of the resistivity wasunreliable. Besides, it was impossible to analyze the low-temperature functional dependence of the resistivity, which isimportant for comparison with the high-pressure power-lawdependence of the resistivity in the metallic phase of BaVS3

b

a

a) b)

FIG. 1. �Color online� �a� A VSe3 chain of BaVSe3 is shown inthe orthorhombic �Cmc21� phase, as well as �b� the arrangement ofthe chains in the ab plane. Barium atoms are located in the 12coordinated sites between the chains. In the hexagonal �P63 /mmc�phase vanadium atoms are aligned along the c axis and b=a�3.

PHYSICAL REVIEW B 78, 235111 �2008�

1098-0121/2008/78�23�/235111�11� ©2008 The American Physical Society235111-1

http://dx.doi.org/10.1103/PhysRevB.78.235111

and the transition from non-Fermi-liquid to Fermi-liquidbehavior.11 Furthermore, in order to ascertain the crossing ofTMI and TX in the phase diagram of BaVS3,10 it is importantto investigate the behavior of Tc in BaVSe3 under pressure.When pressure is applied to ceramic samples, the main effectis the compression of grain boundaries. This leads to unreli-able pressure dependence of the resistivity. It also turns outthat from transport measurements done on such samples, it isdifficult to extract the precise pressure dependence of theferromagnetic transition temperature Tc.

In this paper we report a comprehensive study of mag-netic and transport properties of high-quality single crystalsof BaVSe3. To compare our results with the theoretical pre-dictions, we discuss the density-functional theory �DFT� cal-culations of the band structure in BaVSe3. The main result isthat in many of its properties BaVSe3 bears a strong resem-blance to the high-pressure phase of BaVS3. However, find-ings such as pressure enhancement of the power-law expo-nent n of resistivity or the pressure and magnetic-fielddependence of the residual resistivity �0 challenge our under-standing of the electrical transport at low temperatures.

II. METHODS

Single crystals were grown using a method similar to theone described in the work of Kelber et al.9 The crystals usedin this study were in form of shiny black needles with typicaldimensions of 1�0.1�0.1 mm3. The high quality of thecrystals was reflected in a high residual resistivity ratio��RRR�=��300 K� /�0� of typically 50.

For electrical transport measurements, we used severalneedle-shaped crystals with typical dimensions of 0.4�0.05�0.01 mm3. A sample with four silver paint contactswas mounted on a homemade thermopower sample holder,fitting into a clamped pressure cell. Small metallic heatersinstalled at both ends of the sample generated the tempera-ture gradient which was measured with a Chromel-Constantan differential thermocouple. Such a setup enabled asimultaneous measurement of the resistivity and the ther-mopower. The pressure medium used in this study was kero-sene, and the maximum pressure attained was 2.8 GPa. Thepressure was measured using a calibrated InSb pressuregauge.

Magnetic susceptibility was measured on a collection of ahundred single crystals of BaVSe3 by a Faraday method. Thecrystals with total mass of 4 mg were randomly placed in asample holder. The susceptibility was measured in the tem-perature range from Tc�42 to 330 K in magnetic fields up to0.9 T. At temperatures below Tc, field and temperature de-pendence of magnetization was measured by zero-field cool-ing.

All band-structure calculations were done using DFT.Spin-dependent generalized gradient approximation �GGA�,in the Perdew-Burke-Ernzerhof �PBE� functional form,12 andscalar-relativistic ultrasoft pseudopotentials are employed asimplemented in the QUANTUM ESPRESSO computerpackage.13 Electron wave functions and augmented densitiesare expanded in-plane waves with cutoff energies of 35 and400 Ry, respectively. Sampling of the Brillouin zone �BZ� is

done using 8�8�8 k-point grid.14 Starting atomic configu-ration is taken from experiment and full atomic relaxation isperformed in order to find an equilibrium structure. Mur-naghan equation of state15 is then used to find the equilib-rium lattice constant. Pressures are determined by the stresstensors, which are calculated for the systems with unit cellsscaled isotropically to the volumes that are 0.97 and 0.94 ofthe equilibrium one. Validity of this approach was tested forthe last case with Parrinello-Rahman variable-cell moleculardynamics16 at the constant pressure. During the simulationsymmetry of the unit cell remained unchanged as well as thec /a ratio.

III. AMBIENT PRESSURE

A. Transport properties

The temperature dependence of the transport coefficients,resistivity, and thermoelectric power was determined at am-bient pressure from 1.5 to 650 K. Given the morphology ofthe crystals, all the measurements were performed along thec axis. The resistivity is shown in the top panel of Fig. 2. Inthe previously studied ceramic samples, the room-

FIG. 2. �Color online� Temperature dependence of resistivity isshown in the top panel. The arrows mark the temperature of theferromagnetic phase transition Tc, which can be better distinguishedfrom the inset showing the derivative of the resistivity. The bottompanel demonstrates the clear T2 dependence of resistivity below 15K.

AKRAP et al. PHYSICAL REVIEW B 78, 235111 �2008�

235111-2

temperature value of the resistivity was approximately threetimes larger than the present value �ceramics�1.8 m� cm.4

The ceramic samples had a residual resistivity ratio of �3,whereas for our single crystal RRR�50.

The overall shape of the resistivity curve greatly re-sembles the high-pressure resistivity in BaVS3. At 300 K, thevalue of resistivity is 0.57 m� cm, which compares verywell to the high-pressure value of resistivity in BaVS3,��300 K,2.8 GPa�=0.55 m� cm.11,17 Such a high value ofthe resistivity indicates that BaVSe3 is a bad metal. In theresistivity one cannot discern any signatures of a structuraltransition from hexagonal to orthorhombic symmetry whichsupposedly occurs around 300 K.9 Instead, our data showthat above 200 K, the resistivity is linear, indicating that thedominant mechanism in the high-temperature range is scat-tering on phonons. As shown in the inset of Fig. 2, an abruptchange in the slope of the resistivity appears below 42 K,where ferromagnetic ordering takes place. Below 200 K anddown to Tc, the resistivity drops with a more pronouncedslope, which seems to be correlated with the change in thesymmetry seen by the magnetic moments.5 This point will beaddressed in more detail later.

The low-temperature part is particularly interesting withrespect to BaVS3. Above pcr�2.0 GPa the low-temperatureresistivity of BaVS3 may be described by a power-law tem-perature dependence,

� = �0 + ATn, �1�

with n�1.5 in the very beginning of the metallic phase andn→2 when the system is tuned far from pcr.

8,11 In BaVSe3,the ambient-pressure-temperature dependence of resistivitybelow �15 K may be described by Eq. �1�. The values ofthe parameters extracted from such a fit are the following:�0=12.9 �� cm, A=1.16�10−4 m� cm, and n=2.00�0.01. Indeed, a clear T2 dependence may be seenfrom the lower panel of Fig. 2.

Figure 3 shows the temperature dependence of thermo-

electric power in BaVSe3. Again, the shape of the curve isqualitatively very similar to the high-pressure phase ofBaVS3.18 The high-temperature part of the curve �100 KT500 K� is linear, just as it is expected in a metal. Thehigh absolute value of this transport coefficient confirms thebad metallicity of BaVSe3. To obtain an estimate of the valueof Fermi energy EF, we may apply the formula describingthe thermopower of a free-electron gas with an energy-independent scattering rate,19

S = −2kB

2T

2�e�EF. �2�

This gives EF�0.52 eV. However, the thermopower ofBaVSe3 has a significant offset 11.2 �V /K instead of ex-trapolating into zero for T=0 as the above Mott formulawould predict. The origin of this temperature-independentcontribution may be polaronic or might be more general,which has so far not been discussed in the literature.20 Apartfrom the high-temperature linear behavior, thermopower dis-plays a wide hump centered around 100 K and a low-temperature maximum at �20 K. The corresponding low-temperature maximum in BaVS3 under high pressure p� pcr has been attributed to phonon drag.18 However, thislocal maximum in BaVS3 has a strong magnetic-field depen-dence, which suggests that there may also be a magnon con-tribution present.

Besides the qualitative similarity of the sulfide and theselenide resistivity curves, the fact that their thermopower isalso very similar firmly establishes BaVSe3 as a high-pressure counterpart of BaVS3. The high-temperature part ofthe high-pressure phase of BaVS3 is presently experimen-tally inaccessible since the clamped pressure cell which hasbeen employed so far cannot be heated above 350 K. Mea-suring BaVSe3 is in this sense also interesting because itindicates what sort of temperature dependence of the trans-port coefficients is expected up to 650 K in the sulfide com-pound under �3 GPa.

B. Magnetization and susceptibility

Figure 4 shows the temperature dependence of inversemagnetic susceptibility, 1 /�, in the paramagnetic regimefrom 43 to 330 K. We note that neither in this property can astructural transition be discerned in the vicinity of 300 K.Paramagnetic susceptibility obeys Curie-Weiss law �=C / �T− �, practically in the entire temperature range. Thefit to Curie-Weiss plot 1 /�=T /C− /C gives the followingvalues for Curie constant C and Curie-Weiss temperature :C=0.244 emu K /mol and = +44 K. Positive signifiesferromagnetic interaction of spins which results in ferromag-netic ordering below 43 K. Effective magnetic moment ob-tained from Curie constant in the paramagnetic regime is�eff=1.40�B / f.u. Effective magnetic moment reported previ-ously is slightly larger, 1.42�B.4 The reason for this discrep-ancy is that the authors subtracted the temperature-independent diamagnetism �dia=−1.5�104 emu /mol, thusincreasing the value of susceptibility. To fully incorporate thetemperature-independent part of susceptibility, the Van Vleckparamagnetic susceptibility should also be subtracted. The

FIG. 3. �Color online� The ambient-pressure-temperature depen-dence of the thermoelectric power of BaVSe3 is shown for tempera-tures up to 600 K. The inset shows a zoom on the ferromagnetictransition, and the arrow marks Tc, the temperature of the ferromag-netic ordering.

TRANSPORT AND MAGNETIC PROPERTIES OF BaVSe3 PHYSICAL REVIEW B 78, 235111 �2008�

235111-3

value of this contribution is usually �10−4 emu /mol, so thatdiamagnetic and paramagnetic temperature-independent sus-ceptibilities nearly cancel. This is why here Curie-Weiss fitwas done on measured susceptibility without subtracting anytemperature-independent parts. The effective moment issomewhat higher than the ambient-pressure value in theparamagnetic phase of BaVS3, �eff=1.2�B.

Below 43 K magnetization increases rapidly with decreas-ing temperature. Figure 5 shows temperature dependence ofM /H measured in several different fields ranging from 0.02to 0.12 T. Figure 6 shows field dependence of magnetizationat several different temperatures below Tc. In both cases, thesample was cooled below Tc in zero field. Magnetizationdisplays saturating behavior after a very rapid increase inlow fields �H0.1 T�. Similar field dependence was alsoobserved in Ref. 4. As can be seen from Fig. 5, M /H atcertain temperature is larger for smaller fields, which is theeffect of the rapidly saturating behavior of the magnetizationshown in Fig. 6. This is the reason why M /H measured here

in small fields is almost 2 orders of magnitude larger than theone shown in Ref. 4, where the applied field was 1 T com-pared to 0.12 T in our case. Also shown in Fig. 5 is theparamagnetic susceptibility of BaVSe3 in the temperaturerange 43T60 K.

The properties of the ferromagnetic phase below Tc werealso investigated by means of torque magnetometry and themeasurement of susceptibility anisotropy, as reported byHerak et al.5 The angular dependence of torque in the mag-netic field disclosed that the system is a ferromagnet withuniaxial polarization. The absolute value of the torque deter-mined at 4.2 K was found to be about 20 times higher whenthe magnetic field is directed parallel to the c axis then in theorthogonal configuration. In the case of a uniaxial ferromag-net, this implies that the large component of the magneticmoment is oriented along the c axis, which contrasts thetheoretical predictions based on group theory and symmetryarguments, claiming that the large component is in the abplane.21 The torque measurement also allowed us to deter-mine the effective moment of the ferromagnetic phase, giv-ing �eff= �0.6�0.2��B per vanadium atom.5 The correlationbetween the magnetic susceptibility and the torque in theparamagnetic phase implies that below 200 K, the magneticmoments experience a changing symmetry. Interestingly, thisis precisely the temperature below which the resistivity startsdecreasing with a larger slope.

IV. BAND-STRUCTURE CALCULATIONS

In order to compare the experimental results obtained forthe BaVSe3 single crystals with the theoretical predictions,the DFT-based band-structure calculations were performed.Since the DFT is a ground-state theory, it is reasonable tocompare quantitatively only those experimental resultswhich reflect the ground-state properties.

Calculations of the lattice constant in the hexagonal phaseagree well with experimental results. Calculated values for

χ

χ Θ

Θµ µ

FIG. 4. �Color online� Temperature dependence of the inversemagnetic susceptibility of BaVSe3.

0 10 20 30 40 50 600

1

2

3

4

5

6

M/H

(em

u/m

ol)

T (K)

H=0.2kOeH=0.4kOeH=0.8kOeH=1.2kOe

χparamagnetic

FIG. 5. Temperature dependence of M /H at several differentfields below Tc. Also shown is paramagnetic susceptibility aboveTc.

0.0 0.5 1.0 1.5 2.00.0

0.5

1.0

1.5

2.0

2.5

M(1

03

em

uO

e/m

ol)

H (kOe)

4.4K

10.5K

23K

31K

35K

40K

43K

FIG. 6. Field dependence of magnetization M at several differ-ent temperatures below Tc.


235111-4

a=7.01 Å and c=5.87 Å differ only by 0.15% from thosereported in experiments: a=6.9990�11� Å and c=5.8621�13� Å.9,22 Measurements show that slightly abovethe room-temperature crystal structure of BaVSe3 belongs tothe P63 /mmc symmetry, while it is not clear what happens atlower temperatures. Some notions that BaVSe3 undergo,similarly to the sulfide, a phase transition to the orthorhom-bic structure somewhere between 290 and 310 K exists in theliterature; but measured values of the lattice parameters forthis phase are not, to our knowledge, available in the litera-ture. Kelber et al.9 speculated about orthorhombic phase ofBaVSe3, but they reported only the structural parameters forthe hexagonal one. On the other hand Poulsen22 has foundthat at room temperature BaVSe3 becomes orthorhombicwhen some of barium is replaced by a small amount of po-tassium. In order to clarify the issue of the structure, wecarried out a set of calculations and found that—as in thecase of the sulfide—the phase with the Cmc21 symmetryindeed has a lower total energy than the hexagonal one forabout 0.1 eV/f.u. Calculated lattice parameters in the ortho-rhombic phase are a=7.06 Å, b=12.00 Å, and c=5.85 Å.23

Vanadium atoms are no longer aligned along the c axis butare displaced in the b direction forming a zigzag chain �seeFig. 1�. In both phases the unit cell contains two vanadiumatoms which are equivalent by symmetry and therefore nogap is opened.

We also find that the bulk modulus at the equilibriumvolume differs considerably for the two phases. The value of62 GPa in the orthorhombic phase is almost double com-pared to the one in the hexagonal phase �38 GPa� indicatingthat the low-temperature structure is much less sensitive toexternal pressure.

Theoretical results for the electronic ground state agreeboth qualitatively and quantitatively with the experiments.As shown in Fig. 7, where the spin-resolved density of states�DOS� is presented for both phases, the system is correctly

predicted to be metallic and ferromagnetic. Vanadium d or-bitals split in the octahedral field into the T2g and Eg multi-plets. By forming the chains and placing them into theP63 /mmc structure, the octahedral symmetry is broken andthe T2g triplet splits into the A1g singlet and Eg doublet. TheA1g orbitals are able to interact along the chains and formnearly quasi-one-dimensional band. On the other hand, theorbitals from the Eg doublet do not interact appreciably withtheir environment and therefore they form almost dispersion-less bands which are responsible for the sharp peak structureof DOS just below the Fermi energy. Interaction of theatomic orbitals from the second Eg doublet with 4p orbitalsof the neighboring Se atoms is stronger and is responsible forthe formation of bands which are located further below andabove the Fermi energy. Figure 8 shows the electronic statesformed by the vanadium A1g and Eg orbitals at the � point ofthe hexagonal Brillouin zone. The states are labeled accord-ing to the irreducible representations of the correspondingcrystal point group �D3h�.24 Two types of Eg states areshown. The first one is entirely composed of the vanadiumEg orbitals and the other one mixes with the selenium porbitals. Eg states which have nonzero projection on the or-bitals of the selenium atoms are positioned about 2 eV belowthe Fermi energy, while the states constituted out of the Egorbitals coming from the T2g splitting lay only 0.12 eV belowthe Fermi energy.

In the octahedral phase the hexagonal symmetry is brokenand the vanadium Eg doublets split in the crystal field. Thisenhances the mixing with the selenium orbitals and the sharppeak structure in the DOS is smeared out. Mixing is strongerin the spin-majority channel due to the smaller energy differ-ence compared to the selenium p bands. The effect of thesymmetry breaking can also be seen in the band structures ofthese two BaVSe3 phases as shown in Fig. 9. Flat doublydegenerate bands near the Fermi energy in the hexagonalphase split due to the lower symmetry of the orthorhombicphase into nondegenerate bands whose bandwidth increases.In both phases, the glide planes in the direction of the chainsexist �mirror symmetry in the ac plane combined with thehalf-period translation� and the translational period along the

-10

0

10

TotalV (A

1g)

V (Eg)

Se (p)

-6 -4 -2 0 2E - E

F(eV)

-10

0

10DO

S(1

/eV

)

P63/mmc

Cmc21

spin maj.

spin min.

spin maj.

spin min.

FIG. 7. �Color online� Spin-resolved DOS, in the region aroundthe Fermi energy, is shown for P63 /mmc and Cmc21 BaVSe3 crys-tal structures. Projections on the vanadium A1g and Eg and theSe 4p orbitals are also shown.

E g

E g

A 1g

FIG. 8. �Color online� VSe3 chains are shown together with theA1g and Eg electronic states of the hexagonal BaVSe3 at the � pointin the Brillouin zone. The A1g and Eg orbitals coming from thesplitting of the T1g triplet do not interact with the Se 4p orbitals,while there is some mixing of the second Eg doublet and the Seorbitals.


235111-5

chains contains two full symmetry elementary units�symcells25�. Therefore, the folded structure of the bands canclearly be seen along the �-A and �-Z directions of bothP63 /mmc and Cmc21 phases, respectively.

In Refs. 26 and 27 Lechermann et al. showed that thefilling of the vanadium A1g and Eg orbitals in the case ofsulfide compound is not correctly predicted by DFT meth-ods. They prove that results obtained in the local-densityapproximation �LDA� to DFT need to be corrected by thedynamical mean-field theory �DMFT�, which includes theeffects of strong correlations, in order to come closer to theunderstanding of the metal to insulator phase transition inBaVS3. Otherwise the filling of the vanadium A1g �Eg� orbit-als is overestimated �underestimated� and the LDA picturedoes not provide a Fermi-surface nesting needed for thecharge-density wave instability. However, qualitative LDApicture of both phases, which predicts that the low-energysector is almost completely determined by the vanadium dbands, remains valid. Our GGA band structure of the sulfideis similar to the one obtained within the LDA approximation.In the case of selenide compound we find that bigger disper-sion of the p bands caused by the size difference between Sand Se ions leads to the appearance of a purely seleniumband which cuts the Fermi surface. In Fig. 10 band structureof the hexagonal BaVSe3 along the �-A direction is showntogether with the corresponding DOS. Three types of bandsthat determine low-energy behavior of BaVSe3 can beclearly distinguished: the nearly dispersionless E bands,quasi-one-dimensional A1 band formed by the vanadium A1gorbitals, and A2 band formed exclusively of selenium 4p or-bitals. In the case of BaVS3 the A2 band lays completelybelow the Fermi energy. Therefore, the low-energy sector ofBaVSe3 compound has more of the selenium p and less Egcharacter than the corresponding energy sector of the sulfide.

This influences the filling of vanadium d orbitals and maystabilize the orthorhombic phase as it is seen in experiments.

In the spin minority channel, Eg bands are shifted aboveFermi surface due to exchange interaction leading to nonzeromagnetic moment which is localized around vanadium atomsand amounts to 1.63�B per unit cell in the orthorhombicphase. This gives a moment of 0.82�B per vanadium atom,which is a reasonable value in comparison with the experi-mental result for the ferromagnetic phase �0.6�0.2��B.5

For the high-pressure transport measurements which fol-low, it is important to consider the changes in the band struc-ture upon applying pressure. The method which was usedgave no dramatic changes. At pressures lower than 3 GPa,the lattice parameters of the orthorhombic phase are expectedto change not more than 2% which does not affect the elec-tronic ground state considerably. As expected, the orbitalsoverlap more and the spectra broaden. In Fig. 11, DOS oftwo groups of bands of the orthorhombic BaVSe3 is shownas well as how it changes with applied pressure. The firstgroup located at the energies between −15 and −10 eV be-

M Γ A

-2

0

2

E-

EF

(eV

)

Y Γ Z

MΓ

A

YΓ

Z

a) b)

FIG. 9. �Color online� The Brillouin zone and the spin-majorityband structure along the high-symmetry directions of the �a� hex-agonal and �b� orthorhombic BaVSe3 crystal structures.

Γ A 10 20DOS (1/eV)

-2

0

2

E-

EF

(eV

)

TotalV (A

1g)

V (Eg)

Se (p)

Eg

E

A1g

A1

A1u

A2

A2u

A1

Eu

E

EE

A2g

A2

Eg

E

A1

A1g

Eg

Eg,

FIG. 10. �Color online� Electronic bands along the c axis to-gether with the corresponding DOS. Bands are labeled according tothe symmetry properties of the � point and �-A direction �see text�.Arrows indicate the states at � which are shown in Fig. 8.

0

10

20

0

10

20

DO

S(1

/eV

)

-15 -10 -5 0E - E

F(eV)

0

10

20

0 GPa

1.95 GPa

4.23 GPa

FIG. 11. �Color online� Spin-majority DOS of the orthorhombicBaVSe3 at different pressures is shown.


235111-6

low the Fermi energy consists of barium 5p and selenium 4sorbitals. Their interaction is enhanced and the DOS broadenswith the pressure. The same occurs with the second group ofbands located around the Fermi energy and formed by vana-dium 3d and selenium 4p orbitals. It is evident that thebroadening, although quite small, occurs mainly in the low-energy sector �below −2.5 eV� within the selenium p bands.On the other hand, the structure of the DOS in the vicinity ofthe Fermi energy almost does not change up to the pressureof 4.23 GPa. We also find that the magnetic moment de-creases only slightly upon applying pressure from the valueof 0.82�B at zero pressure to the 0.79�B and 0.73�B at 1.95and 4.23 GPa, respectively.

V. HIGH-PRESSURE TRANSPORT PROPERTIES

The metal-insulator transition in BaVS3 or the PM-FMtransition in MnSi exhibits a remarkable sensitivity topressure.8,10,11,28 In both systems moderate pressures of1.5–2.0 GPa drive the system into a non-Fermi-liquid state.This was the prime motivation to investigate BaVSe3 underhydrostatic pressure. Furthermore, since BaVSe3 at ambientpressure resembles to BaVS3 at �3 GPa, it could give a hinthow the latter compound would evolve at even higher pres-sures.

Figure 12 displays the temperature dependence of resis-tivity of BaVSe3 under high pressures up to 2.8 GPa. Thevalue of resistivity monotonously decreases as pressure isapplied and by 2.8 GPa its room-temperature value hasdropped by more than 20%. The resistivity of metals is nor-mally reduced under pressure due to the effects of enhancedbandwidth and/or because the relaxation time � becomeslonger. The RRR value in BaVSe3 increases from 50 at am-bient pressure to 55 under 2.8 GPa, which implies that therelative change in �0 is larger than in ��300 K�. Like inBaVS3, such pressure dependence of �0 hints that this quan-tity may contain other contributions apart from impurityscattering.

From the position of the kink in the resistivity measure-ments, one may extract the pressure dependence of the tem-perature of the ferromagnetic ordering Tc, which is shown in

Fig. 13. There seems to be a weak increase in Tc at a rate of�0.9 K /GPa. This indicates that the pressure strengthensthe ferromagnetic interaction between the localized mo-ments. The increase in Tc in BaVSe3 is at variance with thebehavior of the low-pressure insulating phase of BaVS3,where a feeble decrease in TX up to �0.5 GPa wasobserved.29 However, both the decrease in TX in BaVS3 andthe increase in Tc in BaVSe3 are unified in the phase diagramof Ba1−xSrxVS3, where a part of barium atoms is substitutedby smaller but isovalent strontium atoms.30 Because of thesize differences between barium and strontium atoms, in-creasing the strontium content x causes a decrease in theinterchain spacing and thus leads to an effective chemicalpressure. As x grows from 0 to 0.07, the antiferromagnetictransition is slowly suppressed, just as it happens in the pureBaVS3 under hydrostatic pressure. At xcr=0.07, the unit cellsuddenly shrinks and the antiferromagnetic ground stategives way to ferromagnetism. When the strontium content xincreases from xcr until the solubility limit x�0.18, the tem-perature of the ferromagnetic transition shows a weak in-crease, which may be compared to our present observationson BaVSe3 under hydrostatic pressure.

In the 3d transition-metal compound MnSi, the ferromag-netic metallic phase collapses under a moderate pressure of1.5 GPa and the power-law exponent of the resistivitychanges from n=2 to a non-Fermi-liquid value of 1.5.28 InBaVSe3, pressure also influences the resistivity coefficient ndescribing the power-law behavior of the resistivity below�15 K according to Eq. �1�, but in a surprisingly differentway. The evolution of n under pressure is shown in Fig. 13.Upon the application of pressure the exponent n is enhancedbeyond its Fermi-liquid value of n=2 and reaches the valueof 2.3 under 2.8 GPa, the maximum applied pressure. It ispossible that the increase in exponent continues under higherpressures toward the next meaningful exponent 3. A plau-sible interpretation of the observed increase in n is that thepressure reduces the temperature range where electron-electron scattering dominates and makes some other scatter-ing mechanism, for instance, electron-phonon interaction,shows up through the exponent n.

One additional reason for unclarity regarding the origin ofa low-temperature exponent 2n3 is the phonon-drag ef-

FIG. 12. �Color online� The temperature dependence of resistiv-ity under various pressures.

FIG. 13. �Color online� The pressure dependence of the tem-perature of magnetic ordering Tc �left scale� and of the resistivityexponent n �right scale�.


235111-7

fect which can further suppress resistivity by pulling the pho-non distribution off equilibrium.31 At low temperatures,electron-phonon scattering produces quasiparticle relaxationrates going as T3. This term in the resistivity is suppressedbecause the scattering is mainly restricted to small angles,which results in Bloch’s T5 dependence of the electron-phonon contribution to resistivity. However, in 1935, Mott32

suggested a somewhat naive sd model in which there are twotypes of valence electrons: nearly free s electrons and tightlybound d electrons. He assumed that the transport arises fromthe motion of the s electrons and that the current is primarilylimited by their scattering into d states. In his model, large-angle scattering was allowed at fairly low temperatures, lead-ing to a possible T3 dependence of the resistivity forelectron-phonon scattering. Since then several calculationshave been performed on magnetic systems, bothferromagnetic33 and antiferromagnetic,34 and it has becomequantitatively clear that electron scattering on spin wavesinfluences the power law of the temperature dependence ofthe low-temperature resistivity. It is reasonable to expect thatpressure stiffens the ferromagnetic order which could alterthe electron-magnon scattering and could lead to power-lawbehavior such as what we observe in BaVSe3 under highpressure.

The thermoelectric power under pressure is shown in Fig.14. The slope of the linear part appears not to be significantlyinfluenced by pressure. This means according to Eq. �2� thatthe value of EF remains unchanged. Therefore, the pressuredoes not influence the bandwidth. Combining this result withthe observed resistivity decrease, we may conclude that theprimary effect of the pressure is enhancing the relaxationtime �. Such a conclusion is coherent with the fact that ther-mopower is independent of � in the first approximation,where the energy dependence of the relaxation time is ne-glected. It is also consistent with the band-structure calcula-tions, which suggest very little pressure dependence of theDOS at the Fermi level.

On the contrary, the temperature-independent offset is in-creased under pressure by more than 3 �V /K, as shown inthe inset of Fig. 14. We define S0 for a given pressure as theoffset of the linear part of thermopower with respect to thehighest-pressure thermopower,

S0�p� = S�2.3 GPa,T� − S�p,T� ,

where 150 KT300 K. In BaVS3, S0 changes by14 �V /K under 2.7 GPa.18 In BaVSe3 the change in S0 issmaller, but the trend is continued. The existence of such anoffset in thermoelectric power is nontrivial to understand. Asmentioned earlier, one possibility is that its origin is po-laronic. In that case, as the pressure improves the metallicityof the system, the polaronic contribution should diminish andS0 should eventually converge to a pressure-independentvalue.

The wide hump which appears around 100 K in the ther-mopower at ambient pressure shifts to slightly higher tem-peratures when pressure is applied at an approximate rate of7 K/GPa. This suggests that the feature may have a phononicorigin. The increase in the characteristic temperature wouldin that case come from the pressure-induced stiffening of therelevant vibrational modes. Finally, the low-temperature fea-ture ascribed to phonon drag becomes more pronounced un-der pressure but the temperature of the maximum valueshows no pressure dependence.

VI. MAGNETOTRANSPORT

Due to its ferromagnetic ground state, the transport prop-erties of BaVSe3 are expected to be fairly sensitive to anexternal magnetic field. Figure 15 shows a comparison be-tween the resistivity measured in zero field and the one mea-sured in magnetic field B=12 T oriented parallel to the crys-tal c axis. Indeed, there is a large response of the carrierscattering to the applied field. The slope change at Tc asso-ciated with the magnetic transition is completely wiped outin the magnetic field. To quantify magnetoresistance, we em-ploy the usual definition

��

�=

��B� − �0 T

�0 T, �3�

where �0 T is the zero-field resistivity. The temperature de-pendence of �� /� is shown in the inset of Fig. 15. At high

FIG. 14. �Color online� Temperature dependence of thermoelec-tric power under various pressures. The inset shows the offset S0, asdiscussed in the text.

FIG. 15. �Color online� Ambient-pressure resistivity at 0 and 12T. The magnetic field is directed along the VSe3 chains, B c axis.Inset shows the relative magnetoresistance, �� /�, as defined in thetext.


235111-8

temperatures, above �120 K, the magnetoresistance van-ishes. The negative �� /� below this temperature is attributedto the ordering of magnetic moments by the external field.Magnetic field suppresses spin fluctuations and in this waydecreases scattering in the conduction electrons on the mag-netic moments. The extremum value of magnetoresistivityamounts to �−13% and occurs precisely at Tc. Below 10 Kthe magnetoresistance starts to increase steeply.

Similar behavior of the resistivity is observed when pres-sure is applied and if the direction of the magnetic field ischanged. Figure 16 shows the temperature dependence ofmagnetoresistance under two different high pressures, 1.9and 2.8 GPa, in a field orientation such that B is perpendicu-lar to the c axis. The high-temperature behavior of �� /� at1.9 GPa �top panel� is similar to the ambient-pressure depen-dence from Fig. 15. However, the peak at Tc is somewhatless pronounced. This seems to be correlated with the weak-ening of the signature of the ferromagnetic transition in re-sistivity. In the low-temperature part, magnetoresistancechanges the sign at �12 K for the field B=12 T. Under 2.8GPa, the maximum value of magnetoresistance approaches20% for the maximal magnetic field applied �Fig. 16, bottompanel�.

In an ordinary paramagnetic metal, the magnetoresistanceis negative in the temperature region where the external field

can align magnetic moments and thus reduce the scatteringof the conduction electrons off these moments. At low tem-peratures, the magnetic moments in BaVSe3 are morealigned and fluctuate less, which is why the field has littleadditional effect on their ordering. Hence, a positive magne-toresistance takes over, characteristic of normal metals.

In BaVS3 the field dependence of the resistivity is a non-monotonous function.10 To establish whether such behaviorextends to BaVSe3, we have determined the field dependenceof the magnetoresistance at several fixed temperatures forp=2.3 GPa and B perpendicular to c axis. Figure 17 dis-plays the results. The magnetoresistance changes characterbetween 8 and 15 K, in agreement with the data discussedabove: at high temperatures it is negative, whereas for lowtemperatures it becomes positive. Notably, at 4.5 K a smalllocal maximum appears at B�3 T, after which magnetore-sistance decreases slightly, and then increases linearly aboveB�5 T. A feature of similar shape in magnetoresistancemay still be seen at 25 K, but for T=44 K there is no traceof a local maximum, only a monotonous decrease in thewhole field range. A comparable distinction between the low-and high-temperature behaviors of magnetoresistance wasalso observed in BaVS3 at pressures above �2.1 GPa.11 Thetemperature where the character of magnetoresistivitychanges was also found to be rather close to what we observehere, namely, in the range between 8 and 15 K. However, thelocal maximum at low temperatures in BaVS3 is much morepronounced. In BaVS3, it can be argued that the nonmonoto-nous field dependence of the resistivity comes from the cant-ing of the Eg spins and their strong interaction with the A1gelectrons. This explanation may also be applied to BaVSe3,providing another point of comparison between the selenideand the sulfide.

Finally, Fig. 18 illustrates the pressure and magnetic-fielddependence of coefficient �0 which describes the zero-temperature extrapolation of resistivity. Residual resistivity�0 is monotonously diminished under pressure. In a normalmetal, �0 bears no great importance, as it is merely a measureof the impurity concentration. However, in BaVS3 andBaVSe3 its origin is certainly not so simple. The pressuredependence of �0 in BaVS3 is anomalous: a sharp decrease in

FIG. 16. �Color online� High-pressure-temperature dependenceof magnetoresistance at 1.9 and 2.8 GPa. The magnetic-field orien-tation is B�c axis.

FIG. 17. �Color online� The field dependence of magnetoresis-tance at 2.3 GPa at several temperatures. The field is perpendicularto VSe3 chains, B�c axis.


235111-9

�0 occurs simultaneously with the tuning of the power-lawcoefficient n toward the Fermi-liquid value.11 This may beexplained by the fact that close to the pressure where theinsulating phase is suppressed, both n and �0 issue from thescattering of conduction electrons on the charge fluctuationsin the A1g sector. When pressure is increased toward 3 GPa,BaVS3 approaches the n=2 value, which is observed at am-bient pressure in BaVSe3. The decrease in �0 under pressurein BaVSe3 presumably comes from the fact that pressuremodifies the interaction of magnetic moments and thus influ-ences the scattering of conduction electrons on spin waves.

Contrary to pressure, applied magnetic field enhances �0,approximately following �0�B2. When an external magneticfield is present, in k space it separates the Fermi spheres ofthe spin-majority and spin-minority channels by �BB. Thefield can change the configuration of the Eg electrons. Thematrix element describing the transition from one spin orien-tation to the other is proportional to B2. When random spinflips occur, the electronic orbitals of Eg electrons are influ-enced too. Since the conduction electrons from the A1g sectorscatter on the Eg electrons, when Eg electrons are canted ortheir distribution among minority and majority channels ischanged, this may affect the scattering. The fact that thetransition probability between the two spin orientations isproportional to B2 may be related to the similar field depen-dence of �0.

VII. DISCUSSION AND CONCLUSIONS

There is a considerable similarity between the high-pressure BaVS3 and the ambient-pressure BaVSe3. Whensulfur is replaced by selenium, the overlaps between thechains are enhanced, producing as an effect the chemicalpressure. The aftermath is that there exists a set of physicalproperties which behave in a very similar manner. This isparticularly clear in the case of the transport coefficients. Theambient-pressure-temperature dependence of the resistivityin BaVSe3 has the same qualitative shape as the resistivity inthe sulfide for p� pcr and the same holds for the thermoelec-tric power. What is more, the low-temperature resistivity in

the selenide is described by the canonical Fermi-liquid expo-nent n=2.

Experimenting on BaVSe3 allows an insight into the high-pressure phase of BaVS3, warranting the use of many tech-niques which are normally inaccessible other than at ambientpressure. The measurements on BaVSe3, besides confirmingwhat we already know about BaVS3, have also given someuseful hints for understanding the magnetic ground state ofthe sulfide compound. The magnetic susceptibility infers thatbelow 43 K, BaVSe3 is ferromagnetic. The ferromagneticmetallicity of the sister selenide suggests that the high-pressure ground state of BaVS3 is also likely to be ferromag-netic. However, the magnetic ground state of high-pressureBaVS3 is not yet experimentally accessible. From the high-temperature behavior of the resistivity and thermoelectricpower of BaVSe3, one is enticed to believe that the high-temperature phase of BaVS3 is also a bad metal character-ized by linear temperature dependencies of the resistivity andthe thermoelectric power.

In view of the band-structure calculations, it seems that itis not crucial to take into account the strong correlations inorder to reproduce the main experimental observations thatBaVSe3 is a ferromagnetic system of itinerant electrons.Band-structure calculations give a fairly correct estimate ofthe magnetic moment in the ferromagnetic phase. In addi-tion, they predict that the bandwidths are not significantlyinfluenced by our experimentally attainable pressures.

The correlation between the magnetic torque and the sus-ceptibility allowed to see that the symmetry seen by the mag-netic ions is changing below 200 K.5 Moreover, the tempera-ture dependence of the susceptibility anisotropy implies thatbelow 62 K the system becomes most paramagnetic alongthe c axis, suggesting that a rotation of the magnetic axestakes place at this temperature. Consequently, there may be astructural transition happening at low temperatures or alter-natively a deformation of the ligand cage. The resistivitydeparts from the linear temperature dependence and startsdecreasing more steeply below 200 K. Again, this findingmay also prove to be relevant for the high-pressure BaVS3,in which the resistivity above pcr has a very similar shape tothat of BaVSe3; in that it also exhibits a change in slopearound 200 K and a precipitous decrease below.8,11

Lastly, some of our observations induced us to believethat there is more complexity to the phenomena occurring inBaVSe3 than just what seems to be the continuation of high-pressure phase diagram of BaVS3. One of the initial motivesin the study of BaVSe3 was a possibility of stabilizing anon-Fermi-liquid state by pressure, just as it happens in thecase of MnSi. There, the ferromagnetic transition is sup-pressed for pressures beyond 1.5 GPa, and the non-Fermi-liquid phase suddenly sets in as the power-law exponentjumps from n=2 to 3/2.28 In BaVSe3, we have not observedsuch a sudden drop in n. Instead, the power-law exponent nshows a decided increase under pressure. The residual resis-tivity �0 is dependent on pressure and magnetic field. Pres-ently, we attribute these unexpected dependencies to thestrong interaction between the Eg and the A1g electrons.

ACKNOWLEDGMENTS

The experimental work in Lausanne was sponsored by the

FIG. 18. �Color online� Pressure and magnetic-field �B�c axis�dependence of the residual resistivity �0.


235111-10

Swiss National Science Foundation and its NCCR MaNEP.Calculations were performed at the Computer Center of theEcole Polytechnique Fédérale de Lausanne and at the SwissCenter for Scientific Computing in Manno. A part of thiswork was supported by the Swiss National Science Founda-

tion under Grant No. 200020-112318. The work in Zagrebwas supported by the resources of the SNSF-SCOPESproject �Scientific Cooperation between Eastern Europe andSwitzerland� and by the Croatian Ministry of Science, Edu-cation and Sports under Grant No. 035-0352843-2846.

*[email protected] Y. Tokura, Rep. Prog. Phys. 69, 797 �2006�.2 C. Pfleiderer, S. R. Julian, and G. G. Lonzarich, Nature �London�

414, 427 �2001�.3 C. Pfleiderer, D. Reznik, L. Pintschovius, H. von Löhneysen, M.

Garst, and A. Rosch, Nature �London� 427, 227 �2004�.4 T. Yamasaki, S. Giri, H. Nakamura, and M. Shiga, J. Phys. Soc.

Jpn. 70, 1768 �2001�.5 M. Herak, M. Miljak, A. Akrap, L. Forró, and H. Berger, J. Phys.

Soc. Jpn. 77, 093701 �2008�.6 G. Mihaly, I. Kezsmarki, F. Zamborszky, M. Miljak, K. Penc, P.

Fazekas, H. Berger, and L. Forro, Phys. Rev. B 61, R7831�2000�.

7 H. Nakamura, T. Yamasaki, S. Giri, H. Imai, M. Shiga, K.Kojima, M. Nishi, K. Kakurai, and N. Metoki, J. Phys. Soc. Jpn.69, 2763 �2000�.

8 L. Forró, R. Gaál, H. Berger, P. Fazekas, K. Penc, I. Kézsmárki,and G. Mihály, Phys. Rev. Lett. 85, 1938 �2000�.

9 J. Kelber, A. H. Reis, A. T. Aldred, M. H. Mueller, O. Massenet,G. Depasquali, and G. Stucky, J. Solid State Chem. 30, 357�1979�.

10 N. Barišić, A. Akrap, H. Berger, and L. Forró, arXiv:0712.3395�unpublished�.

11 N. Barišić, A. Akrap, H. Berger, and L. Forró, arXiv:0712.3393�unpublished�.

12 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77,3865 �1996�.

13 P. Giannozzi, http://www.quantum-espresso.org14 H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 �1976�.15 C.-L. Fu and K.-M. Ho, Phys. Rev. B 28, 5480 �1983�.16 M. Parrinello and A. Rahman, Phys. Rev. Lett. 45, 1196 �1980�.17 A. Akrap, A. Rudolf, F. Rullier-Albenque, H. Berger, and L.

Forró, Phys. Rev. B 77, 115142 �2008�.18 N. Barišić, Ph. D. thesis, Lausanne, 2004, https://

nanotubes.epfl.ch/nbarisic19 R. D. Barnard, Thermoelectricity in Metals and Alloys �Taylor &

Francis, London, 1972�.20 Note that platinum, a conventional metal, has also a large inter-

cept of thermoelectric power at T=0 K, whose origin has neverbeen elucidated. See, for example, J.-S. Zhou and J. B. Good-enough, Phys. Rev. B 51, 3104 �1995�.

21 P. Balla and P. Fazekas �unpublished�.22 N. J. Poulsen, Mater. Res. Bull. 32, 1673 �1997�.23 In the hexagonal phase b=a�3=12.14 Å.24 The local symmetry of the vanadium atoms coincides with the

point group of the BaVSe3 in the hexagonal phase. Therefore thesame labeling is used for the atomic orbitals and electronic statesin the bulk at the � point.

25 M. Damnjanovic, T. Vukovic, and I. Milosevic, J. Phys. A 33,6561 �2000�.

26 F. Lechermann, S. Biermann, and A. Georges, Phys. Rev. B 76,085101 �2007�.

27 F. Lechermann, S. Biermann, and A. Georges, Phys. Rev. Lett.94, 166402 �2005�.

28 C. Pfleiderer, G. J. McMullan, S. R. Julian, and G. G. Lonzarich,Phys. Rev. B 55, 8330 �1997�.

29 H. Nakamura and T. Kobayashi �unpublished�.30 A. Gauzzi, N. Barišić, F. Licci, G. Calestani, F. Bolzoni, P. Faze-

kas, E. Gilioli, and L. Forró, arXiv:cond-mat/0601286 �unpub-lished�.

31 P. B. Allen �private communication�.32 N. F. Mott, Proc. Phys. Soc. London 47, 571 �1935�.33 J. Mathon, Proc. R. Soc. London, Ser. A 306, 355 �1968�.34 A. Ishikawa, J. Phys. Soc. Jpn. 51, 441 �1982�.


235111-11

Documents

Transport and magnetic properties of