Table Of ContentAnisotropy in the magnetic and electrical transport properties of Fe Cr Sb
1−x x 2
Rongwei Hu,1,2 V. F. Mitrovi´c,2 and C. Petrovic1
1Condensed Matter Physics and Materials Science Department,
Brookhaven National Laboratory, Upton, NY 11973
2Department of Physics, Brown University, Providence, RI 02912
(Dated: February 2, 2008)
We have investigated anisotropy in magnetic and electrical transport properties of Fe1−xCrxSb2
(0 ≤ x ≤ 1) single crystals. The magnetic ground state of the system evolves from paramagnetic
to antiferromagnetic with gradual substitution of Fe with Cr. Anisotropy in electrical transport
8 diminishes with increased Cr substitution and fades away by x = 0.5. We find that the variable
0 range hopping(VRH)conduction mechanism dominates at low temperatures for 0.4≤x≤0.75.
0
2 PACSnumbers: 71.20.Nr,71.28.+d,75.30.-m,75.50.Pp
n
a
J I. INTRODUCTION Pnnm.9 Neutron diffraction studies of CrSb2 indicate a
high spin d2 configuration,an antiferromagnetic ground
1
statewithNeeltemperatureT =273±2K,andamag-
1 The magnetic resemblance of FeSb to FeSi suggests N
that FeSb could be another model sy2stem to study the neticmomentperCrof1.94µB.10 Inthisworkweexam-
l] possible ap2plicability of the Kondo insulator scenario to inethemagneticandelectricalpropertiesofFe1−xCrxSb2
e (0≤ x ≤ 1) and discuss the possible conduction mecha-
transitionmetalcompoundswith3d electrons.1,2,3,4The
- nism of this binary system.
r magneticsusceptibilityofFeSb isnearlytemperaturein-
t 2
s dependent atlow temperatures,followedby diamagnetic
.
t to paramagnetic crossover around 100 K and thermally
a
activatedbehaviorathightemperatures.5 Anotherstrik-
m
ing similarity to FeSi comes from the result of ab ini-
d- tio LDA+U electronic calculations that show near de-
n generacy of small gap semiconductor and metallic ferro-
o magnetic state.4 Electrical transport in FeSb is rather
2
c anisotropic and nearly quasi one-dimensional. Whereas
[ resistivity along the ba- and bc- axes is semiconducting
2 showing activated temperature dependence below room
v temperature, the bb- axis resistivity is metallic above 40 6.8
1 K and semiconducting below that temperature.1 Opti- b
35 cstaaltceo,nzdeuroctDivriutydemweaeisguhrtemofenσt(sωs)haotwelodwafrteruqeueinncsiuelsatainndg nt (¯ ) 6.4
1 a
1. tawneaenni1so0t0ro-p3i5c0ecnmer−g1yignaopveErgalilnagtrheeemspeencttrwailthrarnegseistbive-- Const 6.0 a
80 itymeasurements. Thermalexcitationsofchargecarriers Cell 3.25
0 through Eg in conventional MIT transitions produce re- 3.20
: distribution of the spectral weight just above the gap. c
iv However, a full recovery of spectral weight in FeSb2 oc- 3.150.0 0.2 0.4 0.6 0.8 1.0
X cursabove1eV,suggestingcontributionsoflargerenergy X
r scales.3 Electrondoping onFe site induced a weak ferro- 136
a magneticmetallicstateandcolossalmagnetoresistancein
aFree1−oxfCpoaxrStibc2u.laTrhinutseroetshte.5r,6doping studies in this system 3 e (¯) 132
m
u
Hole doping, on the other hand, induces a heavy Vol 128
fermion metallic state in FeSb2−xSnx7, analogous to the ell
coafsteheinhFoeleSid1−opxAinlgx.o8nTtohebegtrtoeurnudndstearstteaonfdFtehSebin,flwueenince- nit C 124
2 U
vestigate the effects of Cr substitution on Fe site of this
material. ThesignificanceofCrsubstitutionisthatholes 120
0.0 0.2 0.4 0.6 0.8 1.0
are introduced in narrow energy bands with 3d charac-
X
ter, unlike in the case of Co and Sn substitution. CrSb
2
is an antiferromagnetic semiconductor that crystallizes FIG. 1: Lattice constants and unit cell volume of
into the marcasite structure with the same space group Fe1−xCrxSb2 versus nominal Cr concentration x.
2
II. EXPERIMENTAL METHOD
The samples investigatedin our experiments were sin- 0.1
glecrystalsgrownfromhightemperaturemelt.11,12Pow- 1 ) x=0.4 (a)
der X-ray diffraction (XRD) spectra of the ground sam- - ol x=0.5
ples were taken with Cu Kα radiation (λ = 1.5418 ˚A) u m0.01 x=0.6
using a Rigaku Miniflex X-ray machine. The lattice pa- em x=0.25
rameterswereobtainedbyfittingtheXRDspectrausing H (1E-3 x=0.75
the Rietica software.13 Single crystals were oriented us- M/a x=0.1
ing a Laue Camera and were polished into rectangular
bars along specific crystalline axes. Thin Pt wires were x=1
1E-4
attached to electrical contacts made with Epotek H20E 0 100 200 300
T ( K)
silver epoxy for a standard 4-wire resistance measure- 0.1 U.)60
mticeanlt.miScraomscpolpeedNimikeonnsioSnMsZw-8e0re0 wmietahsu10reµdmwirtehsoaluntioopn-, -1 mol) x=x0=.40(.b5) -3 10/F.B300
andtheaveragevalueswereusedtoestimateageometric mu 0.01 x=0.6 M (-a30 xx==00..245
factor. Magnetization,resistivityandheatcapacitymea- (e -6-010 -5 0 5 10
surementswerecarriedoutinaQuantumDesignMPMS- H x=0.25 H (kOe)
5 and a PPMS-9 for temperatures from 1.8 K to 350 K. M/b x=0.75
1E-3
x=0.1
x=1
III. RESULTS AND DISCUSSION 0 100 200 300
T (K)
0.1
)
-1 ol x=0.4 (c)
Thelatticeparametersofdopedsamplesfromthepow- m
u x=0.5
derX-raydiffractionspectraareshowninFig. 1. Linear m
0.01
dependence on Cr concentration in accordance with Ve- (e x=0.6
H
gard’s law demonstrates that Cr uniformly substitutes x=0.25
Fe in the entire doping range. All axes increase linearly M/c x=0.75
1E-3
with increasing x and the lattice constants of the end x=0.1
members are consistent with the reported values, FeSb x=1
2
(a=5.8253(2)˚A, b=6.5313(2)˚A, c=3.1952(2)˚A) and 0 100 200 300
CrSb (a = 6.0250(1) ˚A, b = 6.8708(1) ˚A, c = 3.2711(1) T ( K)
˚A).1,124,16 -1 ol) 6
The magnetic susceptibility along the three crystal m (d)
axes of Fe1−xCrxSb2 (0 ≤ x ≤ 1) in temperature range mu 4
1.8 to 350 K is shown in Fig. 2. FeSb exhibits a dia- e
magnetic to paramagnetic crossover at2about 100 K for -4 0 x=0 H || a
1 2 H || b
field applied along the bc axis. The temperature depen- H ( H || c
dence of the susceptibility along the ba- and bb- axes is M/a
0
virtually identical: nearly temperature independent at Magnetic susceptibility of FeSb2
lowtemperaturesandthermallyactivatedathighertem- 0 100 200 300
peratures. The magnetic susceptibility of CrSb is con- T (K)
2
sistentwithmagneticorderingbelowT =275K. Afree
N
ionmodelEq.(1)proposedbyJaccarinoappliedtoFeSb FIG.2: (a)-(c)TemperaturedependanceofM/H forfieldof
2
gives a spin gap ∆ =527±4 K.17 H = 1000 Oe applied along 3 crystalline axes. Inset shows
χ
the hysteresis loops for 0.25 ≤ x ≤ 0.4. (d) M/H versus
J(J +1) 2J +1 temperature (T)of pureFeSb2.
χ = Ng2µ2 +χ (1)
FI B 3k T 2J +1+exp(∆ /k T) 0
B χ B
Nµ2 substitution, long range antiferromagnetic order is in-
χ = eff (2)
CW 3k (T −Θ) duced for x ≥ 0.25 and the Neel temperature gradually
B
increases toward T =275 K, of CrSb (x = 1). The
N 2
For x = 0.1, the temperature dependence of suscep- high temperature effective magnetic moment is some-
tibility is comprised of a reduced thermally activated whatlowerthanexpected,µ (Cr4+)=2µ fortheend
eff B
term, Eq.(1), with gap value ∆ = 441± 8 K, and a concentrationsofx=0.1andx=0.75,assummarizedin
χ
low-temperature Curie-Weiss term, Eq.(2), with µ = Table I. This deviation could arise due to contributions
eff
1.08± 0.06 µ due to Cr substitution. With further Cr ofthe thermallyactivated FeSb -like Paulisusceptibility
B 2
3
TABLEI:Parameters of thefitstotheCurie-Weiss lawof thehigh temperatureM/H and semiconductingenergy gaps ofthe
resistivity.
x µeff(µB) Θ(K) χ0(emu/mol) TC/TN(K) Ms(10−3µB) ∆ρ(K)
0.10 1.08(6) 22(8) 1.3×10−4 302(9)
0.25 1.13(5) 26(4) 8.2×10−4 6.6(5) 45(1) 321(2)
0.40 1.85(6) 18(3) 3.8×10−4 14(1) 72(1) 434(8)
0.50 1.88(2) 2.5(8) 2.2×10−4 25 425(1)
0.60 1.82(4) −12(3) 6.3×10−4 65(2) 397(6)
0.75 1.44(3) −18(1) 12.2×10−4 150(5) 251(4)
for low Cr doping and to temperature limitations of our ing that the magnetization M(H) consists of a satura-
magneticsusceptibilitymeasurement,whereχ(T)curves tion moment(M ) and paramagnetic component (χH),
s
were fitted in close proximity to the antiferromagnetic we obtain the canting angle φ of 2.2 ∼ 4.1◦. The angle
transition for x=0.75. is defined as 2sin−1(M /2M ) where M = 2µ
S max max B
Parametersdeduced from the fit to the Eq. (1) model is the magnetic moment of the Cr4+. The saturation
are listed in Table I. Clearly, the Curie-Weiss temper- moment MS ∼ 0.09µB/Cr accounts for the ordering
ature changes sign from positive to negative indicating of 4.5% of Cr atoms. Hysteresis loops with coercive
thatthemagneticcouplingevolvesfromferromagneticto fields of HC = (230 ∼ 1100) Oe and remnant fields of
antiferromagnetic. However, the field dependence of the HR = (10 ∼ 63) Oe emu/mol were observed with field
transition, as depicted in Fig. 3, reveals a canted anti- applied along all three crystalline axes in this doping
ferromagneticstructurefor0.25≤x≤0.45. Inthis dop- range. With further Cr substitution for 0.6 ≤ x ≤ 1,
ing range, in a predominantly antiferromagnetic phase thesystemhasthe antiferromagneticstructureofCrSb2,
a small spontaneous magnetization is present due to a consistent with the results of Kjekshus et al..14
slight deviation from a strictly antiparallel arrangement The temperature dependence of the resistivity of
or to parasitic ferromagnetism. Since there is an inver- Fe1−xCrxSb2 for current applied along individual axes
sion symmetry at the Fe site in the Pnnm space group of the crystal structure is shown in Fig. 4. Electrical
b
of FeSb2, we can exclude the presence of Dzayloshinsky- transport along the b - axis shows a substantial metallic
Moriya type of interaction.18 The seemingly ferromag- regionfor0≤x≤0.25. Theregionofmetallicresistivity
netic tail is sensitive to the applied field, changing to gradually shifts down in temperature with increasing x,
a characteristic antiferromagnetic peak in lower fields. yielding a metallic state at the lowest measured temper-
Magnetism in Fe1−xCrxSb2 is most likely attributable ature for x = 0.25. At high temperatures, however, the
to the ordering of Cr atoms since the electronic config- regionofmetallicresistivityisprogressivelyreducedwith
uration of Fe in FeSb2 is the nonmagnetic 3d4. Assum- the increasing x, giving way to semiconducting behavior
above150K.Above150Kactivatedtemperaturedepen-
dence of resistivity is isotropic for all x≥0.1, except for
ρ of x=0.75.
b
Theevolutionoftheintrinsicbandsemiconductingen-
10kO e 5kOe 1kOe 0.5kOe 0.1kOe
ergy gap is listed in Table I. The gap values increase in
-3 0emu/mol)3405 x=0.25 -3 10emu/mol)6900 x=0.4 r∆neoρancm=heos8n3oit4tso±nloi3ccaKflasmhfoaiorxnixmfr=uomm1..∆SFρeom=rixc2o2=n5d±0u.c54t,iKntghfeoenrgeaxrpg=yva0glautpoe
M/H (115 M/H (30 dfourexto=se0m.7i5medteavlilaictetsrafnrospmormtoonbosetorvneicdbfoerhbba-vaixoirspreossissitbivly-
ity at hightemperatures. There is a lossof spin disorder
0 10 20 30 40 50 0 10 20 30 40 50
T( K) T( K) scattering at the TN for 0.25 ≤ x ≤ 0.1, in good agree-
2.3 ment with magnetization measurements.
ol)60 ol)
m m The resistivity data for an intermediate range of x,
mu/55 mu/2.2 0.25≤x≤0.75, is depicted in Fig. 5. Low temperature
e e
-3 1050 -3 10 x=0.75 resistivity is described by ρ = ρ0exp(T0/T)1/4, imply-
H ( H (2.1 ing a variable range hopping (VRH) conduction mecha-
M/45 x=0.5 M/ nism. The characteristic temperatures T0 and the cor-
2.0 responding localization lengths ξ are summarized in Ta-
0 5 10 15 100 120 140 160 180 200
T(K) T(K) ble II. The length is given by ξ3 = 19/[kBT0N(EF)]15,
where the density of states at the Fermi level N(E )
F
FIG. 3: Field dependance of the magnetic transitions for of 3×1037J−1cm−3 is estimated using low temperature
0.25≤x≤0.75 specific heat measurements (Fig. 5 inset).
4
T(K)
350 100 40 16 8 4 2.5
1 2 2K)00
9 x=1 ol
m
cm) 6 x=0.25 m) 0.1 1C/T (mJ/P00 a x=0.4
(ma x=0.4 x=0.5 x=0.6 TN (c 00 10T2(K220) 30 x=0.6
3 x=0.5
0.01
x=0.75 x=0 a x=0.25
00 100 200 300 a x=0.75
T(K) 1E-3
0.3 0.4 0.5 0.6 0.7 0.8
) 6 x=0.6 x=1 T-1/4(K-1/4)
m
x=0.5
c x=0 FIG. 5: ρ versus T−1/4 curves for 0.25 ≤ x ≤ 0.75 on a
m 4 semilog scale. Inset: Cp/T versus T2 for T <6 K.
( x=0.4
b
2
x=0.25 is present for intermediate alloys for 0.25 ≤ x ≤ 0.75.
The low temperature insulating region in FeSb dimin-
x=0.75 2
0 ishes with increasing x in Fe1−xCrxSb2 and disappears
0 100 200 300 by x=0.25.
T( K) FeSb andCrSb crystallizeinanorthorhombicmarc-
2 2
x=0.6 asitePnnm structure,whereasCoSb hasapseudomarc-
2
6 x=1 asitemonoclinicP21/c symmetryinducedbyanincrease
m) ofba-axis,doublingofthebc-axisandasmallmonoclinic
c 4 x=0.5 x=0.75 angle β = 90.4◦. FeSb2, CoSb2 and CrSb2 are all semi-
conducting materials and continuously miscible on their
m
x=0.25 respective binary alloy phase diagrams. Thus, it is pos-
(c x=0.4 sible to control a rich formation of ground states by car-
2
rierconcentration. BothFe1−xCoxSb2 andFe1−xCrxSb2
electronic systems are noteworthy in that although the
x=0
two end members are semiconducting, metallic regions
0
0 100 200 300 exist in their binary alloy systems. In contrastto the in-
T(K) termediateFe1−xCoxSb2 system,whereametallicregion
appears with as small an electron doping as x=0.05, in
Fe1−xCrxSb2groundstatemetallicityisobservedonlyfor
FIG. 4: Resistivity of Fe1−xCrxSb2 for current applied along x = 0.25. This is consistent with LDA+U band struc-
threecrystallineaxes. ArrowindicatestheNeeltemperatures. turecalculations.4Thedensityofstates(DOS)abovethe
Fermi levelis largely determined by the occupancy of 3d
orbitals. Electron doping readily moves the Fermi level
The rich phase diagrams of the electronic system in into the large peak just above the Fermi energy, in con-
the Fe1−xCrxSb2 alloys are displayed in Fig. 6. With trast to hole doping which moves the Fermi level to the
the increase of x, the paramagnetic ground state evolves depleted region of the DOS toward the valence band.
toward an antiferromagnetic one, see Fig. 6(a). In
the antiferromagnetic part of the phase diagram we dis-
tinguish a canted antiferromagnetic (CAF) region for
0.2 ≤ x ≤ 0.45. The phase diagram compiled from the TABLEII:T0 and ξ of variable rangehoppingand Sommer-
feld coefficient from specific heat measurements.
electricaltransportpropertiesisshowninFig. 6(b). The
b x 0.25 0.4 0.5 0.6 0.75
b - axis transport is metallic for 0 ≤ x ≤ 0.25. In addi-
tion, there are two semiconducting regions. The system T0(K) 2723 4657 7063 7750 57
ξ(A˚) 215 193 198 254 1758
is band gap semiconductor for 0.25< x at high temper-
γ(mJ/molK2)33.1 17.7 10.7 2.1 0.1
ature. The variable range hopping (VRH) mechanism
5
tution of Cr for Fe induced a rich phase diagram. Mag-
netically ordered ground states are formed for 0.25 ≤
x ≤ 1. The canted antiferromagnetism of intermedi-
ate alloys for x ≤ 0.5 evolves into the antiferromagnetic
(a)
PM state of CrSb with a Neel temperature gradually in-
100 2
creasing up to T =275 K for x = 1. The material is
N
AF b
K) semiconducting, with a metallic regionfor b - axis trans-
T( port in the paramagnetic region for 0 ≤ x ≤ 0.25. The
10
isostructuralFe1−xCrxSb2 alloysareaninterestingplay-
ground for studying intermediate electronic states be-
CAF tween small gap, nearly magnetic (or “Kondo”) semi-
1 conductor (x = 0) and antiferromagnetic semiconductor
0.0 0.2 0.4 0.6 0.8 1.0
x (x = 1). Further optical and X-ray scattering measure-
200 ments could be useful to study this problem in more de-
(b) tail.
Semiconductor
150
I || a
T(K)100 M II |||| bc
50
0 I VRH V. ACKNOWLEDGMENTS
0.0 0.2 0.4 0.6 0.8 1.0
x
FIG. 6: Phase diagram of Fe1−xCrxSb2, compiled from mea- We thank W.-G. Yin and Myron Strongin for use-
surements of magnetic properties (a) and from electrical ful communication and critical reading. This work was
transport (b). carried out at the Brookhaven National Laboratory,
which is operated for the U.S. Department of Energy by
Brookhaven Science Associates (DE-Ac02-98CH10886).
IV. CONCLUSION This work was supported by the Office of Basic Energy
Sciences of the U.S. Department of Energy. This work
We have studied anisotropy in the magnetic and elec- wasalsosupportedinpartbytheNationalScienceFoun-
trical transport properties of Fe1−xCrxSb2. The substi- dation DMR-0547938 (V. F. M.).
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