Evidence for electron-phonon interaction in Fe$_{1-x}$M$_{x}$Sb$_{2}$ (M=Co, Cr) single crystals

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by  N. Lazarević

Evidence for electron-phonon interaction in Fe1−xMxSb2 (M=Co, Cr) single crystals
N. Lazarevi´c, Z. V. Popovi´c
Center for Solid State Physics and New Materials,
Institute of Physics, Pregrevica 118, 11080 Belgrade, Serbia
Rongwei Hu, C. Petrovic
∗
Condensed Matter Physics and Materials Science Department,
Brookhaven National Laboratory, Upton, New York 11973-5000, USA
We have measured polarized Raman scattering spectra of the Fe1−xCoxSb2 and Fe1−xCrxSb2
1 (0≤x≤0.5) single crystals in thetemperature range between 15 K and 300 K. The highest energy
1 B1gsymmetrymodeshowssignificantlineasymmetryduetophononmodecouplingwidthelectronic
0
background. Thecouplingconstantachievesthehighestvalueatabout40Kandafterthatitremains
2
temperature independent. Origin of additional mode broadening is pure anharmonic. Below 40 K

n thecouplingisdrastically reduced,inagreementwithtransportpropertiesmeasurements. Alloying
a of FeSb2 with Co and Cr produces the B1g mode narrowing, i.e. weakening of the electron-phonon
J interaction. In thecase of Ag symmetry modes we havefound a significant mode mixing.

8
2 PACSnumbers: 78.30.Hv;72.20.-;75.20.-g;73.63.-b;

]
el I. INTRODUCTION Alloying of FeSb2 with Co and Cr also reduces the cou-
- pling, i.e. leads to the B1g mode narrowing. We have
r
t also observed strong Ag symmetry mode mixing.
s FeSb2 is a narrow-gap semiconductor which attracted
t. a lot of attention because of its unusual magnetic,1
a thermoelectric2 andtransportproperties.3 Themagnetic
m
susceptibility of FeSb is nearly constant at low temper-
2
- atures with paramagnetic to diamagnetic crossover at II. EXPERIMENT
d
around 100 K for a field applied along the c-axis, sim-
n
o ilar to FeSi.4 The electrical resistivity along the a- and
Single crystals of FeSb , Fe Co Sb and
c b - axes shows semiconducting behavior with rapid in- 2 1 x x 2
[ creaseforT<100K.Alongthec-axisresistivityexhibits Fe1 xCrxSb2 (0< x ≤0.5) were gr−own using the
a metal to semiconductor transition at around 40 K.1,4 high−-temperature flux method, which is described in de-
1 tails in Refs.9,10 Sample structure and composition were
v Based on the measurements of the electrical resistivity,
determined by analyzing the powder X-ray diffraction
1 magnetic susceptibility, thermal expansion, heat capac-
1 ity and optical conductivity the FeSb has been charac- data of Fe(Co,Cr)Sb2 single crystals collected using a
5 terized as a strongly correlatedsemico2nductor.1–6 It was Rigaku Miniflex diffractometer with Cu Kα radiation.4
5 The samplesstoichiometrywasdetermined by anenergy
also shown that FeSb has colossal Seebeck coefficient S
1. at10K andthe larges2tpowerfactorS2σ everreported.2 dispersive JEOL JSM-6500 SEM microprobe. Analysis
0 Thermalconductivityκ ofFeSb isrelativelyhighandis of several nominal x=0.25 samples showed that the
2
1 uncertainty in Co and Cr concentrationsamong samples
dominated by phonons around 10 K with phonon mean
1 freepathl ∼102µmseveralordersofmagnitudelarger grown from different batches was ∆x=0.04. The Raman
v: than electrpohnic mean free path.2 scattering measurements were performed using Jobin
i Yvon T64000 Raman system in micro-Raman configu-
X In the recent room temperature study we have ob- ration. The 514.5 nm line of an Ar+/Kr+ mixed gas
r served, for the first time, all six Raman active modes of laser was used as an excitation source. Focusing of the
a FeSb predictedbytheory.7 Racuet al.8 measuredpolar-
2 laser beam was realized with a long distance microscope
izedRamanscatteringspectraofFeSb2singlecrystalsbe- objective (magnification50×). We have found thatlaser
low room temperature and found only anharmonicity of
power level of 0.02 mW on the sample is sufficient to
A andB symmetrymodeswithnoadditionalelectron-
g 1g obtainRamansignaland,exceptsignaltonoiseratio,no
phonon coupling.
changes of the spectra were observed as a consequence
In this work we have measured at different tempera- of laser heating by further lowering laser power. The
tures polarized Raman scattering spectra of pure FeSb correspondingexcitationpowerdensity was less then 0.1
2
singlecrystalsandFeSb crystalsalloyedwithCoandCr. kW/cm2. AllRamanscatteringmeasurementspresented
2
TheB modeasymmetryandbroadeningisanalyzedus- in this work were performed using the (10¯1) plane of
1g
ing Breit-Wigner-Fano profile model. The coupling be- FeSb orthorhombic crystal structure. Low temperature
2
tween single phonon and the electronic background is measurements were performed between 15 K and 300 K
drastically reduced for temperatures bellow 40 K, fully using KONTI CryoVac continuous Helium flow cryostat
in agreement with transport properties measurements.3 with 0.5 mm thick window.
2

FeSb2 TABLEI. Parameters obtained by fittingof theB1g symme-
try mode spectra of pure FeSb2 with the BWF line shape
260K model.
s) Temperature (K) ωp (cm−1) Γ (cm−1) q
nit 210K 15 187.7(2) 1.4(3) 16(1)
u
b. 30 188.4(1) 1.8(3) 12(1)
r 180K
(a 85 187.0(1) 2.7(2) 9.6(8)
y
sit 150K 120 185.6(1) 3.3(3) 9.8(9)
en 150 183.6(1) 3.8(3) 9.8(9)
n Int 120K 180 182.1(1) 3.9(3) 9.9(9)
a 210 180.4(1) 4.3(3) 9.8(9)
m
a 85K 260 178.1(1) 4.7(3) 9.8(8)
R

30K
188 4.5 0.18
15K )
1
- 1m86 4.0 0.16
165 170W1a75ve1n8u0mb18e5r (1c9m0-1)195 200 er (c 3.5 -1 m)0.14
1b84 c
iFnIGth.e1(.xT,yh)ecRonafimgaunrastciaotnte(rBin1ggssypmecmtreatoryfFmeoSdbe2ss)inmgeleascurryesdtaalst 1enum82 23..50 WHM (0.12 1/q
different temperatures. v 0.10
a F
W
180 2.0
0.08
III. RESULTS AND DISCUSSION 1/q 1.5
178 0.06
40 80 120 160 200 240
FeSb crystallizes in the orthorhombic marcasite-type
2 Temperature (K)
structureofthecentrosymetricPnnm(D12)spacegroup,
2h
with twoformulaunits (Z=2)per unit cell.4 Basicstruc- FIG. 2. Wavenumber, FWHM and the degree of coupling
tural unit is built up of Fe ion surrounded by de- (1/q)oftheB1g modeasafunctionoftemperatureforFeSb2
sample.
formed Sb octahedra. These structural units form edge
sharing chains along the c- axis. According to the
factor-group analysis there are 6 Raman active modes
sity and ω and Γ/2 are the real and imaginary part of
(2A +2B +B +B ), which were observed and as- p
g 1g 2g 3g
phonon self energy, respectively. The spectra calculated
signedinourpreviouswork.7 The A andB symmetry
g 1g
usingEq. (1)areshownassolidlinesinFig. 1. Thebest
modes are bond stretching vibrations, whereas the B
2g
fitparametersarepresentedinTable I. Decreaseofq in-
and B symmetry modes represent librational ones.11
3g
dicates an increase in electron-phonon coupling. Nearly
Fig. 1 shows Raman scattering spectra of FeSb sin-
2
gle crystals in the (x,y) configuration (x, = 1 [101], the same value for q above 40 K (Table I) corresponds
√2 to temperature independent electron-phononinteraction
y = [010])7 measured at different temperatures in the
contribution (see Fig. 2). These results are completely
spectralrangeofthehighestenergyB symmetrymode.
1g inagreementwiththetransportpropertiesmeasurements
ForthisconfigurationB andB modesareRamanac-
1g 3g whichalsoshowedthatcarriersconcentrationrapidlyde-
tive, see Ref 7. One can notice an asymmetry of the B
1g creases for T<40 K, and is nearly constant above this
mode towards lower wave numbers. This broad, asym- temperature.3
metric structure is analyzed using a Breit-Wigner-Fano
In general, structural disorder, isotopic and/or anhar-
(BWF)interferencemodel.12,13Theresonanceusuallyin-
moniceffectsandelectron-phononinteractioncancausea
volves an interference between Raman scattering from
change of linewidth, among which only the last two can
continuum excitations and that from a discrete phonon,
introduce temperature dependence. Fig. 2 shows tem-
providedtwoRaman-activeexcitationsarecoupled. The
perature dependance of energy and linewidth of the B
1g
BWF model line shape is given by:
mode for pure FeSb sample experimentally obtained as
2
(1−ǫ/q)2 peak position and full width at half maximum (FWHM)
I =I0 1+ǫ2 , (1) of the Raman mode, respectively. As can be seen from
Fig. 2, in the temperature range between 15 K and
where ǫ = (ω−ω )/(Γ/2) and 1/q is the degree of cou- 40 K, the linewidth drastically increases with temper-
p
plingwhichdescribesthedepartureofthelineshapefrom ature increase. Because the phonon linewidth change
a symmetric Lorentzian function. The I is the inten- due to the phonon-phonon interactions (anharmonicity)
0
3

-1 1m)88 Fe1-xMxSb2 q 45 TABLEII.Best fitingparameters for FWHMandwavenum-
1ber (c84 x=45%Co Ebeqr.t(e2m)paenrdat(u3r)e.dependanceoftheB1g symmetrymodeusing
m R
u q 26 a
11Waven7860 q = 9.8x=25%Coman Inten CoFmepSobu2nd Γ02(.0cm(2−)1) A0.(5c3m(4−)1) Ω109(2c.4m(−3)1) C3(.c8m(1−)1)
-1 m)22..48 CCCrro252505%%% q 19 x=0sity (arb. u FFee00..7555CCoo00..2455SSbb22 11..15((11)) 00..2059((24)) 118990..99((22)) 11..8205((66))
M (c2.0 Co45% x=25%Crnits) Fe0.75Cr0.25Sb2 0.8(2) 0.43(7) 183.2(3) 1.93(11)
WH q 35 Fe0.5Cr0.5Sb2 1.4(1) 0.26(5) 176.2(3) 0.64(11)
F
1.6 x=50%Cr
80 100 120 140 160 180 200 220 240 260 165 170 175 180 185 190 195 200
-1
Temperature (K) Wavenumber (cm ) FeSb2 Fe0.75Cr0.25Sb2
FIG. 3. Wavenumber and FWHM as a function of tempera- nits) 260K nits) 260K
toufrteh(eleBft1gpamnoedl)eafnodr Fthee1−BxW(CFo,aCnra)xlySsbis2aatll2o1y0sKam(prilgehs.tpanel) arb. u 210K arb. u 210K
itbeshleealucottswrudoarn4lal0-ymphKvaoetnirccyoonmcshmienasatnlefglrreoaamctotfiloosBwntr.1ogtSneugmmpoptpedeomreratptlieufnorrearewtstuihwdrietsehcdcoeoonpnfcecFlnluuedsSdeiobennd2t Raman Intensity ( 111528000KKK Raman Intensity ( 111852000KKK
we found in a perfect mapping of the FWHM and 1/q

temperature dependance for T<40 K and the transport 85K 85K
properties measurements,3 whichshows dramaticcarrier
140 150 160 170 180 190 200 140 150 160 170 180 190 200
-1 -1
concentration decrease for T<40 K. At higher tempera- Wavenumber (cm ) Wavenum ber (cm )
tures (in our caseabove 40K) majorcontributionto the
FIG. 4. The Raman scattering spectra of FeSb2 (left panel)
temperaturedependanceofthelinewidthcomesfromthe and Fe0.75Cr0.25Sb2 (right panel) single crystals in the(x,x,)
phonon-phonon interaction because the electron-phonon configuration (Ag symmetry modes) measured at different
contribution for T>40 K is temperature independent temperatures.
(1/q∼const.).
Having this in mind, for T>40 K we consider energy
andlinewidthchangeoftheB modevs. temperatureas
1g one can see a large increase of the q with an increase of
pure temperature induced anharmonic effect. Influence
x,indicatingadecreaseofelectron-phononinteractionby
of the anharmonic effects on the Raman mode linewidth
Co and Cr alloying. Temperature dependance of energy
and energy can be taken into account via three-phonon
and linewidth for Fe (Co,Cr) Sb alloys are shown in
1 x x 2
processes:14,15 the left panel of Fig.−3. Experimental data are repre-
sented by symbols. Calculated spectra, obtained using
2
Γ(T)=Γ +A 1+ , (2) Eqs. (2) and (3), are represented by dashed and solid
0 (cid:18) ex−1(cid:19)
lines. Best fit parameters are presented in Table II. Γ
0
decreases significantly in Fe (Co,Cr) Sb alloys com-
whereΓ includesintrinsiclinewidth,structuraldisorder, 1 x x 2
0 paredto the pure FeSb (Tab−le II), althoughcrystaldis-
isotopic effect and temperature independent electron- 2
order increases with increasing Co and Cr concentration
phonon interaction contribution. A is the anharmonic
(for x ≤ 0.5). This is a consequence of drastic decrease
constant and x=h¯Ω /2k T.
0 B ofelectron-phononinteractioncontributionwithincreas-
Phonon energy is given by:
ing x. One can also notice that values of anharmonic
2 constantsdecreasewithincreasingCoandCr concentra-
Ω(T)=Ω0−C(cid:18)1+ ex−1(cid:19), (3) tions, what can be a consequence of change of electronic
structure of material by alloying.
whereΩ is temperatureindependentcontributions,C is ThepolarizedRamanscatteringspectraforpureFeSb
0 2
theanharmonicconstant.14,15 Eq. (2)andEq. (3)givea and Fe Cr Sb single crystals in the (x,x,) configu-
0.75 0.25 2
rather good fit (dashed and solid lines in the Fig. 2, re- ration (A symmetry modes) measured at different tem-
g
spectively) of the experimental data for the temperature peratures, are presented in Fig. 4. We have observed
region above 40 K. Fit parameters are presented in the structureatabout155cm 1 whichshowsasymmetryto-
−
Table II. wards higher wavenumbers. However, this asymmetry
From the BWF analysis of the experimental data for cannot be ascribed to the electron-phonon interaction,
Fe (Co,Cr) Sb (solidlinesattherightpanelofFig3), but is a consequence of the existence of two A sym-
1 x x 2 g
−
4
metry modes, as we have already reported in our previ- highest value at about 40 K and after that remains
ously published paper.7 Low temperature measurement temperature independent. Additional broadening comes
confirmedourpreviousassignation. TheLorentzianline- from the temperature induced anharmonicity. With in-
shape profile has been used for extraction of mode en- creasingconcentrationofCoandCrinFe (Co,Cr) Sb
1 x x 2
ergy and linewidth. These modes have nearly the same alloys the electron-phonon interaction is−drastically re-
energieswhatimposes the existenceof the mode mixing, duced. We have also observed mixing of the A symme-
g
manifested by energy and intensity exchange. The mix- try phonon modes in pure and Cr doped sample.
ing is specially pronounced when the intensities of the
modes are nearly the same.16 For FeSb the mixing is
2
strongest in the temperature range between 200 K and
ACKNOWLEDGMENT
250KandforFe Cr Sb between120Kand180K,
0.75 0.25 2
see Fig. 4.
We have pleasure to thank Dr Zorani Dohˇcevi´c-
Mitrovi´cforhelpfuldiscussion. Thisworkwassupported
IV. CONCLUSION bytheSerbianMinistryofScienceandTechnologicalDe-
velopment under Project No. 141047. Part of this work
The temperature study of polarizedRamanscattering was carried out at the Brookhaven National Laboratory
spectra of the Fe M Sb (M=Cr, Co) single crystals whichisoperatedfortheOfficeofBasicEnergySciences,
1 x x 2
has been performe−d. The linewidths and energies of the U.S. Department of Energy by Brookhaven Science As-
Ramanmodes wereanalyzedasafunctionofxandtem- sociates (DE-Ac02-98CH10886).
perature. Strong electron-phonon interaction, observed Present address Ames Laboratory and Department
∗
for the B symmetry mode ofpure FeSb , producessig- of Physics and Astronomy,Iowa State University, Ames,
1g 2
nificantmodeasymmetry. Thecouplingconstantreaches Iowa 50011,USA
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