Combined resistivity and Hall effect study on NaFe$_{1-x}$Rh$_x$As single crystals

2.2 MB·

by  Frank Steckel

Combined resistivity and Hall effect study on NaFe Rh As single crystals
1−x x
Frank Steckel,1,∗ Robert Beck,1 Maria Roslova,2 Dirk Bombor,1 Igor
Morozov,1,3 Sabine Wurmehl,1,4 Bernd Bu¨chner,1,4,5 and Christian Hess1,5,†
1Leibniz-Institute for Solid State and Materials Research, IFW-Dresden, 01069 Dresden, Germany
2Department of Chemistry and Food Chemistry, TU Dresden, 01062 Dresden, Germany
3Department of Chemistry, Lomonosov Moscow State University, 119991 Moscow, Russia
4Institut fu¨r Festko¨rperphysik, TU Dresden, 01069 Dresden, Germany
5Center for Transport and Devices, Technische Universita¨t Dresden, 01069 Dresden, Germany
6
(Dated: January 6, 2016)
1
0 ElectricaltransportmeasurementsareusedtostudytheRh-dopedNaFeAssuperconductorseries
2 with a focus on the tetragonal phase. The resistivity curvature has an anomalous temperature de-
n pendenceevidencinginthephasediagramtwocrossoverregionsofchangesinthescatteringrate,the
a effectivemassaswellasofthechargecarrierdensity. Thefirstcrossoverregionisdirectlyconnected
J to the structural transition and resembles the onset of resistivity anisotropy. The second crossover
5 region can as well be deduced from the temperature dependent Hall coefficient. A comparison to
literature NMR data suggests this region to be connected with nematic fluctuations far above the
] tetragonal to orthorhombic phasetransition.
n
o PACSnumbers: 74.25.fc,74.25.Dw,74.70.Xa
c
-
r
p I. INTRODUCTION spectroscopy,21 point contact spectroscopy22 as well as
u angle resolved photoemission spectroscopy (ARPES)23
s wereabletodetectafluctuationregimeindoped111and
. Most of the FeAs-based superconductors share the
t 122 compounds. However, the question about the tem-
a same principles of their electronic phase diagram, i.e. i)
m an antiferromagnetic order following a structural transi- perature and doping evolution of the fluctuation regime
in the phase diagram of the Fe-based superconductors
- tionintheundopedcompoundsii)asuppressionofthese
d remains open. Therefore, a method highly sensitive to
phasesuponchemicaldopingorpressure,andiii)adome-
n subtle fluctuations of the incipient transition is needed.
like behaviorofa superconductingphase. The supercon-
o The transport coefficients are capable of probing even
ducting critical temperature T is the highest at the in-
c c
tiny changes of the electronic structure and thus should
[ stance when complete suppression of the structural and
be suited to detect fluctuations in the electronic system.
magneticphaseisreached. Recentphasediagramstudies
1 Theelectricalresistivityhasbeenprovenpowerfulforde-
show,thatessentiallythedopedchargeseemstoinfluence
v thephasediagram. Thus,CoandRh-dopinginNaFeAs1 tectingandanalyzingsimilarlysubtleelectronicstructure
9
2 and in BaFe2As22 as well as Ni and Pd doping com- cShr-adnogpeesd. LFoarCeuxOam2p4l,e2,5iansLwae-ldloapsedinBFi-2dSorp2CeduOL6a+FδeAasnOd
8 parably affect the transition temperatures. The phase 2 4
and SmFeAsO26 the analysis of the resistivity slope and
0 transitions in the undoped and underdoped compounds
0 came recently into focus because the rotational symme- curvatureallowedtodetectapseudogap-regimeaswellas
. the crossover from non-Fermi-liquid to Fermi-liquid be-
1 try breaking seems to be triggered from the electronic
0 system in the Fe-based superconductors.3,4 This transi- havior. Intimately connected with the resistivity is the
6 tion is called nematic5 and happens naturally in twins Hallcoefficientandis,thus,anaturalcandidatetocross-
1 check such subtle electronic structure changes.27
such that only microscopic probes can locally detect
: In this paper, we report a detailed analysis of the re-
v the lowered two-fold symmetry in the Fe-plane of these
i materials.6,7Byapplyingasmallstraintothecrystallat- sistivity curvature and the Hall coefficient of Rh-doped
X NaFeAs single crystals. Our results clearly show a
tice an easy axis for the electronic distortion is defined
ar and, thus, the material becomes detwinned. In this case crossoverregionintimately connected to TS and further-
more another crossoverat very high temperatures trace-
even macroscopic methods can probe the difference in
able through the whole accessible electronic phase dia-
the orthogonalnematic a- and b-directions. For example
gram. We show that the first region tracks the onset
in resistivitymeasurementsofdetwinned crystalsa large
of the resistivity anisotropy whereas the second region
anisotropiy between ρ and ρ is observed in many dif-
a b
ferent Fe-based superconductors.8–15 It turned out, that evidences the incipient electronic fluctuations.
already far above the structural transition temperature
T such an anisotropy is measurable if uniaxial strain is
S
applied. However,thestrainfieldsmearsthetransition16 II. EXPERIMENTAL
and enhances the fluctuation regime. Thus, in order to
study the zero-strain fluctuations other methods were Crystal growth and characterization of the
applied. Nuclear magnetic resonance (NMR),15,17,18 Na Fe Rh As single crystals with x = 0 − 0.043
1−δ 1−x x
magnetic torque measurements,19,20 X-ray absorption is elaborated in detail in Ref. 1. Due to the high
2
III. RESULTS
A. Resistivity
x = 0
Fig. 1 displays the resistivity of the NaFe Rh As
1−x x
x = 0.01
single crystals. At high temperatures T > 250 K a lin-
ear fit to the resistivity data is possible and extrapo-
x = 0.013 lated to lower temperatures. Already here a deviation
from the linear extrapolation is visible in the tempera-
u.) ture range below ∼225 K. Resulting from the canonical
a. x = 0.018 picture of a metal for T > Θ /4 ∼ 75 K (with Θ the
( D D
K) Debye-temperatureofNaFeAs28,29)theelectron-phonon-
0 x = 0.019 scattering rate is expected to be linear in temperature
0
3 (cf. the Bloch-Gru¨neisen formula30) and thus with zero
(
/ x = 0.028 chuigr hvatteumrepoerfaρt(uTre)s. pAoninytsdedviiraetcitolny ftroomuntuhsiusableshcaavttieorrinagt
or additional changes in the charge carrier density n or
their effective mass m.
x = 0.041
Allcrystalsshowastrongdeviationfromthecanonical
linear behavior independent of the doping level. The de-
x = 0.043 viationhasitsmaximumintheintermediatetemperature
regime of approximately 150 K. Interestingly, this maxi-
mal deviation does not shift with increasing Rh content
and, thus, seems to be unaffected from the suppression
of the structural and magnetic phase. Upon lowering
the temperature further, the deviation from the linear
extrapolation becomes smaller. Below temperatures of
0 50 100 150 200 250 ∼ 50 K the temperature dependence of the resistivity is
T (K) dominatedby thephase transitionsofthe structuraland
FIG. 1. (Color online) Normalized and shifted resistivity of magneticorderingandsuperconductivityyieldingtypical
theNaFe1−xRhxAssinglecrystalsfromRef.1. Togetherwith hump and dip anomalies. In our analysis, we therefore
the resistivity a linear fit to the high temperature region is focusonthetemperature-range&50Kandbelow175K
shown as a black solid line. Thus, the deviation from this in the tetragonal phase. In Ref. [31] similar deviations
linearbehaviorasabroaddipintheintermediatetemperature
havebeenreportedforCo-dopedNaFeAsandareargued
regime becomes visible.
ashavinganotiontowardsachangeoftheeffectivemass
and chargecarrierdensity. Nevertheless,all these effects
can naturally be ascribed to changes of the scattering
rate, too.
The inflection point in the electrical resistivity curves
is known as indicator for changes of the electronic
structure.25,26 Thus, to investigate the temperature
regime of changes in the electronic structure in more de-
sensitivity to air of Na Fe Rh As, all preparations
1−δ 1−x x tailweplot the curvatureofthe resistivitydatagivenby
and subsequent transportmeasurements have been done
the second derivative in a color-coded scheme in Fig. 2.
either in inert gas atmosphere (Argon) or in vacuum.
In particular, we identify the inflection points by zero
curvature.
Thephasediagramyieldstwoinflectionpointregimes.
Thecrystalswerecontactedwithatwocomponentsil- A first one T∗1 in the underdoped regime at ∼ 20 K
ver epoxy in the standard four point contact geometry higher than T . The structural transition seems to fol-
S
inside an argon box and afterwards securely closed in- low T∗1 and both vanish upon doping towards the op-
side a homemade probe rod. The evacuated probe rod timal doping level. The second inflection point regime
had then been inserted to a Helium bath cryostat. The T∗2 is remarkably high in temperature. At first it in-
resistivity measurements have been already presented in creases slightly from 125 K in the undoped NaFeAs up
Ref. 1 to determine the phase transition temperatures. to125Kintheoptimallydoped(x=0.013)crystal,then
The Halleffectmeasurementswereconductedwithmag- T∗2 decreasesdownto 75K with further increasingx up
netic fields up to ±15 T. The perpendicular resistivity to the highest doping levels, i.e. T∗2(x) changes slope
ρ has been antisymmetrized with respect to the mag- at about optimal doping. Thus, in contrast to T∗1, the
xy
netic field. second inflection point regime is traceable through the
3
2 2
d / dT x = 0
-2
150 (K ) x = 0.01
x = 0.013
T
10 S
-6
22E -1006
-6 )
1T (K)00 T*2 --22 E 1-006 -103 0m/C100 cm) 0.0 280K
T*1 R (1H -2 10m -0.5 130K
50 - (xy 80K
TS TRH -1.0 x = 0.013 50K
TN Tnem 40K
-1 1000 0 5 10 15
T (T1T) 0H (T)
C
0
0 50 100 150 200 250 300
0.00 0.01 0.02 0.03 0.04
x in NaFe1-xTxAs with T = Co, Rh T (K)
FIG. 2. (Color online) Color-coded phase diagram of FIG. 3. (Color online) Hall coefficient RH from the under-
NaFe1−xTx with T = Co and Rh. The curvature of the re- doped NaFe1−xRhxAs crystals at 8 T. The arrow marks the
sistivity of the NaFe1−xRhxAs single crystals is shown. Red structural transition temperature TS from Ref. 1. The in-
color marks a positive, yellow nearly no curvature and blue set shows the diagonal resistivity ρxy in dependence of the
color a negative curvature of the resistivity data sets. The absolute magnetic field of thex=0.013 underdoped sample.
grey dotted lines are guides to the eye to mark the transi-
tion regions T∗1 and T∗2. The grey solid and green lines
mark the phase transition temperatures from Ref. 1. The smeared structural phase transition anomaly in analogy
dark yellow triangles mark the nematic transition tempera- to the magnetic susceptibility χ. For Rh contents higher
ture found by Ref. 9 by analyzing the resistivity anisotropy than x=0.013the nonlinearity ofρ (|B|) vanishes and
xy
of detwinned NaFe1−yCoyAs single crystals with the nomi- no kink appears which provides more evidence that the
nal Co-doping level y rescaled to match optimal doping of
optimally doped NaFe Rh As sample with x = 0.018
our samples with x = 0.018. The half-open turquoise dots 1−x x
mark the 1/T1T = 0.22 (sK)−1 data points from NMR has no structural transition.1 The origin of the kink can
measurements15 on NaFe1−xCoxAs single crystals (see Dis- bAeRuPnEdSermsteoaosdurwemithentthseohnelNpaoFfeAtesm.3p3erTahtuesree-ddeaptaenhdaevnet
cussion). The black squares mark the deviation temperature
TRH atwhichtheHallcoefficientdeviatesfromthehightem- shownthatabigpartofthebandstructurestartstoshift
perature phenomenological fit. at TS prior to the electronic reconstruction due to the
magnetic ordering. Such a reconstruction at the Fermi
surface involves naturally a strong change of the charge
whole accessible phase diagram. carrier density and, thus, a direct signal in the Hall co-
efficient.
The R of the overdoped samples, i.e. x ≥ 0.018,
H
B. Hall effect plotted in Fig. 4 has nearly the same weak temperature
dependence as the underdoped crystals down to ∼ 50 K
TheHallcoefficientRH (seeFig.3and4)iscalculated where|RH|hasamaximumanddecreasesforlowertem-
fromtheslopeofρ (|B|). Pleasenotethattheundoped peratures. This temperature dependence is highly com-
xy
NaFeAs has a nonlinear ρ (not shown) in agreement parable to that measured on Co-doped NaFeAs.34–36
xy
with an earlier report32. R of NaFeAs is negative in Aninterestingquantitytogetmoreinsighttothetem-
H
the complete measuredtemperature rangeand the abso- perature dependence of the multiband Hall coefficient
lutevalue|R |increasesweaklywithdecreasingtemper- is the cotangent of the Hall angle which is defined as
H
ature. At T ≥TS the temperature dependence of RH is cotθH =ρxx/ρxy. Inthe Drude one-bandpicture, where
relativelysmallwhileatthestructuraltransitiontemper- RH =1/nq and ρxx =m/nq2τ, it follows:
atureTS theHallcoefficienthasakinkandrisesstrongly ρ m
to high negative values without any further anomaly cotθH = = . (1)
R B qτB
H
down to the lowest accessible temperatures. Especially,
at the magnetic ordering temperature no anomaly is re- Inthisquantitytheinfluenceofthechargecarrierdensity
vealed. This shape of R is similar for the underdoped n cancels, and the cotangent of the Hall angle is direct
H
crystals x ≤ 0.013 (Fig. 3) except for a shifted and proportional to the effective scattering rate. In the case
4
--21000 xxxxx ===== 00000.....000001124489813 1000 a) 00000....00001111389 3.96 = (cot +138.67) / T 1H02468b) x T= =R 0H3.96 3.45 b = (cot +211.2) / T112H-050055 c)Tx R=H 0= .30.1458
C) H b 0
3 m/-30 cot 0 50100150200250 -1050 100150200250
-10 0 0 - T (K) T (K)
1 5
R (---H654000 (cm)xy------6543210 x = 05.018 10 40K 152182220550KKKK 100 00..002481 3.6 --bT = (cot +52) / 11H-5050 dT)xR H= 0.041 3.1 b = (cot +95.3) / T ----H43210000 e)TxR H= 0.043
0H (T) 0.043 = 3.6 = 3.1
-70 10 -20 50 100 150 200 -5050 100 150 200
0 50 100 150 200 250 300 0 50 100 150 200 250 T (K) T (K)
T (K) T (K)
FIG. 4. (Color online) Hall coefficient RH from the optimal FIG.5. (Coloronline)ThenegativecotangentoftheHallan-
and overdoped NaFe1−xRhxAscrystals. The inset shows the gleθH forallNaFe1−xRhxAssinglecrystalsinasemilogarith-
diagonal resistivity ρxy in dependence of the absolute mag- mic plot (a). On the right side (b)-(e), for selected composi-
netic field of thex=0.018 optimally doped sample. tions,thedeviationfromthehightemperaturefitbyEq.(2),
plotted as b = (cotθH −a)/Tβ. The fit range was chosen
as T ≥ 100 K. TRH marks the temperature, where the data
ofmorethanonecontributingbandto the chargecarrier points deviatefrom thehigh temperaturefit.
transportthe dependencies are not easily revealed. Nev-
ertheless, in high-temperature superconductors typically
Remarkably, the Hall coefficient deviation tempera-
a phenomenological function of the form
tures T , additionally plotted in Fig. 2, reflect as well
RH
cotθ =a+bTβ (2) the aforementioned trend of the second inflection point
H
region T∗2. Thus, we have a second, independent de-
fits the temperature dependence of the cotangent of the termination of T∗2. Additionally, the comparison with
Hallangleverywell.27,35,37–39 InthemultibandFe-based Co-dopedNaFeAsshowsthatbothmaterialshaveasim-
superconductors, in particular doped BaFe As 27,39 and ilar transition region as well as similar phase transition
2 2
Co-dopedNaFeAs35 β-valuesbetween4 and2havebeen temperatures upon formal electron doping.
reported. Motivated by these findings we address now
theanalysisoftheHalleffectdataonourNaFe Rh As
1−x x
single crystals. IV. DISCUSSION
The cotangentofthe Hallangleofthe NaFe Rh As
1−x x
singlecrystalsisdisplayedinFig.5(a). Thehightemper- After having established the experimental finding of
ature behavior (T >125 K) is well described by Eq. (2). twotransitionregionsT∗1andT∗2intheelectronicphase
However, below a certain temperature the curves shown diagram of electron-doped NaFeAs above the known
in Fig. 5(b)-(e) deviate from this power law. To illus- phase transition temperatures the natural question of
trate this behavior, we subtracted the high temperature the origin of these inflection points has to be answered.
fitfromEq.(2)fromthedatapointstoclearlydefinethe Therefore, we discuss our results in the light of other
deviation temperature T (cf. Fig. 5). Additionally, experimentalresults for the tetragonalphase in this ma-
RH
the values for β are given in the plots and they vary be- terial.
tween 4 and 3, while β consistently with previous data In a resistivity anisotropy study on detwinned
sets,27,35,39 decreases with increasing doping level. NaFe Co As in Ref. 9 the onset of the anisotropy is
1−x x
Nevertheless,suchadeviationfromatemperaturelaw definedasthekinkappearinginρ −ρ slightlyaboveT .
a b S
which is valid for a larger temperature regime, points TheonsettemperaturesT oftheresistivityanisotropy
nem
towards an unusual change in the physical properties of ofNaFe Co AsnearlycoincideswithT∗1inunstrained
1−x x
the charge carriers, i.e. effective mass or scattering rate NaFe Rh As single crystals (cf. Fig. 2). Thus, it is
1−x x
following Eq. (1). Indeed, also the charge carrierdensity possible to track the onset temperature T of a strong
nem
n can be responsible for the changes, because Eq. (1) is anisotropy between ρ and ρ by carefully studying the
a b
strictly valid only in a one-band metal. stress-free average resistivity curvature. Note that, we
5
found small deviations especially in the undoped crystal seem to be quite more sensitive to nematic fluctuations
where T is located at a slightly higher temperature in the tetragonal phase of the iron-based superconduc-
nem
thanT∗1,whichmighteitherhaveitsoriginintheuncer- tors than other probes such as NMR and STM6 experi-
taintyofδ in Na FeAs orinthe smearingofthe struc- ments, which found anisotropies up to 90 K. In view of
1−δ
turalphase transitionby uniaxially stressingthe crystal. this strong sensitivity it is remarkable that we can re-
All the shown data, i.e. T and T∗1 have in common, solve the aforementioned slope change of T∗2(x) at opti-
nem
that they are tightly connected to the structural transi- mal doping. Such an anomaly in the doping dependence
tion and are suppressed upon doping equally to T . at optimal doping has been reported before in resistiv-
S
We ascribed the second inflection point T∗2 at much ity anisotropy measurements.10,45 The corroboration of
highertemperaturestoachangeofeitherthechargecar- these findings by our results calls for a further investiga-
rier density, the effective mass, the scattering rate or tionofthe fluctuation regimeto disentanglewhether the
a combination of those. From the cotθ analysis we nematic fluctuation channels or the coupling constants8
H
know that this transition region cannot be assigned to possess a hidden doping dependence including a clarifi-
the multiband nature of the Fe-based superconductors. cation of the role of the impurity density in the nematic
Besides,no other phase transitionatsuch hightempera- fluctuation regime.
tures in these materials are known. Another correlation
could be the influence of fluctuations on the transport
which could be fluctuations of the spins, the orbitals or
V. CONCLUSION
the structure. We compareourresults withspin fluctua-
tions in the tetragonal state and therefore consult NMR
dataofCo-dopedNaFeAs,inparticularweusethequan- WeperformedacombinedstudyofresistivityandHall
tity 1/T T.15 This quantity is proportional to the imag- effect measurements on NaFe Rh As single crystals.
1 1−x x
inary part of the dynamical spin susceptibility and thus In total we found the typical anomalies of the phase
measures spin fluctuations in the whole Brillouing zone. transitions and additional deviations from the expected
1/T T rises significantly far above the structural tran- hightemperaturebehaviorattemperaturesfarabovethe
1
sition temperature and thus reveals a slow-down of the phasetransitions. Weappliedthemethodoftheresistiv-
spin fluctuations. By definition, this includes q = 0 ne- itycurvatureanalysisandfoundtworegionsofinflection
matic fluctuations and indeed a scaling of 1/T T18 with points. The first inflection point T∗1 at temperatures
1
the elastic moduli,40 showing the softness of the crystal slightly above T points towards the onset of resistivity
S
lattice aboveT ,hasbeen reported.41 Forapropercom- anisotropy. Comparisons to NMR data suggest that T∗2
S
parisonwe choosea certain1/T T value (see Fig. 2) and from the resistivity as well as the Hall coefficient indi-
1
mark the temperatures at which the 1/T T of a partic- cate the onset of fluctuations connected to the nematic
1
ular Co-doped NaFeAs crystal crosses this value. Inter- phase in the tetragonal state. This method is thus ca-
estingly, the doping dependence in the electronic phase pable of revealing not only the broad fluctuation regime
diagram of T∗2 and of the 1/T T values is similar. In athightemperatures inthe complete phase diagrambut
1
particular, T∗2 and 1/T T as a function of doping have also the real onset of resistivity anisotropy induced by
1
the same slope for doping levels above optimal doping. the nematic rotational symmetry breaking which is con-
We therefore ascribe the inflection point to a sensitivity nected with the structural phase transition.
of the resistivity to the onset of nematic fluctuations. It
still remains to be clarified which quantities, i.e. charge
carrier density, effective mass and scattering rate, are
ACKNOWLEDGMENTS
dominantly influenced. Conflicting results about the im-
portance of the impurity density and their anisotropy
have been reported. While transport measurements in This work has been supported by the Deutsche
magnetic field32 and after annealing42 suggest a domi- Forschungsgemeinschaft through the Priority Program
nant role of the observed anisotropic impurity states43 SPP1458 (Grants No. BU887/15-1 and HE3439/11),
another strain dependent resistivity anisotropy experi- and through the Emmy Noether Program in project
mentpointstowardsanegligibleinfluenceoftheimpurity WU595/3-3. We thank the BMBF for support in the
density above T .44 frame of the ERA.Net RUS project (project 01DJ12096,
S
We point out that the electrical transport coefficients FeSuCo).
∗ [email protected] Shevelkov, A. U. B. Wolter, C. Hess, S. Wurmehl, and
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