Power-law Temperature Dependent Hall Angle in the Normal State and its Correlation with Superconductivity in iron-pnictides

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by  Y. J. Yan

Power-law Temperature Dependent Hall Angle in the Normal State and its
Correlation with Superconductivity in iron-pnictides
Y. J. Yan1, A. F. Wang1, X. G. Luo1, Z. Sun2†, J. J. Ying1, G. J. Ye1, P. Chen1, J. Q. Ma1 and X. H. Chen1∗
1Hefei National Laboratory for Physical Science at Microscale and Department of Physics,
University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
2National Synchrotron Radiation Laboratory, University of Science and Technology of China,
Hefei, Anhui 230029, People’s Republic of China
3 We report Hall measurement of the normal state in K- and Co-doped BaFe2As2, as well
1 NaFe1−xCoxAs. We found that a power-law temperature dependence of Hall angle, cotθH∝ Tβ,
0 prevails in normal state with temperature range well above the structural, spin-density-wave and
2 superconducting transitions for the all samples with various doping levels. The power β is nearly
4 for the parent compounds and the heavily underdoped samples, while around 3 for the super-
n
conducting samples. The β suddenly changes from 4 to 3 at a doping level that is close to the
a
emergenceof superconductivity. It suggests that theβ of ∼3is clearly tied tothesuperconductiv-
J
ity. Ourdatasuggest that,similartocuprates,thereexistsaconnectionbetweenthephysicsinthe
9
normal state and superconductivity of iron-pnictides. These findings shed light on the mechanism

of high-temperaturesuperconductivity.
]
n
o PACSnumbers: 74.62.-c;74.25.F-;74.70.Xa
c
-
r
p As a second family of high-Tc superconducting ma- ments can determinately uncover anomalous behavior in
u terials, iron-pnictides have been frequently compared to thenormalstates. Here,wewillshowthatresistivityand
s high-T cuprates [1–4]. There are many similarities be- Hall measurements hint a connection between the high-
c
.
t tween them, such as: an antiferromagentism in the par- temperature normal state and the low-temperature su-
a
m ent compounds and the quasi-two-dimensionalnature of perconductingstate. Wehaveinvestigatedaseriesofsin-
- superconducting CuO2 and FeAs layers. Superconduc- gle crystals of Ba1−xKxFe2As2 and Ba(Fe1−xCox)2As2,
d tivity is realized by suppressing the antiferromagnetic as well NaFe1−xCoxAs. The cotangent of Hall angle,
n (AFM) ground state in both of these superconductors. cotθH, from resistivity and Hall measurements was ob-
o
In cuprates, one of the central puzzles is the unusual served to vary with a simple but systematic trend. The
c
[ properties of the normal states, for instance, pseudogap, cotθH shows a fashion of Tβ in the paramagnetic state
linear-temperature dependent resistivity, T2 behavior of well above the structural, SDW and superconducting

1 Hall angles, which can give clues to the underlying mi- transitions. The magnitude of β is ∼ 4 in the heav-
v
croscopic interactions and the mechanism of supercon- ily underdoped regime near the parent compound, while
4
3 ductivity [5, 6]. Comparing the two high-Tc families, it drops to ∼ 3 when the superconducting ground state
7 we are curious about whether the normal states in iron- emerges. With further doping, β remains ∼ 3 in a small
1 pnictides can provide some hints and help to uncover dopingrangeandthendecreasesgraduallywiththe van-
.
1 the high-Tc physics. In deed, unusual behavior, such as ishing of superconducting ground state. Together with
0 linear-temperature dependence of magnetic susceptibil- the similar behavior observed in NaFe1−xCoxAs, our
3 ity abovethe AFM transition[7, 8], strongtemperature- datashow a consistentbehaviorinthe high-temperature
1
dependent Hall coefficients [9–13], has been observed in behavior in the normal state, which bears a connection
:
v iron-pnictides. Although the underlying physics is still with the emergence of superconducting ground state.
Xi under debate, these properties are closely related to the
Figure 1(a) shows the temperature dependence of
multibandcharacterofiron-pnictidesthatisacrucialkey
r
a to the understanding of the superconductivity in these resistivity for single crystalline Ba1−xKxFe2As2 and
materials. Ba(Fe1−xCox)2As2 with various doping, with a marked
asymmetric changes of transport properties induced by
While de Haas-van Alphen and angle-resolved pho-
electron and hole doping. Our data are similar to pre-
toemission spectroscopy (ARPES) can precisely deter-
vious reports of resistivity in doped BaFe2As2 crystals
mine the Fermi surface topology and the band struc-
[14, 15]. It is evident that the high-temperature resis-
ture, the electronic transport measurements are more
tivity exhibits distinct curvatures for electron and hole
sensitive to the subtle and complicated interactions in
dopings. Inthe hole-dopedregion(Fig. 1(a),toppanel),
the multiband system. In particular,transportmeasure-
the high-temperature curvature is downwards, while it
is upwards in the electron-doped region (Fig. 1(a), bot-
tom panel). It is interesting that the high-temperature
∗E-mailofX.H.C:[email protected] resistivity of the parent compound bears a similarity to
† E-mailofZ.S:[email protected] that of electron-doped compounds, which suggests that
2

(a)0.5 x = 0 x = 0.08 (b)10 x = 0.08 at 5T 0 x = 0 0 x = 0.021 0.0 x = 0.032 0.0 x = 0.045
0.4 xxx === 000...135320 xxx === 000...235378 8 xxx === 000...123332 3 (10)H-1 -1 -0 .5 --00.. 42
0.3 xx == 01..605 6 xxx === 000...355708 cot --320 5 10-20 2 4 6-1.00 5 10 15-0.60 3 6 9 12 15
0.2 4 xx == 01..605 5T0.0 T4 (10 9 K4) 0.0 T3.91 (10 9 K3.91) 0.0 T2.9 (10 6 K2.9) 0.0 T3.0 (10 6 K3.0)
(m cm)000...501 xx == 00 . 0 3 2 xx == 00..002415 -93 (10 m / C)H002 3 (10) at cot--H00..420 2x =4 0.0569 8 --00.. 840 x2 = 0.0472 6 ---000... 6420 5 x 1=0 01.152520 2 5---000... 6420 4x =8 0.1128516
0.4 x = 0.059 x = 0.072 R -5 T2.89 (1 06 K2.89) T3.09 (10 7 K3.09) T2.60 (1 05 K2.60) T2.50 (10 5 K2.50)
x = 0.125 x = 0.185
0.3 -10 x = 0 FIG. 3: (Color online) cotθH vs. Tβ for Ba(Fe1−xCox)2As2
x = 0.021 singlecrystalswithvariousdoping. Themagnitudeofβvaries
0.2 -15 xx == 00..003425 from sample to sample. The solid red lines show the Tβ de-
-20 xx == 00..005792 pendenceof cotθH.
0.1 x = 0.125
-25 x = 0.185
0.0
0 50 100 150 200 250 300 0 50 100 150 200 250 300 novel properties in the electronic systems [16]. In this
T (K) T (K) paper, we focus on the data at high temperatures well
FIG. 1: (Color online) (a): Temperature dependence of re- above the structural and SDW transitions. We stress
sistivity for Ba1−xKxFe2As2 (top) and Ba(Fe1−xCox)2As2 that, without the driving forcesfrom those orderingten-
(bottom) single crystals, respectively; (b): Temperature de-
dency, the high-temperature transport data are able to
pendence of Hall coefficient for Ba1−xKxFe2As2 (top) and provide information on the fundamental changes in the
Ba(Fe1−xCox)2As2 (bottom) single crystals, respectively.
prime band structure, which can supply valuable infor-
mation on the physics of iron-pnictides.

3 10) at 5T -01 x = 0 105 x = 0.08 48 x = 0.13 24 xx == 00..2332 BcrayF1s−itgaxulKsrexwF1iet(2hbA)vsa2srhi(ootwoupss)dtaohnpedinHBga.al(lIFnceo1a−effitxyCcpioeicxna)t2lARcosH2m(pfboeorntstbaootmethd)
(H-2
ot semimetal, where the densities of electron and hole car-
c-3 0 0 0 riers are roughly equal to each other, a vanishing Hall
0 2 4 6 8 10 0 10 0 2 4 6 8 10 0 5 10 15 20
T T4.0 (1 09 K4.0) 0.4 T4.08 (10 9 K4.08) 0.9 T4.0 (10 9 K4.0) T3.0 (1 06 K3.0) coefficient RH is usually expected. However, similar to
3 (10) at 501H..50 x = 0.37 0. 2 x = 0.50 00.. 36 xx == 00..5685 00.. 24 x = 1.0 leRaaHrr,listehhroerwetpsraoanrtsssptroboryntgopttrheoemprepgrertorieaustpussree[e9md–1etp3o]e,nbtdheeednHocema.lilnIcnaotpeeffiadrctbiiyecnuat-
ot
c0.0 0.0 0.0 0.0 single type of carriersin these multiband systems, and a
0.0 0.5 1.0 0 1 2 3 0 3 6 9 12 15 0 1 2 3 4 5 6
2.57 6 2.57 1.84 4 1.84 1.30 2 1.30 1.62 3 1.62 remarkable electron or hole character of transport prop-
T (10 K ) T (10 K ) T (10 K ) T (10 K )
erties can be induced by a slight electron or hole dop-
FIG. 2: (Color online) cotθH vs. Tβ for thesingle crystals of
Ba1−xKxFe2As2 system with different x. The magnitude of ing. It is evident that the RH of Ba(Fe1−xCox)2As2 is
β varies from sample tosample. The solid redlines show the always negative, suggesting the dominance of electron
Tβ dependenceof cotθH. carriers. In Ba1−xKxFe2As2, the RH turns to be posi-
tive with slight hole doping (x≥0.08), showing that the
holecarriersgovernthe transportproperties. The signif-
at high temperatures the parent compound can be con- icant rise in the magnitude of RH is associated with the
sidered as an electron doped compound. This argument structural/SDWtransitions,whichisnotthefocusofthe
isfurtherreinforcedbytheresultsofHallmeasurements, our study here. How to explain the unconventional Hall
whichshowsthatathightemperaturestheelectroncarri- properties is still under debate. In this paper, we focus
ersdominatethetransportpropertiesintheparentcom- onthehightemperatureregionwellabovethestructural,
pound (Figure 1(b)). SDW and superconducting transitions.
On the other hand, the transport measurements show Despite of its complicated properties, we found that
complex behavior at low temperatures below the struc- the resistivityandHalldatareveala intrinsic butsimple
tural and SDW transitions. The resistivity shows dif- behavior. Using the resistivity and Hall data displayed
ferent temperature-dependence in the Co and K doping in Figs. 1(a) and (b), we can calculate the cotangent
regimes. In fact, it has been found that SDW, electronic of Hall angles, cotθH=ρ/ρxy, for both Ba1−xKxFe2As2
nematicity and orbital ordering etc. take place below and Ba(Fe1−xCox)2As2 crystals. The Hall angle reveals
the structural/SDW transitions [16], which can signifi- apower-lawtemperaturedependence,cotθH=A+BTβ,
cantly reconstruct the band structure and give rise to in the temperature range well above SDW, structural
3

been observedin cuprate superconductors, which is con-
4 (a) (b) 4 sideredtobe apeculiarpropertiesofthe unusualnormal
3 3 state,thoughtheexplanationforthis behavioriscontro-
2
versial. In most cuprates, T dependence of the cotθH
2 2
holds for a wide doping range in the normal state above

1 1 the pseudogap-opening temperature [6, 18]. In contrast,
200 200
our data show that the power β varies with doping in
150 * 150 iron-pnictides. Together with the phase diagrams, the
K) T* T K) powers β for the K- and Co-doped BaFe2As2 and Co-
T (100 100 T ( doped NaFeAs are summarized in Fig. 4. Moreover,
we have marked in the phase diagrams the T∗ temper-
50 50
SDW SDW atures, below which the Hall angles deviate from the
0 SC SC 0 Tβ behavior. It is very interesting that the evolutions
1.0 0.8 0.6 0.4 0.2 0.0 0.05 0.10 0.15 0.20
of T∗ with doping show a highly consistent behavior
x (K content) x (Co content)

in both of the doped BaFe2As2 and NaFeAs families,
5
and further studies are required to show what happens
(c)
4 at these crossover temperatures. Systematic measure-
3 ments by ARPES have shown that the carrier doping
2 induced by K and Co dopants leads to a rigid-band-like
change of the valence band structure [19–21]. Therefore,
1
Fig. 4 displays a systematic change of electronic prop-
120
erties due to the variation of electron and hole carriers
*
K) 80 T in BaFe2As2 and NaFeAs. It is worth noting that the
(
T power-law behavior occurs in high temperature region
SDW
40 above the structural, SDW and superconducting transi-
tions, which reveals the fundamental electronic proper-
SC
0 ties of the iron-pnictides without the complexity due to
0.00 0.03 0.06 0.09 0.12
the low-temperature electronic reconstructions.
x (Co content)
In Fig. 4, it is remarkable that the variation of the
FIG. 4: (Color online) The doping dependenceof thepower-
lawexponentβandphasediagramsfor(a): Ba1−xKxFe2As2, power β behaves in a highly similar fashion in BaFe2As2
and NaFeAs families. In the parent compounds of
(b): Ba(Fe1−xCox)2As2 and (c): NaFe1−xCoxAs, respec-
tively. The data of NaFe1−xCoxAs are taken from Ref.17. BaFe2As2 and NaFeAs, β ∼ 4, and the magnitude of β
The T∗ is the characteristic temperature at which the Hall persists until the emergence of superconductivity. In the
angles deviate from thehigh-temperature Tβ behavior. doping range where the superconducting ground state
prevails, β drops to ∼ 3. Then, β∼3 holds for a wide
range of superconducting compounds. With further
and superconducting transitions. Figures 2 and 3 show doping, superconductivity fades away, β decreases to a
the plots of cotθH vs. Tβ for both Ba1−xKxFe2As2 and smaller value. With the emphasis on the consistentvari-
Ba(Fe1−xCox)2As2, respectively. A T-power law depen- ation of β in these materials, we also notice some excep-
dence holds for all the crystals at high temperatures. In tions. IntheparentcompoundofNaFeAsfamily,thereis
Figure 2, the cotθH of the parent compound BaFe2As2 nobulksuperconductivity,wethereforeconsideritanon-
decreases with increasing temperature, which is similar superconducting compound. In addition, the significant
tothebehaviorofelectron-dopedcompoundsasshownin decrease of β in the overdoped Ba1−xKxFe2As2 is likely
Fig. 3. Together with the resistivity data, this behavior coincident with the fact that the isotropic gap structure
suggeststhatBaFe2As2 canbe consideredasanelectron gradually changes to a nodal one with K doping[22, 23],
doped compound in the high-temperature normal state. though it is unclear how such a variationcan change the
Incontrast,thecotθH inhole-dopedsamplesforx≥0.08 magnitude of β.
increases with temperature. Our data indicate that the As already shown in Fig. 1, the electronic trans-
temperature dependence of the cotθH can provide infor- port in electron and hole doped region of BaFe2As2 is
mation onwhether electronor hole carrierspredominate quite different. Moreover, many properties of NaFeAs
the transportproperties. Moreover,one may notice that family are distinct from those of BaFe2As2 compounds.
themagnitudeofthepowerβ variesfromsampletosam- However, the similar doping-dependent variation of β in
ple. Moreover, such a Tβ behavior of Hall angle in the these materials suggests that there is a connection be-
normal state has also been found in Co-doped NaFeAs tween the high-temperature transport data and the low-
family, as reported by us in Ref. 17. temperature electronic ground states. At high temper-
For a comparison, the Tβ behavior of Hall angle has atures, the electronic band structure and underlying in-
4
teractions are relatively simple, without the complexity superconductivity has been found in Ru and P doped
duetotheelectronicreconstructionororderingtendency BaFe2As2, in which Ru and P change local interactions
atlowtemperatures. With the electronandholedoping, intheelectronicsystem. Itwouldbeinterestingtoinves-
ARPESdatahaveshownthatthebandstructurechanges tigatewhetherβ ∼3isauniversalbehaviorandholdsfor
in a rigid-band-likefashion, without significant variation thesematerials. Thesestudies,togetherwithourresults,
oflocalcorrelations[19–21]. Thus,itisreasonabletobe- willshed lightonthe rolesof chargeitinerancy andlocal
lievethat,athightemperatures,thefundamentalchange interactions in iron-pnictides.
in the electronic system is the shifting of Fermi energy.
In summary, the Hall angle of Ba1−xKxFe2As2,
Generally, one may expect β evolves gradually with car- Ba(Fe1−xCox)2As2 shows a power-law behavior, cotθH∝
rier doping, since the rigid-band-like change in the band Tβ,athightemperatureswellabovethestructural,SDW
structureis smooth[19–21]. However,the reductionofβ andsuperconductingtransitions. β ∼4wasobservedfor
from 4 to 3 seems to be a sudden drop, which suggests a
the parent compound and the heavily underdoped sam-
particularchange of the band structure by either hole or
ples on both the electron and hole doped sides. With
electron doping. It is worth noting that, the electronic
increasingdoping,asthesuperconductivityoccurs,theβ
properties of electron and hole pockets in iron-pnictides suddenlydecreasesto∼3. Thecloseconnectionbetween
are remarkably different, while our data shows that the
the change of β magnitude and the emergence of su-
Hallanglesintheelectron-andhole-dopedBaFe2As2 be- perconductivity suggest that some important electronic
have in a similar fashion. This counterintuitive finding
property at high temperatures is crucial for the under-
suggests that the normal-state electronic structure and
standing of the superconductivity in iron-pnictides.
its interactions with various degrees of freedom contain
Acknowledgements:
important messages about iron-pnictide physics. Un-
fortunately, there is no high-temperature ARPES data This work is supported by the National Natural
available to unambiguously show the critical change in Science Foundation of China (Grants No. 11190021,
the band structure [19–21]. We can only infer such a 11174266, 51021091), the ”Strategic Priority Research
change by the variation of β. The close connection be- Program(B)”oftheChineseAcademyofSciences(Grant
tween this reduction of β and the emergence of super- No. XDB04040100), the National Basic Research Pro-
conducting ground state suggests that the change of the gramofChina(973Program,GrantsNo. 2012CB922002
bandstructurebydopingfavorsthesuperconductivityin and No. 2011CBA00101), and the Chinese Academy of
iron-pnictides. Moreover,Fig. 3 shows that β∼3 is asso- Sciences.
ciated with the superconducting ground state, though
β decreases continuously with K doping in overdoped
Ba1−xKxFe2As2, which is probably associated with the
variationofthegapstructurefromisotropictonodalone.
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