Magnetic anisotropy in hole-doped superconducting Ba 0.67K 0.33Fe 2As2 probed by polarized inelastic neutron scattering

0.33 MB·English

by  Chenglin Zhang

Magnetic anisotropy in hole-doped superconducting Ba K Fe As probed by
0.67 0.33 2 2
polarized inelastic neutron scattering
Chenglin Zhang,1 Mengshu Liu,1 Yixi Su,2 Louis-Pierre Regnault,3 Meng Wang,1,4
Guotai Tan,1,5 Th. Bru¨ckel,6 Takeshi Egami,1,7,8 and Pengcheng Dai1,4,∗
1Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA
2 Ju¨lich Centre for Neutron Science JCNS-FRM II,
Forschungszentrum Ju¨lich GmbH, Outstation at FRM II,
Lichtenbergstrasse 1, D-85747 Garching, Germany
3 3Institut Laue-Langevin, 6, rue Jules Horowitz, BP 156, 38042 Grenoble Cedex 9, France
1 4Beijing National Laboratory for Condensed Matter Physics,
0
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2 5Physics Department, Beijing Normal University, Beijing 100875, China
n 6Ju¨lich Centre for Neutron Science JCNS and Peter Gru¨nberg Institut PGI,
a JARA-FIT, Forschungszentrum Ju¨lich GmbH, 52425 Ju¨lich, Germany
J 7Department of Materials Science and Engineering,

8 The University of Tennessee, Knoxville, Tennessee 37996-1200, USA
8Joint Institute of Neutron Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

] (Dated: December 11, 2013)
n
o We use polarized inelastic neutron scattering (INS) to study spin excitations of optimally hole-
c doped superconductor Ba0.67K0.33Fe2As2 (Tc = 38 K). In the normal state, the imaginary part of
- the dynamic susceptibility, χ′′(Q,ω), shows magnetic anisotropy for energies below ∼7 meV with
r
p c-axispolarizedspinexcitationslargerthanthatofthein-planecomponent. Uponenteringintothe
u superconductingstate,previousunpolarizedINSexperimentshaveshownthatspingapsat∼5and
s 0.75 meVopen at wavevectorsQ=(0.5,0.5,0) and(0.5,0.5,1),respectively,with abroad neutron
.
t spin resonance at Er =15 meV.Our neutron polarization analysis reveals that thelarge difference
a
inspingapsispurelyduetodifferentspingapsinthec-axisandin-planepolarizedspinexcitations,
m
resulting resonance with different energy widths for the c-axis and in-plane spin excitations. The
- observation of spin anisotropy in both opitmally electron and hole-doped BaFe2As2 is due to their
d
proximity tothe AFordered BaFe2As2 where spin anisotropy exists below TN.
n
o
PACSnumbers: 74.70.Xa,75.30.Gw,78.70.Nx
c
[

1 Neutronpolarizationanalysishasplayedanimportant with pure paramagnetic scattering. Upon entering into
v role in determining the magnetic structure and excita- the superconducting state, a quasi-isotropic spin reso-
7 tions of solids1. For high-transition temperature (High- nance occurs at E = 40 meV to within the precision of
r
9 T ) copper oxide superconductors derived from hole or the measurements and a spin anisotropy develops in the
c
3
electron-doping from their antiferromagnetic (AF) par- lower energy 10≤E ≤30 meV, resulting in a clear spin
1
ent compounds, neutron polarization analysis have con- gap below 22 meV for the c-axis polarized dynamic sus-
.
1 clusively shown that the collective magnetic excitation ceptibility χ′′ and in-plane χ′′ for E ≥ 10 meV6. The
0 c a/b
coupled to superconductivity at the AF wave vector of low-energyspinanisotropyislikelyduetospin-orbitcou-
3
the parent compounds, termed neutron spin resonance2, plinginthesystem. Foroptimallyelectron-dopedcopper
1
: has a magnetic origin3–9. Furthermore, by carrying out oxide superconductor Pr0.88LaCe0.12CuO4−δ, spin exci-
v neutron polarization analysis with a spin-polarized in- tations are isotropic both above and below T 8. There-
i c
X cident neutron beam along the scattering wave vector fore, the spin anisotropy in the superconducting state of
r Q = ki −kf (where ki and kf are the incident and fi- hole-dopedYBa2Cu3O6.9isunrelatedtothenormalstate
a nalwavevectorsofthe neutron,respectively),xˆ||Q; per- paramagnetic scattering.
pendicular to Q but in the scattering plane, yˆ⊥Q; and
perpendicular to Q and the scattering plane, zˆ⊥Q, one Like copper oxide superconductors, superconductivity
can use neutron spin flip (SF) scattering cross sections in iron pnictides also arises when electrons or holes are
σSF,σSF, and σSF to determine the spatial anisotropyof doped into their AF parent compounds10–14. Further-
xx yy zz
spin excitations1. If the resonance is an isotropic triplet more, unpolarized neutron scattering experiments have
excitation of the singlet superconducting ground state, shown that both hole and electron-doped iron pnictides
oneexpectsthatthedegeneratetripletwouldbeisotropic exhibits a neutron spin resonance similar to copper ox-
inspaceaspureparamagneticscattering9. Foroptimally idesuperconductors15–20. Intheinitialpolarizedneutron
hole-doped copper oxide superconductor YBa Cu O scatteringexperimentonoptimallyelectron-dopedsuper-
2 3 6.9
′′
(Tc = 93 K), neutron polarization analysis reveals that conductor BaFe1.9Ni0.1As2 (Tc = 20 K), χc was found
′′
spinexcitationsinthenormalstatearespatiallyisotropic to be much larger than χ for energies 2 ≤ E ≤ 6
a/b
andfeaturelessforenergies10≤E ≤60meV,consistent meV below T , while the resonance at E = 7 meV
c r
2
is only weakly anisotropic21. In a subsequent polarized 8 8
45 K k =2.66 Å-1 k =3.84 Å-1
neutron scattering measurement on undoped AF parent f f
6 6
compound BaFe As 22, isotropic paramagnetic scatter- [0.5,0.5,0] [0.5,0.5,2]
2 2
ing at low-energy (E = 10 meV) were found to become 4 M 4
001
anisotropic spin waves below th′e′ N´eel temperature TN 2 M 2
with a much larger in-plane (χ ) spin gap than that 110 (a)
a/b 0 0
′′
of the out-of-plane gap (χc). These results indicate a 8 2 K 8
strongsingle-ionanisotropyandspin-orbitcoupling,sug- n n
gestingthatmoreenergyisneededtorotateaspinwithin 1 mi 4 4 1 mi
oathnxeise2ol2er.ctthHrooornhw-ooemvveebrrid,cospiame-bdilapBrlaapnFoeel1a.tr8hi5zaNendi0.rn1o5etAuattsri2nong(Teictxp=teor1itm4heeKntc)s-, monitors ~ 0 E(rb)0 monitors ~
wisohticrohpiics pfaarraamwaagyneftriocmscathtteerAinFg borodthereadbopvheaasned, rbeevleoawl 250 4 2 K - 45 K 4 133
Trecs2o3n.aVnecrey-lrikeceenextlcyi,taSttieoffnesnsinettahle. rseuppoerrtcoevnidduecntcinegforsttawtoe Counts/ 0 E 0 Counts/
r
Kof)o.pIntimadadlliytioelnecttoroann-disoopterdopBicaFrees1o.8n8aCnoc0e.1a2tAEs2=(T8c =me2V4 -4 (c) -4
with weak dispersion along the c-axis, there is a reso- 40 σSF+σSF+σSF 40
xx yy zz
nanceatE =4meVpolarizedonlyalongthec-axiswith
strong intensity variation along the c-axis24. In the nor- 20 45 K 20
E
mal state, there are isotropic paramagneticscattering at 2 K r
AF wave vectors with L = 0 and weak anisotropic scat- 0 (d) 0
M M M M
teringwithalargerc-axispolarizedintensityatL=124. 001 110 001 110
0 5 10 15
If the observed anisotropic magnetic scattering in E (meV)

the superconducting state of optimally electron-doped
BaFe Ni As 21 and BaFe Co As 24 are in- FIG. 1: (Color online) Neutron polarization analysis deter-
1.9 0.1 2 1.88 0.12 2
deed associated with the anisotropic spin waves in mined c-axis (χ′c′ ∝ M001) and in-plane (χ′a′/b ∝ M110) com-
BaFe2As222, one would expect similar anisotropic spin ponentsofspinexcitationsinBa0.67K0.33Fe2As2 fromrawSF
constant-QscansatQ=(0.5,0.5,0) andand(0.5,0.5,2). To
excitationsinhole-dopedmaterialsnottoofarawayfrom
the parent compound. In this paper, we report neu- extract M001 and M110, we use methods described in Ref.23
tron polarization analysis on spin excitations of the op- and assume M1¯10 = M110 in the tetragonal crystal. (a) En-
ergy dependence of M001 and M110 at T = 45 K. (b) Iden-
timally hole-doped superconducting Ba K Fe As .
0.67 0.33 2 2 tical scans at T = 2 K. (c) The solid and open circles show
From the previous unpolarized INS work on the same the temperature difference (2 K−45 K) for M001 and M110,
sample, we know that spin excitations in the supercon- respectively. (d) The sum of σSF +σSF+σSF at 45 and 2
xx yy zz
ducting state have a resonance at Er =15 meV, a small K.Sincebackgroundscatteringisnotexpectedtochangebe-
spin gap (E ≈ 0.75 meV) at Q = (0.5,0.5,0) and a tween these temperatures16, such a procedure will increase
g
large gap (E = 5 meV) at (0.5,0.5,1)16. In the nor- statistics of magnetic scattering. The black data points are
malstate, spign excitations at both wavevectorsare gap- collected at Q = (0.5,0.5,0) with kf = 2.66 ˚A−1, while the
less and increase linearly with increasing energy16. Our red data points are at Q = (0.5,0.5,1) with kf = 3.84 ˚A−1.
The solid and dashed lines are guided to theeyes.
polarizedINSexperimentsrevealthatthepersistentlow-
energyspinexcitationsattheAFwavevector(0.5,0.5,1)
below T are entirely c-axis polarized. Although there
c
◦
is also superconductivity-induced spin anisotropy simi- ity3 atfullwidthhalfmaximum)withatetragonalunit
lar to optimally electron-doped BaFe Ni As 21 and cell for which a = b = 3.93 ˚A, and c = 13.29 ˚A. In this
1.9 0.1 2
BaFe Co As 24,thelow-energyc-axispolarizedspin notation, the vector Q in three-dimensional reciprocal
1.88 0.12 2
excitationsdonotchangeacrossT andthereforecannot spacein˚A−1 is definedas Q=Ha∗+Kb∗+Lc∗, where
c
have the same microscopic origin as the spin isotropic H, K, and L are Miller indices and a∗ = aˆ2π/a,b∗ =
resonance at Er = 15 meV. We suggest that the per- bˆ2π/b,c∗ = cˆ2π/c are reciprocal lattice vectors. Our
sistent c-axis polarized spin excitations in the supercon- polarized INS experiments were carried out on the IN22
ducting state of optimally hole and electron-doped iron triple-axis spectrometer with Cryopad capability at the
pnictide superconductorsisduetotheirproximitytothe Institut Laue-Langevin in Grenoble, France. The fixed
AF ordered parent compound. Their coupling to super- final neutron wave vectors were set at k = 2.66 ˚A−1
f
conductivity mayarisefromdifferentcontributionsofFe and k =3.84˚A−1 in order to close the scattering trian-
f
3dX2−Y2 and 3dXZ/YZ orbitals to superconductivity25. gles. To compare with previous polarized INS results on
Single crystals of Ba K Fe As are grown by a iron pnictides21–24, we converted the measured neutron
0.67 0.33 2 2
self-fluxmethod16. About10gramsofsinglecrystalsare SFscatteringcrosssectionsσSF,σSF,andσSF intoc-axis
xx yy zz
coalignedin the [H,H,L] scattering plane (with mosaic- (M ) and in-plane (M ) components ofthe magnetic
001 110
3

8 45 K kf=2.66 Å-1 kf=3.84 Å-1 8 6 45 K kf=2.66 Å-1 kf=3.84 Å-1 6
[0.5,0.5,1] [0.5,0.5,1] [0.5,0.5,0] [0.5,0.5,2]
3 3

4 M 4
001 0 0
M
0 110 (a)0 -3 M001-M11 0 M001-M11 0 (a)-3
10 10 62 K 6
2 K
n n
Counts/250 monitors ~ 1 min 0405 2 K - 45 K EErr (b)0504 Counts/133 monitors ~ 1 min Counts/250 monitors ~ 1 mi -03603345 K K[ Mf0=.5200,1.0-6M.65 ,1Å11 0 ]- 1 [K0f. =5M,30.0.0851-4,M1 Å]11- 01 (b)-030363Counts/133 monitors ~ 1 mi
-4 (c) -4 -3 M001-M11 0 M001-M11 0 (c) -3
50 σSF+σSF+σSF (d) 50 6 2 K (d)6
xx yy zz
3 3
25 45 K E 25
r
2 K 0 0
0 0
M M M M -3 M -M M -M -3
001 110 001 110 001 110 001 110
0 5 10 15 20 0 5 10 15 20
E (meV) E (meV)

FIG.2: (Color online) Constant-Qscansat Q=(0.5,0.5,1) FIG.3: (Coloronline)Energydependenceofspinanisotropy
below and above Tc. (a) Energy dependence of M001 and asdeterminedbythedifferencebetweenM001−M110fortem-
M110 at T = 45 K and (b) at 2 K. The superconductivity- peratures(a)45Kand(b)2KatwavevectorQ=(0.5,0.5,0)
induced spin gaps are at ≤2 and 7 meV for M001 and M110, andQ=(0.5,0.5,2). Similardifferencesabove(c)andbelow
respectively. At resonance energy of E =15 meV, the scat- (d)T atQ=(0.5,0.5,1). Theenergywidthisbroaderin(d)
r c
tering is isotropic. (c) The solid and open circles show the compared with (b). Thesolid and dashed lines are guided to
temperature difference (2 K−45 K) for M001 and M110, re- theeyes.
spectively. (d) The sum of σSF+σSF+σSF at 45 and 2 K.
xx yy zz
The solid and dashed lines are guided to theeyes.
spin anisotropy (M > M ) appearing near E ≈ 8
001 110
meV[Fig. 1(b)]. Thisissimilartothespinanisotropyin
scattering23. BaFe Co As 24. Figure1(c)showsthe temperature
1.88 0.12 2
Figure 1 shows energy scans above and below T at difference of magnetic scattering, revealing net intensity
c
wave vectors Q=(0.5,0.5,0) and (0.5,0.5,2). We chose gainsfor M001 and M110 only above∼7 and10 meV, re-
these two equivalent wave vectors with different fixed fi- spectively. Figure1(d)showsthesumoftheSFmagnetic
nal neutron energies to satisfy the kinematic condition scatteringintensitiesforthreedifferentneutronpolariza-
for the large covered energy range. Since the iron mag- tions, which improve the statistics, above and below Tc.
netic formfactors, geometricalfactors, and instrumental ConsistentwithFig. 1(c),thesuperconductivity-induced
resolutionsaredifferentatthesetwowavevectors,weuse netmagneticintensitygainappearsonlyabove∼7meV,
left and right scales for Q=(0.5,0.5,0)and (0.5,0.5,2), forming a resonance at Er =15 meV.
respectively. In the normalstate (45 K),spin anisotropy Figure2summarizesthe identicalscansasthatofFig.
′′
for energies below E ≈ 7 meV is clear with M001 (χc) 1 at the AF wave vector Q = (0.5,0.5,1) above and be-
′′
largerthanM110 (χa/b)[Fig. 1(a)]. ForE >7meV,spin low Tc. At T =45 K, we see clear spin anisotropy below
excitations are nearly isotropic. This is different from E ≈ 7 meV with M > M similar to the spin exci-
001 110
electron-doped BaFe Co As , where paramagnetic tations at Q = (0.5,0.5,0) [Fig. 2(a)]. Upon cooling to
1.88 0.12 2
scattering at Q = (0.5,0.5,0) is isotropic above T 24. 2 K, a large spin gap opens below E ≈ 7 meV in M ,
c 110
In the superconducting state (2 K), M and M in but there is still magnetic scattering in M extending
001 110 001
Ba K Fe As vanish below 5 meV, consistent with toatleast2meV.Therefore,thelow-energysignalabove
0.67 0.33 2 2
opening of a superconductivity-induced spin gap [Fig. ∼1 meV at Q = (0.5,0.5,1) reported in the earlier un-
1(b)]16. From E = 5 meV to the resonance energy at polarizedneutronmeasurements16 areentirelyc-axispo-
E =15meV,bothM andM increasewithincreas- larized magnetic scattering. The neutron spin resonance
r 001 110
ing energy, but with different slope resulting significant atE =15isisotropic. Thetemperaturedifferenceplots
r
4
12 σ xSxF σ ySyF σ zSzF (a) Tsphineregfaopres,itnheMdifferaenndceMs in suapteQrcon=du(c0t.i5v,i0ty.5-,in0d)uacnedd
001 110
E =4 meV (0.5,0.5,1) are causing peaks in (M −M ).
001 110
45 K
8 Finally, to confirmthe low-energyspin anisotropydis-
cussed in Figs. 1-3, we show in Figs. 4(a)-4(c) constant-
energy scans with three different neutron polarizations
min 4 at E = 4 meV along the [H,H,0] and [H,H,1] direc-
~ 1 0.25 [H,H0., 500] (r.l.u) 0.75 tions. In the normal state, σxSxF shows clear peaks at
onitors 8 E =4σ mxSxFeV σ ySyF σ zSzF (b) QIn b=ot(h0.c5a,s0e.5s,,0w)eaanldso(fi0n.5d,0σ.5xSxF,1≥) [σFzSigzFs.>4σ(ySayF),atnhdus4c(co)n]-.
0 m 6 2 K firmingtheanisotropicnatureofthemagneticscattering
5 with M > M . In the superconducting state, while
2 001 110
nts/ σxSxF and σzSzF are peaked at (0.5,0.5,1), σySyF is feature-
ou 4 less. These results againconfirmthe presence of a larger
C
superconductivity-inducedspingapinM thanthatin
(c) 110
12 M [Fig. 2(b)].
001
E =4 meV From Figs. 1-4, we see anisotropic spin suscepti-
45 K
9 bility in both the normal and superconducting state
of Ba K Fe As , different from optimally electron-
0.67 0.33 2 2
6 doped BaFe Co As where the anisotropy is be-
1.88 0.12 2
lieved to emerge only with the opening of the supercon-
0.25 0.50 0.75 ducting gap24. Furthermore, our data reveal that large
[H,H,1] (r.l.u)
differencesinthesuperconductivity-inducedspingapsat
Q = (0.5,0.5,0) and (0.5,0.5,1)16 arise from the differ-
FIG. 4: (Color online) Constant-energy scans along the
ences in spin gaps of c-axis polarized spin excitations.
[H,H,0] and [H,H,1] directions at an energy transfer of
E = 4 meV for different neutron polarization directions. (a) Theseresultsaresimilartothepreviousworkonelectron-
Neutron SF scattering cross sections σxSxF, σySyF, and σzSzF at doped BaFe1.9Ni0.1As221 and BaFe1.88Co0.12As224, sug-
45 K along the [H,H,0] direction. Similar scans along the gesting that the influence of a strong spin anisotropy in
[H,H,1] direction at (b) 2 K and (c) 45 K. All data are ob- undoped parent compound BaFe As 22 extends to both
2 2
tainedwithk =2.66˚A−1. ThesolidlinesarefitbyGaussian. optimally electron and hole-doped iron pnictide super-
f
conductors. For comparison, we note that spin excita-
tionsinsuperconductingironchalcogenidesaredifferent,
between2and45Kdisplayabroadandnarrowpeakfor having slightly anisotropic resonance with isotropic spin
M andM ,respectively[Fig. 2(c)]. Fig. 2(d) shows excitations below the resonance26,27.
001 110
the sum of SF magnetic scattering below and above T . In Ref.24, it was suggested that the observed spin
c
Consistent with unpolarized work16, we see net inten- anisotropy in BaFe1.88Co0.12As2 can be understood as a
sity gain of the resonance in the superconducting state c-axispolarizedresonancewhoseintensitystronglyvaries
for energies above E ≈ 7 meV, different from that of with the c-axis wave vector. This is not the case in
BaFe1.88Co0.12As2 where the magnetic intensity starts Ba0.67K0.33Fe2As2sincewefindmuchweakerc-axismod-
to gain above E = 4 meV in the superconducting state ulation of the magnetic intensity16. Therefore, the spin
[Fig. 4(b) in24]. anisotropyseeninoptimally electronandhole-dopedsu-
To further illustrate the effect of spin anisotropy, we perconductors is a consequence of these materials being
plot in Figs. 3(a)-3(d) the differences of (M001−M110) close to the AF ordered parent compound BaFe2As2,
above and below T at wave vectors Q = (0.5,0.5,0) where spin-orbit coupling is expected to be strong28–30,
c
and (0.5,0.5,1). In the normal state, we see clear mag- andisnotfundamentaltosuperconductivityofthesema-
netic anisotropy with M > M for energies below terials. To understand how spin anisotropy in optimally
001 110
∼7 meV [Figs. 3(a) and 3(c)]. In the superconducting hole and electron-doped iron pnictide superconductors
state, the (M −M ) differences revealsimilar inten- might be coupled to superconductivity via spin-orbit in-
001 110
sity peaks centered around ∼7 meV at Q = (0.5,0.5,0) teraction,wenotethatholeandelectron-dopedironpnic-
and (0.5,0.5,1), but with a much broader width for tides are multiband superconductors with different su-
Q=(0.5,0.5,1)[Figs. 3(b)and3(d)]. Sincetherearees- perconducting gaps for different orbitals. If c-axis and
sentiallynointensitygaininM acrossT near∼7meV in-plane spin excitations arise from quasiparticle excita-
001 c
[Figs. 1(c)and2(c)],theapparentpeaksin(M −M ) tionsofdifferentorbitalsbetweenholeandelectronFermi
001 110
arisefromdifferentresponsesofM andM acrossT . pockets31, the large differences in superconducting gaps
001 110 c
WhiletheintensityofM acrossT issuppressedbelow for Fermi surfaces of different orbital characters might
001 c
∼7meVandenhancedaboveit,similarcrossoverenergy induce the observed large spin anisotropy.
occursaround10meVinM ,thusresultingpeaksnear We are grateful to W. C. Lv for helpful discussions
110
7 meV in (M −M ) at 2 K [Figs. 3(b) and 3(d)]. and H.F. Li, K. Schmalzl, and W. Schmidt for their as-
001 110
5
sistance in the neutron scattering experiment. The work theUSDOEBESthroughtheEPSCoRgrant,DE-FG02-
atUTKissupportedbytheUSDOEBESNo. DE-FG02- 08ER46528. Work at IOP is supported by the MOST of
05ER46202. C.L.Z and T.E are partially supported by China 973 programs (2012CB821400).
∗ Electronic address: [email protected] 17 M. D. Lumsden, A. D. Christianson, D. Parshall, M. B.
1 R.M.Moon,T.Riste,andW.C.Koehler,Phys.Rev.181, Stone, S. E. Nagler, G. J. MacDougall, H. A. Mook, K.
920 (1969). Lokshin, T. Egami, D.L. Abernathy,E. A.Goremychkin,
2 J. Rossat-Mignod, L. P. Regnault, C. Vettier, P. Bourges, R.Osborn,M.A.McGuire,A.S.Sefat,R.Jin,B.C.Sales
P. Burlet,J. Bossy, J. Y.Henryand G. Lapertot, Physica and D. Mandrus, Phys. Rev.Lett.102, 107005 (2009).
C (Amsterdam) 185, 86 (1991). 18 S. Chi, A. Schneidewind, J. Zhao, L. W. Harriger, L. Li,
3 H.A.Mook,G.AeppliandT.E.MasonandT.Armstrong, Y. Luo, G. Cao, Z. Xu, M. Loewenhaupt, J. Hu and P.
Phys. Rev.Lett. 70, 3490 (1993). Dai, Phys. Rev.Lett. 102, 107006 (2009).
4 H. F. Fong, B. Keimer, D. Reznik, D. L. Milius and I. A. 19 D. S. Inosov, J. T. Park, P. Bourges, D. L. Sun, Y. Sidis,
Aksay,Phys. Rev.B 54, 6708 (1996). A.Schneidewind,K.Hradil,D.Haug,C.T.Lin,B.Keimer
5 Pengcheng Dai, H. A. Mook, R. D. Hunt and F. Dog˘an, and V. Hinkov,Nat.Phys. 6, 178 (2010).
Phys. Rev.B 63, 054525 (2001). 20 H.Q.Luo,Z.Yamani,Y.C.Chen,X.Y.Lu,M.Wang,S.
6 N. S. Headings, S. M. Hayden, J. Kulda, N. Hari Babu, L.Li, T.A.Maier, S.Danilkin,D.T.Adroja, and P.Dai,
and D.A. Cardwell. Phys. Rev.B 84, 104513 (2011). Phys. Rev.B 86, 024508 (2012).
7 S. D. Wilson, P. Dai, S. Li, S. Chi, H. J. Kang and J. W. 21 O. J. Lipscombe, L. W. Harriger, P. G. Freeman, M. En-
Lynn,Nature(London) 442, 59 (2006). derle, C. L. Zhang, M. Y. Wang, T. Egami, J. P. Hu, T.
8 J.Zhao,F.C.Niestemski,ShankarKunwar,ShiliangLi,P. Xiang, M. R. Norman, and Pengcheng Dai, Phys. Rev. B
Steffens,A.Hiess,H.J.Kang,S.D.Wilson,ZiqiangWang, 82, 064515 (2010).
P. C. Dai, and V. Madhavan,Nat. Phys. 7, 719 (2011). 22 N. Qureshi, P. Steffens, S. Wurmehl, S. Aswartham, B.
9 M. Eschrig, Adv.Phys. 55, 47 (2006). Bu¨chner,andM.Braden,Phys.Rev.B86,060410(2012).
10 Y.Kamihara,T.Watanabe,M.Hirano,andH.Hosono,J. 23 M. S. Liu, C. Lester, J. Kulda, X. Y. Lu, H. Q. Luo, M.
Am. Chem. Soc. 130, 3296 (2008). Wang, S. M. Hayden, and Pengcheng Dai Phys. Rev. B
11 M. Rotter, M. Tegel, and D. Johrendt, Phys. Rev. Lett. 85, 214516 (2012).
101, 107006 (2008). 24 P. Steffens, C. H. Lee, N. Qureshi, K. Kihou, A. Ayo, H.
12 L.J.Li,Y.K.Luo,Q.B.Wang,H.Chen,Z.Ren,Q.Tao, Eisaki, and M. Braden, arXiv:1210.6386.
Y.K.Li,X.Lin,M.He,Z.W.Zhu,G.H.Cao, andZ.A. 25 W. Malaeb et al.,Phys. Rev.B 86, 165117 (2012).
Xu,New J. Phys.11, 025008 (2009). 26 P. Babkevich,B. Roessli, S. N.Gvasaliya, L.-P. Regnault,
13 C.delaCruz,Q.Huang,J.W.Lynn,J.Li,W.RatcliffII, P. G. Freeman, E. Pomjakushina, K. Conder, and A. T.
J. L. Zarestky, H. A. Mook, G. F. Chen, J. L. Luo, N. L. Boothroyd, Phys. Rev.B 83, 180506(R) (2011).
Wang, and P. Dai, Nature(London) 453, 899 (2008). 27 K. Prokeˇs, A. Hiess, W. Bao, E. Wheeler, S. Landsgesell,
14 P.Dai,J.P.Hu,andE.Dagotto,Nat.Phys.8,709(2012). and D. N.Argyriou, Phys. Rev.B 86, 064503 (2012).
15 A. D. Christianson, E. A. Goremychkin, R. Osborn, S. 28 F. Kru¨ger, S. Kumar, J. Zaanen, and J. van den Brink,
Rosenkranz, M. D. Lumsden, C. D. Malliakas, I. S. Phys. Rev.B 79, 054504 (2009).
Todorov, H. Claus, D. Y. Chung, M. G. Kanatzidis, R. I. 29 C. C. Lee, W. G. Yin, and W. Ku, Phys. Rev. Lett. 103,
Bewley, and T. Guidi, Nature(London) 456, 930 (2008). 267001 (2009).
16 C.L.Zhang,M.Wang,H.Q.Luo,M.Y.Wang,M.S.Liu, 30 W.C.LvandP.Phillips,Phys.Rev.B84,174512(2012).
J. Zhao, D. L. Abernathy, T. A. Maier, K. Marty, M. D. 31 J. H. Zhang, R. Sknepnek, and J. Schmalian, Phys. Rev.
Lumsden,S.Chi,S.Chang,J.A.Rodriguez-Rivera,J.W. B 82, 134527 (2010).
Lynn, T. Xiang, J. P. Hu, and Pengcheng Dai, Scientific
Report 1, 115 (2011).