Orbital Order and Spin Nematicity in the Tetragonal Phase of Electron-doped Iron-Pnictides NaFe$_{1-x}$Co$_{x}$As

1.3 MB·

by  R. Zhou

APS/123-QED
Orbital Order and Spin Nematicity in the Tetragonal Phase of
Electron-doped Iron-Pnictides NaFe Co As
1 x x
−
R. Zhou,1 L. Y. Xing,1 X. C. Wang,1 C. Q. Jin,1 and Guo-qing Zheng1,2
6
1 1Beijing National Laboratory for Condensed Matter Physics,
0
2 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

n
2Department of Physics, Okayama University, Okayama 700-8530, Japan
a
J
0 (Dated: January 21,2016)
2
Abstract

]
n
o In copper-oxide and iron-based high temperature (high-Tc) superconductors, many physical properties
c
- exhibitin-planeanisotropy,whichisbelievedtobecausedbyarotationalsymmetry-breakingnematicorder,
r
p
u whoseoriginanditsrelationship tosuperconductivity remainelusive. Inmanyiron-pnictides, atetragonal-
s
.
at to-orthorhombic structuraltransitiontemperatureTs coincideswiththemagnetictransitiontemperatureTN,
m
making the orbital and spin degrees of freedom highly entangled. NaFeAsis asystem where T = 54 K is
s
-
d
well separated from T = 42 K, which helps simplify the experimental situation. Here we report nuclear
n N
o
c magnetic resonance (NMR) measurements on NaFe1 xCoxAs (0 x 0.042) that revealed orbital and
[ − ≤ ≤

1 spinnematicity occurring atatemperature T∗ faraboveTs inthetetragonal phase. WeshowthattheNMR
v
spectra splitting and its evolution can be explained by an incommensurate orbital order that sets in below
3
9
T andbecomescommensurate belowT ,whichbringsabouttheobserved spinnematicity.
2 ∗ s
5
0
.
1
0
6
1
:
v
i
X
r
a
1
Understandingthenormalstateoutofwhichhigh-T superconductivity(SC)developsisanim-
c
portant task in condensed-matterphysics. In copper-oxide high-temperaturesuperconductors, the
normalstatedeviatesfromtheconventionalstatedescribedbyLandauFermiliquidtheory. Inpar-
ticular,belowacertaintemperatureT ,aso-calledpseudogapstateemerges,breakingtherotation
∗
symmetry of the underling lattices [1, 2]. In iron-pnictide or iron-selenide high-T superconduc-
c
tors,manyphysicalpropertiesinthenormalstatealsoshowstronganisotropy(nematicity),break-
ingthefour-fold rotation(C4)symmetry[3–5]. Forexample,intheparentFe-pnictideBaFe As ,
2 2
electronically-driven nematicity was discovered in the in-plane resistivity below a tetragonal-to-
orthorhombic structural transition temperature T [3, 6]. Soon after the transport measurements,
s
angle resolved photo-emission spectroscopy (ARPES) found that the degeneracy of the Fe-3d
xz
and 3d orbitals is lifted [4]. Later on, nematicity was also found in other properties rang-
yz
ing from magneto-elastic property in chemically-pressurized BaFe As [5], to spin dynamics in
2 2
carrier-doped BaFe As [7], and to local electronic structure around defects even above T [8, 9].
2 2 s
Theoretically, both spin [10] and orbital origin [11–14] have been proposed for the cause of the
experimentally-observed nematicity. In the BaFe As family, however, antiferromagnetism (AF)
2 2
sets in simultaneouslyat T or slightlybelow[15]. As a result, it is unclear whether thetransition
s
isdrivenbyspindegreeoffreedom[10]orbyorbitaldegreeoffreedom[11–14]. Neitherisitclear
whether the nematicity is caused by a static [5] or a fluctuating order [7]. Therefore, identifying
the origin of the nematicity has become an urgent issue, since it is believed that the interaction
leadingto suchanematicitymayalso beresponsibleforthehigh-T superconductivity[16,17].
c
NaFeAs is a uniquesystem where T = 54 K is well aboveT = 42 K. Only 2.7 percent of Co
s N
substitutingforFegivesrisetothemaximumT =21K[18],whichmakesthesystemacleanone
c
with much less doping-induced disorder than other systems. In this Communication, we report
evidencepointingtowardorbitalorderatatemperatureT (as highas90K)thatisfaraboveT in
∗ s
NaFe Co Asby75Asand23NaNMRspectroscopy. Wefurtherrevealedaspinnematicityinthis
1 x x
−
systembythespin-latticerelaxationrate(1/T )measurements,andshowthatitcanbeunderstood
1
as adirect consequenceoftheorbitalorder.
The single crystals of NaFe Co As used for the measurements were grown by the self-flux
1 x x
−
method[8]. Inordertopreventsampledegradation,ThesampleswerecoveredbyStycast1266rin
agloveboxfilledwithhigh-purityArgas[19]. Thetypicalsamplesizeis3mm 3mm 0.1mm. The
× ×
Co content xwasdeterminedbyenergy-dispersivex-rayspectroscopy. TheT wasdeterminedby
c
DC susceptibility measured by a SQUID device. The NMR spectra were obtained by integrating
2
the spin echo as a function of frequency at H = 11.998 T. The T was measured by using the
0 1
saturation-recoverymethod,and determinedby agoodfittingtothetheoreticalcurve[20].
The 75As or 23Na nucleus with spin I = 3/2 has a nuclear quadrupole moment Q that cou-
ples to the electric field gradient (EFG) V (α = x,y,z), relating to the NQR frequency tensors
αα
ν = eQ V . Therefore, both75As-and23Na-NMRaregoodprobesforastructuralphasetran-
α 4I(2I 1) αα
−
sitionasshowninNaFeAswheretheprincipalaxesarealongthecrystalaxes[21]. Inaddition,the
As site is very close to the Fe plane so that the As-p and Fe-d orbitals strongly hybridize, which
makes75AsNMRalsoasensitiveanduniqueprobefordetectinganorbitalordersinceadisparate
occupationinAs-p orbitalswillproducean asymmetricEFG.
When amagneticfield H isapplied along i-axis(i =a or b), theNMRresonance frequency f
0
isexpressed by[22]
1 1
f = γ H (1+K)+ ν m (n η 1)+a δf (1)
m m 1,i N 0 i c i m i
↔ − 2 − 2! · −
, where Ki is the Knight shift, m = 3/2, 1/2 and -1/2, and ni = ∓ 1. η ≡ |VxxV−zzVyy|=(cid:12)ννaa+−ννbb(cid:12) is the
(cid:12) (cid:12)
asymmetry parameter of the EFG, which measures a nematicity in the ab-plane. Fina(cid:12)lly, a(cid:12) δf is
(cid:12) (cid:12)m i
thesecond-orderquadrupolarshiftwhen H is appliedparallel toi-axis,and isgivenas,
0
(v v )2 3v2 η 2
δf = b − c = c 1
a 12(1+Ka)γNH0 16(1+Ka)γNH0(cid:18) − 3(cid:19) (2)
(v v )2 3v2 η 2
δf = a − c = c 1+
b 12(1+K )γ H 16(1+K )γ H 3
b N 0 b N 0(cid:18) (cid:19)
Thiscorrection onlyneedstobeconsideredforthecentraltransition(m=1/2)line,soa =1 and
1/2
a =a =0. ForamaterialwithC4rotationsymmetry,η = 0. However,η > 0ifC4symmetry
3/2 1/2
−
is broken. Therefore, for a twined single crystal with C2 symmetry, the field configurations of
H a-axisand H b-axiswillgiveadifferent f ,leadingtoasplittingofbothsatelliteand
0 0 m m 1,i
k k ↔ −
central peaks.
Figure 1 shows the evolution of the NMR spectra in NaFeAs. At high temperature (T), only
onecentraltransitionandapairofsatellitesareobserved. BelowT =90K,abroadeningofboth
∗
centralandsatellitelineswasseeninthe75As-NMRspectra,butnotinthe23Na-NMRlines. With
further decreasing T, all the 75As-NMR lines become narrower below T , and a clear splitting is
s
observed. Sameistruefor23Na-NMRlinesbelowT . NotethatT ismuchhigherthantheT 54
s ∗ s
∼
K confirmed bybothpreviousneutronscatteringmeasurement[23]and ourresistivitydata[19].
One apparent possibility for the 75As-NMR lines broadening (splitting) is that there are some
small local orthorhombicdomains existingaboveT formed by tiny uniaxial pressure from disor-
s
3
(a) (b)
(c) (d)
FIG. 1: (a-b) 75As- and 23Na-NMR spectra. The three peaks at T = 100 K respectively correspond to the
lowfrequencysatellite(LFS),centraltransitionandhighfrequencysatellite(HFS).Themiddlepanelin(a)
showsthesimulationof2D-incommensurate orbitalordermodelforT =60Kspectra. Green(red)shadow
area represents the transitions with H a-axis (b-axis). The green and red arrows show the positions at
0
k
which1/T and1/T wasmeasured,respectively. AtT =100K,1/T measuredatlow-andhigh-frequency
1a 1b 1
tailsgivesrisetothesamevalue. (c-d),T-dependence ofthefullwidthathalfmaximum(FWHM)ofeach
peak.
ders [9, 24] or uniaxial strains due to epoxy encapsulation. However, this can be ruled out since
23Na-NMR spectra do not change below T and there is no angular dependence of T [19]. The
∗ ∗
other is that orbitals order in the real tetragonal phase. In this case, the origin of EFG asymmetry
istheFeorbitalorderparameter∆. Forexample,fortheorbitalsplittingfoundinARPES[4], one
can write ∆ (n3d n3d), where n is the electron density. It will produce a population disparity
∝ xz − yz
between As-4p and 4p , (n4p n4p), throughFe-As orbitalhybridization. Such disparitywas ex-
x y x y
−
plained by electronic mechanism [10–14], as well as by local-density approximations calculation
[25]. Atthemoment,wecannotruleoutotherformof∆thatcan produceafinite(n4p n4p). The
x y
−
4
NaFe1 -xCoxAs
x = 0
100K
60K
42K

x = 0.0089
)
t. 90K
ni 60K
u 40K
.
b
r
A

(

y
it x = 0.018
s
n 80K
e 60K
t
n 20K
I

R
M
N
- x = 0.027
s
A 50K
5 35K
7
20K

x = 0.042
50K
20K
82 83 84 92 93
Frequency (MHz)
FIG. 2: T-evolution of the 75As-NMR satellite peaks. For x = 0, 0.0089, 0.018 and 0.027, the peaks are
broadenedbelowT ,andsplitbelowT . Forx=0.042,however,noclearchangeinthespectrumisdetected
∗ s
downtoT =20K.
As-NQRfrequency tensorν isrelated ton4p as [26]
x,y,z x,y,z
ν n4p n4yp+n4zp
x x − 2
 ννyz  = ν0nn4y4zpp −− nn44xxpp++22nn4z4ypp  (3)
whereν istheNQRfrequencywhenthereisoneelectron(hole)ineach4p-orbital. Itfollowsthat
0
ν ν = 3ν0 n4p n4p , thereforeη n4p n4p ∆.
x − y 2 x − y As ∝ x − y ∝
(cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12)
(cid:12) Belo(cid:12)w we s(cid:12)how that(cid:12)an incommensura(cid:12)te orbital(cid:12)order in the tetragonal phase, which becomes
(cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12)
commensuratebelowT ,canconsistentlyaccountfortheobservedresults. Theobservedbehavior
s
5
(a) (c)
(d)
(b)
FIG.3: TheevolutionoftheEFGasymmetryparameterη. (a)T-dependenceofη forvarious x. Thesolid
As
and dotted arrows indicate T and T , respectively. (b) T-dependence of η for x=0. The green curve is
∗ s Na
the contribution due to the structure change obtained by all-electron full-potential linear augmented plane
wave method [27, 28], by using the lattice parameter from neutron scattering [23] and X-ray diffraction
[29]. (c)Experimental,calculated andthesubtracteddataofη for x=0. (d)η normalizedbyitsvalueat
As As
T against √1 T/T forvarious x.
s − ∗
is very similar to the crossover of commensurate to incommensurate antiferromagnetic order in
NaFeAs[21]. Generally speaking, in a commensurate density-wave state, the NMR line reflects
thesmallnumberofphysicallynon-equivalentnuclearsitesintheunitcellsothatthelinewidthis
small. In an incommensuratestate,however,sincethetranslationalperiodicityislost,thenumber
of non-equivalentnuclear sites is larger which gives rise to a larger linewidth [30]. In the present
case,Amodulationduetoorbitalorderwillcauseanadditionaltermintheresonancefrequencyat
As site(x,y). Letthisterm beacosinefunctionas cos 2πq x+θ +cos 2πq y+θ , where
a x · x b y · y
h (cid:16) (cid:17) (cid:16) (cid:17)i
q andq arethetwo-dimensional(2D)wavevectorsandθ isthephase. Then,forcommensurate
x y x,y
order, the additional term becomes cosθ +cosθ , which is site-independent. For incommensu-
x y
h i
rate order, however, this term is site-dependent, which leads to a broadening of the spectrum. By
convoluting with a Gaussian function [19], we can reproduce the spectra as shown in Fig. 1 (a).
Inpassing,wenotethatT =90Kfor x=0isconsistentwiththetemperaturebelowwhichscanning
∗
tunnelingmicroscopefound localelectronicnematicitybyquasiparticleinterference [8].
Below T , the 75As-NMR spectra become narrower and each peak is well resolved. Moreover,
s
6
no NMR intensityloss is observed below T ord T [19]. All theseimplythat all theAs sites have
s ∗
thesameenvironment. That is,theorbitalorderbecomes commensurate. Thedopingdependence
of the spectra is shown in Fig. 2. As for x=0, a peak splitting was also found above T for x =
s
0.0089, 0.018and 0.027,which get well resolvedat T . For x =0.042, however,no change of the
s
spectrawas founddowntoT = 20K.
More quantitative data are shown in Fig. 3 where the evolution of η is demonstrated. The η
As
develops continuously below T , showing a saturation tendency approaching T . In contrast, η
∗ s Na
showsuponlybelowT andtheabsolutevalueismuchsmallerthanη ,indicatingthatitispurely
s As
due to the structural transition. There are two contributions to the observed η, η= η + η ,
lattice orbital
where η is due to surrounding lattice and η is due to orbital order on Fe site. By the first
lattice orbital
principle calculation, we find that the observed η is well explained by the change in η ; the
Na lattice
discrepancy is about 10%. Another remarkable feature of η is that it increases steeply again
As
below T , which cannot be accounted by the calculated η . The red circles in Fig. 3 (d) is the
s lattice
net increase after subtracting the effect due to the lattice change. A clear kink can be seen at T ,
s
which is true even after multiplying the calculated result by a factor of 1.1 1.15. The increase
∼
is consistent with the incommensurate-to-commensuratetransition. In the incommensurate state,
n4p n4p is inhomogeneous and η probes the averaged n4p n4p . In the commensurate state,
x y As x y
− −
(cid:12) (cid:12) (cid:12) (cid:12)
(cid:12)η measu(cid:12)resthehomogeneous n4p n4p , whichcan bela(cid:12)rger [19].(cid:12)
(cid:12) As (cid:12) x y (cid:12) (cid:12)
−
(cid:12) (cid:12)
Finally, it is worthwhile poi(cid:12)nting out(cid:12)that η shows a linear relationship with √1 T/T
(cid:12) (cid:12) As ∗
−
for all samples in the vicinity of T , as shown in Fig. 3 (d), suggesting that the nematic order
∗
undergoes a Landau-type-like second-order phase transition. The T and T results obtained by
∗ s
NMRaresummarizedin thephasediagramshowninFig. 4.
Next we turn to the spin dynamics of this system. which was also clearly seen below T in
∗
1/T . Figure 5 (a) shows the 1/T results for x = 0, 0.0089 and 0.018. Below T , 1/T measured
1 1 ∗ 1
at thepositionscorresponding to H [100] (a-axis) and H [010] (b-axis)shows oppositeT-
0 o 0 o
k k
dependence. Herewe assign thedirectionwith larger NQRfrequency tensorto the a-axis. Figure
5 (b) shows the ratio of the two T . As in Ba(Fe [Ni,Co] ) As [15, 31], 1/T arises from the
1 1 x x 2 2 1
−
antiferromagnetic spin fluctuations and the contribution due to the intra-band (DOS at the Fermi
level), but the former is dominant [19]. We show below that the anisotropy of 1/T is a natural
1
consequenceoftheorbitalorder.
ThemagneticorderontheFeatomsbelowT isofstripetypewithorderingvectorsQ =(π,0)
N X
[23]. Above T , however, magnetic fluctuations from Q = (0,π) also exist and have the equal
N Y
7
100
) NaFe1-xCoxAs
K
e ( Orbital Tc
r
u and Spin TN
t
a Nematic
r 50 , Ts
e
p *
m T
e Tetra
T
Ortho
AF
SC
0
0 0.02 0.04 0.06 0.08
Co doping x
FIG. 4: The obtained phase diagram. For x <0.027, T agrees well with that from resistivity [19]. For x
s
= 0.027, the T coincides with T so that direct comparison with resistivity is unavailable. To distinguish
s c
with other compositions, the data point is represented by an open triangle. Ortho and Tetra represent the
orthorhombic andtetragonal phase,respectively.
amplitudeasthosefrom Q . SinceAssitsaboveorbelowthecenterofthesquareformed byfour
X
irons, 1/T of 75As along the orthorhombic a-direction or b-direction sees antiferromagnetic spin
1
fluctuationsfromboth Q and Q as follows[32]
X Y
1 QX
A2χ
T ! ∝ ′′a
1 a (4)
1 QX
A2 χ +χ
T ! ∝ ′′a ′′c
1 b (cid:0) (cid:1)
and
1 QY
A2 χ +χ
T ! ∝ ′′b ′′c
1 a (cid:0) (cid:1) (5)
1 QY
A2χ
T ! ∝ ′′b
1 b
HereAisthehyperfinecouplingconstantandχ (j=a,b,c)istheimaginarypartofthestaggered
′′j
susceptibility. Themeasured(1/T ) (i = a,b)can then bewrittenas
1 i
1 1 QX 1 QY
= N +N (6)
X Y
T ! T ! T !
1 i 1 i 1 i
where N (N ) is the relative weight of contribution from Q (Q ), with N + N = 1. It then
X Y X Y X Y
follows
(1/T1)b = χ′′c +χ′′a + NNXYχ′′b (7)
(1/T1)a χ′′a + NNXY(χ′b′ +χ′c′)
8
FIG.5: (a)T-dependence of1/T forvarious x. (b)T dependence of1/T ratio. Solid, dashed anddotted
1 1
arrows indicate T , T and T , respectively. (c) Schematics of the Fermi surface (FS)obtained by ARPES
∗ s c
[35]andthespinfluctuationswavevectors. TheouterFScenteredatΓisomittedhereforclarity. Thecolor
represents theFe-3d orbitalcharacter.
xz,yz,xy
whichmeasuresachangeintheratio NY. The1/T ratiowillalwaysbeaunityaslongasN =N .
NX 1 X Y
On the other hand, in the limit of N 1 and N 0, the ratio will be 2, since polarized inelastic
X Y
∼ ∼
neutron scattering found that the anisotropy in the low-energy spin excitations above T is small,
s
ifany[33].
Asseen inFig. 5(b), theobservedratio (1/T1)b increasesbelowT ,indicatingthat N increases
(1/T1)a ∗ X
and N decreases. These results are a natural consequence of orbital order with the occupation
Y
of Fe-3d becoming larger than Fe-3d which changes the FS nesting condition so that spin
xz yz
fluctuations with Q becomes dominant [34]. This is because Q connects the Fermi pocket
X X
centered at Γ = (0,0) with that centered at M = (π,0) consisting of d orbital, and Q connects
X xz Y
the Γ Fermi pocket with that centered at M = (0, π) consisting of d orbital (see Fig. 5 (c)).
Y yz
Finally,wenotethatananomalyisfoundatT in1/T ofbothdirections,whichisconsistentwith
s 1
a change in the character of orbital order, but the detailed analysis of the anomaly and theoretical
explanationare atopicoffutureinvestigation.
Previously, electronic nematicity was found in BaFe As [4, 5, 15] and FeSe [36–40] sys-
2 2
tems, but it occurs right at T . Above T , only fluctuations were observed [41, 42]. In Ni-doped
s s
9
BaFe As , although anisotropy was found in the spin susceptibilityabove T , the system was un-
2 2 s
der a uni-axial pressure and it was attributed to a fluctuating order [7]. By contrast, no external
drivingforcewasappliedinthepresentcase,thustheobservationofastaticorderatthetimescale
of10 8 secis unprecedented.
−
In summary, we have presented the systematic NMR measurements on single crystals of
NaFe Co As. The 75As-spectra were broadened at T far above T and get well split below T .
1 x x ∗ s s
−
The EFG asymmetry parameter η emerges below T and increases abruptly below T . However,
∗ s
the 23Na-NMR spectra showed no change until T . These results can be explained by an incom-
s
mensurate orbital order formed in the tetragonal phase which becomes commensurate below T .
s
AspinnematicityisalsofoundbelowT , whichcan beunderstoodas adirectconsequenceofthe
∗
orbitalorder.
Acknowledgments
WethankT.Xiangforhelpfuldiscussionandcomments,M.-H.JulienandS.Onariforacritical
reading of the manuscript, S. Maeda and T. Oguchi for advice and help in the EFG calculation,
Z. Li and J. Yang for assistance in some of the measurements. This work was partially supported
by CAS Strategic Priority Research Program, No. XDB07020200 and by a 973 project National
BasicResearch Program ofChina, No. 2012CB821402.
[1] M. J. Lawler, K. Fujita, Jhinhwan Lee, A. R. Schmidt, Y. Kohsaka, Chung Koo Kim, H. Eisaki, S.
Uchida, J. C. Davis, P. Sethna and Eun-Ah Kim, Intra-unit-cell electronic nematicity of the high-T
c
copper-oxide pseudogap states.Nature466,347-351 (2010).
[2] R. Daou, J. Chang, David LeBoeuf, O. Cyr-Choinie`re, F. Laliberte´, N. Doiron-Leyraud, B. J.
Ramshaw, R. Liang, D. A. Bonn, W. N. Hardy and L. Taillefer, Broken rotational symmetry in the
pseudogap phaseofahigh-T superconductor. Nature463,519-522 (2010).
c
[3] J.-H. Chu, J. G.Analytis, K.DeGreve, P. L McMahon, Z.Islam, Y. Yamamoto, and I. R.Fisher, In-
PlaneResistivity Anisotropy inanUnderdoped IronArsenide Superconductor. Science 329, 824-826
(2010).
10