ARTICLESPUBLISHED ONLINE: 10 NOVEMBER 2014 | DOI: 10.1038/NMAT4138

Orbital-driven nematicity in FeSeS-H. Baek1*, D. V. Efremov1, J. M. Ok2, J. S. Kim2, Jeroen van den Brink1,3 and B. Büchner1,3

A fundamental and unconventional characteristic of superconductivity in iron-based materials is that it occurs in the vicinityof two other instabilities. In addition to a tendency towards magnetic order, these Fe-based systems have a propensityfor nematic ordering: a lowering of the rotational symmetry while time-reversal invariance is preserved. Setting the stagefor superconductivity, it is heavily debated whether the nematic symmetry breaking is driven by lattice, orbital or spindegrees of freedom. Here, we report a very clear splitting of NMR resonance lines in FeSe at Tnem = 91K, far above thesuperconducting Tc of 9.3K. The splitting occurs for magnetic fields perpendicular to the Fe planes and has the temperaturedependence of a Landau-type order parameter. Spin–lattice relaxation rates are not a�ected at Tnem, which unequivocallyestablishes orbital degrees of freedom as driving the nematic order. We demonstrate that superconductivity competes withthe emerging nematicity.

Even if the existence of nematic order in the different classesof iron-based superconductors is by now a well-establishedexperimental fact, its origin remains controversial1–7. It

is related either to a lattice instability that causes a regularstructural phase transition, to the formation of time-reversal-invariant magnetic order, for instance an Ising spin-nematic8–10state, or to the ordering of orbital degrees of freedom11–15. As thenematic instability is a characteristic feature of the normal statefrom which at lower temperatures the superconductivity emerges,the different possible microscopic origins of nematicity are directlylinked to the properties of the superconducting state16,17. From asymmetry point of view it is clear that when one of these threeorderings (lattice/spin/orbital) develops, it must affect the othertwo—the crucial challenge thus lies in establishing which orderingis primary, and to determine to which extent this primary orderaffects the two other degrees of freedom. It has been establishedthat the lattice distortion, which at Tnem reduces the crystallographicsymmetry from tetragonal to orthorhombic, is an unlikely primaryorder parameter, not only because the distortion is weak, but alsobecause measurements of the resistance anisotropy have shownthat the structural distortion is a conjugate field to a primaryorder parameter, therefore not the order parameter itself 2. Thisbasically restricts the driving force for the nematicity to be ofelectronic origin: either due the electron’s spin or its orbital degreeof freedom.

FeSe is an attractive iron-based superconductor to study thisissue, as it is a binary system with a rather simple structure(see Fig. 1), while sharing many common features with other Fe-based superconductors18. Our bulk FeSe single crystals undergoa clear tetragonal to orthorhombic transition at Tnem = 91K andat Tc = 9.3 K superconductivity sets in, which is consistent withprevious reports5. In single-layer FeSe films a much higher Tchas been reported, 65K (refs 19–23) and above24, which is evenhigher than in any other iron-based superconductor. The highquality of our FeSe single crystals is confirmed by their very sharpsuperconducting transition and large residual resistivity ratio (seeSupplementary Methods).

To establish whether spins or orbitals are responsible for itsnematic instability we have measured 77Se NMR spectra as afunction of temperature. The Se atoms in FeSe sit centrally above

and below the Fe4 plaquettes that form an almost square lattice(see Fig. 1b). For the NMR measurements we used an externalfield H=9 T applied in a direction either parallel or perpendicularto the crystallographic c axis, which is normal to the Fe planes(Fig. 1a). In the high-temperature tetragonal phase the spectra areextremely narrow with the full-width at half-maximum of ∼1 kHzfor H ‖a and ∼1.5 kHz for H ‖ c, which is characteristic of a highlyhomogeneous sample (see Fig. 2). Below Tnem we observe that the77Se line splits into two lines with equal spectral weight for in-planefields,H ‖a. Note that in the orthorhombic phase our crystal is fullytwinned. The notation H ‖ a thus means that actually one type ofdomain in the crystal experiences a magnetic field H ‖ a and theother type of domain hasH ‖b. These two domains occur with equalprobability.We shall refer to the split lines as l1 and l2 with frequencyν1 and ν2, respectively (ν1<ν2). In contrast, the 77Se spectrum forH ‖ c consists of a single line l3 at frequency ν3 that does not splitand remains narrow down to low temperatures. From this, one canalready conclude that the l1–l2 line splittingmust be the consequenceof an in-plane symmetry change.

We note that the 77Se nuclear spin is 1/2 so that the observedsplitting cannot be due to a quadrupolar-type coupling to locallattice distortions. This is in contrast to LaFeAsO, in which thequadrupolar splitting of the 75As line in twinned single crystalsfor H ⊥ c reflects the presence of orthorhombic domains7. Ontwo further grounds it can be excluded that the orthorhombiclattice distortion causes the l1–l2 splitting. First, the splitting changessignificantly when FeSe enters the superconducting state (seeFig. 3b), where the lattice structure does not change notably25. Thatthe splitting is of electronic origin is attested also by a more detailedconsideration of the temperature dependence of the resonancefrequency νi (i= 1 . . . 3) for each of the three NMR lines. TheT dependence is shown in Fig. 2 in terms of the Knight shiftKi = (νi − ν0)/ν0 of νi away from an isolated nucleus (ν0 = γnHwith the nuclear gyromagnetic ratio γn). In a paramagnetic stateK=Ahfχspin+Kchem so that K is directly related to the local spinsusceptibility χspin. Here Ahf is the hyperfine coupling constantand Kchem is the temperature-independent chemical shift. It isclear that the splitting between l3 and the degenerate l1, l2 pairin the tetragonal structure (that is, for T > Tnem) is caused bythe in-plane (‖a)–out-of-plane (‖c) anisotropy of the hyperfine

1IFW Dresden, Helmholtzstr. 20, 01069 Dresden, Germany, 2Department of Physics, Pohang University of Science and Technology, Pohang 790-784,Korea, 3Department of Physics, Technische Universität Dresden, 01062 Dresden, Germany. *e-mail: sbaek.fu@gmail.com

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ARTICLES NATUREMATERIALS DOI: 10.1038/NMAT4138

Se

Fe

a ab

bc

a b

Figure 1 | Schematic crystallographic structure of FeSe. a,b, Fe–Se layersstacked along the c direction (a) and the in-plane Fe atoms forming analmost square lattice with Se atoms centred alternatively above and belowFe4 plaquettes (b).

coupling and the spin susceptibility. This anisotropy is caused bythe crystallographic structure being very different in the directions‖a and ‖c, owing to the manifestly layered lattice structure of FeSe.From the data in Fig. 3a it is clear that the l3–l1,2 splitting ν3− ν1,2above Tnem is similar in size to the l2–l1 splitting 1ν=ν2−ν1 inthe low-temperature orthorhombic state. It is evident that sucha very large splitting 1ν cannot be caused by the small latticedisplacements in the orthorhombic state, involving atoms thatmove distances less than 0.5% of the lattice constant5,25. This isexemplified by the average Kav

‖a = (K1 +K2)/2 of the two H ‖aand H ‖ b lines (for the two different orthorhombic domains)having the same temperature dependence as K‖c=K3 in the entiretemperature range. This is very different from the behaviour ofthe Knight shift splitting 1K‖a = (K2 −K1)/2∝1ν between l2and l1 below Tnem. From the temperature dependence of 1K‖a(shown in Fig. 3b), one sees that it exhibits the typical

√Tnem−T

behaviour of a Landau-type order parameter close to a second-orderphase transition.

Having established an order parameter type of behaviourof splitting 1ν and having excluded it is of lattice origin,we consider next the possibility that spin degrees of freedomcause the observed in-plane anisotropy of the Knight shift inthe orthorhombic state. We have therefore measured the spin–lattice relaxation rate T−11 as a function of temperature (seeFig. 3). The quantity (T1T )−1 is proportional to the q-sumof the imaginary part of the dynamical susceptibility, that is,(T1T )−1∝

∑qA2

hf(q)χ ′′(q,ω)/ω, thereby probing antiferromagnetic(AFM) spin fluctuations. We observe that when crossing thenematic phase transition, (T1T )−1 barely changes, indicating thatAFM fluctuations are not enhanced around Tnem and the systemis evidently very far away from any magnetic instability. Onlywhen further lowering the temperature we observe that (T1T )−1gradually increases and that at Tc, when superconductivity sets in,the AFM fluctuations are significantly enhanced. This observationis in agreement with previous (T1T )−1 measurements on FeSepowders26 and evidences that spin fluctuations are not driving thenematic transition. Moreover, the extremely narrow 77Se NMR linesbeing well preserved down to 4.2 K indicates the complete absenceof static magnetism27.

The remaining degree of freedom that can drive the nematicordering is the orbital one, in particular in the form of ferro-orbitalorder (FOO). It is clear that such an orbital ordering breaks thein-plane local symmetry at the Se sites (see Fig. 4), and generatestwo non-equivalent directions ⊥ c: the a and b direction. We firstconsider FOO from a theoretical point of view, defining the FOOorder parameter as ψ= (nx−ny)/(nx+ny), where nx ,y correspondsto the occupation of x = dxz and y = dyz orbitals indicated inFig. 4 (z corresponds to the crystallographic c axis). Given thesymmetries of the system, the free energy in the vicinity of the orbital

160a bFeSe

77Se NMR9 T

H || c H || a

140

120

100

80

60

40

20

0

160

140

120

100

80

60

40

20

073.24 73.26

T (K

)

l3 l1 l2

Tnem

Tc

73.28 73.30 73.26Frequency (MHz)Frequency (MHz)

73.28 73.30

H || [110]

Figure 2 | 77Se NMR spectra for the FeSe single crystal. a, Measured at afield of 9 T applied parallel to either the crystallographic a axis or c axis, as afunction of temperature. The 77Se line splits into two lines (l1 and l2) atTnem=91 K for H‖a, whereas the line l3 for H‖c remains narrow at alltemperatures. To avoid an overlap, the spectra for H‖c are o�set by−10 kHz. b, For an in-plane magnetic field where H‖[110]. The absence ofthe line splitting for this field orientation is direct proof for a breaking of thelocal four-fold rotational symmetry. The broadening of the line is attributedto the strain induced by glueing this crystal inside the NMR coil.

ordering transition in the presence of a magnetic field H can beexpanded as:

F=a2ψ 2+

b4ψ 4+

12χ⊥

M 2−γψ(M 2

x −M2y )+

g2M 2

z +MH (1)

where M is the magnetic moment. An important quantity is γ , thecoupling between the orbital order parameter and magnetization.For localized 3d states it is perturbatively related to the strengthof spin–orbit interaction λ and energy difference ∆d between thex and y , z states as γ ∝ λ2/∆d . From equation (1) one obtainssusceptibilities of the formχxx ,yy=χ⊥/(1±γψχ⊥)≈χ⊥(1∓γψχ⊥)and χzz =χ⊥/(1+χ⊥g ). Owing to the linear coupling the orbitalorder parameter is directly proportional to the anisotropy in themagnetic susceptibility: χxx−χyy∝ψ∝

√TOO−T in the vicinity of

the ferro-orbital ordering transition.Now the question arises how such a ferro-orbital ordering affects

the Knight shifts Kα = Ahfααχαα , where α = x , y , z . Owing to the

orthorhombic symmetry only the three diagonal terms are present2.This is in agreement with the experiments showing Kx ,y 6=Kz . Itis useful to consider the average, isotropic part of the in-planeKnight shift

Kav‖a=A

hfxxχxx+Ahf

yyχyy=1/2(Ahfxx+A

hfyy)(χxx+χyy)

+1/2(Ahfxx−A

hfyy)(χxx−χyy)

separately from the difference, the anisotropic in-plane Knight shift

1K‖a=Ahfxxχxx−Ahf

yyχyy=1/2(Ahfxx+A

hfyy)(χxx−χyy)

+1/2(Ahfxx−A

hfyy)(χxx+χyy)

An analysis of the hyperfine constants establishes thatAhfxx−Ahf

yy∝ψ ,so that 1K‖a∝ψ ∝

√TOO−T . Thus, the anisotropic Knight shift

is directly proportional to the orbital ordering parameter but thesame analysis shows that K av

‖a and Kz may depend on ψ only inhigher order.

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NATUREMATERIALS DOI: 10.1038/NMAT4138 ARTICLES

0.28 0.000

0.0

0.2

0.4

0.6

0.8

Inte

nsity

(a.u

.)

73.26 73.27 73.28

0

0

00 2 4

51015

20

1

2

3

4

20 40 60 80 100 120 140

0.005

0.010

10 K

4.5 K

0.015

0.020

0.025

0 20 40 60T (K) T (K)

0 20 40 60

00.0

0.2

0.4

0.6

0.8

2010 30

80 100 120 140T (K)

T (K)(T1T

)−1 (s

−1 K

−1)

(T1T

)−1 (s

−1 K

−1)

TnemTnem

Tnem

Tc

Tc

l3

l2

l1

Tc

Tc

80 100 120 140

0.29

0.30

0.31

0.32 (%)

(MHz)ν

Δ ||a

(%)

Δ ||a

(10−5

)

0.33

0.34

0.35

0.36a b

c

H || a (l1)H || a (l2)

H || c (l3)H || a (average)

√Tnem − T

Figure 3 | Emergence of orbital-driven nematic state in FeSe. a, Temperature dependence of the 77Se NMR Knight shift K for fields ‖a and ‖c. Whereas atTnem, K‖a splits into lines l1 and l2, both K‖c and Kav

‖a, the average position of lines l1 and l2, show a smooth T-dependence. b, Temperature dependence ofthe l1–l2 line splitting below Tnem in terms of the di�erence in Knight shift1K‖a. Insets: (upper right) below Tnem the splitting1K‖a is proportional to√

Tnem−T, as is expected for an order parameter at a second-order phase transition; (lower left) the comparison of two 77Se spectra at 10 K (>Tc) and4.5 K (<Tc) reveals that the splitting between the l1 and l2 lines clearly decreases in the superconducting state. The intensities of two spectra werenormalized for comparison. c, Temperature dependence of the spin–lattice relaxation rate divided by T, (T1T)−1. The error bars reflect the uncertainty in thefitting procedure. At around Tnem the spin-relaxation rate barely changes, indicating the absence of a magnetic instability. Approaching Tc enhances(T1T)−1, signalling that AFM spin fluctuations develop. Below Tc, as is conventional in the superconducting state, (T1T)−1 strongly drops. The inset showsan enlargement of the low-temperature regime.

We can now compare the theoretical analysis for an orbital-driven nematic state with our experimental results. Clearly themeasured splitting 1K‖a shows the

√Tnem−T behaviour close to

the critical temperature, so that we conclude that Tnem=TOO. At thesame time the measured Kav

‖a and K‖c (Fig. 3a) indeed barely showan anomaly in their temperature dependence. In the normal state,between∼50–60K and Tc the splitting1K‖a decreases. This is dueto the two distinct contributions to 1K‖a: the temperature depen-dence of the hyperfine constant Ahf

xx −Ahfyy and of the susceptibility

χxx−χyy . The former saturates below 50–60K, as the nematic orderparameter tends to a constant25. At the same time the anisotropicpart of the transverse susceptibility changes owing to non-Fermiliquid effects caused by the enhanced spin fluctuations28, leading tothe observed decrease in 1K‖a in the normal state. The issue thatremains open from the NMR data is the precise pattern of orbitalordering that is formed. The NMR data do not fix the directionsof x and y with respect to the crystallographic axes. Any rotationof the FOO ordering pattern around the c axis is therefore possiblein principle. However, the orthorhombic lattice distortion inducedby the FOO ordering leaves all Fe–Se distances equivalent6, whichimplies that x ‖a and y ‖b, leading to the FOO pattern in Fig. 4.

The conclusion above, that below Tnem the orbital order as shownin Fig. 4 renders the electronic structure along the a and b directioninequivalent, resulting in clearly different NMR responses for H ‖a

andH ‖b, can be tested.When themagnetic field is applied in the abplane in the diagonal direction, that is,H ‖[110], the field has equalprojections on a and b (see Fig. 4). Therefore, the two domains in ourtwinned crystal should now yield the sameNMR response, implyingthat for this field orientation the splitting between l1 and l2 in theorthorhombic state below Tnem should be absent. We performedthe experiment with H ‖ [110], using a different single-crystallineplatelet glued in the required orientation. As shown in Fig. 2b nowa splitting of the line below Tnem is indeed clearly absent, which isdirect proof that below Tnem the rotational (C4) symmetry is broken.We note that our NMR experiments do not provide informationon the size of the domains, which might in principle be orderedor disordered at a microscopic scale, which implies the presenceof a certain amount of antiferro-orbital ordering. The relevance ofsuch secondary orderingsmight be probed byNMR experiments ondetwinned crystals.

Having established that orbital order drives the nematic ordering,the question arises how the orbital ordering affects not only thelattice and spin degrees of freedom, but also the superconductingstate. The relation to the secondary orthorhombic lattice distortionhas been discussed above. From the NMR data also the couplingbetween the orbital order to the spin degrees of freedom is directlyevident. The spin–lattice relaxation rate, measuring the strengthof low-energy spin fluctuations, shows that in the vicinity of Tnem

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ARTICLES NATUREMATERIALS DOI: 10.1038/NMAT4138

a

H || a

H || [110]

b

b

a

dxy dyz dxz

Figure 4 | Top view of the FOO in FeSe with the two di�erent domains thatare present in a twinned crystal. The three orthogonal orbitals dxy , dyz anddxz are indicated. The double-headed arrows indicate the nematicorder parameter.

there is little, if any, enhancement of the magnetic excitations, anenhancement that would be expected from Fermi-liquid theoryin the vicinity of a spin-density wave transition. This impliesthat the characteristic energy of the degrees of freedom drivingthe nematic transition considerably differs from the characteristicenergy of magnetic degrees of freedom: orbital and spin degrees offreedom are well separated. When going below Tnem the spin–latticerelaxation rate increases steadily, approaching Tc in a manner that isquantitatively different for the lines l1 and l2 (see Fig. 3c). This is tobe expected because the spin-relaxation rate in the FOO state picksup the anisotropies in its hyperfine couplings and susceptibilities, asthe Knight shift does.

Finally, we analyse the interplay of the orbital ordering andsuperconductivity. Previously, scanning tunnelling spectroscopymeasurements have found a two-fold breaking of the Cooper-pairsymmetry in FeSe, which implies that the superconducting orderparameter is directly affected by the nematicity29. Here we observethe complementary effect: the splitting1K‖a (which is proportionalto the orbital order parameter) changes significantly below Tc (seeSupplementary Methods). Thus, the nematic order parameter isdirectly affected by superconductivity. The splitting1K‖a becomingsmaller while the Knight shifts K‖c and Kav

‖a barely change indicatesthat in our bulk FeSe crystals superconductivity and nematicitycompete—superconductivity tends to suppress orbital ordering andvice versa. It is interesting to note that in the single layers of FeSefor which spectacularly high Tc values have been reported19–24 atetragonal–orthorhombic transition is absent, evidencing a muchweaker nematic tendency. It will have to be established whether thesuppressed nematicity is a cause for the strongly enhancedTc in FeSesingle layers.

MethodsSingle crystals of FeSe (Tc∼9.3 K) were grown using a KCl–AlCl3 flux techniqueas described in detail elsewhere30. The mixture of Fe, Se, AlCl3 and KCl wassealed in an evacuated Pyrex ampoule. The samples were heated to 450 ◦C in ahorizontal tube furnace, held at this temperature for 40 days. The temperature ofthe hottest part of the ampoule was 450 ◦C and the coolest part was 370–380 ◦C.The obtained product was washed with distilled water to remove flux and otherby-products and then the tetragonal-shaped single crystals were mechanicallyextracted. The typical size of the obtained crystals was 1×1×0.1mm3. Thetemperature dependence of the resistivity of FeSe single crystals was measuredusing a conventional four-probe configuration in a 14 T physical propertymeasurements system and the magnetic susceptibility was measured in a 5 Tmagnetic property measurements system.

77Se (nuclear spin I=1/2) NMR was carried out in a FeSe single crystal(0.7×0.7×0.1mm3) at an external field of 9 T and in the range of temperature4.2–140K. The sample was rotated using a goniometer for the exact alignmentalong the external field. The 77Se NMR spectra were acquired by a standard

spin-echo technique with a typical π/2 pulse length 2–3 µs. The nuclearspin–lattice relaxation rate T−11 was obtained by fitting the recovery of the nuclearmagnetization M(t) after a saturating pulse to a single exponential function,1−M(t)/M(∞)=Aexp(−t/T1), where A is a fitting parameter.

Received 29 July 2014; accepted 9 October 2014;published online 10 November 2014

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AcknowledgementsThe authors thank G. Prando and H-J. Grafe for discussion. This work has beensupported by the Deutsche Forschungsgemeinschaft (Germany) through DFG ResearchGrants BA 4927/1-1 and the Priority Program SPP 1458. Financial support through theDFG Research Training Group GRK 1621 is gratefully acknowledged. The work atPOSTECH was supported by the National Research Foundation (NRF) through theMid-Career Researcher Program (No. 2012-013838), SRC Center for Topological Matter(No. 2011-0030046), and the Max Planck POSTECH/KOREA Research InitiativeProgram (No. 2011-0031558), and also by the Institute of Basic Science (IBS) through theCenter for Artificial Low Dimensional Electronic Systems.

Author contributionsS-H.B. performed the main NMR measurements, analysed data, and participated inwriting of the manuscript; J.M.O. and J.S.K. synthesized the sample; D.V.E. and J.v.d.B.provided theoretical support and participated in writing of the manuscript; B.B.supervised and guided the study and participated in the writing of the manuscript. Allauthors discussed the results and commented on the manuscript.

Additional informationSupplementary information is available in the online version of the paper. Reprints andpermissions information is available online at www.nature.com/reprints.Correspondence and requests for materials should be addressed to S-H.B.

Competing financial interestsThe authors declare no competing financial interests.

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