Intra-unit-cell nematic charge order in the titanium-oxypnictide family of superconductors

Abstract

Understanding the role played by broken-symmetry states such as charge, spin and orbital orders in the mechanism of emergent properties, such as high-temperature superconductivity, is a major current topic in materials research. That the order may be within one unit cell, such as nematic, was only recently considered theoretically, but its observation in the iron-pnictide and doped cuprate superconductors places it at the forefront of current research. Here, we show that the recently discovered BaTi₂ Sb₂ O superconductor and its parent compound BaTi₂ As₂ O form a symmetry-breaking nematic ground state that can be naturally explained as an intra-unit-cell nematic charge order with d-wave symmetry, pointing to the ubiquity of the phenomenon. These findings, together with the key structural features in these materials being intermediate between the cuprate and iron-pnictide high-temperature superconducting materials, render the titanium oxypnictides an important new material system to understand the nature of nematic order and its relationship to superconductivity.

ARTICLE

Received 9 Jun 2014 | Accepted 5 Nov 2014 | Published 8 Dec 2014

Benjamin A. Frandsen1,*, Emil S. Bozin2,*, Hefei Hu2,w, Yimei Zhu2, Yasumasa Nozaki3, Hiroshi Kageyama3, Yasutomo J. Uemura1, Wei-Guo Yin2 & Simon J.L. Billinge2,4

Understanding the role played by broken-symmetry states such as charge, spin and orbital orders in the mechanism of emergent properties, such as high-temperature super-conductivity, is a major current topic in materials research. That the order may be within one unit cell, such as nematic, was only recently considered theoretically, but its observation in the iron-pnictide and doped cuprate superconductors places it at the forefront of current research. Here, we show that the recently discovered BaTi2Sb2O superconductor and its parent compound BaTi2As2O form a symmetry-breaking nematic ground state that can be naturally explained as an intra-unit-cell nematic charge order with d-wave symmetry, pointing to the ubiquity of the phenomenon. These ndings, together with the key structural features in these materials being intermediate between the cuprate and iron-pnictide high-temperature superconducting materials, render the titanium oxypnictides an important new material system to understand the nature of nematic order and its relationship to superconductivity.

DOI: 10.1038/ncomms6761

Intra-unit-cell nematic charge order in the titanium-oxypnictide family of superconductors

1 Department of Physics, Columbia University, New York, New York 10027, USA. 2 Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA. 3 Department of Energy and Hydrocarbon Chemistry, Graduate School of Engineering, Kyoto University, Nishikyo, Kyoto 615-8510, Japan. 4 Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA. * These authors contributed equally to this work. w Present address: Intel Corporation, Folsom, California 95630, USA. Correspondence and requests for materials should be addressed to S.J.L.B. (email: mailto:[email protected]

Web End [email protected] ).

NATURE COMMUNICATIONS | 5:5761 | DOI: 10.1038/ncomms6761 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 1

& 2014 Macmillan Publishers Limited. All rights reserved.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6761

Rather than being an anomalous side effect in one or two cuprate systems, broken-symmetry states are now thought to be widespread in strongly correlated electron systems

and other complex materials. Extensive study of the manganites1,2, cuprates3,4, iron pnictides5 and a variety of other systems has made it increasingly evident that local and global symmetry breaking in the charge, orbital, lattice and spin degrees of freedom are associated with the appearance of emergent phenomena, such as colossal magnetoresistance and high-temperature superconductivity (HTSC), but the exact relationship is not understood. Historically, the study of such broken-symmetry states has been very challenging. Taking the cuprates as an example, 8 years elapsed from the initial discovery of superconductivity to the rst observation of symmetry-broken charge order (stripes) in one system6, another 7 years passed before hints were found in others7,8 and only within the last 3 years has charge order begun to emerge as a possibly ubiquitous feature of the cuprates9,10.

Several possibilities arise when considering the symmetries that can be broken by these states. Most charge-/spin-density waves (C/SDWs) break the translational symmetry of the lattice, folding the Brillouin zone and resulting in superlattice diffraction peaks. On the other hand, orbital ordering, where charge transfers between orbitals centred at the same site, can break the metric rotational symmetry without lowering the translational symmetry. Examples are charge-nematic11 and loop-current12,13 orders in the doped cuprates. In this context, nematic order is dened as one that breaks the rotational point group symmetry while preserving the lattice translational symmetry. The fact that nematic symmetry-broken states have recently been discovered experimentally in both the cuprate11 and iron-based14 superconductors raises the importance and relevance of this observation to HTSC. It is, therefore, critically important to understand the role and ubiquity of symmetry breaking, including intra-unit-cell nematicity, to the superconducting phenomenon.

Standard theoretical treatments of HTSC, such as the effective single-band tJ model, have typically ignored the possibility of intra-unit-cell orders15. When multiple atoms per unit cell are explicitly included in the theory, qualitatively different ground-state solutions may be found16, underscoring the subtlety and importance of accounting correctly for this phenomenon. Hence, nding related but distinct systems that exhibit this phenomenon is expected to shed new light on this critical question.

Very recently, superconductivity was discovered1719 in titanium-oxypnictide compounds, such as ATi2Pn2O (A Na2,

Ba, (SrF)2, (SmO)2; Pn As, Sb, Bi), which are close structural

and chemical cousins to the cuprates and iron-pnictides2024. In particular, in isovalent BaTi2(Sb1xBix)2O and aliovalent Ba1

xNaxTi2Sb2O (ref. 25), muon spin rotation and heat capacity measurements point to fully-gapped s-wave superconductivity2628.

Interestingly, a number of compounds in this family also show strong anomalies in resistivity and/or magnetic susceptibility that are thought to be signatures of symmetry-breaking charge- or spin-ordered ground states21,24,25,29,30, suggesting that these materials are excellent candidates for studying the interplay between broken-symmetry states and superconductivity. In light of these strong transport anomalies, it is then quite surprising that subsequent experiments have failed to uncover any direct evidence for a conventional spin- or charge-density wave ground state26,27,31, leaving open the question of whether these materials do possess symmetry-broken ground states.

Here, we show that superconducting BaTi2Sb2O, and its non-superconducting parent compound BaTi2As2O, do indeed undergo a tetragonal-orthorhombic phase transition, corresponding to a C4C2 symmetry lowering, that occurs at

the temperature of the transport anomaly. On the other hand, high-sensitivity electron diffraction measurements failed to detect any superlattice peaks in the bulk at low temperature, indicating that this transition does not break translational symmetry. The low-temperature phase, therefore, constitutes a nematic state. In light of the pronounced upturn in resistivity accompanying this nematic transition, together with the absence of any ordered SDW26, we attribute the nematicity to an intra-unit-cell charge order with d-wave symmetry by charge transfer between neighbouring Ti sitessimilar to that between neighbouring oxygen sites in cuprate superconductorsand nd that it naturally explains the temperature dependence of the lattice constants. These results establish this family of materials as another playground for studying symmetry-breaking electronic phases and their relationship to superconductivity.

ResultsStructural and electronic properties of BaTi2Pn2O. The basic structural unit of BaTi2Pn2O is a planar square net of titanium and oxygen, in analogy with the cuprates (Fig. 1a,b), with the crucial difference that the positions of the metal and oxygen ions are switched between the structures (the complete titanate structure is shown as an inset in Fig. 2b). In Fig. 1, the square net is shown by solid lines along the nearest neighbour bonds, with dashed lines showing the net joining second neighbour ions. This second-nearest-neighbour square net connects oxygen ions in the cuprates, but metal ions in the titanate compounds and also in the iron-based superconductors (Fig. 1c). Thus, in terms of chemistry and structure, the titanate compounds bridge between the ferrous and cuprate superconductors. The Ti 3d orbitals are occupied by one electron per Ti atom, which is found to reside in a nominally 1/4-lled band formed via hybridization of the dxy and dy2 z

2 =dx2 z

2 orbitals for the Ti(1)/Ti(2) ions (dened in Fig. 1b). The local geometry of the Ti(1) site is shown in Fig. 1d and the arrangement of the d-energy levels is shown in Fig. 1e.

Furthermore, the phase diagram (Fig. 2b) is highly reminiscent of the cuprates and iron-based superconductors, with super-conductivity appearing on doping and transport behaviour that is strongly suggestive of a competing electronic transition such as the formation of a CDW or SDW21,24. The transport is metallic at high temperature21, with a positive resistivity slope versus temperature (Fig. 2a). However, on cooling, a pronounced upturn in the resistivity is found for all x in the solid solution BaTi2As1 xSbxO. The feature occurs at a temperature Ta that

decreases monotonically from 200 K for x 0 to 50 K for

x 1, with superconductivity appearing below B1 K for the

antimony endmember and increasing to 5 K for BaTi2Bi2O (refs 19,24). Anomalies in the magnetic susceptibility and specic heat are also observed21 at Ta.

Density functional theory (DFT) calculations for BaTi2Sb2O predicted an instability towards a bicollinear SDW formation32,33 or a commensurate CDW ground state driven by an unstable phonon mode that doubles the unit cell by distorting the Ti squares and preserves the tetragonal symmetry34. The possibility of SDW formation in BaTi2(As,Sb)2O, either commensurate or incommensurate, was subsequently ruled out by muon spin relaxation and 121/123Sb nuclear resonance measurements, which show conclusively that no magnetic order develops at any temperature probed26,27,31. On the other hand, a conventional CDW should be evident through an associated structural distortion. However, initial electron and neutron diffraction studies on the Sb endmember26 found no broken symmetry or any signature of superlattice formation at low temperatures, nor was a CDW gap formation observed in angle-resolved photoemission measurements of the nested Fermi surfaces

2 NATURE COMMUNICATIONS | 5:5761 | DOI: 10.1038/ncomms6761 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

& 2014 Macmillan Publishers Limited. All rights reserved.

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6761 ARTICLE

a b c

O

Ti(2)

O

As As

Fe

Cu

b

Ti(1)

a

y z

Pn

d e

3x2 3y 2 r 2

r 2 yz

eg

t 2g

xz

xy xy

y2 x 2

z2 z2

x

xz

yz

Ti(1)

Ti(1)

Ti(2)

Figure 1 | Planar geometries of cuprate, titanium-oxypnictide, and iron-pnictide superconducting families. (ac) Planar motifs in cuprates, titanium oxypnictides and iron pnictides, respectively. Solid grey lines show the metal-anion square net, and dotted black lines show the square net of second-nearest-neighbour atoms. The and signs in b and c denote As atoms that are above and below the plane, respectively. (d) TiO2Pn4

octahedral motif found in BaTi2Pn2O. (e) Schematics of the Ti 3d-orbital energy levels for the two distinct Ti sites labelled in b, Ti(1) and Ti(2). The two lowest-lying orbitals marked in red form two bands occupied by one electron per Ti.

a b

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3 0 50 100 150 200 250 300

200

150

100

50

0 2.0 2.1 2.2 2.3 0

10

Pn

O

Ba

c

8

b

[afii9845]/[afii9845] 300K

6

a

BaTi2(As1xSbx)2O x=0 x=0.4 x=0.6 x=1

Temperature (K)

TiTi

4

Resistivity anomaly

Superconducting Tc

Bi3

Sb3

2

As3

Temperature (K)

Temperature (K)

Pn3 ionic radius ()

Figure 2 | Transport characteristics and phase diagram of BaTi2Pn2O with Pn As, Sb, Bi. (a) Electrical resistivity of BaTi2(As1

xSbx)2O, normalized

by the room temperature resistivity. Arrows indicate the anomaly discussed in the text. (b) Phase diagram of BaTi2Pn2O shown as a function of Pn3 ionic diameter. Broken lines are guides to the eye. The error bars accompanying the red circles arise from the instrumental low-temperature limitof 1.8 K. Inset: tetragonal crystal structure of BaTi2Pn2O.

(although a slight depression of the density of states at other momenta was found to correlate in temperature with the resistivity anomaly35). The possibility of an incommensurate CDW was also ruled out by 121/123Sb nuclear resonance measurements31.

Neutron powder diffraction measurements. In the absence of evidence for a long-range ordered CDW, we undertook a neutron diffraction and total scattering measurement on BaTi2Sb2O with a dense set of temperature points to search for evidence for a possible short-range ordered CDW36,37. We also extended the investigation to the previously unstudied BaTi2As2O endmember.

Unexpectedly, we found a long-range structural phase transition at Ta. Room temperature measurements of BaTi2As2O conrm the tetragonal P4/mmm space-group symmetry previously reported from X-ray diffraction21. However, on cooling through Ta, we observe a distinct splitting of the (200)/(020) and

(201)/(021) Bragg peaks, representing the rst observation of a symmetry lowering at the same temperature as the resistivity anomaly in BaTi2As2O. This is shown in Fig. 3, which compares the high- and low-temperature Bragg peaks in panel (a) and displays their temperature evolution in panel (b). The (200) peak at 2.02 begins to broaden below 200 K, coinciding with Ta, and appears to split at the lowest temperatures. Similarly, the (201) peak at 1.94 displays apparent splitting as the temperature is lowered. These observations demonstrate that BaTi2As2O undergoes a long-range ordered structural phase change at Ta, lowering its symmetry from tetragonal to orthorhombic.

To investigate the structural transition in greater detail, we performed Le Bail38 renements at all temperatures. We used the parent P4/mmm model for TZ200 K. The simplest possible symmetry-breaking distortion mode of the parent P4/mmm structure consistent with the observed peak splitting is a mode that breaks the degeneracy of the a- and b-axes without otherwise shifting atoms within the unit cell, resulting in a space-group

NATURE COMMUNICATIONS | 5:5761 | DOI: 10.1038/ncomms6761 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 3

& 2014 Macmillan Publishers Limited. All rights reserved.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6761

0.1

0

0.6

0.4

0.2

00.10.2

[afii9834](%)

P4/mmm

a

(200)

300 K20 K

(201)

7.27

7.26

200

100 300

Pmmm P4/mmm

c()

a,b()

T (K)

b

Normalized intensity (arb.units)

300 K

118.4118.8

V(3 )

275 K 250 K

220 K 200 K 180 K 160 K 140 K 120 K 100 K75 K

50 K20 K

7.25

4.04

4.03

a

150 300

T (K)

210 K

190 K 170 K 150 K

130 K 110 K

b

0

1.95

2 2.05

Figure 3 | Temperature evolution of BaTi2As2O neutron diffraction pattern. (a) Comparison of normalized intensities of 300 K (red) and 20 K (blue) data around (200) and (201) reections in P4/mmm setting.(b) Waterfall plot across the temperature range studied. The 20 K data (blue symbols) are shown with a t (blue solid line) of the rened Pmmm model. The corresponding difference curve is shown as the green solid line below. The asterisk marks the (200)/(020) reections of the BaTiO3 impurity phase.

50 100 150 200 300

250 Temperature (K)

Figure 4 | Temperature evolution of BaTi2As2O structural parameters. (a) Lattice parameter c (red). (b) Lattice parameters a, b (blue). Insets: orthorhombicity Z 2 (ab)/(a b) (left) and unit cell volume (right).

Vertical dashed grey line indicates transition temperature. Dashed red line is a guide for the eyes. Error bars represent the estimated standard deviation of the corresponding rened parameter.

d-spacing ()

symmetry of Pmmm, which was used for To200 K. We also explored other candidate orthorhombic structures with lower symmetry, but since these structures do not improve the t quality within the resolution limitations of the current data, Pmmm is the most appropriate choice. We display the results of these renements in Fig. 4. As seen in panel (b), the tetragonal a axis clearly splits below TB200 K, with a maximum orthorhombic splitting of B0.01 . The orthorhombicity parameter Z 2 (ab)/(a b) is shown in the inset of panel

(a), indicating a maximum orthorhombicity of B0.22%. Panel (a) also displays the temperature dependence of the c axis parameter, which exhibits an upturn below the structural transition deviating from the linear thermal contraction trend seen for T4200 K. This same type of c axis response also accompanies long-range ordered stripe formation in the nickelates36. Additional details regarding Rietveld renement of BaTi2As2O can be found in Supplementary

Note 1. The superconducting BaTi2Sb2O shows qualitatively the same behaviour, albeit with an amplitude decreased by a factor of

B5, with an orthorhombic splitting (0.05%) and a small but observable c axis upturn appearing on cooling through Ta 50 K.

The undistorted P4/mmm model can be used with moderate success at all temperatures, but the Pmmm model yields a better t below 50 K (see Supplementary Note 2). Pair distribution function analysis is consistent with these observations for both compounds and can be found in Supplementary Note 3.

These results offer compelling evidence that the observed structural response is intimately related to the transport anomaly and may be driven by a broken symmetry of the electronic system forming at that temperature. The small distortion amplitude in BaTi2Sb2O explains why this long-range structural phase change escaped notice in previous neutron diffraction measurements26.

Electron diffraction measurements. Since CDW formation is implicated, we made a special effort to search for the appearance of weak superlattice peaks associated with a nite CDW wave-vector in electron diffraction (ED) patterns below Ta. The original study on the antimony endmember failed to observe superlattice peaks26. Here, we concentrated on the arsenic endmember where the structural distortion is ve times larger, and the ED patterns were heavily overexposed to search for any weak response at intensities close to background. Despite these efforts, the ED patterns taken along the [001] and [011] directions revealed no superlattice peaks in the bulk at low temperature, as shown in Fig. 5. However, in a very small fraction of the sample in the immediate vicinity of grain boundaries, weak superlattice peaks with Q (1/2, 0, 0) are observed at low temperature. This non-

bulk behaviour is explored further in Supplementary Note 4.

DiscussionA picture emerges of a C4C2 symmetry breaking occurring with an accompanying strong upturn in resistivity, but with no corresponding CDW superlattice peaks appearing. The resistivity upturn is larger than would be expected as a passive response of the electronic system to the structural transition, borne out by a standard DFT calculation with the observed orthorhombicity parameter Z 0.22%, which showed that merely 0.0003 electrons

are transferred from Ti(1) to Ti(2). Therefore, in common with earlier discussion18,21, we propose that the structural transition is a response to an instability of the electronic system. The earlier muon spin relaxation results26,27, together with the ED measurements, allow us to rule out the existing proposals of SDW formation32,33 or a phonon-driven CDW34. Instead, an intra-unit-cell charge-nematic electronic symmetry breaking is implicated, similar to that proposed for doped cuprates39.

In the current case, a charge redistribution between the on-site orbital states at the Fermi level, dx2 z

2 =dy2 z

2 to dxy, does not

4 NATURE COMMUNICATIONS | 5:5761 | DOI: 10.1038/ncomms6761 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

& 2014 Macmillan Publishers Limited. All rights reserved.

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6761 ARTICLE

a b

[011]

[001]

89 K

89 K

010

01-1

11-1

100

100

Figure 5 | Electron diffraction patterns of BaTi2As2O. (a) Diffraction pattern with the incident beam along the [001] and (b) along the [011] directions. No superlattice peaks are observed at low temperature even after heavy overexposure.

break the rotational symmetry, so can be ruled out. Instead, a simple but novel intra-unit-cell charge order (IUC-CO) naturally explains the observed phenomenology. A transfer of charge from Ti(1) to Ti(2) (see Fig. 1b) lowers the rotational symmetry of the Ti2O plaquette locally from C4 to C2, with the effect on the overall lattice symmetry depending on the ordering pattern of the distinct Ti ions in neighbouring unit cells. Repeating the symmetry-lowered plaquette uniformly along the a and b directions results in no change of the unit cell, but breaks the metric symmetry from C4 in P4/mmm to C2 in Pmmm, as observed experimentally. This arrangement of charges can accordingly be described as a nematic IUC-CO. Our data are therefore consistent with the formation of this type of charge order on cooling through Ta. Such a model is also consistent with the breaking of C4 symmetry at the Pn site that has been observed from 121/123Sb nuclear resonance measurements31.

This nematic IUC-CO is energetically favoured on Coulombic grounds if the on-site Hubbard energy U is sufciently small, which is a reasonable assumption as the system is a metal rather than a Mott insulator. The small Hubbard U arises from signicant screening due to the solvation effect of the high polarizabilities of the As3 and Sb3 anions, which are an order of magnitude larger than that of O2 . Moreover, the As and Sb ions reside on a lower symmetry site in the Pmmm structure, which enhances the effects of their polarizabilities. This physics was proposed in an earlier study of the iron-pnictide super-conductors40. Returning to the present system, the transfer of a charge of d from Ti(1) to Ti(2) will result in a lowering of the electrostatic energy, V(1d)(1 d) V(1d2), where V is the

screened Coulombic interaction between Ti sites and is positive. The result is charge order with a d-wave symmetry41 with the sign of the modulated charge density varying as around

the plaquette. From plaquette to plaquette, the orientation of the axis of the distortion can be parallel or perpendicular, forming a ferro- or anti-ferro- type ordering, which would preserve or break translational symmetry, respectively. The former is consistent with the experimental observations in this material. We suggest that the rather rigid face-shared octahedral topology in each layer favours the uniform ferro- over the anti-ferro- ordering. It is noteworthy that this V is the counterpart of the Coulumbic repulsion Vpp between neighbouring oxygen atoms in the CuO2 plane, which was shown to drive IUC nematic order in nonstoichiometric doped cuprates42. Hence, the present results obtained on these stoichiometric materials (thus having less ambiguity such as disorder effects) yield insight into the origin of IUC nematic order in the cuprates.

This nematic IUC-CO naturally explains the observed changes in the a- and c-lattice parameters. The transfer of charge from the Ti(1) dy2 z

2 results in increased electrostatic repulsion between the charge-rich dx2 z

2 orbital to Ti(2) dx2 z

2 orbitals

extending along the a axis, breaking the tetragonal degeneracy of the a and b axes and leading to the observed orthorhombic distortion. Furthermore, a uniform stacking of the IUC-CO in each layer can also explain the response of the c-lattice parameter, which expands upon entering the charge-ordered state (Fig. 4a). This lattice expansion may be attributed in part to increased electrostatic repulsion between inter-layer Ti ions from the transferred charge. The net energy contribution is V0[(1 d)2 (1d)2] V0(2 2d2), where V0 is the inter-layer screened

Coulombic interaction. This acts in addition to other elastic energy contributions.

The structural effects observed on cooling are much smaller in BaTi2Sb2O than BaTi2As2O, suggesting that the IUC-CO is relatively suppressed both in amplitude and temperature. This may be a result of the larger unit cell in the Sb compound, due to its larger Sb3 ionic diameter (2.25 versus 1.98 for As3 ;

ref. 18), resulting in a smaller V.

To identify the microscopic driving force of this nematic instability, we present a symmetry-based zero-order analysis in which only the leading energy scales are retained. Ti atoms reside at the centre of a distorted octahedron with oxygen at the apices and pnictide atoms around the equatorial plane, as shown in Fig. 1d for Ti(1). The Ti 3d-energy levels are illustrated in Fig. 1e, similar to the case of nearly isostructural (LaO)2CoSe2O (ref. 43).

The nominal electron occupation is one electron per Ti atom, which would have been assigned to the locally lowest-lying dy2 z

2

and dx2 z

2 orbitals on the Ti(1) and Ti(2) ions, respectively. However, the s-bonding between the Ti(1) and Ti(2) dxy orbitals forms a relatively wide band that overlaps the locally lowest level. Therefore, the minimum model for the titanium oxypnictides involves the two orbitals: dy2 z

2 and

dxy on Ti(2). Since the dxy orbital has the same impact on both the a and b direction, the C4C2 symmetry lowering around the central oxygen atom is mainly determined by the charge imbalance between the quasi-one-dimensional dy2 z

2 and dxy on Ti(1) and dx2 z

2 band on

2 on Ti(2) as a result of the Stoner instability42. No doubt this mechanism will be complicated by hybridization and other issues, but this symmetry-based analysis provides the appropriate realistic starting point. Since the proposed nematic intra-unit-cell charge order elegantly explains all the observed structural effects, it is anticipated to be the electronic ground state of BaTi2Pn2O.

Ti(1) and dx2 z

NATURE COMMUNICATIONS | 5:5761 | DOI: 10.1038/ncomms6761 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 5

& 2014 Macmillan Publishers Limited. All rights reserved.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6761

Methods

Neutron powder diffraction. Powder specimens of BaTi2As2O and BaTi2Sb2O were prepared via conventional solid state reaction methods. Details of the synthesis are provided in a previous study26. Time-of-ight neutron total scattering experiments were performed at the Neutron Powder Diffractometer at Los Alamos Neutron Science Center (LANSCE) at Los Alamos National Laboratory. Data were collected using a closed-cycle He refrigerator at temperatures ranging from 10300 K in steps of 10 K near the structural transition and 25 K away from the transition over a wide range of momentum transfer Q. Le Bail38 ts to the intensity proles were performed with GSAS44 on the EXPGUI platform45. Pair distribution function (PDF) proles were obtained by Fourier transforming the measured total scattering intensity up to a maximum momentum transfer of Qmax 24 1 using

established protocols46,47 as implemented in the programme PDFgetN48. The Le Bail ts were used to extract lattice parameters and space-group symmetry, the PDF ts to extract atomic displacement parameters. Symmetry mode analysis using the programme ISODISTORT49 was conducted to identify candidate distorted structures.

Electron diffraction and DFT calculations. Electron diffraction patterns were recorded using a JEOL ARM 200CF transmission electron microscope (TEM), operated at 200 keV, at Brookhaven National Laboratory. The TEM samples were prepared by crushing powder specimens into thin akes transparent to the electron beam, which were supported by a lacey carbon copper grid. DFT calculations were performed within the generalized gradient approximation implemented in the Wien2k software package50.

References

1. Dagotto, E. et al. Nanoscale phase Separation and Colossal Magnetoresistance (Springer-Verlag, 2003).

2. Dagotto, E. Complexity in strongly correlated electronic systems. Science 309, 257262 (2005).

3. Orenstein, J. & Millis, A. J. Advances in the physics of high-temperature superconductivity. Science 288, 468474 (2000).

4. da Silva Neto, E. H. et al. Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates. Science 343, 393396 (2014).

5. Fernandes, R., Chubukov, A. & Schmalian, J. What drives nematic order in iron-based superconductors? Nat. Phys. 10, 97104 (2014).

6. Tranquada, J. M., Sternlieb, B. J., Axe, J. D., Nakamura, Y. & Uchida, S. Evidence for stripe correlations of spins and holes in copper oxide superconductors. Nature 375, 561563 (1995).

7. Hoffman, J. E. et al. A four unit cell periodic pattern of quasi-particle states surrounding vortex cores in Bi2Sr2CaCu2O8d. Science 295, 466469 (2002).

8. Vershinin, M. et al. Local ordering in the pseudogap state of the high-Tc superconductor Bi2Sr2CaCu2O8d. Science 303, 19951998 (2004).

9. Chang, J. et al. Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67. Nat. Phys. 8, 871876 (2012).

10. Comin, R. et al. Charge order driven by Fermi-arc instability in Bi2Sr2

xLaxCuO6d. Science 343, 390392 (2014).

11. Lawler, M. J. et al. Intra-unit-cell nematicity of the high-Tc copper-oxide pseudogap states. Nature 466, 374377 (2010).

12. Varma, C. Non-Fermi-liquid states and pairing instability of a general model of copper oxide metals. Phys. Rev. B 55, 14554 (1997).

13. Li, Y. et al. Hidden magnetic excitation in the pseudogap phase of a high-Tc superconductor. Nature 468, 283285 (2010).

14. Chuang, T. et al. Nematic electronic structure in the parent state of the iron-based superconductor Ca(Fe1xCox)2As2. Science 327, 181184 (2010).

15. Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a mott insulator: Physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 1785 (2006).

16. Fernandes, R., Chubukov, A., Knolle, J., Eremin, I. & Schmalian, J. Preemptive nematic order, pseudogap, and orbital order in the iron pnictides. Phys. Rev. B 85, 024534 (2012).

17. Yajima, T. et al. Synthesis and physical properties of the new oxybismuthides BaTi2Bi2O and (SrF)2Ti2Bi2O with a d1 square net. J. Phys. Soc. Jpn 82, 013703 (2013).

18. Yajima, T. et al. Two superconducting phases in the isovalent solid solutions BaTi2Pn2o (Pn As, Sb, and Bi). J. Phys. Soc. Jpn 82, 033705 (2013).

19. Zhai, H.-F. et al. Superconductivity, charge- or spin-density wave, and metal-nonmetal transition in BaTi2(Sb1xBix)2O. Phys. Rev. B 87, 100502 (2013).

20. Ozawa, T. C. & Kauzlarich, S. M. Chemistry of layered d -metal pnictide oxides and their potential as candidates for new superconductors. Sci. Technol. Adv. Mater. 9, 033003 (2008).

21. Wang, X. F. et al. Structure and physical properties for a new layered pnictide-oxide: BaTi2As2O. J. Phys: Condens. Mater. 22, 075702 (2010).

22. Liu, R. H. et al. Structure and physical properties of the layered pnictide-oxides: (SrF)2Ti2Pn2O (Pn As, Sb) and (SmO)2Ti2Sb2O. Chem. Mater. 22, 15031508

(2010).

23. Johrendt, D., Hosono, H., Hoffmann, R.-D. & Pttgen, R. Structural chemistry of superconducting pnictides and pnictide oxides with layered structures. Z. Kristallogr. 226, 435446 (2011).

24. Yajima, T. et al. Superconductivity in BaTi2Sb2O with a d1 square lattice.J. Phys. Soc. Jpn 81, 103706 (2012).25. Doan, P. et al. Ba1xNaxTi2Sb2O (0.0 r x r 0.33): a layered titanium-based pnictide oxide superconductor. J. Am. Chem. Soc. 134, 1652016523 (2012).

26. Nozaki, Y. et al. Muon spin relaxation and electron/neutron diffraction studies of BaTi2(As1xSbx)2O: Absence of static magnetism and superlattice reections.

Phys. Rev. B 88, 214506 (2013).27. von Rohr, F., Schilling, A., Nesper, R., Baines, C. & Bendele, M. Conventional superconductivity and charge-density-wave ordering in Ba1xNaxTi2Sb2O. Phys.

Rev. B 88, 140501 (2013).28. Gooch, M. et al. Weak coupling BCS-like superconductivity in the pnictide oxide Ba1xNaxTi2Sb2O (x 0 and 0.15). Phys. Rev. B 88, 064510 (2013).

29. Axtell, III E. A., Ozawa, T., Kauzlarich, S. M. & Singh, R. R. Phase transition and spin-gap behavior in a layered tetragonal pnictide oxide. J. Solid State Chem. 134, 423426 (1997).

30. Liu, R. H. et al. Physical properties of the layered pnictide oxides Na2Ti2P2O (P As,Sb). Phys. Rev. B 80, 144516 (2009).

31. Kitagawa, S., Ishida, K., Nakano, K., Yajima, T. & Kageyama, H. s-wave superconductivity in superconducting BaTi2Sb2O revealed by 121/123Sb-NMR/

nuclear quadrupole resonance measurements. Phys. Rev. B 87, 060510 (2013).32. Singh, D. J. Electronic structure, disconnected fermi surfaces and antiferromagnetism in the layered pnictide superconductor NaxBa1xTi2Sb2O.

New J. Phys. 14, 123003 (2012).33. Wang, G., Zhang, H., Zhang, L. & Liu, C. The electronic structure and magnetism of BaTi2Sb2O. J. Appl. Phys. 113, 243904 (2013).

34. Subedi, A. Electron-phonon superconductivity and charge density wave instability in the layered titanium-based pnictide BaTi2Sb2O. Phys. Rev. B 87, 054506 (2013).

35. Xu, H. C. et al. Electronic structure of the BaTi2As2O parent compoundof the titanium-based oxypnictide superconductor. Phys. Rev. B 89, 155108 (2014).

36. Abeykoon, M. et al. Evidence for short-range-ordered charge stripes far above the charge-ordering transition in La1.67Sr0.33NiO4. Phys. Rev. Lett. 111, 096404 (2013).

37. Boin, E. S., Billinge, S. J. L., Takagi, H. & Kwei, G. H. Neutron diffraction evidence of microscopic charge inhomogeneities in the CuO2 plane of superconducting La2xSrxCu4 (0 r x r 0.30). Phys. Rev. Lett. 84, 58565859 (2000).

38. Le Bail, A., Duroy, H. & Fourquet, J. L. Ab-initio structure determination of LiSbWO6 by X-ray powder diffraction. Mater. Res. Bull. 23, 447452 (1987).

39. Fujita, K. et al. Direct phase-sensitive identication of a d-form factor density wave in underdoped cuprates. Proc. Natl Acad. Sci. USA 111, E3026E3032 (2014).

40. Sawatzky, G., Elmov, I., van den Brink, J. & Zaanen, J. Heavy-anion solvation of polarity uctuations in pnictides. Europhys. Lett. 86, 17006 (2009).

41. Fradkin, E., Kivelson, S. A., Lawler, M. J., Eisenstein, J. P. & Mackenzie, A. P. Nematic fermi uids in condensed matter physics. Annu. Rev. Condens. Matter Phys. 1, 153 (2010).

42. Fischer, M. H. & Kim, E.-A. Mean-eld analysis of intra-unit-cell order in the Emery model of the CuO2 plane. Phys. Rev. B 84, 144502 (2011).

43. Wu, H. Electronic structure, spin state, and magnetism of the square-lattice mott insulator LaCo2Se2O3 from rst principles. Phys. Rev. B 82, 020410(R)

(2010).44. Larson, A. C. & Von Dreele, R. B. General structure Analysis System. Report No. LAUR-86-748, 87545 (Los Alamos National Laboratory, 1994).

45. Toby, B. H. EXPGUI, a graphical user interface for GSAS. J. Appl. Crystallogr. 34, 201213 (2001).

46. Egami, T. & Billinge, S. J. L. Underneath the Bragg Peaks: Structural Analysis of Complex Materials 2nd edn (Elsevier, 2012).

47. Chupas, P. J. et al. Rapid acquisition pair distribution function analysis (RA-PDF). J. Appl. Crystallogr. 36, 13421347 (2003).

48. Peterson, P. F., Gutmann, M., Proffen, T. & Billinge, S. J. L. PDFgetN:a user-friendly program to extract the total scattering structure function and the pair distribution function from neutron powder diffraction data. J. Appl. Crystallogr. 33, 11921192 (2000).

49. Campbell, B., Stokes, H., Tanner, D. & Hatch, D. ISODISPLACE: an internet tool for exploring structural distortions. J. Appl. Crystallogr. 39, 607614 (2006).

50. Blaha, P., Schwarz, K., Madsen, G., Kvasnicka, D. & Luitz, J. WIEN2k: An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties (Vienna University Technology, 2001).

Acknowledgements

Work at Brookhaven National Laboratory was supported by the U.S. Department of Energy, Ofce of Basic Energy Sciences, under contract No. DE-AC02-98CH10886.

6 NATURE COMMUNICATIONS | 5:5761 | DOI: 10.1038/ncomms6761 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

& 2014 Macmillan Publishers Limited. All rights reserved.

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6761 ARTICLE

Work at Columbia University was supported by the U.S. National Science Foundation (NSF) Partnership for International Research and Education (PIRE) Super-PIRE project (grant OISE-0968226). Y.J.U. also acknowledges support from NSF DMR-1105961, the Japan Atomic Energy Agency Reimei project, and the Friends of Todai Inc. The work at Kyoto University was supported by the FIRST program, Japan Society of the Promotion of Science (JSPS). Neutron scattering experiments were carried out on NPDF at LANSCE, funded by DOE Ofce of Basic Energy Sciences. LANL is operated by Los Alamos National Security LLC under DOE Contract No. DE-AC52-06NA25396.

Author contributions

Y.J.U., S.J.L.B. and B.A.F. initiated this work. Y.N. and H.K. carried out sample preparation and characterization. E.S.B. carried out the neutron diffraction measurements and analysed the data with assistance from B.A.F. H.H. performed the electron diffraction measurements with help from Y.Z. W.-G.Y. proposed the charge-ordering

model and provided theoretical support. B.A.F., W.-G.Y. and S.J.L.B. wrote the paper, with input from all the authors.

Additional information

Supplementary Information accompanies this paper at http://www.nature.com/naturecommunications

Web End =http://www.nature.com/ http://www.nature.com/naturecommunications

Web End =naturecommunications

Competing nancial interests: The authors declare no competing nancial interests.

Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/

Web End =http://npg.nature.com/ http://npg.nature.com/reprintsandpermissions/

Web End =reprintsandpermissions/

How to cite this article: Frandsen, B. A. et al. Intra-unit-cell nematic charge order in the titanium-oxypnictide family of superconductors. Nat. Commun. 5:5761 doi: 10.1038/ ncomms6761 (2014).

NATURE COMMUNICATIONS | 5:5761 | DOI: 10.1038/ncomms6761 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 7

& 2014 Macmillan Publishers Limited. All rights reserved.