Charge-ordering cascade with spin-orbit Mott dimer states in metallic iridium ditelluride

Abstract

Spin-orbit coupling results in technologically-crucial phenomena underlying magnetic devices like magnetic memories and energy-efficient motors. In heavy element materials, the strength of spin-orbit coupling becomes large to affect the overall electronic nature and induces novel states such as topological insulators and spin-orbit-integrated Mott states. Here we report an unprecedented charge-ordering cascade in IrTe₂ without the loss of metallicity, which involves localized spin-orbit Mott states with diamagnetic Ir⁴⁺ -Ir⁴⁺ dimers. The cascade in cooling, uncompensated in heating, consists of first order-type consecutive transitions from a pure Ir³⁺ phase to Ir³⁺ -Ir⁴⁺ charge-ordered phases, which originate from Ir 5d to Te 5p charge transfer involving anionic polymeric bond breaking. Considering that the system exhibits superconductivity with suppression of the charge order by doping, analogously to cuprates, these results provide a new electronic paradigm of localized charge-ordered states interacting with itinerant electrons through large spin-orbit coupling.

ARTICLE

Received 19 Sep 2014 | Accepted 28 Apr 2015 | Published 10 Jun 2015

K.-T. Ko1,2,3, H.-H. Lee1,2, D.-H. Kim1,2, J.-J. Yang2,4, S.-W. Cheong4,5, M.J. Eom6, J.S. Kim6, R. Gammag6,

K.-S. Kim6, H.-S. Kim6,7, T.-H. Kim6,7, H.-W. Yeom6,7, T.-Y. Koo8, H.-D. Kim8,9 & J.-H. Park1,2,10

Spinorbit coupling results in technologically-crucial phenomena underlying magnetic devices like magnetic memories and energy-efcient motors. In heavy element materials, the strength of spinorbit coupling becomes large to affect the overall electronic nature and induces novel states such as topological insulators and spinorbit-integrated Mott states. Here we report an unprecedented charge-ordering cascade in IrTe2 without the loss of metallicity, which involves localized spinorbit Mott states with diamagnetic Ir4Ir4 dimers. The cascade in cooling, uncompensated in heating, consists of rst order-type consecutive transitions from a pure Ir3 phase to Ir3 Ir4 charge-ordered phases, which originate from Ir 5d to Te 5p charge transfer involving anionic polymeric bond breaking. Considering that the system exhibits superconductivity with suppression of the charge order by doping, analogously to cuprates, these results provide a new electronic paradigm of localized charge-ordered states interacting with itinerant electrons through large spinorbit coupling.

1 c_CCMR & Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Korea. 2 Max Plank POSTECH Center for Complex Phase Materials, Pohang University of Science and Technology, Pohang 790-784, Korea. 3 Max Plank Institute for Chemical Physics in Solid, 01187 Dresden, Germany. 4 l_PEM & Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Korea. 5 Department of Physics and Astronomy, Rutgers Center for Emergent Materials, Rutgers University, Piscataway, New Jersey 08854, USA. 6 Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Korea. 7 Center for Articial Low Dimensional Electronic Systems, Institute for Basic Science, Pohang 790-784, Korea.

8 Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang 790-784, Korea. 9 Center for Correlated Electron Systems, Institute for Basic Science (IBS) & Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea. 10 Division of Advanced Materials Science, Pohang University of Science and Technology, Pohang 790-784, Korea. Correspondence and requests for materials should be addressed to J.-H.P. (e-mail: mailto:[email protected]

Web End [email protected] ).

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DOI: 10.1038/ncomms8342

Charge-ordering cascade with spinorbit Mott dimer states in metallic iridium ditelluride

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8342

Interplay between spinorbit coupling (SOC) and Coulomb interaction has become a challenging subject in condensed matter physics since it may realize novel superconductivity

competing with charge ordering (CO) of spinorbit Mott states as in the high TC cuprates13. On the other hand, a charge modulation can be induced by electronic Peierls instability, the so called charge density wave (CDW)4,5. As electron states are localized as in the Mott states, it appears as a charge order-type modulation due to intersite Coulomb interactions68. In a system with heavy elements, the large SOC can stabilize the localized spinorbit Mott state as observed in iridates9, and then the charge-ordered Mott state naturally leads a novel electronic framework of the interplay. Further, if the localized Mott state interacts with itinerant conduction electrons, the system possibly experiences valence uctuations as in the 4f rare-earth materials10 and exhibits unprecedented physical phenomena. IrTe2 was reported as a new CDW material with a modulation vector q (1/5 0 1/5) below a CDW transition temperature TCB260 K

and also as a mother compound of Ir based superconductors1113. Various efforts have been conducted to elucidate electronic mechanisms of the charge modulation11,13,14, but the CDW like nature was disputable. A recent X-ray diffraction (XRD) study suggested charge modulations not only in the Te site but also in the Ir site with dimerization below TC15, suggesting a possibility of the Ir site CO.

IrTe2 is crystallized in a CdI2-type layered hexagonal structure (P3m1) with van der Waals bond gap (Fig. 1a). The lattice constants at 300 K are a 3.93 and c 5.39 with c/a 1.37,

which is much smaller than c/a 1.61.8 in other isostructural

dichalcoginides16,17. The interlayer TeTe distance (3.50 ) is also greatly shorter than the expected van der Waals bond length 2RvdW 4.12 , twice of the atomic radius, indicating strong

interlayer coupling through the TeTe covalent bonding. The short bond length is considered as formation of Te23 polymeric bonds17. The band calculations predict a three dimension-like

Fermi surface with a nesting instability near q (1/5 0 1/5) and

Ir3 and Te1.5 valences in the high temperature (HT) phase11.

Here we report unprecedented CO behaviours without losing metallicity in a hexagonal layered IrTe2. The CO behaviours are investigated by using comprehensive experimental and theoretical studies. The experimental results obtained from a variety of transport and spectroscopic measurements manifest that the system undergoes rst order-type consecutive transitions from a pure Ir3 to Ir3 Ir4 charge-ordered phases with q1/5 (1/5 0 1/5) and q1/8 (1/8 0 1/8) on cooling while it

directly transits from the low temperature (LT) q1/8 phase to the HT Ir3 phase on heating. The transitions involve Ir 5d to Te 5p charge transfer with Te anionic polymeric bond breaking.

Theoretical free energy model analyses show that the charge-ordered phases are stabilized by localized Ir 5d spinorbit Mott states together with diamagnetic Ir4 Ir4 dimerization. These results provide a new electronic paradigm of the spinorbit driven charge-ordered Mott states interacting with itinerant conduction electrons.

Results and DiscussionsElectrical and magnetic behaviours. The resistivity of high-quality IrTe2 single crystals exhibits remarkably different behaviours for cooling and heating processes (Fig. 1b). On cooling, it shows consecutive resistivity jumps at TC1E280 K and at

TC2E180 K without losing metallicity. Meanwhile, on heating, the LT phase directly transits into the HT phase at THE280 K with the corresponding resistivity drop. All the transitions are rst order-type transitions with B1 K narrow temperature windows, indicating minimal defects in the crystal.

The magnetic susceptibility also displays the uncompensated thermal hysteretic behaviour (Fig. 1c). In the HT phase, it shows weak Pauli paramagnetism, which is well explained by the non-magnetic Ir3 (5d6) with the t2g band full and Te23 with 5p conduction electrons (one hole per formula unit). On cooling across TC1, it drops to be negative and the intermediate phase is diamagnetic. The diamagnetism becomes stronger below TC2. In a heating process, it shows the direct LT to HT phase transition at TH as can be seen in the resistivity results. Considering the IrIr dimerization across TC1 (ref. 15), one can suspect the formation of diamagnetic Mott dimer states in analogous to diamagnetic Ti2O3 with dimerized S 1/2 Mott states18 so that the enhanced

diamagnetism reects increase of the dimer population in the LT phase.

Structural identication. We performed XRD measurements along a (0 0 4) to (1 0 5) direction (Fig. 2a,b) and monitored the ordering peak intensities (Fig. 2c,d) at different temperatures. At 300 K, only the Bragg peaks are observable. On cooling (Fig. 2a,c,e), the q1/5 (1/5 0 1/5) ordering peaks additionally

appear at TC1/5E280 K (TC1) with a rst-order HT to q1/5 phase transition. The peak intensity maintains nearly constant down to TC1/8E180 K (TC2). For further cooling below TC1/8, the q1/5 peaks are suddenly replaced with q1/8 (1/8 0 1/8) ordering

peaks, and the system undergoes another rst order q1/5 to q1/8

phase transition. The appearance of the q1/8 peaks accompanies large increase of a diffusive scattering background, which is due to lack of regularity in the q1/8 modulation. The peak intensity barely varies with temperature down to 10 K. On heating (Fig. 2b,d,f), the q1/8 peak intensity remains up to TH1/8E280 K (TH) without appearance of the q1/5 peaks. Meanwhile, the background is somewhat reduced, indicating certain improvement of the q1/8 regularity. For further heating, the q1/8 peaks nally disappear across TH1/8, and the q1/8 phase directly transits

to the HT phase. One can notice gradual increase of the peak intensity in heating, especially from 200 to 280 K, mainly due to improvement of the modulation regularity. An additional 1/11 ordering of a minor faction was observed in LT phase in the scanning tunnelling microscope (STM)19. However, any hint of this order is not observable in the XRD, indicating that it is a surface phenomenon. The q1/8 regularity degradation may be attributed to smaller domain formation, but can also be considered as a hint of valence uctuations of the localized Ir 5d Mott states interacting with the Te 5p conduction electrons.

Figure 2e,f shows variations of the hexagonal lattice constants determined from the Bragg peaks. On cooling (Fig. 2e) across the HT to q1/5 transition, a (in-plane) decreases while c (out-of-plane) increases, resulting in increase of the c/a ratio from 1.37 to1.401.41. The ratio further increases to 1.42 across the q1/5 to

q1/8 transition. Meanwhile, on heating (Fig. 2f) across TH1/8, it is reduced back to 1.37 in the HT phase. Considering that the small c/a ratio in the HT phase involves the Te23 polymeric bonding, the increased ratios in the q1/5 and q1/8 phases imply certain

degrees of the Te23 bond breaking, which leads the Ir valence change from Ir3 (d6) to Ir4 (d5).

SOC assisted electronic transition. The Ir valence change is examined by using the Ir 4f core-level photoemission spectroscopy (Fig. 3a). At 300 K (HT phase), the Ir 4f spectrum displays a simple two-peak feature representing the 4f7/2 and 4f5/2 core-hole

nal states. Their binding energies correspond to those of Ir3 , conrming the Te23 formation. At 260 K (q1/5 phase), each peak splits into double peaks with a 0.41-eV separation, showing that

IrTe2 becomes an Ir3 Ir4 mixed valence state. This binding energy (EB) shift, the so called chemical shift, is similar to that

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a = 3.93 c = 5.39

(P3m1)

3.4984 Ir Te

bh

3.9284

3.5580

ch

ah

Sample A Cooling Heating

Sample B Poly crystal

[afii9845](cm)

50

50

100

50

[afii9851](106 emu mole1 )

0

X 0.1

50

0 0 100 200

150 250 300

50

Figure 1 | Crystal structure and physical properties of IrTe2. On cooling, IrTe2 crystals exhibit remarkable thermal hysteretic electrical and magnetic behaviours with consecutive transitions at B280 and B180 K but only a single transition at B280 K on heating, differently from the polycrystalline sample. (a) Each hexagonal layer consists of edge-shared IrTe6 octahedrons. The hexagonal axes are presented with red (ah), green (bh) and blue (ch) arrows. Blue and yellow ball symbols are represents Ir and Te atoms, respectively. The interlayer TeTe bond length (3.4984 ) is much shorter than the expected van der Waals bond length 2RvdW 4.12 . (b) The resistivity results of the single-crystal samples (orange and dotted black lines) display the

consecutive transitions accompanied with abrupt changes on cooling, while it does only a single transition on heating. In the resistivity of the polycrystalline sample (green line), which is scaled down to 0.1, the second transition does not appear, indicating that it suppressed by impurities or defects. (c) Magnetic susceptibility is measured with a bunch of IrTe2 crystals grown in a single batch to compensate the low magnetic signal. Blue and red lines are measured in cooling and heating, respectively. The susceptibility shows the Pauli paramagnetism above B280 K but does diamagnetism below B280 K. On cooling, the susceptibility is further reduced in the second transition, which is not recovered in heating cycle, consistently with the resistivity.

100 200

150 250 300

Temperature (K) Temperature (K)

observed in CuIr2S4 with an Ir3 Ir4 CO state20,21. At 100 K (q1/8 phase), the Ir4 high binding peak intensity overwhelms the Ir3 one. Figure 3b shows the Ir4 fractions for different temperatures and phases estimated from the Ir3 and Ir4 relative peak intensities (Supplementary Fig. 1). The transitions accompany the Ir average valence changes from a pure Ir3 in the HT phase to an Ir3 Ir4 mixed valence with a 3:2 xed ratio in the q1/5 phase. In the q1/8 phase, the ratio becomes (4 x):(4 x) with monotonic increase of the x-value from zero

near TH1/8 to about one below 50 K, indicating the Ir 5d valence uctuation. The appearance of Ir4 , which reects the Te23

polymeric bond break to yield Te2 , veries that the q1/5 and

q1/8 modulations involve Ir3 Ir4 charge orders.

Figure 4ad show the Fermi surface topology around the G-point at 300 K obtained by using the angle-resolved photo-emission spectroscopy (ARPES) and the G-cross ARPES spectra in three different phases, respectively. The predicted electronic structure well agrees with the ARPES results in the HT phase (Supplementary Fig. 2). The transitions accompany considerable spectral changes not only at the Fermi level (EF) but also in the 03 eV valence band region. The spectral weight at EF gradually decreases with cooling from 300 to 260 K and to 100 K without losing the metallic EF feature as shown in Fig. 4e, consistently with the optical results across the HT to q1/5 phase transition14. These results well explains the resistivity jumps across the

transitions (see Fig. 1b). The electronic changes across the transitions are also observable in the G-cross band dispersions (Fig. 4bd). The overall dispersions are mostly maintained across the transitions. However, one can notice that an additional at band feature appears at EBB0.8 eV in the q1/5 phase and is extended in the q1/8 phase.

The electronic structures in the three different phases can be described schematically in Fig. 4fh. The Ir 5d state is split into a triplet t2g and a doublet eg states with a splitting energy10 DqB3 eV under the octahedral Oh symmetry. The large SOC energy (B0.5 eV) of Ir 5d splits again the low lying t2g states into the spinorbit Jeff 3/2 and Jeff 1/2 states9. In the HT

phase with pure Ir3 (5d6), both the Jeff 3/2 and Jeff 1/2

bands are fully occupied while the Te 5p wide band crosses EF with one hole per Te23 . On cooling across TC1/5 (q1/5 phase), the

Te23 bonds are partially broken with Ir 5d to Te 5p electron transfer, and the system becomes a 3:2 Ir3 Ir4 charge-ordered state. At the Ir4 (5d5) site, the Jeff 1/2 state becomes half-full,

and the electronic state is expected to become the localized Jeff 1/2 Mott state as in Sr2IrO4. The dimerization leads the

diamagnetic spinorbit Mott dimer states, and the Hubbard U, which is o1 eV in Sr2IrO4, is effectively enlarged by the dimerization energy (D) to be Ueff( U D) B1.5 eV. The

newly appearing at band at EBB0.8 eV seems to represent the low Hubbard band of the spinorbit Mott dimer state.

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Intensity (count s1)

1011

109

285 K 100 K 250 K 250 K 100 K 285 K

107

105

103

101

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 (h 0 4+h)

(h 0 4+h)

0.0

Lattice c() Peak area (arb. unit)

1 8

1 8

0 15

1 5

0 18

0

1 8

0 100 200 300 0 100 200 300

0 100 200 300 0 100 200 300

5.45

5.43

5.41

5.39

c

a

3.96

3.92

3.88

3.84

3.80

Lattice a()

c

a

Temperature (K) Temperature (K)

Figure 2 | Superlattice peaks in IrTe2 in cooling and heating processes. XRD data in cooling (a,c,e) and heating (b,d,f) processes. (a) On cooling, q1/5 (1/5 0 1/5) peaks at 250 K (below TC1/5E280 K) are replaced with the q1/8 (1/8 0 1/8) peaks at 100 K (below TC1/8E180 K). (b) On heating,

the q1/8 peaks are maintained at 250 K and disappear at 300 K (above TH1/8E280 K). Ordering peak intensities as a function of temperature are displayed. Dashed vertical lines indicate phase boundaries. (c) The q1/5 peaks switch into the q1/8 peaks across TC1/8 on cooling. (d) On heating, the q1/8 intensity gradually increases above 200 K mainly due to improvement of the modulation regularity. The in-plane (a) and out-of-plane (c) hexagonal lattice constants are displayed as a function of temperature (e) in cooling and (f) heating processes. The c/a ratio change across the transitions involves partial breaks of Te23 polymeric bonds accompanying Ir average valence changes.

2:6

4:4

3:2

Temperature (K)

The characteristic orbital occupation ratio nxy:nyz:nzx 1:1:1 for

the t2g xy, yz and zx orbitals in the Jeff 1/2 state4 should be

adjusted by the dimerization, which relatively lowers the energy of xy orbital along the dimer direction. A molecular eld calculation for an Ir4 Ir4 dimer shows that the occupation ratio becomes roughly nxy:nyz:nzx 2:1:1 for DB0.70.8 eV, as

predicted in the band calculations for the q1/5 phase15. The Ir 5d to Te 5p charge transfer reduces the density of state at EF to drive the resistivity jump. In the q1/8 phase, the Ir4 fraction increases and the carrier density further decreases.

Real space ordering patterns and phase diagrams. The real space ordering patterns are investigated by using the STM measurements from a cleaved (001) surface as shown in Fig. 5. The stripe type modulations are clearly observable along the [100] direction in the ordered phases. The layered structure naturally yields the Te layer at the surface, and the STM image reects the tunnelling current through the Te 5p states, which is determined by the local charge carrier density and relative vertical heights of

Intensity (arb. unit)

300 K

Ir 4f5/2

Ir 4f7/2

Ir4+ fraction

0.8

0.6

0.4

0.2

0.0

260 K

100 K

Ir4+ / (Ir4+ + Ir3+)

66 64 62 60 58 0 100 200 300

Binding energy (eV)

Figure 3 | Ir valence changes in IrTe2. (a) Ir 4f core-level photoemission spectra at 300 K (HT), 260 K (q1/5) and 100 K (q1/8) are demonstrating Ir

valence changes. Single peaks at 300 K indicate pure Ir3 , while mixed Ir3Ir4 at 260 and 100 K is evident in high binding peaks (that is, high valence state). (b) Ir4 fractions obtained from the Ir 4f core-level spectra are displayed as a function of temperature. The fraction stays at 2/5 (Ir3 :Ir4 3:2) in the q1/5 phase, while it varies in a range from 0.5 to 0.6

in the q1/8 phase. The green lines indicate characteristic ratio of q1/5 (3:2), (3212)-type q1/8 (4:4) and (12212)-type q1/8 (2:6) orderings.

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0.0

0.5

Binding energy (eV)

0

1

2

3

0.8 0.4 0.4

Binding energy (eV)

0

1

2

Binding energy (eV)

0

1

2

1 )

k y (

T=300 K

3

260 K 160 K

High

Low

3

1.5 1.0 0.5 0.0 0.5 1.0

kx (1) ky (1)

0.8 0.4 0.4

0.8 0.4 0.4

ky (1) ky (1)

HT phase

q1/5 phase q1/8 phase

300 K 260 K 160 K

Ir3+Te2 Ir4+Te2

Ir4+Te2 4x 4+x

8

8UHB

3 5

Ir3+Te2

2 5

Ir3+Te2

Intensity (arb. unit)

EF

Ueff

Jeff=

1

2

Jeff=

1

2

Jeff=

1

2

Jeff=

3 2

Jeff=

3 2

Jeff=

3 2

3.0 2.0 0.0

1.0

Binding energy (eV)

Te 5p Te 5p

LHB

Te 5p

Figure 4 | Electronic structure of IrTe2. (a) Fermi surface topology in the G-sheet (kz 5c*) obtained from ARPES at 300 K. It displays a sixfold ower

shape as predicted in a band calculation. (bd) Angle-resolved spectra for the G-cut (red dotted line on a) at different temperatures. At 300 K (HT phase), the spectra are much coherent because the system has no CO. An additional at band at EBB0.8 eV, which represents the spinorbit low Hubbard band (LHB), appears around the G-point at 260 K and is extended at 160 K in the k-space. The spectra below TC1/5 (260 K) become less coherent because of an alternating potential difference of Ir3 and Ir4 as well as the monoclinic distortion. Further broadening at 160 K is attributed to the irregular domain formation of q1/8 charge order. (e) Angle-integrated spectra are displayed. The spectral weight at EF decreases below TC1/5 and does more below TC1/8 (fh) Schematic energy diagrams in the three different phases. At HT phase (f), the spinorbit coupled Jeff 3/2 and Jeff 1/2 bands are fully occupied by six electrons at Ir3 (5d6) sites, while the Te 5p band crosses EF with one hole per formula unit. At q1/5 phase (g), the hole transfers into the Ir 5d and Ir4 (5d5) forms the spinorbit Mott state with the upper and lower Hubbard bands (UHB and LHB) separated by Ueff, which is enhanced by the dimer formation. At q1/8 phase (h), the population of Ir4 dimer increases and the valence uctuation is exhibited as a function of temperature.

Te ions on the surface. The CO occurs at the Ir sites and the Te 5p local charge density and vertical height are affected by the neighbouring Ir states. Thus, the observed modulation in the Te layer reects the Ir3 Ir4 charge order in the underneath Ir layer. The STM image in the q1/5 phase (Fig. 4a) is well explained by the Te 5p charge modulation formed by a (32)-type [Ir3

Ir3 Ir3][Ir4Ir4 ] q1/5 charge order. This pattern represents the two-dimensional charge order in the Ir layer projected from the q1/5 (1/5 0 1/5) three-dimensional order (Supplementary

Fig. 3), and well matches with the Ir arrays determined from the XRD analyses15 (Supplementary Fig. 4). In the q1/8 phase, two types of the 1/8 modulations are observable and understood with the modulations by a (3212)-type [Ir3 Ir3 Ir3 ][Ir4 Ir4 ]

[Ir3][Ir4Ir4 ] order with 4Ir3 :4Ir4 (Fig. 5b) and a (12212)-type [Ir3][Ir4 Ir4][Ir4 Ir4 ][Ir3][Ir4Ir4] with 2Ir3 :6Ir4 (Fig. 5c). The (3212)-type is dominant but the (12212)-type fraction increases on cooling to yield Ir3 :Ir4

(4 x):(4 x) with increasing x as observed in the Ir 4f core-

level study (see Fig. 3b). The Ir 5d valence uctuation admixes the two q1/8 order types and likely degrades the modulation regularity to enhance the scattering background (see Fig. 2a).

Now we compare free energies, F E TS, for the charge

conguration states of the uniform Ir3 (HT), and the Ir3 Ir4 -ordered states with the q1/5 (32)-type, q1/8 (3212)-type and q1/8 (12212)-type (Supplementary Table 1, Supplementary Note 1). Within a mean-eld description, the energy E for each state with the spinorbit Mott dimer states can be simply expressed in terms of the Te 5p (Ir 5d) hole energy ep(d), the

Ir4 Ir4 dimerization energy D, the nearest neighbor intersite dd Coulomb energy Vdd, the pd valence sharing energy Upd and the lattice energy eL (see equation (1) in Methods). The entropy

changes across the transitions are estimated from the specic heat measurements (Supplementary Fig. 5).

In spite of simplicity, the free energy analysis, in which Vdd and

D play critical roles to drive the CO, can successfully reproduce the transitions observed in IrTe2. The resulting phase diagrams are presented for cooling (Fig. 6a) and heating (Fig. 6b) processes. On cooling, the system undergoes consecutive transitions at kBTC1/5/Vdd 0.100 (HT to q1/5) and at kBTC1/8/Vdd 0.063

(q1/5 to q1/8) for (D/2 ep ed)/Vdd 0.98, yielding TC1/5 278 K

and TC1/8 175 K for Vdd 0.24 eV in a good agreement with the

observed TC1/5B280 K and TC1/8B180 K. In the heating process,

we additionally introduced a small q1/8 pinning energy of0.0013Vdd (0.31 meV) per formula unit, which completely suppresses the q1/5 phase and leads to the direct q1/8 to HT phase transition at TH1/8 282 K, 4 K higher than TC1/5 as

observed in the resistivity and specic heat data (see Fig. 1b and Supplementary Fig. 5). In the q1/8 phase, the free energies of the (12212)- and (3212)-type ordered states are close to each other, reecting their coexistence. Suppose the Ir 5d to Te 5p charge transfer energy ed epB0.1 eV, which corresponds to the Ir 5d

binding energy at the Ir3 site (d6-d5), the dimerization energy D is B0.7 eV with Vdd 0.24 eV.

DiscussionIrTe2 exhibits unprecedented physical properties with various unusual features such as the uncompensated thermal hysteretic transition behaviour, multiple charge-ordered states without losing metallicity, anionic polymeric bond breaking, dimerization and charge uctuation. It is noticed that the q1/5 to q1/8 phase

transition is a commensurate to commensurate rst-order

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[Ir3+Ir3+Ir3+][Ir4+Ir4+]

[Ir3+Ir3+Ir3+][Ir4+Ir4+][Ir3+][Ir4+Ir4+]

[Ir3+][Ir4+Ir4+][Ir4+Ir4+][Ir3+][Ir4+Ir4+]

Ir3+:Ir4+ = 2:6

38 pm

0 pm

Ir3+

Ir4+

q1/8 (2:6) q1/8 (2:6)

q1/8 (4:4) q1/8 (4:4)

q1/5

q1/5

HT HT

Cooling Heating

0.98

0.96

0.94

0.00 0.05 0.10 0.00 0.05 0.10 kBT/Vdd kBT/Vdd

(/2 + [afii9830] p [afii9830] d)/V dd

Te

C

/8 T1

T1

T1

C

/5

H

/8

Ir4+dimer Ir3+:Ir4+ = 3:2

(32)

Figure 6 | Phase diagrams of IrTe2. Phase diagrams obtained from free energy analyses for (a) cooling and (b) heating. Model parametersTe 5p energy (ep), Ir 5d energy (ed), dimer formation energy (D) and temperature (T)are renormalized with an intersite Coulomb interaction (Vdd).

Blue and pink regions denote the non-ordered HT and q1/5 ordered phases, respectively. Light and dark green regions represent q1/8 (4:4) and q1/8 (2:6) ordered phases with the (3212)- and (12212)-type charge orders, respectively.

53 pm

65 pm

0 pm

0 pm

(3,212)

(12,212)

Ir3+:Ir4+ = 4:4

Methods

Single-crystal preparation and transport measurements. High-quality IrTe2 single crystals were grown by using a chemical vapour transport method from the Te ux. The electrical resistivity and magnetic susceptibility were measured by using commercial physical property measurement system and magnetic property measurement system, respectively. The second transition temperature TC2 is sensitive to the sample quality and varies in a range from 185 to 170 K among the crystals even from a single batch. The second transition is even not observable in the crystals prepared through fast cooling from the growth temperature. We obtained the magnetic signal from a bunch of single crystals (13 mg) grown in a single batch to improve the signal to noise ratio so that it displays a multi-domain behaviour for the second transition in the magnetic susceptibility.

XRD measurements. The superstructure in IrTe2 was investigated by using hard XRD measurement at the 3A beamline in Pohang Light Source with six-circle PSI diffractometer. The photon energy was set to be 10.8 keV (l 1.148 ), a pre-edge

of Ir L3 white line (11.2 keV). The temperature was controlled within 0.5 K. The diffracted photon ux were monitored through a scintillator (NaI:Tl). The order parameters were estimated from the (1/5 0 4 1/5) and (1/8 0 4 1/8) ordering

peak intensities in the q1/5 and q1/8 phases, respectively.

ARPES and STM measurements. For ARPES and STM measurements,the single crystals were cleaved in situ at 300 K in a ultrahigh vacuum better than 8 10 11 Torr by using a post method to expose a clean (001) surface with the

Te layer termination. ARPES was performed at the 4A1 beamline in Pohang Light Source with a Scienta SES-2002 electron spectrometer. We used linearly polarized light in the photoelectron scattering plane. The inner potential was found to be V0 13 eV for the crystal momentum kz 0:512

p Ekin V0 ( 1) along the

crystal c-axis, which yields Ekin 116.89 eV at G(E5c*) point and Ekin 92.33 eV

at A point (E4.5c*) for the lattice parameter c 5.386 . The total energy

resolution was set to be B85 meV. The STM images were obtained in a constant-current mode with the tunnelling current of B0.1 nA. The atomic arrays are drawn by using VESTA software24.

Free energy model analysis. Considering the ordered structures, in which each (1 0 1) plane consists of IrTe6 octahedrons with purely either Ir3 or Ir4 , the system is effectively reduced to a one-dimension (1D) chain along the [1 0 1]

direction. Suppose that the system is a 1D chain with N-unit (IrTe2) cell lattice sites, the energy per unit cell is expressed within a mean-eld description as

E epnp ednd

1

2 ndD

Figure 5 | STM images with atomic arrangements. STM images of each phase are displayed with atomic arrangement. Red and blue spheres represents Ir3 and Ir4 ion, respectively. Two neighbouring Te ions get closer to each other due to the underneath Ir4 Ir4 dimer (blue ellipse).

The lattice distortion changes the height of Te ions, which locates between two dimerized Ir4 ions and results bright signal on STM image. (a) STM image in the q1/5 phase is compared with the atomic arrangements for the(32)-type q1/5 order. (b,c) STM images in (3212)-type q1/8 phase and (12212)-type q1/8 phase are displayed with relevant atomic arrangement.

The Ir4 ions always appear in pair (diamagnetic dimer formation).

transition and can be considered as a rare harmless stair case22, distinguishable from the commonly observed devils stair case23. The commensurate q1/8 phase seems to be pinned by the lattice, and directly transits into the HT phase without appearance of the q1/5 phase on heating. The unique behaviour in IrTe2 is driven by the localized spinorbit Mott dimer states. The results offer a novel electronic paradigm, in which localized charge-ordered states interact with conduction electrons introduced by the large SOC and the interplay between SOC and Coulomb interaction plays essential roles. Pd or Pt doping, introducing additional electrons, suppresses the charge order and the system becomes a superconductor at LT1113. It indicates that the superconducting order competes with the charge order, similarly as in the cuprates13 although the mechanism can be different, and suggests a possibility for realization of superconductivity involving the spinorbit Mott state.

1N Vdd X

N

i1

ndindi1 Udpnpnd eL; 1

where np(d) denote the average number of the Te 5p (Ir 5d) holes. The d hole number at the i-site is set to be ndi 0 for Ir3 and ndi 1 for Ir4 , and the total

number of holes is constrained to be one, that is, np nd 1.

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Acknowledgements

We appreciate the kind support of S.-Y. Park for the XRD measurements. This work was supported by the National Creative Initiative (2009-0081576) and Max Plank POSTECH/ KOREA Research Initiative (2011-0031558) programme through NRF by MSIP of Korea. J.S.K. is also supported by Basic Pesearch Program (2012-013838) through NRF by MSIP of Korea. K.-S.K. is also supported by Basic Research Programs (2012R1A1B3000550 and 2011-0030785) through NRF by MSIP of Korea and by TJ Park Science Fellowship.H.-S.K., T.-H.K., and H.-W.Y. are supported by Institute for Basic Science (IBS) in Korea. The work at Rutgers University was supported by the NSF (NSF-DMREF-1233349) of US. The Pohang Accelerator Laboratory is supported by POSTECH and MSIP of Korea.

Author contributions

K.-T.K. and T.-Y.K. carried out XRD. K.-T.K., H.-D.K., H.-H.L., and D.-H.L. performed the photoemission spectroscopies. J.-J.Y. and S-W.C. synthesized the crystals. M.J.E. andJ.-S.K. performed the magnetic measurements. R. G., K.-S.K. and J.-H.P. developed the free energy theoretical models. H.-S.K., T.-H.K. and H.-W.Y. performed STM. K.-T.K. and J.-H.P. analysed the data and wrote the manuscript. J.-H.P. initiated and supervised the research.

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How to cite this article: Ko, K.-T. et al. Charge-ordering cascade with spinorbit Mott dimer states in metallic iridium ditelluride. Nat. Commun. 6:7342doi: 10.1038/ncomms8342 (2015).

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