Emergent Nematic State in Iron-based Superconductors S. Kasahara1,2, H.J. Shi2, K. Hashimoto2, S. Tonegawa2, Y. Mizukami2, K. Sugimoto3, T. Fukuda4, A. Nevidomskyy5, T. Terashima1, T. Shibauchi2, Y. Matsuda2 1. Thank you Mr. Chairman. First I would like to thank the organizers for this opportunity. I am going to talk on the electronic nematic state which appears in the iron-based high-temperature superconductors. I’m Kasahara from kyoto university and here are my collaborators, particularly Shi hongjie san, who is now graduating master course, had made a great contribution on the magneto-torque measurements. 1) Research Center for Low Temperature & Materials Sciences, Kyoto University 2) Department of Physics, Kyoto University 3) Japan Synchrotron Radiation Research Institute, SPring-8 4) Quantum Beam Science Directorate, JAEA SPring-8 5) Department of Physics and Astronomy, Rice University,

Outline *Introduction: High Temperature Superconductivity in Fe-pnictides & Possible Nematic State in This Class of Materials *Experimental Magnetic Torque Measurements Single Crystalline Synchrotron XRD *Results & Discussion Evidence for the Electronic Nematic State 2. Here is the outline of my talk. First I would like to introduce the High Temperature Superconductivity in Iron-pnictides, which are actually the second generation materials showing high Tc superconductivity other than cuprates, Then I will introduce you the possible nematic state, which is the novel electronic state in the condensed matter physics, and its presence is suggested in the iron-baesd superocnductors. After introducing our experimental methods, I would show you the evidence for the nematic order in this class of materials. *Summary

Superconductivity in Fe-Pnictides ― Discovery Tc ~ 55 K Y. Kamihara, et al., JACS, 130, 3296 (2008). Fe-pnictides LaFeAs(O,F) (“1111”) 3. Here is a historical plot of the superconducting transition temperature Tc, below there the materials undergo superconducting sate. The very first discovery of the superconductivity goes back to 1911, and there had been only the conventional superconductors which show superconductivity only at low temperatures. The first high-temperature superconductivity in cuprates is found in 1986, whose Tc is now about 160 K. After some gap after the cuprates, the superconductivity in Fe-pnicitides is found in LaFePO, then their high-temperature superconductivity is triggered by the discovery of Florin doped LaFeAsO in 2008. Their Tc is now up to 55K, which is actually the highest other than cuprates and this class of materials is thought as a second generation system of the high temperature superconductivity. The Second Generation Materials of High-Tc Superconductivity H. Takahashi et al., Nature 453, 376 (2008).

Superconductivity in Fe-Pnictides ― Family Tc ~ 55 K “1111” “122” Fe-pnictides “111” 3. Up to now, several Fe-based materials are found to show superconductivity, which crystallize in the different structures. The common feature in this class of materials is they all have the tetrahedral networks which is based on the 2 dimensional square lattice of the Fe atoms and , The Second Generation Materials of High-Tc Superconductivity “42622” “11”

Superconductivity in Fe-Pnictides ― Family 2D square lattice of Fe-atoms From c-axis Fe “1111” “122” Pnictogen (Chalcogen) “111” 3.5 Up to now, several Fe-based materials are found to show superconductivity, which crystallize in the different structures. The common feature in this class of materials is that they all have the tetrahedral networks which is based on the 2-dimensional square lattice of the Fe atoms, as we can see in their top view from the c-axis, and Pnictogen atoms are placed above and below the Fe-plane as you can see in the view from the a-axis. From a-axis Fe “42622” Pnictogen (Chalcogen) “11”

Superconductivity in a close proximity to magneto-structural order. Phase Diagram Parent compounds Structural transition (Ts) & AFM transition (TN) “1111” “122” 4. In most Fe-based superconductors, they commonly have the parent phase which shows the magneto-structural transition at low temperatures. The transition is suppressed by chemical doping or applying pressure, then in the close proximity to the ordered state superconducting phase appears. H. Luetkens et al., Nature Materials 8, 305 (2009). S. Nandi et al., PRL 104, 057006 (2010). The magneto-structural transition is suppressed by doping or applying pressure. Superconductivity in a close proximity to magneto-structural order.

Phase Diagram Parent compounds Structural transition (Ts) & AFM transition (TN) “1111” “122” Understanding the underlying physics of spin/orbital & its connection to the superconductivity is particularly important. 4.5 In most Fe-based superconductors, they commonly have the parent phase which shows the magneto-structural transition at low temperatures. The transition is suppressed by chemical doping or applying pressure, then in the close proximity to the ordered state superconducting phase appears. So therefore, the phase diagram suggests that understanding the physics of spin/orbital and its connection to the superconductivity is of primal importance. H. Luetkens et al., Nature Materials 8, 305 (2009). S. Nandi et al., PRL 104, 057006 (2010). The magneto-structural transition is suppressed by doping or pressure. Superconductivity in a close proximity to magneto-structural order.

Phase Diagram Symmetry Breaking Parent compounds Structural transition (Ts) & AFM transition (TN) High-T Low-T “122” Ba Ba Tetragonal Paramagnetic Orthorhombic. Antiferromagnetic 5. In the parent phase, it is know that the system is paramagnetic at high temperature and takes the tetragonal crystal symmetry, On the other hand, it undergoes Antiferromagnetic-orthorhombic phase at low temperatures, where the stripe type antiferromagnetism appears. the system spontaneously four fold symmetry and takes the ground state which has the lower symmetry. Obviously, understanding the origin of the magneto-structural transition is important for the understanding of pnictides. S. Nandi et al., PRL 104, 057006 (2010). Fe Symmetry Breaking Stripe type AFM

Good nesting between hole and electron sheets Theoretical approach: Itinerant Picture Fermi Surface Five-fold degenerate Fe 3d orbitals participate: XZ/YZ, XY, 3Z2-R2, X2-Y2 Multiband electronic structure with well-separated hole and electron sheets Good nesting between hole and electron sheets Original BZ Original BZ Unfolded BZ electron Q ~ (π,π) 6.5 The nesting between the hole and electron induces spin-density wave, which has the wave vector along Q = (pi,pi) and this corresponds to the stripe type modulation of the antiferromagnetic state. hole D.J. Singh and M.H. Du, Phys. Rev. Lett. 100, 237003 (2008). K. Kuroki et al., New J. Phys. 11, 025017 (2009).

Electronic Nematic State Theoretical approach: Localized Picture Frustration between J1 and J2 and its removal by orbital ordering J1a=J1b J1a<J1b J1a>J1b Lv et al., PRB 80, 224506 (2009). PRB 82, 045125 (2010). Broken Rotational Symmetry Chen et al., PRB 80, 180418(R) (2009). Electronic Nematic State 7. Another approach is the localized picture where we consider the interaction of the iron square lattice. For a square lattice, the ground state is expected to have this configuration, which is not the stripe type observed in the real system. So something is different. The idea is that when J1 and J2 are close, some frustration exist in the triangular lattice and to remove this frustration, the electronic state can spontaneously lower its symmetry. For example, it is proposed that the polarization of the dxz and dyz orbitals can remove this frustration. Such an orbital ordering can proceed the magneto-structural transition and could be their origin. We note that the ordering breaks rotational symmetry at high temperatures, and this is called as an electronic nematic state in analogy to the liquid crystals. Nematic & Smectic in Liquid Crystals E. Fradkin et al., Science 327, 155 (2010). (Wikipedia)

Experiments Suggesting the Electronic Nematic State Experiments Suggesting the Nematic State Resistivity J. Chu et al. Science (2010). ARPES M. Yi et al., PNAS (2011). BaFe2As2 Ba(Fe0.975Co0.025)As2 rb > ra above Ts 8. Experimentally there are some reports suggesting the possible nematic state above the magneto-structural transition. In the detwinned samples with applying uniaxial stress, it is reported that the resistivity along a and b axes are much different and the in-plane anisotropy appears even above the structural transition temperatures. Also in the ARPES of detwinned samples, significant difference in the dxz and yz orbitals is reported. These experiments suggest possible electronic nematic state above the magneto-structural transition. However, it is of course the problem that the detwiining by uniaxial stress may already break the tetragonal symmetry. Finite in-plane anisotropy above Ts in detwinned crystals.

Questions on the Electronic Nematic State 1. Intrinsic? 2. Thermodynamic phase? 3. Connections to the Magneto-Structural transition and Superconductivity? Electronic Nematic Ultra-Precise Torque Magnetometry & Single Crystalline Synchrotron XRD 9. Now We have several questions for the possible electronic nematic state in iron pnictides. 1stly, if this is intrinsic or not, and to confirm this, we need to examine the nematic state without uniaxial pressures. 2ndly, whether this is a thermodyanamic phase or not. So we need thermodyanmic probe to detect the electronic nematic state. 3rdly, what is the connection to the magnet-structural transition and also the connection to the superconductivity. So to under those questions, we have performed ultra-precise torque magnetometry and synchrotoron XRD analysis for tiny single crystalline crystals.

Change in the piezoresistance Experiment 1: Magnetic torque measurements Micro-piezoresistive cantilever torque 5x10-12 e.m.u. Very high sensitivity SQUID 10-8 e.m.u. (at m0H=4T) t : magnetic torque V: sample volume M: magnetization H: applied Field Change in the piezoresistance Magnetic Torque Thermodynamic Quantity 10. The magnetic torque is a thermodynamic quantity which is defined by M cross H. In our experiments, we use micro-piezoresistive cantilever to measure the torque. We put a tiny single crystal on the top of the lever, then rotate it in a magnetic field. Since the resistance value of the piezo-lever changes due to the magnetic torque, we are able to measure the torque by reading the pieze resistance. This enable us very precise measurements which exceeds four orders beyond the commercial SQUID magnetometer.

Experiment 1: Magnetic torque measurements q scan f scan a b c t  b c a H H Field Rotation within the ac-plane Field Rotation within the ab-plane 11. There are roughly two different measurements for the torque magnetometry. One is the ordinal measurement, called theta scan, which is already appeared in this morning and examine the out-of-plane anisotropy of the susceptibility. Another one is the what we call phi scan. If we put the sample vertically on the lever and then rotate the field within the plane, we can examine the in-plane anisotropy of the susceptibility whose where magnetic torque is expressed by this equation.

Direct probe of the In-plane Anisotropy without detwining Experiment 1: Magnetic torque measurements Preserved tetragonal symmetry caa = cbb, cab = 0 t2f = 0 f scan b c a H t Preserved C4 Symmetry f p/2 Broken rotational symmetry caa ≠ cbb, or cab ≠ 0 t2f ≠ 0 t Broken C4 Symmetry f Field Rotation within the ab-plane 12. This torque phi scan provides stringent test for the rotational symmetry breaking. Because the magnetic torque is expressed like this, when the system preserves tetragonal symmetry, the susceptibility in a and b are equivalent so the first term should be zero. Also the off-diagonal component of the susceptibility is also zero for the preserved tetragonal symmetry. Thus, there is no 2 fold oscillation in the torque signal. On the other hand, if the rotational symmetry is broken, there appears the difference between chi_aa and chi_bb or finite-offdiagonal chi_ab. This leads to the oscillations in the torque signal with the period of pi. Therefore, this provides a direct probe for the in-plane anisotropy. We also note that by putting a tiny crystal, we can examine the in-plane anisotropy without detwining. p Direct probe of the In-plane Anisotropy without detwining

Experiment 1: Magnetic torque measurements Vector magnet and mechanical rotator system We can rotate H continuously within the ab plane with a misalignment less than 0.02 deg. t : magnetic torque V: sample volume M: magnetization H: applied Field Single crystal Thermodynamic Quantity b c a H 13. In the experiments, we put the sample as in this picture, and then we apply the field precisely within the ab-plane.

Experiment 2: Single Crystalline Synchrotron XRD BL02B1 14. Another experiment we run is the single crystalline synchrotron X-ray diffractions. The experiments are performed at spring-8, where w use a large cylindrical imaging-plate, which covers the very high angle of the 2theta values.

Experiment 2: Single Crystalline Synchrotron XRD BL02B1 (h h 0)T 14.5 Another experiment we run is the single crystalline synchrotron X-ray diffractions at spring-8. When the system undergoes orghorhombic phase, it is known that this structural transition accompanies twinning of the orhthorhmbic domains, which leads to the splitting of the Bragg peak. Here we analyze the temperature dependence of the higher order peaks such as tetragonal (7 7 0) or (8 8 0) which is sensitive to the orthorhombic distortions. We also use a large cylindrical imaging-plate, which covers the high 2theta values, which also enables the experiments sensitive to the tiny distiortions. Equipped with a large cylindrical image-plate camera 2q values: -60 deg < 2q < 145 deg (350 mm x 683 mm) Higher order peaks (7 7 0)T or (8 8 0)T Sensitive experiments to the orthorhombic distortions.

System: BaFe2(As1-xPx)2 An ideal system to study Iron-pnictides TSDW Tcon x = 0 0.07 0.14 0.20 0.23 0.27 0.33 0.41 0.56 0.64 0.71 BaFe2(As1-xPx)2 Paramagnetic -Tetragonal Antiferromagnetic -Orthorhombic Superconducting SK et al., PRB 81, 184519 (2010). H. Shishido et al., PRL 104, 057008 (2010). ・Clear Anomalies at Ts & TSDW 15. As a target system, we chose phosphorous doped Ba122 whose resistivity is presented here, and shows representative phase diagram of the Fe-pnictides. One of the advantage of this system is the clear anomalies related to the magneto-structural transitions. Also we note that very pure single crystals, which are clean and homogeneous, are available in this system, as evident by the quantum oscillation in the wide range of substitutions. So we believe this is an ideal system to study Fe-pnictides. ・Pure crystals are available Quantum oscillations are observed in a wide range (0.38 < x < 1.0) An ideal system to study Iron-pnictides

Data are omitted because they are unpublished.