Hadrien Mayaffre

Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa2Cu3Oy.

Electronic charges introduced in copper-oxide (CuO2) planes generate high-transition-temperature (Tc) superconductivity but, under special circumstances, they can also order into filaments called stripes. Whether an underlying tendency towards charge order is present in all copper oxides and whether this has any relationship with superconductivity are, however, two highly controversial issues. To uncover underlying electronic order, magnetic fields strong enough to destabilize superconductivity can be used. Such experiments, including quantum oscillations in YBa2Cu3Oy (an extremely clean copper oxide in which charge order has not until now been observed) have suggested that superconductivity competes with spin, rather than charge, order. Here we report nuclear magnetic resonance measurements showing that high magnetic fields actually induce charge order, without spin order, in the CuO2 planes of YBa2Cu3Oy. The observed static, unidirectional, modulation of the charge density breaks translational symmetry, thus explaining quantum oscillation results, and we argue that it is most probably the same 4a-periodic modulation as in stripe-ordered copper oxides. That it develops only when superconductivity fades away and near the same 1/8 hole doping as in La2−xBaxCuO4 (ref. 1) suggests that charge order, although visibly pinned by CuO chains in YBa2Cu3Oy, is an intrinsic propensity of the superconducting planes of high-Tc copper oxides.

Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy

The pseudogap regime of high-temperature cuprates harbours diverse manifestations of electronic ordering whose exact nature and universality remain debated. Here, we show that the short-ranged charge order recently reported in the normal state of YBa2Cu3Oy corresponds to a truly static modulation of the charge density. We also show that this modulation impacts on most electronic properties, that it appears jointly with intra-unit-cell nematic, but not magnetic, order, and that it exhibits differences with the charge density wave observed at lower temperatures in high magnetic fields. These observations prove mostly universal, they place new constraints on the origin of the charge density wave and they reveal that the charge modulation is pinned by native defects. Similarities with results in layered metals such as NbSe2, in which defects nucleate halos of incipient charge density wave at temperatures above the ordering transition, raise the possibility that order–parameter fluctuations, but no static order, would be observed in the normal state of most cuprates if disorder were absent.

Emergence of charge order from the vortex state of a high-temperature superconductor

Evidence is mounting that charge order competes with superconductivity in high Tc cuprates. Whether this has any relationship to the pairing mechanism is unknown as neither the universality of the competition nor its microscopic nature has been established. Here, we show using nuclear magnetic resonance that charge order in YBa2Cu3Oy has maximum strength inside the superconducting dome, similar to compounds of the La2-x(Sr,Ba)xCuO4 family. In YBa2Cu3Oy, this occurs at doping levels of p=0.11-0.12. We further show that the overlap of halos of incipient charge order around vortex cores, similar to those visualised in Bi2Sr2CaCu2O8+δ, can explain the threshold magnetic field at which long-range charge order emerges. These results reveal universal features of a competition in which charge order and superconductivity appear as joint instabilities of the same normal state, whose relative balance can be field-tuned in the vortex state.

Controlling Luttinger liquid physics in spin ladders under a magnetic field.

We present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 (BPCB) consisting of weakly coupled spin-1/2 Heisenberg antiferromagnetic ladders. Treating ladders in the gapless phase as Luttinger liquids, we are able to fully account for (i) the magnetic field dependence of the nuclear spin-lattice relaxation rate T1(-1) at 250 mK and for (ii) the phase transition to a 3D ordered phase occurring below 110 mK due to weak interladder exchange coupling. BPCB is thus an excellent model system where the possibility to control Luttinger liquid parameters in a continuous manner is demonstrated and the Luttinger liquid model tested in detail over the whole fermion band.

Homogeneous vs. inhomogeneous coexistence of magnetic order and superconductivity probed by NMR in Co- and K-doped iron pnictides

In Ba(Fe0.95Co0.05)2As2 all of the 75As NMR intensity at the paramagnetic resonance position vanishes abruptly below TonsetSDW=56 K, indicating that magnetic (spin-density wave) order is present in all of the sample volume, despite bulk superconductivity below Tc=15 K. The two phases thus coexist homogeneously at the microscopic scale. In Ba0.6K0.4Fe2As2, on the other hand, the signal loss below TonsetSDW75 K is not complete, revealing that magnetic order is bound to finite-size areas of the sample, while the remaining NMR signal shows a clear superconducting response below Tc=37 K. Thus, the two phases are not homogeneously mixed, at least for this potassium concentration. For both samples, spatial electronic and/or magnetic inhomogeneity is shown to characterize the NMR properties in the normal state.

77Se NMR Evidence for the Jaccarino-Peter Mechanism in the Field Induced Superconductor, λ-(BETS)2FeCl4

We performed 77 Se NMR on a single crystal sample of the field-induced superconductor λ-(BETS) 2 FeCl 4 . Our result obtained in the paramagnetic state provide a microscopic insight on the exchange interaction J between the spins s of the BETS π conduction electrons and the Fe localized d spins S . The absolute value of the Knight shift K decreases when the polarization of the Fe spins increases. This reflects the “negative” spin polarization of the π electrons through the exchange interaction J . The value of J has been estimated from the temperature and the magnetic field dependence of K and found to be in good agreement with that deduced from transport measurements [Balicas et al. : Phys. Rev. Lett. 87 (2001) 067002]. This provides direct microscopic evidence that the field-induced superconductivity is due to the compensation effect predicted by Jaccarino and Peter [Phys. Rev. Lett. 9 (1962) 290]. Furthermore, an anomalous broadening of the NMR line has been observed at low temperatures, which suggests...

Emergence of Orbital Nematicity in the Tetragonal Phase of BaFe2(As1−xPx)2

We report on 75As-NMR measurements in single crystalline BaFe2(As0.96P0.04)2 for magnetic fields parallel to the orthorhombic [110]o and [100]o directions above the structural transition temperature TS \( \simeq \) 121 K. A large difference in the linewidth between the two field directions reveals in-plane anisotropy of the electric field gradient, even in the tetragonal phase. This provides microscopic evidence of population imbalance between As-4px and 4py orbitals, which reaches |nx − ny|/|nx + ny| ∼ 15% at T → TS and is a natural consequence of the orbital ordering of Fe-3dxz and dyz electrons. Surprisingly, this orbital polarization is found to be already static near room temperature, suggesting that it arises from the pinning of anisotropic orbital fluctuations by disorder. The effect is found to be stronger below ∼160 K, which coincides with the appearance of nematicity in previous torque and photoemission measurements. These results impose strong constraints on microscopic models of the nematic state.

Attractive Tomonaga-Luttinger liquid in a quantum spin ladder.

We present NMR measurements of a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder compound (C7H10N)2CuBr4 under magnetic fields up to 15 T in the temperature range from 1.2 K down to 50 mK. From the splitting of NMR lines, we determine the phase boundary and the order parameter of the low-temperature (three-dimensional) long-range-ordered phase. In the Tomonaga-Luttinger regime above the ordered phase, NMR relaxation reflects characteristic power-law decay of spin correlation functions as 1/T1∝T(1/2K-1), which allows us to determine the interaction parameter K as a function of field. We find that field-dependent K varies within the 1<K<2 range, which signifies attractive interaction between the spinless fermions in the Tomonaga-Luttinger liquid.

Uniform and staggered magnetizations induced by Dzyaloshinskii-Moriya interactions in isolated and coupled spin- 1 ∕ 2 dimers in a magnetic field

We investigate the interplay of Dzyaloshinskii-Moriya interactions and an external field in spin-

Quantum-critical spin dynamics in quasi-one-dimensional antiferromagnets.

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