Giacomo Prando Phase Diagrams of REFeAsO 1-x F x Materials. Macroscopic and Nanoscopic Experimental Investigation

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3 Giacomo Prando Phase Diagrams of REFeAsO 1-x F x Materials Macroscopic and Nanoscopic Experimental Investigation

4 Copyright MMXIII ARACNE editrice S.r.l. via Raffaele Garofalo, 133/A B Roma (06) ISBN I diritti di traduzione, di memorizzazione elettronica, di riproduzione e di adattamento anche parziale, con qualsiasi mezzo, sono riservati per tutti i Paesi. Non sono assolutamente consentite le fotocopie senza il permesso scritto dell Editore. I edizione: maggio 2013

5 A Lara e alla mia famiglia

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7 «E cos è questa?» domandò vivacemente Guglielmo toccando una pietra che giaceva sullo scaffale. «Questa? Mi è stata donata tempo fa. Credo sia lopris amatiti o lapis ematitis. Pare abbia varie virtù terapeutiche, ma non ho ancora scoperto quali. La conosci?» «Sì,» disse Guglielmo, «ma non come medicina.» Trasse dal saio un coltellino e lo appressò lentamente alla pietra. Come il coltellino, mosso dalla sua mano con estrema delicatezza, giunse a poca distanza dalla pietra, vidi che la lama compiva un movimento brusco, come se Guglielmo avesse mosso il polso, che invece aveva fermissimo. E la lama aderì alla pietra con un lieve rumore di metallo. «Vedi,» mi disse Guglielmo, «è un magnete.» «E a che serve?» chiesi. «A varie cose, di cui ti dirò (... )» U. Eco, Il nome della rosa La scienza, come la poesia, si sa che sta ad un passo dalla follia (... ) L. Sciascia, La scomparsa di Majorana Sapientia, cum probitate morum conjuncta, humanae mentis perfectio Motto of Collegio Ghislieri, Pavia

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9 Contents List of Figures 13 List of Tables 23 Preface by Prof. Pietro Carretta 25 Preface by Prof. Philippe Mendels 27 Preface by the Author 29 Introduction to Fe-based pnictide and chalcogenide materials Pnictide and chalcogenide materials. Overview of the main features Structural properties of RETmPnO compounds Magnetic RETmPnO compounds and f d interaction High-T c superconductivity in REFeAsO 1 xf x compounds and in other pnictide and chalcogenide materials Problems associated with the synthesis of REFeAsO 1 xf x Outline of the dissertation I Properties of superconductivity in REFeAsO 1 x F x deduced by measurements of macroscopic susceptibilities 53 I Macroscopic dc susceptibility of REFeAsO 1 xf x compounds 55 I.1 Contributions to dc magnetization in 1111 materials I.1.1 Static magnetization in non-superconducting CeFeAsO 1 xf x I.1.2 Static magnetization in superconducting CeFeAsO 1 xf x I.1.3 Coexistence region for spin density wave and superconductivity I.2 Superconducting phase fluctuations for T T c I.2.1 The model of phase superconducting fluctuations I.2.2 Experimental results I.3 Conclusions

10 10 Contents II Phase diagram of vortices in REFeAsO 1 xf x superconductors 77 II.1 Phase diagram of flux lines and depinning energy barriers II.1.1 Preliminary magnetic characterization of the samples II.1.2 Temperature dependence of the upper critical field H c II.1.3 Irreversibility line H irr(t ) II.1.4 Depinning energy barriers U 0(H) pwd II.2 Analysis of the experimental results II.2.1 Anisotropic Ginzburg-Landau model of collective pinning II.2.2 Linking data relative to different H-regimes II.2.3 Results of the analysis II.3 Conclusions II Local features of magnetism in REFeAsO compounds scanned by chemical substitutions and external hydrostatic pressure 101 III Phase diagram of CeFeAsO 1 xf x by means of µ + SR measurements 103 III.1 µ + SR investigation of CeFeAsO 1 xf x III.1.1 Undoped sample III.1.2 Lightly doped x =0.03 and x =0.04 samples III.1.3 Coexistence of spin density wave and superconductivity for x = III.1.4 Superconductivity for x = Comparison with SmFeAsO 0.8F III.1.5 Phase diagram of CeFeAsO 1 xf x III.2 Conclusions IV Magnetism of rare earth ions in CeFeAsO 1 xf x studied by means of 19 F-NMR 127 IV.1 19 F-NMR across the electronic phase diagram IV.1.1 Line-shape and paramagnetic shift. Experimental results IV.1.2 Theory and simulation of the 19 F-NMR absorption line IV.1.3 Spin-lattice relaxation rate IV.1.4 Phase diagram IV.2 Conclusions V Effects of hydrostatic pressure on REFeAsO 1 xf x compounds 143 V.1 µ + SR measurements upon applied hydrostatic pressure V.2 Crossover between magnetism and superconductivity in REFeAsO 1 xf x (RE = La, Ce and Sm) V.2.1 Experimental results on the La-based sample V.2.2 Experimental results on the RE-based samples (RE = Sm, Ce) V.2.3 Effects of pressure in superconducting CeFeAsO 0.94F V.3 Conclusions

11 Contents 11 III Conclusions and open perspectives 157 IV Appendices 165 A Basics of nuclear magnetic resonance 167 A.1 Larmor precession and magnetic resonance A.2 Static local magnetic fields and paramagnetic shift A.3 Dynamical properties and relaxation times A.3.1 Bloch s equations. T 1 and T 2 relaxation times A.3.2 Statistical description of the spin-lattice relaxation rate A.3.3 Microscopic interpretation. Relaxation mechanisms B NMR quantification of real F content 177 C Basics of µ + spin spectroscopy 179 C.1 Positive muons µ +. Production, implantation and decay C.2 Zero magnetic field measurements C.2.1 Static distributions C.2.2 Dynamical processes C.3 Longitudinal magnetic field measurements D Physical Constants 189 Bibliography 191 Acknoledgements 207

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13 List of Figures 1 Sketchy crystalline structures of typical Fe-based pnictide and chalcogenide compounds (reprinted from [Lum10] with permissions both of Authors and of IOP Publishing. Copyright IOP Publishing. All rights reserved). From left to right: 1111, 122, 111 and 11 families. As Fe As and Se Fe Se tri-layers are drawn with green and blue balls Upper image: crystallographic structure of RETmPnO compounds at room T around the tetragonal primitive cell represented by the black box (space group P 4/nmm). Tm and Pn ions are indicated with ochre and green spheres, respectively. The red dots and the big violet spheres represent the O 2 ions and the RE 3+ ions, respectively. Lower image: view along the c-axis of the same image plotted in the upper image. Both the images have been drawn by using the software VESTA, see [Mom08] Phase diagrams for the SmFeAsO 1 xf x family reporting quite contradictory behaviours for the x-dependence of the structural transition temperature. The equivalent labels T s and T T-O are used to refer to such critical temperature in the left graph (reprinted from [Mar09] with permissions both of Authors and of the American Physical Society, Copyright 2009 from the American Physical Society) and right graph (reprinted from [Mar11] with permissions both of Authors and of the American Physical Society, Copyright 2011 from the American Physical Society), respectively Left graph (reprinted from [Luo10] with permissions both of Authors and of the American Physical Society, Copyright 2010 from the American Physical Society): phase diagram of the magnetic ground states for both Fe and Ce sublattices in CeFeAs 1 xp xo. Left graph, inset: comparison of the different scales for the overall exchange constant among RE ions and the Kondo temperature represented as blue and red lines, respectively. Right graph (reprinted from [Jia09] with permissions both of Authors and of IOP Publishing. Copyright IOP Publishing. All rights reserved): phase diagram for the ground state of BaFe 2(As 1 xp x) 2 where the progressive As 1 xp x substitution suppresses the magnetic phase and drives the system towards a superconducting state for x 0.2. Right graph, inset: power-law exponent for the T -dependence of resistivity ρ in the normal state

14 14 List of Figures 5 Left graph (reprinted from [Arm10] with permissions both of Authors and of the American Physical Society, Copyright 2010 from the American Physical Society): sketchy phase diagram of the electron-doped cuprate superconductors RE 2 xce xcuo 4. Right graph (courtesy of Dr. S. Sanna, see also [San09a]): phase diagram of SmFeAsO 1 xf x obtained from µ + SR and magnetization measurements displaying the same phenomenology presented in the case of RE 2 xce xcuo Left graph (reprinted from [Les09] with permissions both of Authors and of the American Physical Society, Copyright 2009 from the American Physical Society): phase diagram of Ba(Fe 1 xco x) 2As 2 obtained from heat-capacity, resistivity and neutron diffraction measurements. Left graph, inset: suppression of the Fe ordered moment with increasing the Co concentration. Right graph (reprinted from [Kat10] with permissions both of Authors and of the Journal of the Physical Society of Japan): phase diagram of Fe 1+ySe xte 1 x obtained from magnetization and neutron scattering measurements. The yellow SG area indicated the emergence of a spin-glass-like phase Left graph: phase diagram of LaFeAsO 1 xf x obtained from µ + SR measurements and displaying a sharp first-order-like crossover between the magnetic and the superconducting phases (courtesy of Dr. H. Luetkens. See also [Lue09]). Right graph: phase diagram obtained from neutron scattering measurements for CeFeAsO 1 xf x, claiming that a quantum critical point is present at x values close to 0.06 (courtesy of Dr. J. Zhao and Prof. P. Dai. See also [Zha08]) Left graph (reprinted from [Lee10] with permissions both of Authors and of the American Physical Society, Copyright 2010 from the American Physical Society): phase diagram for the flux lines in a SmFeAsO 0.85 single crystal obtained by means of magnetoresistivity measurements. Right graph (reprinted from [Pan10] with permissions both of Authors and of the American Physical Society, Copyright 2010 from the American Physical Society): comparison among the irreversibility lines obtained in different cuprate and pnictide superconductors, showing a wide region for the glassy phase of vortices in SmFeAsO 1 xf x Left graph (reprinted from [Dag09] with permissions both of Authors and of the American Physical Society, Copyright 2009 from the American Physical Society): T -dependence of the superconducting gaps from Andreev-reflection spectroscopy in SmFeAsO 1 xf x. Right graph (reprinted from [Umm09] with permissions both of Authors and of the American Physical Society, Copyright 2009 from the American Physical Society): reduced Brillouin zone reporting hole (1, 2) and electron bands (3) employed in the modeling of s ± -like superconductivity I.1 Inverse magnetic susceptibility of CeFeAsO 0.96F 0.04 at H = 100 Oe as a function of T (volume units). The continuous red line is a best-fit according to equation (I.1). Upper inset: M vs. H at 2.8 K for CeFeAsO 0.96F The red curve is a best-fit according to a linear function. Lower inset: magnetic susceptibility of CeFeAsO at different applied H in the region of low T

15 List of Figures 15 I.2 FC magnetization of CeFeAsO 0.945F as a function of T (volume units) at different H in the high-h regime (the low-h regime is plotted in the inset). Continuous lines are best-fits according to equation (I.5). The green curves indicate that χ sc is fixed to I.3 Upper graph: M vs. H curve at 40 K for CeFeAsO 0.945F (volume units). The red curve is a best-fit according to a linear function. Upper graph, inset: enlargement at low H values evidencing a component associated with magnetic impurities and saturating at µ 0H 0.5 T. Lower graph: values of M 0 vs. H for CeFeAsO 0.945F after the fitting procedure to M vs. T data according to equation (I.5). Data are plotted after the subtraction of the T -independent saturated contribution associated with magnetic impurities. The red curve is a best-fit according to a linear function. Lower graph, inset: H-dependence of N eff per Ce 3+ ion resulting from the fitting procedure according to equation (I.5). The weak H-dependence should be considered as an artifact from the fitting procedure I.4 Upper graph: M vs. T at different H for optimally-doped SmFeAsO 0.8F 0.2 (FC). The red continuous curves are best-fits according to equation (I.5). The low-t anomalies are related to the AFM ordering of Sm 3+ magnetic moments. Lower graph: values of M 0 = χ 0H vs. H for SmFeAsO 0.8F 0.2 after the fitting procedure to M vs. T data according to equation (I.5). Data are plotted after the subtraction of a T -independent saturated contribution associated with magnetic impurities. The red curve is a best-fit according to a linear function. Lower graph, upper inset: M vs. H curve at 56 K (volume units). The red curve is a best-fit according to a linear function. Lower graph, lower inset: H-dependence of N eff resulting from the fitting procedure according to equation (I.5) I.5 M/H vs. T at H =5Oe for SmFeAsO 0.8F 0.2 (volume units). The presence of a small volume percentage of magnetic impurities is inferred from the separation of ZFC and FC curves already far above T c(0). Inset: linear extrapolation procedure to deduce the value of T c(0) 52.3 K from the FC curve (Copyright 2011 from the American Physical Society) I.6 M vs. T curves for five samples of CeFeAsO 1 xf x across the spin density wave - superconductivity coexistence region of the phase diagram. The measurements were performed at H =5Oe (FC) for all the measurements. The data are shifted along the vertical axis for the sake of clarity, with the only exception of CeFeAsO 0.945F I.7 N eff vs. H estimated by a fitting procedure according to equation (I.5). See also the relative raw experimental curves at H =5Oe displayed in figure I I.8 M vs. H curves for SmFeAsO 0.8F 0.2 at K and 56 K before the subtraction procedures (enlargement in the low-h regime). Inset: isothermal diamagnetic contributions M dia vs. H at K (seetext) I.9 M dia vs. H for SmFeAsO 0.8F 0.2 at representative T values above T c. The curves are obtained after the subtraction procedures described in the text. Continuous lines are best-fits obtained by means of numerical integration of equation (I.9). Inset: T -dependence of H up. The dashed line is a guide for the eye (Copyright 2011 from the American Physical Society)

16 16 List of Figures I.10 Reduced magnetization m c vs. T for SmFeAsO 0.8F 0.2 in the low-h regime. No crossing of curves at T c is observed (Copyright 2011 from the American Physical Society) I.11 m c vs. T for SmFeAsO 0.8F 0.2 in the high-h regime. The crossing of curves at T 53.2 K suggests that in this H-range the GL framework is valid (Copyright 2011 from the American Physical Society) II.1 Left graph: simplified sketchy phase diagram for the superconducting phase in type-ii superconductors (reprinted from [Bla94] with permissions both of Author and of the American Physical Society, Copyright 1994 from the American Physical Society). Right graph: refinement of the phase diagram presented in the left graph with the addition of the irreversibility line, here denoted as B m(t ) (reprinted from [Bla94] with permissions both of Author and of the American Physical Society, Copyright 1994 from the American Physical Society) II.2 Magnetic susceptibility curves (volume units) at H =5Oe (FC) as a function of T for the three samples. Data are plotted after subtracting a linear term roughly accounting for the contribution from impurities (Copyright 2012 from the American Physical Society) II.3 H c2 vs. T/T c(0) curves for the three samples as obtained from M vs. T data. The continuous lines are best-fits to data in the high-h regime according to linear functions II.4 Upper graph: raw data of the imaginary and the real components of χ ac in volume units relative to CeFeAsO 0.945F (upper and lower subgraphs, respectively). Measurements were performed at H ac =1.5 Oe and ν m = 478 Hz and at different applied H (Copyright 2012 from the American Physical Society). Lower graph: raw data for the real component of χ ac vs. T in SmFeAsO 0.8F 0.2 (volume units). Measurements have been performed at H = 250 Oe and ν m = 1488 Hz and at different amplitudes of the alternating magnetic fields H ac = Oe II.5 FLs phase diagram in SmFeAsO 0.8F 0.2. Both the criteria for the determination of H irr(t ) are presented (onset in χ ac: signs, maximum in χ ac at ν m = 37 Hz: signs. H ac =1.5 Oe for all the measurements). The dashed lines are best fits to data according to equation (II.16). The different signs at fixed H are relative to estimates at different ν m. H c2(t ) is denoted by signs (see figure II.3) II.6 Upper graph, upper subgraph: enlargement of raw data presented in the upper graph of figure II.4 for CeFeAsO 0.945F displaying χ ac vs. T curves around T p. Upper graph, lower subgraph: dχ ac/dt vs. T curves, whose maxima clearly display a precise correlation with T p (Copyright 2012 from the American Physical Society). Lower graph: FLs phase diagram relative to the three studied samples (Copyright 2012 from the American Physical Society). Open symbols track H irr(t ) as deduced from the χ ac-criterion at ν m = 37 Hz (dashed-dotted lines are guides for the eye). Full symbols track H c2(t ) as deduced from M vs. T curves (continuous lines are the best-fits reported in figure II.3) II.7 Dependence of 1/T p on ν m in CeFeAsO 0.945F (H ac =1.5 Oe and µ 0H = 1.5 T). The dashed line is a best fit to data according to equation (II.18)

17 List of Figures 17 II.8 H-dependence of U 0(H) pwd in the three investigated samples. Continuous lines are best-fits to data according to a 1/H dependence II.9 3D plot displaying the dependence of U 0(H, T) pwd (blue full circles) on both T and H relatively to LaFeAsO 0.9F 0.1. The projections on the H T plane track H irr(t ) while the projections on the U 0 H plane correspond to data plotted in figure II.8. With the additional points (+ signs) relative to the T - dependence of H c2, the H T plane represents the phase diagram of FLs shown in the lower graph of figure II II.10 H irr(t ) relative to the three samples normalized with respect to the relative value of H c2(0) pwd. Continuous lines are best-fits according to equation (II.34) (Copyright 2012 from the American Physical Society) II.11 Representation of the quantity between curly brackets in equation (II.43) in the low-h limit. The dashed lines are guides for the eye and they are used to extrapolate the intercept values back to H = 0Oe (Copyright 2012 from the American Physical Society) II.12 Collapse of 1/λ 2 ab(0) vs. H data after a proper normalization according to the value of 1/λ 2 ab(0) at H = 250 Oe. Inset: H-dependence of the λ ab (0) values. Open (full) symbols are relative to data from the low-h (high-h) regime III.1 Electrostatic potential of REFeAsO materials (reprinted from [Mae09] with permissions both of Authors and of the American Physical Society, Copyright 2009 from the American Physical Society). The µ + crystallographic site A, equivalent to 1, is positioned right on the FeAs layers III.2 Upper graph: ZF-µ + SR spectra for CeFeAsO. Continuous lines are best-fits according to equation (III.5) and to table III.1. Lower graph: short-t enlargement of the ZF-µ + SR spectra shown in the upper graph III.3 Upper graph: T -dependence of V m for CeFeAsO. The continuous black line is a best-fit function according to equation (III.3). The red filled circles represent λ L (T ). Lower graph: T -dependence of B µ1 (T ) in CeFeAsO measured by a cosine-like fitting to the transversal component of the spectra shown in figure III.2. The continuous line is a best-fit according to equation (III.10). The red full triangles represent λ Tr 1 (T ) III.4 Upper graph: ZF-µ + SR spectra for CeFeAsO 0.97F Continuous lines are best-fits according to equation (III.5) and to table III.1. Lower graph: B µ1 vs. T in CeFeAsO 0.97F 0.03 measured by a Bessel-like fitting to the transversal component of the spectra shown in the upper graph (red full triangles). The continuous red line is a best-fit according to equation (III.10). Lower graph, inset: V m(t ) for CeFeAsO 0.97F The continuous line is a best-fit function according to equation (III.3) III.5 Upper graph: ZF-µ + SR spectra for CeFeAsO 0.96F Continuous lines are best-fits according to equation (III.5) and to table III.1. Lower graph: λ Tr 1 (T ) for CeFeAsO 0.96F Lower graph, inset: V m(t ) for CeFeAsO 0.96F The continuous line is a best-fit function according to equation (III.3) III.6 Upper graph: ZF-µ + SR spectra for CeFeAsO 0.94F Continuous lines are best-fits according to equation (III.5) and to table III.1. Lower graph: λ Tr 1 (T ) in the x = 0.04 and x = 0.06 samples. Lower graph, inset: V m(t ) for CeFeAsO 0.94F The line is a best-fit function according to equation (III.3). 117

18 18 List of Figures III.7 Sketchy representation of the model of phase segregation of superconductivity and magnetism (reprinted from [Par09] with permissions both of Authors and of the American Physical Society, Copyright 2009 from the American Physical Society). The nanoscopic coexistence is realized whether the order-ofmagnitude of the mean distance among magnetic domains (green droplets) is close to d 1 nm, namely the spatial range of the magnetic dipolar field generated by uncompensated Fe moments on the domain walls (red arrows). Under these circumstances, both µ 1- and µ 2-like implanted muons feel a static magnetic local field giving rise to the phenomenology observed in figure III III.8 Upper graph: TF-µ + SR spectra for CeFeAsO 0.94F 0.06 (H = 200 Oe). Upper graph, upper subgraph: data in the paramagnetic regime T >T c. Upper graph, lower subgraph: superconducting mixed regime T <T c. Continuous red lines are best-fits according to equation (III.13). Lower graph: fitting results according to equation (III.13). Lower graph, upper subgraph: λ(t ) for the non-magnetic oscillating term. Lower graph, lower subgraph: B µ(t ) at the µ + site. The red dashed line is a guide to the eye according to a double-exponent mean-field-like function III.9 ZF-µ + SR spectra for CeFeAsO 0.945F Continuous lines are best-fits according to equation (III.5) and to table III III.10TF-µ + SR spectra for CeFeAsO 0.945F (H = 150 Oe). Upper graph: paramagnetic regime at 40 K. Lower graph: mixed regime at 5 K. Continuous red lines are best-fits according to equation (III.12) III.11Upper graph: fitting results for TF-µ + SR spectra of CeFeAsO 0.945F reported in figure III.10 according to equation (III.15). Upper graph, upper subgraph: σ sc vs. T. Upper graph, lower subgraph: B µ vs. T. Lower graph: fitting results for TF-µ + SR spectra of SmFeAsO 0.8F 0.2 (not shown) according to equation (III.15). Lower graph, upper subgraph: σ sc vs. T. Lower graph, lower subgraph: B µ vs. T III.12Phase diagram of CeFeAsO 1 xf x family resulting from the µ + SR measurements reported in this chapter (Copyright 2011 from the American Physical Society). The labels M and SC stands for magnetic spin density wave and superconductivity, respectively, while the meaning of LR and SR is longand short-range order for the magnetic phase, respectively. The x =0.07 sample is not discussed in the thesis since its behaviour is extremely similar to the x = 0.06 one. The point deep into the superconducting region is extracted from the phase diagram reported in [Zha08] IV.1 Main graph: inverse magnetic susceptibility of CeFeAsO 0.965F as a function of T at H = 20 Oe (volume units). The continuous line is a best-fit according to equation (IV.1). Inset: magnetic susceptibility of CeFeAsO 0.95F 0.05 as a function of T at H =5Oe (volume units). The continuous line is a best-fit according to equation (IV.2)

19 List of Figures 19 IV.2 Upper graph: fitting results for the 19 F-NMR absorption line at different representative T for CeFeAsO 0.965F (experimental points are not shown for the sake of clarity). Upper graph, inset: raw data relative to representative T values. Lower graph: shape of the 19 F-NMR line for CeFeAsO 0.95F 0.05 at T = 30 K. The continuous black curve is a best-fit to data according to the function reported in equation (IV.3). The two single contributions are also reported as continuous coloured lines and labelled correspondingly to the relative components of the anisotropic K f tensor IV.3 Main graph: T -dependence for the ab and c components of the K f tensor for all the investigated samples at µ 0H =3.9 T (main graph and inset, respectively) IV.4 Main graph: K ab and K c as a function of the M/H curve reported in figure IV.1 with T as an implicit parameter (data relative to CeFeAsO 0.965F 0.035). The continuous curves are best-fits according to linear functions. The black dashed line roughly accounts for the contribution to K from a transferred contact term IV.5 Main graph: 19 F-NMR resonance line of CeFeAsO 0.965F at T = 45 K and µ 0H = 5 T. The continuous line is a simulation of experimental data according to the procedure explained in the text (partial powder average with π/6 ϕ 5π/6). The dashed line is obtained by extending the powder average procedure to the whole solid angle IV.6 Main graph: recovery laws for CeFeAsO 0.965F at selected T. The continuous curves are best-fits according to a single-exponential function, see equation (IV.22). Inset: enlargement at short-t values displaying the good quality of the fitting procedure IV.7 Main graph: T -dependence of 1/T 1. The black dashed line is guide to the eye according to the trend T 4/3. The two arrows indicate the anomalies associated with the transition to the spin density wave phase. No anomaly is observed in CeFeAsO 0.95F 0.05 and CeFeAsO 0.945F in correspondence to the onset of superconductivity IV.8 Main graph: T -dependence of 1/T 1 in the three investigated samples. The continuous lines are best-fits according to the phenomenological function reported in equation (IV.23). Inset: fitting results for the parameter CF expressed in K degrees. The black dashed line is a linear extrapolation back to x = IV.9 Phase diagram of CeFeAsO 1 xf x after the 19 F-NMR measurements. The labels M and SC stands for spin density wave and superconductivity, respectively. The dashed red line relative to T c in the coexistence region is indicative of some uncertainty in the positioning of the emergence of superconductivity. The point relative to the undoped sample is borrowed from the phase diagram reported in figure III.12 obtained by means of µ + SR on the sample series from the University of Genova. On the other hand, the point deep into the superconducting region is extracted from the phase diagram reported in [Zha08] V.1 The MP35N double-wall piston-cylinder pressure cell developed at the Laboratory for Muon Spin Spectroscopy (Paul Scherrer Institut) and used for µ + SR measurements

20 20 List of Figures V.2 Upper graph: TF-µ + SR spectra for SmFeAsO at P =2.05 GPa (H = 50 Oe). The two curves are relative to T values well below and well above T N K. The continuous lines are best-fits according to the function reported in equation (V.3). Upper graph, inset: short-t enlargement displaying an oscillating transverse signal from the magnetic phase of the sample. Lower graph: ZF- µ + SR spectra for SmFeAsO at P =2.05 GPa. The continuous lines are best fits to data according to the function reported in equation (V.5) while the dashed line is a rough estimate of the contribution from the PC itself. Lower graph, inset: short-t enlargement displaying an oscillating transverse signal from the magnetic phase of the sample V.3 Main graph: magnetic susceptibility of LaFeAsO 0.945F at two different values of applied P (H =5Oe, ZFC, volume units). The label 10 4 GPa corresponds to ambient P conditions with the sample mounted in the unloaded PC. Inset: enhancement of T c upon increasing P estimated from FC curves (not shown). The dashed line is a guide for the eye V.4 V m for LaFeAsO 0.945F at several values of P up to 2.35 GPa. Blue square signs represent measurements at ambient P, where the open symbols are relative to the calibration measurement while the filled ones are relative to the measurement with the sample mounted in the unloaded PC. The continuous lines are best-fits according to equation (V.6). Inset: gradual suppression of T N on increasing P V.5 Main graph: V m for SmFeAsO 0.925F estimated from TF-µ + SR data for several values of P up to 1.6 GPa. The dashed line is a guide to the eye according to equation (V.6). Upper inset: short-t ZF-µ + SR depolarization at ambient P. The continuous red line is a best-fit according to the function reported in equation (V.5). Lower inset: B µ(t ) at the µ + site estimated from ZF-µ + SR data for two values of P. Continuous lines are best-fits according to the function reported in equation (V.9) V.6 Upper graph: V m for CeFeAsO 0.96F 0.04 estimated from TF-µ + SR data. Filled symbols are relative to GPD measurements while open ones are relative to the GPS characterization (already shown in the lower graph of figure III.5, inset). The dashed line is a guide to the eye according to equation (V.6). Upper graph, inset: TF-µ + SR depolarization at 15 K and 100 K at ambient P (sample mounted in the unloaded PC). Continuous lines are best-fits according to equation (V.3). Lower graph: λ Tr vs. T at two different values of P. Open and filled squares are relative to the ambient P measurements at GPS and GPD, respectively. No dependence on the applied P is deduced within the experimental error. Lower graph, inset: ZF-µ + SR spectra at some representative T values for the measurement at 2.35 GPa

21 List of Figures 21 V.7 Upper graph: M/H for CeFeAsO 0.94F 0.06 at two values of P (H =5Oe, ZFC, volume units). Continuous lines are best-fits according to equation (V.10). The label 10 4 GPa corresponds to ambient P with the sample mounted in the unloaded PC. Upper graph, upper inset: T c vs. P estimated from FC curves (not shown). The dashed line is a guide for the eye. Upper graph, lower inset: suppression of the value of the magnetic moment of Ce 3+ ions upon increasing P. Lower graph: V m in CeFeAsO 0.94F 0.06 estimated from TF-µ + SR (see also the lower graph of fig. III.8, lower subgraph). The continuous lines are best-fits according to equation (V.6). Lower graph, inset: B µ vs. T in the superconducting phase from TF-µ + SR (see also the lower graph of figure III.8, lower subgraph). 154 B.1 Integrated intensity of the spin echo as a function of t in SmOF (left graph) and in CeFeAsO 0.93F 0.07 Ge (right graph). Both the measurements are performed at room temperature. The two continuous lines are best-fits of data according to a Gaussian-like decay in SmOF and to a exponential-like decay in CeFeAsO 0.93F 0.07 Ge C.1 ISIS particles accelerator scheme C.2 π + meson decay according to equation (C.1) (reprinted from [Cox87] with permissions both of Author and of IOP Publishing. Copyright IOP Publishing. All rights reserved) C.3 Larmor precession of s µ + around the local magnetic field B (reprinted from [Cox87] with permissions both of Author and of IOP Publishing. Copyright IOP Publishing. All rights reserved) C.4 µ + decay corresponding to the emission of the positron with maximum linear momentum and energy according to equation (C.4) (reprinted from [Cox87] with permissions both of Author and of IOP Publishing. Copyright IOP Publishing. All rights reserved) C.5 µ + asymmetric decay (reprinted from [Cox87] with permissions both of Author and of IOP Publishing. Copyright IOP Publishing. All rights reserved). Curve labeled as a =1: only the positron s maximum emission energy is considered. Curve labeled as a =1/3: the positron emission is averaged on all the possible energies C.6 Position of the detectors of positrons around the sample in the longitudinal configuration (reprinted from [Dal97] with permissions both of Authors and of IOP Publishing. Copyright IOP Publishing. All rights reserved). The position of the µ + spin is rotated by 180 with respect to its initial direction C.7 Zero-field relaxation functions caused by different distributions of static local magnetic fields: (a) Gaussian Kubo-Toyabe, (b) Lorebtzian Kubo-Toyabe (reprinted from [Cox87] with permissions both of Author and of IOP Publishing. Copyright IOP Publishing. All rights reserved) C.8 Depolarization functions caused by a dynamical Gaussian process in the strong collision limit (reprinted from [Dal97] with permissions both of Authors and of IOP Publishing. Copyright IOP Publishing. All rights reserved)

22 22 List of Figures C.9 Effect of the application of an external longitudinal magnetic field in the case of a static distribution of local fields (reprinted from [Dal97] with permissions both of Authors and of IOP Publishing. Copyright IOP Publishing. All rights reserved) C.10 Comparison between the effects of the application of an external longitudinal magnetic field H LF on (a) a static distribution of local magnetic fields of width σ and (b) on a dynamical process with frequency ν ν c (reprinted from [Cox87] with permissions both of Author and of IOP Publishing. Copyright IOP Publishing. All rights reserved)