Magnetism Group

Prof. Amit Keren's Group Technion

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High Tc Superconductivity

Common energy scale for magnetism and superconductivity in the cuprates

One of the most challenging tasks of solid-state physics today is to understand the mechanism for superconductivity in cuprates. These materials, which have a relatively high critical temperature Tc, are based on doped CuO2 planes. Since at zero doping they are antiferromagnets, several theories ascribe their superconductivity to holes interacting via a magnetic medium. Yet the phenomenon of superconductivity begins at doping levels in which magnetism almost disappears, and therefore there is no clear evidence relating the two. Fortunately, there is a narrow doping range in which superconductivity and magnetism, in the form of randomly oriented static spins, co-exist below a critical temperature Tg<Tc. We thus focus on this doping range and examine Tg and Tc in numerous superconducting families. We find that in all cases a common energy scale controls both critical temperatures. This is demonstrated in the figure where we plot both Tc/Tcmax and Tg/Tcmax as a function of holes in the system. In this normalized plot all data points of Tc and Tg, for various materials, collapse into a single curve. This clearly indicates that superconductivity and magnetism in the cuprates share a common energy scale.

We have published the following papers on the subject:

Abstract:
Electronic spin and orbital (dd) excitation spectra of (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy samples aremeasured by resonant inelastic x-ray scattering (RIXS). In this compound, Tc of samples with identical hole dopings is strongly affected by the Ca/Ba substitution x due to subtle variations in the lattice constants, while crystal symmetry and disorder as measured by linewidths are x independent. We examine two extreme values of x and two extreme values of hole-doping content y corresponding to antiferromagnetic and superconducting states. The x dependence of the spin-mode energies is approximately the same for both the antiferromagnetic and superconducting samples. This clearly demonstrates that RIXS is sensitive to the superexchange J even in doped samples. A positive correlation between J and the maximum of Tc at optimal doping (Tcmax) is observed. We also measured the x dependence of the dxy → dx2-y2 and dxz/yz → dx2-y2 orbital splittings. We infer that the effect of the unresolved d3z2-r2 → dx2-y2 excitation on Tcmax is much smaller than the effect of J . There appears to be dispersion in the dxy → dx2-y2 peak of up to 0.05 eV. Our fitting furthermore indicates an asymmetric dispersion for the dxz/yz → dx2-y2 excitation. A peak at ~ 0.8 eV is also observed and attributed to a dd excitation in the chain layer.

Abstract:
We present an investigation of charge-compensated antiferromagnetic (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy single crystals using Raman scattering as well as muon spin rotation. In this system the parameter x controls the Cu-O-Cu superexchange interaction via bond distances and buckling angles. The oxygen content y controls the charge doping. In the absence of doping the two-magnon peak position is directly proportional to the superexchange strength J. We find that both x and y affect the peak position considerably. The Néel temperature determined from muon spin rotation on the same samples independently confirms the strong dependence of the magnetic interaction on x and y. We find a considerable increase in the maximum superconducting transition temperature Tcmax with J. This is strong evidence of the importance of orbital overlap to superconductivity in this family of cuprates.

Abstract:
We report systematic 17O-NMR measurements on the high-Tc cuprate (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy, for four different families (different x). Using Knight shift data, we show that the pseudogap opening temperature T* is much higher than Tc near optimal doping, unlike structurally similar YBCO. In addition, at constant doping the pseudogap temperature does not vary with x, in contrast to Tc. This puts constraints on the nature of the pseudogap and position of the quantum critical point inside the superconducting dome.

Abstract:
We report angle-resolved photoemission spectroscopy on two families of high-temperature superconductors (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy with x = 0.1 (Tcmax = 56 K) and x = 0.4 (Tcmax = 82 K). The Fermi surface (FS) is found to be independent of x or y, and its size indicates extreme sample-surface overdoping. This universal FS allows the comparison of dynamical properties between superconductors of similar structure and identical doping, but different Tcmax. We find that the high-energy (|E| > 50 meV) nodal velocity in the x = 0.4 family is higher than in the x = 0.1 family. The implied correlation between Tcmax and the hopping rate t supports the notion of kinetic energy driven superconductivity in the cuprates. We also find that the antinodal gap is higher for the x = 0.4 family.

Abstract:
The origin of the pseudogap and its relationship with superconductivity in the cuprates remains vague. In particular, the interplay between the pseudogap and magnetism is mysterious. Here we investigate the newly discovered nodal gap in hole-doped cuprates using a combination of three experimental techniques applied to one, custom made, single crystal. The crystal is an antiferromagnetic La2-xSrxCuO4 with x = 1.92%. We perform angleresolved photoemission spectroscopy measurements as a function of temperature and find: quasi-particle peaks, Fermi surface, anti-nodal gap and below 45 K a nodal gap. Muon spin rotation measurements ensure that the sample is indeed antiferromagnetic and that the doping is close, but below, the spin-glass phase boundary. We also perform elastic neutron scattering measurements and determine the thermal evolution of the commensurate and incommensurate magnetic order, where we find that a nodal gap opens well below the commensurate ordering at 140 K, and close to the incommensurate spin density wave ordering temperature of 30 K.

Abstract:
Absolute resistivity measurements as a function of temperature from optimally doped YBa2Cu3O7-δ , La2-xSrxCuO4, Bi2Sr2Ca1Cu2O8-x, and (Ca0.1La0.9)(Ba1.65La0.35)Cu3Oy thin films are reported. Special attention is given to the measurement geometrical factors and the resistivity slope between Tc and T*. The results are compared with a strong-coupling theory for the resistivity derivative near Tc, which is based on hard core bosons, and with several weak-coupling theories, which are BCS based. Surprisingly, our results agree with both paradigms. The implications of these findings and the missing calculations needed to distinguish between the two paradigms are discussed.

Abstract:
Using angle-resolved photoemission spectroscopy (ARPES), it is revealed that the low-energy electronic excitation spectra of highly underdoped superconducting and nonsuperconducting La2-xSrxCuO4 cuprates are gapped along the entire underlying Fermi surface at low temperatures. We show how the gap function evolves to a dx2-y2 form with increasing temperature or doping, consistent with the vast majority of ARPES studies of cuprates. Our results provide essential information for uncovering the symmetry of the order parameter(s) in strongly underdoped cuprates, which is a prerequisite for understanding the pairing mechanism and how superconductivity emerges from a Mott insulator.

Abstract:
We report the successful growth of a large (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy (CLBLCO) single crystal. In this material, x controls the maximum of Tc (Tcmax), with minimal structural changes. Therefore, it allows a search for correlations between material properties and Tcmax. We demonstrate that the crystals are good enough for neutron scattering and cleave well enough for Raman scattering. These results open new possibilities for cuprate research.

Abstract:
We report direction-dependent susceptibility and resistivity measurements on La2-xSrxCuO4 single crystals. These crystals have rectangular needle-like shapeswith the crystallographic “c” direction parallel or perpendicular to the needle axis, which, in turn, is in the applied field direction. At optimal doping we find finite diamagnetic susceptibility above Tc, namely fluctuating superconductivity (FSC), only when the field is perpendicular to the planes. In underdoped samples we find FSC in both field directions. We provide a phase diagram showing the FSC region, although it is sample dependent in the underdoped cases. The variations in the susceptibility data suggest a different origin for the FSC between underdoping (below 10%) and optimal doping. Finally, our data indicate that the spontaneous vortex diffusion constant above Tc is anomalously high.

Abstract:
A limiting factor in the ability to interpret isotope effect measurements in cuprates is the absence of sufficiently accurate data for the whole phase diagram; there is precise data for Tc , but not for the antiferromagnetic transition temperature TN. Extreme sensitivity of TN to small changes in the amount of oxygen in the sample is the major problem. This problem is solved here by using the novel compound (Ca0.1La0.9)(Ba1.65La0.35)Cu3Oy for which there is a region where TN is independent of oxygen doping. Meticulous measurements of TN for samples with 16O and 18O find the absence of an oxygen isotope effect on TN with unprecedented accuracy. A possible interpretation of our finding and existing data is that isotope substitution affects the normal state charge carrier density.

Abstract:
A systematic angle-resolved photoemission study of the electronic structure of La2-xSrxCuO4 in a wide doping range is presented in this paper. In addition to the main energy band, we observed a weaker additional band, the (π, π) folded band, which shows unusual doping dependence. The appearance of the folded band suggests that a Fermi surface reconstruction is doping dependent and could already occur at zero magnetic field.

Abstract:
The critical doping levels in cuprates, where the ground state changes its nature (from an antiferromagnet to a spin glass to superconductor to metal), are not universal. We investigate the origin of these critical doping variations by measuring the in-plane oxygen pσ hole density in the CuO2 layers as a function of the oxygen density y in (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy. This is done using the oxygen 17 nuclear quadrupole resonance parameter νQ. We compare compounds with x=0.1 and 0.4 which have significant critical y variations and find that these variations can be explained by a change in the efficiency of hole injection into the pσ orbital. This allows us to generate a unified phase diagram for the CLBLCO system across the entire doping range, with no adjustable parameters.

Abstract:
A proper understanding of the mechanism for cuprate superconductivity can emerge only by comparing materials in which physical parameters vary one at a time. Here, we present a variety of bulk, resonance and scattering measurements on the (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy high temperature superconductors, in which this can be done. We determine the superconducting, Néel, glass and pseudopage critical temperatures. In addition, we clarify which physical parameter varies, and, equally important, which does not, with each chemical modification. This allows us to demonstrate that a single energy scale, set by the superexchange interaction J , controls all the critical temperatures of the system. J , in turn, is determined by the in plane Cu-O-Cu buckling angle.

Abstract:
We describe two different nuclear quadrupole resonance (NQR) based techniques, designed to measure the local asymmetry of the internal electric field gradient η and the tilt angle α of the main NQR principal axis z^ from the crystallographic axis c^. These techniques use the dependence of the NQR signal on the duration of the radio frequency (rf) pulse and on the direction of the rf field H1 with respect to the crystal axis. The techniques are applied to oriented powder of YBa2Cu3Oy fully enriched with 63Cu. Measurements were performed at different frequencies, corresponding to different in-plane copper sites with respect to the dopant. Combining the results from both techniques, we conclude that oxygen deficiency in the chain layer lead to a rotation of the NQR main principal axis at the nearby Cu on the CuO2 planes by α ≂ 20° ∓ 5°. This occurs with no change to η. The axis rotation associated with oxygen deficiency means that there must be electric field inhomogeneities in the CuO2 planes only in the vicinity of the missing oxygen.

Abstract:
We investigate the coupling between the magnetic and superconducting order parameters in an 8-m-long meander line (“wire”) made of a La1.94Sr0.06Cu4 film with a cross section of 0.5 ✕ 100 μm2. The magnetic order parameter is determined using the low-energy muon spin relaxation technique. The superconducting order parameter is characterized by transport measurements and modified by high current density. We find that when the superconducting order parameter is suppressed by the current, the magnetic transition temperature, Tm, increases. The extracted sign and magnitude of the Ginzburg-Landau coupling constant indicate that the two orders are repulsive, and that our system is located close to the border between first- and second-order phase transition.

Abstract:
Using muon spin rotation we determine the zero-temperature staggered antiferromagnetic order parameter M0 versus hole doping measured from optimum Δpm, in the (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy system. In this system the maximum Tc and the superexchange J vary by 30% between families (x). M0(x,Δpm) is found to be x independent. Using neutron diffraction we also determine the lattice parameters variations for all x and doping. The oxygen buckling angle is found to change with x, implying a change in the holes kinetic energy. We discuss the surprising insensitivity of M0(x,Δpm) to the kinetic-energy variations in the framework of the t-J model.

Abstract:
We investigate the crossover temperature T* as a function of doping in (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy, where the maximum T* (Tcmax) varies continuously by 30% between families (x) with minimal structural changes. T* is determined by dc-susceptibility measurements. We find that T* scales with the maximum Néel temperature TNmax of each family. This result strongly supports a magnetic origin of T* and indicates that three dimensional interactions play a role in its magnitude.

Abstract:
We present extensive magnetic measurements of the (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy system with its four different families (x) having a Tcmax(x) variation of 28% and minimal structural changes. For each family, we measured the Néel temperature, the anisotropies of the magnetic interactions, and the spin-glass temperature. Our results exhibit a universal relation Tc=cJns for all families, where c ~ 1, J is the in-plane Heisenberg exchange, and ns is the superconducting carrier density. This relates cuprate superconductivity to magnetism in the same sense that phonon-mediated superconductivity is related to atomic mass.

Abstract:
We report charge density measurements, using NMR, in the superconducting compound (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy, which has two independent variables, x (family) and y (oxygen). For underdoped samples we find the rate at which holes are introduced into the plane upon oxygenation to be family independent. In contrast, not all carriers contribute to either antiferromagnetic or superconducting order parameters. This result is consistent with a two-fluid phenomenology or intrinsic mesoscopic inhomogeneities in the bulk. We also discuss the impact of weak chemical disorder on Tc.

Abstract:
We report in-plane 63Cu nuclear magnetic resonance measurements for a series of fully enriched (Ca0.1La0.9)(Ba1.65La0.35)Cu3Oy powder samples, which belong to the YBa2Cu3Oy (YBCO) family, but the doping could vary from very underdoped to extremely overdoped. From these measurements, we determine the average nuclear quadrupole resonance frequency νQ and its second moment ΔνQ, both set by the in-plane hole density n, as a function of oxygen level y. We find that in the overdoped side n is saturated, but ΔνQ rapidly increases with increasing y. The relevance of these results to the increasing penetration depth in overdoped cuprates is discussed.

Abstract:
The origin of charge inhomogeneity in YBa2Cu3Oy is investigated using an experimental method designed to determine the nuclear quadrupole resonance (NQR) asymmetry parameter η for very wide NQR lines at different positions on the line. The method is based on the measurement of the echo intensity as a function of the angle between the radio frequency field H1 and the principal axis of the electric field gradient. Static charge inhomogeneity deduced from η>0 is found in this compound, but only in conjunction with oxygen deficiency. This limits considerably the possible forms of charge inhomogeneity in bulk YBa2Cu3Oy.

Abstract:
We develop an experimental method for measuring the intrinsic susceptibility χ of the powder of cuprate superconductors in the zero-field limit using a dc magnetometer. The method is tested with lead spheres. Using this method, we determine χ for a number of cuprate families as a function of doping. A universal linear χ and not proportionality χ relation between Tc and χ is found. We suggest possible explanations for this phenomenon.

Abstract:
Zero-field muon spin-relaxation (µSR) measurements in 63Cu isotope enriched and natural YBa2Cu4O8 powders are presented. The µ+ relaxation rate is characterized by a sizeable enhancement as the temperature is lowered below the superconducting transition temperature Tc. The comparison of the asymmetry decay in the two samples reveals that the µ+ relaxation is driven by nuclear dipole interaction from 300 K down to 4.2 K. It is argued that the increase in the relaxation rate below Tc originates from a change either of the µ+ site or of the orientation of the electric-field gradient at the Cu nuclei, due to a modification in the charge distribution within CuO chains.

Abstract:

Using the transverse field muon spin relaxation technique,we measure the temperature dependence of the magnetic field penetration depth ,i n the Nax CoO2 y H2 O system.We find that ,which is determined by the superfluid density n s and the effective mass m ,is very small and on the edge of the TF-mSR sensitivity.Nevertheless,the results indicate that this system obeys the Uemura relation.By comparing with the normal state electron density,we conclude that m of the superconductivity carrier is 70 times larger than the mass of bare electrons.Finally,the order parameter in this system cannot be described by a complete gap over the entire Fermi surface.

Abstract:
Many compounds based on CuO2 planes (cuprates) superconduct below a critical temperature Tc. Some of them show a second phase where a spontaneous static magnetic field appears below a critical temperature Tg, which is lower than Tc. By comparing Tc and Tg in numerous superconducting families,each with its own maximum Tc,we find that the same energy scale determines both critical temperatures. This clearly indicates that the origin of superconductivity in the cuprates is magnetic.

Abstract:
The (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy  system is ideal for testing theories of high temperature superconductivity, since nearly the full range of doping is controlled by y, and Tcmax is continuously controlled by x, with minimal structural changes. We investigate this system with both transverse and longitudinal field mSR. This allows us to re-examine the Uemura relation, the nature of the spontaneous magnetic fields below Tc, and the relation between their appearance temperature Tg and Tcmax. Our major findings are: (1) the Uemura relation is respected by this system more adequately than by other cuprates, (2) Tg and Tc are controlled by the same energy scale, (3) the phase separation between hole poor and hole rich regions is a microscopic one, and (4) spontaneous magnetic fields appear gradually with no moment size evolution.

Abstract:
We characterize the spontaneous magnetic field, and determine the associated temperature Tg, in the superconducting state of (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy using zero and longitudinal field mSR measurements for various values of x and y. Our major findings are: (I) Tg and Tc are controlled by the same energy scale, (II) the phase separation between hole poor and hole rich regions is a microscopic one, and (III) spontaneous magnetic fields appear gradually with no moment size evolution.

Abstract:
NMR transverse relaxation (TR) measurements of 17O in the O(2,3) sites of YBa2Cu3(16O1-c17Oc)7 are presented. A Gaussian-like relaxation is found. The origin of this relaxation is investigated by varying the isotopic concentration of the oxygen, the temperature, the external field, and by comparing it with the O(4) site. Our results are consistent with a model in which this relaxation is caused by the dynamical fluctuation of copper nuclei, including both spin lattice and flip-flop processes. With this model we can explain consistently the TR of 89Y and 63,65Cu(1) as well. We use our results to re-analyze previous NMR 63,65Cu(2) TR data.

Abstract:
We have performed zero-field muon spin rotation (mSR) measurements of the “infinite layer” cuprate compound Ca0.86Sr0.14CuO2and the “infinite chain” system Sr2CuO3. A spontaneous magnetic field from the ordered Cu moments is observed below TN=540(5)K in Ca0.86Sr0.14CuO2: below T=360 K, we observe muon spin precession with a frequency n (T-> 0)=16 MHz (corresponding to a local field of 1.2 kG). The precession signal is replaced by a rapid depolarization above T=360~K due to the onset of muon diffusion. The hopping rate followed an Arrhenius law, with an activation energy of Ea=0.39(1) eV. The sub-lattice magnetization Ms, proportional to n(T), showed a slower decay with increasing temperature in Ca0.86Sr0.14CuO2, compared with that observed in La2CuO4 and Sr2CuO2Cl2, indicating that a wider CuO2 layer separation results in more 2-dimensional magnetic behavior. In the “infinite chain” system Sr2CuO3, the onset of magnetic order was found at T~5 K with a local field of ~30 G at the muon site at T->0. The exchange interaction, inferred from susceptibility measurements is on the order of 103 K, implying a remarkable suppression of the ordering temperature with kBTN/J<=0.01 in Sr2CuO3. These results demonstrate clear signatures of low dimensional magnetic behavior in the CuO chains.

Abstract:
We performed zero-field muon-spin-rotation measurements of the “infinite-chain” compound Ca2CuO3. A spontaneous magnetic field is observed below 13 K. The exchange interaction inferred from susceptibility measurements and two-magnon Raman scattering is approximately 103 K, which implies a remarkable suppression of the ordering temperature kBTN/J1d~0.01. We discuss the relevance of these measurements to the problem of one dimensional spin-1/2 antiferromagnets.