Anomalous behavior of the complex conductivity of Y1-xPrxBa2Cu3O7 observed with THz spectroscopy.

We have measured the electrodynamic properties of Y1−xPrxBa2Cu3O7 single crystal thin films as a function of temperature using coherent THz-time-domain spectroscopy. We obtain directly the complex conductivity σ = σ1 + iσ2, the London penetration depth λL, the plasma frequency ωp, and the quasiparticle scattering rate 1/τ . We find that 1/τ drops exponentially rapidly with T below the critical temperature in all the superconducting samples, implying that this behavior is a signature of highTc superconductivity. The plasma frequency decreases with increasing Pr content, providing evidence that Pr depletes carriers, leaving the CuO planes underdoped. Both the conductivity in the THz region and the dc resistivity yield evidence for the opening of a spin gap above Tc. Typeset using REVTEX 1 The large body of vital spectroscopic data on the high-Tc superconducting compound Y1Ba2Cu3O7−δ (YBCO) measured in the far infrared (FIR) as well as the GHz-region has revealed many interesting features. Among them are: the presence of one [1] or more [2] energy gaps in the superconducting state, a temperature dependent penetration depth that is indicative of d-wave pairing [3], and a quasiparticle scattering rate which is proportional to frequency in the normal state [1] and which drops by four orders of magnitude at Tc [4]. The new technique of THz-time-domain spectroscopy bridges the gap between the FIR and the GHz regime. THz measurements of YBCO display a peak in the temperature dependence of σ1 below Tc, which appears to be related to a temperature-dependent scattering rate 1/τ rather than to BCS coherence effects [5]. Other experiments using the same technique have revealed that the penetration depth λL, has a temperature-dependence inconsistent with BCS theory [6]. Here we report results of a THz investigation into the Y1−xPrxBa2Cu3O7 (YPrBCO) system. These measurements are of great interest because samples covering a wide range of critical temperatures can be obtained simply by varying the Y/Pr ratio [7]. Also, because YPrBCO is fully stoichiometric in the oxygen content, it is more homogeneous than oxygen-depleted YBCO and does not change from an orthorhombic to a tetragonal lattice upon decreasing Tc. Several mechanisms have been proposed for the Tc suppression, including a magnetic pair breaking effect [8] and depletion of holes in the CuO2 planes [9]. Recently, the opening of a spin gap at temperatures above Tc in oxygen-deficient YBCO has been deduced from various experiments e.g. dc resistivity and Hall coefficient [10,11], neutron scattering [12], and NMR measurements [13]. However, until now only one electro-magnetic measurement on underdoped YBCO has been linked to the presence of a spin gap [1]. In this paper, we report evidence for a spin gap obtained from measurements both at dc and at THz frequencies in YPrBCO, which is consistent with Pr depleting holes from the CuO planes [9]. Our spectroscopic technique involves a coherent time-domain measurement of a ps microwave impulse E(t) transmitted through the sample [14]. A Fourier transform yields the complex transmission spectrum t(ω) and the complex conductivity σ(ω), without the use of Kramers-Kronig analysis. The London penetration depth λL(T ), the plasma frequency ωp in the clean limit, and the scattering time τ(T ) are obtained with the aid of a two-fluid model. 2 The microwave source is a biased 30 μm transmitting antenna fabricated on low temperature grown GaAs, triggered with ∼100 fs optical pulses from a colliding-pulse modelocked dye laser. The emitted microwave pulses have spectral components spanning the 0.1 – 1.0 THz spectral region which is difficult to access with conventional electronics [15]. The receiver is a 30 μm antenna, fabricated on ion-implanted silicon-on-sapphire and gated with a second pulse from the laser. The receiver photocurrent is proportional to the incident microwave field. We investigated five YPrBCO samples having Pr composition x = 0.0, 0.2, 0.3, 0.4, and 1.0. The films are grown by pulsed laser deposition [16] onto NdGaO3 substrates. The film thicknesses are approximately 150 nm (Table I). NdGaO3 is the ideal substrate because it remains transparent and nondispersive over the entire spectral bandwidth of our pulses, as well as over the entire range of temperatures investigated here. The excellent lattice match of NdGaO3 to YPrBCO is a prerequisite for a low density of misfit dislocations on the film-substrate interfaces. The substrates have a (001) orientation, yielding ĉ oriented, twinned films. The critical temperatures T dc c (Table I) are determined from the temperature dependent resistivity, as measured with a four-point probe. To calculate the conductivity, we make use of the multiple reflection formula for the field transmitted through a layer of (complex) index n2, thickness d, bounded by media of index n1 and n3: t(ω) = t12t23 exp(in2(ω/c)d) 1 + r12r23 exp(2in2(ω/c)d) (1) where tij = 2ni/(ni + nj) is the field transmission coefficient at the ijth interface, and rij = (ni − nj)/(ni + nj) is the field reflection coefficient. In our geometry, n1 represents vacuum, n2 = √ 1 + iσ(ω)/(ǫ0ω) is the index of the superconducting layer, and n3 is the measured index of the substrate. As n2(ω/c)d ≪ 1, and n2 ≫ n3 > 1 in our samples, Eq. (1) reduces to t(ω) = 1 + n3 1 + n3 + Zoσ(ω)d (2) where Z0 is the impedance of free space. The effect of varying Pr content x (hereafter [Pr]) on the conductivity spectra σ(ω) at T = 50 K is similar to the effect of varying the temperature for a given alloy (Fig. 1). The addition of Pr has at least two interrelated effects: a) The suppression of Tc changes the partitioning between normal and superconducting carriers. b) The total number of carriers N (or their mobility) may be reduced. 3 To the extent that the superconducting carriers make the largest contribution to σ2, both factors a) and b) lead one to expect that at a given temperature, pure YBCO would have the largest σ2, and it does. Samples with 20% and 30% Pr have smaller values of σ2, since they are only slightly below their Tc. The sample with 40% Pr has σ2 ≈ 0 because it is above Tc at 50 K. Only normal carriers contribute to σ1 for ω 6= 0, but now factors a) and b) compete. At 50 K, σ1 decreases with [Pr], therefore the effect of a reduction in N dominates the effect of the shift in Tc which increases the fraction of normal carriers. The data for pure YBCO and 20% Pr have been fit to a frequency-dependent Drude form, and one can see that 1/τ lies in our spectral range. For 30% and 40% Pr, we observe frequency independent σ1 and can conclude that 1/τ is large compared to 1 THz. Pure PrBCO is a dielectric at 50 K, as seen by a conductivity proportional to frequency, i.e. a dielectric constant independent of frequency. Examining σ2 at a fixed frequency, e.g. 480 GHz, we see that it is close to zero at high temperature, but rises sharply at the onset of superconductivity, thus providing an independent ac measurement of Tc (Table I). In all of the superconducting alloys, below Tc, σ1 displays a peak, which has been previously observed only in fully oxygenated YBCO using microwave techniques [5,17] as well as measuring the thermal conductivity [18]. It has been attributed to a sharp rise in the scattering time τ of normal carriers below Tc offsetting the decrease in the fraction of normal carriers, although coherence effects remain a possibility. For pure YBCO, the peak value is about 20 times higher than σ1(100 K). With increasing [Pr] the peak height in σ1 decreases but the temperature corresponding to the peak position does not shift significantly. The normal state behavior of our samples is particularly interesting because underdoped materials such as (124)YBCO and oxygen deprived (123)YBCO undergo a phase transition associated with the opening of a spin gap at a temperature TD > Tc. Evidence for the presence of a spin gap has been seen in neutron scattering [12,19], as well as in dc resistivity measurements [10,11]. Recent experimental [20] and theoretical [9] work confirms that YPrBCO alloys are also underdoped, i.e. superconductivity is suppressed, because holes are removed from the CuO2 planes. If the normal carriers couple strongly to spin fluctuations, the opening of a spin gap should be accompanied by an increase in the scattering time τ , giving rise to an enhancement in σ1 below TD 4 for ω < 1/τ . For pure (optimally doped) YBCO, at 480 GHz, σ1 shows only a single transition at Tc (Fig. 2b). For the (underdoped) alloys, σ1 has two transitions, one at Tc, the other at a higher temperature which increases with [Pr]. To accentuate the two transitions, Fig. 2b is shaded in the region bounded by Tc, the experimental curve, and a dashed line representing 1/(α+ βT ) behavior. The higher transition temperature seen at 480 GHz matches that of a transition also observed in the dc resistivity (Fig. 3a). The transition is manifested as a deviation from a linear T dependence. To show the deviation more clearly, the resistivity is first fit to a line ρ = α + βT between 250 and 300 K, and then the experimental values are normalized to the value determined by the line as follows: