Nonlinear dielectric microwave losses in MgO substrates

Hein, Matthias; Oates, D.E.; Hirst, P.J.; Humphreys, R.G.; Velichko, A. V.

doi:10.1063/1.1447000

Cited by 38 publications

(32 citation statements)

References 23 publications

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“…41 In our measurements of MgB 2 these signatures of TLS are completely absent. None of the MgB 2 resonators show anomalous power or temperature dependence of the Q.…”

Section: B Two-level Systemsmentioning

confidence: 66%

Evidence for non-s-wave symmetry of theπgap inMgB2from intermodulation distortion measurements

Agassi

Oates

Moeckly³

2009

Phys. Rev. B

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We present low-temperature low-power intermodulation-distortion ͑IMD͒ measurements of high-quality MgB 2 thin films that are inconsistent with presumed s-wave symmetry of the order parameter. The measurements were carried out in a stripline resonator at approximately 2 GHz between 1.8 K and T c . The IMD arises from the nonlinear Meissner effect in which the penetration depth is dependent on the RF magnetic field. Specifically, the observed IMD vs temperature T for T Ӷ T c / 2 varies as T −2 , while for an s-wave gap symmetry in the clean limit, the low-temperature IMD decreases exponentially with decreasing temperature. We calculate the IMD from first principles for different order-parameter symmetries using a Green's function approach and compare the results with the measured data. We propose that the observed upturn in the low-temperature IMD implies an admixture of an order parameter with nodal lines into the energy gaps of MgB 2 . Most likely, this admixture is prominent for the gap. Within the constraints of the hexagonal crystal symmetry of MgB 2 , the best fit with our IMD measurements is obtained with a gap ⌬͑ , T͒ = ⌬ 0 ͑T͒sin͑6͒, where is the azimuthal angle in the ab plane, and ⌬ 0 ͑T͒ is the amplitude, weakly temperature dependent at low temperatures. This gap symmetry entails six nodal lines. We also present low-temperature penetration-depth measurements that are consistent with the proposed nodal gap symmetry. To relate our proposition with existing literature, we review other low-temperature probes of the order-parameter symmetry. The literature presents conflicting results, some of which are in direct support of the symmetry proposed here.

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“…41 In our measurements of MgB 2 these signatures of TLS are completely absent. None of the MgB 2 resonators show anomalous power or temperature dependence of the Q.…”

Section: B Two-level Systemsmentioning

confidence: 66%

Evidence for non-s-wave symmetry of theπgap inMgB2from intermodulation distortion measurements

Agassi

Oates

Moeckly³

2009

Phys. Rev. B

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“…4,5 YBCO films deposited on other substrates, such as sapphire and MgO, do not exhibit intrinsic nonlinearity due to induced defects in the YBCO film for a sapphire substrate 9 and due to substrate nonlinearities in the case of an MgO substrate. 13 The films were patterned using standard photolithography and wet etching. All resonators were patterned simultaneously in a single process step to assure uniformity.…”

Section: Methodsmentioning

confidence: 99%

Nonlinear Meissner effect in a high-temperature superconductor: Local versus nonlocal electrodynamics

et al. 2008

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Measured intermodulation distortion ͑IMD͒ power at 1.5 GHz in a series of YBa 2 Y 3 O 7−␦ stripline resonators of varying strip widths is compared to the predictions of two qualitatively distinct theories of the nonlinear Meissner effect. The stripline resonators are patterned from a single wafer to ensure uniformity of the material properties. According to the first theory ͓T. Dahm and D. J. Scalapino, Phys. Rev. B 60, 13125 ͑1999͔͒, the IMD power is dominated by contributions from the strip edges, while according to the second theory ͓D. Agassi and D. E. Oates, Phys. Rev. B 72, 014538 ͑2005͔͒ it is dominated by contributions from the body of the strip. The parameter-free comparison of the measured data with the theoretical predictions clearly favors the latter theory. We conclude that the nonlinear component of the penetration depth must be treated with nonlocal electrodynamics. The origins of this outcome are discussed briefly in the framework of a Green's-function approach.

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“…15. This hysteretic behavior enables an experimental separation of the vortex contribution to R i from reversible mechanisms due to sound generation 78 , dielectric losses in the substrate 79,80 etc. The total surface resistance R s can be written as a sum of the vortex component R i and the BCS resistance…”

Section: B Residual Surface Resistance At B0 ≪ Bvmentioning

confidence: 99%

Dynamics of vortex penetration, jumpwise instabilities, and nonlinear surface resistance of type-II superconductors in strong rf fields

2008

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We consider nonlinear dynamics of a single vortex in a superconductor in a strong rf magnetic field B0 sin ωt. Using the London theory, we calculate the dissipated power Q(B0, ω), and the transient time scales of vortex motion for the linear Bardeen-Stephen viscous drag force, which results in unphysically high vortex velocities during vortex penetration through the oscillating surface barrier. It is shown that penetration of a single vortex through the ac surface barrier always involves penetration of an antivortex and the subsequent annihilation of the vortex antivortex pairs. Using the nonlinear Larkin-Ovchinnikov (LO) viscous drag force at higher vortex velocities v(t) results in a jump-wise vortex penetration through the surface barrier and a significant increase of the dissipated power. We calculate the effect of dissipation on nonlinear vortex viscosity η(v) and the rf vortex dynamics and show that it can also result in the LO-type behavior, instabilities, and thermal localization of penetrating vortex channels. We propose a thermal feedback model of η(v), which not only results in the LO dependence of η(v) for a steady-state motion, but also takes into account retardation of temperature field around rapidly accelerating vortex, and a long-range interaction with the surface. We also address the effect of pinning on the nonlinear rf vortex dynamics and the effect of trapped magnetic flux on the surface resistance Rs calculated as a function or rf frequency and field. It is shown that trapped flux can result in a temperature-independent residual resistance Ri at low T , and a hysteretic low-field dependence of Ri(B0), which can decrease as B0 is increased, reaching a minimum at B0 much smaller than the thermodynamic critical field Bc. We propose that cycling of rf field can reduce Ri due to rf annealing of magnetic flux which is pumped out by rf field from the thin surface layer of the order of the London penetration depth.

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Nonlinear dielectric microwave losses in MgO substrates

Abstract: We have investigated the nonlinear surface impedance and two-tone intermodulation distortion of ten epitaxial YBa 2 Cu 3 O 7-δ films on MgO substrates, using stripline resonators, at frequencies

Cited by 38 publications

References 23 publications

Evidence for non-s-wave symmetry of theπgap inMgB2from intermodulation distortion measurements

Evidence for non-s-wave symmetry of theπgap inMgB2from intermodulation distortion measurements

Nonlinear Meissner effect in a high-temperature superconductor: Local versus nonlocal electrodynamics

Dynamics of vortex penetration, jumpwise instabilities, and nonlinear surface resistance of type-II superconductors in strong rf fields

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