Thermal and electrical conductivity of approximately 100-nm permalloy, Ni, Co, Al, and Cu films and examination of the Wiedemann-Franz Law

Abstract

We present measurements of thermal and electrical conductivity of polycrystalline permalloy (Ni-Fe), aluminum, copper, cobalt, and nickel thin films with thickness < 200 nm. A micromachined silicon-nitride membrane thermal isolation platform allows measurements of both transport properties on a single film and an accurate probe of the Wiedemann-Franz (WF) law expected to relate the two. Through careful elimination of possible effects of surface scattering of phonons in the supporting membrane, we find excellent agreement with WF in a thin Ni-Fe film over nearly the entire temperature range from 77 to 325 K. All other materials studied here deviate somewhat from the WF prediction of electronic thermal conductivity with a Lorenz number, L, suppressed from the free-electron value by 10 − 20%. For Al and Cu we compare the results to predictions of the theoretical expression for the Lorenz number as a function of T . This comparison indicates two different types of deviation from expected behavior. In the Cu film, a higher than expected L at lower T indicates an additional thermal conduction mechanism, while at higher T lower than expected values suggests an additional inelastic scattering mechanism for electrons. We suggest the additional low T L indicates a phonon contribution to thermal conductivity, and consider increased electron-phonon scattering at grain boundaries or surfaces to explain the high T reduction in L.

Spin‐Driven Emergent Antiferromagnetism and Metal–Insulator Transition in Nanoscale p‐Si

“…The V 3ω response shows a magnetic field‐dependent behavior, and this can be interpreted as a spin influenced thermal transport in p‐Si since p‐Si is significantly more thermally conducting than Ni 81 Fe 19 . We estimate that the thermal resistance of the p‐Si layer will be ≈26 times (assuming a = 30 W mK −1 ) of Ni 81 Fe 19 layer ( = 21 W mK −1 ). In addition, the magnetic field‐dependent measurements of V 2ω and V 3ω responses show temperature‐dependent minima between 20 and 50 K.…”

Thermal spin injection and interface insensitivity in permalloy/aluminum metallic nonlocal spin valves

“…Here we take the value of the Lorenz number, L Al = 2.0 × 10 −8 WΩ/K 2 from a measurement of a similar Al thin film made using our micromachined thermal isolation platform [33].…”

“…As discussed in detail below, this allows description of each device using a simple analytic thermal model that includes Joule heating and Peltier heating or cooling. With knowledge of the thermal conductivity and Seebeck coefficients of representative films that we measure using our technology for thin film thermal measurements [27][28][29][30][31][32][33], we determine an upper limit on the thermal gradient driving spin injection without recourse to complicated simulations or assumptions of bulk thermal properties. We also use a 2d finite element approach based on purely diffusive heat flow, though again informed by measured values of thermal conductivity and Seebeck coefficients, to approach a more realistic estimate of the thermal gradient and the SDSE.…”

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

“…Other examples for phonons in various situations include Refs. [39,40,[63][64][65][66][67], while examples for photons in nanostructures include Refs. [68,69].…”