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

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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%4.pt0exto4.pt0ex20%. 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-T4pt0exL 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.