Inter-grain tunneling in the half-metallic double-perovskites Sr$_2$BB'O$_6$ (BB'-- FeMo, FeRe, CrMo, CrW, CrRe

The zero-field conductivities ($\sigma$) of the polycrystaline title materials, are governed by inter-grain transport. In the majority of cases their $\sigma$(T) can be described by the"fluctuation induced tunneling"model. Analysis of the results in terms of this model reveals two remarkable features: 1. For \emph{all} Sr$_2$FeMoO$_6$ samples of various microstructures, the tunneling constant (barrier width $\times$ inverse decay-length of the wave-function) is $\sim$ 2, indicating the existence of an intrinsic insulating boundary layer with a well defined electronic (and magnetic) structure. 2. The tunneling constant for \emph{all} cold-pressed samples decreases linearly with increasing magnetic-moment/formula-unit.

Half-metallic ordered double-perovskites with fully polarized conduction bands and Curie temperatures (T c ) above room temperature (RT) are of interest for devices which depend on spin polarized transport. Therefore their magnetic, electronic and in particular their magneto-resistive properties 1 have been investigated intensively over the past two decades.
The grain boundaries in these materials act in most cases as tunnel barriers. The early theories of inter-grain tunneling magneto-resistance addressed the problem of tunneling through a non-magnetic barrier separating two ferromagnetic grains (including vacuum). 2-4 These theories could not explain inter-grain magneto-resistance in half metals. In Ref. 5 the magneto-resistive behaviour of (BaSr) 2 FeMoO 6 was explained in terms of tunneling between two correlated spin glass-like surfaces separated by a thin insulating layer. In Ref. 6 it was suggested that the pinned ferromagnetic spins at the core/skin interface should be taken as being solely responsible for the tunneling magneto-resistance in half-metallic doubleperovskites. A spin-glass-like surface layer surrounding each soft ferromagnetic (FM) grain of Sr 2 FeMoO 6 has been detected also in Ref. 7 by careful ac susceptibility measurements on a highly ordered polycrystalline sample; these measurements were able to separate the barrier layer signal from the bulk. The presence of an intrinsic insulating boundary layer around FM grains of (LaSr)MnO 3 (LSMO), with magnetic properties different from those of the bulk, has been recently revealed by means of x-ray linear dichroism and transport measurements. 8 This phase, about 2 unit cells thick, is held responsible for the observed depressed magneto-transport properties in manganite based magnetic tunneling junctions.
Unlike the difficulty in separating the magnetic properties of the layers from those of the bulk, 7 it is relatively easy to study the electronic properties of the grain skin layers when the electronic transport is dominated by inter-grain tunneling as is the case in most of the polycrystalline samples of the title materials. In this report we focus on the zero-field conductivity of various samples of the five title compounds; this comparative study revealed some important features of the grain-boundaries of these half metals. Table I shows the five title double-perovskites (with abbreviations), their ionic configuration, nominal (ideal) saturation magnetization (M i ) and T c . While their bulk is metallic, as confirmed by their metallic-like thermopower, 10 the zero-field conductivities (σ(T )) of polycrystalline samples are non-metallic (the conductivity increases with increasing T).
Metallic-like resistivity was found in a single crystal of SFMO. 11 The inter-grain tunneling conductivity depends strongly on preparation conditions and often exhibits unusual T-dependence. The most remarkable behaviors are the linear-in-T conductivities from liquid He temperatures up to RT, for all our sintered and granular samples of SFMO , irrespective of preparation conditions, for some samples of SFRO and of SCMO, and the linear-in-T 2 conductivity over the same range of T, for some samples of SCMO. 12 The temperature dependence of the conductivity for all our samples, except for porous SCRO, can be derived from the "fluctuation induced tunneling" (FIT) model. 13 This model applies to metallic grains embedded in an insulating medium. Tunneling occurs across small gaps (width w and area A) between large metallic grains; the small gaps are subject to large thermal fluctuations of the voltage. σ(T) predicted by this model is: All SFMO samples exhibit linear σ(T ). In other compounds conductivity linear-in-T or linear-in-T 2 (over a wide temperature range) are special cases. However, except for SCRO, σ(T ) for all sintered samples obeys the FIT model with parameters within a wide range that depend on the preparation conditions. Our sintered SCRO samples were porous and their conductivity over an unprecedentedly wide range of T was of Berthelot-type (ln(σ(T )/σ(0)) = T /T B where T B is a constant of the order of a few tens of K). 14 This behavior can be derived from Tredgold's "vibrating barrier tunneling" model. 15 Eq. (1) can be reduced to a Berthelot-type formula for T 1 /T o >> 1 and T /T o << 1 with T B = T 2 o /T 1 but then the values of the fitting parameters to our data become non-physical. Interestingly, σ(T ) for cold-pressed (c.p.) SCRO obeys the FIT model with reasonable parameters (see below).
The FIT model has been extended to electric-field dependent conductivities. The nonlinear I-V characteristics measured on some SFMO samples (using pulsed currents in order to avoid Joule heating) are consistent with the extended FIT model, at least qualitatively . 16 The FIT model does not address magnetic interactions. Since it was applied successfully to at least three groups of magnetic materials (our title materials, CrO 2 and its composites 17,18 and Co-based nanocomposites 19 ), it may be assumed that the influence of the magnetic interactions is on the nature of the tunneling barrier and on the pre-exponent.
Since M i of our samples varies between 1 and 4, we attempted to detect correlations between the tunneling parameters of the exponent of Eq. (1) and M i . Table II  The upper curve in Fig. 1(a) shows σ(T ) of a sintered SFRO sample that underwent a short heat treatment at 500 o C in Ar5%H 2 . The maximum indicates mixed grain-boundary and metallic conductivity. A similar behavior is seen in Fig. 2 Fig.  1(a)). The solid line represents Eq. (1) fitted to the experimental data. Fig. 1(b) shows three more plots of σ(T ) for SFRO samples, including one for a c.p. sample. The data for the c.p. sample exhibit unusual behavior at high temperatures and Eq. (1) could be fitted to this line only up to 250 K.  Table I). The possibility that such a simple analytical function fits the dependence of πχw/2 on M i for this set of half-metallic c.p. samples requires further experimental and theoretical support.
Our analysis shows that the quality of the tunneling barriers in inter-grain conductivity depends on T o . The higher T o relative to RT, the closer is inter-grain tunneling to elastic tunneling. Table II and Fig. 3(b) show that, for only 3 samples out of 19, T o > 1000 K, i.e.
for two polycrystalline samples of SFMO (in Fig. 3(b) the two symbols coincide) and for one c.p. sample of SFRO. Note that for SFMO(N1) the ratio σ(RT )/σ(0) is only 1.25. The wide spread of the FIT parameters implies a broad range of interactions governing magnetoresistance (magneto-conductance). Results in Ref. 21 show that for sintered SFMO samples the magneto-conductance is much higher than that for a c.p. sample at all temperatures.
This requires a more systematic investigation.   Fig. 2 Fig. 1 represent Eq. 1 fitted to experimental data.