# Magnetothermopower in A2−xLaxFeMoO6 (A = Sr, Ba)

Authors: G. V. M. Williams; J. Stephen
Journal: Advances in Condensed Matter Physics
 (2017)

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## Abstract

A magnetothermopower has been observed in electronically spin-polarized polycrystallineSr2-xLaxFeMoO6 and Ba2FeMoO6. The magnetothermopower is linear up to ~50 K for Sr2-xLaxFeMoO6 and linear up to ~270 K for Ba2FeMoO6. We suggest that the magnetothermopower may arise from a spin-tunneling magnetothermopower between the grains.


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## Body

## 1. Introduction

The double perovskites are an interesting class of compounds where some of them are predicted to display 100% electronic spin polarization and hence they are called half-metals [1]. Most research has focused on Sr2FeMoO6 and Ba2FeMoO6 [1–11] where the Curie temperature is above room temperature and hence there are potential device applications that include magnetic field sensing [12, 13]. The appearance of electronic spin polarization in ferromagnetic metals means that spin-dependent tunneling can occur in thin films that are separated by a thin insulating layer [13–15]. Spin-dependent tunneling also occurs in Sr2FeMoO6 and Ba2FeMoO6 polycrystalline samples [1, 2, 8, 11, 12] where it has been shown that the resultant magnetoresistance can be modeled in terms of tunneling between the grains and through a thin insulating layer on the surface of the grains [8]. It has recently been shown that ferromagnetic/insulating/ferromagnetic tunneling junctions containing ferromagnetic metallic layers with some degree of electronic spin polarization can also display a spin-tunneling magnetothermopower [16, 17]. Since spin-tunneling is also known to occur between the grains in Sr2FeMoO6 and Ba2FeMoO6, then it might be expected that a spin-tunneling magnetothermopower also occurs in these compounds.In this paper we report the results from magnetothermopower and magnetoresistance measurements on polycrystallineSr2-xLaxFeMoO6 and Ba2-xLaxFeMoO6. We show that magnetothermopower is observed and it may possibly be due to a spin-tunneling magnetothermopower between the grains.


## 2. Materials and Methods

TheSr2-xLaxFeMoO6 and Ba2-xLaxFeMoO6 polycrystalline samples were made using a method described elsewhere [10]. X-ray diffraction (XRD) measurements showed that the samples were phase pure within the limit of detectability. Magnetothermopower, magnetoresistance, and magnetization measurements were made at different magnetic fields and temperatures using a Quantum Design PPMS. The magnetothermopower measurements were made using the TTO option where the applied magnetic field was parallel to the thermal gradient. The magnetoresistance measurements were done using a four-terminal configuration and with the applied magnetic field parallel to the current.Some high field magnetization measurements were done to estimate the Fe/Mo antisite disorder (ASD). The saturation magnetic moment per formulae unit (f.u.) was 2.66, 1.74, and 1.13μB/f.u. for Sr2-xLaxFeMoO6 with x=0, 0.2, and 0.4, where μB is the Bohr magneton. The maximum measured value for no ASD and x=0 is 4 μB/f.u. [18]. The resultant ASD is 15%, 25%, and 32% for x=0, 0.2, and 0.4 using the correlation between the saturation magnetic moment per f.u. and the ASD [15, 18]. These estimates of the ASD are close to those obtained from the XRD data using a ratio of the (101) peak divided by the (200) peak and using the correlation between ASD and this XRD ratio [10]. The saturation moment for Ba2FeMoO6 is much higher and it is 3.78 μB/f.u., which corresponds to a low ASD of 3%.


## 3. Results and Discussion

TheSr2-xLaxFeMoO6 thermopower,S, is plotted in Figure 1 for x=0, 0.2, and 0.4 at 6T and for no applied magnetic field. The thermopower in the absence of an applied magnetic field systematically increases with increasing x. This has been noted before and it has been suggested by comparison with the superconducting cuprates that it is indicative of the expected electron doping by La [10]. We have previously shown that the temperature dependence of the thermopower can be modeled with a diffusion term and a phonon-drag term where it was assumed that phonon-electron scattering is still significant at 300 K when compared with phonon-phonon scattering [10].Figure 1
Plot of the thermopower fromSr2-xLaxFeMoO6 with (a) x=0.4, (b) x=0.2, and (c) x=0 at 0T (filled circles) and 6T (filled up triangles).
(a) (b) (c)It is apparent in Figure1 that there is a magnetic field induced decrease in the Sr2-xLaxFeMoO6 thermopower for temperatures up to 300 K, which is still below the Curie temperature of ~425 K [5]. This change can be seen more clearly in Figure 2 where the difference in thermopower, ΔS=S6T-S(0T), is plotted and it is apparent that ΔS is linear in temperature up to ~50 K. A linear ΔS is also observed in Ba2FeMoO6 up to a higher temperature of ~270 K, as can be seen in Figure 3. We note that the Ba2FeMoO6 thermopower at 0T is similar to that reported in another study where there is an anomalous peak in the thermopower near the Curie temperature of 321 K [19].Figure 2
Plot of theSr2-xLaxFeMoO6 thermopower at 6T minus the thermopower at 0T for x=0 (filled circles), x=0.2 (filled up triangles), and x=0.4 (filled down triangles). The lines are guides to the eye.Figure 3
(a) Plot of the thermopower fromBa2FeMoO6 at 8T (filled up triangles) and 0T (filled circles). (b) The resultant thermopower difference S(8T)-S(0T). Also shown is the best fit line with a zero intercept.
(a) (b)There are a number of possible mechanisms that can lead to a magnetothermopower below the magnetic ordering temperature. For example, a spin-entropy thermopower can occur in compounds with strong electron-electron interactions [20, 21]. If these interactions are large enough then there will exist a very narrow band and the spin degrees of freedom can result in a spin-entropy thermopower, S=-σ/e, where σ is the entropy per electron [21]. At high temperatures the spin-entropy thermopower can be described by the Heikes function, S=kB×ln⁡gs×gc, where gs is the spin degeneracy, gc is the configurational degeneracy, and kB is Boltzmann’s constant [21]. This produces a positive contribution to the thermopower. For high applied magnetic fields, gs will tend towards 1 and hence there will be a reduction in the spin-entropy thermopower. A spin-entropy thermopower is unlikely to occur in Sr2-xLaxFeMoO6 because the conduction band is too broad [22] and the magnetothermopower strongly depends on temperature.Magnon-drag is another mechanism that can lead to a magnetothermopower [23]. It is analogous to phonon-drag in nonmagnetic metals. It should increase at low temperatures as the magnon density increases and it will decrease at high temperatures due to magnon-magnon and magnon-phonon scattering. It has been argued that the magnon populations can be low when the applied magnetic field is parallel to the magnetization and high when it is antiparallel to the magnetization. The net result can be a reduction in the magnon-drag thermopower at high magnetic fields and when all magnetic domains are aligned in the direction of the applied magnetic field. At low temperatures the magnon-drag thermopower, SMD, is proportional to T3/2/2/(nD3/2), where T is the temperature,n is the carrier concentration, and D is the exchange stiffness constant [23]. This predicts that SMD will be proportional to T3/2 at low temperatures and SMD should decrease with increasing carrier concentration. However, it is apparent in Figure 2 that S is linear below ~50 K for Sr2-xLaxFeMoO6 and linear below ~270 K for Ba2FeMoO6 rather than being proportional to T3/2, and S is still finite at 300 K. This suggests that magnon-drag thermopower is not the origin of the magnetothermopower in Sr2-xLaxFeMoO6 or Ba2FeMoO6.It may be that the magnetothermopower from polycrystallineSr2-xLaxFeMoO6 and Ba2FeMoO6 arises from a spin-dependent Seebeck effect. This type of magnetothermopower has been reported in magnetic tunneling junctions where one or more of the layers are ferromagnetically ordered and display electronic spin polarization [16, 17]. In the case of magnetic tunnel junctions with an insulating barrier between the two spin-polarized metallic layers or if there is no exchange coupling between the layers, the spin-tunneling magnetothermopower, ST, can be written as [16](1)ST=-ekBTG∫tEE-EF-∂f∂EdE,wheree is the electron charge,G is the tunneling conductance,t(E) is the tunneling transmission function,E is the energy, and f is the Fermi function. The tunneling conductance can be written as [16](2)G=e2h∫tE-∂f∂EdE,where h is Planck’s constant.IftE does not strongly depend on energy within a few kBT of EF, where kB is Boltzmann’s constant and EF is the Fermi energy, then it can be shown using (1) and (2) that ST reduces to the Mott formulae [17](3)ST=-π23kB2Te1G∂GE∂EEF,whereG(E) is the energy-dependent tunneling conductance. The change in the magnetothermopower is then [17](4)ΔST=SP-SAP=-π23kB2Te1GP∂GPE∂EEF-1GAP∂GAPE∂EEF,where SP and GP are the spin-tunneling thermopowers for the magnetization parallel to both layers and SAP and GAP are the spin-tunneling thermopowers when the magnetization from both layers is antiparallel. Equation (4) predicts that ΔST will be linearly dependent onT.If a spin-tunneling magnetothermopower occurs inSr2-xLaxFeMoO6 and Ba2FeMoO6 at the grain boundaries then the thermopower can be written as S(B)=ST(B)+SBulk, where SBulk is the thermopower away from the grain boundaries that is assumed be independent of the applied magnetic field. Thus, ΔS(B)=ΔST(B). Since ΔS(B) is linear in temperature up to ~50 K for Sr2-xLaxFeMoO6 and up to ~270 K in Ba2FeMoO6 as predicted from (4), then our data suggests that the magnetic field dependence of ΔS is due to a spin-tunneling magnetothermopower.The slope of ΔS below ~50 K for Sr2FeMoO6 is nearly the same for x=0 and x=0.2 and it is smaller for x=0.4. It is possible that this is due to a change in EF for x=0.4. The effect of changes in EF on ΔS can be illustrated using a simple model where tp(E) can be written as tPE=N↑N↑+N↓N↓t and tAPE=2N↑N↓t, where N↑ is the majority carrier DOS, N↓ is the minority carrier DOS, and tP(E) and tAP(E) are the energy independent tunneling transmission functions for the parallel and antiparallel configurations, respectively [24]. It can then be shown from (2) and (3) that (5)SP=-π23kB2Te1N↑N↑+N↓N↓2N↑∂N↑E∂EEF+2N↓∂N↓E∂EEF,SAP=-π23kB2Te1N↑N↓N↑∂N↓E∂EEF+N↓∂N↑E∂EEF.If we take a simple DOS with N↑=a1E0.5 and N↓=a2E-E00.5 then from (5)(6)ΔS=SP-SAP=-π26kB2TeEF21-zx-2-x1-x,where x=E0/EF, x<1, and z=a22/a12+a22. This is negative provided that z>1/(2-x). This simple example shows how a negative spin-tunneling magnetothermopower can occur purely from majority and minority DOS effects. ΔS will decrease if EF increases or if the spin polarization decreases. The smaller ΔS gradient for Sr2-xLaxFeMoO6 with x=0.4 may suggest that EF is larger for x=0.4, which would appear to be consistent with electron doping by La.The departure from linearity for ΔS above ~50 K for Sr2-xLaxFeMoO6 can occur ift(E) is energy-dependent. The envelope functions E-EF-∂f/∂E and -∂f/∂E in (1) and (2) probet(E) with ~± kBT of EF. Thus, ift(E) displays large energy dependence for E-EF>~6 meV then ΔS will be approximately linear only for low temperatures, which is what is observed. The departure from linearity for Ba2FeMoO6 only occurs above ~270 K and close to the Curie temperature. This suggests that the lower temperature departure seen in Sr2-xLaxFeMoO6 may be due to the ASD. It is also possible that the departure in ΔS from linearity in Sr2-xLaxFeMoO6 above ~50 K is due to inelastic scattering that has not been included in the simple model above.The discussion above concerns the relatively well defined conditions where there is no applied magnetic field or when the magnetic field is high enough so that the magnetization directions are the same in the regions close to the grain boundaries. For intermediate magnetic fields, it is reasonable to assume thatS(B) will vary smoothly between SAP and SP as the magnetic field is increased. This is indeed observed as can be seen in Figure 4 where ΔS(B) is plotted as a function of the applied magnetic field for Sr2FeMoO6 at 77 K.Figure 4
Plot of the thermopower difference,S(B)-S(0T) (left axis, circles), and the magnetoresistance (right axis, solid curve) from Sr2FeMoO6 against the applied magnetic field at 77 K.If there is a spin-tunneling magnetothermopower then there should also be a spin-tunneling magnetoresistance. We show in Figure4 that a magnetoresistance is observed where the magnetoresistance from Sr2FeMoO6 at 77 K is plotted as a function of the applied magnetic field. Here we define the magnetoresistance as MR=RB-R0/R0, whereR(B) is the resistance for an applied magnetic field andR(0) is the resistance with no applied magnetic field. The magnetic field dependence and the magnitude of the magnetoresistance are similar to those found in other studies on polycrystalline Sr2FeMoO6 and Ba2FeMoO6 where it has been attributed to spin tunneling between the grains [2, 8, 11, 12]. We find that the magnetoresistance and ΔS(B) have similar magnetic field dependence.


## 4. Conclusions

In conclusion, we observed a magnetothermopower in polycrystallineSr2-xLaxFeMoO6 and BaFeMoO6 that is linear up to ~50 K in Sr2-xLaxFeMoO6 and ~270 K in Ba2FeMoO6. The magnetothermopower may be due to a spin-tunneling thermopower where the magnetothermopower can be linear when the tunneling transmission function is only weakly dependent on energy within a few kBT of EF. In this scenario, the magnetothermopower may arise from spin tunneling across the grain boundary. The departure from linearity above ~50 K in Sr2-xLaxFeMoO6 may be due to a tunneling transmission function that has significant energy dependence only for (E-EF)>~6 meV. It is also possible that there is significant inelastic scattering at higher temperatures.



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*Source: 7578930-2017-01-05.xml*