Advances in Condensed Matter Physics
Volume 2017 (2017), Article ID 7578930, 5 pages
https://doi.org/10.1155/2017/7578930

Research Article

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

G. V. M. Williams and J. Stephen

MacDiarmid Institute, SCPS, Victoria University of Wellington, P.O. Box 600, Wellington 6012, New Zealand

Correspondence should be addressed to G. V. M. Williams; grant.williams@vuw.ac.nz

Received 20 November 2016; Accepted 15 December 2016; Published 5 January 2017

Academic Editor: Jörg Fink

Copyright © 2017 G. V. M. Williams and J. Stephen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

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

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 polycrystalline and . We show that magnetothermopower is observed and it may possibly be due to a spin-tunneling magnetothermopower between the grains.

2. Materials and Methods

The and 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 1.13 μ B/f.u. for with , 0.2, and 0.4, where μ B is the Bohr magneton. The maximum measured value for no ASD and is 4 μ B/f.u. [18]. The resultant ASD is 15%, 25%, and 32% for , 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 is much higher and it is 3.78 μ B/f.u., which corresponds to a low ASD of 3%.

3. Results and Discussion

The thermopower, S, is plotted in Figure 1 for , 0.2, and 0.4 at 6 T and for no applied magnetic field. The thermopower in the absence of an applied magnetic field systematically increases with increasing . 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].

(a)

(b)

(c)

Figure 1: Plot of the thermopower from with (a) , (b) , and (c) at 0 T (filled circles) and 6 T (filled up triangles).

It is apparent in Figure 1 that there is a magnetic field induced decrease in the 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, , is plotted and it is apparent that ΔS is linear in temperature up to ~50 K. A linear ΔS is also observed in up to a higher temperature of ~270 K, as can be seen in Figure 3. We note that the thermopower at 0 T 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 the thermopower at 6 T minus the thermopower at 0 T for (filled circles), (filled up triangles), and (filled down triangles). The lines are guides to the eye.

(a)

(b)

Figure 3: (a) Plot of the thermopower from at 8 T (filled up triangles) and 0 T (filled circles). (b) The resultant thermopower difference . Also shown is the best fit line with a zero intercept.

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, , where is the entropy per electron [21]. At high temperatures the spin-entropy thermopower can be described by the Heikes function, , where is the spin degeneracy, is the configurational degeneracy, and is Boltzmann’s constant [21]. This produces a positive contribution to the thermopower. For high applied magnetic fields, 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 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, , is proportional to /2/(nD 3/2), where is the temperature, n is the carrier concentration, and is the exchange stiffness constant [23]. This predicts that will be proportional to at low temperatures and should decrease with increasing carrier concentration. However, it is apparent in Figure 2 that is linear below ~50 K for and linear below ~270 K for Ba₂FeMoO₆ rather than being proportional to , and is still finite at 300 K. This suggests that magnon-drag thermopower is not the origin of the magnetothermopower in or .

It may be that the magnetothermopower from polycrystalline 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, , can be written as [16]

where e is the electron charge, G is the tunneling conductance, t(E) is the tunneling transmission function, E is the energy, and is the Fermi function. The tunneling conductance can be written as [16]

where is Planck’s constant.

If does not strongly depend on energy within a few of , where is Boltzmann’s constant and is the Fermi energy, then it can be shown using (1) and (2) that reduces to the Mott formulae [17]

where G(E) is the energy-dependent tunneling conductance. The change in the magnetothermopower is then [17]

where and are the spin-tunneling thermopowers for the magnetization parallel to both layers and and are the spin-tunneling thermopowers when the magnetization from both layers is antiparallel. Equation (4) predicts that ΔS T will be linearly dependent on T.

If a spin-tunneling magnetothermopower occurs in and at the grain boundaries then the thermopower can be written as , where is the thermopower away from the grain boundaries that is assumed be independent of the applied magnetic field. Thus, . Since ΔS(B) is linear in temperature up to ~50 K for and up to ~270 K in 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 and and it is smaller for . It is possible that this is due to a change in for . The effect of changes in on ΔS can be illustrated using a simple model where (E) can be written as and , where is the majority carrier DOS, is the minority carrier DOS, and (E) and (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

If we take a simple DOS with and then from (5)

where , , and . This is negative provided that . This simple example shows how a negative spin-tunneling magnetothermopower can occur purely from majority and minority DOS effects. ΔS will decrease if increases or if the spin polarization decreases. The smaller ΔS gradient for with may suggest that is larger for , which would appear to be consistent with electron doping by La.

The departure from linearity for ΔS above ~50 K for can occur if t(E) is energy-dependent. The envelope functions and in (1) and (2) probe t(E) with ~± of . Thus, if t(E) displays large energy dependence for  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 may be due to the ASD. It is also possible that the departure in ΔS from linearity in 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 that S(B) will vary smoothly between and 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, (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 Figure 4 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 , where R(B) is the resistance for an applied magnetic field and R(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 and 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 polycrystalline and that is linear up to ~50 K in 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 of . In this scenario, the magnetothermopower may arise from spin tunneling across the grain boundary. The departure from linearity above ~50 K in may be due to a tunneling transmission function that has significant energy dependence only for 6 meV. It is also possible that there is significant inelastic scattering at higher temperatures.

Competing Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

The authors acknowledge funding support from the New Zealand Ministry of Business, Innovation and Employment (C08X0705, C08X01206) and the MacDiarmid Institute for Advanced Materials and Nanotechnology.

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