Magnetotransport of indium antimonide doped with manganese

Magnetotransport, including the magnetoresistance (MR) and the Hall effect, isinvestigated in polycrystalline In1-xMnxSb samples with x = 0.02 0.06, containing nanosize MnSb precipitates. The relative MR, / , is positive within the whole range of B= 0 10 T and T ~ 20 300 K. The Hall resistivity, H, exhibits a nonlinear dependence on B up to the room temperature.MR is interpreted with the two-band model, suggesting two types of holes with different concentration and mobility. In addition, analysis of H (B, T) is performed by taking into account both the normal and the anomalous contributions. The latter is attributable to the effect of MnSb nanoprecipitates, having the ferromagnetic Curie temperature well above 300 K.


Introduction
Interest to the group III-V Mn-doped diluted magnetic semiconductors (DMS) is connected mainly to their potential applicability in spintronics [1].However, utilization of DMS in spintronic devices requires high values of the ferromagnetic (FM) Curie temperature, T C .On the other hand, intrinsic limitations existing in homogeneous III-V DMS permit to obtain materials only with T C lyingwell below the room temperature, as far as a carrier-mediated ferromagnetism is considered [2].An effective way to overcome such limitations is creation of inhomogeneous materials by alloying III-V DMS with FM compounds of the Mn-V group,havingT C well above the room temperature, such as MnSb withT C = 585 K [3].
This way has been realized recently by doping InSbwith Mnat a non-equilibrium preparation conditions (direct alloying of InSb, Mn and Sb, followed by a fast cooling of the melt) [4].The resulting compound, with a nominal formula In 1-x Mn x Sb andx = 0.01 0.06,is referred below simplyas InMnSb due to a complicated magnetic system and only a minority(~ 10 20 %) of substitutional Mn entering directly the InSb lattice.Two other magnetic components were found to be atomic-size Mn dimers and MnSb nanoparticles with sizes ~ 100 600 nm and volume fraction ~ 1 4 %, which provided interesting magnetic properties of the material, including saturation of the magnetizationM (B) up to T = 300 K already above the fields of B ~ 1 2 T [4].
Here are reported measurements of the magnetoresistance and the Hall effect in the same InMnSb samples as those investigated in Ref. 4 and their detailed quantitative analysis.

Preparation and characterization of polycrystalline
InMnSb samples with x = 0.02, 0.03 and 0.06 referred below as # 2, # 3 and # 4, respectively, is described in detail in Ref. 4. The magnetotransport measurements of the samples were performed using the standard six-point geometry in pulsed magnetic fields B up to 10 T at temperatures between T=16 320 K.
The Hall resistivity, H , exhibits a non-linear dependence onB up to room temperature (see top panel of figure 1).The typical behavior of the relative magnetoresistance (MR), / [ (B) (0)]/ (0), is exhibited in the bottom panel of figure 1.

Analysis of the results
In FM materials the Hall resistivity satisfies the expression whereR N and R A are the normal and the anomalous Hall coefficients, respectively.The normal contribution to H is connected to the transverse electric field due to the Lorenz force, whereas the anomalous one to generation of the transverse electric field of another nature, governed by the influence of the spin-orbit interaction on the electron transport [5].The latter is attributable to the effect of MnSb nanoprecipitates (see Introduction), which is one of the reasons to non-linearity of H (B) [4].The second reason is possible contribution of two types of charge carriers with different concentration and mobility, addressed to the two-band model [6,7].In such conditions R N becomes a function of B [7], which can be presented with the expression are functions of R j and j , wherej = 1 and 2 is the band number [8].Similar to Eq. (2), the resistivity in the two-band model can be expressed as [7,8] 2 ) [8].If neither of j and R j depends on B, then 0 = (T) at B = 0 [7,8] and MR in figure 1 can be fitted with Eq. ( 3)taking , 0 and independent of B,yielding the values of and .The plots of / vs. B (lines in the bottom panel of figure 1), evaluated with Eq. ( 3) using the dependences of (T) in zero field (not shown), exhibit a good agreement with the experimental data.Hence, the two-band model used above provides a reasonable explanation of positive MR in the investigated material.
Because M (B) saturates already atB S ~ 1 2 T [4], for B>B S one can put M M S =M (B S ) = const.Then, combining Eq. ( 1) and ( 2) one finds the expression which suggests that Y is a linear function of ( B) 2 for a correctly chosen value of R A M S .Such R A M S value can be obtainedunder condition of the best linearity of the plots With the expressions of R 0 , R , 0 , and listedbelow Eq. ( 2) and ( 3), the values of j the Hall concentrations p j = (eR j ) 1 and the mobilities j (j = 1 and 2), as well as those ofR A M S are evaluated.The dependences of these parameters on T for # 3 are displayed in the bottom panel of figure 2 and in the top, middle and bottom panel of figure 3, respectively.Temperature dependences of p j , j and R A M S in other samples are similar to those shown in figure 3 for # 3. Therefore, these data are given at some selected temperatures.Namely, p 2 2.3 10 20 and 3.3 10 20 cm 3 , and 2 35 and 32 cm 2 /Vs for # 2 and # 4, respectively, exhibit no significant dependence on T within the error.In # 2 the values of p 1 2.5, 7.5 and 6.6 (in units of 10 16 cm 3 ), 1 = 2500, 1600 and 1470 cm 2 /Vs, and R A M S 6.5, 17 and 2.7 cm at T = 20, 90 and 270 K, respectively, are obtained.Those in # 4 are as follows: p 1 3, 8.6 and 9.7 (in units of 10 16 cm 3 ), 1 3060, 1600, 1320 cm 2 /Vs and R A M S 3.5, 16.5 and 7.5 cm at T = 16, 100 and 320 K, respectively.Eventually, the relations of 1 >> 2 and 2 observed in # 3 (bottom panel of figure 3) are fulfilled in # 2 and # 4, as well.
Finally, as can be seen in the top panel of figure 1,the dependences of H (B) tends to linear functions above B ~ 5 T. Therefore, the analysis of the Hall resistivity can be performed already within a single-band approximation, as made often in literature (see e. g.Refs.6,[9][10][11].Namely, at B > 5 TM (B) is [4], permits determination of R N and R A M S (both independent of B) by linear fits of H (B) in the high-field limit [11].This yields the data of p H = (eR N ) 1 and R A M S exhibited for # 3 in the top and bottom panels of figure 3, respectively.In other samples, the behavior of p H and R A M S in the singleband approximation is similar to that in figure 3.

2.3Discussion
As follows from the results above, the two-band model permits interpretation of the positive MR and the Hall effect in the investigated InMnSb samples simultaneously, provided that all the partial contributions of j and R j ( j = 1 and 2) do not depend on the magnetic field [7].Such supposition is well supported by the good agreement between the experimental (symbols) and the calculated (lines) dependences of / on B(see the bottom panel of figure 1).Additional support is given by thebroad linear intervals on the plots of Y vs. ( B) 2 , which is evident in the top panel of figure 2. The obtained relations of 1 >> 2 and p 1 <<p 2 permits us to attribute the bands 1 and 2 to the light-holeband and the heavy-hole band of InSb [12], respectively.Indeed, the ratios of 1 / 2 ~ 40 90 (see figure 3 and text below it) are comparable with that of the heavy-hole (hh) and the light hole (lh) effective masses,m hh /m lh ~ 30 [12].On the other hand, the strong inequality p 1 <<p 2 is consistent with the same relation between the density of states, determined by the effective mass ratio, as well.
Another interpretation of the origin of two bands with quite different concentration and mobility of the holes has been proposed recently to analyse the positive MR in InMnSb [6].Such interpretation is based on spin-splitting of a single p-d hybridized valence band due to the kinetic p-d exchange, leading to shifts of the spin-up and spindown bands towards energies above and below the Fermi energy, respectively [6].Therefore, such shifts can lead to different hole concentrations in the bands.However, the ratio of 1 / 2 ~ 40 90 observed here already in zero magnetic field looks overestimated, if it isascribed to different scattering of carriers with different spin polarization [6,13].Indeed, in such a case the values of the ratio of 1 / 2 only up to ~ 4 5 have been predicted at B as high as 10 T [13].
As can be seen in the bottom panel of figure 2, the resistivity of the investigated InMnSb samples is governed only by the contribution of the holes of the At this point, the difference between the behaviours of the anomalous contribution to the Hall effect in the bottom panel of figure 3 is noticeable.Indeed, the temperature maximum of R A M S following from the twoband model analysis is rather unusual, whereas no such a maximum appears within a single-band consideration.On the other hand, as discussed above the two-band model analysisis substantiated well enough to attribute the nonmonotonic behavior of R A M S to intrinsic properties of the material.
Finally, we discuss briefly possible influence of the metallic FM MnSb nanoinclusions on the normal Hall contribution, taking into account the values of the resistivity [14] and the normal Hall constant [14,15]

Conclusions
We have investigated the positive magnetoresistance and the Hall effect in InMnSb containing nanosize MnSb precipitates.Both effects are interpreted with the twoband model, suggesting contributions of two types of holes with different concentration and mobility.The values of p j and j addressed to each type of charge carriers are obtained, attributing them presumably to the light and heavy holes of InSb.In addition, the anomalous contribution to the Hall effect is observed up 300 K.This is attributable to the effect of FM MnSb nanoprecipitates, having T C well above the room temperature.

DOI: 10 5 Fig. 1 .
Fig. 1.The magnetic field dependences of H (top panel) and of / (bottom panel).The lines are calculated as described in the text.

Fig. 2 .
Fig. 2.The plots of Y vs. ( B) 2 (top panel) and the dependences of 1 , 2 and on T (bottom panel).The lines are linear fits (top panel) and guides for the eye (bottom panel).

2 of
Y vs. ( B)2 .This is achieved for all samples within the whole interval of T and between B ~ 2 10 T (examples are shown in the top panel of figure2).Eventually, the linear fit of the obtained plots of Y vs. ( B) 2 yields the values of R 0 and R , where the data of (T), obtained from the analysis of MR aboveand shown in the middle panel of figure3,have been used.

Fig. 3 .
Fig. 3. Temperature dependences of p 1 , p 2 andp H (top panel), of 1 , 2 and (middle panel) and of R A M S (bottom panel) in # 3. The linesare to guide the eye.

band 2 (
presumably the heavy-hole band).At the same time, the analysis of the Hall effect within a single-band approximation yields the values of p H , practically coinciding with those of p 2 (circles and crosses in the top panel of figure3, respectively).In this sense, the twoband model analysis of the Hall effect, being much more complicated, seems to give no advantage with respect to the more simple one considering only a single type of charge carriers.However, both analyses can be performed only within a field interval, where the magnetization is saturated, to satisfy the condition of R A M R A M S = const.As can be seen in the top panel of figure2, the onset of the linear part on the plots of Y vs. ( B) 2 at B 2 T is close to the onset of saturation of the magnetization, B S ~ 1 2 T[4] (see Introduction).At the same time, the plots of H (B) tend to linearity only at B> 5 T being evidently higher thanB S .Such contradiction provides additional support to the benefit of the two-band model approach above.

5 )
of bulk MnSb, R N (MnSb), being much smaller those of our samples.With the results of Refs.16 and 17, it can be shown that the value of p H * corrected to presence of a fraction << 1 of MnSb precipitates, is connected to p H with the expression .(With the values of R N (MnSb) ~ 10 3 10 4 cm 3 /C [14, 15] and the data of in Ref. 4, one can find only a small reduction of the Hall concentration by ~ 10 20 %.