Anwar, M.S.
Citation
Anwar, M. S. (2011, October 19). Spin triplet supercurrents in thin films of ferromagnetic CrO2. Casimir PhD Series. Retrieved from https://hdl.handle.net/1887/17955
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Transport properties of CrO 2
In this chapter we investigate the transport properties of the CrO2 thin films deposited on both TiO2 and sapphire substrates. The films are good metal at low temperatures with residual resistivity of the order of 6 µΩcm for films deposited on TiO2 and two times higher for sapphire substrates. The mag- netoresistance (MR) changes sign from negative to positive at temperature around 100 K. At low temperature the MR is a linear function of applied field, which might derive from intergrain tunneling magnetoresistance. This is also suggested by rotational scans (rotation of applied magnetic field) of the MR.
Planar Hall effect measurements reveal that the CrO2 thin films are not in a single magnetic domain state even for films deposited on isostructural TiO2 substrate.1
1Parts of this chapter have been published in,
M. S. Anwar and J. Aarts, Inducing supercurrents in thin films of ferromagnetic CrO2, Supercond. Sci. Technol. 24, 024016 (2011).
44
4.1 Introduction
In Chapter 3 the growth and magnetic properties of CrO2thin films were dis- cussed. The main objective behind the growth of these films is to use them in heterostructures with superconductors (SFS devices) and study the long range proximity effects as discussed in Chapters 1 and 2. For this, it is also useful to extensively characterize the normal state transport properties of the films. Generally, this will reveal how clean the films are, and allow under- standing of the electronic properties of the material. It has been observed that CrO2 is a good metal at low temperatures with residual resistivity of the order of 10 µΩcm and a poor metal at room temperature with resistivity more that 300 µΩcm [27, 50, 51]. Moreover, there is the question of the role and/or influence of the grain structure. It was observed in Chapter 3 that all films are deposited in the form of rectangular grains, and it is important to know whether the grains boundaries are barriers for transport. The ori- entation of these grains is strongly dependent on the type of the substrate used in deposition. It has been shown by magnetotrasport investigations that at low temperatures the intergrain tunneling magnetoresistance (ITMR) is dominant [42, 44]. Intergrain tunneling suggests the presence of a barrier in between the grains. If such a barrier is present in our devices, it can strongly suppress the supercurrent. So, it is important to study the transport proper- ties along with the morphology and magnetic properties of CrO2before using it in the fabrication of the required SFS devices.
This chapter starts with a description of the sample structuring and then reports on the transport properties in two parts. First, measurements of the temperature dependent resistance R(T ), of the high field magnetoresistance and of the Hall effect are presented and discussed. Next, data are given on the low field (anomalous) magnetoresistance, with emphasis on the angular dependence with respect to the applied field and on the Planar Hall effect.
4.2 Sample preparation
To investigate the transport properties of CrO2 thin films, microbridges were structured in the films. For films deposited on both pretreated and untreated TiO2substrates, L-shaped bridges were used which allowed probing the trans- port along both in-plane crystal directions (current along b- and c-axis) at the same time. They were made with e-beam lithography, were 40 µm wide, with 200 µm separation between the voltage contacts and 100 nm thickness of the film. For the lithography step, a negative resist (MaN2405) was used, which was spin coated at 4000 rpm for 60 sec. and baked for 10 min at 90oC. Next
is the etching of L-structure in the CrO2 films. It is difficult to etch the film with Ar ions etcher because of a rather slow etch rate. So, etching was done with reactive ions etching (RIE), where a mixture of CF4 (30 sccm) and O2 (15 sccm) was utilized with a background presure of 10−6mbar. The RIE etch rate was of the order of 0.8 nm/sec. An optical microscope image is given in Fig. 4.1. For the sapphire substrate, a 200 nm thick film was grown, in which a Hall bar (200 µm wide, 2 mm between the voltage contacts) was structured with optical lithography.
Figure 4.1: An optical microscope image of ’L’ shaped bar etched into a 100 nm thick CrO2 film deposited on a pretreated TiO2 substrate to measure the transport along both in-plane axes (the c-axis and the b-axis).
4.3 Results: Resistivity, magnetoresistance, Hall ef- fect
4.3.1 Resistivity
Figure 4.2a shows the specific resistance as a function of temperature for a 100 nm thick CrO2film deposited on a pretreated TiO2substrate, along both the c-axis and the b-axis. The residual resistivity (ρo) is of the order of 9 µΩcm along the b-axis while along the c-axis it is found 6 µΩcm. These values are quite similar the literature values [27, 50]. It is noticeable that ρ(T ) at 4 K is lower for the c-axis than for the b-axis, while it reverses at room temperature, with a crossover at 110 K (see Fig. 4.2b). We observed an unexpected bump in ρ(T ) between 75 - 105 K along both in-plane axes that is
very clear in the derivative of the resistivity as function of temperature. The derivative also shows the transition temperature of the order of 374 K (see Fig. 4.2c). Qualitatively, the results are the same for CrO2 films deposited on untreated TiO2 and pretreated TiO2substrates although there is rather a small quantitative difference.
Figure 4.2: (a) Resistivity versus temperature for a 100 nm thick CrO2 film deposited on a pretreated TiO2 substrate, along the in-plane crystallographic c-axis (open squares) and the b-axis (open circles). The solid lines are a fit to Eq. 4.1, given in the text. (b) The cross-over between the resistivities at 110 K. (c) dρ/dT is showing the ferromagnetic transition temperature at 374 K and a dip around 75-100 K along both c- (dashed line) and b-axes (solid line). (d) Resistivity as a function of temperature for a 200 nm thick CrO2
film deposited on a sapphire substrate. The solid line is the fit.
Figure 4.2d presents the data on ρ(T ) of a 200 nm thick CrO2film deposited on a sapphire substrate. At low temperature, the ρ(T ) becomes almost con- stant (temperature independent), with ρoof the order of 12 µΩcm, larger than the ρoof the films deposited on TiO2. At room temperature, ρ is significantly lower than for films on TiO2.
In the literature, an accepted phenomenological expression used to describe ρ(T ) is given by [27, 51],
ρ(T ) = ρo+ AT2e(−∆T) (4.1) where ρois the residual resistivity and A is a coefficient. As shown in Fig.
4.2 this expression fits the ρ(T ) data well. Table 4.1 gives typical numbers for ρo, A and ∆. The low values for ρo show that the films behave as a good metals at low temperatures. The mean free path le can be estimated from free electron model using the relation le= e2ρ3
oυFN, where N is the density of states at the Fermi level, υF is the Fermi velocity and e is the charge of the electron. Using N = 7.55×1046states/J/cm3and υF = 2.5×105m/s [30], leis about 100 nm, which shows that the grain boundaries are not dominating the transport behavior. The values of ∆ are around 100 K, which does not seem to be related easily to a characteristic energy scale of the material. This will be discussed further below, but here we note that 100 K is the temperature where ρ(T ) shows an anomaly.
Figure 4.3: Resistivity versus T2 for a 100 nm thick CrO2 film deposited on TiO2, (a) along the b-axis and (b) along the c-axis. The solid lines are a fit to T2 behavior.
As the physical significance of ∆ is not clear, we also tried to simply fit a T2 behavior without exponential term. The results are shown in Fig. 4.3.
For the films deposited on TiO2, resistivity shows a quite good fit to the T2 dependence along the b-axis between 100 K to 350 K, similar to the results of Suzuki et al. [52] for CrO2 film deposited on ZrO2 substrate, while along
the c-axis it is quite poor and only exist between 215 K and 312 K. It also emphasizes the anisotropic behavior of resistivity as a function of temperature.
Table 4.1: Some important parameters ρo, ∆ and A for CrO2 thin films de- posited on pretreated, untreated TiO2 and sapphire substrates.
Samples ρo ∆ A
µΩcm (K) nΩcm K2 pretreated-TiO2 (c-axis) 6 80 2.8
(b-axis) 9 150 5.2
untreated-TiO2 (c-axis) 7 75 2.6
(b-axis) 11 140 3.9
sapphire 12 90 2.2
4.3.2 Magnetoresistance: High field MR
Magnetoresistance (MR) is the measure of the relative change in the resis- tance of a material (particularly, magnetic materials) to the resistance in the externally applied magnetic field at a constant temperature, i.e. given by [49],
M R = ∆ρ
ρ = R(H) − R(0)
R(0) (4.2)
where R(0) is the resistance in zero field and R(H) is the resistance in the field. High field magnetoresistance (MR) is measured at different temperatures in a PPMS with field (maximum 9 T) oriented out-of-plane for CrO2 films deposited on both pretreated and untreated TiO2substrates.
Figure 4.4 shows the data for magnetoresistance (MR) measured in per- pendicular configuration (out-of-plane field) for various temperatures between 10 to 250 K. The sample is a 100 nm thick CrO2 film deposited on a pre- treated TiO2 substrate etched in an L-shaped structure so that the current can simultaneously pass along the b-axis and the c-axis. At low fields, the MR shows variations which have to do with changes in the magnetization. When the magnetization saturates, above about 1.5 T, monotonic behavior sets in, which is different in sign for low temperatures and high temperatures. At 10 K and 50 K, the MR is positive that reached at values of 4% (1%) in 5 T with current along the c-axis (b-axis). At 100 K, the sign changes to negative although a cross-over to positive behavior is visible at about 4 T, where MR changes quadratically. The change in MR is linear below and above 100 K.
Above 100 K the MR is negative, with values around -2% at 5 T around room
Figure 4.4: The magnetoresistance as a function of applied field for a 100 nm thick CrO2 film deposited on a pretreated TiO2 substrate, for various tem- peratures. The field is perpendicular to the normal of the substrate and the current I is either along the b- or the c-axis.
temperature (250 K). These observations are quite similar for an untreated CrO2 film, except the lower field curves are not symmetric, which might re- lated with the quality of the films.
Figure 4.5 shows the MR for the 200 nm thick film on sapphire, again with the field applied out-of-plane. The data show the same features; positive MR at 10 K, a cross-over at 100 K, negative MR at 300 K. Noteworthy are the large values at 10 K, of the order of 30% at 8 T.
4.3.3 Anomalous Hall Effect
Figure 4.6-a shows the transverse resistivity ρxy = Vyw/Ix (where w is the width of the Hall bar) as a function of externally applied field in out-of-plane configuration, for various temperatures between 10 K to 400 K. The sample is a 100 nm thick CrO2 film deposited on a pretreated TiO2 substrate. We
Figure 4.5: Magnetoresistance for a 200 nm thick CrO2thin film deposited on a sapphire substrate up to ±9 T magnetic field at different temperatures, (a) the MR at 10 K is positive with 30% increase at 8 T, (b) at 100 K the MR changes sign and (c) at 300 K the MR is negative.
measured Hall resistance for films deposited on both pretreated and untreated TiO2 substrates and for current passing along both the c- and the b-axis.
We did not measure any difference beyound the experimental error for both directions of current and for both kind of films, in agreement with Onsagers principle that ρxy= ρyx regardless of crystal orientation.
At low temperatures (<50K), ρxy(H) is linear with a slope that corre- sponds to hole-like charge carriers. Between 100 K and 350 K, an extra con- tribution is visible at low fields, which is usually ascribed to the effects of the magnetization, and referred to as the anomalous Hall effect (AHE).
The Hall resistivity can then be written as
ρxy= µo(RoHa+ RSM ) (4.3) with Rothe normal Hall coefficient and RS the anomalous Hall coefficient.
Figure 4.6: (a) Hall resistivity as a function of applied field ρxy(H) for a 100 nm thick CrO2film deposited on a pretreated TiO2substrate, measured at various temperature between 10 K to 400 K. (b) Ordinary Hall coefficient Ro as a function of temperature between 10 - 300 K. (c) nr. of holes/Cr atom versus temperature decreases with the increase in the temperature. (d) Anomalous Hall coefficient RS versus temperature, the solid line is the theoretical fit Eq.
4.4.
The carrier density follows in a one-band model from Ro= −1/en. A positive Rotranslates to holes as carriers.
4.4 Discussion
The discussion on the data given above can be started with the residual re- sistivity ρo. The different values of ρo for different substrates reveal that ρo
is sensitive to the disorder. Principally, for a normal metal, ρo is due to only lattice imperfections or impurities in the metal because the electron-phonon scattering vanishes at low temperatures. The ratio between room tempera- ture resistance and ρo is a measure of the crystal imperfections or impurity
concentration. It is known as the residual resistance ratio (RRR) [3]. For our samples the RRR is 20 along the b-axis and 41 along the c-axis. These values are higher than for the films deposited on an untreated TiO2 and sap- phire substrates, which shows that CrO2 films deposited on a pretreated TiO2
substrate are in better quality.
Another important issue is the description of R(T ) with Eq. 4.1, which is usually interpreted as a T2contribution, modified with a phenomenological exponential. In general, the T2 term comes from electron-electron scatter- ing. The value of the coefficient A of T2 term is in the range of 2.2 - 5.0
× 10−3 µΩcm/K2 and much larger than normal ferromagnetic metals (1.3- 1.6 × 10−5 µΩcmK−2) [52]. The higher value might be related with the contribution of the electron-magnon scattering along with electron-electron scattering [51, 52]. If ρ(T ) also has electron-magnon scattering contributions then the prefactor ∆ of the exponential term might be related with a gap in magnon spectrum. However, the value of ∆ is found about ≈ 150 K (maxi- mum, along the c-axis), which is still very low to be associated with spin flip scattering, since the minority spin band is about 1.5 eV below the Fermi level.
That suggests there is no correlation of ∆ with spin flip scattering in CrO2. So, the physical significance of the ∆ is not clear. It is remarkable that the value of ∆ falls in the temperature range of about 100 K where there is a dip in dR/dT . This may also be correlated with M (T ) measurements presented in Chapter 3 (deviation from Bloch’s law). This strongly suggests some elec- tronic phase change in CrO2 around 100 K. That is reinforced by the high field MR data, which show a change in sign around 100 K. Looking at the Hall data, a plot for Ro is given in Fig. 4.6b and the derived carrier density in Fig. 4.6c. It can be seen that the carriers are holes, and that their number actually is not constant, but drops significantly between 200 k and 100 K.
There appears therefore to be no reason to try describing the resistivity in the whole temperature regime with a single expression. Something can also be said about the anomalous Hall coefficient RS, which is plotted in Fig. 4.6d.
It is not present below 100 K, but then grows exponentially around 150 K and has a peak at 350 K just below the Curie Temperature. The sign of Ro
and RS are different, which is of significance, since conventional ferromagnets they are in the same. These data are quite similar to what is seen in Colossal Magnetoresistance materials such as (La0.7Sr0.3)MnO3 or (La0.7Ca0.3)MnO3
and they seem to rule out the conventional explanations of conventional spin scattering and side jump or skew scattering but a Berry phase might be the possible explanations for these materials. Recently, it was suggested to use topological spin defects or Skyrmion strings [53] to understand the behavior of AHE, in particular for double exchange systems (also the case of CrO2 with
self doped double exchange). The density of Skyrmion strings and RS are related as,
RS∝ 1
T < n >∝exp(EC/kBT )
T (4.4)
where n is the density of Skyrmion strings and ECis the energy of creation of a single Skyrmion string. In our data, RS increases exponentially around 150 K and yields a good fit to Eq. 4.4 with EC ≈ 1100 K (see Fig. 4.6d).
4.5 Results: Low field MR, Rotational scans of MR, Planar Hall Effect
4.5.1 Magnetoresistance: Low field MR
The low field MR was measured in a low temperature (4.2 K) Oxford cryostat (mu metal shielded) with externally applied magnetic field with in-plane con- figuration. For films deposited on a pretreated TiO2, we applied field parallel and perpendicular to the current for both cases of current along the c- and the b-axis. The field H was applied parallel to the current I for the film de- posited on sapphire with the Hall bar structure. For all cases, four probe dc measurements with a current of 100 µA were used. The film was 100 nm thick and deposited on untreated TiO2, pretreated TiO2 and sapphire substrates.
In all cases, the resistance increases when coming from high field, and shows a hysteretic structure when the magnetization direction switches and domain forms. When field is applied along the c-axis (H||c) then for both H||I ( or I||c) and H⊥I (or I||b) the data show a jump-like decrease of R at the presumed coercive field Hc (see Fig. 4.7a,b). when the field is applied along the b-axis (H||b) then the H⊥I (or I||c) resistance shows a dip-like structure, with the dip before Hc is reached and the peak around Hc (see Fig. 4.7c). For H||I (or I||b) a plateau-peak structure is seen with the plateau before Hc is reached and the peak at Hc (see Fig. 4.7d).
The MR behavior was already studied before by Konig et al. [44], with results similar to these. They are compatible with the c-axis as easy axis;
whether H||I or I⊥H, the magnetization switches sharply with H||c. For H||b domains start to form well before Hc is reached, which leads to a dip or a plateau in the variation of R. On this sample, a magnetization measurement was performed which confirm that the c-axis is the easy axis.
Figure 4.8a presents the low field MR data for a 200 nm thick CrO2 film deposited on a sapphire substrate when the current is parallel to the current.
The MR is negative with a quadratic decrease up to 0.25%, which is similar
Figure 4.7: Low field MR probed on a 100 nm thick CrO2 film deposited on pretreated TiO2 at 4.2 K and simultaneously measured for both cases of current along the c-axis and the b-axis. (a) Field and current both are parallel to the c-axis, (b) current parallel to the c-axis but field is perpendicular to the current (along the b-axis), (c) when current is along the b-axis and field is perpendicular (field parallel to the c-axis) and (d) both current and field are parallel to the b-axis.
to the MR data of CrO2film deposited on TiO2substrate for a perpendicular configuration of applied field. The AMR peaks around the coercive field are obviously present (see the inset of Fig. 4.8a). The MR is two times less with the perpendicular configuration than parallel configuration of applied field and the peaks at the coercive field are also very weak (see Fig. 4.8b) but the decrease is still quadratic.
4.5.2 Rotational scans of MR
We also measured the MR as a function of the angle θ of the applied field with respect the current direction through CrO2bridges along the c- and the b-axis.
Figure 4.8: Low field and low temperature (4.2 K) MR measurements for a 200 nm thick CrO2 thin films deposited on sapphire substrate, with in-plane applied field (a) parallel to the current (b) perpendicular to the current. The insets show the MR for field up to 100 mT.
We probed the R(θ) at different temperatures and also at various magnetic field strengths using a PPMS Quantum design rotational transport sample holder. The R(θ) at different temperatures for 50 mT applied field is given in Fig. 4.9. The data for both configurations of I||c and I||b are simultaneously recorded. When θ = 0 the applied field is along the c-axis as shown in the inset of Fig. 4.9b.
At 300 K, R(θ) for I||c is weakly varying, with signatures of maxima at 0o, 180o, and minima at 90o, 270o. For I||b there is a clear variation with peak-like maxima at 90o and 270o, and rounded minima at 0o and 180o. At 200 K the data are similar, now with a stronger signal for I||c. At 100 K the peaks round somewhat, but there is no qualitative change. At 10 K, however, the data for I||b are still similar, but the data for I||c have strongly changed:
the minima at 90oand 270ohave converted to sharply peaked maxima, similar to the I||b data. The shape of the maxima, and the small hysteresis which can be seen to develop, are partly due to the relatively small applied field. For larger fields the MR-effect becomes stronger, and the maxima more rounded, as shown in Fig. 4.10 for I||c at 4.2 K.
Also these observations are similar to earlier ones [44]. To understand what happens, we contrast the 100 K data with the 10 K data. At 100 K the behavior can be explained with the c-axis being the easy axis. It yields a maximum at 0o for H||c||I, since the magnetization is parallel to the current, which gives a higher R. Also at 0o, the configuration H||c||I gives domains
Figure 4.9: Relative change in the resistivity as a function of rotation of applied field of the order of 50 mT with respect to the magnetization (a) at room temperature (b) 200 K, (c) 100 K and (d) at 10 K. The angle is zero magnetic field is along the c-axis as shown in the inset of (b).
with a magnetization perpendicular to the current, and therefore a minimum in R. At 10 K the effect of the easy axis seems to have disappeared and the parallel alignment of magnetization and current (the situation H||c||I) now leads to minimum. This can be explained by assuming that the dominating transport mechanism now is formed by Intergrain Tunneling Magnetioresis- tance (ITMR). The parallel alignment of the magnetization of neighboring grains reduces the scattering at grain boundaries. It is obvious that this effect can be particularly relevant for fully spin-polarized materials. It also shows a definite influence of the grain boundaries in our thin films on the electrical transport properties.
Figure 4.10: Rotational scans of magnetoresistance at various fields at tem- perature of 4.2 K for current I||c-axis.
4.5.3 Planar Hall effect
The resistance measured along the direction of the current as a function of ap- plied field is known as anisotropic magnetoresistance (AMR), but this physical mechanism is also responsible for a Hall voltage, or Hall resistance, i.e. in the direction perpendicular to the applied current and field. This Hall voltage is commonly called Planar Hall Effect (PHE). We probed PHE using the L structure at 4.2 K in the shielded cryostat with a magnetic field applied in a parallel configuration (H||I). The transverse voltages were recorded for I||c and I||b when the H||c and for the H||b. The results are given in Fig. 4.11 for all four different configurations of current and field.
Comparing Fig. 4.7 with Fig. 4.11 we see that the PHE signal is strongly correlated with the AMR behavior for H||c (the easy axis of magnetization).
Both show narrow peaks, e.g. switching behavior, at the coercive field Hc. For H||b there is less resemblance with AMR. There is no dip-peak structure for H ⊥I; for H ||I there is a weak signature of plateau-peak.
For films deposited on untreated substrates we did not observe any PHE signal. It suggests PHE is quite sensitive to disorder.
The interest in PHE stems from the fact that, if magnetic structures are in a single domain, the longitudinal electric field Ex(measured by AMR) and the transverse field Ey (from PHE) are given by
Figure 4.11: Planar Hall effect for a 100 nm thick CrO2 film deposited on a pretreated TiO2 substrate, (a-b) applied field is parallel to the c-axis (c-d) field is along the b-axis, at 4.2 K.
Ex =
·ρk+ ρ⊥
2 +ρk− ρ⊥ 2 cos 2θ
¸
J (4.5)
Ey =
·ρk− ρ⊥
2 sin 2θ
¸
J (4.6)
Plotting Ey against Ex, the resulting graph is a circle if the magnetization rotated as a single domain. The magnetization angle can then be extracted for every value of (Ex, Ey), This is illustrated in Fig. 4.12 for a 20 nm thick Py film measured at room temperature. Looking at CrO2, it is obvious that the plot of (Ex, Ey) will not form a circle. This might indicate that the material is not in a single domain state at the measured temperature of 4 K. In the view of the rotational scans experiments it seems more logical to conclude that the PHE data confirm the conclusion that the low temperature magnetotransport is dominated by ITMR and not by AMR.
Figure 4.12: Planner Hall effect (ρxy) and AMR (ρxx) at 4.2 K for a 20 nm thick Py thin films deposited on Si substrate. The inset shows the correla- tion between the ρxx and ρxy, the circle formation shown the single domain structure of Py films.
4.6 Conclusion
It can be concluded that CrO2 thin films deposited on a pretreated TiO2 substrate are of better quality than the films deposited on an untreated TiO2or on sapphire substrate. The higher value of the coefficient of the T2dependence of the resistivity might come from the electron-magnon scattering along with the electron-electron scattering. The bump in R(T ) and the sign change in MR around 100 K appear to be related with some phase change in the electronic configuration of CrO2possibly driven by the decrease in carrier concentrations as found in the Hall data. The low-field MR and PHE data reveal the presence of ITMR, and stress that grain boundaries are present in our films. This may be of importance when supercurrents are generated.
