Spin polarization of Fe-rich ferromagnetic compounds in Ru2−xFexCrSi Heusler alloys

Journal of Physics and Chemistry of Solids 72 (2011) 604–607

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Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs

Spin polarization of Fe-rich ferromagnetic compounds in Ru2  xFexCrSi Heusler alloys Iduru Shigeta a,b,, Osamu Murayama b, Toru Hisamatsu b, Alexander Brinkman a, Alexander A. Golubov a, Yukio Tanaka c, Masakazu Ito b, Hans Hilgenkamp a, Masahiko Hiroi b a

Faculty of Science and Technology and MESA + Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands Department of Physics and Astronomy, Kagoshinma University, Kagoshima 890-0065, Japan c Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan b

a r t i c l e i n f o

a b s t r a c t

Available online 16 October 2010

We report spin polarization P of Ru2  xFexCrSi Heusler alloys by the Andreev reflection technique. Ru2  xFexCrSi with L21-type structure and saturation magnetic moment of 2 mB per formula unit is theoretically predicted to be half-metals in the wide range of the composition x. We had clarified that the experimental results of saturation magnetic moment in Fe-rich compounds had coincided with the theoretical prediction. Therefore, we have measured the differential conductance of Ru2  xFexCrSi/Pb planar-type junctions. The P value of Ru2  xFexCrSi was determined by fitting the differential conductance with the modified Blonder–Tinkham–Klapwijk theory. We have found that the behavior of P for Ru2  xFexCrSi was independent of the composition x in the Fe-rich region; P ¼ 0.53 for both of x ¼1.5 and 1.7. The spin polarization is the similar value to Co-based Heusler alloys. & 2010 Elsevier Ltd. All rights reserved.

Keywords: A. Alloys A. Interfaces A. Magnetic materials A. Superconductors D. Transport properties

1. Introduction Tunneling spectroscopy is one of the most powerful measurement methods to understand superconductors and ferromagnets [1]. With regard to ferromagnet/superconductor (F/S) junctions, there are different theoretical models treating F/S contacts in various limits from the ballistic case to the diffusive case [2–8]. The spin polarization of ferromagnetic materials can be determined by the Andreev reflection technique [9,10]. As such ferromagnetic materials, Heusler alloys have been studied for a long time mainly because of their unique magnetism. Alloys that crystallize in cubic L21-type structure are referred to as full-Heusler alloys. Recently, they have been attracting interests by reason of their potential use as half-metals (HMs) [11], ferromagnetic shape memory alloys [12], and thermoelectric materials [13]. HMs are particularly expected to be utilized in so-called spintronics, such as the tunneling magnetoresistance [14] and current-perpendicular-to-plane giant magnetoresistance devices [15]. Although it is of great importance to find idealistic HMs, ferromagnetic metals with high spin polarization, which are insensitive to crystalline disorders, are highly valuable even if they are not complete HMs. For the materials, the density of states

 Corresponding author at: Faculty of Science and Technology and MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands. E-mail address: [email protected] (I. Shigeta).

0022-3697/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2010.10.062

of the majority spin states is supposed to be large at the Fermi level. In this case, the high spin polarization should be preserved even when the minority spin states appear by crystalline disorders [16]. As such a material, Ru2  xFexCrSi Heusler alloys were theoretically predicted to be complete or nearly complete HMs, which are robust against crystalline disorders. This prediction was recently made by the linear muffin tin orbital (LMTO) method and the atomic sphere approximation (ASA) with the local-spin-density approximation (LSDA) [16]. However, in spite of prediction of HMs by theoretical works, HMs have not yet realized for Heusler alloys. We were successful to synthesize Ru2  xFexCrSi polycrystals and the physical properties of Ru2  xFexCrSi were clarified so far [17]. In this paper, we focus on spin polarization P of Ru2  xFexCrSi measured by the Andreev reflection technique using Ru-based Heusler alloy/superconductor junctions. The P value is determined by fitting normalized conductance curves with the modified Blonder–Tinkham–Klapwijk (BTK) theory [18].

2. Experimental procedure Polycrystalline Ru2  xFexCrSi samples were prepared by arcmelting high purity constituent elements under high purity argon atmosphere [19]. The phase characterization was carried out by y-2y X-ray diffraction (XRD) using CuKa radiation. Magnetization M was measured as a function of temperature T and magnetic field H by a commercial superconducting quantum interference device magnetometer (MPMS, Quantum Design). Electrical resistivity

I. Shigeta et al. / Journal of Physics and Chemistry of Solids 72 (2011) 604–607

four-probe method for Ru2  xFexCrSi polycrystals and Pb thin films. We have fabricated planar-type junctions by depositing Pb through a metal mask patterned with counterelectrodes on the polished surface of polycrystalline Ru2  xFexCrSi samples. All Pb thin films were kept to 150 nm thick during our experiments. We have measured differential conductance G(V) of the prepared planartype junctions by the conventional modulation method. Temperature dependence of G(V) was also obtained by using a temperature controller. The temperature ranged from 1.2 to 10 K with a stability of less than 0.05 K.

3. Theoretical model In theory, the finite-temperature spectra are habitually calculated by convoluting zero-temperature curves with the derivative of the Fermi distribution function @f =@E, which is a peaked function with the half-width equal to kBT (the product of Boltzmann constant and the temperature). However, the experimental broadening is often considerably larger than kBT, suggesting that interface scattering which breaks the electron coherence plays a significant role. The associated functional form to describe the effect of scattering is unknown. To account for the combined effect of all broadening mechanisms, we take the convolution function in the form of a Gaussian function. For convenience, we write the Gaussian function as expf½ðEeVÞ=2o2 g [20]. With such notation, when only the thermal effect is present, the Gaussian function approximates @f =@E, so that o ¼ kB T. According to the modified BTK theory [18] with taking account of the broadening effect, the differential conductance G(V) for F/S junctions is given by GðVÞp

Z

(   ) ðEeVÞ 2 exp  ½ð1PÞð1þ AN BN Þ þ Pð1 þ AH BH Þ dE, 2o 1 1

4. Results and discussion We have measured magnetization of Ru2  xFexCrSi. Fig. 1 shows the temperature dependences of magnetization M(T) under m0 H ¼ 1 T for 0:3r x r 1:7. As shown in Fig. 1, the Fe-rich compounds of x 4 1:0 have a ferromagnetic phase and the Curie temperature TC is higher enough than room temperature. The saturation magnetic moment becomes close to 2 mB per formula unit for x ¼1.7 at low temperatures. On the other hand, for Ru-rich compounds, the ferromagnetic behavior is still remained for x ¼0.5, whereas M(T) is found almost constant below 50 K. More clearly a round maximum of M(T) is observed around 40 K for x ¼0.3. For this compound, the second magnetic transition below 40 K was clarified as the state corresponding to antiferromagnetism and spin glass [21]. Fig. 2 shows the magnetic field dependence of magnetization M(H) of Ru0.5Fe1.5CrSi at T¼4 and 300 K. The compound of x ¼1.5 exhibits ferromagnetism. The magnetization curves with increasing and decreasing magnetic fields coincide with each other, then the hysteresis is not observed. As shown in the inset of Fig. 2, the saturation magnetic moment is almost constant up to m0 H ¼ 6 T. The saturation magnetic moment is 1:82 mB per formula unit at T¼4 K and falls by 37.6% at T¼300 K to 1:14 mB per formula

2.5 x = 1.7

2.0

M (B/f.u.)

r was measured as a function of temperature T by the usual

x = 1.5

1.5

1.0

x = 1.0

ð1Þ

1 þAN BN ¼

8 > > > > <

x = 0.5 0.5

2

2ð1 þ b Þ 2

b þð1 þ 2Z 2 Þ2 > 2b > > > : 1 þ b þ 2Z 2 , 8 > < 0,

,

jeVj o D, ð2Þ

0

100

200

300

T (K)

jeVjo D, jeVjZ D,

ð3Þ

Fig. 1. Magnetization M(T) of Ru2  xFexCrSi as a function of temperature under m0 H ¼ 1 T for 0:3 r x r 1:7.

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jD2 E2 j, A and B stand for probabilities of the Andreev

1X ½g GðVi ; D,Z,P, oÞ2 , N i i

ð4Þ

where the analyzed conductance-voltage g(V) curve is comprised of N points (Vi, gi), and the fitting function G(Vi) is computed in the modified BTK theory, which is written by Eqs. (1)–(3). The algorithm allows us to optimize in all four parameters, or in any subset, while the others are kept fixed. We imposed natural physical constraints on the parameters, keeping them always positive.

2

1 M (μB/f.u.)

reflection and the normal reflection, and those suffixes N and H represent nonmagnetic channel and half-metallic channel, respectively. Further, P is spin polarization, D is superconducting energy gap, and Z is dimensionless barrier height. The fitting procedure we use is based on an optimization algorithm with the target function being the normalized sum of squared deviations between the fitted data and the trial function [20]:

w2 ðD,Z,P, oÞ ¼

x = 0.3

0.0

jeVj Z D,

1 þ bð1 þ2Z 2 Þ 1 þAH BH ¼ > : ð1 þ bÞð1 þ 2Z 2 Þ þ 2Z 4 , where, b ¼

605

4K 300 K

0

-1

-2 -0.10

-0.05

0.00 μ 0H (T)

0.05

0.10

Fig. 2. Magnetization M(H) of Ru0.5Fe1.5CrSi as a function of magnetic field at T¼ 4 and 300 K. The hysteresis is not observed at both temperatures. Inset: Magnetization M(H) up to m0 H ¼ 6 T at T¼ 4 K.

I. Shigeta et al. / Journal of Physics and Chemistry of Solids 72 (2011) 604–607

25 ρ (nΩ·m)

300

ρ (nΩ·m)

20

15

200 100 0

0

100

200

300

T (K)

10 RRR = 58.7 Tc0 = 7.23 K

5

Δ Tc = 0.15 K

0 5

10

15

20

25

30

T (K) Fig. 3. Resistivity rðTÞ of the Pb thin film as a function of temperature. The Pb thin film is of good superconducting property because of Tc0 ¼ 7.23 K and DT ¼ 0:15 K. Inset: Resistivity rðTÞ in the wide scale of temperature. The rðTÞ in the normal state linearly increases up to T¼300 K, which is typically metallic behavior.

1.10 Ru0.5Fe1.5CrSi

1.05 G (V)/Gn

unit. For fully ordered Ru2  xFexCrSi, the predicted saturation magnetic moment should be 2 mB per formula unit [16]. The XRD measurements for these samples, which are presented elsewhere [17], indicate that Ru2  xFexCrSi is completely L21 structure. We have also measured the resistivity of Pb thin films. It is necessary to check transport properties of Pb thin films as well as magnetic properties of Ru2  xFexCrSi. This is because the Andreev reflection occurs at the F/S junction interface. Fig. 3 shows the typical resistivity rðTÞ of a Pb thin film as a function of temperature. The superconducting transition temperature Tc0 of the Pb thin film was determined to be Tc0 ¼7.23 K, where Tc0 was defined as the temperature becoming completely zero resistivity. The transition width DT was also obtained as DT ¼ 0:15 K. As shown in the inset of Fig. 3, the resistivity rðTÞ in the normal state increased linearly up to 300 K, which is typically metallic behavior. The residual resistivity ratio (RRR) was also acquired as RRR  r300 K =r7:4 K ¼ 58:7 from the inset of Fig. 3. This result signifies that the impurity scattering of electrons is small in the Pb thin film. From the experimental results of Figs. 1 and 2, TC is higher enough than room temperature for Fe-rich compounds and the saturation magnetic moment of the Fe-rich compounds with x ¼1.7 is close to 2 mB per formula unit, which is coincide with the theoretical prediction [16]. Hence, HMs are expected for the Fe-rich compounds of Ru-based Heusler alloys, then we have measured spin polarization P of Fe-rich compounds for Ru2  xFexCrSi by using the Andreev reflection technique. Figs. 4 and 5 show the resulting normalized conductance G(V)/Gn of Ru2  xFexCrSi/Pb planar-type junctions in the compositions of x ¼1.5 and 1.7 at lowest temperatures achieved by pumping liquid helium, where differential conductance G(V) is in the superconducting state and Gn is in the normal state. The good fitting results were obtained as shown in Figs. 4 and 5. In addition, the temperature dependence of differential conductance was measured. The structures of differential conductance in Figs. 4 and 5 disappeared above Tc0. This behavior of the temperature dependence obviously vouches that the structure of G(V) comes from the Andreev reflection, which occurs at the F/S junction interface. Therefore, we tried to analyze experimental conductance using the modified BTK theory. From analysis by using Eqs. (1)–(3), we were able to determine spin polarization P¼0.53 for both of x¼1.5 and 1.7. This result indicates that the spin polarization is independent of different compositions in Fe-rich compounds. The resulting values of fitting parameters are also presented in Figs. 4 and 5.

1.00 P = 0.53 Z = 0.95 meV Δ = 0.95 meV ω = 0.36 meV

0.95

χ 2 = 4.3×10−4

0.90 -10

-5

0 V (mV)

5

10

Fig. 4. Normalized conductance G(V)/Gn measured at T¼ 1.5 K for Ru0.5Fe1.5CrSi. The open circles are the experimental data. The solid line is the fitting result of the modified BTK theory using four independent parameters: P, Z, D and o. All the junction resistances were in the range of 1210 O.

1.10 Ru0.3Fe1.7CrSi 1.05

G(V )/Gn

606

1.00

0.95

P = 0.53 Z = 0.19 Δ = 0.85 meV ω = 0.36 meV

0.90

χ 2 = 2.2 ×10−3

0.85 -10

-5

0 V (mV)

5

10

Fig. 5. Normalized conductance G(V)/Gn measured at T¼ 1.3 K for Ru0.3Fe1.7CrSi. The open circles are the experimental data. The solid line is the fitting result of the modified BTK theory using four independent parameters: P, Z, D and o.

In comparison with previous measurements of the Andreev reflection technique for other Heusler alloys, the spin polarization of Ru2  xFexCrSi was the similar values to other Heusler alloys; for example, Co-based Heusler alloys [22]. The fitting results of Z¼0.1–0.2 mean that the potential barrier height Z is sufficiently low for the fabricated Ru2  xFexCrSi/Pb planar-type junctions. Hence, the Andreev reflection can occur for most of the incident electrons at the junction interface. In this case, the P values can be close to the ideal value of spin polarization at the surface because the P value becomes smaller with the increase of Z [23]. With regard to the energy gap, D ¼ 0:8520:95 meV is smaller than D ¼ 1:36 meV in the previous report [24]. The reduction of D can be comprehended by the proximity effect at F/S junction interface. Using Eq. (4) for w2 as degree of accuracy in the fitting results, we have obtained w2 ¼ 4:3 104 for x ¼1.5 and w2 ¼ 2:2  103 for x¼1.7, respectively. Finally, we note the origin that the experimental P value is lower than the theoretical prediction, such as 100% spin polarization could be achieved for Ru2  xFexCrSi compounds. The suppression of P values in the experiments likely comes from surface reconstructions [25] and the presence of small chemical disorders, such as nonstoichiometric compositions in the L21-type structure.

I. Shigeta et al. / Journal of Physics and Chemistry of Solids 72 (2011) 604–607

5. Conclusion We have determined spin polarization P of Ru2  xFexCrSi Heusler alloys in Fe-rich compounds by the Andreev reflection technique. The spin polarization of Ru2  xFexCrSi was P¼0.53 for both of x¼1.5 and 1.7. The P values were independent of different compositions in Fe-rich compounds. The spin polarization of Ru2  xFexCrSi was the similar values to Co-based Heusler alloys, but HMs did not realized yet in Ru-based Heusler alloys against the theoretical prediction. The suppression of P values likely comes from some reasons, such as surface reconstructions and the presence of small chemical disorders.

Acknowledgments We would like to thank S. Fujii and Y. Miyoshi for their helpful advice and discussion. This research was partially supported by the JGC-S Scholarship Foundation (No. 2133) and the Grant-in-Aid for Young Scientists (B) (No. 21740259) from the Ministry of Education, Culture, Sports, Science and Technology, Japan. References [1] E.L. Wolf, Principles of Electron Tunneling Spectroscopy, Oxford University Press, Oxford, 1985. [2] M.J.M. de Jong, C.W.J. Beenakker, Phys. Rev. Lett. 74 (1995) 1657. [3] S. Kashiwaya, Y. Tanaka, N. Yoshida, M.R. Beasley, Phys. Rev. B 60 (1999) 3572. ˇ ´ , O.T. Valls, Phys. Rev. B 60 (1999) 6320. [4] I. Zutic

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