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Sign reversal of the Hall coefficient in amorphous Co-Zr thin films
Journal of Magnetism and Magnetic Materials 101 (1991) 211-212 North-Holland
Sign reversal of the Hall coefficient in amorphous Co-Zr thin films * T. Stobiecki a, P. Kossacki b and H. Szymczak b a Department of Physics and Electron Technology, Institute of Electronics, Academy of Mining and Metallurgy, 30-059 Krakbw, Poland b Institute of Physics, Polish Academy of Sciences, Warszawa, Poland
The slope of the Hall curve, above saturation, for all ferromagnetic samples is negative and a change of the sign of R, to positive value appears for Co,_,Zr, at x = 0.50 where films are paramagnetic. This anomalous behaviour is associated with the electronic band structure of these alloys. Above saturation be written as
1. Introduction Using sputtering technique for thin films preparation, Zr can be melted with all the late 3d-TM (Cu, Ni, Co and Fe) as a homogeneous noncrystalline phase in a very wide range of concentration [l]. However, liquid-quenched ribbons of these alloys are stable in amorphous phase in a limited range of concentration. For that reason CO~_~ZT~ amorphous films give a unique opportunity to study the Hall effect over a wide composition range. The Hall effect can give us important information about the dynamical properties of electrons in 3d- and 4d-band amorphous transition metals and also is closely related to their electronic structure. 2. Experimental Our Co-Zr films were prepared by the rf sputtering technique. Electrical measurements were carried out in the temperature range from 4 to 300 K. The resistivity was measured by the conventional four contacts dc method and the Hall effect by the ac method of lock-in technique, in a magnetic field up to 6 T.
RH
=
(H > p&J
l/~CLo(aPH/aH)H>~LoM,=Ro
the Hall coefficient
+XHF&,
can
(2)
where xHF is a high field susceptibility. The slope of the Hall curve, above saturation, for all of the Hall curve, above saturation, for all ferromagnetic samples is negative and change of the sign of R, to positive value appears (fig. 2) where films are paramagnetic (x > 0.42). The concentration dependence of R, (fig. 3), where R, was calculated from eq. (2) after xHF correction [2], shows the sign reversal of R, around x = 0.5. The results collected in fig. 3 show that the normal Hall coefficient extrapolated to pure amorphous Co (R, z -7 x lo-” m3/A s) is greater than the R, of liquid Co (R, = - 16 X 10-l’ m3/A s> [3]. The results presented above cannot be explained by the free electron approach. The sign reversal is associated with the sign of the derivative of the density of states (DOS) at the Fermi level (R,+x -g’(E,)/ g2(E,)> [4]. In Zr-rich amorphous alloys, according to the specific heat [5] and photo-emission studies [6] and also band calculations, E, is located at the Zr 4d-band
3. Results and discussion The magnetic field dependence of the Hall resistivity in ferromagnetic materials can be written as PH
=
dR,H
+
WW,
(1)
where R, and R, are the ordinary and spontaneous Hall coefficients, respectively. The typical variation of pH with magnetic field for different Col_xZrX amorphous films (fig. 1) shows that the anomalous Hall effect dominates over the normal Hall effect (RJR, = 103) [l]. The anomalous Hall effect in Co-Zr originates from the quantum side-jump mechanism [l].
* Supported by grant number CPBP 01.04.
2 HIT1
3
Fig. 1. The Hall resistivity pH as a function of magnetic field for amorphous Co, _xZrx films at T = 4 K.
0312~8853/91/$03.50 0 1991 - Elsevier Science Publishers B.V. All rights reserved
T. Stobiecki et al. / Hall coefficient in amorphous Co-B
212
thin films
T 1Kl Fig. 2. The Hall resistivity pH as a function of magnetic for amorphous Co, _xZrx films at T = 300 K.
field
where g’(EF) < 0, hence R, > 0. When the Zr concentration decreases we believe that the 3d-band of Co increases and moves E, gradually to the position where now g’(E,) > 0, hence R, < 0. Our explanation was confirmed by measurements of the electronic specific heat where the DOS at the Fermi level increases when the Zr content is decreasing [S]. The sign reversal takes place also in Cu-Zr [7] and Ni-Zr [8] amorphous alloys where the TM 3d-band and Zr 4d-band are well separated from each other. In the case of Fe-Zr the overlap of the Zr 4d-band with the Fe 3d-band and additionally a large side-jump effect (due to significant spin-orbit coupling [1,9]> are responsible for the fact that we do not observe any sign reversal of R, in Fe-Zr amorphous films. The Hall coefficients R,>CII,M of Co-rich (ferromagnetic) and R, of Zr-rich (pa&magnetic) films are shown in fig. 4 as functions of the temperature be-
8[ T=4K
1
Fig. 3. The normal Hall coefficient R, as a function of Zr contents for amorphous Co, mxZrx films at T = 4 K.
Fig. 4. The Hall coefficient R, as a function of temperature for amorphous Co, _xZrx films.
tween 4 and 300 K. The weak temperature variation of indicates for isotropic scattering in Co-Zr films. It would be unreasonable to expect strong temperature variations in the Hall constant while resistivities of these films have very small temperature derivatives. We conclude that, according to electronic band structure experiments, the normal Hall effect in the ferromagnetic range of concentration of amorphous CO~_~ZT~ is negative and changes its sign to positive around x = 0.50. For a better understanding, this anomalous behaviour requires exact band calculations for various alloy concentrations. R,
References
illT. Stobiecki,
G. Bayreuther and H. Hoffmann, in: Proc. Symp. on Magnetic Properties of Amorphous Metals, eds. A. Hernando, V. Madruga, M.C. Sanchez-Trujillo and M. Vazquez (North-Holland, Amsterdam, 1987) p. 188. Bl F.R. de Boer, P. Kossacki, R. Puiniak, T. Stobiecki, H. Szymczak and X.P. Zhong, J. Magn. Magn. Mater. 101 (1991) 3. The Hall Effect and its [31 H.U. Kiinzi and H.-J. Giintherodt, Applications (Plenum, New York, 1980) p. 215. [41 D. Nguyen Manh, D. Mayou, G.J. Morgan and A. Pasturel, J. Phys. F 17 (1987) 999. [51S. Kanemaki, 0. Takehira, K. Fukamichi and U. Mizutani, J. Phys. Condens. Matter 1 (1989) 5903. [61P. Oelhafen, E. Hauser and H.-J. Giintherodt, Solid State Commun. 35 (1980) 1017. [71 J. Ivkov, E. Babic and R.L. Jacobs, J. Phys. F 14 (1984) L53. [81 R.W. Cochrane, J. Destry and M. Trudeau, Phys. Rev. B 27 (1983) 5955. 191 M. Trudeau, R.W. Cochrane, D.V. Baxter, J.O. Strom-Olsen and W.B. Muir, Phys. Rev. B 37 (1988) 4499.
Sign reversal of the Hall coefficient in amorphous Co-Zr thin films * T. Stobiecki a, P. Kossacki b and H. Szymczak b a Department of Physics and Electron Technology, Institute of Electronics, Academy of Mining and Metallurgy, 30-059 Krakbw, Poland b Institute of Physics, Polish Academy of Sciences, Warszawa, Poland
The slope of the Hall curve, above saturation, for all ferromagnetic samples is negative and a change of the sign of R, to positive value appears for Co,_,Zr, at x = 0.50 where films are paramagnetic. This anomalous behaviour is associated with the electronic band structure of these alloys. Above saturation be written as
1. Introduction Using sputtering technique for thin films preparation, Zr can be melted with all the late 3d-TM (Cu, Ni, Co and Fe) as a homogeneous noncrystalline phase in a very wide range of concentration [l]. However, liquid-quenched ribbons of these alloys are stable in amorphous phase in a limited range of concentration. For that reason CO~_~ZT~ amorphous films give a unique opportunity to study the Hall effect over a wide composition range. The Hall effect can give us important information about the dynamical properties of electrons in 3d- and 4d-band amorphous transition metals and also is closely related to their electronic structure. 2. Experimental Our Co-Zr films were prepared by the rf sputtering technique. Electrical measurements were carried out in the temperature range from 4 to 300 K. The resistivity was measured by the conventional four contacts dc method and the Hall effect by the ac method of lock-in technique, in a magnetic field up to 6 T.
RH
=
(H > p&J
l/~CLo(aPH/aH)H>~LoM,=Ro
the Hall coefficient
+XHF&,
can
(2)
where xHF is a high field susceptibility. The slope of the Hall curve, above saturation, for all of the Hall curve, above saturation, for all ferromagnetic samples is negative and change of the sign of R, to positive value appears (fig. 2) where films are paramagnetic (x > 0.42). The concentration dependence of R, (fig. 3), where R, was calculated from eq. (2) after xHF correction [2], shows the sign reversal of R, around x = 0.5. The results collected in fig. 3 show that the normal Hall coefficient extrapolated to pure amorphous Co (R, z -7 x lo-” m3/A s) is greater than the R, of liquid Co (R, = - 16 X 10-l’ m3/A s> [3]. The results presented above cannot be explained by the free electron approach. The sign reversal is associated with the sign of the derivative of the density of states (DOS) at the Fermi level (R,+x -g’(E,)/ g2(E,)> [4]. In Zr-rich amorphous alloys, according to the specific heat [5] and photo-emission studies [6] and also band calculations, E, is located at the Zr 4d-band
3. Results and discussion The magnetic field dependence of the Hall resistivity in ferromagnetic materials can be written as PH
=
dR,H
+
WW,
(1)
where R, and R, are the ordinary and spontaneous Hall coefficients, respectively. The typical variation of pH with magnetic field for different Col_xZrX amorphous films (fig. 1) shows that the anomalous Hall effect dominates over the normal Hall effect (RJR, = 103) [l]. The anomalous Hall effect in Co-Zr originates from the quantum side-jump mechanism [l].
* Supported by grant number CPBP 01.04.
2 HIT1
3
Fig. 1. The Hall resistivity pH as a function of magnetic field for amorphous Co, _xZrx films at T = 4 K.
0312~8853/91/$03.50 0 1991 - Elsevier Science Publishers B.V. All rights reserved
T. Stobiecki et al. / Hall coefficient in amorphous Co-B
212
thin films
T 1Kl Fig. 2. The Hall resistivity pH as a function of magnetic for amorphous Co, _xZrx films at T = 300 K.
field
where g’(EF) < 0, hence R, > 0. When the Zr concentration decreases we believe that the 3d-band of Co increases and moves E, gradually to the position where now g’(E,) > 0, hence R, < 0. Our explanation was confirmed by measurements of the electronic specific heat where the DOS at the Fermi level increases when the Zr content is decreasing [S]. The sign reversal takes place also in Cu-Zr [7] and Ni-Zr [8] amorphous alloys where the TM 3d-band and Zr 4d-band are well separated from each other. In the case of Fe-Zr the overlap of the Zr 4d-band with the Fe 3d-band and additionally a large side-jump effect (due to significant spin-orbit coupling [1,9]> are responsible for the fact that we do not observe any sign reversal of R, in Fe-Zr amorphous films. The Hall coefficients R,>CII,M of Co-rich (ferromagnetic) and R, of Zr-rich (pa&magnetic) films are shown in fig. 4 as functions of the temperature be-
8[ T=4K
1
Fig. 3. The normal Hall coefficient R, as a function of Zr contents for amorphous Co, mxZrx films at T = 4 K.
Fig. 4. The Hall coefficient R, as a function of temperature for amorphous Co, _xZrx films.
tween 4 and 300 K. The weak temperature variation of indicates for isotropic scattering in Co-Zr films. It would be unreasonable to expect strong temperature variations in the Hall constant while resistivities of these films have very small temperature derivatives. We conclude that, according to electronic band structure experiments, the normal Hall effect in the ferromagnetic range of concentration of amorphous CO~_~ZT~ is negative and changes its sign to positive around x = 0.50. For a better understanding, this anomalous behaviour requires exact band calculations for various alloy concentrations. R,
References
illT. Stobiecki,
G. Bayreuther and H. Hoffmann, in: Proc. Symp. on Magnetic Properties of Amorphous Metals, eds. A. Hernando, V. Madruga, M.C. Sanchez-Trujillo and M. Vazquez (North-Holland, Amsterdam, 1987) p. 188. Bl F.R. de Boer, P. Kossacki, R. Puiniak, T. Stobiecki, H. Szymczak and X.P. Zhong, J. Magn. Magn. Mater. 101 (1991) 3. The Hall Effect and its [31 H.U. Kiinzi and H.-J. Giintherodt, Applications (Plenum, New York, 1980) p. 215. [41 D. Nguyen Manh, D. Mayou, G.J. Morgan and A. Pasturel, J. Phys. F 17 (1987) 999. [51S. Kanemaki, 0. Takehira, K. Fukamichi and U. Mizutani, J. Phys. Condens. Matter 1 (1989) 5903. [61P. Oelhafen, E. Hauser and H.-J. Giintherodt, Solid State Commun. 35 (1980) 1017. [71 J. Ivkov, E. Babic and R.L. Jacobs, J. Phys. F 14 (1984) L53. [81 R.W. Cochrane, J. Destry and M. Trudeau, Phys. Rev. B 27 (1983) 5955. 191 M. Trudeau, R.W. Cochrane, D.V. Baxter, J.O. Strom-Olsen and W.B. Muir, Phys. Rev. B 37 (1988) 4499.