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A SANS study of the magnetic phase transition in amorphous (FexNi1−x)78B10Si12
PHYSICA k
Physica B 180 & 181 (lYY2) 230-232 North-Holland
A SANS RNi,
study of the magnetic
phase
transition
in amorphous
-*ML&
A.C. Hannon”, M. Hagen”.“, R.A. “ISISFutility. Rutherford Appleton Laborutory,
Cowley’,
H.B.
Stanley”.d
and N. Cowlamc
Didcot. Oxon OX11 OQX. UK hDepartment of Physics. Krele University. Keele. Stuffordshire ST.5 5BG. UK ‘Oxford Physics. Clarendort Laboratory. Parks Road. Oxford OX1 3PU. UK ‘Corporute Colloid Science. ICI, The Heath. Runcorn. Cheshire WA7 3QE. UK ‘Department of Physics, University of Sheffield, Sheffield S3 7RH. UK
The magnetic critical scattering from amorphous (Fe,Ni, I ),,B ,,,Si ,~ with x = 0.125 and 0.25 has been studied by small angle neutron scattering (SANS). For the x = 0.125 sample, the SANS suggests a ferromagnetic phase transition at TG= 132.33 + 0.33 K with d = 3 Heisenberg model critical exponents ahove Tc and gapless spin waves below T,. However. the x = 0.25 sample does not undergo a ferromagnetic transition and the inverse correlation length saturates at 0.007 A ’ for temperatures below 333 K.
1. Introduction The effects of random anisotropies in amorphous magnets have been of interest for some time. The original random anisotropy model was proposed by Harris et al. [l] as a possible explanation for results observed in rare earth/transition metal amorphous alloys. This model consists of a system of spins with nearest neighbour ferromagnetic exchange but with an anisotropy on each magnetic site whose direction is random. In the rare earth/transition metal amorphous magnets. this effect was expected to arise through the “crystal field” effect on the rare earth electrostatic ions, which because of the amorphous nature of the lattice would be randomly directed on different sites. Theoretical work on this model (21 has shown that in zero applied magnetic field the ground state is a disordered domain state. This has been confirmed experimentally by small angle neutron scattering (SANS) measurements on Tb,Fe,_, [3] and Dy,Ni, [4]. The situation for transition metal/metalloid amorphous magnets is not so clear, and there have been many experiments which have been successfully interpreted on the basis of a ferromagnetic ground state in these systems [3]. However, recent work has shown that this may not always be the case. SANS measurements on Fe,,,Zr,,, [5] have shown the existence of a domain state as the low temperature magnetic order. Polarised neutron diffraction measurements for wave vectors around the first peak in the structure factor for FeX7BII and (Fe,Ni_?),,B,,,Si,, [6] have shown the existence of a disordered transverse magnetic moment at low temperature. The existence of a random anisotropy effect in Fe based amorphous alloys has recently been suggested by Elsasser et al. [7] from computaOY21-4526/92/$05.00
0
1992 - Elsevier
Science
Publishers
tional calculations of the electronic and magnetic interactions in model amorphous systems. In this paper we report the results of SANS measurements of the magnetic critical scattering from samples of amorphous (Fe,Ni,_ ,),,B,,,Si,, with x = 0.125 and 0.25. These measurements were carried out using the LOQ diffractometer at the ISIS Facility. Rutherford Appleton Laboratory. UK. 2. Experimental The samples of amorphous (FerNi, ,),,B,,,Si,, used were the same as those used by Cowley et al. [6] and were ribbons of width 1.5 mm and thickness 50 pm made by the melt spinning technique at the University of Sheffield. The ribbons were wound on an aluminium frame in such a way that the transmission of the ribbons (which included natural boron) when mounted on the frame was of order 70%. For the x = 0.125 sample, this frame was attached to the copper block of a closed cycle refrigerator (CCR) and for the x = 0.25 sample to the centre stick of a vacuum furnace. During the measurements the sample temperature was continuously controlled and recorded by the instrument control computer. 3. Results Measurements for the x = 0.125 sample were carried out for a range of temperatures between IO K and 180 K. A “high temperature background” measurement was performed at 200 K and an ‘*empty CCR at 273 K. These two background runs background” were virtually identical, suggesting that any small angle nuclear scattering was extremely small and that
B.V. All rights
reserved
A.C.
Hannon et al. I Magnetic phase transition in amorphous
(Fe,Ni,
231
,),,B,,Si,,
consequently the samples are homogeneous. The high temperature background was subtracted from the other data sets in order to obtain the magnetic scattering. The same procedure was followed for the x = 0.25 sample with measurements taken for a range of temperatures from 298 K to 373 K and a background at 391 K. The data for both samples were fitted at all temperatures with a Lorentzian lineshape given by I(Q)
=
A Q'+
(1)
K’
The amplitude A in eq. (1) is related to the isothermal susceptibility by the relation x = A/K~. In fig. I we show a plot of K and x ’ against temperature for the x = 0.125 sample for temperatures T > 133 K. The solid lines are least squares fits to the equations K = TCIITC is the reKJ” and x = ,y,,tmYwhere t=]Tduced temperature. The best fit values are K, = 0.116? 0.027 A-‘, v = 0.67 ? 0.08, x = 0.0193 ” 0.0012 (arbitrary units), y = 1.4 * 0.1 and T, = 132.33 * 0.33 K. The measured values of Y and y are in good agreement with the theoretical values for the d = 3 Heisenberg model [8] of v = 0.71 and y = 1.39. Below TC in the x = 0.125 sample I(Q) is best fitted with a l/Q’ dependence (i.e. K = 0). with an amplitude which for temperatures below 120 K varies linearly with temperature. This behaviour is consistent with a gapless (or nearly gapless) spin wave cross section. In fig. 2 we plot K and x ’ against temperature for the x = 0.25 sample. For temperatures T > 343 K we are able to fit these results to the power law forms
. .
.
.
L
280
300
320
‘I’ernperaturr
360
340
380
(K)
Fig. 2. The temperature dependence of the inverse correlation length K (circles, left hand scale) and the inverse susceptibility x ’ (triangles. right hand scale) for the x =0.25 sample is shown. The solid lines are power law fits as described in the text.
with the best fit parameters K, = 0.108 +- 0.090 A- ‘, Y = 0.70 f 0.03, x,, = 0.131 * 0.009 (arbitrary units), y = 1.41 2 0.03 and TC = 342.37 * 0.60 K. Again these exponents are consistent with the d = 3 Heisenberg model in this temperature range. However the inverse correlation length does not go to zero at T, but instead saturates at 0.007 A-’ down to a temperature of 323 K. This corresponds to a real-space correlation length of 140 A. Similarly the isothermal susceptibility also saturates. Throughout this temperature range the scattering cross-section I(Q) can be fitted by a single Lorentzian line shape. However, below 323 K it cannot be successfully fitted in this way, nor can it be fitted by a sum of two Lorentzians or a Lorentzian plus a Lorentzian squared or a Lorentzian plus a Lorentzian raised to a non-integral power. This is a different behaviour to the previous measurements on Tb,Fe, I [3] and Fe,,,Zr ,I) [5] but is reminiscent of the low temperature behaviour of Dy,Ni, [4]. 4. Discussion
130
140
Temperature
150
160
(K)
Fig. 1. The temperature dependence of the inverse tion length K (circles, left hand scale) and inverse tibility x ’ (triangles, right hand scale) for the x sample is shown. The solid lines are power law described in the text.
correlasuscep= 0.125 fits as
To summarise the results reported in this paper we note that for (Fe,, ,?,Ni, X75)7XB,,,Si,2 the magnetic small angle scattering is consistent with the existence of ferromagnetic long range order while in it is not. It should be noted that (Fe,, riNi ,, ,,),,B,,,Si,, the existence of a ferromagnetic state in is not necessarily inconsistent (Fe,, ,,sNi ,, ,,T),,B,,,Si,,
A.C.
232
Hannon et al.
I Magnetic phase transition in amorphous (Fe,Ni,
with the previous polarised neutron diffraction measurements [6]. The possibility of “wandering axis ferromagnets” magnetic
where
there
component
and
is an
ordered
a disordered
[3] See
for example, J.W. Lynn and J.J. Rhyne, Spin dynamics of amorphous magnets. in: Spin Waves and
longitudinal transverse
com-
has been postulated theoretically [2] for amorphous magnets and this could be an explanation of the observed results. ponent
[4]
[S]
Acknowledgement This work has been supported by the UK Science and Engineering Research Council.
[6]
References [l]
R. Harris, M. Phschke and M.J. Zuckermann, Rev. Lett. 31 (1973) 160. [2] E. Chudnovsky, W.M. Saslow and R.A. Serota, Rev. B 33 (1986) 251 and references therein.
Phys. Phys.
,),,B,,,Si,,
[7] [8]
Magnetic Excitations 2. eds. A.S. Borovik-Romanov and S.K. Sinha (North-Holland, Amsterdam, 198X). A.C. Hannon. R. Cywinski, R.N. Sinclair, D.I. Grimley and A.C. Wright, Physica B 156 & 157 (1989) 210. A.C. Hannon. A.C. Wright and R.N. Sinclair, Mater. Sci. Eng. A 134 (1991) 883. J.A. Fernandez-Baca, J.J. Rhyne, R.W. Erwin and G.E. Fish. J. Phys. Colloq. C8 (1988) 1207. J.J. Rhyne. R.W. Erwin, J.A. Fernandez-Baca and G.E. Fish, J. Appl. Phys. 63 (1988) 3080. R.A. Cowley, N. Cowlam and L.D. Cussens. J. Phys. Colloq. C8 (198X) 1285: J. Phys. Condens. Mat.. in press. C. Elsasser, M. Fahnle, E.H. Brandt and M.C. Bohm. J. Phys. F 18 (1988) 2463. See for example, M.F. Collins. Magnetic Critical Scattering (Oxford University Press. 1989) p. 29.
Physica B 180 & 181 (lYY2) 230-232 North-Holland
A SANS RNi,
study of the magnetic
phase
transition
in amorphous
-*ML&
A.C. Hannon”, M. Hagen”.“, R.A. “ISISFutility. Rutherford Appleton Laborutory,
Cowley’,
H.B.
Stanley”.d
and N. Cowlamc
Didcot. Oxon OX11 OQX. UK hDepartment of Physics. Krele University. Keele. Stuffordshire ST.5 5BG. UK ‘Oxford Physics. Clarendort Laboratory. Parks Road. Oxford OX1 3PU. UK ‘Corporute Colloid Science. ICI, The Heath. Runcorn. Cheshire WA7 3QE. UK ‘Department of Physics, University of Sheffield, Sheffield S3 7RH. UK
The magnetic critical scattering from amorphous (Fe,Ni, I ),,B ,,,Si ,~ with x = 0.125 and 0.25 has been studied by small angle neutron scattering (SANS). For the x = 0.125 sample, the SANS suggests a ferromagnetic phase transition at TG= 132.33 + 0.33 K with d = 3 Heisenberg model critical exponents ahove Tc and gapless spin waves below T,. However. the x = 0.25 sample does not undergo a ferromagnetic transition and the inverse correlation length saturates at 0.007 A ’ for temperatures below 333 K.
1. Introduction The effects of random anisotropies in amorphous magnets have been of interest for some time. The original random anisotropy model was proposed by Harris et al. [l] as a possible explanation for results observed in rare earth/transition metal amorphous alloys. This model consists of a system of spins with nearest neighbour ferromagnetic exchange but with an anisotropy on each magnetic site whose direction is random. In the rare earth/transition metal amorphous magnets. this effect was expected to arise through the “crystal field” effect on the rare earth electrostatic ions, which because of the amorphous nature of the lattice would be randomly directed on different sites. Theoretical work on this model (21 has shown that in zero applied magnetic field the ground state is a disordered domain state. This has been confirmed experimentally by small angle neutron scattering (SANS) measurements on Tb,Fe,_, [3] and Dy,Ni, [4]. The situation for transition metal/metalloid amorphous magnets is not so clear, and there have been many experiments which have been successfully interpreted on the basis of a ferromagnetic ground state in these systems [3]. However, recent work has shown that this may not always be the case. SANS measurements on Fe,,,Zr,,, [5] have shown the existence of a domain state as the low temperature magnetic order. Polarised neutron diffraction measurements for wave vectors around the first peak in the structure factor for FeX7BII and (Fe,Ni_?),,B,,,Si,, [6] have shown the existence of a disordered transverse magnetic moment at low temperature. The existence of a random anisotropy effect in Fe based amorphous alloys has recently been suggested by Elsasser et al. [7] from computaOY21-4526/92/$05.00
0
1992 - Elsevier
Science
Publishers
tional calculations of the electronic and magnetic interactions in model amorphous systems. In this paper we report the results of SANS measurements of the magnetic critical scattering from samples of amorphous (Fe,Ni,_ ,),,B,,,Si,, with x = 0.125 and 0.25. These measurements were carried out using the LOQ diffractometer at the ISIS Facility. Rutherford Appleton Laboratory. UK. 2. Experimental The samples of amorphous (FerNi, ,),,B,,,Si,, used were the same as those used by Cowley et al. [6] and were ribbons of width 1.5 mm and thickness 50 pm made by the melt spinning technique at the University of Sheffield. The ribbons were wound on an aluminium frame in such a way that the transmission of the ribbons (which included natural boron) when mounted on the frame was of order 70%. For the x = 0.125 sample, this frame was attached to the copper block of a closed cycle refrigerator (CCR) and for the x = 0.25 sample to the centre stick of a vacuum furnace. During the measurements the sample temperature was continuously controlled and recorded by the instrument control computer. 3. Results Measurements for the x = 0.125 sample were carried out for a range of temperatures between IO K and 180 K. A “high temperature background” measurement was performed at 200 K and an ‘*empty CCR at 273 K. These two background runs background” were virtually identical, suggesting that any small angle nuclear scattering was extremely small and that
B.V. All rights
reserved
A.C.
Hannon et al. I Magnetic phase transition in amorphous
(Fe,Ni,
231
,),,B,,Si,,
consequently the samples are homogeneous. The high temperature background was subtracted from the other data sets in order to obtain the magnetic scattering. The same procedure was followed for the x = 0.25 sample with measurements taken for a range of temperatures from 298 K to 373 K and a background at 391 K. The data for both samples were fitted at all temperatures with a Lorentzian lineshape given by I(Q)
=
A Q'+
(1)
K’
The amplitude A in eq. (1) is related to the isothermal susceptibility by the relation x = A/K~. In fig. I we show a plot of K and x ’ against temperature for the x = 0.125 sample for temperatures T > 133 K. The solid lines are least squares fits to the equations K = TCIITC is the reKJ” and x = ,y,,tmYwhere t=]Tduced temperature. The best fit values are K, = 0.116? 0.027 A-‘, v = 0.67 ? 0.08, x = 0.0193 ” 0.0012 (arbitrary units), y = 1.4 * 0.1 and T, = 132.33 * 0.33 K. The measured values of Y and y are in good agreement with the theoretical values for the d = 3 Heisenberg model [8] of v = 0.71 and y = 1.39. Below TC in the x = 0.125 sample I(Q) is best fitted with a l/Q’ dependence (i.e. K = 0). with an amplitude which for temperatures below 120 K varies linearly with temperature. This behaviour is consistent with a gapless (or nearly gapless) spin wave cross section. In fig. 2 we plot K and x ’ against temperature for the x = 0.25 sample. For temperatures T > 343 K we are able to fit these results to the power law forms
. .
.
.
L
280
300
320
‘I’ernperaturr
360
340
380
(K)
Fig. 2. The temperature dependence of the inverse correlation length K (circles, left hand scale) and the inverse susceptibility x ’ (triangles. right hand scale) for the x =0.25 sample is shown. The solid lines are power law fits as described in the text.
with the best fit parameters K, = 0.108 +- 0.090 A- ‘, Y = 0.70 f 0.03, x,, = 0.131 * 0.009 (arbitrary units), y = 1.41 2 0.03 and TC = 342.37 * 0.60 K. Again these exponents are consistent with the d = 3 Heisenberg model in this temperature range. However the inverse correlation length does not go to zero at T, but instead saturates at 0.007 A-’ down to a temperature of 323 K. This corresponds to a real-space correlation length of 140 A. Similarly the isothermal susceptibility also saturates. Throughout this temperature range the scattering cross-section I(Q) can be fitted by a single Lorentzian line shape. However, below 323 K it cannot be successfully fitted in this way, nor can it be fitted by a sum of two Lorentzians or a Lorentzian plus a Lorentzian squared or a Lorentzian plus a Lorentzian raised to a non-integral power. This is a different behaviour to the previous measurements on Tb,Fe, I [3] and Fe,,,Zr ,I) [5] but is reminiscent of the low temperature behaviour of Dy,Ni, [4]. 4. Discussion
130
140
Temperature
150
160
(K)
Fig. 1. The temperature dependence of the inverse tion length K (circles, left hand scale) and inverse tibility x ’ (triangles, right hand scale) for the x sample is shown. The solid lines are power law described in the text.
correlasuscep= 0.125 fits as
To summarise the results reported in this paper we note that for (Fe,, ,?,Ni, X75)7XB,,,Si,2 the magnetic small angle scattering is consistent with the existence of ferromagnetic long range order while in it is not. It should be noted that (Fe,, riNi ,, ,,),,B,,,Si,, the existence of a ferromagnetic state in is not necessarily inconsistent (Fe,, ,,sNi ,, ,,T),,B,,,Si,,
A.C.
232
Hannon et al.
I Magnetic phase transition in amorphous (Fe,Ni,
with the previous polarised neutron diffraction measurements [6]. The possibility of “wandering axis ferromagnets” magnetic
where
there
component
and
is an
ordered
a disordered
[3] See
for example, J.W. Lynn and J.J. Rhyne, Spin dynamics of amorphous magnets. in: Spin Waves and
longitudinal transverse
com-
has been postulated theoretically [2] for amorphous magnets and this could be an explanation of the observed results. ponent
[4]
[S]
Acknowledgement This work has been supported by the UK Science and Engineering Research Council.
[6]
References [l]
R. Harris, M. Phschke and M.J. Zuckermann, Rev. Lett. 31 (1973) 160. [2] E. Chudnovsky, W.M. Saslow and R.A. Serota, Rev. B 33 (1986) 251 and references therein.
Phys. Phys.
,),,B,,,Si,,
[7] [8]
Magnetic Excitations 2. eds. A.S. Borovik-Romanov and S.K. Sinha (North-Holland, Amsterdam, 198X). A.C. Hannon. R. Cywinski, R.N. Sinclair, D.I. Grimley and A.C. Wright, Physica B 156 & 157 (1989) 210. A.C. Hannon. A.C. Wright and R.N. Sinclair, Mater. Sci. Eng. A 134 (1991) 883. J.A. Fernandez-Baca, J.J. Rhyne, R.W. Erwin and G.E. Fish. J. Phys. Colloq. C8 (1988) 1207. J.J. Rhyne. R.W. Erwin, J.A. Fernandez-Baca and G.E. Fish, J. Appl. Phys. 63 (1988) 3080. R.A. Cowley, N. Cowlam and L.D. Cussens. J. Phys. Colloq. C8 (198X) 1285: J. Phys. Condens. Mat.. in press. C. Elsasser, M. Fahnle, E.H. Brandt and M.C. Bohm. J. Phys. F 18 (1988) 2463. See for example, M.F. Collins. Magnetic Critical Scattering (Oxford University Press. 1989) p. 29.