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Magnon contributions to low-temperature thermal conductivity of amorphous ferromagnets
Journal of Magnetism and Magnetic Materials lOl(l991) North-Holland
M
37-39
M M
Magnon contributions to low-temperature of amorphous ferromagnets S. Welzel-Gerth,
B. Franz,
H.W. Gronert
thermal
md ? z
conductivity
and E.F. Wassermann
Tieftemperaturphysik, Universitiit Duisburg, 4100 Duisburg, Germany We report about measurements of the thermal conductivity on different amorphous ferromagnetic alloys in the temperature range 0.3 K i T < 25 K in magnetic fields up to 5 T. The results give further experimental evidence of magnon thermal transport in ferromagnetic glassy metals.
1. Introduction The existence of spin-wave-like excitations in ferromagnetic metallic glasses at low temperatures has been well established by magnetic and inelastic neutron scattering experiments [l]. Recently magnons have also been found in the thermal conductivity of amorphous Fe-Ni-metalloid alloys; ~~~~ - T3” [2,3]. The discussion of different scattering mechanisms has shown that the observed magnon heat transport is limited as in crystalline ferromagnets mainly by magnon-electron interaction [2-41. In the present work we give further evidence of magnon contributions to low-temperature thermal conductivity in amorphous ferromagnets. Significant magnon thermal conductivity is found in aCo,,Si,,B,,, a-Fe,,Si,,B,,, a-Fes,B,, and a-Co,,Zr,,. 2. Experimental details The amorphous alloys were prepared by melt-spinning or splat-cooling technique. The amorphous state of the samples was checked by X-ray diffraction and by measurements of the residual resistivity ratio, which is nearly one in metallic glasses. The thermal conductivity was measured in a He3-cryostat with a superconducting solenoid by a stationary method. The absolute accuracy in the total conductivity KIot is limited by the uncertainty of the geometry of the samples to & 108, whereas the relative accuracy is better than *OS’%. Further details have been given elsewhere [5]. 3. Results and discussion The measured total thermal conductivity amorphous metallic magnets is given by K’O’= Kph + Kel + Kmas
Ktot
of
(1)
where ~~~ is the phonon thermal conductivity, K~’ the electron thermal conductivity and ~~~~ the magnetic contributions. K~’ can be separated by using the Wiedemann-Franz law; this leads to: K = K’Of- Kel.
0312-8853/91/$03.50
(2)
Since the application of a magnetic field shifts the spin-wave excitation energies to higher values, the number of magnons and therefore K”‘~~decreases for a fixed temperature, when the field is raised. Assuming that for sufficiently low temperatures and high magnetic fields here T I 2.5 K and B = 5 T [2] - all magnons are “blocked”, i.e. tc”“*(T, B = 5 T) = 0 or Key = K(T, B = 5 T), the thermal conductivity of the spin-wave excitations can be obtained by K~~~=K(T,
B=OT)-K(T,
B=5T);
(3)
~~~~ > 0 is a sign of essential magnon contributions to the thermal conductivity [2-41, whereas ~~~~ < 0 indicates the dominance of phonon scattering by magnons as found earlier in a-Fe,,B,, [6] or phonon scattering by magnetic two-level systems as typical of spin-glasses [7]. Figure 1 shows for example the thermal conductivity K according to eq. (2) as a function of temperature T in a double logarithmic plot in the zero-field (dots) and in an external field of B = 5 T for three a-TM,,Si,,B,, samples with TM = Fe, Co, Ni. Whereas the Pauli-type paramagnet a-Ni,,Si,,B13 [8] shows no field effect in K, in the amorphous ferromagnets a-Fe,,Si,,B,, (Curie temperature T, = 720 K [8]) and a-Co,,Si,OB,, (T, = 700 K [9]) a significant decrease in the magnetic field is found as a sign of magnon heat transport. The plateau in the range 5 K I T I 15 K typical of amorphous solids is reduced by magnetic ions. A similar field effect is also found in a-C%Zr,, (T, > 770 K [lo]), a-Fe,,Si,, B,, (Vitrovac 7505) (T, = 693 K [ll]) and in a-FessB,, (T, = 556 K [12]). The decrease in field for Vitrovac 6025 (T, = 523 K [ll]) is too small to analyse. No field effect is found in a-Al,,Co,,,Gd,,,, the existence of superconductivity below 0.5 K seems possible. Figures 2 and 3 show K”‘@ after eq. (3) as a function of T for a-Fes,B,,, a-Co,Zr,,, a-Fe,.$i,zB,,, aFe,,S1,,B,3 [2] and a-Co,,Sl,,B,,. Below T = 2.5 K for all of these samples (without a-Fe,,Si,,B,, [13]) ~~~~ shows the same power law as in crystalline ferromagnets Kmas _ T3j2 [2,4]. The deviation from this regularity at T < 0.5 K seems to indicate the energy gap of the quadratic energy dispersion, the typical order of which
0 1991 - Elsevier Science Publishers B.V. All rights reserved
38
S. Welzel-Gerth
.
et al. / Magnon contributions
to thermal conductivity
of a-Fe magnets
x IB=OTI
o- Fe765112812-
A
I
I
III1
I,
,,,I
10
1 T(K) Fig. 1. K = rcto’ - ae’ as function of the temperature T in the zero-field and in an external field of 5 T for TM,,Si,,B,, (TM = Fe, Co, Ni)
Fig. 3. rcmag as a function of the temperature T for different amorphous ferromagnets as in fig. 2.
in glassy ferromagnets T = 0.46 K [12].
I
“I”“1
’
’
’ lb”“1
’
is 0.04
meV corresponding
to
These results give further evidence of a significant energy transport via long-range non-localised magnons in amorphous ferromagnets. The discussion in ref. [2] has shown that the observed magnon transport is limited mainly by magnon-electron scattering mediated by the s-d exchange interaction in the so-called “dirty limit”, which leads to a T 3/2-law. Magnon scattering by boundaries, phonons [4], magnetic [5] or structural twolevel systems [14] is not dominant in ferromagnetic metallic glasses. References
. a-Fe86B,L
+ 0 - cog, Zr,,
Fig. 2. ~~~~ as a function of the temperature and a-Co,Zr,, in a double-logarithmic
T for a-FessBId plot
[l] J.J. Rhyne, J. Non-C+. Solids 76 (1985) 129. [2] H.W. Gronert, D.M. Herlach and E.F. Wassermann, Europhys. Lett. 6 (1988) 641. [3] P. Svoboda and P. Vasek, J. Magn. Magn. Mater. 72 (1988) 194. [4] Y. Hsu and L. Berger, Phys. Rev. B 14 (1976) 4059, B 18 (1978) 4856. [5] R. Willnecker, D.M. Herlach and E.F. Wassermann, Phys. Rev. B 31 (1985) 6324. [6] H. Miiller and G. Pompe, Solid State Commun. 59 (1986) 35. (71 D.M. Herlach, E.F. Wassermann and R. Willnecker, Phys. Rev. Lett. 50 (1983) 529.
S. Welzel-Gerth
et al. / Magnon contributions to thermal conductivity of a-Fe magnets
[8] M. Goto, T. Tokunaga, H. Tange and T. Hamatake, Jpn. J. Appl. Phys. 19 (1980) 51. [9] M. Goto, H. Tange and T. Tokunaga, Jpn. J. Appl. Phys. 17 (1978) 1877. [lo] H. Tange, K. Inoue and K. Shirakuwa, J. Magn. Magn. Mater. 54-57 (1986) 303. [ll] Vacuumschmelze GmbH, Hanau, Germany. 1121 J.A. Femandez-Baca, J.W. Lynn, J.J. Bhyne and G.E. Fish, J. Appl. Phys. 57 (1985) 3545.
39
[13] However, for the moment the results below T= 2 K are still unclear, but after the measurement of this sample one of our Allen-Bradley resistivity thermometers must be prepared and calibrated again. [14] D.M. Herlach, H.W. Gronert and E.F. Wassermann, Europhys. Lett. 1 (1986) 23.
M
37-39
M M
Magnon contributions to low-temperature of amorphous ferromagnets S. Welzel-Gerth,
B. Franz,
H.W. Gronert
thermal
md ? z
conductivity
and E.F. Wassermann
Tieftemperaturphysik, Universitiit Duisburg, 4100 Duisburg, Germany We report about measurements of the thermal conductivity on different amorphous ferromagnetic alloys in the temperature range 0.3 K i T < 25 K in magnetic fields up to 5 T. The results give further experimental evidence of magnon thermal transport in ferromagnetic glassy metals.
1. Introduction The existence of spin-wave-like excitations in ferromagnetic metallic glasses at low temperatures has been well established by magnetic and inelastic neutron scattering experiments [l]. Recently magnons have also been found in the thermal conductivity of amorphous Fe-Ni-metalloid alloys; ~~~~ - T3” [2,3]. The discussion of different scattering mechanisms has shown that the observed magnon heat transport is limited as in crystalline ferromagnets mainly by magnon-electron interaction [2-41. In the present work we give further evidence of magnon contributions to low-temperature thermal conductivity in amorphous ferromagnets. Significant magnon thermal conductivity is found in aCo,,Si,,B,,, a-Fe,,Si,,B,,, a-Fes,B,, and a-Co,,Zr,,. 2. Experimental details The amorphous alloys were prepared by melt-spinning or splat-cooling technique. The amorphous state of the samples was checked by X-ray diffraction and by measurements of the residual resistivity ratio, which is nearly one in metallic glasses. The thermal conductivity was measured in a He3-cryostat with a superconducting solenoid by a stationary method. The absolute accuracy in the total conductivity KIot is limited by the uncertainty of the geometry of the samples to & 108, whereas the relative accuracy is better than *OS’%. Further details have been given elsewhere [5]. 3. Results and discussion The measured total thermal conductivity amorphous metallic magnets is given by K’O’= Kph + Kel + Kmas
Ktot
of
(1)
where ~~~ is the phonon thermal conductivity, K~’ the electron thermal conductivity and ~~~~ the magnetic contributions. K~’ can be separated by using the Wiedemann-Franz law; this leads to: K = K’Of- Kel.
0312-8853/91/$03.50
(2)
Since the application of a magnetic field shifts the spin-wave excitation energies to higher values, the number of magnons and therefore K”‘~~decreases for a fixed temperature, when the field is raised. Assuming that for sufficiently low temperatures and high magnetic fields here T I 2.5 K and B = 5 T [2] - all magnons are “blocked”, i.e. tc”“*(T, B = 5 T) = 0 or Key = K(T, B = 5 T), the thermal conductivity of the spin-wave excitations can be obtained by K~~~=K(T,
B=OT)-K(T,
B=5T);
(3)
~~~~ > 0 is a sign of essential magnon contributions to the thermal conductivity [2-41, whereas ~~~~ < 0 indicates the dominance of phonon scattering by magnons as found earlier in a-Fe,,B,, [6] or phonon scattering by magnetic two-level systems as typical of spin-glasses [7]. Figure 1 shows for example the thermal conductivity K according to eq. (2) as a function of temperature T in a double logarithmic plot in the zero-field (dots) and in an external field of B = 5 T for three a-TM,,Si,,B,, samples with TM = Fe, Co, Ni. Whereas the Pauli-type paramagnet a-Ni,,Si,,B13 [8] shows no field effect in K, in the amorphous ferromagnets a-Fe,,Si,,B,, (Curie temperature T, = 720 K [8]) and a-Co,,Si,OB,, (T, = 700 K [9]) a significant decrease in the magnetic field is found as a sign of magnon heat transport. The plateau in the range 5 K I T I 15 K typical of amorphous solids is reduced by magnetic ions. A similar field effect is also found in a-C%Zr,, (T, > 770 K [lo]), a-Fe,,Si,, B,, (Vitrovac 7505) (T, = 693 K [ll]) and in a-FessB,, (T, = 556 K [12]). The decrease in field for Vitrovac 6025 (T, = 523 K [ll]) is too small to analyse. No field effect is found in a-Al,,Co,,,Gd,,,, the existence of superconductivity below 0.5 K seems possible. Figures 2 and 3 show K”‘@ after eq. (3) as a function of T for a-Fes,B,,, a-Co,Zr,,, a-Fe,.$i,zB,,, aFe,,S1,,B,3 [2] and a-Co,,Sl,,B,,. Below T = 2.5 K for all of these samples (without a-Fe,,Si,,B,, [13]) ~~~~ shows the same power law as in crystalline ferromagnets Kmas _ T3j2 [2,4]. The deviation from this regularity at T < 0.5 K seems to indicate the energy gap of the quadratic energy dispersion, the typical order of which
0 1991 - Elsevier Science Publishers B.V. All rights reserved
38
S. Welzel-Gerth
.
et al. / Magnon contributions
to thermal conductivity
of a-Fe magnets
x IB=OTI
o- Fe765112812-
A
I
I
III1
I,
,,,I
10
1 T(K) Fig. 1. K = rcto’ - ae’ as function of the temperature T in the zero-field and in an external field of 5 T for TM,,Si,,B,, (TM = Fe, Co, Ni)
Fig. 3. rcmag as a function of the temperature T for different amorphous ferromagnets as in fig. 2.
in glassy ferromagnets T = 0.46 K [12].
I
“I”“1
’
’
’ lb”“1
’
is 0.04
meV corresponding
to
These results give further evidence of a significant energy transport via long-range non-localised magnons in amorphous ferromagnets. The discussion in ref. [2] has shown that the observed magnon transport is limited mainly by magnon-electron scattering mediated by the s-d exchange interaction in the so-called “dirty limit”, which leads to a T 3/2-law. Magnon scattering by boundaries, phonons [4], magnetic [5] or structural twolevel systems [14] is not dominant in ferromagnetic metallic glasses. References
. a-Fe86B,L
+ 0 - cog, Zr,,
Fig. 2. ~~~~ as a function of the temperature and a-Co,Zr,, in a double-logarithmic
T for a-FessBId plot
[l] J.J. Rhyne, J. Non-C+. Solids 76 (1985) 129. [2] H.W. Gronert, D.M. Herlach and E.F. Wassermann, Europhys. Lett. 6 (1988) 641. [3] P. Svoboda and P. Vasek, J. Magn. Magn. Mater. 72 (1988) 194. [4] Y. Hsu and L. Berger, Phys. Rev. B 14 (1976) 4059, B 18 (1978) 4856. [5] R. Willnecker, D.M. Herlach and E.F. Wassermann, Phys. Rev. B 31 (1985) 6324. [6] H. Miiller and G. Pompe, Solid State Commun. 59 (1986) 35. (71 D.M. Herlach, E.F. Wassermann and R. Willnecker, Phys. Rev. Lett. 50 (1983) 529.
S. Welzel-Gerth
et al. / Magnon contributions to thermal conductivity of a-Fe magnets
[8] M. Goto, T. Tokunaga, H. Tange and T. Hamatake, Jpn. J. Appl. Phys. 19 (1980) 51. [9] M. Goto, H. Tange and T. Tokunaga, Jpn. J. Appl. Phys. 17 (1978) 1877. [lo] H. Tange, K. Inoue and K. Shirakuwa, J. Magn. Magn. Mater. 54-57 (1986) 303. [ll] Vacuumschmelze GmbH, Hanau, Germany. 1121 J.A. Femandez-Baca, J.W. Lynn, J.J. Bhyne and G.E. Fish, J. Appl. Phys. 57 (1985) 3545.
39
[13] However, for the moment the results below T= 2 K are still unclear, but after the measurement of this sample one of our Allen-Bradley resistivity thermometers must be prepared and calibrated again. [14] D.M. Herlach, H.W. Gronert and E.F. Wassermann, Europhys. Lett. 1 (1986) 23.