- Email: [email protected]
Magnetic properties of inequivalent iron atoms in Fe2Ti
Solid State Communications,
Vol. 8, PP. 2173—2176, 1970.
Pergamon Press.
Printed in Great Britain
MAGNETIC PROPERTIES OF INEQUIVALENT IRON ATOMS IN Fe
2Ti
G.K. Wertheim, D.N.E. Buchanan and J.H. Wernick Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey 07974 (Received 7 October 1970 by N.B. Wannay)
High-field Mössbauer measurements show that the a-site iron in Fe2Ti has a vanishing magnetic moment. This accounts for the absence of a-site magnetic hyperfine splitting in the antiferromagnetic compound below the Néel temperature.
IT HAS been recently shown that the magnetic properties of the MgZn2 type, hexagonal Laves phase compound Fe2Ti are a sensitive function of deviations from stoichiometry. Within the single-phase region Ti-rich material ferromagnetic while Fe-rich material is is antiferro-
contributions are small. The occurrence of atoms of one kind both with and without magnetic moment in a single metallic phase is not without precedent having been previously reported in 4 a-Mn.
magnetic with a saturation magnetization which rises linearly with the amount of excess iron. In an earlier publication we have suggested, in part
We have examined this question by studying the Mössbauer absorption of near-stoichiometric Fe 2Ti in an external magnetic field provided by a 100 koe superconducting solenoid. The absorber was prepared from a slightly Ti-rich sample to avoid complications from magnetic clusters. The preparation and Mössbauer spectra The of this sample have been previously published.2 absorber
on the basis of evidence obtained from a Mössbauer effect study, that the ferromagnetism is due to the formation of ferromagnetically coupled 2clusters which form aroundtwo Fetypes atomsofin The iron atoms occupy Ti sites. inequivalent sites. There are six h- sites with mm symmetry which order antiferromagnetically and two a-sites with ~m symmetry which show only quadrupole splitting. It was noted in reference 2 that the intensity of the a-site absorption is greatly reduced in Fe-rich specimens, i.e. this normally nonmagnetic iron apparently develops a hyperfirie field when it is in a magnetic cluster. The observation that the a-site iron normally has a vanishing hyperfine field 3even at 4.2°K has not been previously explained. It could arise from an accidental cancellation of contributions from core and conduction electron polarization and dipolar fields. Another possibility is that the Fe atom itself does not have a magnetic moment and that the other
for the present experiment was prepared from finely crushed powder, rigidly held by a polymethylmethacrylate binder to prevent motion of the particles in the external field. The sample was mounted in a chamber filled with He exchangegas whose walls were in direct contact with liquid helium. The Mössbauer spectrometer was of the conventional parabolic motion type. A 1024 channel analyzer operating in a triggered up-down scan mode ~ was used to accumulate the data. The source consisted of ~Co in a metallic palladium matrix and was at room temperature. Data at 0, 50 and 100 koe are shown in Fig. 1. Perhaps the most striking aspect, and one which must be understood in detail before the spectrum of the a-site iron can be discussed, is the broadening of the h-site spectrum with applied
2173
2174
MAGNETIC PROPERTIES OF INEQUIVALENT IRON ATOMS IN Fe
2Ti
tOE
Vol. 8, No. 24
probability of the occurrence of a particular
—
value of net field is simply proportional to the 00
Ti0 3.4 Fe066 O~ 0.88 He,t ~0kOe
o 82 _______________
1.00 >C
0.94 \~I6ho 0 C
~ 088
z
too..
z
field itself, see appendix. It is qualitatively clear that this will lead to the type of broadening which is actually observed. For direct comparison with the data we have computer-simulated the spectra resulting from this case. One important aspect of the behavior of a polycrystalline absorber in an external field resides in the line intensities. With increasing external field, H, the resultant field at the nucleus becomes more and more aligned in the direction of F!. Since the gamma rays pass through the sample parallel to H, the intensity of the Am 0 lines will decrease with increasing external field. In the calculations this effect was accurately taken into account for the full range of crystal
~ 0.94 lOok 0 e 0.88
I
20
orientation in the polycrystalline absorber. A complication which cannot be treated accurately arises from the quadrupole splitting. Because of the iow site symmetry the Mössbauer data do not suffice to specify the properties of the electric field gradient, EFG, tensor. But even if it is
1.00
0.94 298~i< 088
450 relative to the major axis of the EFG tensor.
tOO koe
The crystallographic direction remains unknown.
082 -03
assumed to be symmetrical, a further ambiguity remains because the spin direction can only be specified to lie on a cone with a half-angle of
I
.1
-0.2 -01 0 0 02 DOPPLER VELOCITY (cm/SeC)
03
FIG. 1. Mössbauer absorption spectra of polycrystalline Fe2Ti at 4.2°K in longitudinal external field. The spectrum of nonmagnetic dilute ~Fe ~fl metallic Ti in 100 koe at 298°Kis shown for comparison at the bottom.
Consequently the quadrupole interaction cannot be rigorously introduced in the simulation of the spectra. Fortunately it is sufficiently small so that this does not seriously compromise the results which are shown as dashed lines in Fig. 1, and serve to separate the h-site absorption from that of the a-site which is of primary concern here.
field. The behavior of an antiferromagnet in an external field depends on the magnitude of the magneto-crystalline anisotropy. If it is small the antiferromagnetic spin-system will flop, i.e. the spin rotate perpendicular to the applied field. The external field, H, then adds in quadrature to the internal field, H0, and all nuclei will experience the same total field. This case produces no broadening and clearly does not apply. Alternately we may assume that the anisotropy is sufficiently largeeasy so that the spin remains aligned the direction. In asystem polycrystalline samplein
The a-site spectrum consists of four slightly broadened lines. This is exactly the spectrum expected for the nuclear Zeeman effect of an iron atom in a longitudinal external field, i.e. the Am = 0 lines are suppressed. The quadrupole coupling, which is know~nto be present from the zero-field spectrum, produce line broadening but causes no line shift. This may be shown rigorously by averaging over all field directions relative to the symmetry axis1~’2time of thethe EFG tensor. quadrupole The zero-field broadening 5~ 50 and 100 koe the field splitting. Atisboth
the net field at the nucleus will now range from H 0—H to H0+H, It can be readily shown that the
calculated from the Zeeman splitting is equal to the externally applied field, which indicates that
Vol. 8, No. 24
MAGNETIC PROPERTIES OF INEQUIVALENT IRON ATOMS IN Fe
the a-site iron has no moment. For comparison we show in the bottom half of Fig. 1 the absorption spectrum of dilute ~Fe in metallic Ti at room temperature in an external field of 100 koe. 6Iron The here is known to have no magnetic moment. similarity of the a-site iron spectrum is immediately apparent.
2Ti
2175
difference in the spatial arrangement. The nonmagnetic a-site has the iron atoms in a relatively small solid angle close to the 3 axis, and the Tih-site atomshas around the atoms equator~The magnetic the iron less symmetrically arranged with the Ti atoms less exposed. The steric differences are apparently sufficient to influence the moment formation by iron. The
If the a-site iron had a magnetic moment the application of an external magnetic field would produce additional broadening because of the large anisotropy, similar to that of the h-site iron. Broadening, over and above that attributable to the quadrupole splitting was not found.
fact that the substitution of an iron atom on a Ti site makes the neighboring a-site irons magnetic 2 provides an additional path for the coupling between the layers of h-site iron atoms. This mechanism may play art important role in the formation of magnetic clusters. 2It might also be noted that the critical nature in which the
The conclusion that the a-site iron has no magnetic moment seems inescapable. Since it is likely that the Ti atoms are also nonmagnetic the direct magnetic interaction between h-site iron atoms are confined to planes perpendicular to the six-fold symmetry axis. However, because of coupling via polarized conduction electrons this compound is not a two-dimensional magnet.
appearance of the moment depends on coordination is in agreement with the assumption made in the discussion of moment formation in Mo—Nb alloys.7
The vanishing moment of the a-site iron should be viewed from the vantage point of the magnetic behavior of the whole Ti—Fe system. As previously mentioned dilute iron in h.c.p. and 6 b.c.c. Ti is known to have no magnetic moment. In fact, even the equiatomic b.c.c. alloy FeTi is nonmagnetic. In the ordered state iron atoms in this compound would have eight Ti near neighbors. The next stable phase with increasing iron content is Fe2Ti. The coordination of the two, iron sites in this compound are similar. Both have six Fe near neighbors and six Ti next-near . - . neighbors. There is, however, a significant
APPENDIX Let the external field, H, define the z-axis. For a polycrystalline sample the direction of the internal field can then be specified by the polar angle, 0. The net resultant field, H~,is given by H = (H 2~~~ H2 + 2H H cos 0)1/2 (1) °
The magnitude of H,~ ranges from H H 0 0 +H.
—
H
to
The probability p (H70) dHr~ for the occurrence of a value between H70 and H70 + dH70 is given by the fraction of solid angle between 0 and 0 + dO which is sin 0 dO /2. Using equation (1) to eliminate 0 yields p(H
)
=
H /2H0H
which is valid in the range of ~
(2)
specified above.
REFERENCES 1.
NAKAMICHI T., J. Phys. Soc. Japan 25, 1189 (1968); BRUCKNER W., PERTHEL B., KLEINSTUCK K. and SCHULZE G.E.R., Phys. Stat. So!. 29, 211 (1968).
2.
WERTHEIM G.K., WERNICK J.H. and SHERWOOD R.C., Solid State Commun. 7, 1399 (1969); J. .appl. Phys. 41, 1325 (1970). See also BRUCKNER W., KLEINSTUCK K. and SCHULZE G.E.R., Phys. Slat. Sal. (a) 1, Ki (1970).
3.
KOCHER C.W. and BROWN P.J., J. appl. Phys. 33, 1091 (1962); WALLACE W.E., J. Chem. Phys. 41, 3857 (1964).
4.
KASPER J.S., Theory of Alloy Phases, p 266 ff. American Society of Metals, Cleveland, (1956).
S.
COHEN R.L. and WEST K.W., (unpublished).
2176
MAGNETIC PROPERTIES OF INEQUIVALENT IRON ATOMS IN Fe
2Ti
6.
RUPP G., Z. Phys. 230, 265 (1970) and references therein.
7.
JACCARINO V. and WALKER L.R., Phys. Rev. Leit. 15, 258 (1965).
Des mesures de l’effet Mössbauer a champ élevé montrent que l’atorne de fer sur le site a dans Fe2Ti posséde un moment magnétique évanouissant. Ainsi s’explique l’absence de separation magnétique hyperfine du site a dans le compose antiferromagnétique au-dessous du point de Née!.
Vol. 8, No. 24
Vol. 8, PP. 2173—2176, 1970.
Pergamon Press.
Printed in Great Britain
MAGNETIC PROPERTIES OF INEQUIVALENT IRON ATOMS IN Fe
2Ti
G.K. Wertheim, D.N.E. Buchanan and J.H. Wernick Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey 07974 (Received 7 October 1970 by N.B. Wannay)
High-field Mössbauer measurements show that the a-site iron in Fe2Ti has a vanishing magnetic moment. This accounts for the absence of a-site magnetic hyperfine splitting in the antiferromagnetic compound below the Néel temperature.
IT HAS been recently shown that the magnetic properties of the MgZn2 type, hexagonal Laves phase compound Fe2Ti are a sensitive function of deviations from stoichiometry. Within the single-phase region Ti-rich material ferromagnetic while Fe-rich material is is antiferro-
contributions are small. The occurrence of atoms of one kind both with and without magnetic moment in a single metallic phase is not without precedent having been previously reported in 4 a-Mn.
magnetic with a saturation magnetization which rises linearly with the amount of excess iron. In an earlier publication we have suggested, in part
We have examined this question by studying the Mössbauer absorption of near-stoichiometric Fe 2Ti in an external magnetic field provided by a 100 koe superconducting solenoid. The absorber was prepared from a slightly Ti-rich sample to avoid complications from magnetic clusters. The preparation and Mössbauer spectra The of this sample have been previously published.2 absorber
on the basis of evidence obtained from a Mössbauer effect study, that the ferromagnetism is due to the formation of ferromagnetically coupled 2clusters which form aroundtwo Fetypes atomsofin The iron atoms occupy Ti sites. inequivalent sites. There are six h- sites with mm symmetry which order antiferromagnetically and two a-sites with ~m symmetry which show only quadrupole splitting. It was noted in reference 2 that the intensity of the a-site absorption is greatly reduced in Fe-rich specimens, i.e. this normally nonmagnetic iron apparently develops a hyperfirie field when it is in a magnetic cluster. The observation that the a-site iron normally has a vanishing hyperfine field 3even at 4.2°K has not been previously explained. It could arise from an accidental cancellation of contributions from core and conduction electron polarization and dipolar fields. Another possibility is that the Fe atom itself does not have a magnetic moment and that the other
for the present experiment was prepared from finely crushed powder, rigidly held by a polymethylmethacrylate binder to prevent motion of the particles in the external field. The sample was mounted in a chamber filled with He exchangegas whose walls were in direct contact with liquid helium. The Mössbauer spectrometer was of the conventional parabolic motion type. A 1024 channel analyzer operating in a triggered up-down scan mode ~ was used to accumulate the data. The source consisted of ~Co in a metallic palladium matrix and was at room temperature. Data at 0, 50 and 100 koe are shown in Fig. 1. Perhaps the most striking aspect, and one which must be understood in detail before the spectrum of the a-site iron can be discussed, is the broadening of the h-site spectrum with applied
2173
2174
MAGNETIC PROPERTIES OF INEQUIVALENT IRON ATOMS IN Fe
2Ti
tOE
Vol. 8, No. 24
probability of the occurrence of a particular
—
value of net field is simply proportional to the 00
Ti0 3.4 Fe066 O~ 0.88 He,t ~0kOe
o 82 _______________
1.00 >C
0.94 \~I6ho 0 C
~ 088
z
too..
z
field itself, see appendix. It is qualitatively clear that this will lead to the type of broadening which is actually observed. For direct comparison with the data we have computer-simulated the spectra resulting from this case. One important aspect of the behavior of a polycrystalline absorber in an external field resides in the line intensities. With increasing external field, H, the resultant field at the nucleus becomes more and more aligned in the direction of F!. Since the gamma rays pass through the sample parallel to H, the intensity of the Am 0 lines will decrease with increasing external field. In the calculations this effect was accurately taken into account for the full range of crystal
~ 0.94 lOok 0 e 0.88
I
20
orientation in the polycrystalline absorber. A complication which cannot be treated accurately arises from the quadrupole splitting. Because of the iow site symmetry the Mössbauer data do not suffice to specify the properties of the electric field gradient, EFG, tensor. But even if it is
1.00
0.94 298~i< 088
450 relative to the major axis of the EFG tensor.
tOO koe
The crystallographic direction remains unknown.
082 -03
assumed to be symmetrical, a further ambiguity remains because the spin direction can only be specified to lie on a cone with a half-angle of
I
.1
-0.2 -01 0 0 02 DOPPLER VELOCITY (cm/SeC)
03
FIG. 1. Mössbauer absorption spectra of polycrystalline Fe2Ti at 4.2°K in longitudinal external field. The spectrum of nonmagnetic dilute ~Fe ~fl metallic Ti in 100 koe at 298°Kis shown for comparison at the bottom.
Consequently the quadrupole interaction cannot be rigorously introduced in the simulation of the spectra. Fortunately it is sufficiently small so that this does not seriously compromise the results which are shown as dashed lines in Fig. 1, and serve to separate the h-site absorption from that of the a-site which is of primary concern here.
field. The behavior of an antiferromagnet in an external field depends on the magnitude of the magneto-crystalline anisotropy. If it is small the antiferromagnetic spin-system will flop, i.e. the spin rotate perpendicular to the applied field. The external field, H, then adds in quadrature to the internal field, H0, and all nuclei will experience the same total field. This case produces no broadening and clearly does not apply. Alternately we may assume that the anisotropy is sufficiently largeeasy so that the spin remains aligned the direction. In asystem polycrystalline samplein
The a-site spectrum consists of four slightly broadened lines. This is exactly the spectrum expected for the nuclear Zeeman effect of an iron atom in a longitudinal external field, i.e. the Am = 0 lines are suppressed. The quadrupole coupling, which is know~nto be present from the zero-field spectrum, produce line broadening but causes no line shift. This may be shown rigorously by averaging over all field directions relative to the symmetry axis1~’2time of thethe EFG tensor. quadrupole The zero-field broadening 5~ 50 and 100 koe the field splitting. Atisboth
the net field at the nucleus will now range from H 0—H to H0+H, It can be readily shown that the
calculated from the Zeeman splitting is equal to the externally applied field, which indicates that
Vol. 8, No. 24
MAGNETIC PROPERTIES OF INEQUIVALENT IRON ATOMS IN Fe
the a-site iron has no moment. For comparison we show in the bottom half of Fig. 1 the absorption spectrum of dilute ~Fe in metallic Ti at room temperature in an external field of 100 koe. 6Iron The here is known to have no magnetic moment. similarity of the a-site iron spectrum is immediately apparent.
2Ti
2175
difference in the spatial arrangement. The nonmagnetic a-site has the iron atoms in a relatively small solid angle close to the 3 axis, and the Tih-site atomshas around the atoms equator~The magnetic the iron less symmetrically arranged with the Ti atoms less exposed. The steric differences are apparently sufficient to influence the moment formation by iron. The
If the a-site iron had a magnetic moment the application of an external magnetic field would produce additional broadening because of the large anisotropy, similar to that of the h-site iron. Broadening, over and above that attributable to the quadrupole splitting was not found.
fact that the substitution of an iron atom on a Ti site makes the neighboring a-site irons magnetic 2 provides an additional path for the coupling between the layers of h-site iron atoms. This mechanism may play art important role in the formation of magnetic clusters. 2It might also be noted that the critical nature in which the
The conclusion that the a-site iron has no magnetic moment seems inescapable. Since it is likely that the Ti atoms are also nonmagnetic the direct magnetic interaction between h-site iron atoms are confined to planes perpendicular to the six-fold symmetry axis. However, because of coupling via polarized conduction electrons this compound is not a two-dimensional magnet.
appearance of the moment depends on coordination is in agreement with the assumption made in the discussion of moment formation in Mo—Nb alloys.7
The vanishing moment of the a-site iron should be viewed from the vantage point of the magnetic behavior of the whole Ti—Fe system. As previously mentioned dilute iron in h.c.p. and 6 b.c.c. Ti is known to have no magnetic moment. In fact, even the equiatomic b.c.c. alloy FeTi is nonmagnetic. In the ordered state iron atoms in this compound would have eight Ti near neighbors. The next stable phase with increasing iron content is Fe2Ti. The coordination of the two, iron sites in this compound are similar. Both have six Fe near neighbors and six Ti next-near . - . neighbors. There is, however, a significant
APPENDIX Let the external field, H, define the z-axis. For a polycrystalline sample the direction of the internal field can then be specified by the polar angle, 0. The net resultant field, H~,is given by H = (H 2~~~ H2 + 2H H cos 0)1/2 (1) °
The magnitude of H,~ ranges from H H 0 0 +H.
—
H
to
The probability p (H70) dHr~ for the occurrence of a value between H70 and H70 + dH70 is given by the fraction of solid angle between 0 and 0 + dO which is sin 0 dO /2. Using equation (1) to eliminate 0 yields p(H
)
=
H /2H0H
which is valid in the range of ~
(2)
specified above.
REFERENCES 1.
NAKAMICHI T., J. Phys. Soc. Japan 25, 1189 (1968); BRUCKNER W., PERTHEL B., KLEINSTUCK K. and SCHULZE G.E.R., Phys. Stat. So!. 29, 211 (1968).
2.
WERTHEIM G.K., WERNICK J.H. and SHERWOOD R.C., Solid State Commun. 7, 1399 (1969); J. .appl. Phys. 41, 1325 (1970). See also BRUCKNER W., KLEINSTUCK K. and SCHULZE G.E.R., Phys. Slat. Sal. (a) 1, Ki (1970).
3.
KOCHER C.W. and BROWN P.J., J. appl. Phys. 33, 1091 (1962); WALLACE W.E., J. Chem. Phys. 41, 3857 (1964).
4.
KASPER J.S., Theory of Alloy Phases, p 266 ff. American Society of Metals, Cleveland, (1956).
S.
COHEN R.L. and WEST K.W., (unpublished).
2176
MAGNETIC PROPERTIES OF INEQUIVALENT IRON ATOMS IN Fe
2Ti
6.
RUPP G., Z. Phys. 230, 265 (1970) and references therein.
7.
JACCARINO V. and WALKER L.R., Phys. Rev. Leit. 15, 258 (1965).
Des mesures de l’effet Mössbauer a champ élevé montrent que l’atorne de fer sur le site a dans Fe2Ti posséde un moment magnétique évanouissant. Ainsi s’explique l’absence de separation magnétique hyperfine du site a dans le compose antiferromagnétique au-dessous du point de Née!.
Vol. 8, No. 24