- Email: [email protected]
Mössbauer study of the low temperature phases of CeSn3
Volume 27A, number 2
PHYSICS
eq. (3) into eq. (1) yields just one excitation branch which is the analog of the high-frequency branch for an ionic crystal. Now consider a slab. If eq. (3) is used in the general dispersion relations, all of the excitations are virtual modes [3]; there are no polaritons since < 1 for all w. Physically, eq. (3) represents the contribution to (w) from intraband transitions occurring in the conduction band. Interband effects can be included [4] by adding a term OEb(w) (assumed real for simplicity) to eq. (3) such that c(w)
=
1
-
+
&b(W)
3June 1968
0s of the modes on the The starting frequencies ~ line w = kxc are given by ~ = Wp2 [1+(m -1 )2ir2c 2/ Up2L2}/oeb, where m = 1, 2,..., is the mode label in fig. 1. For S-polarization, the modes do not differ significantly from those of fig. 1. In practice Ob(W) will always be frequencydependent [4}. The w-k~dependence of the modes will then reflect the frequency dependence of öE b( w). Some very approximate values of 5 b(w) for w Wp are -0.3 for aluminum (indicating that Al is not of interest here), 2 for silver, 0.7 for copper, and 0.2 for potassium [4].
(4)
If S~(w)is predominantly negative so that < 1 for all w, all excitations are still virtual modes. However, if Ob(w) is positive for w> Wp, striking changes occur. The properties of the virtual modes change sharply, particularly for optical experiments performed at large angles of incidence [3] and polariton modes having w > now appear in the region between i~&’ = k~cand W = k~~.C/f, where > 1. The lowest frequency modes for P-polarization, are sketched in fig. 1 for a constant value of SEb(w) equal to 1.0, and for a slab thickness Wp L/c =4.0. There exists an infinite set of solutions, the integers in the label indicating roughly the number of half-wave-lengths in the electric field occurring across the slab.
MOSSBAUER
LETTERS
References i. j. j. Hopfield. J. Phys. Soc. Japan 21, Supplement, 77 (1966). 2. K. L. Kliewer and R. Fuchs, Phys. Rev. 144 (1966) ~ ~ .Rev 150 6573. Rev. 153 (1967) 498. 4. H. Raether, Springer tracts in modern physics (Springer-Verlag, Berlin, 1965), Vol.38, p. 84.
STUDY OF THE LOW TEMPERATURE
PHASES OF CeSn 3
C. R. KANEKAR, K. R. P. MALLIKABJUNA RAO* and V. UDAYA SHANKAR RAO Tata Institute of Funda,nental Research, Bombay -5, India Received 25 April 1968 119Sn in CeSn The M’Ossbauer study of 3 at 4.2°Khas revealed the presence of two phases, one of which is ferromagnetic. These results are compared with earlier Knight shift and susceptibility data in the paramagnetic state.
Earlier, susceptibility study [1] of the intermetallic compound CeSn3 had revealed that this substance has quite unusual magnetic properties, Below 300°K, the observed magnetic susceptibi3~ lity isThis ion. far has lessbeen thaninterpreted that expected to be for due a free to the Ce * Bhabha Atomic Research Centre, Trombay, Bombay.
conversion of some of the trivalent cerium ions into the non-magnetic quadrivalent state. The susceptibility decreases to a minimum around 60°K; rapidlybelow indicating this temperature the onset of itsome increases incipient very ferromagnetism at low temperatures. We wish to report that the Mössbauer study at 85
Volume 27A, number 2
PHYSICS
LETTERS
3 June 1968
w 780 740
Z
Ce Sn
3 at 300’k
‘ ~
0440. w
~
‘
.~“
~t~=
,./~.
/
.,‘~.
.r”.
~
>
‘
:~.
—“
420
.
~
r
CeSn3at42K
(b)
\...,;/
~ 400 I
-6
I
-4
I
-2
I
I
I
0
+4
+6
DOPPLER VELOCITY (mm/Sec) 9Sn in CeSn Fig. 1. M~ssbauer spectra of ~ 3 a) at 3000K b) at 4.2°K.
4.2°Khas revealed two phases, one of which is ferromagnetic and the other is non-magnetic. At room temperature the Mössbauer spectrum (fig. la) is a simple quadrupole doublet showing that the material is in a single phase as expected for CeSn3 which has a f.c.c. structure of the Cu3Au (L12) type. At 4.2°K, in addition to a quadrupole doublet, a Zeeman split six-line spectrum is obtamed ferromagnetic (fig. ib).phase It is logical at 4.2°Kis to assume due to cerous that the ions while the quadrupole doublet arises due to the presence of ceric ions. The internal field at 119Sn in the magnetic phase is 65 kOe. The magnetic field at the tin site can be calculated by combining the Knight shift and the susceptibility data observed for this alloy in the paramagnetic state. The Knight shift at the tin site arises as a consequence of the conduction electron polarization caused through their exchange interaction with the cerium (4f) spins. In a simple model in which the conduction electrons are assumed to be free and possessing a spherical Fermi surface, the spatial variation of the conduction electron spin polarization around the localized moment is oscillatory and is given by the Ruderman-Kittel-Kasuya-Yosida (RKKY) theory [21. The Knight shift of 119Sn may then be written [3] as K(T)
=
[~o
-
XXm(T)1
the rare-earth alloy RSn3 in the absence of localized spins (e.g. in LaSn3), T is the exchange coupling constant between the conduction electron and the rare-earth ion spins, Z is the average number of conduction electrons per atom in the alloy, XM(T) is the magnetic susceptibility of the alloy at temperature T, kF is the Fermi wave vector, and R~is the9Sn distance site. of the i th rareearth From ion the from value the of ll X obtained from the gradient of the K(T) versus XM(T) curve, the expected hyperfine magnetic field Heff in the ferromagnetic phase can be calculated from the following expression assuming that saturation magnetization has been reached. H
-
eff
—
~J~B ~~‘)
z
The value calculated from the Knight shift and susceptibility data [4] is 61 kOe. The agreement between this value and that observed from the Mössbauer data clearly vindicates our suggestion that the phase with Ce3+ ions becomes ferromagnetic at low temperatures. Further experiments are currently underway to determine the hyperfine field at temperatures above and below 4.2°Kin order to understand the nature of the transition in still greater detail.
where gj4
(g -1)r~F(2kFRj) 1
In this expression the function F(x) = = (xcosx -sin x)/x4 gives the oscillatory nature of the polarization; gjis the Lande g-factor of the Ce-ion, and K 0 is the Knight shift expected for 86
References 1. T.Tsuchida and W.E.Wallace, J.Chem.Phys.43 2. K.Yosida, Phys. Rev. 106 (1957) 893. 3. P.G.de Gennes, J.Phys.Radium 23(1962)510. 4. V. Udaya Shankar Rao and R. Vijayaraghavan, Phys.
Letters 19 (1965)168.
PHYSICS
eq. (3) into eq. (1) yields just one excitation branch which is the analog of the high-frequency branch for an ionic crystal. Now consider a slab. If eq. (3) is used in the general dispersion relations, all of the excitations are virtual modes [3]; there are no polaritons since < 1 for all w. Physically, eq. (3) represents the contribution to (w) from intraband transitions occurring in the conduction band. Interband effects can be included [4] by adding a term OEb(w) (assumed real for simplicity) to eq. (3) such that c(w)
=
1
-
+
&b(W)
3June 1968
0s of the modes on the The starting frequencies ~ line w = kxc are given by ~ = Wp2 [1+(m -1 )2ir2c 2/ Up2L2}/oeb, where m = 1, 2,..., is the mode label in fig. 1. For S-polarization, the modes do not differ significantly from those of fig. 1. In practice Ob(W) will always be frequencydependent [4}. The w-k~dependence of the modes will then reflect the frequency dependence of öE b( w). Some very approximate values of 5 b(w) for w Wp are -0.3 for aluminum (indicating that Al is not of interest here), 2 for silver, 0.7 for copper, and 0.2 for potassium [4].
(4)
If S~(w)is predominantly negative so that < 1 for all w, all excitations are still virtual modes. However, if Ob(w) is positive for w> Wp, striking changes occur. The properties of the virtual modes change sharply, particularly for optical experiments performed at large angles of incidence [3] and polariton modes having w > now appear in the region between i~&’ = k~cand W = k~~.C/f, where > 1. The lowest frequency modes for P-polarization, are sketched in fig. 1 for a constant value of SEb(w) equal to 1.0, and for a slab thickness Wp L/c =4.0. There exists an infinite set of solutions, the integers in the label indicating roughly the number of half-wave-lengths in the electric field occurring across the slab.
MOSSBAUER
LETTERS
References i. j. j. Hopfield. J. Phys. Soc. Japan 21, Supplement, 77 (1966). 2. K. L. Kliewer and R. Fuchs, Phys. Rev. 144 (1966) ~ ~ .Rev 150 6573. Rev. 153 (1967) 498. 4. H. Raether, Springer tracts in modern physics (Springer-Verlag, Berlin, 1965), Vol.38, p. 84.
STUDY OF THE LOW TEMPERATURE
PHASES OF CeSn 3
C. R. KANEKAR, K. R. P. MALLIKABJUNA RAO* and V. UDAYA SHANKAR RAO Tata Institute of Funda,nental Research, Bombay -5, India Received 25 April 1968 119Sn in CeSn The M’Ossbauer study of 3 at 4.2°Khas revealed the presence of two phases, one of which is ferromagnetic. These results are compared with earlier Knight shift and susceptibility data in the paramagnetic state.
Earlier, susceptibility study [1] of the intermetallic compound CeSn3 had revealed that this substance has quite unusual magnetic properties, Below 300°K, the observed magnetic susceptibi3~ lity isThis ion. far has lessbeen thaninterpreted that expected to be for due a free to the Ce * Bhabha Atomic Research Centre, Trombay, Bombay.
conversion of some of the trivalent cerium ions into the non-magnetic quadrivalent state. The susceptibility decreases to a minimum around 60°K; rapidlybelow indicating this temperature the onset of itsome increases incipient very ferromagnetism at low temperatures. We wish to report that the Mössbauer study at 85
Volume 27A, number 2
PHYSICS
LETTERS
3 June 1968
w 780 740
Z
Ce Sn
3 at 300’k
‘ ~
0440. w
~
‘
.~“
~t~=
,./~.
/
.,‘~.
.r”.
~
>
‘
:~.
—“
420
.
~
r
CeSn3at42K
(b)
\...,;/
~ 400 I
-6
I
-4
I
-2
I
I
I
0
+4
+6
DOPPLER VELOCITY (mm/Sec) 9Sn in CeSn Fig. 1. M~ssbauer spectra of ~ 3 a) at 3000K b) at 4.2°K.
4.2°Khas revealed two phases, one of which is ferromagnetic and the other is non-magnetic. At room temperature the Mössbauer spectrum (fig. la) is a simple quadrupole doublet showing that the material is in a single phase as expected for CeSn3 which has a f.c.c. structure of the Cu3Au (L12) type. At 4.2°K, in addition to a quadrupole doublet, a Zeeman split six-line spectrum is obtamed ferromagnetic (fig. ib).phase It is logical at 4.2°Kis to assume due to cerous that the ions while the quadrupole doublet arises due to the presence of ceric ions. The internal field at 119Sn in the magnetic phase is 65 kOe. The magnetic field at the tin site can be calculated by combining the Knight shift and the susceptibility data observed for this alloy in the paramagnetic state. The Knight shift at the tin site arises as a consequence of the conduction electron polarization caused through their exchange interaction with the cerium (4f) spins. In a simple model in which the conduction electrons are assumed to be free and possessing a spherical Fermi surface, the spatial variation of the conduction electron spin polarization around the localized moment is oscillatory and is given by the Ruderman-Kittel-Kasuya-Yosida (RKKY) theory [21. The Knight shift of 119Sn may then be written [3] as K(T)
=
[~o
-
XXm(T)1
the rare-earth alloy RSn3 in the absence of localized spins (e.g. in LaSn3), T is the exchange coupling constant between the conduction electron and the rare-earth ion spins, Z is the average number of conduction electrons per atom in the alloy, XM(T) is the magnetic susceptibility of the alloy at temperature T, kF is the Fermi wave vector, and R~is the9Sn distance site. of the i th rareearth From ion the from value the of ll X obtained from the gradient of the K(T) versus XM(T) curve, the expected hyperfine magnetic field Heff in the ferromagnetic phase can be calculated from the following expression assuming that saturation magnetization has been reached. H
-
eff
—
~J~B ~~‘)
z
The value calculated from the Knight shift and susceptibility data [4] is 61 kOe. The agreement between this value and that observed from the Mössbauer data clearly vindicates our suggestion that the phase with Ce3+ ions becomes ferromagnetic at low temperatures. Further experiments are currently underway to determine the hyperfine field at temperatures above and below 4.2°Kin order to understand the nature of the transition in still greater detail.
where gj4
(g -1)r~F(2kFRj) 1
In this expression the function F(x) = = (xcosx -sin x)/x4 gives the oscillatory nature of the polarization; gjis the Lande g-factor of the Ce-ion, and K 0 is the Knight shift expected for 86
References 1. T.Tsuchida and W.E.Wallace, J.Chem.Phys.43 2. K.Yosida, Phys. Rev. 106 (1957) 893. 3. P.G.de Gennes, J.Phys.Radium 23(1962)510. 4. V. Udaya Shankar Rao and R. Vijayaraghavan, Phys.
Letters 19 (1965)168.