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The band magnetism of MnSi
Journal of Magnetism and Magnetic Materials 54-57 (1986) 957-958
957
THE B A N D M A G N E T I S M OF MnSi L. T A I L L E F E R ,
G.G. LONZARICH
Cavendish Laboratory, Cambridge CB3 0HE, UK
a n d P. S T R A N G E H.H. Wills Physics Laboratoo,, Bristol BS8 1 TL, UK
We present an investigation of the electronic spectrum of MnSi through band structure calculations and de Haas-van Alphen (dHvA) measurements. The calculated Stoner T~ is high but shown to be suppressed dramatically by the strong spin fluctuations characteristic of MnSi. The unusually high mass enhancement observed is consistent with the strength of these fluctuations.
The transition metal compound MnSi orders magnetically below 30 K to a helical structure in zero magnetic field or to an induced ferromagnetic state with an unsaturated magnetic moment of 0 . 4 f f J M n atom in a field greater than 6.2 kG [1]. This material differs essentially from typical very weak itinerant ferromagnets in exhibiting very low energy magnetic fluctuation modes over large portions of the Brillouin zone [2]. Such modes are expected to lead to a strong renormalisation of the electronic mass and of the Curie temperature. For a realistic analysis of these effects, a knowledge of the quasiparticle energies must be acquired. The first step towards this end was to calculate the ~ band structure of ferromagnetic MnSi. This was done using the local approximation to Density Functional Theory and applying the standard Linear Muffin Tin Orbital (LMTO) method [3] with the Von B a r t h - H e d i n Approximation for the exchange-correlation energy.
M MnSi
/ ~
Majority (~) spin Minority (i') spin
/ ' ~ ~A \\/
s
),,1
}
(00[)
\,
×1
R [
I/
W---} P
;\ E
M
Fig. 1. Predicted sections of the majority and minority spin Fermi surfaces of MnSi in high symmetry planes. The corresponding sections along planes including Z' rather than Z, the two points being unrelated by symmetry, are only negligeably different from the above (see ref. [4] for crystallographic details). 0304-8853/86/$03.50
Table 1 Identification of the three dominant dHvA frequencies ~. rt and p. with three orbits of the predicted Fermi surface normal to the [100] crystal direction. F22 is the small electron pocket centred on F; X21 is a hole neck centred on X; M21 is a large electron loop centred on M (see fig. 1). Identification is based on the relative amplitude of the dHvA signal, on the magnitude and orientation dependence of the frequencies and on the magnitude of the masses
Frequency (MG) Cyclotron masses (ma) ~: I'22 -9:X21 ,a: M21
Exp
Calc
Exp
Calc
Exp/Calc
0.7 29 64
0.3 30.7 68
2.4 8.0 14.5
0.5 2.4 3.0
4.8 3.3 4.8
Spin-orbit coupling was neglected, but other relativistic effects were included. Our self-consistent spin polarised calculation yields a nearly uniform exchange splitting of majority and minority spin bands, which are individually generally similar to those reported previously for the paramagnetic state [4], and predicts a stable magnetic moment of 0.25ffB/Mn atom in fair agreement with the measured value. The bands near the Fermi energy E v consist mainly of the ten very flat 3d-bands of manganese. To produce as realistic a band structure as possible, the self-consistent splitting was further increased artificially until the calculated magnetic moment was equal to the experimental value, a reasonable procedure with uniformly split bands. The Fermi surface predicted by the resulting band structure is shown in fig. 1. The areas and cyclotron masses of three typical extremal orbits in a plane normal to the [100] crystal direction are listed in table 1. The spin-resolved density of electronic states is shown in fig. 2, where the exchange splitting ,~ is indeed seen to be essentially uniform and approximately equal to 21 toRy. The calculated band structure was given experimental support through a study of the de H a a s - v a n Alphen
© E l s e v i e r S c i e n c e P u b l i s h e r s B.V.
958
L. Taille]er et aL
/ Band magnetism of MnSi
I
Table 2 Comparison of the transition temperatures of MnSi calculated using the conventional Stoner model and the spin fluctuation (SF) model of Lonzarich and Taillefer [6]. The Stoner model uses the density of states shown in fig. 2 in the paramagnetic limit ( J 4 0 ) and an interaction parameter 1-13.1 toRy as discussed in the text. The SF model uses four parameters derived from the equation of state at T = 0 and from inelastic neutron scattering data
0-80 i¸
u :>. ry60
~. ,, jq'~,
"'
,
i, i ,
i
@ ~
40t
," ~ 2 0 m R y
T~(K) >,
Stoner model
SF model
measured
400-500
32
29.5(5)
MnSi
g 20
--Majority , Minorily
(~) spin ('~) spin
21 toRy I
i
ol
-40
20
1
~~
51 mRy I
20
0
40
Fig. 2. Calculated density of electronic states of MnSi near the Fermi energy E v for majority ( t ) spins (solid line) and minority (~,) spins (dashed line) separately. The nearly uniform exchange splitting is approximately 21 mRy. The spin resolved density of states at E v is N t (EF) = 74.9 and N~ ( E v ) = 79.2 states/Ry cell spin and the narrow band gap just above E v has a width of 31 toRy.
(dHvA) effect. Preliminary investigations were performed on a high purity sample of MnSi (residual resistivity ratio O [293 K] p [4.2 K] of 230) at temperatures down to 0.35 K and in magnetic fields up to 130 kG. As many as 15 fundamental) d H v A frequencies
m* - 8 . 0 m o m*:
2.4m o
m*- 14.5 rn o
m* ~ 18 m ~
I51. The Curie temperature was estimated by conventional Stoner theory using our calculated density of states in the paramagnetic limit (A ~ 0) and an interaction parameter I = 13.1 toRy derived from the exchange splitting. Note that this value of 1 agrees with the e n h a n c e m e n t of the longitudinal susceptibility in the ferromagnetic state. As seen in table 2 the resulting T~ is much too high. However, when spin fluctuations are taken into account, T~ is dramatically suppressed to a value in close agreement with experiment [6].
r'fii
/L__ OVIG
were observed, most of which are resolved in the frequency spectrum of fig. 3. The effective cyclotron masses were measured to be unusually high, extending from 2.4m 0 at the lowest frequencies to beyond 14.5m 0 at high frequencies. The masses of the K and F branches are in fact the highest ever observed in a transition metal. A n identification of the three d o m i n a n t d H v A frequencies measured experimentally with three of the predicted orbits is given in table 1. The measured and calculated cyclotron masses are also given, along with their ratio m * / r n , the mass e n h a n c e m e n t factor. The average factor of approximately 4, a very large value for a transition metal, is comparable to the e n h a n c e m e n t of the linear coefficient of the heat capacity Y/T0 = 5.2 evaluated using the specific heat data of Fawcett et al.
70
MG
Fig. 3. Amplitude spectrum of typical dHvA oscillations in MnSi at T = 0.35 K in the [100] field orientation and in the range 102.8 kG ~
[1] D. Bloch, J. Voiron, V. Jaccarino and J.H. Wernick, Phys. Left. 51A (1975) 259. [2} Y. Ishikawa, Y. Noda, C. Fincher and G. Shirane, Phys. Rev. B25 (1982) 254. [3] H.L. Skriver, The LMTO Method (Springer, New York, 1984). [4] O. Nakanishi, A. Yanase and M. Kataoka, in: Electron Correlation and Magnetism in Narrow-Band Systems, ed. T. Moriya (Springer, New York, 1981). [5] E. Fawcett, J.P. Maita and J.H. Wernick, Intern. J. Magn. 1 (1970) 29. [6] G.G. Lonzarich and L. Taillefer J. Phys. C 18 (1985) 4339. G.G. Lonzarich, J. Magn. Magn. Mat. 45 (1984) 43.
957
THE B A N D M A G N E T I S M OF MnSi L. T A I L L E F E R ,
G.G. LONZARICH
Cavendish Laboratory, Cambridge CB3 0HE, UK
a n d P. S T R A N G E H.H. Wills Physics Laboratoo,, Bristol BS8 1 TL, UK
We present an investigation of the electronic spectrum of MnSi through band structure calculations and de Haas-van Alphen (dHvA) measurements. The calculated Stoner T~ is high but shown to be suppressed dramatically by the strong spin fluctuations characteristic of MnSi. The unusually high mass enhancement observed is consistent with the strength of these fluctuations.
The transition metal compound MnSi orders magnetically below 30 K to a helical structure in zero magnetic field or to an induced ferromagnetic state with an unsaturated magnetic moment of 0 . 4 f f J M n atom in a field greater than 6.2 kG [1]. This material differs essentially from typical very weak itinerant ferromagnets in exhibiting very low energy magnetic fluctuation modes over large portions of the Brillouin zone [2]. Such modes are expected to lead to a strong renormalisation of the electronic mass and of the Curie temperature. For a realistic analysis of these effects, a knowledge of the quasiparticle energies must be acquired. The first step towards this end was to calculate the ~ band structure of ferromagnetic MnSi. This was done using the local approximation to Density Functional Theory and applying the standard Linear Muffin Tin Orbital (LMTO) method [3] with the Von B a r t h - H e d i n Approximation for the exchange-correlation energy.
M MnSi
/ ~
Majority (~) spin Minority (i') spin
/ ' ~ ~A \\/
s
),,1
}
(00[)
\,
×1
R [
I/
W---} P
;\ E
M
Fig. 1. Predicted sections of the majority and minority spin Fermi surfaces of MnSi in high symmetry planes. The corresponding sections along planes including Z' rather than Z, the two points being unrelated by symmetry, are only negligeably different from the above (see ref. [4] for crystallographic details). 0304-8853/86/$03.50
Table 1 Identification of the three dominant dHvA frequencies ~. rt and p. with three orbits of the predicted Fermi surface normal to the [100] crystal direction. F22 is the small electron pocket centred on F; X21 is a hole neck centred on X; M21 is a large electron loop centred on M (see fig. 1). Identification is based on the relative amplitude of the dHvA signal, on the magnitude and orientation dependence of the frequencies and on the magnitude of the masses
Frequency (MG) Cyclotron masses (ma) ~: I'22 -9:X21 ,a: M21
Exp
Calc
Exp
Calc
Exp/Calc
0.7 29 64
0.3 30.7 68
2.4 8.0 14.5
0.5 2.4 3.0
4.8 3.3 4.8
Spin-orbit coupling was neglected, but other relativistic effects were included. Our self-consistent spin polarised calculation yields a nearly uniform exchange splitting of majority and minority spin bands, which are individually generally similar to those reported previously for the paramagnetic state [4], and predicts a stable magnetic moment of 0.25ffB/Mn atom in fair agreement with the measured value. The bands near the Fermi energy E v consist mainly of the ten very flat 3d-bands of manganese. To produce as realistic a band structure as possible, the self-consistent splitting was further increased artificially until the calculated magnetic moment was equal to the experimental value, a reasonable procedure with uniformly split bands. The Fermi surface predicted by the resulting band structure is shown in fig. 1. The areas and cyclotron masses of three typical extremal orbits in a plane normal to the [100] crystal direction are listed in table 1. The spin-resolved density of electronic states is shown in fig. 2, where the exchange splitting ,~ is indeed seen to be essentially uniform and approximately equal to 21 toRy. The calculated band structure was given experimental support through a study of the de H a a s - v a n Alphen
© E l s e v i e r S c i e n c e P u b l i s h e r s B.V.
958
L. Taille]er et aL
/ Band magnetism of MnSi
I
Table 2 Comparison of the transition temperatures of MnSi calculated using the conventional Stoner model and the spin fluctuation (SF) model of Lonzarich and Taillefer [6]. The Stoner model uses the density of states shown in fig. 2 in the paramagnetic limit ( J 4 0 ) and an interaction parameter 1-13.1 toRy as discussed in the text. The SF model uses four parameters derived from the equation of state at T = 0 and from inelastic neutron scattering data
0-80 i¸
u :>. ry60
~. ,, jq'~,
"'
,
i, i ,
i
@ ~
40t
," ~ 2 0 m R y
T~(K) >,
Stoner model
SF model
measured
400-500
32
29.5(5)
MnSi
g 20
--Majority , Minorily
(~) spin ('~) spin
21 toRy I
i
ol
-40
20
1
~~
51 mRy I
20
0
40
Fig. 2. Calculated density of electronic states of MnSi near the Fermi energy E v for majority ( t ) spins (solid line) and minority (~,) spins (dashed line) separately. The nearly uniform exchange splitting is approximately 21 mRy. The spin resolved density of states at E v is N t (EF) = 74.9 and N~ ( E v ) = 79.2 states/Ry cell spin and the narrow band gap just above E v has a width of 31 toRy.
(dHvA) effect. Preliminary investigations were performed on a high purity sample of MnSi (residual resistivity ratio O [293 K] p [4.2 K] of 230) at temperatures down to 0.35 K and in magnetic fields up to 130 kG. As many as 15 fundamental) d H v A frequencies
m* - 8 . 0 m o m*:
2.4m o
m*- 14.5 rn o
m* ~ 18 m ~
I51. The Curie temperature was estimated by conventional Stoner theory using our calculated density of states in the paramagnetic limit (A ~ 0) and an interaction parameter I = 13.1 toRy derived from the exchange splitting. Note that this value of 1 agrees with the e n h a n c e m e n t of the longitudinal susceptibility in the ferromagnetic state. As seen in table 2 the resulting T~ is much too high. However, when spin fluctuations are taken into account, T~ is dramatically suppressed to a value in close agreement with experiment [6].
r'fii
/L__ OVIG
were observed, most of which are resolved in the frequency spectrum of fig. 3. The effective cyclotron masses were measured to be unusually high, extending from 2.4m 0 at the lowest frequencies to beyond 14.5m 0 at high frequencies. The masses of the K and F branches are in fact the highest ever observed in a transition metal. A n identification of the three d o m i n a n t d H v A frequencies measured experimentally with three of the predicted orbits is given in table 1. The measured and calculated cyclotron masses are also given, along with their ratio m * / r n , the mass e n h a n c e m e n t factor. The average factor of approximately 4, a very large value for a transition metal, is comparable to the e n h a n c e m e n t of the linear coefficient of the heat capacity Y/T0 = 5.2 evaluated using the specific heat data of Fawcett et al.
70
MG
Fig. 3. Amplitude spectrum of typical dHvA oscillations in MnSi at T = 0.35 K in the [100] field orientation and in the range 102.8 kG ~
[1] D. Bloch, J. Voiron, V. Jaccarino and J.H. Wernick, Phys. Left. 51A (1975) 259. [2} Y. Ishikawa, Y. Noda, C. Fincher and G. Shirane, Phys. Rev. B25 (1982) 254. [3] H.L. Skriver, The LMTO Method (Springer, New York, 1984). [4] O. Nakanishi, A. Yanase and M. Kataoka, in: Electron Correlation and Magnetism in Narrow-Band Systems, ed. T. Moriya (Springer, New York, 1981). [5] E. Fawcett, J.P. Maita and J.H. Wernick, Intern. J. Magn. 1 (1970) 29. [6] G.G. Lonzarich and L. Taillefer J. Phys. C 18 (1985) 4339. G.G. Lonzarich, J. Magn. Magn. Mat. 45 (1984) 43.