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Properties, units and constants in magnetism
Journal of Magnetism and Magnetic Materials 100 (1991) 573-575 North-Holland
Properties, units and constants in magnetism L y d o n J. S w a r t z e n d r u b e r National Institute of Standards and Technology, Gaithersburg, MD 20234, USA
The accompanying table (table 1) consists of data and numbers designed to be useful as a pocket data card for workers in the fields of magnetism and magnetic materials. They have been selected from a number of sources [1-6]. The symbols used in the table are: the ferromagnetic Curie temperature; the magnetic m o m e n t of each atom in Bohr magnetons; the specific saturation magnetization. The saturation magnetization 4"rrMs in gauss can be ~rS obtained by multiplying o-s by 4"rr and by the density; the ferromagnetic resonance frequency. There are two isotopes for Gd: 155Gd (14.9% Vr abundance) and 157Gd (15.7%). Other isotopes are: 57Fe (2.14%), 61Ni (1.1%) and 59C0 (100%); the density. Densities given are calculated densities from X-ray results. Actual densities can P vary a few percent from the values given, even for very pure materials; the atomic weight, or the number of grams per mole; A the volume susceptibility; Xv the mass susceptibility; Xg the permeability of free space; /z0 the Bohr magneton; the nuclear magneton; tXB/k the ratio of the Bohr magneton to the Boltzmann constant. This is useful because the ration ~BH/kT appears quite often; NA~ZB the product of Avogadro's constant and the Bohr magneton; the magnetic flux quantum. 40
L
]Zat
The value of Tc for hcp Co given in table 1 is estimated. The ferromagnetic nuclear magnetic resonance ( F N R ) frequencies listed are for 57Fe, 59C0, 61Ni, ~55Gd and 157Gd. The two relationships noted are useful for converting the magnetic induction or in e m u / g to the magnetic m o m e n t per atom in Bohr magnetons or to the magnetic induction in gauss. The susceptibility values and their temperature coefficients for several N I S T standard reference materials are included since many workers have these standards in their laboratory but may no longer have the certificate. Further, if great care is used in the selection of materials, one can probably use these numbers to fabricate special standards at the 1% accuracy level. The t e m p e r a t u r e coefficients have a limited range of validity but can be considered valid f o r normal variations in room temperature. Conversions between cgs Gaussian units and mks (SI) units seem to have been designed to torment both the novice and the seasoned professional alike. Both unit systems have their advantages and both 0304-8853/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved
574 Table 1 Data and numbers in the field of magnetism and magnetic materials Ferromagnetic elements:
Fe (bcc)
Co (fcc)
Co (hcp)
Ni (fcc)
Gd (hcp)
TO [K] izat at 0 K [/zB] o"s at 0 K [Tm3/kg 4~" 10 -7] a) trs at 298 K [Tm3/kg 4~" 10 -7] a) NMR ~'r at 0 K [MHz] p at 298 K [g/cc] A [g/tool]
1044 2.217 221.7 217.2 46.64 7.875 55.847
1388 1.753 166.1 164.8 228 8.793 58.933
1360 1.721 163.1 161.8 217 8.804 58.933
627.4 0.6157 58.57 55.09 28.46 8.912 58.71
293.4 7.56 268.4 0 48.6, 64.2 7.898 157.25
NIST calibration samples, SI units, T = 298 K SRM SRM SRM SRM SRM SRM
772 (Ni sphere) b) 766 (MnF 2) 764 (Pt) 765 (Pd) 763 (AI) 763 (AI) @ 77.7 K
o- = Xg = Xg = gg = Xg = Xg =
54.95 X 4~- X 10-7 (1 -- 9 5 5 / H ) 123.0 x 4~" x 10- 9 0.991 x 4~" x 10- 9 5.24 x 4~r × 10 -9 0.604X4zr x 10 9 0.696x4~r x 10 9
- 0.03%/K - 0.28%/K - 0.07%/K -0.19%/K -0.06%/K -0.07%/K
( 5: 0.4%) ( + 0.5%) ( 5: 0.5%) (5:0.5%) (5:0.5%) (5:0.5%)
Gaussian to SI:
multiply no. of
by
to obtain no. of
Flux density, B Field strength, H Magnetization, M Magnetization, 4wM Susceptibility (M/H), Xv c) Mass susceptibility, Xg c) Magnetic moment, tz c) Specific magnetization, tr c) Demagnetizing factor, N Flux, • Anisotropy constant, K
G Oe G or Oe G emu cm - 3 0 e - 1 emu g - i O e - 1 e r g / G ( -= emu) emu/g (no dim.) maxwell erg/cm 3
10 -4 103/4~r 103 10 4 4~r 41r. 10 -3 10 3 4"n-. 10 -7 1/4"rr 10 - s 10 1
T A/m
A/m T (no dim.) m3/kg J / T ( -- A m 2) Tm3/kg (no dim.) Wb j/m 3
Useful constants:
Gaussian
SI
/~0 /x a /x N
1 (no dim.) 9.274015 x 10 -21 e r g / G 5.050787 x 10 24 e r g / G 0.671710X 10 4 K / G 5.584939 X 103 erg G - 1 m o l - i 2.067835 x 10 -7 maxwell
4rr × 10 -7 H / m ( =- T m / A ) 9.274015 x 10 -24 J / T 5.050787 × 10 -27 J / T 0.671710 K / T 5.584939 J T 1 mol-1 2.067835 x 10-15 Wb
IxB/k NA/Z B q~0 ( = h / 2 e )
a) Note for ~ in e m u / g : /~at (in /~B ) = o'A//NA//,B; B s (in G ) = 4rr~rsp. b) Valid for H between 280 and 795 k A / m . c) G cm 3 is often substituted for emu (which is not a unit). In the Gaussian system B = H + 4~M, in SI (mks) B = ~0 ( H + M).
will n o d o u b t b e u s e d f o r s o m e t i m e t o c o m e . T h e c o n v e r s i o n s g i v e n a r e t h e o n e s w e h a v e f o u n d m o s t o f t e n u s e f u l . T h e o f t e n u s e d " u n i t " , e m u , is n o t r e a l l y a u n i t t o w h i c h d i m e n s i o n a l a n a l y s i s c a n b e a p p l i e d . A s a n a i d t o o v e r c o m i n g t h i s , e m u is s o m e t i m e s r e p l a c e d b y G c m 3. ( I t c o u l d a l s o b e r e p l a c e d b y e r g / G . ) S u s c e p t i b i l i t i e s i n t h e G a u s s i a n s y s t e m , s u c h a s Xg, a l t e r n a t e l y a p p e a r w i t h t h e u n i t s e m u / g , e m u / g O e , e m u / g G , G c m 3 / g a n d c m 3 / g . A l t h o u g h v o l u m e s u s c e p t i b i l i t y is d i m e n s i o n l e s s in b o t h s y s t e m s , it is o f t e n a s s i g n e d a u n i t i n t h e G a u s s i a n r e f . [5].
system. For further discussion of magnetic
units see
575
References [1] [2] [3] [4] [5]
G.C. Carter, L.H. Bennett and D.J. Kahan, Metallic Shifts in NMR (Pergamon, New York, 1977). J.J. Rhyne, Bull. Alloy Phase Diagrams 3 (1982) 401. E.R. Cohen and B.N. Taylor, Rev. Mod. Phys. 59 (1987) 1121. E.P. Wohlfarth, Ferromagnetic Materials, vol. 1 (North-Holland, Amsterdam, 1980). L.H. Bennett, C.H. Page and L.J. Swartzendruber, AlP Conf. Proc. 29 (American Institute of Physics, New York, 1976); J. Res. Nat. Bur. Stds. 83 (1978) 9. [6] H.P.J. Wijn, Landolt-B6rstein Numerical Data, Group III, vol. 19, subvoL A, (Springer, Berlin, 1986).
Properties, units and constants in magnetism L y d o n J. S w a r t z e n d r u b e r National Institute of Standards and Technology, Gaithersburg, MD 20234, USA
The accompanying table (table 1) consists of data and numbers designed to be useful as a pocket data card for workers in the fields of magnetism and magnetic materials. They have been selected from a number of sources [1-6]. The symbols used in the table are: the ferromagnetic Curie temperature; the magnetic m o m e n t of each atom in Bohr magnetons; the specific saturation magnetization. The saturation magnetization 4"rrMs in gauss can be ~rS obtained by multiplying o-s by 4"rr and by the density; the ferromagnetic resonance frequency. There are two isotopes for Gd: 155Gd (14.9% Vr abundance) and 157Gd (15.7%). Other isotopes are: 57Fe (2.14%), 61Ni (1.1%) and 59C0 (100%); the density. Densities given are calculated densities from X-ray results. Actual densities can P vary a few percent from the values given, even for very pure materials; the atomic weight, or the number of grams per mole; A the volume susceptibility; Xv the mass susceptibility; Xg the permeability of free space; /z0 the Bohr magneton; the nuclear magneton; tXB/k the ratio of the Bohr magneton to the Boltzmann constant. This is useful because the ration ~BH/kT appears quite often; NA~ZB the product of Avogadro's constant and the Bohr magneton; the magnetic flux quantum. 40
L
]Zat
The value of Tc for hcp Co given in table 1 is estimated. The ferromagnetic nuclear magnetic resonance ( F N R ) frequencies listed are for 57Fe, 59C0, 61Ni, ~55Gd and 157Gd. The two relationships noted are useful for converting the magnetic induction or in e m u / g to the magnetic m o m e n t per atom in Bohr magnetons or to the magnetic induction in gauss. The susceptibility values and their temperature coefficients for several N I S T standard reference materials are included since many workers have these standards in their laboratory but may no longer have the certificate. Further, if great care is used in the selection of materials, one can probably use these numbers to fabricate special standards at the 1% accuracy level. The t e m p e r a t u r e coefficients have a limited range of validity but can be considered valid f o r normal variations in room temperature. Conversions between cgs Gaussian units and mks (SI) units seem to have been designed to torment both the novice and the seasoned professional alike. Both unit systems have their advantages and both 0304-8853/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved
574 Table 1 Data and numbers in the field of magnetism and magnetic materials Ferromagnetic elements:
Fe (bcc)
Co (fcc)
Co (hcp)
Ni (fcc)
Gd (hcp)
TO [K] izat at 0 K [/zB] o"s at 0 K [Tm3/kg 4~" 10 -7] a) trs at 298 K [Tm3/kg 4~" 10 -7] a) NMR ~'r at 0 K [MHz] p at 298 K [g/cc] A [g/tool]
1044 2.217 221.7 217.2 46.64 7.875 55.847
1388 1.753 166.1 164.8 228 8.793 58.933
1360 1.721 163.1 161.8 217 8.804 58.933
627.4 0.6157 58.57 55.09 28.46 8.912 58.71
293.4 7.56 268.4 0 48.6, 64.2 7.898 157.25
NIST calibration samples, SI units, T = 298 K SRM SRM SRM SRM SRM SRM
772 (Ni sphere) b) 766 (MnF 2) 764 (Pt) 765 (Pd) 763 (AI) 763 (AI) @ 77.7 K
o- = Xg = Xg = gg = Xg = Xg =
54.95 X 4~- X 10-7 (1 -- 9 5 5 / H ) 123.0 x 4~" x 10- 9 0.991 x 4~" x 10- 9 5.24 x 4~r × 10 -9 0.604X4zr x 10 9 0.696x4~r x 10 9
- 0.03%/K - 0.28%/K - 0.07%/K -0.19%/K -0.06%/K -0.07%/K
( 5: 0.4%) ( + 0.5%) ( 5: 0.5%) (5:0.5%) (5:0.5%) (5:0.5%)
Gaussian to SI:
multiply no. of
by
to obtain no. of
Flux density, B Field strength, H Magnetization, M Magnetization, 4wM Susceptibility (M/H), Xv c) Mass susceptibility, Xg c) Magnetic moment, tz c) Specific magnetization, tr c) Demagnetizing factor, N Flux, • Anisotropy constant, K
G Oe G or Oe G emu cm - 3 0 e - 1 emu g - i O e - 1 e r g / G ( -= emu) emu/g (no dim.) maxwell erg/cm 3
10 -4 103/4~r 103 10 4 4~r 41r. 10 -3 10 3 4"n-. 10 -7 1/4"rr 10 - s 10 1
T A/m
A/m T (no dim.) m3/kg J / T ( -- A m 2) Tm3/kg (no dim.) Wb j/m 3
Useful constants:
Gaussian
SI
/~0 /x a /x N
1 (no dim.) 9.274015 x 10 -21 e r g / G 5.050787 x 10 24 e r g / G 0.671710X 10 4 K / G 5.584939 X 103 erg G - 1 m o l - i 2.067835 x 10 -7 maxwell
4rr × 10 -7 H / m ( =- T m / A ) 9.274015 x 10 -24 J / T 5.050787 × 10 -27 J / T 0.671710 K / T 5.584939 J T 1 mol-1 2.067835 x 10-15 Wb
IxB/k NA/Z B q~0 ( = h / 2 e )
a) Note for ~ in e m u / g : /~at (in /~B ) = o'A//NA//,B; B s (in G ) = 4rr~rsp. b) Valid for H between 280 and 795 k A / m . c) G cm 3 is often substituted for emu (which is not a unit). In the Gaussian system B = H + 4~M, in SI (mks) B = ~0 ( H + M).
will n o d o u b t b e u s e d f o r s o m e t i m e t o c o m e . T h e c o n v e r s i o n s g i v e n a r e t h e o n e s w e h a v e f o u n d m o s t o f t e n u s e f u l . T h e o f t e n u s e d " u n i t " , e m u , is n o t r e a l l y a u n i t t o w h i c h d i m e n s i o n a l a n a l y s i s c a n b e a p p l i e d . A s a n a i d t o o v e r c o m i n g t h i s , e m u is s o m e t i m e s r e p l a c e d b y G c m 3. ( I t c o u l d a l s o b e r e p l a c e d b y e r g / G . ) S u s c e p t i b i l i t i e s i n t h e G a u s s i a n s y s t e m , s u c h a s Xg, a l t e r n a t e l y a p p e a r w i t h t h e u n i t s e m u / g , e m u / g O e , e m u / g G , G c m 3 / g a n d c m 3 / g . A l t h o u g h v o l u m e s u s c e p t i b i l i t y is d i m e n s i o n l e s s in b o t h s y s t e m s , it is o f t e n a s s i g n e d a u n i t i n t h e G a u s s i a n r e f . [5].
system. For further discussion of magnetic
units see
575
References [1] [2] [3] [4] [5]
G.C. Carter, L.H. Bennett and D.J. Kahan, Metallic Shifts in NMR (Pergamon, New York, 1977). J.J. Rhyne, Bull. Alloy Phase Diagrams 3 (1982) 401. E.R. Cohen and B.N. Taylor, Rev. Mod. Phys. 59 (1987) 1121. E.P. Wohlfarth, Ferromagnetic Materials, vol. 1 (North-Holland, Amsterdam, 1980). L.H. Bennett, C.H. Page and L.J. Swartzendruber, AlP Conf. Proc. 29 (American Institute of Physics, New York, 1976); J. Res. Nat. Bur. Stds. 83 (1978) 9. [6] H.P.J. Wijn, Landolt-B6rstein Numerical Data, Group III, vol. 19, subvoL A, (Springer, Berlin, 1986).