Part C: Hexagonal Ferrites. Special Lanthanide and Actinide Compounds

628 Pages·1982·32.91 MB·English

by  K.-H. Hellwege, A. M. Hellwege (eds.), D. Bonnenberg, K. A. Hempel, W. Roos (auth.)

Ref. p. 371 5.0 Introduction
5 Hexagonal ferrites
5.0 Introduction *)
Since the discovery in 1951 of the, technically, very important magnetic properties of the ferrite BaFe,,O,,
with hexagonal crystal structure, many related compound; have been synthesized, and the properties of these
mostly completely new structures have been investigated. At room temperature the magnetic moments of most
of these compounds can be ordered in groups in such a way that the magnetic moments of the ions of one group
are mutually parallel oriented, whereas the magnetic moments of the ions of different groups are oriented anti-
parallel to each other. Such an incompletely compensated antiferromagnetism was called ferrimagnetism by
NCel, who was the first to describe this type of magnetism in order to explain the magnetization of ferrites with
spine1s tructure [48N]. The technical interest in the oxides with hexagonal crystal structure is shown by the fact
that some of these materials show a very high uniaxial magnetic anisotropy, so that they can be used as a ceramic
permanent magnetic material which for some applications can compete technically, and economically, with the
metallic permanent magnets of the AlNiCo-type. Other hexagonal ferrites have interesting properties as magnetic
cores at frequencies above about 100 MHz. In electronic equipments for microwaves, single crystals and poly-
crystalline samples of hexagonal ferrites with still other chemical compositions are used successfully, because
of their exceptionally high internal magnetic field, or becauseo f the non-linear effects which appear at already
relatively low amplitude of the high frequency field. For the h.f. applications it is essential that theses emi-conduct-
ing ferrites can be prepared in such a way that their conductivity at room temperature is very low.
The chemical compositions and the crystal structures of the’hexagonal ferrites show many similarities, and
they are reviewed in sections 7.3 and 7.4 of volume 111/4bS. ection 5.5 (7.5 in vol. 111/4b)in cludes the paramagnetic
properties of the hexagonal ferrites while sections 5.6..=5.10( 7.6...7.10 in vol. 111/4b)d eal with the properties
of the compounds of each crystal structure separately. Becauseo f the various uncertainties regarding the crystal
structures of the calcium ferrites and the substituted calcium ferrites, the properties of these ferrites are given
separately in section 5.11 (7.11 in vol. 111/4b).
In sections 5.12..e 5.14,p roperties of some hexagonal ferrites of increasing significance are to be found which
have been taken out of the above mentioned sections and arranged into groups. Apart from this, further hexag-
onal ferrites which do not belong to the above mentioned sections are listed in section 5.15.
5.1 Quantities and units
In today’s literature the magnetic properties are discussedi n the SIU (S&me International dUnit&) or in
units of the cgs-emu= electromagnetic cgs system.T herefore, and contrary to vol. 111/4b,in tables and figures of
this volume, the various quantities are given in cgs-emuo r in SI units, i.e. in the units as used in the original pa-
pers. In this section 5.1.,h owever, equations are given in both, cgs-emua nd SIU system,i n the second casei ndi-
cated by a light shade,t hough in the original papers from which somee quations have been taken, only the electro-
magnetic cgs system has been used. The relation between the magnetic induction, B, the magnetic field strength,
H, and the magnetization, M, is given by
B=H+4xM;
a) Conductivity
The temperature-dependenceo f the conductivity Q of hexagonal ferrites can usually be described by the equa-
tion :
g=g,
5.1 Quantities and units [Ref. p. 37
where Q denotes the density of the porous sample.T he specific saturation magnetization at 0 K, a:, is a measure
of the magnetic moment p, per molecule of the substance.T he quantity p, is usually expressedi n number of
Bohr magnetons according to the equation:
(4)
where (IV,,) is the molar mass of the substanceA , NA the number of molecules per mole (Avogadro number) and
uB the Bohr magneton:
NA = 6.02. 1O23m ole- ‘,
~-I. _ _--__- .__-__ .--_---.-
pB=g=9.27.1e0rg- G2a1us s- ’ ; $B=$9.27. lo-a4A m2
and
“““~)_^_,- _ _ ,......I_ ..-...
NA pB = 5580.5 erg Gauss mole- ’ ; pB= 5.58014m 2 mole- ‘.
c) Magneto-crystalline anisotropy of hexagonal crystals
Becauseo f the symmetry of the hexagonal crystal lattice, the magneto-crystalline anisotropy energy density
is given by the equation:
n~,=K,sin26+K2sin48+K;sin60+K3sin60cos6(~+$). (5)
The angles 0 and 4 are polar coordinates and the constants Ki are the coefficients of the magneto-crystalline
anisotropy. The phase angle $ is zero for a particular choice of the axis of the coordinate system.T he term with
the coefficient K; can usually be neglected. In casesw here the term with K, is predominant, the spontaneous
magnetization is oriented parallel to the c-axis for K, >O, the crystal has a so-called preferential direction of
magnetization. For K ~0, the spontaneous magnetization is oriented perpendicular to the c-axis, the crystal has
a so-called preferential plane of magnetization. In general the angle 0e between the direction of the spontaneous
magnetization and the c-axis is a function of K, and K,, as illustrated in Fig. A. In casesw here 0<8,<90” the
crystal shows a preferential cone for the spontaneous magnetization with a vertex 24, which is given by the equa-
tion :
sin e,=fq. (6)
Fig. A. The relation between the preferential direction of )
the magnetization vector in a hexagonal crystal and the
corresponding values of the magneto-crystalline anisotropy
coefhcients K, and K,. For 0,=0 the c-axis is the preferen-
tial direction, for Be= 90” the basal plane is the preferential -K, -
plane for the magnetization. In the sector of the diagram
for which sin 0a =I/-K,/2K, all directions of the magneti- .ZK,=-K,
zation which make an angle of B0w ith the c-axis of the crystal
have the lowest energy (preferential cone for the magneti-
zation). In the region -2K,>K,>O the spontaneous
magnetization has metastable orientations [59CSEF].
The magneto-crystalline anisotropy field strength HA is defined as the effective field strength that causest he same
stiffness for a rotation of the magnetization over a small angle out of its preferential direction as the magneto-
crystalline anisotropy does. In the case of a rotation with constant angle 4 we get:
^_^._ _.. ‘ . _. ”, .-_,--- - .-”. ”x ._ . _._ _
(7)
so that for
t&=0: H,A=HA=2K,fMS; (74
e&o”: H$= -(K,+K,)/& H:= -(K, +K,)/poMS, (W
__-..-_- I” .. - “__^.____ - ._ ” ..-
sin&,=]/-K,/2K,: H~=2(K,/K,)(K, +2K,)/M,; H~=WWWK, +~WIGK. (7c)
2 Bonnenberg/Hempel/Roos
Ref. p. 371 5.1 Quantities and units
Ihe effective anisotropy field strength for a rotation of the magnetization out of its equilibrium orientation along
the surface of the preferential cone is given by:
H~=(1/M,sin28,)(a2w,/a~‘),=,=36~K,~sin4B,/M,;
i’y” 7- -“wywy”-pi--y’m~ - qe;“=” eqo- tyy-nw~~~-+~~-~“~‘7‘~y ”q-y (8)
f=[~/poM6sm &,)(a
5.1 Quantities and units [Ref. p. 37
and
for
HzH*-(N,-NJM,
HA>4nM;
Fig. B shows the graphs for the eqs. (12), (13a) and (13b) for the casesw here demagnetizing fields do not appear.
Fig. B. The angular frequency for ferromagnetic resonance, b
CO,,,,a s a function of the external magnetic field strength
H parallel or perpendicular to the preferential direction for
the magnetization (c-axis) of a crystal with hexagonal
symmetry [59SW].
II. Hexagonal crystals with planar anisotropy.
a) When the magnetic field strength H is oriented parallel to the y-direction in the preferential plane, which
will also be the xy-plane, of the orthogonal system the resonancef requency given by (10) is as follows:
2nl,,,=y[H-(NY-Nx)M]1'2~[H+H,A+(Nz-NY)M-J1'2;
I_---
,=yp,[H-(NY-NJMj1'2+i+H~+(NI-N,)hfJ112 (14)
If only magneto-crystalline energy is considered, according to [59BK] this equation reduces to:
where the minus and the plus signs in the second factor correspond to an instable and a stable equilibrium ori-
entation of the magnetization in the plane, respectively,a nd K, is another constant in the serial development
of the anisotropy energy.
b) For a magnetic field parallel to the direction for difficult magnetization (c-axis) the resonance frequency
is given by:
2xf,,,=y[(H-H,A)-(Nz-Nx)M]1'2[(H-H~)-(Nz-NY)M-J1'2; (1%
--v--.-v --._-~_--"-
-H~)-(Nz-NJM1112[(H-H$)-(Nz-N;)MJ'n
for
H>H*+N,M;
4 Ronnenberg/Hempel/Roos
Ref. p. 371 5.2 List of symbols and abbreviations
In the derivation of eqs.( 14) and (15) the anisotropy field strength H$ is neglected with respectt o H and Ht since
it is usually lower by several orders of magnitude. In the special casew here only magneto-crystalline energy has
to be considered, [59BK], the eq. (15) reduces to:
~KL,=YH
M M M
5.2 List of symbols and abbreviations
4) Symbols
a, c CA1 lattice parameters
B I31 magnetic induction
W%,x CG.e el maximum energy product of permanent magnetic materials
d [mm] crystal thickness
f L-Hz1 frequency
fres CHzl resonancef requency
H [A ~‘1, PI magnetic field strength
HA [@I magnetocrystalline anisotropy field strength
dfc Dl coercive field strength for magnetization
Ki [erg cm- ‘1 magnetocrystalline anisotropy constant
M [A-m-?], [Oe] magnetization
Pm CPBI saturation magnetic moment (per formula unit)
POL -Pi3 spontaneous magnetic moment (per formula unit)
4 CW activation energy
AR
reluctance
R
S [VK-‘1 Seebeckc oefficient
T WI, CKI temperature
Tc c”Cl Curie temperature
TN CKI NCel temperature
tan 6 dielectric loss factor
&=&‘-if complex dielectric constant
0, CKI paramagnetic Curie temperature
I magnetostriction constant
~=p’-ip” complex magnetic permeability
Pi initial magnetic permeability
e Pcml resistivity
ex Cgc m- 3l X-ray density
0 [Cl-l cm-r] electrical conductivity
CT[ G cm3 g-l] specific magnetization
6, [G cm3g -7 specific saturation magnetization
x=x’-ix”. complex magnetic susceptibility
x8 [cm3g - ‘1 susceptibility per gram
x, [cm3 mole-l] susceptibility per mole
w [rad s-l] angular frequency
b) Abbreviations
d.c. direct current
FMR ferromagnetic resonance
Me, M metal
NMR nuclear magnetic resonance
Note: In this contribution figure and table numbers which refer to Vol. 111/4ba re characterized by an asterisk.
Bonnenberg/Hempel/Roos
Ref. p. 371 5.2 List of symbols and abbreviations
In the derivation of eqs.( 14) and (15) the anisotropy field strength H$ is neglected with respectt o H and Ht since
it is usually lower by several orders of magnitude. In the special casew here only magneto-crystalline energy has
to be considered, [59BK], the eq. (15) reduces to:
~KL,=YH
M M M
5.2 List of symbols and abbreviations
4) Symbols
a, c CA1 lattice parameters
B I31 magnetic induction
W%,x CG.e el maximum energy product of permanent magnetic materials
d [mm] crystal thickness
f L-Hz1 frequency
fres CHzl resonancef requency
H [A ~‘1, PI magnetic field strength
HA [@I magnetocrystalline anisotropy field strength
dfc Dl coercive field strength for magnetization
Ki [erg cm- ‘1 magnetocrystalline anisotropy constant
M [A-m-?], [Oe] magnetization
Pm CPBI saturation magnetic moment (per formula unit)
POL -Pi3 spontaneous magnetic moment (per formula unit)
4 CW activation energy
AR
reluctance
R
S [VK-‘1 Seebeckc oefficient
T WI, CKI temperature
Tc c”Cl Curie temperature
TN CKI NCel temperature
tan 6 dielectric loss factor
&=&‘-if complex dielectric constant
0, CKI paramagnetic Curie temperature
I magnetostriction constant
~=p’-ip” complex magnetic permeability
Pi initial magnetic permeability
e Pcml resistivity
ex Cgc m- 3l X-ray density
0 [Cl-l cm-r] electrical conductivity
CT[ G cm3 g-l] specific magnetization
6, [G cm3g -7 specific saturation magnetization
x=x’-ix”. complex magnetic susceptibility
x8 [cm3g - ‘1 susceptibility per gram
x, [cm3 mole-l] susceptibility per mole
w [rad s-l] angular frequency
b) Abbreviations
d.c. direct current
FMR ferromagnetic resonance
Me, M metal
NMR nuclear magnetic resonance
Note: In this contribution figure and table numbers which refer to Vol. 111/4ba re characterized by an asterisk.
Bonnenberg/Hempel/Roos
5.5 Paramarrnetic
1D ro.D erties of ferrites with hexagonal crystal structure [- Ref. -D . 37
5.3 Chemical compositions and phase diagrams of hexagonal ferrites
(SeeV ol. III/4b, p. 555).
5.4 Crystal structures
(SeeV ol. III/4b, p. 557).
5.5 Paramagnetic properties of ferrites with hexagonal crystal structure
Table 1. (Seea lso Vol. 111/4b,T able 3* and Figs. 16*...19*, p. 561).
Compound Ref. Remarks Fig.
BaFed49 73F theoretical x of ferrimagnet with five sublattices
BaZnxTi,Fe,,- 2xO19 70DWA f'/& vs. H for x = 2.25 at 295 K
PbFe&9 66ABB 1
SrFe12019 70BKMG anisotropy of x
SrAI,Fe,,-,O,, 73FPG l/x vs. T for different x, Ntel parameters
SrCO%.a% 69BKM anisotropy of x 2
70BK, 70BKMG anisotropy of x
10
@
cm3
6
I 5
-s 10
-4 .lO'
g/cm3
3
6
I
2
$ L
1
2
0
710 720 730 740 K 750 0 100 200 300 400 500 600 “C 700
I- I-
Fig. 1. PbFe,zO,,. The inverse of the molar suscepti- Fig. 2. SrCr,,,Fe,,,O,,. Temperature dependence of the
bility, l/x,. vs. temperature, T. paramagnetic inverse susceptibility per gram, l/xs, vs. tem-
Open circles: measured 11to the r-axis; perature, T, along the c-axis (II) and in the basal plane (I)
full circles: measured 1 to the c-axis [66ABB]. [69BKM].
6 Ronnenberg/Hempel/Roos
Ref. p. 371 5.6 M-type ferrites
5.6 M (magnetoplumbite)-type ferrites
56.1 Survey of the chemical substitution in the M structure and
room temperature lattice constants
Table 2. Survey of the chemical substitution in the M structure. (See also Vol. 111/4b, Table 4*, p. 562 and
Figs. 20*.‘.23*, p. 564).
Compound Ref. Remarks Properties
zi i
Tables Fig.
BaFe1201g 71GS addition of L3,4, 5, 3913,
rare-earth 6,798 20,21,
22,23
BaAl,Fe,,- .Olg 68BS-3 4, 5, 6, 7 5, 9,15
7ovz see Fig. 20*, 21*
71HK-2 see Fig. 20*, 21*
BaAs,Fe,,- r019 73KG 4
74EK-1 ,H,,avs.T
75EK-1
BaCr,Fe,,- xOlg 71KH see Fig. 20*, 21” 4,5,6 4,10,15
Bal-xWe12-xWlg 74G a vs. T 4
D=K’+, Bi3+
P= Cu2+, Ni2+
Mn4+, Zn’;,
Ti4+
BaGa,Fe,,- xO1g 73HK-1 4, 5, 6 15
BaGa2Scl.2Fes.sOlg 23.63 5.95 73ACCY 4
BaIn,Fe,2-,0,, 70EM 4, 537 4, 5,10,
71KH 11
71 PVZS
71vz
BaIndes.dAg 23.790 6.000 72ALNY
Bal-xPbxFe1201g 74AFS 4 12
Ba,Pb,Srl-~,+,,Fe1201g 76MMO-1 4
BaSb,Fe,,- .O,, 72EK 4,5
75EK-1
75EK-2
BaSbi,:Fe:,iFe3+ 10.5 0 19 74L 5
BaSc,Fe,,- xO,g 69AY 435
69ASYL
71vz 5,17
Ba%.5Felo.501g 71 PSSF 4
Ba,Srl-.Fe1201g 69JM 435
Ba o.75Sro.25Fe1201g 70WK admixtures of 4
B,03,A1,03,
Ga203
Ba,-,Sr,Al,Fe,,-.O,, 68BS-3 a vs. x, y 4
BaTio,,FeisFe3+ 10.8 0 19 74L 5 19
BaTi,Co,Fe,,- 2xOlg 76KG 495, 7
BaTi,Co,Fe,O,, 73BKSZ 4
. .
WTl, WPn,AW12 - x- ty+ zJ0 1g 69D 7
BaZnli2~Ge1,2~Fe12-x0,, 71KH 4 4,lO
BaZn2,3xNb1,3~Fe12-.01g 71KH 4 4,10,13
BaZn2~Jali3%Olg 71KH 4 13
BaZn,Ti,Fe,,- 2xO1g 72MTS-2 127
BaZnTiMnFeaO,, 73MASE 4,5
continued
Bonnenberg / HempelI Roos
5.6 M-type ferrites [Ref. p. 37
Table 2 continued
Compound Ref. Remarks Properties
i 1
Tables Fig.
BaZnxTi,Mn,Fe,,- I- y- z019 72MTS-1 4 18
Ba(Zn2~~~VlIV,i~,)Fe12-,01g 71KH 4 4,13
CaFe1201g 22.01 5.566 71MSK0
CaW, W1201g 71MSK0 4
CaLa,Fe,,-,O,, 79YKN a, c vs. x
J-aFe12019 74DL 4,s
Lao.sAo.sFe1201g 68LV
A=Na,K,Ag
LaFe2+Fe3+0 78SKZS 4
La3+Me2:;e’:90
70MS 4
Me = Zn, Cd, I%, di, Mg, Co
LaNiFe,,O,, 67KCMS Tc = 572“ C
Lao.s’&.sFe1201g 73DHM 4
PbFe1201g 23.09 5.78 69AFY 1,3,6,
23.11 5.889 67CKBG 798
PbAl,Fe,,-,O,, 67CKBG 67
PbIn,Fe12-,0,g 71P VZS 5
PbInl.gFelo.lOlg 22.50 5.945 71P VZS 4,5 16
SrFe12% 68AAB-2 1,3,4, 5, 14
22.98 5.78 69AFY 6,7,8
78W M-formation study
SrAl,Fe,,-,O,, 67B-2 1,3,4,5,8
SrAs,Fe,,-,O,, 72EK with increasing 4,5
x -+ transition
M to W
S~l-xW%201g 76LS 0.1255 x 5 0.5
SrCoo .42Tio.42Fell.ldh9 70KBSK-2 4
SrColJLFegOlg 69SPC 425
SrCr3.2%&J19 69BKM 1 2
~ro.sCr3.6Fea.401s.s 72BS 7
SrGa,Fe,,-,O,, 68AAB-2 4 8,14
68BS-2
SrSc,Fe,, - =Olg 72CC-1 3
SrSb,Fe,,-,Olg 74EK-1 495
6.000
11
5.975
5.950
5.925
D
b
Fig. 4. BaIn,Fe,,-,O,, (open circles); 5.900
BaZn 213rNb,i3rFe12-x0,9 (full triangles);
BaZn,,,,V,,,,Fe,,_,O,, (full circles);
5.875
BaZn,,,,Ge,:,,Fe,,-,0,, (squares);
BaCr,Fe,,-,O,, (open triangles).
Lattice parameter n vs. concentration of substituted ions, x 5.850
[XKH]. 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
x-
8 Ronnenberg/Hempel/Roos
Ref. p. 371 5.6 M-type ferrites
6.4
H
6.: L
6.2
I I I I I Ye- 1
0I 6.1
6.0
5.878
5.877
5.8
5.876
5.875 Y
0 cl.1 0.2 0.3 0.4 0.5 1.0 Fig. 5. BaIn,Fe,,-,O,,, BaAl,Fe,,-,O,,,
x- BaSc,Fe,,-,O,,. Lattice constants, c and a, and ratio c/a
g. 3. x/2 Me,O, . (1 -x) BaO .5.75 Fe,O,. as a function of composition
lttice constants a and c of ferrites vs. x. (1) c (2) a (3) c/a for BaIn,Fe,,-,O,,
pen circles: Me=La; full circles: Me=Gd; (4) c/a for BaAl,Fe,,-,O,, (5) c/a for BaSc,Fe,,-,O,,
angles: Me=Lu [IJlGS]. [71VZ].
23.2 23.08
A ti
23.05
22.8
23.02
22.4
22.99
I
22.0 u 22.96
22.93
21.61
0 2 4 6 8 IO 12
x- 22.90
:. 6. PbAl,,-,Fe,O,,. Lattice constant c as a function
composition [67CKBG]. 22.87
22.84
3.94
I
s 3.91b
0 3 6 9 12
x-
Fig. 8. SrGa,Fe,,-,O,,. Lattice constants c and a and
ratio c/a vs. composition x [68BS-21.
4
0 2 4 6 8 IO 12 Fig. 7. PbAl,,-,Fe,O,, . Lattice constant a as a function
x- of composition [67CKBG].
Bonnenberg/Hempel/Roos 9