- Email: [email protected]
Domain wall resonance in Ga substituted magnetoplumbite
Journal
of Magnetism
DOMAIN
and Magnetic
Materials
IN Ga SUBSTITUTED
WALL RESONANCE
L. PfJST ‘I), P.E. WIGEN,
1195
54457 (1986) 119551196
M. RAMESH,
Dept. of Phvsrcs, Ohio State Unwersit~y. I74
P. SIROK?
MAGNETOPLUMBITE
” and K. SUK ‘)
West 18th Acw~ue. Columbus,
OH 43210,
USA
DWR in thin plates of the hexaferrite PbFe,,_ ,Ga,O,, for x = 0.1 and 2 was measured with in-plane magnetic field, H,. up to 13 kG. As the stripe period is smaller than thickness, the DWR frequency can be simply expressed analytically as a function of thickness, magnetization M, exchange constant, and uniaxial anisotropy energy. The dependence on H, is incorporated in the dependence of the effective mass, z-component of magnetization M._. and the wall energy on H,. Very good agreement in obtained for both zero field resonance frequency (0.4 to 1.0 GHz) and the dependence of frequency on H,.
1. Introduction The hexagonal ferrite PbFe,,O,, (magnetoplumbite) exhibits a very high uniaxial anisotropy energy and magnetization, and for this reason it is of great importance in applications. Both anisotropy energy and magnetization can be decreased by substitution of some of the Fe atoms by nonmagnetic atoms, in our case Ba. Domain wall resonance (DWR) in single crystals of and PbFe,,O,, was recently measured pure BaFe,,O,, [I], but large difference between experimental values and values calculated according to theory were observed. DW R on magnetoplumbite samples, with different substitutions of Ga PbFe,z_ ,Ga,O,,, (x = 0, 1, and 2) are reported here. The data was supported by independent measurements of FMR and magnetization. The results can be described by appropriate theory at zero field and as a function of the magnetic field. H,, applied parallel to film plane.
cannot be applied. Therefore samples thicker than 60 pm were avoided. DWR was measured using a shorted slot line structure transmission technique [4] with derivative detection. The external field H, was applied parallel to the plane of the sample. The DWR frequencies are plotted in fig. 1. The most diverse set of samples was for composition PbFe,, Ga,O,,. Fig. 1 gives the results of DWR for samples with thicknesses of 17, 29 and 58 pm. Both the 29 and the 58 pm thick samples were cleaved from bulk crystal, while the 17 pm thick samples were produced by
2. Experimental The magnetoplumbite single crystals were prepared by growing from a lead oxide flux [2]. Thin plates with surfaces perpendicular to easy axis were cleaved from bulk crystals. Smaller thicknesses were obtained by polishing, and some of these samples were finally etched in hot phosphoric acid. According to ref. [3] and our direct observation, the domain structure of such platelets consists of stripes with oppositely oriented magnetization and with planar domain walls perpendicular to the surface. With increasing thickness the shape of the domain wall very close to the surface becomes wavy [3], while inside the samples the stripe structure is still preserved. For even thicker plates (over about 60 pm) more complicated domain structure appears, which can no longer be described as a stripe
structure.
For
‘) Permanent address: Academy of Sciences, vakia.
0304-8853/86/$03.50
this
case,
the
usual
DWR
Institute of Physics, Prague 8. Na Slovance
0 Elsevier Science
oc 2
theory
Czechoslovak 2, Czechoslo-
Publishers
4
6
8
10
12
HP,kG
1. DWR frequency for different samples of Fig. PbFe,,_,Ga,O,,: (1) x =O, thickness t =ll pm; (2) x =l, t =14 pm: (3) x = 2, t =17 pm (m-polished on both sides. O-polished on one side, O-polished and etched): (4) x = 2. t = 29 )L; (5) x = 2, t = 58 pm.
B.V.
three methods. All were cleaved at higher thickness and polished down to 17 pm with the following differences: (a) polished on both sides. (b) polished. then etched in phosphoric acid (135°C. 3 min) (the thickness did not change much on etching). or (c) polished on only one aide. The DWR frequencies are the same within experimental error for all these samples with different surface treatment, as can be seen in fig. 1. line 3. However the signal was sharper for the etched sample. especially at higher 11,. The shape of the FMR signal was considerably improved after etching as surface stresses induced by the polishing were removed. 3. Discussion All samples were found to have narrow stripes. wjith the period P smaller than the thickness t. In such cases the demagnetizing factor. N,. is proportional to P/t. and the DWR frequency calculated from the demagnetizing energy can be analytically expressed [5] as
samples as a function of the applied field was me:ibured on a vibrating magnetometer for fields applied both parallel and perpendicular to the easy axis. By compar~ng all these data the material parameters are 4nM, 7 4.X kG and K ,, = 2.9 X 1 Oh erg/cm3 for samples with \ z 0: 4.0 kG and 2.3 x 10h erg/cm’ for .V= 1; and 3.3 h the demagnetizing energy. This correction W;LS then included into the calculation of the force constant and consequently to the DWR frequency. M,/M, in eq. (2) is equal to cos 0. where sin H = H,/H ,,,,. and II,,,, = 2 ~,,/:kf~ ~ 4rM,h’,. The change of domain wall cncrgb with applied field can be expressed [7] ah
= cos 6’~ (~/2
,,,, ) sin 0.
~ 0)( 1 ~ 4vM,N,/H
(3)
O\\,,
(‘=
167 In 2
JAKU
and 5 is the Riemann zeta function. ((3) = 1.2019825 . K,, is the uniaxial anisotropy constant and the exchange constant is A = 5.1 x 10 7 erg/cm according to ref. [6]. The domain wall mass is equal to the Diiring Neglecting the small mass. m,, = 1/(2ay’JA/K,). field dependence of the terms in (lb). the change of DWR frequency with applied magnetic field is given by [51 w/w,, = (M,/My(
m,,/m)
“( uu,,/u,.)’ j.
The domain wall mass 111~~calculated according to Morkowski, et al. [8] decreases very sharply with applied field. reaching ,?I,,/n~ M = IO for II, = It,,,,/‘. The DWR data indicated a slightly leas pronounced field dependence. which could be approximately described 21s 171= ,>~,/(l - t1,/2 II,,,,). The full lines in fig. 1 were calculated using eqs. (1) and (2) with this field depcndence for the domain wall mas>. ‘l’his work was supported # DMR-8304250.
in part
by NSF
[l]
F. Wetm.
.I.
W. Totksdorl’
and
Appt. I’hv\. 51
(1980) 3x16.
(2)
where m is domain wall mass in presence of magnetic field. To find the values of M, and K,,. independent FMR and magnetization measurements were made. The FMR (at 49 GHz) for samples of PbFe,,,G?O,, yielded g= 1.99 and 2 Ku/M,4aM, = 13.0 kG. Peak-to-peak resonance widths were between 100 and 200 Oe. The magnetic moment of both saturated and nonsaturated
H. Dot&,
Grant
Res. Bull. 16 (19X1) 1499. J. Kacnx and R. Gemperle. C‘xch. J. Phqs. BIO (lY60) 505. H. Dibtch. IEEE Trans. Magn. MAC;-14 (1978) 692. L. Pust and P.E. Wigen. to hr puhllahed. R. Grmoerlc. E.V. Shtolts and M. Zeleni. Phw. Stat. Sol. i (1963) io15. M. Ramesh, That\, Ohio State Unlvrrslly (19X5). P.F.. Wigen and R.J. ych. .I [Xl J. Morkowskl. H. Dotwh. Mngn. Magn. Mat. 25 (1981) 39
[3] 141 i5j 161 ’ ’ 171
of Magnetism
DOMAIN
and Magnetic
Materials
IN Ga SUBSTITUTED
WALL RESONANCE
L. PfJST ‘I), P.E. WIGEN,
1195
54457 (1986) 119551196
M. RAMESH,
Dept. of Phvsrcs, Ohio State Unwersit~y. I74
P. SIROK?
MAGNETOPLUMBITE
” and K. SUK ‘)
West 18th Acw~ue. Columbus,
OH 43210,
USA
DWR in thin plates of the hexaferrite PbFe,,_ ,Ga,O,, for x = 0.1 and 2 was measured with in-plane magnetic field, H,. up to 13 kG. As the stripe period is smaller than thickness, the DWR frequency can be simply expressed analytically as a function of thickness, magnetization M, exchange constant, and uniaxial anisotropy energy. The dependence on H, is incorporated in the dependence of the effective mass, z-component of magnetization M._. and the wall energy on H,. Very good agreement in obtained for both zero field resonance frequency (0.4 to 1.0 GHz) and the dependence of frequency on H,.
1. Introduction The hexagonal ferrite PbFe,,O,, (magnetoplumbite) exhibits a very high uniaxial anisotropy energy and magnetization, and for this reason it is of great importance in applications. Both anisotropy energy and magnetization can be decreased by substitution of some of the Fe atoms by nonmagnetic atoms, in our case Ba. Domain wall resonance (DWR) in single crystals of and PbFe,,O,, was recently measured pure BaFe,,O,, [I], but large difference between experimental values and values calculated according to theory were observed. DW R on magnetoplumbite samples, with different substitutions of Ga PbFe,z_ ,Ga,O,,, (x = 0, 1, and 2) are reported here. The data was supported by independent measurements of FMR and magnetization. The results can be described by appropriate theory at zero field and as a function of the magnetic field. H,, applied parallel to film plane.
cannot be applied. Therefore samples thicker than 60 pm were avoided. DWR was measured using a shorted slot line structure transmission technique [4] with derivative detection. The external field H, was applied parallel to the plane of the sample. The DWR frequencies are plotted in fig. 1. The most diverse set of samples was for composition PbFe,, Ga,O,,. Fig. 1 gives the results of DWR for samples with thicknesses of 17, 29 and 58 pm. Both the 29 and the 58 pm thick samples were cleaved from bulk crystal, while the 17 pm thick samples were produced by
2. Experimental The magnetoplumbite single crystals were prepared by growing from a lead oxide flux [2]. Thin plates with surfaces perpendicular to easy axis were cleaved from bulk crystals. Smaller thicknesses were obtained by polishing, and some of these samples were finally etched in hot phosphoric acid. According to ref. [3] and our direct observation, the domain structure of such platelets consists of stripes with oppositely oriented magnetization and with planar domain walls perpendicular to the surface. With increasing thickness the shape of the domain wall very close to the surface becomes wavy [3], while inside the samples the stripe structure is still preserved. For even thicker plates (over about 60 pm) more complicated domain structure appears, which can no longer be described as a stripe
structure.
For
‘) Permanent address: Academy of Sciences, vakia.
0304-8853/86/$03.50
this
case,
the
usual
DWR
Institute of Physics, Prague 8. Na Slovance
0 Elsevier Science
oc 2
theory
Czechoslovak 2, Czechoslo-
Publishers
4
6
8
10
12
HP,kG
1. DWR frequency for different samples of Fig. PbFe,,_,Ga,O,,: (1) x =O, thickness t =ll pm; (2) x =l, t =14 pm: (3) x = 2, t =17 pm (m-polished on both sides. O-polished on one side, O-polished and etched): (4) x = 2. t = 29 )L; (5) x = 2, t = 58 pm.
B.V.
three methods. All were cleaved at higher thickness and polished down to 17 pm with the following differences: (a) polished on both sides. (b) polished. then etched in phosphoric acid (135°C. 3 min) (the thickness did not change much on etching). or (c) polished on only one aide. The DWR frequencies are the same within experimental error for all these samples with different surface treatment, as can be seen in fig. 1. line 3. However the signal was sharper for the etched sample. especially at higher 11,. The shape of the FMR signal was considerably improved after etching as surface stresses induced by the polishing were removed. 3. Discussion All samples were found to have narrow stripes. wjith the period P smaller than the thickness t. In such cases the demagnetizing factor. N,. is proportional to P/t. and the DWR frequency calculated from the demagnetizing energy can be analytically expressed [5] as
samples as a function of the applied field was me:ibured on a vibrating magnetometer for fields applied both parallel and perpendicular to the easy axis. By compar~ng all these data the material parameters are 4nM, 7 4.X kG and K ,, = 2.9 X 1 Oh erg/cm3 for samples with \ z 0: 4.0 kG and 2.3 x 10h erg/cm’ for .V= 1; and 3.3 h the demagnetizing energy. This correction W;LS then included into the calculation of the force constant and consequently to the DWR frequency. M,/M, in eq. (2) is equal to cos 0. where sin H = H,/H ,,,,. and II,,,, = 2 ~,,/:kf~ ~ 4rM,h’,. The change of domain wall cncrgb with applied field can be expressed [7] ah
= cos 6’~ (~/2
,,,, ) sin 0.
~ 0)( 1 ~ 4vM,N,/H
(3)
O\\,,
(‘=
167 In 2
JAKU
and 5 is the Riemann zeta function. ((3) = 1.2019825 . K,, is the uniaxial anisotropy constant and the exchange constant is A = 5.1 x 10 7 erg/cm according to ref. [6]. The domain wall mass is equal to the Diiring Neglecting the small mass. m,, = 1/(2ay’JA/K,). field dependence of the terms in (lb). the change of DWR frequency with applied magnetic field is given by [51 w/w,, = (M,/My(
m,,/m)
“( uu,,/u,.)’ j.
The domain wall mass 111~~calculated according to Morkowski, et al. [8] decreases very sharply with applied field. reaching ,?I,,/n~ M = IO for II, = It,,,,/‘. The DWR data indicated a slightly leas pronounced field dependence. which could be approximately described 21s 171= ,>~,/(l - t1,/2 II,,,,). The full lines in fig. 1 were calculated using eqs. (1) and (2) with this field depcndence for the domain wall mas>. ‘l’his work was supported # DMR-8304250.
in part
by NSF
[l]
F. Wetm.
.I.
W. Totksdorl’
and
Appt. I’hv\. 51
(1980) 3x16.
(2)
where m is domain wall mass in presence of magnetic field. To find the values of M, and K,,. independent FMR and magnetization measurements were made. The FMR (at 49 GHz) for samples of PbFe,,,G?O,, yielded g= 1.99 and 2 Ku/M,4aM, = 13.0 kG. Peak-to-peak resonance widths were between 100 and 200 Oe. The magnetic moment of both saturated and nonsaturated
H. Dot&,
Grant
Res. Bull. 16 (19X1) 1499. J. Kacnx and R. Gemperle. C‘xch. J. Phqs. BIO (lY60) 505. H. Dibtch. IEEE Trans. Magn. MAC;-14 (1978) 692. L. Pust and P.E. Wigen. to hr puhllahed. R. Grmoerlc. E.V. Shtolts and M. Zeleni. Phw. Stat. Sol. i (1963) io15. M. Ramesh, That\, Ohio State Unlvrrslly (19X5). P.F.. Wigen and R.J. ych. .I [Xl J. Morkowskl. H. Dotwh. Mngn. Magn. Mat. 25 (1981) 39
[3] 141 i5j 161 ’ ’ 171