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Influence of GGG substrate on FMR and magnetostatic wave propagation
Journal of Magnetism and Magnetic Materials 101 (1991) 159-161 North-Holland
Influence of GGG substrate on FMR and magnetostatic wave propagation M. MarySko Institute
of Physics, Czech Academy
of Science, 16200 Prague 6, Czechoslovakia
We analyse and review effects concerning the influence of the paramagnetic GGG substrate on FMR at low temperatures and magnetostatic wave propagation in ferrimagnetic garnet films. New experimental data are presented for the permeability of GG6 at X band.
1. Introduction 0,003 Ferrimagnetic garnet films are usually epitaxially grown on Gd,Ga,O,, (GGG) substrates having a thickness of typically 0.5 mm. GGG is a relatively strong paramagnet and therefore its magnetic moment may influence the results measured on the garnet/GGG samples. The aim of this contribution is to study these effects in a more detail. 2. Magnetic properties of GGG
(1) (2) where H, = w/y, and AH, is the linewidth of GGG. The measurements of the microwave losses in GGG were already reported in refs. [2,3] and the temperature dependence of &’ at f = 25.4 GHz in our earlier work [4]. Unfortunately in ref. [4] the absolute value of & was determined only very crudely. At this place we present the more precise measurement of &’ made at f = 9.1 GHz and T = 300 K. The samples were the rectangular GGG substrates of thickness 0.49 mm with an area up to 60 mm2. The cavity perturbation method was used with the cylindrical cavity TEati and the rectangular cavities TE,,,, TE,,,. The value &’ as a 0 1991 - Elsevier Science Publishers
0,002
0,001
For T > 5 K the static susceptibility of GGG obeys the Curie-Weiss law 4axo = C(T - 0)-l, where C = 2.065 K, 0 = -2.3 K [l]. The microwave permeability of the GGG medium magnetized along the z axis is described (neglecting anisotropy) by a gyrotropic tensor p, with the components pi = & - i&‘, Y, = u; - iv;‘. The Larmor and anti-Larmor absorption correspond to the terms & = &’ + Y;’ and &,,_ = &’ - v;’ respectively. It is seen that p y = (&‘r + pyAL)/2. The components pyL, &‘AL can be derived theoretically from the Bloch equations. This yields
0312-X853/91/$03.50
‘i
0
I
I
5
10
Fig. 1. Dependence pi’(H) f = 9. 1 GHz;
5 H( kOe) measured on GGG substrates at
the approximation based on eqs. (1) and (2) is denoted by the dashed line.
function of the static magnetic field is plotted in fig. 1. Let us remark that our experimental value &’ = 0.003 + 0.0005 (H = 2400 Oe) is roughly three times larger than that reported at f= 8.7 GHz by Adam et al. [2]. The measured dependence p;‘(H) can be satisfactorily described in terms of the eqs. (1) and (2) if we take HI = 3000 Oe, AH, = 6800 Oe and replace 47rx0 = 0.00683 by an effective value (47r~e)~rr = 0.00542 (fig. 1). Eqs. (1) and (2) enable us to evaluate &(H), pyAL( H) (e.g. at H = 2400 Oe we get & = 0.0046, & = 0.0014) and also, to some extent, to estimate the frequency dependence of &‘, & and &_. 3. FMR parameters In measuring the resonance field and linewidth at low temperatures two effects should be taken into account : a) A change of the static field Ho due to the magnetic moment of the GGG substrate, as was shown by Danilov et al. [5]. For t >> d (see fig. 2a) the contribu-
B.V. All rights reserved
160
M. MatyZko / Influence of GGG substrate on FMR and MSWpropagation
Fig. 2. (a) sketch of an epitaxial YIG film; the GGG substrates in (b) the perpendicular and (c) parallel applied field H,,.
tion 6H,, is nearly the same over the thickness d of the film, i.e. 6Ha = SH,(x, y). To a first approximation we assume that the substrate is uniformly magnetized and calculate the field in the centre of the endface (x = y = 0) [5,6]. Then, for the square sample, t -=za and 4nxe -=x 1, the measured perpendicular and parallel resonance fields can be expressed as HImea.S= H$ (1 - 4Tx,,2fit/=a),
(3)
Hi,,,
(4)
= H”,(l
+ 4q,,fit,‘aa),
where the fields HO1, H ‘IOcorrespond to the absence of GGG. This effect manifests itself e.g. at low temperatures where we evaluate an apparent positive uniaxial constant which is larger than the actual K, (see the paper by P. Novak et al. in this issue). As a further step it is possible to consider the distribution of 6H, over the area of the endface. The width of the distribution AH, gives an information on the linewidth broadening AHGGG produced by the inhomogeneity in SH,. Because of the dipolar narrowing effect [7] we expect that A HGGG = ( AHr,)2/4~M,. E.g. for a = 3 mm, t = 0.25 mm (the substrate after polishig), T = 20 K, HO1= HI’,-,= 10000 Oe, we obtain 4~x, = 0.0926, H,&, = 9937 Oe, H limeas= 10034 Oe, A HD = 43 Oe, AH, = 16 Oe, (AHGoo)’ = 1 Oe, (AHGGG)II = 0.14 Oe. b) Losses in GGG associated with an external microwave demagnetizing field of the garnet film. Using the results [8] we find that for d > 3 pm, d/a < 0.002 the corresponding AH contribution is roughly given by
where a is the transversal dimension of the film and M, the saturation magnetization. (The shift 6H,,, can be estimated by replacing &‘r + &,_ - 1.) The contribution (5) could be observable only for YIG at T < 10 K. 4. Magnetostatic wave propagation We consider the surface (MSSW), backward volume (MSBVW) and forward volume (MSFVW) magnetostatic waves (MSW) propagating in an infinite garnet (e.g. YIG) slab of thickness d magnetized along the + ( - )z axis. The half-space above the slab is assumed
to be formed by the GGG medium (This case was also analysed by Balinskii et al. [9] for the scalar permeability pi.) The relevant parameter characterizing propagation loss L, per unit delay time (or L per unit length). air, we have [lo] L, = L,, = C,AH,
is In
(6)
where AH is the linewidth of the garnet and C, a constant. Taking into account GGG we obtain a new value of L, which can be written in the form = C, P L, = L,, + LGGG
(
AH + A HGGG =l
(7)
11
where A HzGG represents an equivalent linewidth. (The analogic relation, with the same AHzGG, holds for L.) In the following, we shall characterize damping due to GGG just by the quantity AHzGG. It will be assumed that &-=x 1, &_ -=x 1, &‘*r << 1 and that the MSSW, MSBVW, MSFVW modes are described by the known standard dispersion relations. MSSWs propagate along the y axis in a slab with the surface parallel to the yz plane, in the frequency region between wi = (ai + w,,w~)~/~ and w2 = w,, + w,/2. Here o,=yH, w,= y47rMS and y is the gyromagnetic ratio. For the wave uniform along the z axis we get
and AHGGG( -) can be obtained by substituting: w0 + -%l %l+ --%I, MS -+ -MS and by replacing &,,_ by &‘t_. We see that propagation of MSSWs is nonreciprocal. For the + ( - ) case the wave is localized at the slab-GGG (slab-an) boundary which corresponds to the larger (lesser) damping. MSBVWs propagate along the z axis in a slab with the surface parallel to the yz plane, in the region between w. and wt. For the wave uniform along the y axis the linewidth AHzGG( +) = AHeyG( -)is given by AHGGG
eq
=
&‘417M, 4( w2 - a;) Cy2W;(ti2+W;)[2+)kr]d(l+t2)]
where ~=(w~--~)~‘~(w:--‘)~‘/~ wave vector.
’ and
k,
(9) is the
M. Matyfko
/ Influence of GGG substrate on FMR and MS W propagation
MSFVWs propagate along the y axis in a slab with the surface parallel to the xy plane, in the region between w, and wl. For the wave uniform along the x axis we get the quantity AHpG(+) = AHetGG(-) which can be obtained from eq. (9) substituting k, + k, and replacing the factor 1 + LX*by 1 + l/a*. As an example we take a YIG film with d = 20 pm, k = 100 cm-‘, at 9 GHz and 300 K. Here, we get AHeTGG = 0.37 Oe, AHe_” = 0.016 (MSSW), AHe_GG GGG = 0.21 Oe (MSFVW). Fe:‘:“, ~m$?h~);H(MSElVW, MSFVW) decreases with decreasing fr:quency. It is seen that for the MSSW localized at the substrate as well as for the volume waves the ifluence of GGG cannot be neglected. References [I] W. Gunsser, in: Magnetic Oxides and Related Compounds, Landolt Bomstein 3/12a (Springer, Berlin 1978) p. 275.
161
PI J.D. Adam, J.H. Collins and D.B. Cruikshank, AIP Conf. Proc. (1975) 643. [31 P. KaboS and C.E. Patton, Adv. Ceramics 16 (1986) 67.
141 M. MarySko, Czech. J. Phys. B 39 (1989) 116. [51 V.V. Danilov, D.L. Lyfar, Yu. V. Lynbonon ko, A. Yu. Nechiporuk and S.M. Ryabchenko, Izv. Vyssh. Uchebn. Zaved. Fiz. 32 (1989) 48. 161R.I. Joseph and E. Schlamann, J. Appl. Phys. 36 (1965) 1579. [71 S. Geschwind and A.M. Clogston, Phys. Rev. 108 (1957) 49. PI M. MarySko, Proc. 9th ICMF (Esztergom, 1988) 104. 191 M.G. Balinskii, V.V. Danilov, A. Yu. Nechiporuk and V.M. Talalaevskii, Izv. Vyssh. Uchebn. Zared. Radiofiz. 29 (1986) 1253. WI D.D. Stancil, J. Appl. Phys. 59 (1986) 218.
Influence of GGG substrate on FMR and magnetostatic wave propagation M. MarySko Institute
of Physics, Czech Academy
of Science, 16200 Prague 6, Czechoslovakia
We analyse and review effects concerning the influence of the paramagnetic GGG substrate on FMR at low temperatures and magnetostatic wave propagation in ferrimagnetic garnet films. New experimental data are presented for the permeability of GG6 at X band.
1. Introduction 0,003 Ferrimagnetic garnet films are usually epitaxially grown on Gd,Ga,O,, (GGG) substrates having a thickness of typically 0.5 mm. GGG is a relatively strong paramagnet and therefore its magnetic moment may influence the results measured on the garnet/GGG samples. The aim of this contribution is to study these effects in a more detail. 2. Magnetic properties of GGG
(1) (2) where H, = w/y, and AH, is the linewidth of GGG. The measurements of the microwave losses in GGG were already reported in refs. [2,3] and the temperature dependence of &’ at f = 25.4 GHz in our earlier work [4]. Unfortunately in ref. [4] the absolute value of & was determined only very crudely. At this place we present the more precise measurement of &’ made at f = 9.1 GHz and T = 300 K. The samples were the rectangular GGG substrates of thickness 0.49 mm with an area up to 60 mm2. The cavity perturbation method was used with the cylindrical cavity TEati and the rectangular cavities TE,,,, TE,,,. The value &’ as a 0 1991 - Elsevier Science Publishers
0,002
0,001
For T > 5 K the static susceptibility of GGG obeys the Curie-Weiss law 4axo = C(T - 0)-l, where C = 2.065 K, 0 = -2.3 K [l]. The microwave permeability of the GGG medium magnetized along the z axis is described (neglecting anisotropy) by a gyrotropic tensor p, with the components pi = & - i&‘, Y, = u; - iv;‘. The Larmor and anti-Larmor absorption correspond to the terms & = &’ + Y;’ and &,,_ = &’ - v;’ respectively. It is seen that p y = (&‘r + pyAL)/2. The components pyL, &‘AL can be derived theoretically from the Bloch equations. This yields
0312-X853/91/$03.50
‘i
0
I
I
5
10
Fig. 1. Dependence pi’(H) f = 9. 1 GHz;
5 H( kOe) measured on GGG substrates at
the approximation based on eqs. (1) and (2) is denoted by the dashed line.
function of the static magnetic field is plotted in fig. 1. Let us remark that our experimental value &’ = 0.003 + 0.0005 (H = 2400 Oe) is roughly three times larger than that reported at f= 8.7 GHz by Adam et al. [2]. The measured dependence p;‘(H) can be satisfactorily described in terms of the eqs. (1) and (2) if we take HI = 3000 Oe, AH, = 6800 Oe and replace 47rx0 = 0.00683 by an effective value (47r~e)~rr = 0.00542 (fig. 1). Eqs. (1) and (2) enable us to evaluate &(H), pyAL( H) (e.g. at H = 2400 Oe we get & = 0.0046, & = 0.0014) and also, to some extent, to estimate the frequency dependence of &‘, & and &_. 3. FMR parameters In measuring the resonance field and linewidth at low temperatures two effects should be taken into account : a) A change of the static field Ho due to the magnetic moment of the GGG substrate, as was shown by Danilov et al. [5]. For t >> d (see fig. 2a) the contribu-
B.V. All rights reserved
160
M. MatyZko / Influence of GGG substrate on FMR and MSWpropagation
Fig. 2. (a) sketch of an epitaxial YIG film; the GGG substrates in (b) the perpendicular and (c) parallel applied field H,,.
tion 6H,, is nearly the same over the thickness d of the film, i.e. 6Ha = SH,(x, y). To a first approximation we assume that the substrate is uniformly magnetized and calculate the field in the centre of the endface (x = y = 0) [5,6]. Then, for the square sample, t -=za and 4nxe -=x 1, the measured perpendicular and parallel resonance fields can be expressed as HImea.S= H$ (1 - 4Tx,,2fit/=a),
(3)
Hi,,,
(4)
= H”,(l
+ 4q,,fit,‘aa),
where the fields HO1, H ‘IOcorrespond to the absence of GGG. This effect manifests itself e.g. at low temperatures where we evaluate an apparent positive uniaxial constant which is larger than the actual K, (see the paper by P. Novak et al. in this issue). As a further step it is possible to consider the distribution of 6H, over the area of the endface. The width of the distribution AH, gives an information on the linewidth broadening AHGGG produced by the inhomogeneity in SH,. Because of the dipolar narrowing effect [7] we expect that A HGGG = ( AHr,)2/4~M,. E.g. for a = 3 mm, t = 0.25 mm (the substrate after polishig), T = 20 K, HO1= HI’,-,= 10000 Oe, we obtain 4~x, = 0.0926, H,&, = 9937 Oe, H limeas= 10034 Oe, A HD = 43 Oe, AH, = 16 Oe, (AHGoo)’ = 1 Oe, (AHGGG)II = 0.14 Oe. b) Losses in GGG associated with an external microwave demagnetizing field of the garnet film. Using the results [8] we find that for d > 3 pm, d/a < 0.002 the corresponding AH contribution is roughly given by
where a is the transversal dimension of the film and M, the saturation magnetization. (The shift 6H,,, can be estimated by replacing &‘r + &,_ - 1.) The contribution (5) could be observable only for YIG at T < 10 K. 4. Magnetostatic wave propagation We consider the surface (MSSW), backward volume (MSBVW) and forward volume (MSFVW) magnetostatic waves (MSW) propagating in an infinite garnet (e.g. YIG) slab of thickness d magnetized along the + ( - )z axis. The half-space above the slab is assumed
to be formed by the GGG medium (This case was also analysed by Balinskii et al. [9] for the scalar permeability pi.) The relevant parameter characterizing propagation loss L, per unit delay time (or L per unit length). air, we have [lo] L, = L,, = C,AH,
is In
(6)
where AH is the linewidth of the garnet and C, a constant. Taking into account GGG we obtain a new value of L, which can be written in the form = C, P L, = L,, + LGGG
(
AH + A HGGG =l
(7)
11
where A HzGG represents an equivalent linewidth. (The analogic relation, with the same AHzGG, holds for L.) In the following, we shall characterize damping due to GGG just by the quantity AHzGG. It will be assumed that &-=x 1, &_ -=x 1, &‘*r << 1 and that the MSSW, MSBVW, MSFVW modes are described by the known standard dispersion relations. MSSWs propagate along the y axis in a slab with the surface parallel to the yz plane, in the frequency region between wi = (ai + w,,w~)~/~ and w2 = w,, + w,/2. Here o,=yH, w,= y47rMS and y is the gyromagnetic ratio. For the wave uniform along the z axis we get
and AHGGG( -) can be obtained by substituting: w0 + -%l %l+ --%I, MS -+ -MS and by replacing &,,_ by &‘t_. We see that propagation of MSSWs is nonreciprocal. For the + ( - ) case the wave is localized at the slab-GGG (slab-an) boundary which corresponds to the larger (lesser) damping. MSBVWs propagate along the z axis in a slab with the surface parallel to the yz plane, in the region between w. and wt. For the wave uniform along the y axis the linewidth AHzGG( +) = AHeyG( -)is given by AHGGG
eq
=
&‘417M, 4( w2 - a;) Cy2W;(ti2+W;)[2+)kr]d(l+t2)]
where ~=(w~--~)~‘~(w:--‘)~‘/~ wave vector.
’ and
k,
(9) is the
M. Matyfko
/ Influence of GGG substrate on FMR and MS W propagation
MSFVWs propagate along the y axis in a slab with the surface parallel to the xy plane, in the region between w, and wl. For the wave uniform along the x axis we get the quantity AHpG(+) = AHetGG(-) which can be obtained from eq. (9) substituting k, + k, and replacing the factor 1 + LX*by 1 + l/a*. As an example we take a YIG film with d = 20 pm, k = 100 cm-‘, at 9 GHz and 300 K. Here, we get AHeTGG = 0.37 Oe, AHe_” = 0.016 (MSSW), AHe_GG GGG = 0.21 Oe (MSFVW). Fe:‘:“, ~m$?h~);H(MSElVW, MSFVW) decreases with decreasing fr:quency. It is seen that for the MSSW localized at the substrate as well as for the volume waves the ifluence of GGG cannot be neglected. References [I] W. Gunsser, in: Magnetic Oxides and Related Compounds, Landolt Bomstein 3/12a (Springer, Berlin 1978) p. 275.
161
PI J.D. Adam, J.H. Collins and D.B. Cruikshank, AIP Conf. Proc. (1975) 643. [31 P. KaboS and C.E. Patton, Adv. Ceramics 16 (1986) 67.
141 M. MarySko, Czech. J. Phys. B 39 (1989) 116. [51 V.V. Danilov, D.L. Lyfar, Yu. V. Lynbonon ko, A. Yu. Nechiporuk and S.M. Ryabchenko, Izv. Vyssh. Uchebn. Zaved. Fiz. 32 (1989) 48. 161R.I. Joseph and E. Schlamann, J. Appl. Phys. 36 (1965) 1579. [71 S. Geschwind and A.M. Clogston, Phys. Rev. 108 (1957) 49. PI M. MarySko, Proc. 9th ICMF (Esztergom, 1988) 104. 191 M.G. Balinskii, V.V. Danilov, A. Yu. Nechiporuk and V.M. Talalaevskii, Izv. Vyssh. Uchebn. Zared. Radiofiz. 29 (1986) 1253. WI D.D. Stancil, J. Appl. Phys. 59 (1986) 218.