- Email: [email protected]
Wave front reversal of surface magnetostatic waves
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 300 (2006) e41–e44 www.elsevier.com/locate/jmmm
Wave front reversal of surface magnetostatic waves G.A. Melkova, V.I. Vasyuchkaa, A.V. Chumaka, A.N. Slavinb, a
Faculty of Radiophysics, National Taras Shevchenko University of Kiev, Kiev 01033, Ukraine b Department of Physics, Oakland University, Rochester, MI 48309, USA Available online 17 November 2005
Abstract The wave front reversal (WFR) of non-reciprocal waves has been investigated. The experiment was performed using surface magnetostatic waves (SMSW) excited by a pulsed microwave signal of the carrier frequency 4.7 GHz in an epitaxial yttrium–iron garnet (YIG) film. The WFR was realized by pulsed parametric pumping of a double frequency. It was shown that WFR with high efficiency can be achieved for SMSW having relatively small wavenumbers k102 rad/cm. r 2005 Elsevier B.V. All rights reserved. PACS: 75.30.Ds; 76.50.+g; 85.70.Ge Keywords: Yttrium–iron garnet; Spin waves; Parametric processes
1. Introduction The phenomenon of wave front reversal (WFR) can be successfully used for signal processing in a wide range of frequencies from acoustic to optical frequency bands [1]. This phenomenon was also investigated in detail in microwave frequency range using magnetostatic and dipole-exchange spin waves (DESW) in epitaxial yttrium–iron garnet (YIG) films [2]. In all such experiments, geometry of backward volume magnetostatic waves (BVMSW) [3] was used. The BVMSW, as well as all other waves used for the investigation of WFR, are reciprocal waves, i.e., their properties are identical for the direct and reversed propagation directions. In this paper, we study the possibility of WFR of non-reciprocal waves, using surface magnetostatic waves (SMSW) as an experimental object. The distributions of the microwave magnetic fields h1, h2 and magnetizations m1, m2 for the SMSW depend on the directions of propagation: one wave (h1, m1) is ‘‘pressed up’’ to the free surface of the ferrite film, while the wave propagating in the opposite direction (h2, m2) is ‘‘pressed up’’ to the other surface being in contact with the substrate [3]. In the range of large wavenumbers k41=d, where d is Corresponding author. Tel.: +1 248 370 3401; fax: +1 248 370 3408.
E-mail address: [email protected] (A.N. Slavin). 0304-8853/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2005.10.143
the thickness of the ferromagnetic film, the microwave magnetic fields h1, h2 and magnetizations m1, m2 of SMSW modes decay exponentially with the distance from the surface: m1, h1 expðkxÞ and m2, h2 expðkðd xÞÞ; here x is the normal to the film plane, and x ¼ 0; x ¼ d are the coordinates of the film surfaces. Such localization of SMSW should considerably influence the WFR process, because its interaction efficiency is determined by the R overlap integral m1 m2 dx [3]. 2. Experimental results and discussion The experimental investigations of WFR of nonreciprocal waves were performed on the SMSW propagating in YIG ferrite films. The experiments were performed using experimental setup shown in Fig. 1. It consists of an YIG film waveguide (saturation magnetization 4pM0 ¼ 1750 Oe), epitaxially grown on a gallium–gadolinium garnet (GGG) substrate. The middle part of the YIG waveguide was placed in a rectangular opening inside a dielectric (e80) resonator which was used to supply pumping pulses. SMSW with the wavevector k were excited and received by the input (1) and output (2) microstrip antennas of the width of 50 mm separated by the distance l ¼ 6 mm. The bias magnetic field H0 was applied in the film plane perpendicularly to the direction of the MSW
ARTICLE IN PRESS G.A. Melkov et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e41–e44
e42
Pd
2
Dielectric resonator Pp l k Pr
GGG
Ps
1 YIG
H0
Fig. 1. Experimental setup: 1—input antenna, used to supply the input signal Ps and to receive the front-reversed output signal Pr; and 2—output antenna used to receive the signal of the delayed primary MSW Pd.
propagation (H0?k). This geometry corresponds to the excitation of SMSW [3]. The YIG film waveguide had the width of 1.5 mm, and length of 20 mm. An input electromagnetic signal pulse having the carrier frequency os/2p ¼ 4.7 GHz, duration ts ¼ 30–100 ns, and power Pso1 mW was supplied to the input antenna (1) and excited in the film a packet of SMSW having the carrier wave number k102 rad/cm. The input antenna (1) was also used to receive an output signal Pr formed as a result of the WFR process caused by the pumping pulse. The output antenna (2) received the direct SMSW packet propagating in the film from the input antenna (1). The output signal Pd received by the antenna (2) was delayed by the SMSW propagation time Td relative to the input signal Ps. Without the pumping pulse, this output signal was smaller than the input one, Pd ¼ Ps/L (here L is the propagation losses in the film). Under the action of the pumping, the output signal was amplified and was greater than the input one: Pd ¼ GPs, G41. Pumping pulses of the duration tp ¼ 30–50 ns, carrier frequency opE2os, and the maximum power Pp ¼ 5 W were supplied to the dielectric resonator from a magnetron generator via a standard rectangular waveguide. The microwave magnetic field of the pumping pulse inside of the dielectric resonator was parallel to the bias magnetic field H0, i.e. the case of parallel pumping was realized in our experiment [3]. The length of the dielectric resonator, determining the size of the pumping localization region along the direction of SMSW propagation (see Fig. 1), was equal to 4.5 mm. Signal pulse Ps was supplied to the input antenna (1) at the moment of time t ¼ 0; the output signal Pd at the antenna (2) was received at the time t ¼ Td, which in our experiments was equal to Td100–150 ns. The pumping pulse was supplied at the time t ¼ Tp, and the reversed signal Pr was received at the input antenna (1) at the time t ¼ 2Tp [1,2]. We have investigated two qualitatively different regimes: TppTd and Tp4Td. In the first case the usual WFR of SMSW was realized. In the second case the direct SMSW waves have already passed the film at the moment of pumping application t ¼ Tp4Td, they reached
the output antenna (2) and were out of the spatial region where the interaction with pumping is possible. However, a ‘‘trace’’ of the passed SMSW was still present in the interaction region. This ‘‘trace’’ consists of the shortwavelength DESW created as the result of two-magnon scattering of the primary SMSW on the inhomogeneities [3]. These scattered DESW have large wavenumbers k104 rad/cm and substantially lower relaxation rate ork, than the relaxation rate or of the primary SMSW. Parametric pumping supplied under the condition Tp4Td acts on these DESW, and creates reversed DESW. These reversed DESW propagate back to the inhomogeneities (or scattering centers) where they were originally created and as a result of the inverse scattering on the same inhomogeneities are converted into a secondary SMSW wavepacket having small wavenumbers of the order of k102 rad/cm. The secondary SMSW packet propagates towards the input antenna (1) where it creates a reversed signal Pr [4]. The signal formed by the reversed DESW packet, as well as usual reversed signal, are received at the input antenna at the time t ¼ 2Tp [4]. The results of our experimental investigations on one of the YIG film waveguides are shown in Fig. 2, where the dependence of the output power of the reversed signal Pr is shown as a function of the applied bias magnetic field. In Fig. 2 HC is the upper boundary of existence of SMSW at a given experimental signal frequency: at H0 ¼ HC the SMSW wavenumber is zero, k ¼ 0 [3]. For comparison, we have also shown in Fig. 2 the output power Pd of the delayed signal (received by the antenna 2, see Fig. 1) in the absence of parametric pumping. The maximum power of the reversed signal was observed at the magnetic field H0EHC30 Oe, which corresponds to the excitation SMSW with the wavenumber kE102 rad/cm. For lower fields H0 (i.e., for larger wavenumbers k) the power Pd of the reversed signal decreases. This fact is illustrated by the curve 3 in the Fig. 2, which shows the difference between the lines 1 and 2 of the same plot. The curve 3 is, actually, the amplification factor of the reversed signal relative to the usual delayed signal. In the region of small wavenumbers kE50 rad/cm the amplification factor reaches the magnitude of 12 dB, and rapidly decreases with the increase of the SMSW wavenumber. This effect is explained by the decrease of the overlap integral with the increase of k, which leads to the decrease of efficiency of parametric interaction of direct and reversed SMSW. We should also mention that compared to the case of WFR of reciprocal BVMSW, even the optimum amplification factor of reversed SMSW is about 10 dB lower than for the BVMSW [4]. This substantial reduction in amplification is caused mainly by the low efficiency of the input antenna 1 that serves also as an output antenna for the reversed SMSW pulse, which propagates along the lower (substrate) surface of the YIG film waveguide. The dependence of the output power Pr on the time of pumping application Tp is shown in Fig. 3. In agreement with the above-presented discussion, the time of the
ARTICLE IN PRESS G.A. Melkov et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e41–e44
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Pr/Pd (dB)
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Pr, Pd (dBm)
20
1
3
-50
5 HC 0
-60 920
940
960
980 1000 H0 (Oe)
1020
1040
Fig. 2. Curve 1 shows the dependence of the output power Pr of the reversed signal on the bias magnetic field H0. Curves 2 and 3 show, respectively, the dependence of the direct delayed signal power Pd (see Fig. 1) on the bias field H0 when no pumping was supplied (curve 2), and the difference between the curves 1 and 2: Pr (dB m)–Pd (dB m) ¼ Pr /Pd (dB) (curve 3). The YIG film thickness was d ¼ 6.8 mm, ts ¼ 50 ns, tp ¼ 40 ns, Pp ¼ 5 W, and Ps ¼ 104 W.
-30
Pr (dBm)
-40
-50
-60
200
400
600
800
Tp (ns) Fig. 3. Dependence of the reversed signal power Pr received at the antenna 1 (see Fig. 1) on the time Tp when the pumping pulse was switched on. YIG film thickness d ¼ 6.8 mm, H0EHC, ts ¼ 50 ns, tp ¼ 40 ns, Pp ¼ 5 W, Ps ¼ 104 W.
reversed signal arrival at the antenna (1) is of the order of 2Tp. It is clear from Fig. 3, that the dependence Pr(Tp) consists from two linear segments with different slopes. It is known that these slopes are determined by the relaxation rates of the waves that participate in the process of WFR [5]. For the ‘‘early’’ switching of the pumping pulse (TpT d ffi 120 ns) the WFR is caused by long-wavelength SMSW with the relaxation rate or, while for the ‘‘late’’ switching (T4T d ), the reversal is mediated by the shortwavelength DESW having much smaller relaxation rate
e43
ork5or. In the real experimental situation, due to finite durations of the signal ts and pumping tp pulses, the transition between the two regimes takes place for a somewhat larger value of Tp, namely, at Tp ¼ 180 ns. It follows from Fig. 3, that relaxation rates for SMSW and DESW are equal to or ¼ 2.4 107 s1 and ork ¼ 2.2 106 s1, respectively. Owing to the peculiarities of the two-magnon scattering of spin waves on the YIG film inhomogeneities [3] the effective excitation of DESW by SMSW is possible only in a narrow range of magnetic fields near HC [5]. In some cases, especially in ferrite films with pinned surface spins, we observed similar ‘‘resonance’’ dependencies with the width of several tens of Oe, and, sometimes, having several well-pronounced maxima. Due to the small relaxation rate of DESW, we were able to achieve the delay time Td of the reversed signal larger than 2 ms.
3. Conclusion The possibility of wave front reversal (WFR) for nonreciprocal waves by double-frequency parametric pumping was demonstrated on the example of surface magnetostatic wave propagating in yttrium–iron garnet (YIG) films. For relatively small surface magnetostatic waves (SMSW) wavenumbers of k102 rad/cm the decrease of output power (compared to the case of reciprocal backward volume magnetostatic waves (BVMSW)) is caused only by the small efficiency of reception of the reversed wave packet propagating close to the lower surface of the film by the microstrip antenna situated at the upper surface of the film. In this case the output power is more than 10 dB larger than the output power of a passive ferrite delay line with the same delay time. For the larger values of the SMSW wavenumber the decrease in the output power is also related to the lower efficiency of parametric interaction of the direct and reversed waves with pumping caused by non-reciprocal distributions of microwave magnetization in the direct and reversed waves. We also showed the possibility of using short-wavelength dipole-exchange spin waves (DESW) to increase the delay time up to 2 ms. DESW are excited as a result of twomagnon scattering of SMSW on inhomogeneities of the ferrite film. Two-magnon scattering and DESW-mediated WFR are observed in a narrow range of applied magnetic fields near the upper boundary of the SMSW spectrum.
Acknowledgements This work was supported in part by the Ukrainian Foundation for Fundamental Research, Grant no. 2.07/16, by the Science and Technology Center in Ukraine, Grant no. 3066 and by the MURI Grant W911NF-04-1-0247 from the US Army Research Office.
ARTICLE IN PRESS e44
G.A. Melkov et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e41–e44
References [1] B.Ya. Zeldovich, R.F. Pilipetskii, V.V. Shkunov, Principles of the Phase Conjugation, Springer, Berlin, 1985. [2] G.A. Melkov, A.A. Serga, V.S. Tiberkevich, A.N. Oliynyk, A.N. Slavin, Phys. Rev. Lett. 84 (2000) 3438.
[3] A.G. Gurevich, G.A. Melkov, Magnetization Oscillation and Waves, CRC Press, New York, 1996. [4] G.A. Melkov, Yu.V. Kobljanskyj, A.A. Serga, V.S. Tiberkevich, A.N. Slavin, Phys. Rev. Lett. 86 (2001) 4918. [5] Yu.V. Koblyanskyy, G.A. Melkov, V.S. Tiberkevich, V.I. Vasyuchka, A.N. Slavin, J. Appl. Phys. 93 (2003) 8594.
Journal of Magnetism and Magnetic Materials 300 (2006) e41–e44 www.elsevier.com/locate/jmmm
Wave front reversal of surface magnetostatic waves G.A. Melkova, V.I. Vasyuchkaa, A.V. Chumaka, A.N. Slavinb, a
Faculty of Radiophysics, National Taras Shevchenko University of Kiev, Kiev 01033, Ukraine b Department of Physics, Oakland University, Rochester, MI 48309, USA Available online 17 November 2005
Abstract The wave front reversal (WFR) of non-reciprocal waves has been investigated. The experiment was performed using surface magnetostatic waves (SMSW) excited by a pulsed microwave signal of the carrier frequency 4.7 GHz in an epitaxial yttrium–iron garnet (YIG) film. The WFR was realized by pulsed parametric pumping of a double frequency. It was shown that WFR with high efficiency can be achieved for SMSW having relatively small wavenumbers k102 rad/cm. r 2005 Elsevier B.V. All rights reserved. PACS: 75.30.Ds; 76.50.+g; 85.70.Ge Keywords: Yttrium–iron garnet; Spin waves; Parametric processes
1. Introduction The phenomenon of wave front reversal (WFR) can be successfully used for signal processing in a wide range of frequencies from acoustic to optical frequency bands [1]. This phenomenon was also investigated in detail in microwave frequency range using magnetostatic and dipole-exchange spin waves (DESW) in epitaxial yttrium–iron garnet (YIG) films [2]. In all such experiments, geometry of backward volume magnetostatic waves (BVMSW) [3] was used. The BVMSW, as well as all other waves used for the investigation of WFR, are reciprocal waves, i.e., their properties are identical for the direct and reversed propagation directions. In this paper, we study the possibility of WFR of non-reciprocal waves, using surface magnetostatic waves (SMSW) as an experimental object. The distributions of the microwave magnetic fields h1, h2 and magnetizations m1, m2 for the SMSW depend on the directions of propagation: one wave (h1, m1) is ‘‘pressed up’’ to the free surface of the ferrite film, while the wave propagating in the opposite direction (h2, m2) is ‘‘pressed up’’ to the other surface being in contact with the substrate [3]. In the range of large wavenumbers k41=d, where d is Corresponding author. Tel.: +1 248 370 3401; fax: +1 248 370 3408.
E-mail address: [email protected] (A.N. Slavin). 0304-8853/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2005.10.143
the thickness of the ferromagnetic film, the microwave magnetic fields h1, h2 and magnetizations m1, m2 of SMSW modes decay exponentially with the distance from the surface: m1, h1 expðkxÞ and m2, h2 expðkðd xÞÞ; here x is the normal to the film plane, and x ¼ 0; x ¼ d are the coordinates of the film surfaces. Such localization of SMSW should considerably influence the WFR process, because its interaction efficiency is determined by the R overlap integral m1 m2 dx [3]. 2. Experimental results and discussion The experimental investigations of WFR of nonreciprocal waves were performed on the SMSW propagating in YIG ferrite films. The experiments were performed using experimental setup shown in Fig. 1. It consists of an YIG film waveguide (saturation magnetization 4pM0 ¼ 1750 Oe), epitaxially grown on a gallium–gadolinium garnet (GGG) substrate. The middle part of the YIG waveguide was placed in a rectangular opening inside a dielectric (e80) resonator which was used to supply pumping pulses. SMSW with the wavevector k were excited and received by the input (1) and output (2) microstrip antennas of the width of 50 mm separated by the distance l ¼ 6 mm. The bias magnetic field H0 was applied in the film plane perpendicularly to the direction of the MSW
ARTICLE IN PRESS G.A. Melkov et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e41–e44
e42
Pd
2
Dielectric resonator Pp l k Pr
GGG
Ps
1 YIG
H0
Fig. 1. Experimental setup: 1—input antenna, used to supply the input signal Ps and to receive the front-reversed output signal Pr; and 2—output antenna used to receive the signal of the delayed primary MSW Pd.
propagation (H0?k). This geometry corresponds to the excitation of SMSW [3]. The YIG film waveguide had the width of 1.5 mm, and length of 20 mm. An input electromagnetic signal pulse having the carrier frequency os/2p ¼ 4.7 GHz, duration ts ¼ 30–100 ns, and power Pso1 mW was supplied to the input antenna (1) and excited in the film a packet of SMSW having the carrier wave number k102 rad/cm. The input antenna (1) was also used to receive an output signal Pr formed as a result of the WFR process caused by the pumping pulse. The output antenna (2) received the direct SMSW packet propagating in the film from the input antenna (1). The output signal Pd received by the antenna (2) was delayed by the SMSW propagation time Td relative to the input signal Ps. Without the pumping pulse, this output signal was smaller than the input one, Pd ¼ Ps/L (here L is the propagation losses in the film). Under the action of the pumping, the output signal was amplified and was greater than the input one: Pd ¼ GPs, G41. Pumping pulses of the duration tp ¼ 30–50 ns, carrier frequency opE2os, and the maximum power Pp ¼ 5 W were supplied to the dielectric resonator from a magnetron generator via a standard rectangular waveguide. The microwave magnetic field of the pumping pulse inside of the dielectric resonator was parallel to the bias magnetic field H0, i.e. the case of parallel pumping was realized in our experiment [3]. The length of the dielectric resonator, determining the size of the pumping localization region along the direction of SMSW propagation (see Fig. 1), was equal to 4.5 mm. Signal pulse Ps was supplied to the input antenna (1) at the moment of time t ¼ 0; the output signal Pd at the antenna (2) was received at the time t ¼ Td, which in our experiments was equal to Td100–150 ns. The pumping pulse was supplied at the time t ¼ Tp, and the reversed signal Pr was received at the input antenna (1) at the time t ¼ 2Tp [1,2]. We have investigated two qualitatively different regimes: TppTd and Tp4Td. In the first case the usual WFR of SMSW was realized. In the second case the direct SMSW waves have already passed the film at the moment of pumping application t ¼ Tp4Td, they reached
the output antenna (2) and were out of the spatial region where the interaction with pumping is possible. However, a ‘‘trace’’ of the passed SMSW was still present in the interaction region. This ‘‘trace’’ consists of the shortwavelength DESW created as the result of two-magnon scattering of the primary SMSW on the inhomogeneities [3]. These scattered DESW have large wavenumbers k104 rad/cm and substantially lower relaxation rate ork, than the relaxation rate or of the primary SMSW. Parametric pumping supplied under the condition Tp4Td acts on these DESW, and creates reversed DESW. These reversed DESW propagate back to the inhomogeneities (or scattering centers) where they were originally created and as a result of the inverse scattering on the same inhomogeneities are converted into a secondary SMSW wavepacket having small wavenumbers of the order of k102 rad/cm. The secondary SMSW packet propagates towards the input antenna (1) where it creates a reversed signal Pr [4]. The signal formed by the reversed DESW packet, as well as usual reversed signal, are received at the input antenna at the time t ¼ 2Tp [4]. The results of our experimental investigations on one of the YIG film waveguides are shown in Fig. 2, where the dependence of the output power of the reversed signal Pr is shown as a function of the applied bias magnetic field. In Fig. 2 HC is the upper boundary of existence of SMSW at a given experimental signal frequency: at H0 ¼ HC the SMSW wavenumber is zero, k ¼ 0 [3]. For comparison, we have also shown in Fig. 2 the output power Pd of the delayed signal (received by the antenna 2, see Fig. 1) in the absence of parametric pumping. The maximum power of the reversed signal was observed at the magnetic field H0EHC30 Oe, which corresponds to the excitation SMSW with the wavenumber kE102 rad/cm. For lower fields H0 (i.e., for larger wavenumbers k) the power Pd of the reversed signal decreases. This fact is illustrated by the curve 3 in the Fig. 2, which shows the difference between the lines 1 and 2 of the same plot. The curve 3 is, actually, the amplification factor of the reversed signal relative to the usual delayed signal. In the region of small wavenumbers kE50 rad/cm the amplification factor reaches the magnitude of 12 dB, and rapidly decreases with the increase of the SMSW wavenumber. This effect is explained by the decrease of the overlap integral with the increase of k, which leads to the decrease of efficiency of parametric interaction of direct and reversed SMSW. We should also mention that compared to the case of WFR of reciprocal BVMSW, even the optimum amplification factor of reversed SMSW is about 10 dB lower than for the BVMSW [4]. This substantial reduction in amplification is caused mainly by the low efficiency of the input antenna 1 that serves also as an output antenna for the reversed SMSW pulse, which propagates along the lower (substrate) surface of the YIG film waveguide. The dependence of the output power Pr on the time of pumping application Tp is shown in Fig. 3. In agreement with the above-presented discussion, the time of the
ARTICLE IN PRESS G.A. Melkov et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e41–e44
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2 -40
10
Pr/Pd (dB)
-30
Pr, Pd (dBm)
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1
3
-50
5 HC 0
-60 920
940
960
980 1000 H0 (Oe)
1020
1040
Fig. 2. Curve 1 shows the dependence of the output power Pr of the reversed signal on the bias magnetic field H0. Curves 2 and 3 show, respectively, the dependence of the direct delayed signal power Pd (see Fig. 1) on the bias field H0 when no pumping was supplied (curve 2), and the difference between the curves 1 and 2: Pr (dB m)–Pd (dB m) ¼ Pr /Pd (dB) (curve 3). The YIG film thickness was d ¼ 6.8 mm, ts ¼ 50 ns, tp ¼ 40 ns, Pp ¼ 5 W, and Ps ¼ 104 W.
-30
Pr (dBm)
-40
-50
-60
200
400
600
800
Tp (ns) Fig. 3. Dependence of the reversed signal power Pr received at the antenna 1 (see Fig. 1) on the time Tp when the pumping pulse was switched on. YIG film thickness d ¼ 6.8 mm, H0EHC, ts ¼ 50 ns, tp ¼ 40 ns, Pp ¼ 5 W, Ps ¼ 104 W.
reversed signal arrival at the antenna (1) is of the order of 2Tp. It is clear from Fig. 3, that the dependence Pr(Tp) consists from two linear segments with different slopes. It is known that these slopes are determined by the relaxation rates of the waves that participate in the process of WFR [5]. For the ‘‘early’’ switching of the pumping pulse (TpT d ffi 120 ns) the WFR is caused by long-wavelength SMSW with the relaxation rate or, while for the ‘‘late’’ switching (T4T d ), the reversal is mediated by the shortwavelength DESW having much smaller relaxation rate
e43
ork5or. In the real experimental situation, due to finite durations of the signal ts and pumping tp pulses, the transition between the two regimes takes place for a somewhat larger value of Tp, namely, at Tp ¼ 180 ns. It follows from Fig. 3, that relaxation rates for SMSW and DESW are equal to or ¼ 2.4 107 s1 and ork ¼ 2.2 106 s1, respectively. Owing to the peculiarities of the two-magnon scattering of spin waves on the YIG film inhomogeneities [3] the effective excitation of DESW by SMSW is possible only in a narrow range of magnetic fields near HC [5]. In some cases, especially in ferrite films with pinned surface spins, we observed similar ‘‘resonance’’ dependencies with the width of several tens of Oe, and, sometimes, having several well-pronounced maxima. Due to the small relaxation rate of DESW, we were able to achieve the delay time Td of the reversed signal larger than 2 ms.
3. Conclusion The possibility of wave front reversal (WFR) for nonreciprocal waves by double-frequency parametric pumping was demonstrated on the example of surface magnetostatic wave propagating in yttrium–iron garnet (YIG) films. For relatively small surface magnetostatic waves (SMSW) wavenumbers of k102 rad/cm the decrease of output power (compared to the case of reciprocal backward volume magnetostatic waves (BVMSW)) is caused only by the small efficiency of reception of the reversed wave packet propagating close to the lower surface of the film by the microstrip antenna situated at the upper surface of the film. In this case the output power is more than 10 dB larger than the output power of a passive ferrite delay line with the same delay time. For the larger values of the SMSW wavenumber the decrease in the output power is also related to the lower efficiency of parametric interaction of the direct and reversed waves with pumping caused by non-reciprocal distributions of microwave magnetization in the direct and reversed waves. We also showed the possibility of using short-wavelength dipole-exchange spin waves (DESW) to increase the delay time up to 2 ms. DESW are excited as a result of twomagnon scattering of SMSW on inhomogeneities of the ferrite film. Two-magnon scattering and DESW-mediated WFR are observed in a narrow range of applied magnetic fields near the upper boundary of the SMSW spectrum.
Acknowledgements This work was supported in part by the Ukrainian Foundation for Fundamental Research, Grant no. 2.07/16, by the Science and Technology Center in Ukraine, Grant no. 3066 and by the MURI Grant W911NF-04-1-0247 from the US Army Research Office.
ARTICLE IN PRESS e44
G.A. Melkov et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e41–e44
References [1] B.Ya. Zeldovich, R.F. Pilipetskii, V.V. Shkunov, Principles of the Phase Conjugation, Springer, Berlin, 1985. [2] G.A. Melkov, A.A. Serga, V.S. Tiberkevich, A.N. Oliynyk, A.N. Slavin, Phys. Rev. Lett. 84 (2000) 3438.
[3] A.G. Gurevich, G.A. Melkov, Magnetization Oscillation and Waves, CRC Press, New York, 1996. [4] G.A. Melkov, Yu.V. Kobljanskyj, A.A. Serga, V.S. Tiberkevich, A.N. Slavin, Phys. Rev. Lett. 86 (2001) 4918. [5] Yu.V. Koblyanskyy, G.A. Melkov, V.S. Tiberkevich, V.I. Vasyuchka, A.N. Slavin, J. Appl. Phys. 93 (2003) 8594.