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Methods of relaxation reversal for spin waves and oscillations
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) 991–992
Methods of relaxation reversal for spin waves and oscillations Yu.V. Kobljanskyja, V.S. Tiberkevicha, A.V. Chumaka, V.I. Vasyuchkaa, G.A. Melkova, A.N. Slavinb,* a
Radiophysical Faculty, Kiev Taras Shevchenko National University, Kiev 01033, Ukraine b Department of Physics, Oakland University, Rochester, MI 48309, USA
Abstract Reversal of relaxation for a pulsed microwave signal of the carrier frequency B4:7 GHz propagating in an yttrium– iron-garnet YIG film achieved by application of a double-frequency parametric pumping pulse has been studied theoretically and experimentally. The possibility of formation of a restored output macroscopic signal consisting of not one, but two pulses having different delay times is demonstrated for the first time. r 2003 Elsevier B.V. All rights reserved. PACS: 75.30.Ds; 76.50.+g; 85.70.Ge Keywords: Yttrium–iron-garnet; Spin waves; Parametric processes
There are examples of relaxation processes that are reversible, at least during a certain time interval. One of such processes is the process of phase relaxation responsible for the effects of spin and photon echo [1]. One method of the reversal of phase relaxation based on the excitation of the reversed wave or phase-conjugated oscillation by an additional pulse of parametric pumping is well-known [1]. If Tp —is the time interval between the application of a signal pulse and the short pulse of parametric pumping, the time of appearance of the restored macroscopic phase-conjugated signal (echo signal) is—2Tp : Another method is based on the frequency-selective parametric amplification of the scattered signal wave [2]. The time of appearance of the restored signal in this method is equal to Tp þ tp ; where tp —is the duration of the parametric pumping pulse. Thus, in general, as a result of the action of a parametric pumping pulse two restored signals should appear: the signal caused by the selective parametric amplification at the delay time Tp þ tp and the signal caused by the phase-conjugation process at the delay time 2Tp : *Corresponding author. Tel.: +248-370-3401; fax: +248370-3408. E-mail address: [email protected] (A.N. Slavin).
The experimental verification of this statement and determination of the conditions of existence of each of the restored signals were performed for the case of dipole-exchange backward volume magnetostatic waves (BVMSW) propagating along the direction of the bias magnetic field in a tangentially magnetized yttrium– iron-garnet (YIG) film. Our experimental setup [3] consists of an YIG film waveguide, the middle part of which was placed in a rectangular opening inside a dielectric resonator. A single narrow microstrip antenna (width—10 mm) was used for the excitation of the input and for the reception of the output pulsed signals. YIG film thickness was 7:4 mm; width—1:5 mm; and length— 20 mm: The external bias magnetic field was H0 ¼ 1065 Oe: In our experiments, the input signal pulse of the duration ts ¼ 20 ns and carrier frequency os =2p ¼ 4:7 GHz excited in the film at the time t ¼ 0 a wave packet of dipole-exchange BVMSW having a carrier wave number of kB104 cm1 : Then, at the time t ¼ Tp a pumping pulse of the duration tp ¼ 5–300 ns and power Pp o5 W having carrier frequency op C2os was supplied to the dielectric resonator made of ceramics with dielectric constant eB80: The microwave pumping magnetic field in the resonator was parallel to the bias ~0 : As a result of actions of the signal magnetic field H pulse (having the power Ps ) and then, after a delay of
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.044
ARTICLE IN PRESS 992
Yu.V. Kobljanskyj et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 991–992
Fig. 1. Oscillogramms of pulses in the signal channel (upper trace) and in the pumping channel (lower): (1) input signal pulse; (2) pulse reflected from the pumping resonator; (3,4) output delayed pulses created by selective parametric amplification and phase conjugation correspondingly.
Tp ; of a pumping pulse (having the power Pp ) the restored signal of the power Pout was received at the input microstrip antenna. Fig. 1 shows the relative positions in time of all the above-mentioned pulses for the case Pp ¼ 5 W; tp ¼ 80 ns; Tp ¼ 700 ns: It is clear from Fig. 1 that in this particular case the output signal, indeed, consists of two pulses. The first of them (3) is delayed by the time BTp þ tp ¼ 780 ns relative to the input signal pulse (1). This delay corresponds to the expected time of appearance of the restored macroscopic signal created by frequency-selective parametric amplification. The delay time of the second output pulse (4) is B2Tp ¼ 1400 ns; which corresponds to the expected time of appearance of the restored signal created by the phaseconjugated wave with a reversed wave front. The situation shown in Fig. 1 exists in a limited interval of duration of the pumping pulse tp : When tp p30 ns the signal (3) from selectively amplified waves disappears, while the increase of tp > 80 ns leads to the distortion and, eventually, to the disappearance of the signal (4) from phase-conjugated waves. To explain theoretically the obtained experimental results we used the Landau–Lifshits equation with the effective field consisting of the constant bias magnetic field, demagnetizing and exchange fields, as well as the homogeneous pulsed microwave field of the parallel
pumping and the non-homogeneous pulsed microwave field of the signal. The signal excites in the film a wave packet of primary dipole-exchange BVMSW having eigen-frequencies ok 7Dok and wave numbers k7Dk: The action of pulsed parametric pumping led to the selective parametric amplification of the packet of primary waves excited by the signal and, also, to the parametric excitation and ‘‘phasing’’ of phase-conjugated waves having wave numbers in the interval k8Dk: The first group of these waves created at the time Tp þ tp the output pulse of the power Pk ; while the second group created at the time 2Tp the output pulse of the power Pk : The ratio of powers of the two output pulsed signals has the form Pk 1 8jVk jTp ðt tp Tp Þ ; ð1Þ ¼ exp jVk jt2s þ 2tp Pk a where Vk is the coupling coefficient with parallel R pumping [4], and a ¼ 1=jVk jDkj Dk Vk dkj: According to (1), for tp ; ts -0 we have only the phase-conjugated signal Pk at the output, while the power of the selectively amplified signal Pk ¼ 0: With the increase of tp the bandwidth of the parametric amplification decreases and for tp B30 ns both phase-conjugated and selectively amplified signals are present at the output, which is confirmed experimentally. The suppression of the phase-conjugated signal Pk for tp > 80 ns is caused by the parametric excitation from the thermal level of the spin waves with kX104 cm1 [4] This work was supported in part by the NSF Grants No. DMR-0072017 and INT-0128823, by the Oakland University Foundation.
References [1] A. Abragam, The Principles of Nuclear Magnetism, Clarendon, Oxford, 1961. [2] G.A. Melkov, Yu.V. Kobljanskyj, et al., Phys. Rev. Lett. 86 (2001) 4918. [3] Yu.V. Kobljanskyj, G.A. Melkov, et al., J. Appl. Phys. 93 (2003) 8594. [4] A.G. Gurevich, G.A. Melkov, Magnetization Oscillations and Waves, CRC Press, New York, 1996, p. 256.
Journal of Magnetism and Magnetic Materials 272–276 (2004) 991–992
Methods of relaxation reversal for spin waves and oscillations Yu.V. Kobljanskyja, V.S. Tiberkevicha, A.V. Chumaka, V.I. Vasyuchkaa, G.A. Melkova, A.N. Slavinb,* a
Radiophysical Faculty, Kiev Taras Shevchenko National University, Kiev 01033, Ukraine b Department of Physics, Oakland University, Rochester, MI 48309, USA
Abstract Reversal of relaxation for a pulsed microwave signal of the carrier frequency B4:7 GHz propagating in an yttrium– iron-garnet YIG film achieved by application of a double-frequency parametric pumping pulse has been studied theoretically and experimentally. The possibility of formation of a restored output macroscopic signal consisting of not one, but two pulses having different delay times is demonstrated for the first time. r 2003 Elsevier B.V. All rights reserved. PACS: 75.30.Ds; 76.50.+g; 85.70.Ge Keywords: Yttrium–iron-garnet; Spin waves; Parametric processes
There are examples of relaxation processes that are reversible, at least during a certain time interval. One of such processes is the process of phase relaxation responsible for the effects of spin and photon echo [1]. One method of the reversal of phase relaxation based on the excitation of the reversed wave or phase-conjugated oscillation by an additional pulse of parametric pumping is well-known [1]. If Tp —is the time interval between the application of a signal pulse and the short pulse of parametric pumping, the time of appearance of the restored macroscopic phase-conjugated signal (echo signal) is—2Tp : Another method is based on the frequency-selective parametric amplification of the scattered signal wave [2]. The time of appearance of the restored signal in this method is equal to Tp þ tp ; where tp —is the duration of the parametric pumping pulse. Thus, in general, as a result of the action of a parametric pumping pulse two restored signals should appear: the signal caused by the selective parametric amplification at the delay time Tp þ tp and the signal caused by the phase-conjugation process at the delay time 2Tp : *Corresponding author. Tel.: +248-370-3401; fax: +248370-3408. E-mail address: [email protected] (A.N. Slavin).
The experimental verification of this statement and determination of the conditions of existence of each of the restored signals were performed for the case of dipole-exchange backward volume magnetostatic waves (BVMSW) propagating along the direction of the bias magnetic field in a tangentially magnetized yttrium– iron-garnet (YIG) film. Our experimental setup [3] consists of an YIG film waveguide, the middle part of which was placed in a rectangular opening inside a dielectric resonator. A single narrow microstrip antenna (width—10 mm) was used for the excitation of the input and for the reception of the output pulsed signals. YIG film thickness was 7:4 mm; width—1:5 mm; and length— 20 mm: The external bias magnetic field was H0 ¼ 1065 Oe: In our experiments, the input signal pulse of the duration ts ¼ 20 ns and carrier frequency os =2p ¼ 4:7 GHz excited in the film at the time t ¼ 0 a wave packet of dipole-exchange BVMSW having a carrier wave number of kB104 cm1 : Then, at the time t ¼ Tp a pumping pulse of the duration tp ¼ 5–300 ns and power Pp o5 W having carrier frequency op C2os was supplied to the dielectric resonator made of ceramics with dielectric constant eB80: The microwave pumping magnetic field in the resonator was parallel to the bias ~0 : As a result of actions of the signal magnetic field H pulse (having the power Ps ) and then, after a delay of
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.044
ARTICLE IN PRESS 992
Yu.V. Kobljanskyj et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 991–992
Fig. 1. Oscillogramms of pulses in the signal channel (upper trace) and in the pumping channel (lower): (1) input signal pulse; (2) pulse reflected from the pumping resonator; (3,4) output delayed pulses created by selective parametric amplification and phase conjugation correspondingly.
Tp ; of a pumping pulse (having the power Pp ) the restored signal of the power Pout was received at the input microstrip antenna. Fig. 1 shows the relative positions in time of all the above-mentioned pulses for the case Pp ¼ 5 W; tp ¼ 80 ns; Tp ¼ 700 ns: It is clear from Fig. 1 that in this particular case the output signal, indeed, consists of two pulses. The first of them (3) is delayed by the time BTp þ tp ¼ 780 ns relative to the input signal pulse (1). This delay corresponds to the expected time of appearance of the restored macroscopic signal created by frequency-selective parametric amplification. The delay time of the second output pulse (4) is B2Tp ¼ 1400 ns; which corresponds to the expected time of appearance of the restored signal created by the phaseconjugated wave with a reversed wave front. The situation shown in Fig. 1 exists in a limited interval of duration of the pumping pulse tp : When tp p30 ns the signal (3) from selectively amplified waves disappears, while the increase of tp > 80 ns leads to the distortion and, eventually, to the disappearance of the signal (4) from phase-conjugated waves. To explain theoretically the obtained experimental results we used the Landau–Lifshits equation with the effective field consisting of the constant bias magnetic field, demagnetizing and exchange fields, as well as the homogeneous pulsed microwave field of the parallel
pumping and the non-homogeneous pulsed microwave field of the signal. The signal excites in the film a wave packet of primary dipole-exchange BVMSW having eigen-frequencies ok 7Dok and wave numbers k7Dk: The action of pulsed parametric pumping led to the selective parametric amplification of the packet of primary waves excited by the signal and, also, to the parametric excitation and ‘‘phasing’’ of phase-conjugated waves having wave numbers in the interval k8Dk: The first group of these waves created at the time Tp þ tp the output pulse of the power Pk ; while the second group created at the time 2Tp the output pulse of the power Pk : The ratio of powers of the two output pulsed signals has the form Pk 1 8jVk jTp ðt tp Tp Þ ; ð1Þ ¼ exp jVk jt2s þ 2tp Pk a where Vk is the coupling coefficient with parallel R pumping [4], and a ¼ 1=jVk jDkj Dk Vk dkj: According to (1), for tp ; ts -0 we have only the phase-conjugated signal Pk at the output, while the power of the selectively amplified signal Pk ¼ 0: With the increase of tp the bandwidth of the parametric amplification decreases and for tp B30 ns both phase-conjugated and selectively amplified signals are present at the output, which is confirmed experimentally. The suppression of the phase-conjugated signal Pk for tp > 80 ns is caused by the parametric excitation from the thermal level of the spin waves with kX104 cm1 [4] This work was supported in part by the NSF Grants No. DMR-0072017 and INT-0128823, by the Oakland University Foundation.
References [1] A. Abragam, The Principles of Nuclear Magnetism, Clarendon, Oxford, 1961. [2] G.A. Melkov, Yu.V. Kobljanskyj, et al., Phys. Rev. Lett. 86 (2001) 4918. [3] Yu.V. Kobljanskyj, G.A. Melkov, et al., J. Appl. Phys. 93 (2003) 8594. [4] A.G. Gurevich, G.A. Melkov, Magnetization Oscillations and Waves, CRC Press, New York, 1996, p. 256.