- Email: [email protected]
Low-frequency dynamics of HPD at low pressures
Physica B 284}288 (2000) 258}259
Low-frequency dynamics of HPD at low pressures Alexander Feher *, Emil Gaz\ o, RoH bert HarakaH ly , Martin Kupka, L[ ubos\ Lokner , Marcela MedeovaH , Radovan Scheibel , Peter Skyba, Norbert Smolka Department of Experimental Physics, S[ afa& rik University, Park Angelinum 9, 04154 Kos\ ice, Slovakia Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 04353 Kos\ ice, Slovakia
Abstract Experimental study of low-frequency oscillation modes of a domain wall between the homogeneously precessing domain (HPD) and the stationary domain (SD) in super#uid He}B is presented. Measurements were performed in the temperature range from 0.5¹ to 0.8¹ and at a pressure of 2.7 bar. The small signal of the low-frequency domain wall oscillations on the high-frequency background (the HPD excitation) was measured using an RF-detector and a lowfrequency "lter in combination with a low-frequency lock-in ampli"er. This technique makes it possible to study "ne e!ects of the HPD low-frequency oscillation modes which may be associated with the in#uence of the texture. 2000 Elsevier Science B.V. All rights reserved. Keywords: He}B; Homogeneously precessing domain; Spin dynamics
1. Introduction Nowadays, it is generally accepted that the dynamic spin structure of a homogeneously precessing domain and stationary domain is a powerful tool for investigation of the magnetic relaxation processes and the spinorbital dynamics of the super#uid He}B phase [1]. The HPD is a unique macroscopic manifestation of the socalled magnetic super#uidity as a direct consequence of the orbital p-wave and spin-triplet pairing of the He atoms. Using a cw-NMR technique to excite the HPD, it is possible to compensate the energy losses due to magnetic relaxation processes. As a result, the HPD is maintained in a dynamical equilibrium state, i.e., the state with coherent spin precession corresponds to a minimum of the total energy. Because of the HPD magnetic super#uid state, the phase of the spin precession (i.e. the phase of the order parameter) is very sensitive to any perturbation. Any disturbances or external forces applied to the HPD
* Corresponding author. E-mail address: [email protected] (A. Feher)
will cause it to deviate from the dynamical equilibrium state, creating a gradient in the phase of precession. The gradient excites spin supercurrents } a e!ective feedback mechanism restoring the dynamical equilibrium state. This can result in oscillations of the spin distribution around the equilibrium state [2]. Besides the so-called twisting oscillation mode [1], another two types of lowfrequency oscillations of the HPD can be excited and studied: planar [1] and axial modes. These last two modes are similar to the oscillations on the surface of a liquid in a gravitational "eld. The frequencies of axial or planar oscillation modes of the HPD with length ¸ can be calculated using the equation [2]
(2Qc c Q¸c tanh B, X" 1 RB R(2c
(1)
where B is the magnetic "eld gradient, R is the radius of the cell, Q is the "rst nonzero root of the equation J (x)"0 (J (x) is the Bessel function with i"0 or 1 for G G axial or planar waves, respectively), c "(5c !c )/4 , and c "(5c #3c )/4, where c and c are the spin , , wave velocities with respect to the direction of the magnetic "eld.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 5 1 8 - 1
A. Feher et al. / Physica B 284}288 (2000) 258}259
259
2. Experiment and discussion We continued our study of the dynamics of the HPD oscillation modes [3] at 2.7 bar and in the temperature range from 0.5¹ to 0.8¹ using another more sensitive method of measurement. We applied a small longitudinal alternating magnetic "eld with axial symmetry as a perturbation to the HPD equilibrium state. We can also assume that the expected &#are-out' texture in the SD having axial symmetry should help to excite an axial mode with the same symmetry. The measurements were performed in an experimental cell of cylindrical shape made from Stycast mounted on a di!usion-welded nuclear stage [4]. The method of measurement we used is based on using a RF-detector and a low-frequency "lter in combination with a lowfrequency lock-in ampli"er. The reference signal for the lock-in ampli"er was taken from the generator which provided the longitudinal magnetic "eld. A typical set of absorption and dispersion signals as a function of applied frequency and their dependence on the magnetic "eld gradient is presented in Fig. 1. One can see pure resonance signals corresponding to the excited axial mode which allowed us to determine also the width of absorption signal, which is a measure of damping. So far there is no theoretical model of the HPD oscillation modes which would take into account an additional dissipation process due to dynamic oscillations of the HPD wall. We therefore can only analyze several possible mechanisms, such as the dynamic spin di!usion [5], the Leggett} Takagi relaxation, or even the process of Andreev re#ection. Preliminary analysis of the dependence of the resonance frequencies on the magnetic "eld gradient shows that, contrary to results published in Ref. [3], at low pressures higher axial modes are preferentially excited due to the in#uence of the texture in SD.
Fig. 1. Absorption and dispersion signals of the axial oscillation mode for various magnetic "eld gradients.
Acknowledgements This work was supported by grants of Slovak Grant Agency VEGA No. 2/4178/97 and No. 1/4385/97. Liquid nitrogen needed for experiments was sponsored by VSZ[ Ferroenergy a.s.
References [1] Yu.M. Bunkov, in: W. Halperin (Ed.), Progress in Low Temperature Physics, Vol. 14, Elsevier, Amsterdam, 1995, p. 56. [2] I.A. Fomin, Sov. Phys. JETP 66 (1987) 1142. [3] L. Lokner, A. Feher, M. Kupka, R. HarakaH ly, R. Scheibel, Yu.M. Bunkov, P. Skyba, Europhys. Lett. 40 (1997) 539. [4] P. Skyba, J. NyeH ki, E. Gaz\ o, V. MakroczyovaH , Yu.M. Bunkov, D.A. Sergatskov, A. Feher, Cryogenics 37 (1997) 293. [5] E.V. Poddyakova, Zh. Eksp. Teor. Fiz. 97 (1990) 1166.
Low-frequency dynamics of HPD at low pressures Alexander Feher *, Emil Gaz\ o, RoH bert HarakaH ly , Martin Kupka, L[ ubos\ Lokner , Marcela MedeovaH , Radovan Scheibel , Peter Skyba, Norbert Smolka Department of Experimental Physics, S[ afa& rik University, Park Angelinum 9, 04154 Kos\ ice, Slovakia Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 04353 Kos\ ice, Slovakia
Abstract Experimental study of low-frequency oscillation modes of a domain wall between the homogeneously precessing domain (HPD) and the stationary domain (SD) in super#uid He}B is presented. Measurements were performed in the temperature range from 0.5¹ to 0.8¹ and at a pressure of 2.7 bar. The small signal of the low-frequency domain wall oscillations on the high-frequency background (the HPD excitation) was measured using an RF-detector and a lowfrequency "lter in combination with a low-frequency lock-in ampli"er. This technique makes it possible to study "ne e!ects of the HPD low-frequency oscillation modes which may be associated with the in#uence of the texture. 2000 Elsevier Science B.V. All rights reserved. Keywords: He}B; Homogeneously precessing domain; Spin dynamics
1. Introduction Nowadays, it is generally accepted that the dynamic spin structure of a homogeneously precessing domain and stationary domain is a powerful tool for investigation of the magnetic relaxation processes and the spinorbital dynamics of the super#uid He}B phase [1]. The HPD is a unique macroscopic manifestation of the socalled magnetic super#uidity as a direct consequence of the orbital p-wave and spin-triplet pairing of the He atoms. Using a cw-NMR technique to excite the HPD, it is possible to compensate the energy losses due to magnetic relaxation processes. As a result, the HPD is maintained in a dynamical equilibrium state, i.e., the state with coherent spin precession corresponds to a minimum of the total energy. Because of the HPD magnetic super#uid state, the phase of the spin precession (i.e. the phase of the order parameter) is very sensitive to any perturbation. Any disturbances or external forces applied to the HPD
* Corresponding author. E-mail address: [email protected] (A. Feher)
will cause it to deviate from the dynamical equilibrium state, creating a gradient in the phase of precession. The gradient excites spin supercurrents } a e!ective feedback mechanism restoring the dynamical equilibrium state. This can result in oscillations of the spin distribution around the equilibrium state [2]. Besides the so-called twisting oscillation mode [1], another two types of lowfrequency oscillations of the HPD can be excited and studied: planar [1] and axial modes. These last two modes are similar to the oscillations on the surface of a liquid in a gravitational "eld. The frequencies of axial or planar oscillation modes of the HPD with length ¸ can be calculated using the equation [2]
(2Qc c Q¸c tanh B, X" 1 RB R(2c
(1)
where B is the magnetic "eld gradient, R is the radius of the cell, Q is the "rst nonzero root of the equation J (x)"0 (J (x) is the Bessel function with i"0 or 1 for G G axial or planar waves, respectively), c "(5c !c )/4 , and c "(5c #3c )/4, where c and c are the spin , , wave velocities with respect to the direction of the magnetic "eld.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 5 1 8 - 1
A. Feher et al. / Physica B 284}288 (2000) 258}259
259
2. Experiment and discussion We continued our study of the dynamics of the HPD oscillation modes [3] at 2.7 bar and in the temperature range from 0.5¹ to 0.8¹ using another more sensitive method of measurement. We applied a small longitudinal alternating magnetic "eld with axial symmetry as a perturbation to the HPD equilibrium state. We can also assume that the expected &#are-out' texture in the SD having axial symmetry should help to excite an axial mode with the same symmetry. The measurements were performed in an experimental cell of cylindrical shape made from Stycast mounted on a di!usion-welded nuclear stage [4]. The method of measurement we used is based on using a RF-detector and a low-frequency "lter in combination with a lowfrequency lock-in ampli"er. The reference signal for the lock-in ampli"er was taken from the generator which provided the longitudinal magnetic "eld. A typical set of absorption and dispersion signals as a function of applied frequency and their dependence on the magnetic "eld gradient is presented in Fig. 1. One can see pure resonance signals corresponding to the excited axial mode which allowed us to determine also the width of absorption signal, which is a measure of damping. So far there is no theoretical model of the HPD oscillation modes which would take into account an additional dissipation process due to dynamic oscillations of the HPD wall. We therefore can only analyze several possible mechanisms, such as the dynamic spin di!usion [5], the Leggett} Takagi relaxation, or even the process of Andreev re#ection. Preliminary analysis of the dependence of the resonance frequencies on the magnetic "eld gradient shows that, contrary to results published in Ref. [3], at low pressures higher axial modes are preferentially excited due to the in#uence of the texture in SD.
Fig. 1. Absorption and dispersion signals of the axial oscillation mode for various magnetic "eld gradients.
Acknowledgements This work was supported by grants of Slovak Grant Agency VEGA No. 2/4178/97 and No. 1/4385/97. Liquid nitrogen needed for experiments was sponsored by VSZ[ Ferroenergy a.s.
References [1] Yu.M. Bunkov, in: W. Halperin (Ed.), Progress in Low Temperature Physics, Vol. 14, Elsevier, Amsterdam, 1995, p. 56. [2] I.A. Fomin, Sov. Phys. JETP 66 (1987) 1142. [3] L. Lokner, A. Feher, M. Kupka, R. HarakaH ly, R. Scheibel, Yu.M. Bunkov, P. Skyba, Europhys. Lett. 40 (1997) 539. [4] P. Skyba, J. NyeH ki, E. Gaz\ o, V. MakroczyovaH , Yu.M. Bunkov, D.A. Sergatskov, A. Feher, Cryogenics 37 (1997) 293. [5] E.V. Poddyakova, Zh. Eksp. Teor. Fiz. 97 (1990) 1166.