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Homogeneously precessing spin domain in rotating vortex-free 3HeB
Physica B 165&166 North-Holland
(1990)
671-672
HOMOGENEOUSLY PRECESSING SPIN DOMAIN IN ROTATING VORTEX-FREE sHe-6
J.S. KORHONEN, V.V. DMITRIEV+, Z. JANU*, Y. KONDO, M. KRUSIUS, AND Yu.M. MUKHARSKIY+ Low Temperature Laboratory, Helsinki University of Technology, 02150 Espoo, Finland
Superfluid counterflow in rotating vortex-free sHe-B induces distinct changes in the homogeneously precessing resonance domain: its volume is reduced and the NMR absorption increased. Both effects disappear if the domain fills the whole experimental cell.
3. EXPERIMENTAL RESULTS When the static magnetic field is swept downwards, the HPD is formed in the low field region. At the domain boundary the Larmor frequency becomes equal to that of the rf excitation; therefore by changing the magnitude of H, the boundary can be moved inside the cell. Fig. 1 shows the components of M perpendicular to H. The lowermost curve, measured in the stationary state, gives the trace of M while the domain boundary travels from the top of the cell (origin) to the bottom (A). The total magnetization M = ( Ml2 + M r? )l’s grows proportional to the volume of the HPD. The phase of M is defined by the energy dissipation P: at constant M, AP is proportional to AMI (4). Various relaxation processes in the HPD mode are discussed in Ref. 4; here we note only that energy dissipation connected with spin diffusion through the domain boundary is seen in Fig. 1 as the rapid increase in MI, when the domain wall first enters the cell.
1. INTRODUCTION Unlike in He-II and sHe-A, a vortex-free state can be maintained in sHe-B up to appreciable rotation velocities. In conventional cw NMR spectra the superfluid counterflow vn - vs of the vortex-free state is manifested as a rearrangement of the resonance absorption with frequency, implicating substantial changes in the counterflow dominated n-texture (1). At high rf excitation levels a linear field gradient VH of the static magnetic field stabilizes a resonance mode unique to sHe-B (2). In this mode two domains with uniform spin behavior exist: in the low field homogeneously precessing domain (HPD) the magnetization M makes an angle 8 > 1040 with H, while in the high field domain M is parallel to H. Vortices and counterflow both affect the two domain structure. While vortices interact with the precessing spins in the HPD (3) changes induced by counterflow occur only if the narrow (< 1 mm) boundary region between the two domains is present. EXPERIMENTAL SET-UP Our measurements are performed in a rotating nuclear demagnetization cryostat at 29.3 bar pressure. The experimental chamber consists of two parts. The cylindrical NMR cell (diameter $ = 7 mm, length L = 7 mm is separated from the large heatexchanger volume by a tube ($ = 1.5 mm, L = 5.5 mm) with an orifice ($ = 1 mm, L = 0.5 mm). This construction prevents vortices present in the main sHe volume from entering the NMR cell. The rotation velocity for vortex creation depends on temperature and is = 1 ratis at T = 0.5Tc and >2.8 rad/s at T > 0.6Tc. The magnetic field, H = 14.2 mT, is parallel with the rotation axis R and the symmetry axis of the cell. The field gradient points to the cell bottom, so that the HPD forms first in the upper part of the cell. The NMR spectrometer (4) is operated at the constant frequency of 460 kHz.
2.
017 0
+ Institute for Physical Problems, Moscow, 117 334 USSR. Institute of Physics, Rez, CS-25068 Czechoslovakia. @ 1990 - Elsevier
Science
Publishers
M,,(VI
/ 0.8
1.2
FIGURE 1 Measured components of magnetization M in the plane perpendicular to the external field H. T = 0.7Tc, VH = 3 mT/m.
??
0921-4526/90/$03.50
I 0.4
B.V. (North-Holland)
J.S. Korhonen,
672
V.V. Dmitriev,
Z. Janu, Y. Kondo, M. Krusius,
Yu.M. Mukharskif
VH tmT/m) 0.14
0.4 P=29.3
bar
r c a
:: zi
0
I
o
0.12-0
a 0.10
= 0.2 a I
o_ 0
'IO
20 ’
I
R=1.5rad/s 0 0
Cl 0
0
0.08
1.0
2.0
R (radis.1
FIGURE 2 Reduction AM of the HPD magnetization as a funtion of rotation velocity at different VH. AM is normalized by the maximum value Mmax, measured when the HPD fills the whole cell.
If the domain boundary is swept to point B (see Fig. 1) and the cryostat is accelerated to n = 1 rad/s, curve B-C is traversed and a clear reduction in the total magnetization, or in the volume of the HPD, is seen. Sweeping the magnetic field at a = const. gives the curve with points C, D and A. A similar curve with points E and F is recorded after acceleration to 2 rad/s. Both curves, measured in the rotating state, show an additional absorption independent of total magnetization. The dotted lines depict sudden jumps from D and F to A (when H is reduced) and from A to E (when H is increased). If the magnetic field is further reduced after a jump to A, the trace A-G is independent of G. The disappearance of the additional absorption when the HPD fills the whole cell, the sudden jumps, and the hysteretic behavior reveal that counterflow interacts with the HPD only in the presence of the domain boundary. The reduction in magnetization or in the volume of the HPD and the increase in resonance absorption are plotted in Fi s. 2 and 3, respectively. Both are proportional to Q8 at small VH.Their dependences on VH are such that AM 0~ (VH)-1 while AP decreases rather more slowly with increasing VH. The additional absorption might be explained by an increase in spin diffusion relaxation at the domain wall. Two effects must be considered: a change in the wall thickness and an increase in its surface area due to bending of the domain wall in the inhomogeneous velocity distribution v = -R x r.
0
1.0
1 2.0
n
”
R(rad/s) FIGURE 3 Additional absorption AP as a function of rotation velocity at two magnetic field gradients. The data was measured at constant magnetization M = 0.55Mrnex. The insert shows AP as a function of the field gradient at a = 1.5 rad/s. P, T and H are as in Fig. 2.
Experiments in a magnetic field tilted by 900 with respect to the rotation axis show a similar behavior of the HPD as in the axial field. A qualitative difference is that in the transverse field the additional absorption due to counterflow depends on the total magnetization: no increase in absorption is seen, if the HPD fills approximately half of the cell. ACKNOWLEDGEMENTS We wish to thank LA. Fomin, A.D. Gongadze and G.E. Volovik for discussions. This work has been supported by the Korber Stiftung (Hamburg) and the Academy of Finland and the USSR Academy of Sciences through project ROTA. REFERENCES (1) P.J. Hakonen and K.K. Nummila, Phys. Rev. Lett. 59 (1987) 1006, and A.D. Gongadze, Z. Janu, Y. Kondo, J.S. Korhonen, M. Krusius, Yu. M. Mukharskiy, and E.V. Thuneberg, to be published. (2) A.S. Borovik-Romanov, Yu. M. Bunkov, V.V. Dmitriev, Yu. M. Mukharskiy, and K. Flachbart, Sov.Phys. JETP 61 (1985) 1199, and I.A. Fomin, Sov. Phys. JETP 61 (1985) 1207. (3) V.V. Dmitriev, Y. Kondo, J.S. Korhonen, M. Krus/us, Yu.M. Mukharskiy, E.B. Sonin, and G.E. Volovik, this volume. (4) Y. Kondo, J.S. Korhonen, and M. Krusius, this volume.
(1990)
671-672
HOMOGENEOUSLY PRECESSING SPIN DOMAIN IN ROTATING VORTEX-FREE sHe-6
J.S. KORHONEN, V.V. DMITRIEV+, Z. JANU*, Y. KONDO, M. KRUSIUS, AND Yu.M. MUKHARSKIY+ Low Temperature Laboratory, Helsinki University of Technology, 02150 Espoo, Finland
Superfluid counterflow in rotating vortex-free sHe-B induces distinct changes in the homogeneously precessing resonance domain: its volume is reduced and the NMR absorption increased. Both effects disappear if the domain fills the whole experimental cell.
3. EXPERIMENTAL RESULTS When the static magnetic field is swept downwards, the HPD is formed in the low field region. At the domain boundary the Larmor frequency becomes equal to that of the rf excitation; therefore by changing the magnitude of H, the boundary can be moved inside the cell. Fig. 1 shows the components of M perpendicular to H. The lowermost curve, measured in the stationary state, gives the trace of M while the domain boundary travels from the top of the cell (origin) to the bottom (A). The total magnetization M = ( Ml2 + M r? )l’s grows proportional to the volume of the HPD. The phase of M is defined by the energy dissipation P: at constant M, AP is proportional to AMI (4). Various relaxation processes in the HPD mode are discussed in Ref. 4; here we note only that energy dissipation connected with spin diffusion through the domain boundary is seen in Fig. 1 as the rapid increase in MI, when the domain wall first enters the cell.
1. INTRODUCTION Unlike in He-II and sHe-A, a vortex-free state can be maintained in sHe-B up to appreciable rotation velocities. In conventional cw NMR spectra the superfluid counterflow vn - vs of the vortex-free state is manifested as a rearrangement of the resonance absorption with frequency, implicating substantial changes in the counterflow dominated n-texture (1). At high rf excitation levels a linear field gradient VH of the static magnetic field stabilizes a resonance mode unique to sHe-B (2). In this mode two domains with uniform spin behavior exist: in the low field homogeneously precessing domain (HPD) the magnetization M makes an angle 8 > 1040 with H, while in the high field domain M is parallel to H. Vortices and counterflow both affect the two domain structure. While vortices interact with the precessing spins in the HPD (3) changes induced by counterflow occur only if the narrow (< 1 mm) boundary region between the two domains is present. EXPERIMENTAL SET-UP Our measurements are performed in a rotating nuclear demagnetization cryostat at 29.3 bar pressure. The experimental chamber consists of two parts. The cylindrical NMR cell (diameter $ = 7 mm, length L = 7 mm is separated from the large heatexchanger volume by a tube ($ = 1.5 mm, L = 5.5 mm) with an orifice ($ = 1 mm, L = 0.5 mm). This construction prevents vortices present in the main sHe volume from entering the NMR cell. The rotation velocity for vortex creation depends on temperature and is = 1 ratis at T = 0.5Tc and >2.8 rad/s at T > 0.6Tc. The magnetic field, H = 14.2 mT, is parallel with the rotation axis R and the symmetry axis of the cell. The field gradient points to the cell bottom, so that the HPD forms first in the upper part of the cell. The NMR spectrometer (4) is operated at the constant frequency of 460 kHz.
2.
017 0
+ Institute for Physical Problems, Moscow, 117 334 USSR. Institute of Physics, Rez, CS-25068 Czechoslovakia. @ 1990 - Elsevier
Science
Publishers
M,,(VI
/ 0.8
1.2
FIGURE 1 Measured components of magnetization M in the plane perpendicular to the external field H. T = 0.7Tc, VH = 3 mT/m.
??
0921-4526/90/$03.50
I 0.4
B.V. (North-Holland)
J.S. Korhonen,
672
V.V. Dmitriev,
Z. Janu, Y. Kondo, M. Krusius,
Yu.M. Mukharskif
VH tmT/m) 0.14
0.4 P=29.3
bar
r c a
:: zi
0
I
o
0.12-0
a 0.10
= 0.2 a I
o_ 0
'IO
20 ’
I
R=1.5rad/s 0 0
Cl 0
0
0.08
1.0
2.0
R (radis.1
FIGURE 2 Reduction AM of the HPD magnetization as a funtion of rotation velocity at different VH. AM is normalized by the maximum value Mmax, measured when the HPD fills the whole cell.
If the domain boundary is swept to point B (see Fig. 1) and the cryostat is accelerated to n = 1 rad/s, curve B-C is traversed and a clear reduction in the total magnetization, or in the volume of the HPD, is seen. Sweeping the magnetic field at a = const. gives the curve with points C, D and A. A similar curve with points E and F is recorded after acceleration to 2 rad/s. Both curves, measured in the rotating state, show an additional absorption independent of total magnetization. The dotted lines depict sudden jumps from D and F to A (when H is reduced) and from A to E (when H is increased). If the magnetic field is further reduced after a jump to A, the trace A-G is independent of G. The disappearance of the additional absorption when the HPD fills the whole cell, the sudden jumps, and the hysteretic behavior reveal that counterflow interacts with the HPD only in the presence of the domain boundary. The reduction in magnetization or in the volume of the HPD and the increase in resonance absorption are plotted in Fi s. 2 and 3, respectively. Both are proportional to Q8 at small VH.Their dependences on VH are such that AM 0~ (VH)-1 while AP decreases rather more slowly with increasing VH. The additional absorption might be explained by an increase in spin diffusion relaxation at the domain wall. Two effects must be considered: a change in the wall thickness and an increase in its surface area due to bending of the domain wall in the inhomogeneous velocity distribution v = -R x r.
0
1.0
1 2.0
n
”
R(rad/s) FIGURE 3 Additional absorption AP as a function of rotation velocity at two magnetic field gradients. The data was measured at constant magnetization M = 0.55Mrnex. The insert shows AP as a function of the field gradient at a = 1.5 rad/s. P, T and H are as in Fig. 2.
Experiments in a magnetic field tilted by 900 with respect to the rotation axis show a similar behavior of the HPD as in the axial field. A qualitative difference is that in the transverse field the additional absorption due to counterflow depends on the total magnetization: no increase in absorption is seen, if the HPD fills approximately half of the cell. ACKNOWLEDGEMENTS We wish to thank LA. Fomin, A.D. Gongadze and G.E. Volovik for discussions. This work has been supported by the Korber Stiftung (Hamburg) and the Academy of Finland and the USSR Academy of Sciences through project ROTA. REFERENCES (1) P.J. Hakonen and K.K. Nummila, Phys. Rev. Lett. 59 (1987) 1006, and A.D. Gongadze, Z. Janu, Y. Kondo, J.S. Korhonen, M. Krusius, Yu. M. Mukharskiy, and E.V. Thuneberg, to be published. (2) A.S. Borovik-Romanov, Yu. M. Bunkov, V.V. Dmitriev, Yu. M. Mukharskiy, and K. Flachbart, Sov.Phys. JETP 61 (1985) 1199, and I.A. Fomin, Sov. Phys. JETP 61 (1985) 1207. (3) V.V. Dmitriev, Y. Kondo, J.S. Korhonen, M. Krus/us, Yu.M. Mukharskiy, E.B. Sonin, and G.E. Volovik, this volume. (4) Y. Kondo, J.S. Korhonen, and M. Krusius, this volume.