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NMR absorption in a homogeneously precessing domain of 3HeB
Physica B 1658~166 North-Holland
NMR
(1990)
ABSORPTION
673-674
IN A HOMOGENEOUSLY
PRECESSING
DOMAIN
OF 3He-B
Y. KONDO, J.S. KORHONEN, and M. KRUSIUS
Low Temperature Laboratory, Helsinki University of Technology, 02150 Espoo, Finland The measurement of cw NMR absorption in a homogeneously precessing spin domain of sHe-B is discussed. The absorptron is divided into several contributions, based upon their drfferent dependences on the domain length. Within our experimental accuracy, we found no contribution linear with domain size which would be caused by surface relaxation on the cell wall. 1. INTRODUCTI
N In superfluid BHe-B the homogeneously precessing spin domain (HPD) is created at high rf excitation levels in the presence of a linear field gradient VH superimposed on the static polarization field H. In this domain the spins are uniformly precessing at co,which corresponds to the Larmor frequency at the domain boundary. This has been demonstrated by the Moscow group both theoretically (1) and in a number of beautiful experiments (2 . We have used the FIPD resonance mode for studying the B-phase vortices (3) and counterflow (4) in the rotating liquid. Vortices produce an additional NMR absorption which is proportional to their total length within the domain. When analyzing the mechanism for this additional spin relaxatron it became necessa to compare the NMR absorption in different external 7relds. In this report we discuss the method for extracting the absolute value of the NMR absorption, and divide it into different contributions on the basis of their dependences on the domain size in the stationary liauid. This orocedure has been introduced bv the Moscow group (2), but here we consider #more extensively the term linear with domain length which would be caused by surface relaxation on the cell wall. Our experiments show that this linear contribution is less than 0.01 nW/cm2 at 14.2 mT. 2. TANK CIRCUIT An analysis of the cw NMR tank circuit has been carried out in Fig. 1 to determine the NMR absorption PM. Here vM is the voltage which is induced by the precessing total magnetization M in the pick-up coil, ie., IVM I = cokvlI= m&H in the HPD mode rather than being proportional to the rf excitation field HI as in conventional low level NMR. The volta e v. across the tank circuit, in the absence of the H$ D (vM= 0), is cancelled in the actual measurement with a compensation tank circuit connected to the second input of the differential preamplifier. The remaining signal voltage, -j&M, is measured with a phase sensitive detector where vM’and VM”are the dispersion and absorption signals, respectively. The phase setting of the detector is adjusted by enforcing the requirement that PM is independent of v. (see Fig. l), ie., vM”jvoj = COn.3. Even if we add a
0921-4526/90/$03.50
@ 1990 - Elsevier
Science
Publishers
l-
&t
iOejut
v= rQ2io(l-j/Q)-jQvM r=wL/O
; LC=l/wZ
vo= rQ2(1-j/Q)io
FIGURE 1 Equivalent circuit of our cw NMR tank circuit. resistance to damp the Q value of the tank circuit, our method of calculating PM and adjustin the hase is still valid save for correction terms of or8 er l/ & In our experiments, the error in the phase adjustment’is less than 0.3’. The limiting features are the accuracies of our synthesizer oscillator (Hewlett-Packard #3325A) and lock-in amplifier (Princeton Applied Research #5202). 3. MEASUREMENTS Our NMR cell is a cylinder with diameter = height = 7 mm, with H and VH oriented alon the c linder axis (3 ,4). When H is swept downward, t\ e HP 8. frrst starts forming at that end of the cylinder where the Larmor frequency begins to drop below w. The domain boundary forms at the location where the Larmor frequency equals w. Thus, by sweeping H with VH = const., one can control the size of the domain in such a way that, at each location of the domain boundary, M 0~ length of the domain L and the tipping angle of the precessing spins is = 104’ (1). In Fig. 2 the tank circuit voltage which is calculated from the lock-in amplifier output, while sweeping H, is shown as a plot with c&M” vs (&,$’ (top): at the origin there is no HPD while at point A the domain fills the entire cell. The lower graph in Fig. 2 illustrates the corresponding PM vs GjvMj 0~ M plot. Note the large correction due to -jvMj2/r. The NMR absorption was fitted to a polynomial in M = IM I with
B.V. (North-Holland)
674
Y. Kondo, J.S. Korhonen, M. Krusius
QvM’[mV(rms)]
10
I
I
I
0 0
0 boundary (14.2mT)
r
8
$
6-
“0 Ng
4-
0
0 L-T( 14.2mT)
.E
??
boundary(28.4mT)
+ L-T(28.4mT)
.
?? , 0
*b o c+@ c+
O_
3 a
QlvMllmWms)l FIGURE 2 Plot of the in-phase QvM” vs the out-of-phase QvM’ components of the HPD signal (top) and the corresponding NMR absorption PM vs Q~vM~0~M (bottom) at 14.2 mT, 11 mT/m, 0.48Tc, and 29.3 bar. Circuit constants are L = 80 uH, Q = 58, Iv01 = 15.7 mV(rms).
PM=a,+anM+asMs
"0
A
a2M
o
a&f3
10
20
VH (mT/m)
FIGURE 3 Division of the NMR absorption into three components according to Eq. l), shown here as a function of VH at 14.2 mT, 0.48 \ c and 29.3 bar. The terms = M and M* are shown with their values when the HPD fills the entire cell.
B
0’ 0.4
0.5
0.6
0.7
0.8
TITc
FIGURE 4 The domain boundary and Leggett-Takagi (L-T) components to PM as a function of temperature measured at 10 mT/m and 29.3 bar, in two different fields 14.2 and 28.4 mT.
(1)
where the first constant term corresponds to relaxation in the domain boundary, 0~H7/3VH1/3., the second to relaxation at the cylindrical cell wall wrth an area = P, and the third to Le gett-Takagi relaxation in the bulk domain, =@@VH 9. In Fig. 3 the division into these 3 terms is shown as a function of VH. We found no significant linear term. The worst case phase.error, 0.3’, makes 0.008 nW error in the linear term In this case at 14.2 mT. The current setting of the magnet producing the gradient for optimum field homogenerty was found by ad’usting for minimum line width of the conventional Nd R absorption signal in the normal Fermi liquid phase.
0.10 -
2 -
From these results we can determine the spin diffusion constant and the Leggett-Takagi relaxation time (2) and we find no significant surface relaxation. When the measurements of Fig. 3 were repeated at different temperatures and the results were pfotted in normalized form, PM/H*, then Fig. 4 was obtained. Even in the higher field of 28.4 mT we could not find a meaningful contribution from surface relaxation which has been predicted to have the strong field dependence of H4 (5). ACKNOWLEDGEMENTS We wish to thank V.V. Dmitriev and Yu.M. Mukharskiy for useful discussions. This work has been supported through the Award for the Advancement of European Science by the Korber Stiftung. REFERENCES (1) I.A. Fomin, Sov. Phys. JETP 61 (1985) 1207. (2) AS. Borovik-Romanov, YuM. Bunkov, V.V. Dmitriev, and Yu.M. Mukharskiy, Quantum Fluids and Solids 1989, AIP Conf. Proc. 194 (1989) 15. (3) V.V. Dmitriev, Y. Kondo, J.S. Korhonen, M. Krusius, E.B. Sonin, and G.E. Volovik, this volume. (4) J.S.Korhonen, V.V.Dmitriev, Z.Janu, Y.Kondo, M.Krusius, and Yu.M.Mukharskiy, this volume. (5) T. Ohmi, M. Tsubota, and T. Tsuneto, Proc. 18th Internat. Conf. on Low Temp. Phys., Kyoto, Jap. J. Appl. Phys.26 (1987) 169.
NMR
(1990)
ABSORPTION
673-674
IN A HOMOGENEOUSLY
PRECESSING
DOMAIN
OF 3He-B
Y. KONDO, J.S. KORHONEN, and M. KRUSIUS
Low Temperature Laboratory, Helsinki University of Technology, 02150 Espoo, Finland The measurement of cw NMR absorption in a homogeneously precessing spin domain of sHe-B is discussed. The absorptron is divided into several contributions, based upon their drfferent dependences on the domain length. Within our experimental accuracy, we found no contribution linear with domain size which would be caused by surface relaxation on the cell wall. 1. INTRODUCTI
N In superfluid BHe-B the homogeneously precessing spin domain (HPD) is created at high rf excitation levels in the presence of a linear field gradient VH superimposed on the static polarization field H. In this domain the spins are uniformly precessing at co,which corresponds to the Larmor frequency at the domain boundary. This has been demonstrated by the Moscow group both theoretically (1) and in a number of beautiful experiments (2 . We have used the FIPD resonance mode for studying the B-phase vortices (3) and counterflow (4) in the rotating liquid. Vortices produce an additional NMR absorption which is proportional to their total length within the domain. When analyzing the mechanism for this additional spin relaxatron it became necessa to compare the NMR absorption in different external 7relds. In this report we discuss the method for extracting the absolute value of the NMR absorption, and divide it into different contributions on the basis of their dependences on the domain size in the stationary liauid. This orocedure has been introduced bv the Moscow group (2), but here we consider #more extensively the term linear with domain length which would be caused by surface relaxation on the cell wall. Our experiments show that this linear contribution is less than 0.01 nW/cm2 at 14.2 mT. 2. TANK CIRCUIT An analysis of the cw NMR tank circuit has been carried out in Fig. 1 to determine the NMR absorption PM. Here vM is the voltage which is induced by the precessing total magnetization M in the pick-up coil, ie., IVM I = cokvlI= m&H in the HPD mode rather than being proportional to the rf excitation field HI as in conventional low level NMR. The volta e v. across the tank circuit, in the absence of the H$ D (vM= 0), is cancelled in the actual measurement with a compensation tank circuit connected to the second input of the differential preamplifier. The remaining signal voltage, -j&M, is measured with a phase sensitive detector where vM’and VM”are the dispersion and absorption signals, respectively. The phase setting of the detector is adjusted by enforcing the requirement that PM is independent of v. (see Fig. l), ie., vM”jvoj = COn.3. Even if we add a
0921-4526/90/$03.50
@ 1990 - Elsevier
Science
Publishers
l-
&t
iOejut
v= rQ2io(l-j/Q)-jQvM r=wL/O
; LC=l/wZ
vo= rQ2(1-j/Q)io
FIGURE 1 Equivalent circuit of our cw NMR tank circuit. resistance to damp the Q value of the tank circuit, our method of calculating PM and adjustin the hase is still valid save for correction terms of or8 er l/ & In our experiments, the error in the phase adjustment’is less than 0.3’. The limiting features are the accuracies of our synthesizer oscillator (Hewlett-Packard #3325A) and lock-in amplifier (Princeton Applied Research #5202). 3. MEASUREMENTS Our NMR cell is a cylinder with diameter = height = 7 mm, with H and VH oriented alon the c linder axis (3 ,4). When H is swept downward, t\ e HP 8. frrst starts forming at that end of the cylinder where the Larmor frequency begins to drop below w. The domain boundary forms at the location where the Larmor frequency equals w. Thus, by sweeping H with VH = const., one can control the size of the domain in such a way that, at each location of the domain boundary, M 0~ length of the domain L and the tipping angle of the precessing spins is = 104’ (1). In Fig. 2 the tank circuit voltage which is calculated from the lock-in amplifier output, while sweeping H, is shown as a plot with c&M” vs (&,$’ (top): at the origin there is no HPD while at point A the domain fills the entire cell. The lower graph in Fig. 2 illustrates the corresponding PM vs GjvMj 0~ M plot. Note the large correction due to -jvMj2/r. The NMR absorption was fitted to a polynomial in M = IM I with
B.V. (North-Holland)
674
Y. Kondo, J.S. Korhonen, M. Krusius
QvM’[mV(rms)]
10
I
I
I
0 0
0 boundary (14.2mT)
r
8
$
6-
“0 Ng
4-
0
0 L-T( 14.2mT)
.E
??
boundary(28.4mT)
+ L-T(28.4mT)
.
?? , 0
*b o c+@ c+
O_
3 a
QlvMllmWms)l FIGURE 2 Plot of the in-phase QvM” vs the out-of-phase QvM’ components of the HPD signal (top) and the corresponding NMR absorption PM vs Q~vM~0~M (bottom) at 14.2 mT, 11 mT/m, 0.48Tc, and 29.3 bar. Circuit constants are L = 80 uH, Q = 58, Iv01 = 15.7 mV(rms).
PM=a,+anM+asMs
"0
A
a2M
o
a&f3
10
20
VH (mT/m)
FIGURE 3 Division of the NMR absorption into three components according to Eq. l), shown here as a function of VH at 14.2 mT, 0.48 \ c and 29.3 bar. The terms = M and M* are shown with their values when the HPD fills the entire cell.
B
0’ 0.4
0.5
0.6
0.7
0.8
TITc
FIGURE 4 The domain boundary and Leggett-Takagi (L-T) components to PM as a function of temperature measured at 10 mT/m and 29.3 bar, in two different fields 14.2 and 28.4 mT.
(1)
where the first constant term corresponds to relaxation in the domain boundary, 0~H7/3VH1/3., the second to relaxation at the cylindrical cell wall wrth an area = P, and the third to Le gett-Takagi relaxation in the bulk domain, =@@VH 9. In Fig. 3 the division into these 3 terms is shown as a function of VH. We found no significant linear term. The worst case phase.error, 0.3’, makes 0.008 nW error in the linear term In this case at 14.2 mT. The current setting of the magnet producing the gradient for optimum field homogenerty was found by ad’usting for minimum line width of the conventional Nd R absorption signal in the normal Fermi liquid phase.
0.10 -
2 -
From these results we can determine the spin diffusion constant and the Leggett-Takagi relaxation time (2) and we find no significant surface relaxation. When the measurements of Fig. 3 were repeated at different temperatures and the results were pfotted in normalized form, PM/H*, then Fig. 4 was obtained. Even in the higher field of 28.4 mT we could not find a meaningful contribution from surface relaxation which has been predicted to have the strong field dependence of H4 (5). ACKNOWLEDGEMENTS We wish to thank V.V. Dmitriev and Yu.M. Mukharskiy for useful discussions. This work has been supported through the Award for the Advancement of European Science by the Korber Stiftung. REFERENCES (1) I.A. Fomin, Sov. Phys. JETP 61 (1985) 1207. (2) AS. Borovik-Romanov, YuM. Bunkov, V.V. Dmitriev, and Yu.M. Mukharskiy, Quantum Fluids and Solids 1989, AIP Conf. Proc. 194 (1989) 15. (3) V.V. Dmitriev, Y. Kondo, J.S. Korhonen, M. Krusius, E.B. Sonin, and G.E. Volovik, this volume. (4) J.S.Korhonen, V.V.Dmitriev, Z.Janu, Y.Kondo, M.Krusius, and Yu.M.Mukharskiy, this volume. (5) T. Ohmi, M. Tsubota, and T. Tsuneto, Proc. 18th Internat. Conf. on Low Temp. Phys., Kyoto, Jap. J. Appl. Phys.26 (1987) 169.