Spin dynamics of superfluid3He-B in a slab geometry

The spin dynamics and the spin relaxation mechanisms of the superfluid³He-B were studied by using the NMR method in a slab geometry, where the superfluid3He-B was confined between narrow parallel plates with a gap smaller than the healing length of then-texture and the magnetic field was applied parallel to the plates. The relaxation parameter in the Leggett-Takagi (LT) equations was determined from a line width measurement of the transverse CW NMR. By using the pulsed NMR method, spin dynamics were studied in the nonlinear region. The observed spin dynamics were in good agreement with a numerical calculation of the LT equations together with the relaxation parameter determined by the CW NMR. When the tipping angle became larger than a certain critical value, the superfluid³He-B entered the Brinkman-Smith (BS) state. In this case, we observed the slow relaxation process in the BS state and then the rapid recovery process from the BS state to the initial non-Leggett configuration. The slow process in the BS state was attributed to the surface relaxation mechanism due to the torque from the surface-field energy.     

Theory of the Anomalous Nuclear Spin Relaxation in U2D2 Solid 3He

In pulsed NMR experiments on U2D2 solid ³ He it has been observed that in some cases free induction signals decay very quickly. It was also found that in such cases a large negative frequency shift from the Larmor frequency appears. We investigated the mechanism of this anomalous nuclear spin relaxation theoretically, using the Holstein-Primakoff method for the Hamiltonian including dipole and exchange interaction. It is shown that the Suhl Instability which had been observed only in the electron spin systems occurs also in the nuclear spin systems and these observed behaviors are attributed to the instability of the uniform precession of magnetization due to the excitation of spin waves.     

Transport experiments on dilute,spin-polarized Fermi fluids

A series of experiments has been carried out on very dilute³He-⁴He mixtures and on pure³He liquid at very high field/temperature ratios (H8 T, T4.3mK). In this regime these systems display a strong Leggett-Rice effect, weakly damped paramagnetic spin waves, and significant polarization effects on spin and momentum transport. The dilute mixture experiments used NMR to observe standing spin waves, and vibrating-wire viscometry to measure momentum transport. A very satisfactory agreement is found with the recent kinetic-equation calculations of Jeon and Mullin. The pure³He experiments may provide the first evidence for field-induced relaxation of transverse spin currents.     

NQR on Gallium Single Crystals for Absolute Thermometry at Very Low Temperatures

It is shown that NMR/NQR-thermometry on Ga single crystals can serve the need of absolute thermometry in a temperature range from below 20 K to above 1 mK. Thus, the sensitive range includes all phase transition temperatures around 1 mK of solid and fluid ³ He, a necessity for an extension of the ³ He-melting-pressure temperature scale towards lower temperatures. The experiments were performed in magnetic fields of 50 to 200 mT and at temperatures down to 200 K using single rf-pulses. Special care was taken for the orientation of the magnetic field with respect to crystal orientation which was obtained by in-situ pulsed NMR-experiments. It has been shown that in the investigated parameter range nonlinear effects in NMR due to high spin alignment had no significant influence. In pulsed NMR as well as in specific heat experiments it could be shown that spin-spin interactions are only weak in Ga and do not influence nuclear paramagnetism, at least at temperatures above 100 K. The advantages of using Ga instead other elements for population difference thermometry are discussed.     

Persistent Signal; Coherent NMR state trapped by orbital texture

No Heading The so-called persistent NMR signal, that was found in superfluid ³He-B at very low temperature corresponds to new states of coherent spin precession. They are distinct from the previously known homogeneously precessing domain (HPD), whose stability is supported by the specific profile of the spin-orbital potential. The new states are stabilized by the orbital texture which provides the required feedback mechanism supporting the precession with a single frequency. New precessing states are obtained by pumping the energy into the spin wave modes localized in the potential well formed by the orbital texture. When the intensity of a given spin wave increases, it influences the orbital degrees of freedom. As a result the potential well is modified and hence modifies the eigen-frequency of the spin-wave mode, which in turn affects the orbital texture. The frequency of this self-consistent precessing state thus depends on the longitudinal magnetization, (S_z). If d(S_z)/dS_z < 0 this coherent mode spontaneously arises in pulsed NMR and persists with a continuous drift of the frequency. This state of magnetic superfluidity is similar to the Bose condensate formed the ground state of the potential well, in the case when the well self-consistently depends on the population of the condensate.PACS number: 67.57.Lm     

Collisionless spin waves in normal and superfluid3He

Standing spin-wave modes in liquid³He have been studied by cw NMR at Larmor frequencies of 1, 2, and 4 MHz and pressures of 0, 6.3, and 12.3 bar. The spin waves, which produce peaks in the NMR line, are visible at temperatures below 5 mK at zero pressure. With the assumption of a slightly simplified sample shape and no transverse spin relaxation at the walls, the theory of Leggett fits the spin-wave frequencies in the normal liquid very well, giving a value of the Fermi liquid parameterF ₁ ^a =–0.6±0.2 at zero pressure. The width of some of the peaks is larger than expected from other determinations of the quasiparticle diffusion time _D . This could be due to wall relaxation or to deviations from the assumed sample geometry. In the superfluid A₁ and A phases, where the data cannot be fitted to existing theories, the spin-wave modes are shifted in frequency and suffer additional damping as the temperature is decreased. At still lower temperatures in the B phase an inversion of the spin-wave spectrum from one side of the NMR line to the other is observed, agreeing quantitatively with the predictions of the 1975 theory of Combescot.     

Pulsed NMR study in nuclear ordered solid3He

The nuclear spin dynamics in nuclear spin ordered solid³He in low magnetic fields on the melting curve has been studied by pulsed NMR down to 0.6 mK. The free induction decay signals (FID) were measured in single crystals of solid³He at three operating frequencies of 920, 1380, and 1840 kHz. The FIDs were nonexponential and dependent on the rf pulse strength _p H ₁ t _w , where is the gyromagnetic ratio,H ₁ is the rf field strength, andt _w is the pulse width. At small _p they decayed almost linearly in time with a small exponential tail at the end. When _p was further increased they became shorter and neither exponential nor linear in time. At large _p they decayed very rapidly and sometimes could not be observed at all because of the dead time of the NMR detection system. Such behavior of the FID was observed in many different single crystals in the given temperature range at 920 kHz. Tsubota and Tsuneto have shown by solving the nonlinear equations of motion numerically that the motion of the nuclear spin becomes chaotic when the tipping angle exceeds a critical value. Comparing their result with our experimental results, we concluded that some of the results of the rapid decay of the FID at large _p might be attributed to the onset of the chaotic motion. At 1840 kHz it is expected that the nonlinear effects in the equations of motion become less effective than that at 920 kHz. In fact, at this operating frequency the FIDs even at large _p and the tipping angle-dependent frequency shift could be observed. These frequency shifts were in rather good agreement with Namaizawa's theory provided an effective tipping angle was taken into account.     

An attractor regime for pulsed NMR in3He-B

We have found a new long-lived mode that can be generated in the regime of pulsed NMR in³He-B. The mode has a frequency different from both the Larmor one and that which was generated in the experiment of Corruccini and Osheroff by rf pulses longer than 104°. It does not correspond to stationary solutions of the Leggett-Takagi equations. The mode is due to the existence of an attractor that is a result of an interplay between nonlinear and dissipative effects in the spin dynamics of superfluid³He-B.     

Textures of Rotating Superfluid 3He–A in a Single Narrow Cylinder

We have studied textures of the rotating superfluid ³He–A in a single narrow cylinder by NMR measurement. In a narrow cylinder, the characteristic textures such as Mermin-Ho texture (Mermin and Ho in Phys. Rev. Lett. 36:594, 1976) can be formed in order to minimize the free energy of the system determined by the effect of the wall, the magnetic field, the dipole interaction, the flow of the superfluid and so on. We observed three types of NMR absorption spectra dependent on the processes used to form A-phase in a narrow cylinder. A particular texture shows a characteristic spectrum and we can determine the texture from the observed spectrum by comparing the resonance frequency of the peak in NMR spectrum with the calculated one of the spin wave mode. We present the identification and the phase diagram of textures of the rotating superfluid ³He–A in a single narrow cylinder.     

Evidence for nonsingular vorticity in the Helsinki experiments on rotating3He-A

A theory for the satellite peak in the NMR spectrum of rotating superfluid³He-A is presented. Absorption at the frequency of the satellite is produced by spin waves localized on vortex lines. The peak frequency and total intensity of the satellite are calculated for both singular and nonsingular vortices; a comparison with the Helsinki NMR data strongly suggests that nonsingular vorticity was actually observed in the experiments.     

Orientation of the Angular Momentum in Superfluid 3He-A in a Stretched Aerogel

Superfluid ³He-A in a fully characterized stretched aerogel, used in previous work by Pollanen et al., has been studied for parallel and perpendicular orientations of the magnetic field relative to the anisotropy axis of the aerogel. Consistently, we find that an equal spin pairing state (ESP) is stabilized down to the lowest temperature. From our pulsed NMR frequency shifts as a function of temperature and tip angle, the orientation of the orbital angular momentum $\hat{l}$ has been determined. The aerogel anisotropy introduced by uniaxial stretching tends to align $\hat{l}$ in the axial state parallel to the strain axis, consistent with the theory proposed by Sauls and contrary to Volovik’s prediction based on an impurity calculation of Rainer and Vuorio.     

Textural singularities in superfluid3He-B

The absorption signal occasionally found missing in the middle of resonance absorption lines in NMR is explained on the basis of a textural singularity of the anisotropy axis in the B phase of ³ He. The singularity combines with the field gradient present to give rise to an asymmetric hole in the signal with a singularity on the high-frequency side. The line shapes and temperature dependence are predicted and agree well with experiment. Spin waves are found to be trapped by the potential well formed by the texture and the field gradient. The frequency intervals predicted for the spin waves also agree well with experiment.Work supported in part by National Science Foundation Grant No. NSF DMR 74-18030.     

Systemic Study of Orbital and Spin Nematicity in NaFe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>As by NMR

Nematic order, a self-organized state with rotational symmetry broken, has been observed in both copper-oxide and iron-pnictide high temperature superconductors. However, its origin is still a mystery in the iron pnictides although it is considered as a key to understand the mechanism of superconductivity. Here, we report a systemic nuclear magnetic resonance (NMR) study on NaFe_1?x Co _x As (0 ≤x ≤ 0.042) that an orbital order, accompanied by an instant spin nematicity, occurs at at a temperature T ^? far above structural transition temperature T _s in the tetragonal phase. We show that the observed NMR spectra splitting and its evolution is due to an incommensurate orbital order that sets in below T ^? and becomes commensurate below T _s. We show that the electric field gradient asymmetry parameter is a good measure for the orbital order parameter which undergoes a Landau-like 2nd-order phase transition. We further show that the spin nematicity is well accounted for by the observed orbital order.     

<Superscript>59</Superscript>Co NMR at Pulsed High Magnetic Fields

We report the ⁵⁹Co-NMR observation by spin-echo method at pulsed high magnetic fields up to 48 T. The 22 mm bore-resistive coil magnet with an inductance of 7.59 mH has a total time duration of 50 ms. After discharging the capacitor bank, NMR signals were observed near the maximum field. By repeatedly pulsing the RF sequence around the maximum field, spin echoes at different fields were recorded to give the NMR spectrum.     

Study of surface relaxation mechanism of liquid3He in porous glass by using SQUID NMR

Nuclear spin relaxation of liquid³He in porous glass has been studied. In addition to measurements of the longitudinal spin relaxation timeT ₁ by a usual pulsed SQUID NMR, measurements of the transverse spin relaxation timeT ₂ have been performed by using a newly developed SQUID NMR method to observe a spin echo signal. Temperature and frequency dependences ofT ₁ andT ₂ have been measured. A simple model is proposed which explains the main features of the experimental results.     

Hyperfine enhanced nuclear magnetism of Cs2NaHoCl6

It is known that Ho³⁺ ion in elpasolite compound Cs₂NaHoCl₆, in its electronic ground state, is a ₃ nonmagnetic doublet in a cubic crystal structure at higher temperatures than 0.6 K. A crystal distortion was observed by nuclear magnetic resonance (NMR) and specific heat experiments at lower temperatures. Electronic and nuclear spin ground states in the distorted phase were deduced from our experimental results. Antiferromagnetic state of enhanced nuclear spins of¹⁶⁵Ho in Cs₂NaHoCl₆ was observed following demagnetization cooling. It was studied by magnetic susceptibility, specific heat, and antiferromagnetic resonance measurements. Spin structure and internal field of its state are discussed.     

Analysis of spin wave resonances in3He-4He mixtures

Spin waves have been reported previously in³He-⁴He mixtures using cw-NMR. The spin waves form standing waves in the rf coil used to detect the NMR signal. Only one resonance was observed, corresponding to ak vector of 1 mm^–1. This is in sharp contrast to similar experiments performed on pure³He, where several resonances were seen. An explanation is given of why this occurs and the resonant mode is identified. Furthermore, it is explained why there is an extra width to the resonance for temperatures below 2 mK. This is caused by radiation damping of the resonant mode. The theory is found to be in excellent agreement with the data. Further experiments are suggested, including details of an improved rf coil design, which should lead to information about the quasiparticle interaction.     

Ferromagnetism of 3He Films in Very Low Applied Fields

³ He films on graphite provide a model system for 2D magnetism. At low temperatures, the thermodynamic properties of these films are dominated by exchange interactions. However more subtle interactions such as dipolar coupling and other anisotropies may eventually play a substantial role, especially in small magnetic fields. Our recent experiments use a SQUID system for both pulsed and continuous wave NMR at very low applied fields (B<1mT). The spin polarization can be estimated from both the amplitude and frequency shift. We find that at coverages above 20 atoms/nm ² there is a field independent (zero field) magnetization at finite temperatures. The temperature where this magnetization develops is significantly below J/k where J is the effective exchange energy. Although the apparent ordering occurs over a broad temperature range, there is a trend towards a narrowing of the transition region down to the lowest applied fields. Contrary to recent estimates of exchange parameters which assume a single phase, we find that below 24 atoms/nm ² , only a fraction of the spins contribute to the ferromagnetic behavior. This is more consistent with a mixed phase system in that coverage region.     

Experimental studies of solitons in superfluid 3He-A

Magnetic textures have been created and studied in the A phase of superfluid ³He at several pressures, in magnetic fields from 15 to 20 mT, by intense rf magnetic pulses which invert the magnetization of the fluid. To create this new state we find that the initial large pulse must tip the magnetization by at least 140. In this state the fluid evolves from a condition where the NMR frequency shift -H ₀is smaller than that in the unperturbed superfluid by a factor of 0.54, over a time scale of tens of seconds to a condition where the frequency shift is 0.70 times the unperturbed value. We have studied the fluid's linear response to small-angle sampling pulses as well as the nonlinear response to large-angle pulses. By using two independent NMR coils we have seen this new state move through the fluid; we find that a lower limit on its propagation velocity is around one-half the spin wave velocity. All of our results are generally consistent with the model of solitons in the order parameter proposed by Maki and co-workers.Work supported by the National Science Foundation under Grant No. DMR-7900830.     

NMR experiments on pure3He and3He-4He mixtures in silica aerogel

We have carried out a series of NMR experiments on³He systems filling the pores of silica aerogel with 95% porosity. The systems studied included³He-⁴He mixtures with a wide range of³He concentrations x₃ as well as pure³He. All experiments were conducted in an 8 T field and for temperatures T 6 mK. This resulted in strong spin polarization at the lowest temperatures (up to approximately 80%) for the localized layer observed for a pure³He sample. For pure³He, the magnetic behavior is dominated by the localized spins, which are found to constitute 6% of the sample. The coupled system of localized plus liquid spins displays rapid transverse magnetization relaxation with an anomalous temperature dependence. For intermediate x₃ magnetization measurements provide a preliminary indication of the phase diagram of mixtures filling this porous material. The magnetization is hysteretic over some ranges of x₃.