Effective Minkowski-to-Euclidean signature change of the magnon BEC pseudo-Goldstone mode in polar <Superscript>3</Superscript>He

We discuss the effective metric experienced by the Nambu–Goldstone mode propagating in the broken symmetry spin-superfluid state of coherent precession of magnetization. This collective mode represents the phonon in the RF driven or pulsed out-of-equilibrium Bose–Einstein condensate (BEC) of optical magnons. We derive the effective BEC free energy and consider the phonon spectrum when the spin superfluid BEC is formed in the anisotropic polar phase of superfluid ³He, experimentally observed in uniaxial aerogel ³He-samples. The coherent precession of magnetization experiences an instability at a critical value of the tilting angle of external magnetic field with respect to the anisotropy axis. From the action of quadratic deviations around equilibrium, this instability is interpreted as a Minkowski-to-Euclidean signature change of the effective phonon metric. We also note the similarity between the magnon BEC in the unstable region and an effective vacuum scalar “ghost” condensate.     

Parametric instability in uniform spin precession in superfluid 3He-B

In order to explain the “catastrophic spin relaxation” observed in superfluid ³He-B, the stability of spatially uniform spin precession in this liquid relative to the parametric excitation of spin waves has been analyzed. It is shown that uniform spin precession becomes unstable at low temperatures (Suhl instability). At zero temperature, the growth increments are determined for all spin wave branches. The temperature at which the transition from stable spin precession to instability takes place is estimated.     

Magnon BEC in superfluid <Superscript>3</Superscript>He-A

The new mode of magnetization precession in superfluid ³He-A in a squeezed aerogel has been recently reported. We consider this mode in terms of the Bose-Einstein condensation (BEC) of magnons. The difference between magnon BEC states in ³He-A and in ³He-B is discussed. The article is published in the original.     

Recent results on hyperpolarized<Superscript>3</Superscript>He−<Superscript>4</Superscript>He liquid mixtures

Laser optical pumping in low magnetic field provides very high nuclear polarizations in gaseous helium mixtures, and is used to prepare polarized liquid. Wall relaxation in glass cells is effiently reduced using cesium coatings, and bulk longitudinal relaxation times are measured. In highly magnetized samples, dipolar fields control the spin dynamics in anisotropic volumes and weak external magnetic field inhomogeneities. Long lived magnetostatic modes are observed by pulsed NMR. Detailed analysis of their frequency and damping gives information on magnetization density and spin diffusion coefficient in polarized mixtures. Experiments are performed above 0.2 K on mixtures with³He concentrations of order a few percents or larger. When phase separation occurs, the³He-rich phase retains a high polarization.     

Study of the two-domain processing structure in the superfluid3He-B

The systematic experimental and theoretical investigation of the longlived induction signal, known to exist in the³He-B, has shown that even very small nonuniformity of a steady magnetic fieldH ₀ changes qualitatively the precession pattern arising in the pulsed NMR experiments after tipping of the magnetization. The spin supercurrents redistribute magnetization within the experimental cell to produce the precessing structure, consisting of two domains. In one-domain, situated in the higher field region, magnetizationM has its equilibrium value and is parallel toH ₀. In the other domain the angle betweenM andH ₀ is slightly larger than? ₀=arc cos (?1/4). The structure precesses with frequency, equal to the Larmor frequency at the site of the wall, separating the domains. The relaxation of this structure goes via the growth of the equilibrium domain at the expense of the precessing domain; therefore in the course of the relaxation the frequency of the precession has to decrease with time. The calculated rate decrease agrees with the observed value. Experiments were carried out directly demonstrating the existence of the two-domain structure. After the formation of the two-domain structure, as well as after a perturbation of the structure by short r.f. pulses, low frequency (≈200 Hz) modulation of the induction signal is observed due to vibration of the structure. These vibrations are the standing spin waves in the precessing domain, their frequency being proportional to the size of the domain. The observed dependence of the frequency on other parameters is in agreement with theoretical calculations. The analysis of the data on the vibration and relaxation of the two-domain structure enables us to find the spin wave velocity and the spin diffusion coefficient in³He-B. Further investigation of the two-domain structure enables the study of spin supercurrents in³He-B.     

Nonlinear NMR in a superfluid B phase of <Superscript>3</Superscript>He in aerogel

The properties of liquid ³He in a low-density aerogel preliminarily covered with a few monolayers of ⁴He were studied by pulsed and nonlinear CW NMR techniques. It was found that an NMR frequency shift from the Larmor value exhibits a sharp increase at a magnetization tilting angle exceeding 104°. Nonlinear CW NMR signals related to the formation of a macroscopic region featuring homogeneous precession of the magnetization (homogeneous precession domain) were observed. The experimental results confirm that the low-temperature superfluid ³He phase in the aerogel is analogous to the B-phase in bulk ³He and indicate that the spin supercurrents play an important role in the spin dynamics of superfluid ³He in aerogel.     

Low-temperature stability limit of the coherent spin precession in <Superscript>3</Superscript>He-B

It has been shown that the instability of uniform spin precession in the bulk of the ³He-B superfluid phase is due to the joint action of the anisotropy of the velocities of spin waves and dipole interaction. In the leading approximation in the ratio of the Leggett frequency to the Larmor frequency, the growth increments of the amplitudes of spin waves for all of the possible decay channels have been found. The maximum increment has been determined for all of the angles of spin deviation from the equilibrium orientation. The minimum temperature to which precession is stable has been estimated.     

Free precession and transverse relaxation of hyperpolarized <Superscript>129</Superscript>Xe gas detected by SQUIDs in ultra-low magnetic fields

We studied the free precession of the nuclear magnetization of hyperpolarized ¹²⁹Xe gas in external magnetic fields as low as B₀ = 4.5 nT, using SQUIDs as magnetic flux detectors. The transverse relaxation was mainly caused by the restricted diffusion of ¹²⁹Xe in the presence of ambient magnetic field gradients. Its pressure dependence was measured in the range from 30 mbar to 850 mbar and compared quantitatively to theory. Motional narrowing was observed at low pressure, yielding transverse relaxation times of up to 8000 s.     

Spin dynamics of superfluid<Superscript>3</Superscript>He in non-hydrodynamic regime

We review recent results of experimental and theoretical studies of superfluid³He spin dynamics at ultra low temperature, where density of the normal component is virtually zero. We describe a number of new phenomena: catastrophic relaxation, NMR in the Landau field, surface instability of homogeneous precession, persistent NMR signal etc. We propose that superfluid³He in the ultralow temperature limit may provide a system for the experimental modelling of nonequilibrium quantum field theories.     

New non-Goldstone collective mode of BEC of magnons in superfluid 3He-B

Bose-Einstein condensation of magnons in superfluid 3He-B is experimentally manifested by various states where coherent spin precession is established spontaneously, even in nonhomogeneous magnetic fields. Once such a condensate with coherent spin precession is created, it occupies the state with minimal energy, the ground state. The application of an additional magnetic field to that condensate may cause its deflection from the energy minimum and the condensate responds by creating collective gapless oscillations known as Goldstone modes. This Letter reports the experimental observation of a new (non-)Goldstone mode, which can be viewed as an additional NMR mode of condensed magnons in a rotating frame of reference.     

The <Superscript>55</Superscript>Mn Spin Echo Test of Magnon BEC State in MnCO<Subscript>3</Subscript>

The coherent quantum state of magnons—Bose–Einstein condensate (BEC) has been observed in several types of antiferromagnets. According to the Bose statistics of magnons, BEC appears when the magnon density exceeds the critical density N _BEC and the magnon gas condenses to a quantum liquid. The BEC state is characterized by a coherent precession of the magnetization. In this paper, the first experiments showing the suppression of the spin echo signal by the magnon BEC is presented. These experiments confirm the coherence of magnetic excitations in the BEC state.     

Ultrasensitive 3He magnetometer for measurements of high magnetic fields

We describe a ³He magnetometer capable to measure high magnetic fields (B> 0.1 T) with a relative accuracy of better than 10^-12. Our approach is based on the measurement of the free induction decay of gaseous, nuclear spin polarized ³He following a resonant radio frequency pulse excitation. The measurement sensitivity can be attributed to the long coherent spin precession time T₂ ^? being of order minutes which is achieved for spherical sample cells in the regime of “motional narrowing” where the disturbing influence of field inhomogeneities is strongly suppressed. The ³He gas is spin polarized in situ using a new, non-standard variant of the metastability exchange optical pumping. We show that miniaturization helps to increase T₂ ^? further and that the measurement sensitivity is not significantly affected by temporal field fluctuations of order 10^-4.     

Nonlinear dynamics of semiclassical spin in a time-dependent magnetic field

The dynamics of magnetic nanoclusters (or molecules) with a large spin in a magnetic field whose strength varies in proportion to time is analyzed. Such a field breaks the symmetry relative to rotations through 2π, as well as clockwise and counterclockwise rotations, and induces a number of new coherent quantum effects in the spin dynamics, such as the formation of a band energy spectrum with continuous spin states or the emergence of “Bloch” oscillations in spin precession and interband Zener tunneling. Bloch oscillations are manifested in experiment as equidistant identical jumps on the magnetization curve. The interband Zener tunneling gives rise to additional jumps and peaks on the susceptibility of the system.     

On the problem of catastrophic relaxation in superfluid 3He-B

In this Letter, we discuss the parametric instability of the texture of homogeneous (in time) spin precession and explain how the spatial inhomogeneity of the texture may change the threshold of the instability in comparison with the idealized spatial homogeneous case considered in our JETP Letter 83, 530 (2006). This discussion is inspired by the critical comment of I.A. Fomin (JETP Lett., this issue) related to the above questions. In addition, we considered here the results of direct numerical solution of the full Leggett-Takagi equation of motion for magnetization in ³He-B and experimental data for the magnetic field dependence of the catastrophic relaxation that provide solid support for the theory of this phenomenon presented in our 2006 JETP Letter. The text was submitted by the authors in English.     

Magnetic relaxation of 3He-B after a large tipping pulse

A time dependent precession frequency is observed in ³He-B after a large tipping pulse (>104°) in transverse NMR. Relating the frequency to the tipping angle reveals the time dependence of the longitudinal magnetization. A fit of Fomin's theory to the data yields the Leggett-Takagi collision time at various temperatures.     

Stabilization of homogeneously precessing domains by large magnetic fields in superfluid 3He-B

We have studied the catastrophic relaxation in superfluid 3He-B as a function of magnetic field for a sample pressure of 31 bars. "Catastrophic relaxation" refers to a novel magnetic relaxation process which rapidly disrupts the homogeneous precession of nuclear spins in NMR experiments on the B phase. The catastrophe was observed through its effect on the evolution of a long-lived coherent dynamic state, the homogeneously precessing domain. Our measurements reveal that the onset of catastrophic relaxation is suppressed to lower temperatures by a strong magnetic field.     

Biased quasiballistic spin torque magnetization reversal

We explore the ultrafast limit of spin torque magnetization reversal time. Spin torque precession during a spin torque current pulse and free magnetization ringing after the pulse is detected by time-resolved magnetotransport. Adapting the duration of the pulse to the precession period allows coherent control of the final orientation of the magnetization. In the presence of a hard axis bias field, we find optimum quasiballistic spin torque magnetization reversal by a single precessional turn directly from the initial to the reversed equilibrium state.     

Observation of fractional harmonics in the NMR signal from superfluid 3He-B

Unusual spin-precession states of ³He-B in which the magnetization is half the equilibrium value are investigated by continuous-wave NMR methods. Signals at frequencies equal to 1/2 and 3/2 of the magnetization precession frequency are observed in two such states. Such signals exist because the order parameter of superfluid ³He in these states precesses with frequency equal to half the magnetization precession frequency. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 200–205 (10 February 1999)     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

<Superscript>53</Superscript>Cr NMR study of CuCrO<Subscript>2</Subscript> multiferroic

The magnetically ordered phase of the CuCrO₂ single crystal has been studied by the nuclear magnetic resonance (NMR) method on ⁵³Cr nuclei in the absence of an external magnetic field. The ⁵³Cr NMR spectrum is observed in the frequency range ν_res = 61–66 MHz. The shape of the spectrum depends on the delay tdel between pulses in the pulse sequence τ_π/2–t _del–τ_π–t _del–echo. The spin–spin and spin–lattice relaxation times have been measured. Components of the electric field gradient, hyperfine fields, and the magnetic moment on chromium atoms have been estimated.