Manifestations of nuclear anapole moments in solid-state NMR

Abstract

We suggest to use insulating garnets doped by rare earth ions for measurements of nuclear anapole moments. A parity violating shift of the NMR frequency arises due to the combined effect of the lattice crystal field and the anapole moment of the rare-earth nucleus.We show that there are two different observable effects related to frequency: 1) A shift of the NMR frequency in an external electric field applied to the solid. The value of the shift is about ∆ν1 ∼ 10 −5 Hz with E = 10 kV/cm; 2) A splitting of the NMR line into two lines. The second effect is independent of the external electric field. The value of the splitting is about ∆ν2 ∼ 0.5 Hz and it depends on the orientation of the crystal with respect to magnetic field. Both estimates are presented for a magnetic field of about 10 tesla.We also discuss a radiofrequency electric field and a static macroscopic magnetization caused by the nuclear anapole moment.

Theoretical estimates of the anapole magnetizabilities of C4H4X2 cyclic molecules for X=O, S, Se, and Te

“…29 Attestations of nuclear anapole moments in solid-state nuclear magnetic resonance have been discussed. 30 A magnetic field can induce toroidal flow in the electrons of molecules. [31][32][33] In the terminology of Schmid, 26 the anapole moment is an axio-polar vector, which has opposite sign for the two mirror-images forms of a chiral species, and, in principle, it may be used for chiral discrimination of certain species possessing a magnetic-field induced anapole, e.g., dithiins, associated to toroidal electron flow.…”

Possibility for precise Weinberg-angle measurement in centrosymmetric crystals with axis

“…Rescaling the result of Ref. [18], we find the the singleelectron effective Hamiltonian for 4f -electrons:…”

“…The vertical wavy line on the diagram connecting the two electron lines represents the residual Coulomb interaction between electrons; the weak interaction (3) is shown by the cross on the electron line; the dashed line denotes interaction of electron with the external electric field E. This is but one of a number of diagrams responsible for the effect, in order to find the effective interaction (4) one has to evaluate all of the diagrams. A similar atomic calculation has been performed previously in the paper [18] in regard to the interaction of atomic electrons with the nuclear anapole moment. The effective interaction with the anapole moment appears in the third order of perturbation theory as well, and, although it has different kinematical structure, the part involving atomic radial integrals is practically identical to the present case.…”

“…[17]). The other suggestions for fundamental symmetry violation search in solids include proposed search for manifestations of the nuclear anapole moment in garnets [18] (violation of parity), and the search for the nuclear Schiff moment in the ferroelectric lead titanate compound [19] (violation of T and P symmetries).…”

The Search for Parity Violation in Chiral Molecules

“…suggested recently to use insulating garnets doped by rare earth ions to measure PV shifts in the NMR frequency, which arises from the lattice crystal field and the nuclear anapole moment of the rare earth nucleus such as 169 Tm or 141 Pr [113,114]. Moreover, for the nuclear spin-dependent term in Equation 7.3 the Z scaling might not be as favorable as for the spin-independent case [115,116].…”