Irreducible half-integer rank unit spherical tensors

A new class of half-integer rank spherical tensors is introduced. The motivation for investigating this new class of tensors originated from a desire to be able to partition matrices using mixtures of fictitious integer and half-integer spin labels. However, it is shown that they can also be used as annihilation/creation operators for spin-1/2, 3/2, etc., particles. In particular, half-integer rank tensors can be used to add/subtract a spin-1/2 particle from a given ensemble. Thus they can be viewed as the natural generalization of the raising and lowering operatorsI _±, in that they change bothI andM, simultaneously.The concept of a universal rotator is introduced and it is demonstrated that half-integer rank tensors obey the same contractional and rotational properties as their integer counterparts, but with half-integer rank. In addition, it is shown that half-integer rank tensors can be used to factorize the Pauli spin matrices. Finally, an example of the use of half-integer rank tensors in the block-diagonalization of a simple 3 x 3 matrix is presented and discussed.     

A low temperature study of antiferromagnetic YbVO4 by NMR thermally detected by nuclear orientation

NMR-TDNO results using an external ⁶⁰CoCo (hcp) nuclear orientation thermometer for non-irradiated, single crystal, antiferromagnetic YbVO₄ are compared with those obtained earlier with neutron activated samples using both internal and external γ-ray thermometers. Detailed comparisons are made for the ¹⁷¹Yb (I=1/2, 14.31% abundant) stable nucleus. This strongly asymmetric, largely homogeneous, resonance lineshape was retained and is readily power broadened. Extremely broad, field-dependent homogeneous thermometric responses are observed in the expected frequency range for the quadrupolar stable nucleus ¹⁷³Yb (I=5/2, 16.13% abundant) for both irradiated and non-irradiated samples. This revised version was published online in August 2006 with corrections to the Cover Date.     

Temperature Dependence of the Proton Overhauser DNP Enhancements on Aqueous Solutions of Fremy’s Salt Measured in a Magnetic Field of 9.2?T

The temperature dependence of the water-proton dynamic nuclear polarization (DNP) enhancement from Fremy’s salt nitroxide radicals was measured in a magnetic field of 9.2?T (corresponding to 260?GHz microwave (MW) and 392?MHz NMR frequencies) in the temperature range of 15–65?°C. The temperature could be determined directly from the proton NMR line shift of the sample. Very high DNP enhancements of ?38 (signal integral) or ?81 (peak intensity) could be achieved with a high-power gyrotron MW source. The experimental findings are compared with classical Overhauser theory for liquids, which is based on the translational and rotational motion of the molecules and with molecular dynamics calculations of the coupling factor.     

Coherent spectral enhancement of carrier-envelope-phase stable continua with dual-gas high harmonic generation

Attosecond science is enabled by the ability to convert femtosecond near-infrared laser light into coherent harmonics in the extreme ultraviolet spectral range. While attosecond sources have been utilized in experiments that have not demanded high intensities, substantially higher photon flux would provide a natural link to the next significant experimental breakthrough. Numerical simulations of dual-gas high harmonic generation indicate that the output in the cutoff spectral region can be selectively enhanced without disturbing the single-atom gating mechanism. Here, we summarize the results of these simulations and present first experimental findings to support these predictions.     

Some analytical results forABC,ABCD, andXBCD coupled spin 1/2 systems. II

In the preceding paper, it was shown that the calculation of the density matrix(t) for multiply connectedABC, etc., spin 1/2 spin systems can be greatly simplified by subdividing the Hamiltonian into , where is a suitable linear combination of the constants of the motion. In this paper, a framework for the determination of the time evolution of high-order multipolar quantum states is presented and discussed. It is shown that the necessary mathematical labour is reduced to a minimum by (i) exploiting the fact that is a good quantum number, and (ii) using the theory of partitioned matrices. For example, it is shown that for a generaln-coupled spin 1/2 system, the spin dynamics of the multipolar states, whereK _max is the maximum tensorial rank, can be determined without the need to diagonalize the full 2 ⁿ × 2 ⁿ Hamiltonian matrix, wheren is the number of spins. In fact, to describe the time evolution of the multipolar states it is only necessary to diagonalize twon ×n matrices at most. Finally, some cautionary remarks are made concerning the use of the weak-coupling approximation.     

NMRON studies of MnBr2 \cdot 4H2O in applied magnetic fields

NMRON studies for the ⁵⁴Mn transitions in antiferromagnetic MnBr₂ 4H₂O, in the millikelvin regime, are presented and discussed. New values are given for (i) the sum of the effective molecular exchange and magnetic anisotropy fields acting on the Mn²⁺ ions, =2.23(2) T, and (ii) the magnetic dipole hyperfine splitting, A=-201.99(1) MHz, electric quadrupole hyperfine splitting P=0.049(8) MHz and pseudoquadrupole splitting =1.63(2) MHz for the ⁵⁴Mn nuclei.     

Analytical block-diagonalization of matrices using unit spherical tensors

A new method for block-diagonalizing large Hamiltonian matrices, in closed form, is described. The method is based on (i) a general unitary transformation due to Slichter, and (ii) Fano's unit spherical operatorsÛ _Q ^K (I _i,I _i). The method is illustrated with a simple three spin 1/2 dipolar coupled spin system, characterized by off-block-diagonal unit spherical tensorsÛ ₀ ² (3/2,1/2,) andÛ ₀ ² (3/2,1 /2,). In addition, it is pointed out that any Hamiltonian matrix can be re-labelled in terms of fictitious spin labels, enabling a wide variety of unit spherical tensors to be used in block-diagonalization. For example, a single spin 5/2 matrix can be re-labelled using three spin labels 1/2, 1/2, and 1/2, respectively. Thus the tensor algebra required to block-diagonalize a 6 x 6 matrix is determined solely by the properties of the Pauli spin matrices. Finally, it is shown that re-labelling within the unit spherical tensor framework provides a unifying framework for standard basis operators, fictitious spin 1/2 and 1 operators, and others. The fictitious spin 1 / 2 unit spherical operators discussed in this paper differ from those of Vega and Pines.     

Noncollinear magnetic hyperfine fields in the Ag spacers of Fe/Ag multilayers

Nearly perpendicular magnetic hyperfine fields have been observed for the first time in the Ag "spacers" of Fe/Ag multilayers using low temperature nuclear orientation of (110)Ag(m) at 6 mK. At the same time, vibrating sample magnetometry measurements at temperatures down to 4 K have shown the magnetic anisotropy of the Fe to be in plane. The direction of the Ag hyperfine field is thus noncollinear (nearly orthogonal) to the Fe anisotropy. These results are compared with full potential linearized augmented plane wave calculations using the wien97 code.