NMR study on the stability of the magnetic ground state in MnCr2{}_2O4{}_4

The canting angles and fluctuation of the magnetic ion spins of spinel oxide MnCr${}_2$O${}_4$ were studied by nuclear magnetic resonance (NMR) at low temperatures, which has a collinear ferrimagnetic order below $T_C$ and a ferrimagnetic spiral order below $T_s < T_C$. Contrary to previous reports, only one spin canting angle of Cr ions was observed. The spin canting angles of Mn and Cr ions in the ferrimagnetic spiral obtained at a liquid-He temperature were 43\,^{\circ} and 110\,^{\circ}, respectively. The nuclear spin-spin relaxation was determined by the Suhl-Nakamura interaction at low temperatures but the relaxation rate $T_2^{-1}$ increases rapidly as the temperature approaches $T_s$. This indicates that the fluctuation of the spiral component becomes faster as the temperature increases but not fast enough to leave an averaged hyperfine field to nuclei in the time scale of nuclear spin precession in the ferrimagnetic phase, which is on the order of $10^{-8}$ s. The spiral volume fraction measured for various temperatures reveals that the collinear and the spiral ferrimagnetic phases are mixed below the transition temperature of the spiral order. The temperature hysteresis in the volume fraction implies that this transition has first-order characteristics.Comment: 13 pages, 5 figure

Storing unitary operators in quantum states

We present a scheme to store unitary operators with self-inverse generators in quantum states and a general circuit to retrieve them with definite success probability. The continuous variable of the operator is stored in a single-qubit state and the information about the kind of the operator is stored in classical states with finite dimension. The probability of successful retrieval is always 1/2 irrespective of the kind of the operator, which is proved to be maximum. In case of failure, the result can be corrected with additional quantum states. The retrieving circuit is almost as simple as that which handles only the single-qubit rotations and CNOT as the basic operations. An interactive way to transfer quantum dynamics, that is, to distribute naturally copy-protected programs for quantum computers is also presented using this scheme.Comment: 4 pages, 3 figures, errors in Eq. (8) and Fig. 3 are fixed, to appear in Phys. Rev.