Indirect Coupling of Nuclear Spins in Antiferromagnet with Particular Reference to MnF 2 at Very Low Temperatures

Abstract

Indirect coupling of nuclear spins through hyperfine interaction with spin waves is discussed in the case of antiferromagn.et at very low temperatures. The line width of the p19 nuClear magnetic resonance in MnF2 at 1;4° Kobserved by Shulman and Jaccarino (-14oe) proves to come·mainlY from this coupling. The line width of the Mn 55 resonance in MnF~ is also evaluated to be about 600 oe •.... § 1. Introduction During the past few years, observations of ·the nuclear mllgnetic resonance of non-magnetic ions in paramagnetic iron group fluorides have been reported,1),2),S) and very recently, Shulman and Jaccarin0 4) observed the p19 nuclear magnetic resonance in the antiferro-magnetic state of MnP\!. According to their preliminary report, the resonance at 1.4 OK is Gaussian in shape with a width of.-14 oe. This width is too large to be explained from the nuclear dipole interaction, whose contribution is only 6 oe*) in the presence of the m~netic field along the c-axis. As was shown by Moriya 5) and Kranendonk. and Bloom 6), the spin lattice relaxation time T1 becomes longer and longer with decreasing temperature. In actuality, Shulman and Jaccarino found Tl to be about 20 sec at 4.2°K. In such a temperature region, the thermal motion of the electron m~net is therefore no longer effective for the width of the nuclear spin resonance. Thus, we are compelled to consider an indirect coupling of nuclear spins through hyper:fine interaction. to account for the line width mentioned above. The physical meaning of this indirect coupling is the following: a nuclear m~net polarizes the electron spin component transverse to the direction of the sublattice m~netization through hyper:fine interaction and another nuclear magnet sees this polarization of the electron m~net again through hyper:fine interaction. In the l~e of spin waves, this process can be stated in the way that the· first nucleus virtually excites a spin wave and the second nucleus absorbs it, both through hyper:fine interaction. In this way, the two * Though Shulman and Jaccarino write that the observed width can be explained by the nuclear dipole interaction, it appears that they committed computational errors. 542 Indirect coupling of nuclear spins through hyperfine interaction with spin waves is discussed in the case of antiferromagn.et at very low temperatures. The line width of the p19 nuClear magnetic resonance in MnF2 at 1;4° Kobserved by Shulman and Jaccarino (-14oe) proves to come·mainlY from this coupling. The line width of the Mn 55 resonance in MnF~ is also evaluated to be about 600 oe •.... § 1. Introduction During the past few years, observations of ·the nuclear mllgnetic resonance of non-magnetic ions in paramagnetic iron group fluorides have been reported,1),2),S) and very recently, Shulman and Jaccarin0 4) observed the p19 nuclear magnetic resonance in the antiferro-magnetic state of MnP\!. According to their preliminary report, the resonance at 1.4 OK is Gaussian in shape with a width of.-14 oe. This width is too large to be explained from the nuclear dipole interaction, whose contribution is only 6 oe*) in the presence of the m~netic field along the c-axis. As was shown by Moriya 5) and Kranendonk. and Bloom 6), the spin lattice relaxation time T1 becomes longer and longer with decreasing temperature. In actuality, Shulman and Jaccarino found Tl to be about 20 sec at 4.2°K. In such a temperature region, the thermal motion of the electron m~net is therefore no longer effective for the width of the nuclear spin resonance. Thus, we are compelled to consider an indirect coupling of nuclear spins through hyper:fine interaction. to account for the line width mentioned above. The physical meaning of this indirect coupling is the following: a nuclear m~net polarizes the electron spin component transverse to the direction of the sublattice m~netization through hyper:fine interaction and another nuclear magnet sees this polarization of the electron m~net again through hyper:fine interaction. In the l~e of spin waves, this process can be stated in the way that the· first nucleus virtually excites a spin wave and the second nucleus absorbs it, both through hyper:fine interaction. In this way, the two * Though Shulman and Jaccarino write that the observed width can be explained by the nuclear dipole interaction, it appears that they committed computational errors.