High-field spin dynamics of the one-dimensional spin-½ Heisenberg antiferromagnetα−bis(N-methylsalicylaldiminato copper) (II) (α−CuNSal)

Proton spin-lattice relaxation rates in the one-dimensional (1D) spin-½ Heisenberg antiferromagnet $\alpha -\mathrm{bis}$ (N-methylsalicylaldiminato) copper (II), $\alpha -\mathrm{CuNSal}$, have been measured in applied fields up to 125 kOe in the temperature range 1-4 K. The strong coupling of protons close to the antiferromagnetic (AF) chain serves as a convenient probe to study the dynamics of the AF chain through the field-induced antiferromagnetic to ferromagnetic (F) phase transition. The magnetization of the AF chain, as measured by the proton field shift, is in close agreement with calculations by Bonner and Fisher and yields an exchange interaction $\frac{j}{k}=3.04\mathrm{}\pm 0.04$ K. The proton relaxation rate has isotropic (hyperfine coupled) and anisotropic (dipolar) components. We identify the isotropic relaxation rate with a creation or destruction of one-spin excitations (magnons) and the anisotropic rate with two-magnon processes. The measured one-magnon relaxation rate shows an enhancement near the critical field for the AF → F transition and a strong decrease of more than four decades as the critical field is exceeded. A noadjustable-parameter calculation based on the fermion model quantitatively agrees with the measured one-magnon relaxation rate, both above and below the critical field $H_c$. The enhanced relaxation at $H_c$ is correctly predicted as a consequence of the divergence of the 1D density of magnon states, where a gap in the spin-wave spectrum exists. Above $H_c$ a finite magnon life-time must be included in order to produce a nonzero one-magnon relaxation rate. This is also calculated with no adjustable parameters. The two-magnon relaxation rate also shows a decrease as the critical field is exceeded and the calculated relaxation rate agrees well with experiment at low temperatures, provided, however, that one uses a boson rather than fermion picture.