Ballistic Magnon Transport and Phonon Scattering in the Antiferromagnet ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$

The thermal conductivity of the antiferromagnet ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$ was measured down to 50 mK. Using the spin-flop transition to switch on and off the acoustic Nd magnons, we can reliably separate the magnon and phonon contributions to heat transport. We find that magnons travel ballistically below 0.5 K, with a thermal conductivity growing as $T^3$, from which we extract their velocity. We show that the rate of scattering of acoustic magnons by phonons grows as $T^3$, and the scattering of phonons by magnons peaks at twice the average Nd magnon frequency.

Figure 1

Temperature dependence of the in-plane thermal conductivity $\kappa$ of ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$, in zero magnetic field (circles: $H=0$) and in a field of 10 T applied either in the basal plane (triangles: $H\perp c$) or along the $c$ axis (squares: $H\parallel c$). Inset: Enlargement below 1 K.

Figure 2

Top: Zero-field thermal conductivity $\kappa (0)$ vs $T^{2.6}$. The heat at $H=0$ is carried entirely by phonons: ${\kappa }_p\simeq \kappa (0)$ (see text). The line is a linear fit below 0.4 K. Bottom: The additional thermal conductivity induced by a 10 T in-plane field, $\Delta \kappa =\kappa (10\mathrm{T}\perp c)-\kappa (0)$, plotted as $\Delta \kappa$ vs $T^3$. The line is a linear fit below 0.5 K. The additional heat is carried entirely by acoustic magnons: ${\kappa }_m=\Delta \kappa$ (see text).

Figure 3

Top: Normalized thermal magnetoresistance vs temperature, for $H\parallel c$. This is the field-dependent thermal resistivity of phonons [27]. The arrow indicates the temperature at which magnon scattering is maximum: $T^{*}=3\mathrm{K}$. $T^{*}$ is directly related to the magnon energy $⟨E_{\mathrm{magnon}}⟩$ via the peak phonon frequency, ${\omega }_{\mathrm{phonon}}^{*}$ (see text). Bottom: Difference in thermal conductivity caused by rotating a 10 T field from in plane to $c$ axis, $\Delta {\kappa }^{\prime }=\kappa (10\mathrm{T}\perp c)-\kappa (10\mathrm{T}\parallel c)$, vs temperature. This is the conductivity of magnons. The dotted line is the estimated magnon specific heat (see text) and the solid line is a fit as indicated.