Nonequilibrium dynamical behavior in noncoplanar magnets with chiral spin texture

We observe nonequilibrium dynamical magnetic behavior in the magnetically ordered phase of a Tsai-type Tb-Au-Si quasicrystal approximant system. The magnetic texture in the ordered phase is found to exhibit scalar spin chirality (SSC) order, inferring that SSC is the order parameter of the present magnetic system. We further find that the introduction of “pseudo-Tsai” clusters, associated with additional Tb atoms in the structure, induces spin-glass dynamics. We discuss the observed dynamical magnetic behavior in the Tb-Au-Si systems, considering the effect of the pseudo-Tsai clusters on the magnetic configuration and local spin chirality.

Figure 1

(a) Body-centered periodic arrangement of RE (=Tb) icosahedra (yellow) and pseudo-Tsai RE atoms. The interstitial (distorted) octahedral units named Octa-A (green) and Octa-B (blue) are also presented. (b) The spin configuration on the octahedra of TAS(0) obtained from the previous neutron-scattering experiment [20]. The black and pink arrows (spins) refer to two independent moments RE1_1 and RE1_2, respectively [20]. The SSC is indicated by the red and blue spheres whose size and color represent the absolute value and sign, respectively. (c) A schematic expanded view of the octahedral unit. The sign ($\pm$) indicates the sign of SSC. (d) The spin configuration on the icosahedral unit of TAS(0) with the SSC representations. The green and blue faces are shared with the octahedral units Octa-A and Octa-B, respectively. (e) The periodic arrangement of the octahedral units exhibiting the SSC in the ordered phase of TAS(0). (f) The Hall resistivity of TAS(0) measured below and above the ordering temperature ($T_{\mathrm{m}}\approx 11$ K).

Figure 2

(a) The ZFC (green) and FC (red) magnetization $M$ (plotted as $M/H$) recorded under a magnetic field of $H$ = 10 Oe. (b),(c) The in-phase (${\chi }^{\prime }$) and out-of-phase (${\chi }^{″}$) components of the ac magnetic susceptibility, respectively. The data curves in (a)–(c) are arbitrarily shifted from the origin. The ac susceptibility was recorded using the ac excitation $h$ = 4 Oe at frequencies $f$ = 1.7 (red), 17 (green), and 170 Hz (blue). The data presented for (a)–(c) are from Refs. [15, 20]: note that we remeasured the magnetization for TAS(0) in this study. The schematics in (a) illustrate Tsai-type [TAS(0)] and pseudo-Tsai-type [TAS(14) and TAS(100)] RE clusters. (d)–(f) Time dependence of ${\chi }^{″}$ for (d) TAS(0), (e) TAS(14), and (f) TAS(100) at several temperatures, which was recorded with $h$ = 4 Oe and $f$ = 1.7 Hz.

Figure 3

(a)–(c) The results of the dc memory measurements: $\mathrm{\Delta }M$ vs temperature, where $\mathrm{\Delta }M=M(t_{\mathrm{halt}}\ne 0)-M(t_{\mathrm{halt}}=0)$. (d)–(f) The results of the ac memory measurements: $\mathrm{\Delta }{\chi }^{″}$ vs temperature, where $\mathrm{\Delta }{\chi }^{″}={\chi }^{″}(t_{\mathrm{halt}}\ne 0)-{\chi }^{″}(t_{\mathrm{halt}}=0)$. The inset shows ${\chi }^{″}$ vs temperature for the aging (in the cooling process) and memory (in the warming process) measurements at $T_{\mathrm{halt}}$. Note that the reference curves $\left[{\chi }^{″}(t_{\mathrm{halt}}=0)\right]$ are obtained both in the cooling process (for the reference of the aging curve) and the warming process (for the reference of the memory curve).