Macroscopic Signature of Protected Spins in a Dense Frustrated Magnet

The inability of systems of interacting objects to satisfy all constraints simultaneously leads to frustration. A particularly important consequence of frustration is the ability to access certain protected parts of a system without disturbing the others. For magnets such “protectorates” have been inferred from theory and from neutron scattering, but their practical consequences have been unclear. We show that a magnetic analogue of optical hole-burning can address these protected spin clusters in a well-known, geometrically frustrated Heisenberg system, gadolinium gallium garnet. Our measurements additionally provide a resolution of a famous discrepancy between the bulk magnetometry and neutron diffraction results for this magnetic compound.

Figure 1

(a) Spins at vertices of a triangular Ising antiferromagnetic (AFM) lattice (labeled “?”) are geometrically frustrated (b) Heisenberg AFM on a Kagome lattice. The “local” degree of freedom corresponds to a collective rotation of the red and blue spins around the black spin. (c) One of the Gd sublattices of GGG, showing the ten-membered ring of spins which can rotate about the black spin direction, forming a local degree of freedom analogous to that in (b). (d)–(f) Schematics of spin triads to understand response of local degrees of freedom to small external fields $h_{\mathrm{ac}}$. The black spin sublattice is assumed to be rigid. (a) and (b) are adapted from [7].

Figure 2

(a) Phase diagram (following 11). Our study focuses on the spin liquid phase with $H<4\mathrm{kG}<6\mathrm{kG}$. The red dashed lines indicate the temperatures along which we have conducted detailed dc ($H$) studies. (b) ${\chi }^{\prime \prime }$, as a function of $T$ and $f$ at $H=0$ in the linear regime. (c) $H$ dependence of ${\chi }^{\prime \prime }$. The low $f$ plateau in ${\chi }^{\prime \prime }(f)$ connected to spin ordering at 0.100 K disappears rapidly with the application of $H$.

Figure 3

(a)–(d) Real ($M^{\prime }$, black, left axis) and imaginary ($M^{\prime \prime }$, red, right axis) parts of the magnetization as a function of $h_{\mathrm{ac}}$ at different $T$ for $f=29.9\mathrm{Hz}$. (e) The $T$ dependence of $d{M}^{\prime }/d{h}_{\mathrm{ac}}$ at low ($h_{\mathrm{ac}}=0.04\mathrm{G}$) and high ($h_{\mathrm{ac}}=1.4\mathrm{G}$) drive fields. The line (blue, with solid circles) corresponds to the Curie-Weiss law representing the extrapolated high-temperature susceptibility dominated by the frustrated units of GGG. (f) The analogous plot for $M^{\prime \prime }$. (g) The spectral width of the hole in the susceptibility as a function of temperature. All lines are guides to the eye.

Figure 4

(a)–(c) ${\chi }^{\prime \prime }$ as a function of $f$ at different $T$ bracketing the ordering temperature in the linear (black) and nonlinear (blue) regimes. The nonlinear susceptibility is measured with a pump-probe combination. $f_{\mathrm{pump}}=29.9\mathrm{Hz}$ (blue arrow). (d) The holes in (a)–(c) magnified, sharpest at ordering. (e) Hole-burning at 0.100 K at nonzero $H$. The ability to burn holes disappears by $H=4\mathrm{kG}$ [data shown in the bottom panel of (e) with an added offset for clarity].