Spin freezing in the spin-liquid compound ${\mathrm{FeAl}}_2{\mathrm{O}}_4$

Spin freezing in the $A$-site spinel ${\mathrm{FeAl}}_2{\mathrm{O}}_4$, which is a spin-liquid candidate, is studied using remnant magnetization and nonlinear magnetic susceptibility and isofield cooling and heating protocols. The remnant magnetization behavior of ${\mathrm{FeAl}}_2{\mathrm{O}}_4$ differs significantly from that of a canonical spin glass, which is also supported by analysis of the nonlinear magnetic susceptibility term ${\chi }_3\left(T\right)$. Through the power-law analysis of ${\chi }_3\left(T\right)$, a spin-freezing temperature $T_g=11.4\pm 0.9$ K and critical exponent $\gamma =1.48\pm 0.59$ are obtained. A Cole-Cole analysis of magnetic susceptibility shows the presence of broad spin relaxation times in ${\mathrm{FeAl}}_2{\mathrm{O}}_4$, however, the irreversible dc susceptibility plot discourages an interpretation based on conventional spin-glass features. The magnetization measured using the cooling-and-heating-in-unequal-fields protocol brings more insight into the magnetic nature of this frustrated magnet and reveals unconventional glassy behavior. Combining our results, we arrive at the conclusion that the present sample of ${\mathrm{FeAl}}_2{\mathrm{O}}_4$ consists of a majority spin-liquid phase with “glassy” regions embedded.

Figure 1

The thermoremanent (TRM) and the isothermoremanent (IRM) curves for ${\mathrm{FeAl}}_2{\mathrm{O}}_4$ at 4 K as a function of applied magnetic field. The TRM and IRM responses of ${\mathrm{FeAl}}_2{\mathrm{O}}_4$ are characteristically different from thos of a canonical spin glass or a superparamagnet (see Ref. [14] for a comparison of TRM and IRM curves of different magnetic systems).

Figure 2

(a) The temperature dependence of field-cooled dc magnetization plots of ${\mathrm{FeAl}}_2{\mathrm{O}}_4$ at various applied fields in the range 100 Oe (black open circles, bottom curve) to 50 kOe (black solid circles, top curve). $M$ vs $H$ plots at different temperature values are extracted from these data. (b) Third harmonic of nonlinear susceptibility ${\chi }_3$ along with a power-law fit (solid line) using ${\chi }_3={\chi }_3^0{(T/T_g-1)}^{-\gamma }$.

Figure 3

(a) The nonlinear susceptibilities ${\chi }_{\text{nl}}$ as a function of $H^2$ at different selected temperatures above and below $T_a$ (which is identified as the peak observed in dc magnetization curves in Fig. 2). (b) The scaling plot of the data presented in (a) with $\delta =3.57$ clearly brings out the data collapse conforming to the scaling exponent $\delta$ (see text).

Figure 4

(a)–(d) The Cole-Cole plot (${\chi }^{\prime \prime }\text{−}{\chi }^{\prime }$) at different temperatures below 30 K supports the claim of a broad distribution of relaxation times in ${\mathrm{FeAl}}_2{\mathrm{O}}_4$. The numbers in (a) indicate the applied frequency in Hz. The $x$ axis is offset from zero for clarity. (e) Dependence of ${\chi }^{\prime }$ on frequency. (f) The imaginary part of the magnetic susceptibility ${\chi }^{\prime \prime }$ as a function of frequency along with the theoretical curve according to Eq. (5). (g) The parameter $\alpha$ has a magnitude around 0.8, which indicates a broad relaxation.

Figure 5

The “irreversible” dc susceptibility $\Delta M/H$ of ${\mathrm{FeAl}}_2{\mathrm{O}}_4$ where $\Delta M=(M_{\text{FC}}-M_{\text{ZFC}})$. The irreversibility temperature is shown as $T_{\text{irr}}$ and is indicated by arrows. The dashed-dotted lines are guides to the eye.

Figure 6

(a), (b) Magnetization as a function of temperature using the protocol of CHUF1: The sample was cooled in a constant field of (a) $H_c=50$ kOe or (b) $H_c=10$ kOe and the magnetization is measured while warming in various applied fields $H_w$, as marked in the figure. (c) The magnetic response under the protocol of CHUF2: The sample was cooled in different applied fields $H_c$ while the magnetization was measured in a constant field $H_w=10$ kOe. (d) A field-cooled magnetization measurement in cooling and warming cycles does not give evidence for any thermal hysteresis.