Evidence for cluster spin glass phase with precursor short-range antiferromagnetic correlations in the $B$-site disordered $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ perovskite

The origin of the spin glass (SG) phase in the well-known multiferroic $\mathrm{Pb}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ compound remains controversial due to the complications introduced by the coexistence of SG and long-range ordered (LRO) antiferromagnetic (AFM) phases. We have addressed this controversy through a comprehensive study on a Pb-free system $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ (CFN) which does not exhibit LRO AFM transition. The SG transition in CFN is confirmed by the appearance of a cusp in the temperature dependence of dc magnetization $M\left(T\right)$ with a SG freezing temperature $T_{\mathrm{f}}\sim 25\mathrm{K}$, and bifurcation of the zero-field-cooled and field-cooled magnetization $M\left(T\right)$ below the irreversibility temperature $T_{\mathrm{irr}}\sim 27\mathrm{K}$. Using ac susceptibility $\left[\chi \left(\omega ,T\right)\right]$ measurements, we show that the spin dynamics follows power/Vogel-Fulcher law-type critical dynamics which diverges at $T_{\mathrm{SG}}\sim 24\mathrm{K}$ with an attempt time ${\tau }_{\mathrm{o}}\sim {10}^{-6}\mathrm{s}$ suggesting cluster spin glass (CSG) behavior. The field dependence of $T_{\mathrm{f}}\left(H\right)$ and $T_{\mathrm{irr}}\left(H\right)$ is shown to follow the de Almeida–Thouless line which separates the ergodic and nonergodic phases in the $H-T$ plane and gives $T_{\mathrm{f}}\left(H=0\right)\sim 25\mathrm{K}$, which is in close agreement with $T_{\mathrm{SG}}$ obtained from $\chi \left(\omega ,T\right)$. The existence of the glassy phase below $T_{\mathrm{SG}}$ is further confirmed by the observation of slow nonexponential decay of thermoremanent magnetization with time, memory and rejuvenation effects, and unidirectional exchange-bias effect in the $M-H$ hysteresis loop of field-cooled samples. The neutron powder-diffraction patterns reveal the absence of any magnetic peak due to LRO AFM phase but show a broad diffuse peak due to the presence of $\sim 2-\mathrm{nm}$-size AFM spin clusters which are responsible for the CSG freezing in CFN.

Figure 1

Scanning electron micrograph and EDX spectra of $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$.

Figure 2

(a) Observed (red dots), calculated (black continuous line), and difference (green continuous line) profiles obtained from Rietveld refinement of synchrotron x-ray pattern of $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ at room temperature using $Pbnm$ space group. Vertical tick marks above the difference profile represent the Bragg peak positions. The insets show the superlattice peaks fit on an enlarged scale; (b) depicts the crystal structure of $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ along with tilted octahedra.

Figure 3

Temperature dependence of dc magnetization of $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ measured at 100 Oe field in warming cycle for both ZFC and FC conditions. The inset gives a magnified view of the $M\left(T\right)$ to reveal a small dip (marked with an arrow) in the FCW $M\left(T\right)$ below $T_{\mathrm{f}}$.

Figure 4

(a) Temperature dependence of the real part $\left[{\chi }^{\prime }\left(\omega ,T\right)\right]$ of ac magnetic susceptibility of $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ measured at various frequencies as labeled in the plot for an applied ac drive field of 1 Oe. The main panel (b) depicts $ln\left(\tau \right)$ versus $ln\left(T_{\mathrm{f}}/T_{\mathrm{SG}}-1\right)$ plot, where $\tau =1/\left(2\pi f\right)$. Inset to panel (b) depicts the $ln\left(\tau \right)$ versus $1/T$ plot. The solid line represents the least-squares fit for critical power law and Vogel-Fulcher law.

Figure 5

Temperature dependence of the ZFCW and FCW dc magnetization plots of $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ at various applied magnetic fields.

Figure 6

Plot of $T_{\mathrm{irr}}$ versus $H^{2/3}$ as well as $T_{\mathrm{f}}$ versus $H^{2/3}$ showing the presence of de Almeida–Thouless line.

Figure 7

Time dependence of thermoremanent magnetization of $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ sample at 15 K for 1000 Oe cooling field and wait time of 1000 s. The solid line is the best fit for stretched exponential function to the data.

Figure 8

(a) Temperature dependence of ZFC magnetization of $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ recorded at 100 Oe field with $\left(•\right)$ and without (ο) intermediate stop at $T_{\mathrm{w}}=15\mathrm{K}$ for a wait time ($t_{\mathrm{w}}$) of ${10}^4\mathrm{s}$. (b) Depiction of the difference $\mathrm{\Delta }M\left(T\right)=M_{\mathrm{wait}}^{\mathrm{ZFCW}}\left(T\right)-M_{\mathrm{ref}}^{\mathrm{ZFCW}}\left(T\right)$ vs temperature ($T$) plot from which it is evident that a sharp dip occurs exactly at the waiting temperature ($T_{\mathrm{w}}$).

Figure 9

Temperature dependence of dc magnetization of $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ recorded at 100 Oe field in three different cycles as labeled in the plot. The field is set to zero during the intermittent wait of cooling temperature $T_{\mathrm{w}}=50$, 15 K for 3 h. The cooling and heating rate of measurement is 2 K/min. The pronounced steps in the cooling curve occurs at 15 K and no such step is seen above the spin glass freezing temperature (i.e., at 50 K).

Figure 10

(a) Magnetic-field dependence of isothermal magnetization of $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ sample at 5 and 300 K. Inset depicts the zoomed scale of $M-H$ curve in the low-field region at 5 K. (b) Depiction of magnetization as a function of magnetic field for $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ sample at 5 K in ZFC and 7-T FC conditions to measure the exchange-bias effect. Inset shows the enlarged scale of $M-H$ curve for low-field region.

Figure 11

Panel (a) depicts neutron powder-diffraction patterns of $\mathrm{Ca}\left(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3$ collected at 300, 100, and 5 K. The patterns are shifted vertically for the purpose of presentation. Inset of (a) depicts the enlarged scale of broad diffuse magnetic scattering peak corresponding to short-range antiferromagnetic correlations. Panel (b) depicts the deconvolution of the NPD profile peaks at 5 K. Insets of panel (b) show enlarged scale of deconvoluted peaks at 5 K.