Muon spin relaxation study of the magnetism in unilluminated Prussian Blue analogue photomagnets

We present longitudinal field muon spin relaxation $\left(\mu \mathrm{SR}\right)$ measurements in the unilluminated state of the photosensitive molecular magnetic $\mathrm{Co}\text{−}\mathrm{Fe}$ Prussian Blue analogues $M_{1-2x}{\mathrm{Co}}_{1+x}\left[\mathrm{Fe}\right(\mathrm{CN}{)}_6]\bullet z{\mathrm{H}}_2\mathrm{O}$, where $M=\mathrm{K}$ and Rb with $x=0.4$ and $\simeq 0.17$, respectively. These results are compared to those obtained in the $x=0.5$ stoichiometric limit ${\mathrm{Co}}_{1.5}\left[\mathrm{Fe}\right(\mathrm{CN}{)}_6]\bullet 6{\mathrm{H}}_2\mathrm{O}$, which is not photosensitive. We find evidence for correlation between the range of magnetic ordering and the value of $x$ in the unilluminated state, which can be explained using a site percolation model.

Figure 1

(Color online) Crystal structure of $M_{1-2x}{\mathrm{Co}}_{1+x}\left[\mathrm{Fe}\right(\mathrm{CN}{)}_6]\bullet z{\mathrm{H}}_2\mathrm{O}$: (a) $x=0.5$ and (b) $x\ne 0.5$, with an $\mathrm{Fe}(\mathrm{CN}{)}_6$ vacancy shown in gray coordinated by bound water molecules. Large, medium, and small circles denote Fe, Co, and CN, respectively. The alkali-metal ions which maintain charge neutrality occupy cubic interstitial sites (not shown).

Figure 2

The zero-field- (squares) and field- (circles) cooled dc magnetization of ${\mathrm{Co}}_{1.5}$ measured at $100\mathrm{G}$ in a SQUID magnetometer.

Figure 3

(Color online) The muon spin relaxation as a function of time measured in ${\mathrm{Co}}_{1.5}$ at $100\mathrm{G}$ longitudinal field for different temperatures at (a) early and (b) long times. The solid lines are fits to the function described in the text.

Figure 4

The distribution of static fields (a) and the muon spin relaxation rate (b) in ${\mathrm{Co}}_{1.5}$ as a function of temperature in an applied longitudinal field of $100\mathrm{G}$. The solid lines are a guide for the eye.

Figure 5

The zero-field- (squares) and field- (circles) cooled dc magnetization of ${\mathrm{K}}_{0.2}{\mathrm{Co}}_{1.4}$ measured at $100\mathrm{G}$ in a SQUID magnetometer.

Figure 6

(Color online) The muon spin relaxation as a function of time measured in ${\mathrm{K}}_{0.2}{\mathrm{Co}}_{1.4}$ at $100\mathrm{G}$ longitudinal field for different temperatures at (a) early and (b) long times. The solid lines are fits to the function described in the text.

Figure 7

The distribution of static fields (a) and muon spin relaxation rate (b) in ${\mathrm{K}}_{0.2}{\mathrm{Co}}_{1.4}$ as a function of temperature in a longitudinal field of $100\mathrm{G}$. The solid lines are a guide for the eye.

Figure 8

The inverse susceptibility of ${\mathrm{Rb}}_{0.66}{\mathrm{Co}}_{1.25}$ as a function of temperature measured at $100\mathrm{G}$.

Figure 9

(Color online) The muon spin relaxation in ${\mathrm{Rb}}_{0.66}{\mathrm{Co}}_{1.25}$ at LF $B=40\mathrm{G}$ and different temperatures.

Figure 10

(Color online) The muon spin relaxation in ${\mathrm{Rb}}_{0.66}{\mathrm{Co}}_{1.25}$ at $B=2.4\mathrm{kG}$ and different temperatures.

Figure 11

(Color online) The muon spin relaxation rate in ${\mathrm{Rb}}_{0.66}{\mathrm{Co}}_{1.25}$ as a function of temperature at different longitudinal fields.

Figure 12

The muon spin relaxation time at $T=2.3\mathrm{K}$ as a function of the magnetic field squared. The solid line is a linear fit $T_1=\alpha +\beta B^2$ with $\alpha =0.1147\left(9\right)\mathrm{\mu }\mathrm{s}$ and $\beta =0.401\left(1\right)\mathrm{\mu }\mathrm{s}∕{\mathrm{kG}}^2$.