Magnetic neutron scattering of thermally quenched K-Co-Fe Prussian blue analog photomagnet

Magnetic order in the thermally quenched photomagnetic Prussian blue analog coordination polymer K${}_{0.27}$Co[Fe(CN)${}_6$]${}_{0.73}$[D${}_2$O${}_6$]${}_{0.27}·$1.42D${}_2$O has been studied down to 4 K with unpolarized and polarized neutron powder diffraction as a function of applied magnetic field. Analysis of the data allows the on-site coherent magnetization of the Co and Fe spins to be established. Specifically, magnetic fields of 1 and 4 T induce moments parallel to the applied field, and the sample behaves as a ferromagnet with a wandering axis.

Figure 1

Co-Fe unit cell. Crystallographic positions of atoms within the unit cell are illustrated for Co (blue cubes), Fe (red cubes), Fe-C bonds (red tubes), C (black spheres), N (cyan spheres), coordinated D${}_2$O positions (blue circles), and interstitial D${}_2$O (green contoured isosurfaces), while K ions within the cages cannot be seen in this figure due to masking from D${}_2$O isosurfaces. Details of structure determination are presented in Sec. 3.

Figure 2

Magnetic phase transitions in Co-Fe. Following the temperature bar at the bottom of the figure, (a) a schematic of magnetic states upon warming Co-Fe after a quench achieved by dunking from room temperature into a cryogenic bath, (b) a schematic of magnetic states upon warming Co-Fe after a slow cool of less than 1 K/min to base temperature, and (c) the manifestation of these states as measured by a SQUID magnetometer. The magnetic susceptibility near the ordered state (blue circles) and in a field of 10 mT and the magnetic susceptibility, temperature product (open triangles) in a field of 1 T are shown as a function of warming the sample temperature in a quenched state. The spin-only calculated susceptibility (dotted orange line) and linearized high-temperature susceptibility (dotted black line) are also shown. Uncertainty bars are derived from longitudinal moment scans.

Figure 3

Neutron powder diffraction of Co-Fe at $T=40$ K. Observed scattering is shown as open circles (obs), a full fit including sample mount contributions is shown as a black line (calc'd), the diffuse background is illustrated with a magenta line (bgr), and the residuals of the fit are shown below the zero line with a green line (resid). The signal due to Co-Fe is emphasized with a red filling. Experimental uncertainties derived from counting statistics are smaller than the plotting symbols.

Figure 4

Magnetic neutron powder diffraction of Co-Fe at $T=4$ K as a function of applied magnetic field. The difference between the $T=40$ K diffractogram and the $T=4$ K diffractogram (open circles) along with profile fits to intensities (red line from model 1 for 4 and 1 T data in Table ) are shown for (a) 4 T, (b) 1 T, and (c) 10 mT. Additionally, the difference between the $T=4$ K up-neutron-polarization diffractogram and the $T=4$ K down-neutron-polarization diffractogram (open circles) along with profile fits to intensity (red line from model 5 for polarized data in Table ) are shown for (d) 1 T. Uncertainty bars on experimental data points are statistical in nature representing one standard deviation from the mean, using counting statistics.

Figure 5

SQUID magnetization of Co-Fe at $T=2$ K. Experimental magnetization is shown as open circles (SQUID magnetization) and model fits as a red line (model fit), where FWA and NC are visually indistinguishable; $M\left(1\mathrm{T}\right)=1.1\pm 0.1{\mu }_B$mol${}^{-1}$ and $M\left(4\mathrm{T}\right)=1.6\pm 0.2{\mu }_B$mol${}^{-1}$. The units of $M_S$ are ${\mu }_B$mol${}^{-1}$, and $H_C$, $D_{\text{FWA}}$, and $D_{\text{NC}}$ are all units of Tesla. Uncertainty bars represent one standard deviation from the mean, where statistics are generated by measuring the magnetization of the 14 synthesis batches required to generate 4.37 g for NPD.

Figure 6

An illustration of magnetic structure for different magnetic field regimes. Here the magnetic field points towards the top of the page, short arrows represent iron moments, and long arrows represent cobalt moments. (a) The Co-Fe sample cooled in zero field has a CSG-like state with no average on-site moment, as shown for the measurement of magnetic scattering in 10 mT [Fig. 3c]. (b) The application of magnetic field cants the moments towards the field [Figs. 3b and 3d], and (c) larger fields induce larger average moments [Fig. 3a]. (d) More complicated mesoscopic states that contain texture are also possible, but are not unambiguously determined with our data.

Figure 7

Visual comparison of magnetic configurations for Co-Fe. Here the low angle $H=4$ T data (open circles) are set side by side with model 1 for 4 T from Table (thick solid, red line), model 2 for 4 T from Table (dotted, black line), a ferrimagnetic structure with a 3:1 Co:Fe spin ratio (dashed, blue line), and a ferromagnetic structure with a 3:1 Co:Fe spin ratio (thin solid, black line). Uncertainty bars are representative of one standard deviation from the mean, using counting statistics.