Phase Diagram of a Three-Dimensional Antiferromagnet with Random Magnetic Anisotropy

Three-dimensional antiferromagnets with random magnetic anisotropy (RMA) that have been experimentally studied to date have competing two-dimensional and three-dimensional exchange interactions which can obscure the authentic effects of RMA. The magnetic phase diagram of ${\mathrm{Fe}}_x{\mathrm{Ni}}_{1-x}{\mathrm{F}}_2$ epitaxial thin films with true random single-ion anisotropy was deduced from magnetometry and neutron scattering measurements and analyzed using mean-field theory. Regions with uniaxial, oblique, and easy-plane anisotropies were identified. A RMA-induced glass region was discovered where a Griffiths-like breakdown of long-range spin order occurs.

Figure 1

TRM for ${\mathrm{Fe}}_x{\mathrm{Ni}}_{1-x}{\mathrm{F}}_2$ samples measured in $H=0$ after field cooling in $H_{\mathrm{FC}}=100\mathrm{Oe}$. Data for $x=0$ and 0.10 were measured with $H_{\mathrm{FC}}$ perpendicular to the $c$ axis; all others measured with $H_{\mathrm{FC}}$ parallel to the $c$ axis. Right: Magnetic and crystalline structures of the parent compounds ${\mathrm{NiF}}_2$ ($x=0$) and ${\mathrm{FeF}}_2$ ($x=1$). Yellow, blue, and red dots are ${\mathrm{F}}^{-}$, ${\mathrm{Ni}}^{2+}$, and ${\mathrm{Fe}}^{2+}$ ions, respectively.

Figure 2

(a) TRM data near the phase transition for four representative samples. Symbols are data and red curves are fits to Eq. (3) with two transitions for $x=0.30,0.47$ and one transition for $x=1.0$ and $x=0.0$. Inset: $M$ measured while warming with $H=80\mathrm{Oe}$ applied along the $c$ axis after ZFC from $T=300$ to 5 K and during FC from 300 to 5 K for the $x=0.47$ sample. (b) $\partial M/\partial T$ of the $x=0.47$ TRM and FC data measured under different applied fields. Vertical blue lines indicate transition temperatures $T_1$ and $T_2$.

Figure 3

(a) Neutron scattering intensity as a function of $T$ for the $x=0.3$ (red circles) and $x=0.1$ samples (blue squares). Filled and open symbols indicate (100) and (001) reflections, respectively. Lines are guides to the eye. (b) Intensity near $T_c$. Black curves are best fits to Eq. (3) (with $\beta \to 2\beta$) with the parameters shown in the graph. (c) Angle of $\mathbf{L}$ as a function of $T$ with respect to the $c$ axis for the $x=0.1$ sample calculated from the data in (a). The solid curves are MFT results for the values of $x$ indicated in the graph.

Figure 4

${\mathrm{Fe}}_x{\mathrm{Ni}}_{1-x}{\mathrm{F}}_2$ magnetic phase diagram. Regions are indicated by ${\mathrm{AFM}}_{a\text{−}b}$ (ordering in the $a\text{−}b$ plane), ${\mathrm{AFM}}_c$ (ordering along the $c$ axis), ${\mathrm{AFM}}_{\mathrm{AG}}$ (anisotropy glass phase), ${\mathrm{AFM}}_O$ (oblique phase), and PM (paramagnetic phase). The PM-AFM phase boundary calculated using MFT is denoted by the solid green curve. Horizontal error bars represent uncertainties from quartz-crystal monitor measurements. Vertical error bars are transition widths ${\sigma }_{T_C}$. Measurements for samples that had a response for $H\perp$ to the $c$ axis ($[\overline{1}10]$ direction, $\mathrm{\Delta }$) are also indicated. Magenta lines enclose the MFT ${\mathrm{AFM}}_O$ region. Transitions observed via neutron scattering are indicated. The dark blue curve is a ${\mathrm{AFM}}_c\text{−}{\mathrm{AFM}}_{\mathrm{AG}}$ phase boundary drawn as a guide to the eye.