Magnetization steps in ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{O}:$ Four largest exchange constants and single-ion anisotropy

Magnetization steps from ${\mathrm{Mn}}^{2+}$ pairs in several single crystals of ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{O}$ $(0.0056\mathrm{}<~x<~0.030),$ and in one powder $\mathrm{}(x=0.029\mathrm{}),$ were observed. They were used to determine the four largest exchange constants (largest $J$’s), and the single-ion axial anisotropy parameter D. The largest two exchange constants, $J_1{/k}_{\mathrm{B}}=-18.2\pm 0.5\mathrm{K}$ and $J_1^{\prime }{/k}_{\mathrm{B}}=-24.3\pm 0.5\mathrm{K},$ were obtained from large peaks in the differential susceptibility, $dM/dH,$ measured in pulsed magnetic fields H up to $500\mathrm{kOe}.$ These two largest $J$’s are associated with the two inequivalent classes of nearest neighbors (NN’s) in the wurtzite structure. The 29% difference between $J_1$ and $J_1^{\prime }$ is substantially larger than 13% in ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{S}$ and 15% in ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Se}.$ The pulsed-field data also indicate that, despite the direct contact between the samples and a superfluid-helium bath, substantial departures from thermal equilibrium occurred during the 7.4-ms pulse. The third- and fourth-largest $J$’s were determined from the magnetization M at 20 mK, measured in dc magnetic fields H up to 90 kOe. Both field orientations $\mathbf{H}\Vert \mathbf{c}$ and $\mathbf{H}\Vert \left[101¯0\right]$ were studied. (The $\left[101¯0\right]$ direction is perpendicular to the c axis, $\left[0001\right].)$ By definition, neighbors which are not NN’s are distant neighbors (DN’s). The largest DN exchange constant (third-largest overall) has the value ${J/k}_{\mathrm{B}}=-0.543\pm 0.005\mathrm{K},$ and is associated with the DN at $\mathbf{r}=\mathbf{c}.$ Because this is not the closest DN, this result implies that the $J$’s do not decrease monotonically with the distance r. The second-largest DN exchange constant (fourth-largest overall) has the value ${J/k}_{\mathrm{B}}\approx -0.080\mathrm{K}.$ It is associated with one of the two classes of neighbors that have a coordination number $z_n=12,$ but the evidence is insufficient for a definite unique choice. The dependence of M on the direction of $\mathbf{H}$ gives ${D/k}_{\mathrm{B}}=-0.039\pm 0.008\mathrm{K},$ in fair agreement with $-0.031\mathrm{K}$ from earlier electron paramagnetic resonance work.