Nuclear Magnetic Resonance Studies in Antiferromagnetic CrCl3

Abstract

We have investigated the metamagnetic properties of CrCl₃ by studying the temperature and magnetic field dependences of the Cr⁵³ nuclear magnetic resonance in the temperature range 0.39°–11.5°K. Below 238°K the crystal structure of CrCl₃ is isomorphous with that of CrBr₃ (space group R3̄). A specific heat anomaly occurs at T=16.8°K¹ due to a transition to a magnetically ordered structure in which ferromagnetic (001) sheets alternate in direction along the hexagonal c axis.² The large field‐dependent perpendicular susceptibility arises from the small value of the antiferromagnetic interlayer exchange energy compared to the much larger ferromagnetic intralayer exchange energy. The measured susceptibility below 4°K³ gives an antiferromagnetic exchange field H_E=1450 Oe corresponding to an exchange constant J_Lz_L/k=−0.065°K. From the observed T_c, simple molecular field theory gives an intralayer exchange constant J_Tz_T/k=6.7°K, where z_L and z_T are the number of exchange‐coupled nearest neighbors along the c axis and in the basal plane, respectively. It is apparent from the magnitude of J_T/J_L that the low‐temperature magnetic properties of CrCl₃ should closely approximate those of a two‐dimensional Heisenberg ferromagnet. Among the unusual properties expected for such a system are a nearly linear M(T)/M(0) relation at sufficiently high temperatures and a large parallel magnetic susceptibility. These predictions are in good agreement with our experimental results. We have analyzed the temperature dependence of the Cr⁵³ zero‐field resonance by means of the following isotropic exchange Hamiltonian: $$\mathcal{H}{\mathrm{=-J}}_T{\displaystyle \sum _{\mathrm{i,j}}}\hspace{0.17em}{\mathbf{S}}_i·{\mathbf{S}}_j{\mathrm{-g\beta H}}_A{\displaystyle \sum _i}{\mathrm{\hspace{0.17em}S}}_i^z,$$ where H_A is an effective anisotropy field which includes H_E. We have compared our data with several approximate solutions of (1): (a) simple spin‐wave, long wave (k²) limit; (b) simple spin‐wave, exact calculation of M(T)/M(0) from the dispersion relation; (c) spin‐wave model with approximate treatment of spin‐wave interactions. [The effective anisotropy field was given a temperature dependence H_A(T) = H_A(0)M(T)χ⊥(0)/M(0)χ⊥ (T) and the intralayer interactions were treated by renormalization techniques.] Approximations (a) and (b) were applied to the data below 4°K and (c) to the whole range 0.39°–8.2°K. Agreement within the experimental uncertainty is found in all three cases and the results are: $$\begin{array}{c}(\mathrm{a}{\mathrm{)\hspace{0.17em}J}}_{T^{Z}T}{\text{/k=11.85}}^{\circ }\mathrm{K}{\mathrm{,\hspace{0.17em}H}}_A\text{\hspace{0.17em}\hspace{0.17em}=2700\hspace{0.17em}}\mathrm{Oe},\\ (\mathrm{b}{\mathrm{)\hspace{0.17em}J}}_{T^{Z}T}{\text{/k=13.35}}^{\circ }\mathrm{K}{\mathrm{,\hspace{0.17em}H}}_A\text{\hspace{0.17em}\hspace{0.17em}=2000\hspace{0.17em}}\mathrm{Oe},\\ (\mathrm{c}{\mathrm{)\hspace{0.17em}J}}_{T^{Z}T}{\text{/k=15.03}}^{\circ }\mathrm{K}{\mathrm{,\hspace{0.17em}H}}_A\text{(0)=1525\hspace{0.17em}}\mathrm{Oe}.\end{array}$$ The effect of the intralayer renormalization in (c) is only important above 4°K; the effect of the temperature dependence of H_A, however, is very noticeable even below 4°K as can be seen from the differences in J_T, H_A obtained from (b) and (c). The magnitude of J_T derived from spin‐wave theory is considerably larger than that obtained from the molecular field model. The spin‐wave value, however, is consistent with values derived for two‐dimensional lattices from T_c by the Kramers‐Opechowski method.⁴ The anisotropy in CrCl₃ is very small since H_A(0)≈H_E. One expects a large negative axial dipolar anisotropy; however this anisotropy is almost cancelled by a positive single‐ion term arising from spin‐orbit interactions. This conclusion is in agreement with results of spin‐wave calculations which include these interactions explicitly, as well as direct torque measurements of the anisotropy.⁵ We have investigated the intensity enhancement of the Cr⁵³ resonance in zero field and in weak external fields. In both cases the resonance...