Nuclear Magnetic Resonance Studies in Antiferromagnetic CrCl3

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 HE=1450 Oe corresponding to an exchange constant JLzL/k=−0.065°K. From the observed Tc, simple molecular field theory gives an intralayer exchange constant JTzT/k=6.7°K, where zL and zT 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 JT/JL 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: H=−JT ∑ i,j Si·Sj−gβHA ∑ i Siz,where HA is an effective anisotropy field which includes HE. 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 HA(T) = HA(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: (a) JTZT/k=11.85∘K, HA  =2700 Oe,(b) JTZT/k=13.35∘K, HA  =2000 Oe,(c) JTZT/k=15.03∘K, HA(0)=1525 Oe.The effect of the intralayer renormalization in (c) is only important above 4°K; the effect of the temperature dependence of HA, however, is very noticeable even below 4°K as can be seen from the differences in JT, HA obtained from (b) and (c). The magnitude of JT 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 Tc by the Kramers-Opechowski method.4 The anisotropy in CrCl3 is very small since HA(0)≈HE. 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 is driven by the appropriate antiferromagnetic resonance mode. We have compared the measured intensities with calculations based on the measured static susceptibilities and have obtained a value of K3≈150 erg/cm3 for the weak sixfold anisotropy in the (001) plane. The weak-field enhancement leads to selective excitations in polycrystalline samples resulting in observable splittings of the nuclear resonance when the driving field is parallel to the steady field. These splittings are a result of the expected strong field dependence of the sublattice magnetizations. We have determined χ∥ at several temperatures from these observations. At 4.00°K we find χ∥=0.28 emu/mole which compares with values of 0.227 and 0.289 calculated from spin-wave models (b) and (c), respectively. A complete account of this work appears elsewhere.6