Kazuo Tsuru

Renormalized Spin Wave Theory of Nearly Two-Dimensional Ferromagnet K2CuF4

The temperature and the magnetic field dependences of the magnetization of the ferromagnetic layer-type compound K 2 CuF 4 have been analyzed by the spin wave theory which takes into account the spin wave interaction. It is shown that the spin wave interaction plays rather important role in the nearly two-dimensional magnetic system and gives rise to a logarithmic term in the expansion of the magnetization with respect to the temperature. The apparent T 3/2 temperature dependence of the magnetization can be shown to be realized in a certain temperature region. With the use of the exchange interaction constants estimated in the previous investigations, the present calculation shows excellent agreements with the experiments.

NMR Study of Nearly Two-Dimensional Ferromagnet (CnH2n+1NH3)2CuCl4(n=1∼4) at Low Temperature

NMR of Cl 35 nuclei (within layer) of (C n H 2 n +1 NH 3 ) 2 CuCl 4 is observed at the magnetically ordered state. Through the angular dependence of the NMR frequency, the crystallographic structure of the CuCl 4 layer is determined, which is slightly different from the known crystal structure at room temperature. The existence of various moment directions is shown in (C 3 H 7 NH 3 ) 2 CuCl 4 . The magnetic coupling between layers is discussed. The observed magnetization of (C n H 2 n +1 NH 3 ) 2 CuCl 4 ( n =1, 3 and 4) is compared with the renormalized spin wave theory. It is also shown that the magnetization follows the “T 3/2 -law” given as, /S=1-α(T/T c ) 3/2 , with α∼0.45. The field dependent behavior of the magnetization of (C 2 H 5 NH 3 ) 2 CuCl 4 is discussed at antiferromagnetic state.

Hyperfine Interactions for Cu Nuclei in (C2H5NH3)2CuCl4

From the angular dependence of the Cu 63 NMR frequency in the magnetically ordered state of (C 2 H 5 NH 3 ) 2 CuCl 4 , the parameters in the Cu 63 nuclear spin Hamiltonian are determined as follows; H x =-28.5 kOe, H y =-27.7 kOe, H z =-189.6 kOe, ν Q =6.00 MHz and η=-0.1. From these values, the Fermi contact, dipolar and orbital fields are separately estimated as H F =-114 kOe, H d =+24.4 kOe, H l // =-8.9 kOe and H l ⊥ =-6.3 kOe. The disagreement of the dipolar and orbital fields with the theoretical estimations is found and is interpreted as mainly due to the reduction of 3d spin caused by the electron transfer from the Cl - ions. On the contrary, it is shown that the Fermi contact field is hardly affected by the ligand ions.

Nuclear Relaxation in a Two-Dimensional Ferromagnet with Single-Ion Anisotropy: Application to the System Rb2CrCl4

The nuclear spin-lattice and transverse relaxation times were calculated for a two-dimensional ferromagnet with single-ion anisotropy, using the renormalized spin-wave development. The experimental transverse relaxation rate of 53 Cr nuclei was fairly explained by the Suhl-Nakamura interactions and the two-magnon process. The calculated spin-lattice relaxation due to three-magnon process with exchange enhancement led to an unusual result: the enhancement factor is as high as 29.4 at 25 K i.e. much more than for an easy-axis ferromagnet and a three-dimensional one.

Hyperfine Interactions of Ligand Bromine Nuclei in Ferromagnetic (CH3NH3)2Cu(Cl1-xBrx)4

The bromine NMR studies in the magnetically ordered state of (CH 3 NH 3 ) 2 Cu(Cl 1- x Br x ) 4 (0.03 ≦ x ≦0.85) are carried out. The parameters in the bromine nuclear spin Hamiltonian at 0 K are determined by comparing the NMR shifts with the spin wave theory. The hyperfine fields and the quadrupole frequency are nearly independent of the concentration of Br - ions. In addition to the hyperfine fields due to s - and p σ -orbitals, the anisotropic fields caused by the second order perturbation through the spin-orbit interaction are also observed. The unpaired spin density of Br - ion of the p σ -orbital is estimated. The parameter of π-bond is discussed.

Principle of Corresponding States of Magnetic Phase Diagram of CuCl2·2H2ZO at Low Temperatures and High Pressures

The principle of corresponding states of the magnetic phase diagram of CuCl22H2O (TN=4.35K) at low-temperatures, hydrostatic pressures and magnetic fields has been studied by the low-temperature heat capacity measurements. The Neel temperature TN(p) has changed linearly with pressure p(kbar) as TN(p)=TN(0)(1+0.048p) up to 6 kbar at zero external field. The dependence of magnetic interactions on pressure (or inter-ion distance) is revealed to give the larger value of the magnetic Gruneisen constant than expected for the superexchange mechanism. The phase boundary between paramagnetic and antiferromagnetic phases has been examined at high hydrostatic pressures and magnetic fields applied along the spin easy axis. The principle of corresponding states of the magnetic phase diagram of this compound has been checked by a molecular field approximation in the consideration of the pressure dependence of magnetic interactions and anisotropies.

Nuclear relaxation in a two-dimensional ferromagnet with single-ion anisotropy

Abstract A new method is proposed for computing the spin-wave energy of an easy-plane magnet which satisfies the Goldstone theorem. The method is applied to the calculation of the spin-lattice relaxation time of 53 Cr nuclei in an easy plane ferromagnet Rb 2 CrCl 4 . A large exchange enhancement observed in this system is reasonably explained.

Systematic variation of parameters of Cu nuclear spin Hamiltonian in some cupric compounds

Abstract The concentration dependence of Cu NMR spectra is measured in the mixed crystals (CH 3 NH 3 ) 2 Cu(Cl 1- x Br x . The hyperfine field and the quadrupole frequency of Cu nuclei depend systematically on the number of Br ions in the sorrounding four ligand ions.

Spin-wave theory of the nearly two-dimensional Heisenberg ferromagnet II: (C2H5NH3)2CuCl4

Abstract A renormalized spin-wave theory is developed for the layer-type ferromagnet (C2H5NH3)2CuCl4, and analytical expressions of the magnetization, susceptibilities and phase boundaries for the nearly two-dimensional ferromagnet with a very weak antiferromagnetic interlayer coupling have been obtained. These expressions are compared with the well-known results for conventional three-dimensional magnetic systems. Experimental results can be well explained by the present theory. It is shown that the spin-wave interactions have a significant effect on the susceptibility and that the main terms of the spontaneous magnetization coincide with the results given in the previous paper (I), in which a layer-type ferromagnet with an interlayer ferromagnetic coupling has been discussed.

Spin-wave theory of the nearly two-dimensional ferromagnet (C3H7NH3)2CuCl4

Abstract A renormalized spin-wave theory is developed for the layer-type ferromagnet (C 3 H 7 NH 3 ) 2 CuCl 4 . In contrast with the case of K 2 CuF 4 , the main perturbation to the isotropic intralayer exchange interaction leading to three-dimensional long-range order is here the anisotropy in the intraplanar interaction. An analytical expression for the magnetization of the two-dimensional Heisenberg ferromagnet with a weak anisotropy in the intraplanar exchange as well as interplanar interactions has been obtained. It is shown that an excellent agreement between theory and experiment can be obtained using the interaction constants estimated in previous investigations, and further that the spin-wave interactions have a significant effect on the temperature dependence of the magnetization.