Magnetic properties of EuSe

Journal of Magnetism and Magnetic Materials 31-34 (1983) 431-432

431

MAGNETIC PROPERTIES OF EuSe H. F U K U M A , T. K O M A T S U B A R A *, T. S U Z U K I , S. K U N I I , E. K A L D I S ** a n d T. K A S U Y A

Department of Physics, Tohoku University, Sendai, Japan

To investigate the anomalous magnetic properties of EuSe, we performed the measurements of magnetization and magnetostriction. From the analysis of these results we show that the complex magnetic phase diagram of EuSe can be deduced from biquadratic exchange interaction and magnetoelastic effect.

EuSe with the rock-salt type crystal structure is a wellknown material to show very interest!ng spin structures below the N6el temperature T~ = 4.6 K, even though Eu 2+ is a well known isotropic ion with L = 0 and S = 7/2. The origin of Ising like spin structures, NNSS, NNS, NSNS and NNN, and their transformation mechanism is a very interesting problem attracting many physicists. The fundamental property is the near cancellation of the nearest and the next nearest neighbour exchange constants, Ji + J2 = 0, which causes instability for any Q-vector along [111] and makes the higher order interaction important. Furthermore there are some mysterious evidences and contradictions among the magnetic properties obtained by different authors. To obtain more detailed information, we performed ferri- and ferromagnetic resonances, magnetization and magnetostriction measurements. In this paper, we report the latter two. Free energies of various spin structures are calculated by using the molecular field approximation and compared with the experimental data. Good quality single crystals were grown by the iodine transport technique. The grown crystals were ground into spheres. Magnetization measurements were achieved using a high precision induction method under magnetic field up to 85 kG in the temperature range 0.6 K ~< T ~< 4.2 K. To assure the accuracy, measurements were done in the two different but crystallographically equivalent direction repeatedly. Dilatometric measurements were also done by applying parallel magnetic field up to 85 kG in [100] direction by capacitance method in the temperature range df 1.4 K ~ T g 4.2 K. The M - H curve in the NNS region at 1.4 K is shown in fig. 1. The low and high field regions are the transients regions due to demagnetization for NNS and N N N states, respectively. Here we mention four points. First, the ratio of the initial value of magnetization in NNS with field in the [110], [111] and [100] directions equals to 1 : ~ : (21~, consistent with the model that the spins sit in the (111) plane due to the Material-Engineering Department, Tsukuba University, lbaraki, Japan. ** Laboratorium fiir Festk6rperphysik ETH, Zfirich, Switzerland. *

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2 3 Fig. 1. Magnetization process of EuSe at 1.4 K in three different crystal orientations. The ordinate is normalized to a value for 85 kOe. magnetic dipole interaction but the anisotropy in the plane is very small. Secondary, the initial value of magnetization for [110] is fairly smaller than one third of that of ferromagnetic region. Even at 0.6 K it is smaller than the ideal saturation value or that at 85 kG by about 3%. This seems to suggest that the zero point reduction is large in NNS state. Thirdly, the magnetization for [100] increases much rapidly than those for other directions, exceeding that for the easy direction at about H = 2.7 kOe. This indicates that the NNS state can be easily modified into canted state. The same thing is observed even for the [111] direction, but less impressive. Finally, in spite of the above mentioned complication, no anisotropy of the transition field from NNS to NN states is observed within the experimental accuracy. Our results of the magnetostriction measurement are similar to those of Griessen's but different in detail [1]. At 1.4 K the overall reduction, which means the length change from H = 0 to H = 85 kOe, amounts to 2.0 × 10 -4 . The magnetic measurements under hydrostatic

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pressure by Schwob et al. [2] indicate that Jt is very sensitive to the lattice distance. From this point of view and assuming isotropic volume for the initial and final state, we get ~2/i/Oln r = - 4 . 9 K, in which the bulk modules was obtained from the sound velocity [3]. The obtained value is reasonably smaller than those of EuO and EuS. The same conclusion is also obtained for the tetragonal distortion in the N N S phase. As pointed out before, the magnetic dipole energy plays an important role in the spin ordering, but in the absence of a magnetic field NNSS, NNS, NSNS, N N N and some spiral structures have nearly the same dipole energy and thus other types of higher order interactions should be important. The natural extension is the biquadratic exchange interaction as well as the magnetoelastic effect. Thus we formulate the Hamiltonian with six terms including four parameters, Jl, "/2, "/3 and Jl, in which ,/3 is the third nearest neighbour exchange constant andj~ the nearest neighbour biquadratic constant, and we tried to fit the behavior shown in fig. I and the successive phase diagram in zero field as well as the paramagnetic Curie temperature, Or, = 4.8 K, by the molecular field approximation. Note that the dipole interaction is known and the magnetostriction effect is given by R/i/01n r and the measured elastic constants, which will be given later. As a possible ordering, we assumed ferromagnetic one on each (111) plane. Then for each sublattice the expected values for the dipole and quadrupole moments, < Pi>Q and < qi>Q, and the lattice distortion A + between the parallel and antiparallel spin ordered planes are introduced and then the effective fields for Sz and Qz, h~ and v~, are calculated. The free energy for the molecular field is easily calculated by using the parameters, (p~)Q, Q and ~ +_, which are determined to minimize the free energy as usual. Note that the free energy includes the elastic

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Fig. 3. Calculated spontaneous dilatation change vs. temperature. The dashed line indicates the experimental one. energy for a lattice distortion which are evaluated as follows. There are two kinds of strain, the macroscopic strain, whose energy is evaluated from the given elastic constants, and the microscopic one, for which some microscopic information is necessary, it is clear that the distortion along the [111] direction under consideration has a strong correlation with the LA p h o n o n mode in that direction. We approximate this p h o n o n mode by a one-dimensional linear chain model whose Q-dependent elastic constant C 0 is" determined to fit the experimental values. In the case of N N N , NSNS or spiral structure, only macroscopic distortion exsists. The calculated free energy as a function of temperature is shown in fig. 2 for Jl = +']2 ~ --'/2 and Op = 4.8 K. The sequent phase transition of NSNS, N N S and NNSS is realized by the Q-dependent magnetoelastic effect but the detailed transition temperatures are sensitive to J3. -/3 must have a small negative value, because it makes the N N N state relatively unstable, but a too large negative value stabilizes the N N S state too much at higher temperatures relative to NNSS structure. On the other hand j~ is a sensitive factor to fit fig. 1. Thus the v a l u e s j J J I = 0.01, J~ =0.155 K, ,/2 = - 0 . 1 5 6 K and J 3 = -0.0001 K are obtained. As far as we use the molecular field approximation, the calculated TN, 5.7 K, is too large. This is due to the short range order effect. This is clearly shown in fig. 3 for the magnetoelastic effect. The calculated 8l/1 values for the N S N S - N N S and N N S - N N S S transition agree very well with experiment but the transition to the para state shows a very small change in experiment compared to this calculation. There are still some ambiguities on this transition which need more elaborate experiments. References

[1] R. Griessen, M. Landolt and H.R. Ott, Solid state Commun. 9 (1971) 2219. [2] P. Schwob, Phys. Kondens. Mater. 10 (1969) 186. [3] Y. Shapira and T.B. Reed, AlP Conf. Proc. Magn. and Magn. Mater. 5 (1971) 837.