M A G N E T O C R Y S T A L L I N E A N I S O T R O P Y OF THE FERRIMAGNETIC S E M I C O N D U C T O R CoCr2S 4

A. MARAIS, M. PORTE, L. GOLDSTEIN and P. GIBART Laboratoire de Magn~tisme, CNRS, 1, PLace A. Briand, 92190 Bellevue, France

CoCr2S 4 is a ferrimagnetic n-type semiconductor T c = 227 K. K 1 (77 K) = 3.53 × 105 erg cm -3 for as-grown CoCr2S 4, 3 x 105 for H 2 annealed, and 3.7 × 105 for S 2 annealed. Sulfur vacancies exist in as-grown samples which act as doubly charged donors. They are charge compensated by Cr 2+ metal vacancies and it is assumed that Co 3+ could appear in A site. The main anisotropy ~-- 3 x 105 is due to Co 2+ in A site. A small amount of Co 3+ (3d 6, 5E in Td) and Cr 2+ (3d 4 in D3d symmetry of B site) give large positive K l values.

C o C r 2 S 4 is a ferrimagnetic n-type semiconductor (T c = 227 K). This compound is a normal spinel. Co appears in the A site and Cr in the B site, as was deduced from neutron diffraction data. The high Curie point results from a strong negative A - B interaction, JAB ~ 17 K. The magnetic prop- erties are consistent with localized d-electrons. Nonstoichiometry in magnetic semiconductor spinels is known to change significantly the mag- netic and galvanomagnetic properties. The effect of sulfur (or Se) deficiency in CdCr2S 4 (Se4) on the magnetocrystalline anisotropy has been studied [1] and theoretically interpreted [2].

Nonstoichiometry in CoCr2S 4 was little studied because F MR measurements are not possible; the large spin lattice interaction due to Co 2÷ in the A site gives a large linewidth resonance peak. In FeCr2S 4 the departure from stoichiometry was in- vestigated using M6ssbauer spectroscopy [3] and transport properties [4].

Single crystals of C o C r 2 S 4 w e r e grown from the vapor using H + C1 as the transport component [5]. Different heat treatments were carried out, e.g. sulfur annealing (1-3 atm S 2 at 800°C, 1-2 weeks), and hydrogen annealing ( ~ 800°C, 1-2 weeks). To obtain a low sulfur vapor pressure, a given amount of H 2 was put in a closed tube with COCrES 4, the e q u i l i b r i u m H E - H E S allows us to control the sulfur partial pressure.

1. Resistivity

As-grown CoCr2S 4 is a low mobility n-type semiconductor [5]. A change of the slope log 0 vs. 1 / T appears at T c. Sulfur annealing increases 0 by two orders of magnitude [4, 6] whereas hydrogen annealing only slightly changes 0.

2. Magnetocrystalline anisotropy

Anisotropy data were obtained either from mag- netization measurements on single crystal spheres or from torque measurements. In torque measure- ments, single crystals spheres (1-2 mm in diameter) are rotated in a 100 plane starting from a I1001 direction.

The free energy is given by:

2 2 2 2 F = Kl(alZa~ + a2a 3 + 0~3al) -F Ku sin2(0 -- 0u),

where K t and a 1 have their usual meaning, K u sin 2 (0 - 0~) is a noncubic term, 0 is the angle between the applied field and I1001, and 0 u is the angle of the uniaxial component of the anisotropy and tl00L.

Data are obtained from a Fourrier analysis of the curve

F = f ( O ) (F = torque).

3. Results

Pertinent data for K~ and K~ are given in table 1 for three typical samples: "as-grown", sulfur annealed, and hydrogen annealed. In sample A 0~ = 0, which corresponds to an easis axis along I100l, and in sample CO u = 45 °, which corresponds to the projection of a 11111 direction on a (100) plane.

4. Discussion

In stoichiometric CoCr2S 4 the main anisotropy is due to Co 2÷ in the A site (Cr 3+ makes a contrib- ution of the order of 103-104 erg cm -3 [4]). Co 2+

Journal of Magnetism and Magnetic Materials 15-18 (1980) 1287-1288 ©North Holland 1287

1288 A. Marais et al . / Magnetocrystalline anisotropy of CoCr2S 4

TABLEI

Sulfur annealed As grown Hydrogen annealed A B C

K 1 3.75 × 105 3.45 × 105 2.95 × 105 erg cm- 3 K~ 1.4 × 104 4× 103 0 u 0 45

in the A site (ground state A 2 in T O site) makes a contr ibution to K 1 of 0.2 c m - 1 / i o n [7]. This ex- plains the main anisotropy of the order of 3 × 105 erg cm -3. K l follows the (Ms/MO) 1° law. In previ- ous works [1, 3] it has been shown that deviation f rom stoichiometry occurs in thiospinels. Sulfur vacancies exist which are charge compensated by Cr 2+ (sulfur vacancies act as two charged donors). Heat t reatment results in changing the number of sulfur vacancies.

5. D i r e c t i o n a l order in n o n s t o i c h i o m e t r i c C o C r 2 S 4

As-grown samples do not exhibit directional order. K~ results mainly f rom Co 2+ in the A site. The sulfur annealed sample becomes more insulat- ing by two orders of magnitude. Sulfur vacancies (donors) decrease under sulfur heat treatment. It is further assumed that Cr 2+ are in a narrow d band,

1.6eV above the Cr 3+ level, and act as donors. In all cases the samples are n-type.

The existence on the A site of Co 2+ and possi- bly Co 3÷ in the sulfur annealed sample could ex- plain the important K u value (1.4 × 104 erg cm -3) and the axis of noncubic anisot ropy 1100l arising f rom neighbouring effects. Co 3+, 3d 6, 5D in T a site gives a 5E lowest doublet. This 5E doublet is further split by the exchange field in five doublets. The similar case of Fe 2+ has been discussed in detail by Hoekstra and Van Stapele and the conclusions are basically the same. At low temperature K~ 3KT In cosh (6 /KT) , with 6 = 6XZ/A. Using the data given for C d I n 2 S 4 : C o , 6 ~ 20 -30 cm -~ for Cr 3+. This gives a very large contr ibut ion to the anisotropy. In other words, a concentra t ion of the order of 4 × 10 - 4 C O 3+ could explain the K u value. To be consistent with the n type, it must be assumed that Co 3+ electrons are in deep level far below the Fermi level.

In sample C, hydrogen anneal ing results in in- creasing the number of sulfur vacancies and, con- sequently, the number of Cr 2+. The magnetocrys- talline anisotropy due to Cr 2+ has been discussed

I in detail by Hoekstra et al. [8] who found 11 cm for K 1 when averaged over the four trigonally distorted octahedral sites.

The value of K u can be explained assuming directional order due to the electronic exchange C r 2 + - C r +3. The expression for the separation of the two lowest levels of Cr 2+ given by Hoekstra et al., for a trigonal distortion along ( I l 1)> is

{ 22 AE = 2 62[1 -- 3(a~a~ + ~2c~3 d- 0:20/2)1

+ +

The angular dependence is not the same for the four octahedral sites. When the magnetization rotates in a (110) plane from 100 to l l0, the level of Cr a+ is lowest on the B site with trigonal axis 111, until the angle between M and I I00l reaches 55 ° ( M in the direction [111[). In this case the lowest level appears on the B site with C 3 along l i l . An electron of Cr 2+ when jumping from a B site to another (to lower its energy under rotation of the magnetic field) undergoes an exchange Cr 2+ <--:, Cr +3.

The directional order occurr ing in the 1 10 direc- tion in the 100 plane (projection of the I1 1 axis), which is due to the Cr z+ ~-~ Cr +3 exchange occur- ring on the B sites, could explain the occurrence of K u and the angle 0 u = 45 °.

R e f e r e n c e s

[i] S. B. Berger and H. L. Pinch, J. Appl. Phys. 38 (1967) 949. [2] B. Hoekstra and R. P. van Stapele, Phys. Stat. Sol. (b) 55

(1973) 607. [3] P. Gibart, L. Goldstein and k Brossard, J. Magn. Magn.

Mat. 3 (1976) 109. [4] L. Goldstein, Thesis Paris VI (1974). [5] P. Gibart, L. Goldstein, J. L. Dormann and M. Guittard, J.

Crystal Growth 24/25 (1974) 147. [6] H. Watanabe, Solid State Commun. 12 (1973) 355. [7] T. Jagielinski and H. Szyrnczak, Physica 86-88B (1977) 999. [8] B. Hoekstra, R. P. van Stapele and A. B. Boermans, Phys.

Rev. B 6 (1972) 2762. [9] M. Lleno, H. Nakanishi and T. Irie, J. Phys. Soc. Jap. 44

(1978) 2013.