Phase diagram of Dy3Al5O12 and magnetic linear birefringence

Physica B 162 (1990) 71-73 North-Holland

PHASE DIAGRAM

OF Dy3AI,0,,

N.P. KOLMAKOVA

LINEAR

BIREFRINGENCE

A.I. POPOV

and

Moscow institute of Electronic

AND MAGNETIC

Technics, Moscow,

USSR

Received 17 .4ugust 1989

Dysprosium aluminium garnet is an Ising-like antiferromagnet with a multiaxis magnetic structure and an induced staggered field interaction. It is found that when decreasing the temperature down to about 1.3 K the transition between two antiferromagnetic phases (A’ +A-) should occur. It is shown that magnetic linear birefringence is a convenient method account

of identification of this phase transition. Numerical calculations of the magnetic linear birefringence fully for the experimental field dependence for H (1[l 1 l] and T = 1.35 K < T, = 2.54 K.

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DAG is an ideal system to explore different phase transitions, which may be well described by the Ising model [l] and besides it is a multisublattice noncollinear antiferromagnet. As a consequence of the existence of twelve inequivalent positions for rareearth (RE) ions in a primitive cell of the garnet structure, a field of arbitrary orientation may produce different effects at different sites. So the metamagnetic behavior, which is characteristic for DAG in the ordered state below the tricritical temperature (T, = 1.66 K), reveals itself in a different manner for different field directions. It is important that DAG belongs to an insufficiently explored and numerous enough class of antiferromagnets in which the antiferromagnetic order parameter can interact with the external field (the induced staggered field interaction) [2]. The competition between various mechanisms of staggered field may give rise to a complicated phase diagram, the antiferromagnetic order parameter changing its sign one or more times as a function of temperature and field. Such phase diagrams are interesting by themselves, and they give an opportunity to investigate the dynamics of the order-order transitions. It is of special interest to clarify manifestations of such transitions in the measured thermodynamic properties. pound

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In this work we have considered the complicated phase diagram of DAG, caused by the existence of the induced staggered field, and the peculiarities of the magnetic linear birefringence (MLB) at the phase transitions. For T < TN = 2.54 K and H ]][l 1 l] the magnetic structure of DAG may be depicted by two order parameters: the antiferromagnetic parameter n and the ferromagnetic parameter M. For sufficiently low temperatures (T < T, = 1.66 K) in the field interval ]H] < H,, (H, = 4 kOe, H, is the field of the metamagnetic transition) M = 0, for IH] > H,,; n = 0. The interaction of the antiferromagnetic order parameter with an external field, described by the invariant H,n, where H, is the so-called induced staggered field [2], results in the difference of energies of two antiferromagnetic phases A+(7 > 0) and A-(7 < 0). According to the terminology of ref. [2] phase A’ corresponds to the situation, where the magnetic moments at u-sites (the local H,-component is equal to zero) are antiparallel to the field projection onto the Ising axis, and the magnetic moments at b-sites (the local H,-component is equal to zero) are parallel to the field projection. The stabilization of one of the phases (A’ or A-) by the field occurs as a result of the competition of two mechanisms. The first mechanism is the crystal field (CF) mechanism, caused by the influence of the crystal field. The second mechanism is the staggered interaction (SI) mechan-

ism, which is connected with the different energy of spin excitations in the phases A’ and A- [2]. It is important that the SI mechanism always stabilizes the A+ phase, its contribution to the formation of magnetic structure vanishes when T-+0. The contribution of the CF mechanism is not vanishing for T+O. It is known that at T = 1.35 K a strong external field H )( [ 1 1 l] stabilizes the A’ phase [2]. We have calculated the contribution of the CF mechanism to H,. The calculation was performed on the basis of the following Hamiltonian of the Dy” ion in the k-th position

the paramewhere %& is the CF Hamiltonian, ters of which are well known from the specscopic data [3], %z is the Zeeman term, the last term in (1) is the Hamiltonian of the exchange interaction in the mean-field approximation. the Ising character of the behavior of magnetic moments of the Dy”+ ions being taken into account. The value of He, was determined from the splitting of the ground doublet of the Dy’+ ion for H = 0, which is equal to 7.5 K according to ref. [l], this corresponds to H,, = 6.2 kOe. It turned out that the CF mechanism stabilizes the Aphase, and never the A’ phase. This result is stable in a sufficiently wide region of the CF parameters consistent with spectroscopic data and not differing much from the values determined in ref. [3]. We should note that when considering the CF mechanism we take into account in a natural way the g-value and Van Vleck susceptibility mechanisms, which were discussed separately in ref. [2], and Zeeman effects of the highest orders as well. For the feasible region of the CF parameters this mechanism stabilizes the A- phase regardless of the relation between the values g, and g,.. In ref. [2], where the g-value mechanism is considered separately, the realization of one of the phases is determined by the relation of these values. Our calculation has shown that for the CF parameters listed in ref. [3] the value of the contribution of the CF mechanism to H, for H = 20 kOe is equal to O.O45cm-‘/ion. We

should note that this quantity is rather sensitive to variations of the CF parameters and to the consideration of the influence of the intermediate coupling. From ref. [2] it follows that for T = 1.35 K and H = 20 kOe, the value of the contribution of the SI mechanism to H, is equal to -0.053 cm ~‘/ion. Consequently for T r 1.35 K the A’ phase really exists. For sufficiently low temperatures, when the Sl mechanism which stabilizes the Al phase at 7‘: 1.3SK, is frozen out to a sufficient degree. the CF mechanism becomes dominating, and it stabilizes the A phase. So when lowering the temperature the phase transition A* -+ A should occur. The possibility of the appearance of such a transition was discussed in ref. [2]. Calculating according to ref. [2] the temperature dependence of the SI contribution we have determined the temperature of the A’ -+ A transition: T, = 1.3 K. However. it is necessary to note that rather small deviations of the CF parameters from the values given in ref. [3] can somewhat decrease this value of T,. The very important information on the magnetic structures of DAG and phase transitions may be received from the investigations of the MLB of this compound. For the RE crystals the MLB in the visible region is determined by the allowed electricdipole transitions between the CF levels of the ground 4f configuration and the excited ones. This was used in ref. [4] for the numerical calculations of the MLB for the RE aluminium and gallium garnets in the paramagnetic region. The calculations [4] have allowed to infer that using the available information on the parameters of the interaction of RE ions with the CF we can fully account for the measured field and temperature dependences of the MLB, the signs and anisotropy of the effect for the aluminium and gallium garnets with the Tb”, Dy’++, Er31 and Tm”+ ions. The peculiarities of MLB in the ordered state of DAG are seen very clearly from the formula which is analytically found in the framework of the perturbation theory, analogous to ref. [5] and which determines the dependence of MLB on H, 77 and M:

N.P. Kolmakova and A.I.

An=AHq+BHM.

(2)

Here A and B are the quantities which are determined by the electronic structure of the Dy3+ ion in the CF of DAG. It follows from eq. (2) that MLB is an even (with respect to the sign of an external field) phenomenon in the region IH( > H,, where 77= 0, and M - H; it is an odd phenomenon in the region 1H I< H,, where M = 0. Besides, in the region IHI < H,, for the phase transition A+ -+ A- a change of the MLB sign should occur as the antiferromagnetic parameter 77changes its sign. To account quantitatively for the MLB for T < TN on the basis of the Hamiltonian (1) we have performed the numerical calculations of the field dependences of components of quadrupole moments of the 4f shell of Dy3+ ions, which determine the MLB [4]. In fig. 1 the field dependence of the MLB measured in ref. [6] for T = 1.35 K and H 1)[l 1 l] (continuous curve) and the calculated curves for the A’ phase (dashed curve) and for the phase A- (dotted curve) are shown. It is seen that for the A+

Popov

I Properties

of Dy,Al,O,,

73

phase, which is realized in DAG at T = 1.35 K, the calculated dependence An(H) is in accordance with the experimental one over the whole field interval. The MLB is an odd function of the field for IH I < H, and experiences jumps in the fields of metamagnetic transitions. For H = H,, > 0 the MLB changes its sign. We note that consideration of the exchange splitting essentially influences the field dependence of MLB in the paramagnetic region for H < 10 kOe. As a consequence of the transition A’+ Afor T < T, the change of the MLB sign takes place in the interval (HI
Acknowledgement

We would like to express our thanks to R.Z. Levitin for his interest in this work and valuable remarks.

l@An References

Fig. 1. Field dependence of the MLB at T= 1.35 K, H (1[I 1 l] for a DAG crystal. Continuous curve is An(H) measured in ref. [6], dashed curve is An(H) calculated for the A’ phase, dotted curve is An(H) calculated for the Aphase.

[l] W.P. Wolf, B. Schneider, D.P. Landau and B.E. Keen, Phys. Rev. B 5 (1972) 4472. [2] N. Giordano and W.P. Wolf, Phys. Rev. B 21 (1980) 2008. [3] R.L. Wadsack, J.L. Lewis, B.E. Argyle and R.K. Chang, Phys. Rev. B 3 (1971) 4342. [4] N.P. Kolmakova, R.Z. Levitin, A.I. Popov, N.F. Vedernikov, A.K. Zvezdin and V. Nekvasil, J. de Phys. 49 (1988) C8-9.55; ibid., Phys. Rev. B (to be published). [5] N.F. Vedemikov, A.K. Zvezdin, R.Z. Levitin and A.I. Popov, JETP 93 (1987) 2161. [6] J.F. Dillon, Jr., L.D. Talley and E.Yi Chen, AIP Conf. Proc. N34 (1974) 200.