Journal of Magnetism arid Magnetic Materials 90 & 91(1990) 289-290North-Holland

289

Chiral criticality and multicriticality in triangular antiferromagnets

Hikaru KawamuraDepartment of Physics, College of General Education, Osaka Unioersity, Toyonaka 560. Japan

The phase diagram and critical behavior of weakly-anisotropic antiferromagnets on a stacked-triangular lattice in appliedmagnetic fields are studied by using a scaling theory in connection with recently proposed new chiral universality.Experimental implications for some ABXrtype hexagonal compounds are discussed.

Fig. 1. Schematic 11- T phase diagrams of weakly anisotropicantiferromagnets on a bipartite lattice; (a) uniaxial magnets ina field applied along an easy axis; (b) planar magnets in a field

applied in an easy plane.

phase. In the axial case, three distinct critical lines anda first-order spin-flop line meet at a new type of multi­critical point located at (Tm , H m ) ; see fig. 2a. In theplanar case, two distinct critical lines meet at a zero-fieldmulticritical point. often quoted as a tetracritical point;see fig. 2b. Recently, Kawamura, Caille and Plumer (5)theoretically examined the critical properties of thesesystems, which were determined as given in fig. 2. In theaxial case, new chiral universality appears along thehigh-field phase boundary (11=2 chiral) and at the

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The phase diagram and critical behavior of magneticmaterials exhibiting multicritical points have been ofgreat interest. Consider, for example, weakly-aniso­tropic Heisenberg antiferromagnets on bipartite lattices.Typical magnetic .field-temperaturc phase diagrams areshown in fig. 1 for the cases of axial and planar ani­sotropy. In particular, axial magnets in a field appliedalong an easy axis are known to exhibit a multicriticalpoint, termed bicritical point, at which two distinctcritical lines and a first-order spin-flop line meet. Criti­cal properties of these systems were studied theoreti­cally by Kosterlitz et al. [1), with the results given in fig.1. A noticeable point is that criticality at the multicriti­cal point as well as along the critical line is that of thestandard O(n) Heisenberg universality. Applying a scal­ing theory, Fisher et al. (1) derived various observablepredictions, which were supported by subsequent ex­periments (2). It thus appears that the multicriticalbehavior of unfrustrated antiferromagnets in a field isnow fairly well understood.

On the other hand, in the case of frustrated magnetssuch as antiferromagnets on a stacked-triangular lattice,an entirely new situation may arise. It has been claimedby the author (3) that certain O(n )-symrnetric magnetsexhibiting noncollinear spin ordering should belong tonew universality classes, called O(n) chiral universalityclasses, distinct from the standard O(n) Heisenberguniversality series, with the associated new exponentsa - 0.4, f1- 0.25, y - 1.1, P - 0.53 for II = 2 and a­0.34, f1- 0.28, y - 1.1, P - 0.55 for II = 3. Indeed, re­cent experiments on triangular antiferromagnetsCsMnBr3 , VCI2 • VBr2 and helical magnets Ho, Dy havegiven support to this prediction (4). Under these cir­cumstances, the phase diagram and multicritical behav­ior of such frustrated magnets are of particular interest.

Consider weakly-anisotropic magnets on a three-di­mensional stacked-triangular lattice, in which both interand intraplane couplings are antiferromagnetic.' Mag­netic fields are assumed to be applied along an easy axisor in an easy plane for the axial and planar magnets,respectively. Typical magnetic phase diagrams are shownin fig. 2 together with the spin configuration in each

0304-8853/90/$03.50 <EJ 1990 - Elsevier Science Publishers B.V. (North-Holland) and Yamada Science Foundation

290 H. Kawamura I Critical behacior in triangular antiferromagnets

TFig. 2. Schematic ll-T phase diagrams of weakly amsotropican tiferromagnets on a stacked-triangular latt ice; (a) uniaxialmagnets in a field applied along an easy axis; (b) planar

magnets in a field applied in an easy plane.

multicritical point (n = 3 dural), while in the planarcase, it appears at the zero-field multicritical point(n = 2 chiral) , A scaling theory has led to various ob­servable predictions [5]: for example, in the axial case,three critical lines near the multicritical point behave asIll- Hm 1ex: (T - Tm )9, <P - 1.06 ·being the anisotropy­crossover exponent associated with 11 = 3 chiral class,while in the planar case, two critical lines near thezero-field multicritical point behave as H 2 ex: 1T - Tm 19 ,

<P -1.04 being the anisotropy-crossover exponent asso­ciated with 11 = 2 chiral class. For further details of thescaling predictions see ref. [5].

Now we briefly discuss experimental implications ofthe theory in connection with a class of hexagonalinsulators (stacked-triangular-Iallice antiferromagnets)with the general chemical formula ABX). Althoughthese compounds are magnetically quasi-one-dimen­sional, most of them are known to undergo magnet icphase transitions into a three-dimensionally orderedstate. A well-studied example of axial triangular antifer­romagnets is CsNiCI). The H-T phase diagram of thiscompound was determined by Johnson, Rayne and

Friedberg [6] by means of a susceptibility measurement.Recently, the behavior of phase boundaries near themulticritical point have been studied by Poirier, Cailleand Plumer (7] using ultrasonic velocity measurements.Their results suggest that the associated crossover expo­nent <P is close to but a bit larger than unity, which isconsistent with the theoretical prediction. Other candi­date for axial magnet s may be CsNiBr), RbNiBr) andCsMn1 3• To the author's knowledge, however, the fullmagnetic phase diagram of these compounds have notyet been determined experimentally.

- A typical example of the planar triangular anti ferro­magnet is CsMnnr3• In particular, its criticality at thezero-field transition was extensively studied by neutronscattering [4,8] , the results being consistent with theoccurrence of a new chiral criticality. More recently,magnetization measurements by Goto, Inami and Ajiro[9] have yielded crossover exponents associated with thetwo phase boundaries, <Pupper - 1.02 and <Plower - 1.07,in good agreement with the theoretical value <Pupper =

<Plower - 1.04. RbMnnr) is known to exhibit an incom­mensurate basal-plane spin ordering in zero field, incontrast to esMnBr) which exhibits a 120 0 spin struc­ture. However, the theory predicts a similar behavior atleast concerning its multicritical behavior near zerofield. CsVCI3 may have even weaker magnetic ani­sotropy and thus may exhibit a nearly isotropic (11 = 3chiral) multicritical behavior.

We finally note that essentially similar phen omenacould be expected in other types of magnets includinghelical magnets such as Ho, Dy, Tb and axial sinusoidalmagnets such as Er, although for some axial magnets, amagnetic field needed to reach the multicritical pointmight be beyond the reach of experimental realization.

References

[1J M.E. Fisher and D.R. Nelson, Phys. Rev. Lett . 32 (1974)1350. J.M. KosterIitz, D.R. Nelson and M.E. Fisher, Phys.Rev. B 13 (1976) 412.

[2J See, for example, A.R. King and H. Rohrer, Phys. Rev. B19 (1979) 5864.

[3J H. Kawamura, Phys. Rev. B 38 (1988) 4916; J. Phys. Soc.Jpn. 58 (1989) 584.

[4J See, for example, H. Kawamura, J. App!. Phys. 63 (1988)3086 and refs. cited therein .

(5) H. Kawamura, A. Caille and M.L. Plumer, Phys. Rev. B 41(1990) 4416.

[6J P.B. Johnson, J.A. Rayne and S.A. Friedberg, J. App!.Phys. 50. 50 (1979) 1853.

(7) M. Poirier. A. Caille and M.L. Plumer, Phys, Rev. B 41(1990) 4869.

(8) B.D. Gaulin, T.e. Mason, M.F. Collins and J.Z. Larese,Phys. Rev. Lett. 62 (1989) 1380.

[9J T. Goto, T. Inami and Y. Ajiro, J . Phys. Soc. Jpn. 59 (1990)2328.

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