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It is shown that site disorder induces noncoplanar states, competing with the thermal selection of coplanar states, in the nearest neighbor, classical Kagome Heisenberg antiferromagnet. For weak disorder, it is found that the ground state energy is the sum of energies of separately satisfied triangles of spins. This implies that disorder does not induce conventional spin glass behavior. A transformation is presented, mapping ground state spin configurations onto a folded triangular sheet (a new kind of "spin origami") which has conformations similar to those of tethered membranes.PACS numbers: 75.10.Nr, 75.10.Hk, 75.50.Ee It is well known that geometrical frustration in some nonbipartite lattices prevents long range magnetic order from being established and allows novel kinds of low temperature magnetic states to develop [1-3]. The Heisenberg Kagome antiferromagnet with nearest neighbor couplings is one of the most interesting of such systems. The classical system exhibits a rich, nontrivial ground state degeneracy, with both coplanar and noncoplanar states in the degenerate manifold. For the coplanar states, linear spin-wave theory yields one zero-energy mode for every point in the Brillouin zone [4,5]. All noncoplanar states have fewer zero modes, and, as a result, thermal effects select a nematiclike coplanar ground state [5], an example of the "order by disorder" effect [6,7]. Numerical studies have confirmed the tendency for thermal selection of the nematiclike state [5,8], and there is also evidence [4, 5, 8-10] for a tendency toward \/3 x \/3 ordering in the plane.By far the best-studied experimental Kagome system is the magnetoplumbite, SrCr9jr,Gai2-9pOi9 [11]. For p = 1, this system contains dense Kagome layers, separated by dilute triangular layers, of Cr. Although its CurieWeiss temperature 0cw (foi* P = 1) is over 500 K, no sublattice ordering is found down to helium temperature, where a spin glass, rather than an ordering transition is observed at a temperature T/. The ratio Qcw/Tf is about 130, at least for p > 0.5 [11][12][13]. T/ itself varies rapidly with doping [12,13], having its maximum value of about 4 K near p = 1, where one might expect structural disorder to be least important, and falling monotonically as p is reduced. These observations raise two questions:(1) Why is spin glass behavior, with a temperature scale of order J, not generated by nonmagnetic impurities at the 10% to 20% level and (2) what is the origin of the spin-glass-like behavior which is observed even foip^ 1? It is the first question which is addressed in this Letter, while the second is discussed briefly in our conclusions. Our main results are as follows:(1) Quite generally we find that disorder induces noncoplanarity in the ground state. At low temperatures, the nematiclike state, which is selected by thermal fluctuations, is overwhelmed by this tendency of disorder to induce noncoplanarity [14].(2) For a large class of distributions of spins of random magnitude, including dilute distributions of vacancies, the gro...

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We consider the quantum Heisenberg antiferromagnet on a face-centered-cubic lattice in which J, the secondneighbor (intrasublattice) exchange constant, dominates J′, the first-neighbor (intersublattice) exchange constant. It is shown that the continuous degeneracy of the classical ground state with four decoupled (in a mean-field sense) simple cubic antiferromagnetic sublattices is removed so that at second order in J′/J the spins are collinear. Here we study the degeneracy between the two inequivalent collinear structures by analyzing the contribution to the spin-wave zero-point energy which is of the form H eff /J=C 0 +C 4 σ 1 σ 2 σ 3 σ 4 (J′/J) 4 +O(J′/J) 5 , where σ i specifies the phase of the ith collinear sublattice, C 0 depends on J′/J but not on the σ's, and C 4 is a positive constant. Thus the ground state is one in which the product of the σ's is −1. This state, known as the second kind of type A, is stable in the range |J′|<2|J| for large S. Using interacting spin-wave theory, it is shown that the main effect of the zero-point fluctuations is at small wave vector and can be well modeled by an effective biquadratic interaction of the form ΔE Q eff =−1/ 2Q∑ i,j [S(i)⋅S(j)] 2 /S 3 . This interaction opens a spin gap by causing the extra classical zero-energy modes to have a nonzero energy of order J′√S. We also study the dependence of the zero-point spin reduction on J′/J and the sublattice magnetization on temperature. The resulting experimental consequences are discussed. Disciplines Physics | Quantum Physics CommentsAt the time of publication, author A. Brooks Harris was also affiliated with Tel Aviv University, Tel Aviv, Israel. Currently, he is a faculty member in the Physics Department at the University of Pennsylvania. We consider the quantum Heisenberg antiferromagnet on a face-centered-cubic lattice in which J, the second-neighbor ͑intrasublattice͒ exchange constant, dominates JЈ, the first-neighbor ͑intersublattice͒ exchange constant. It is shown that the continuous degeneracy of the classical ground state with four decoupled ͑in a mean-field sense͒ simple cubic antiferromagnetic sublattices is removed so that at second order in JЈ/J the spins are collinear. Here we study the degeneracy between the two inequivalent collinear structures by analyzing the contribution to the spin-wave zero-point energy which is of the form H eff /JϭC 0 ϩC 4 1 2 3 4 (JЈ/J) 4 ϩO(JЈ/J) 5 , where i specifies the phase of the ith collinear sublattice, C 0 depends on JЈ/J but not on the 's, and C 4 is a positive constant. Thus the ground state is one in which the product of the 's is Ϫ1. This state, known as the second kind of type A, is stable in the range ͉JЈ͉Ͻ2͉J͉ for large S. Using interacting spin-wave theory, it is shown that the main effect of the zero-point fluctuations is at small wave vector and can be well modeled by an effective biquadratic interaction of the form ⌬E Q eff ϭϪ 1 2 Q͚ i, j ͓S(i)•S( j)͔ 2 /S 3 . This interaction opens a spin gap by causing the extra classical zero-energy modes to have ...

We consider a quasi-one-dimensional spin S quantum antiferromagnet as a function of dilution x. We show that in some regimes, dilution suppresses quantum fluctuations. For small enough interchain coupling and integer S, the ground state is disordered for x-0, but antiferromagnetically ordered for x > x c . We estimate that for large S, x c is exponentially small. This is a novel dilution-induced ordering transition.

Quantum effects on magnetic ordering in body-centered-tetragonal antiferromagnets with only nearestneighbor interactions are studied in detail using interacting spin-wave theory. The model consists of M noninteracting (in a mean-field sense) antiferromagnetic planes which together form a body-centeredtetragonal structure. We obtain the leading quantum correction of order 1/S from the zero-point energy for a system of M planes whose staggered moments have arbitrary orientations. The infinite degeneracy of the ground-state manifold of this system is partially removed by collinear ordering in view of effects previously calculated by Shender at relative order J 2 ⊥ /(J 2 S), where J, the antiferromagnetic in-plane exchange interaction, is assumed to dominate J ⊥ , the out-of-plane interaction which can be of either sign. We study the complete removal of the remaining degeneracy of the collinear spin structures by assigning an arbitrary sign σ i (i=1,2,...M) to the staggered moment of the planes. Our result for the zero-point energy (for M>2) up to the sixth order inwhere C>0 and E 1 are constants independent of the σ's, and E G is the classical ground-state energy. (Here sums from i to j when j<i are interpreted to be zero.) Surprisingly, there is no σ-dependent contribution at order j 4 /S. This result shows that for M>4 second-neighboring planes are antiferromagnetically coupled in the ground state and thus the three-dimensional spin structure cannot be described by a single wave vector, as is often assumed. At order j 4 , σ-dependent terms first appear at order 1/S 3 and these also favor antiferromagnetic coupling of alternate planes. Disciplines Physics | Quantum Physics CommentsAt the time of publication, author A. Brooks Harris was also affiliated with Oxford University and Tel Aviv University. Currently, he is a faculty member in the Physics Department at the University of Pennsylvania. Quantum effects on magnetic ordering in body-centered-tetragonal antiferromagnets with only nearestneighbor interactions are studied in detail using interacting spin-wave theory. The model consists of M noninteracting ͑in a mean-field sense͒ antiferromagnetic planes which together form a body-centered-tetragonal structure. We obtain the leading quantum correction of order 1/S from the zero-point energy for a system of M planes whose staggered moments have arbitrary orientations. The infinite degeneracy of the ground-state manifold of this system is partially removed by collinear ordering in view of effects previously calculated by Shender at relative order J Ќ 2 /(J 2 S), where J, the antiferromagnetic in-plane exchange interaction, is assumed to dominate J Ќ , the out-of-plane interaction which can be of either sign. We study the complete removal of the remaining degeneracy of the collinear spin structures by assigning an arbitrary sign i (iϭ1,2, . . . M ) to the staggered moment of the planes. Our result for the zero-point energy ͑for M Ͼ2͒ up to the sixth order in jϭJ Ќ /J iswhere CϾ0 and E 1 are constants indep...

Phase diagrams and magnetic properties of the frustrated metamagnets have been studied. We have shown that strong disorder can narrow the temperature and the magnetic-field interval where the metamagnetic transition takes place. With increasing disorder this discontinuous transition disappears transforming into the second-order phase transition. The magnetic field usually widens the region of the (H, T) phase diagram where the antiferromagnetic nonergodic state exists. The de Almeida-Thouless line has a jump when crossing the metamagnetic phase transition line which results in discontinuous transition into the nonergodic state.

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