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Field-Induced Spin Density Wave and Spiral Phases in a Layered Antiferromagnet

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Field-Induced Spin Density Wave and Spiral Phases in a Layered Antiferromagnet RAPID COMMUNICATIONS PHYSICAL REVIEW B 92, 020415(R) (2015) Field-induced spin density wave and spiral phases in a layered antiferromagnet M. B. Stone,1 M. D. Lumsden,1 V. O. Garlea,1 B. Grenier,2 E. Ressouche,2 E. C. Samulon,3 and I. R. Fisher3 1Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 2INAC-SPSMS, CEA & Universite´ Grenoble Alpes, 38000 Grenoble, France 3Department of Applied Physics and Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA (Received 13 May 2015; revised manuscript received 26 June 2015; published 28 July 2015) We determine the low-field ordered magnetic phases of the S = 1 dimerized antiferromagnet Ba3Mn2O8 using single-crystal neutron diffraction. We find that for magnetic fields between μ0H = 8.80 T and 10.56 T applied along the [110]¯ direction the system exhibits spin density wave order with incommensurate wave vectors of type (η,η,). For μ0H>10.56 T, the magnetic order changes to a spiral phase with incommensurate wave vectors only along the [hh0] direction. For both field-induced ordered phases, the magnetic moments are lying in the plane perpendicular to the field direction. The nature of these two transitions is fundamentally different: the low-field transition is a second-order transition to a spin density wave ground state, while the one at higher field, toward the spiral phase, is of first order. DOI: 10.1103/PhysRevB.92.020415 PACS number(s): 75.10.Jm, 75.30.Et, 75.40.Gb The mapping of Bose-Einstein condensates and quantum diagram in the vicinity of μ0Hc1. A second phase (phase II) was critical points onto the low-temperature magnetic field depen- also found to exist in this region for magnetic fields applied dent phase diagrams of quantum antiferromagnets has allowed perpendicular to the c axis with critical fields μ0Hc1a and for further understanding of the exotic ground states and μ0Hc1b between the quantum paramagnetic phase (QP) and excitations in these systems [1,2]. Although quantum critical phase II and between phase II and phase I, respectively [13]. points exist purely at zero temperature, their influence can be For magnetic fields applied along the c axis, only one phase observed experimentally in these systems at finite temperatures boundary has been observed with thermodynamic measure- with both thermodynamic and spectroscopic probes [3–5]. ments (phase I). These two phases have been proposed to be Dimerized quantum antiferromagnets have become an espe- due to the existence of a finite on-site anisotropy term, D,inthe cially popular testing ground for such behavior. These systems Hamiltonian as well as the existence of significant inter-layer often consist of strongly coupled spin pairs or dimers with exchange interactions along the c axis [14]. The focus of this a series of weaker interdimer interactions [6,7]. The system Rapid Communication is to examine these two phases using we examine, Ba3Mn2O8, has the additional complexity of neutron diffraction techniques in order to understand their competing nearest and next-nearest neighbor interactions and fundamental differences. We find that phase I corresponds of single-ion anisotropy. These effects serve to stabilize an to a long-range-ordered spiral phase with an incommensurate intermediate phase on the magnetic field–temperature phase wave vector. However the order in phase II is due to a spin diagram which has not been observed in other dimer systems. density wave, i.e., an amplitude-modulated uniaxial magnetic 5+ Ba3Mn2O8 is a S = 1 antiferromagnet with the Mn structure. ions forming a rhombohedral network of weakly coupled Single crystals of Ba3Mn2O8 were produced as described dimers. The spin dimers are oriented along the c axis of the in Ref. [11]. Single-crystal magnetic neutron diffraction mea- hexagonal unit cell as shown in the inset of Fig. 1(a). Interdimer surements were performed using the lifting counter two-axis interactions form a frustrated hexagonal network in the ab diffractometer D23 at the Institut Laue-Langevin in Grenoble, plane with additional out of plane couplings. Thermodynamic France. The m = 0.1 g sample was mounted in the (hh) measurements observed a gap in the magnetic excitation scattering plane. This orientation of the sample placed the spectra of approximately 1 meV [8] with a disordered spin- magnetic field perpendicular to the c axis to access both phases liquid ground state supporting well defined singlet-triplet I and II. The sample was mounted within a dilution refrigerator excitations. Inelastic neutron scattering measurements have placed within a 12 T vertical field magnet equipped with large confirmed this and refined the exchange constants illustrated vertical access to probe out-of-plane wave vectors with the in the inset of Fig. 1(a) [9,10]. lifting counter of the diffractometer. Nuclear and magnetic Application of a magnetic field along any direction of the peaks for refinement were measured at a wavelength of λ = crystal structure serves to lift the degeneracy of the triplet 1.2815 A˚ using a copper (200) monochromator. Throughout excitation into its three Sz components. At μ0Hc1 ≈ 9T,the this Rapid Communication, we index reflections using the spin gap is closed and a peak in specific heat and magnetic hexagonal lattice of Ba3Mn2O8. susceptibility indicates a transition to a magnetically ordered The low-temperature nuclear structure was refined at phase [11]. As the magnetic field increases, additional triplet μ0H = 12 T and T = 0.07 K using FullProf software [15]. No excitations condense into the ground state until μ0Hc2 ≈ 26 T change in nuclear Bragg peak position or scattering intensity where the system reenters a disordered paramagnetic phase. was observed as a function of applied magnetic field. This At larger magnetic fields higher order excitations begin to indicates that the nuclear structure does not change with condense into the ground state and a second ordered phase magnetic field and that the sample remained fixed in position as has been found to exist between μ0Hc3 ≈ 32.5 and μ0Hc4 ≈ the magnetic field was varied. The low-temperature high-field 47.9T[8,12]. Figure 1(a) illustrates the low-temperature phase structure agrees well with the previously reported structure 1098-0121/2015/92(2)/020415(5) 020415-1 ©2015 American Physical Society RAPID COMMUNICATIONS M. B. STONE et al. PHYSICAL REVIEW B 92, 020415(R) (2015) found to be incommensurate with the crystal lattice both in the (a) ∗ ∗ ∗ J0 a -b plane and along the c direction. We characterized the Mn5+ J4 propagation vectors as k = (η,η,) with ηII = 0.316 ± 0.01 and II = 0.04 ± 0.009 from reciprocal space scans in phase J2 J 3 II [18]. There are six potential propagation vectors of the type k = (η,η,)fortheR3¯m space group [17]. The six arms of J1 Phase I the k = (η,η,) star are k1 = (η, − 2η,), k2 = (−2η,η,), Phase II k3 = (η,η,), k4 = (η, − 2η, − ), k5 = (−2η,η, − ), k6 = QP (η,η, − ). An extensive search in reciprocal space at μ0H = 10 T found magnetic reflections for only two of these prop- II = − agation vectors which we label as k1 (ηII, 2ηII,) and II = − k2 ( 2ηII,ηII,). The other potential propagation vectors _ ¯ _ I for the R3m space group were examined, but found to not II (102) – K3 (102) – K2 _ have any magnetic scattering intensity. Both the kII and kII _ (003) + K I 1 2 II 3 ◦ (102) + K2 _ ± _ (113) – K I vectors are approximately 30 from the applied magnetic II 3 (102) – K1 __ I field direction. A small misalignment of the magnetic field (018) + K3 relative to the crystallographic axes may be favoring these II − II domains over the k3 k6 domains. The value of ηII agrees well with the location of the minimum in the zero-field magnon dispersion. The incommensurability along the c∗ axis is small but nonzero, and is a likely consequence of a small next-nearest-neighbor bilayer exchange coupling in the system that has not been accounted for in prior models of Ba3Mn2O8. For μ0H = 12 T, we observe a single incommensurate FIG. 1. (Color online) (a) Magnetic field versus temperature propagation vector with greater overall intensity than that ⊥ phase diagram for Ba3Mn2O8 with μ0H c. Open and closed found for either of the two propagation vectors in phase II. black points for T>0.3 K are from the low magnetic field range The incommensurability along the c∗ axis vanishes, = 0 ± of Ref. [11], and were determined from magnetocaloric effect I 0.009, and the incommensurability in the plane shifts slightly (MCE) and heat capacity (C ) measurements. Points for T<0.2K p η = 0.313 ± 0.01. There are three potential propagation correspond to the critical fields observed in neutron scattering I vectors of the type k = (η,η,0) for the R3¯m space group [17]. measurements (e.g., Fig. 2). Phase boundary lines are guides to the = eye. Phase I and phase II are described in the text. Phase QP is An extensive search in reciprocal space at μ0H 12 T found a quantum paramagnetic disordered phase. Inset shows the nuclear magnetic reflections only for propagation vectors of the type + I = crystal structure only illustrating the Mn5 S = 1 sites. Intradimer k3 (ηI,ηI,0). The equivalent propagation wave vectors were (interdimer) exchange is depicted with solid (dashed) lines with examined and found not to exist. The magnetic Bragg peak labeling of exchange paths as in Ref. [10]. (b) Rocking curves of locations observed in phase I are at wave vectors very near the magnetic Bragg peaks at μ0H = 10 T. (c) Rocking curves of magnetic minima of the zero-field dispersion of Ba3Mn2O8 just as in Bragg peaks at μ0H = 12 T.
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