Magnetic and orbital ordering in the spinel MnV2O4
V. O. Garlea, R. Jin, D. Mandrus, B. Roessli, Q. Huang, M. Miller, A. J. Schultz, S. E. Nagler
aa r X i v : . [ c ond - m a t . s t r- e l ] N ov Magnetic and orbital ordering in the spinel MnV O V. O. Garlea, ∗ R. Jin, D. Mandrus, B. Roessli, Q. Huang, M. Miller, A. J. Schultz, and S. E. Nagler Neutron Scattering Science Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA. Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA. Laboratory for Neutron Scattering ETHZ & Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland NIST Center for Neutron Research, Gaithersburg, Maryland 20899, USA IPNS Division, Argonne National Laboratory, Argonne, Illinois 60439, USA. (Dated: October 24, 2018)Neutron inelastic scattering and diffraction techniques have been used to study the MnV O spinel system. Our measurements show the existence of two transitions to long-range ordered ferri-magnetic states; the first collinear and the second noncollinear. The lower temperature transition,characterized by development of antiferromagnetic components in the basal plane, is accompaniedby a tetragonal distortion and the appearance of a gap in the magnetic excitation spectrum. Thelow-temperature noncollinear magnetic structure has been definitively resolved. Taken together, thecrystal and magnetic structures indicate a staggered ordering of the V d orbitals. The anisotropygap is a consequence of unquenched V orbital angular momentum. Understanding the consequences of orbital degeneracy,and the interplay of spin, orbital and lattice degrees offreedom, has emerged as a forefront area of condensedmatter physics. One of the most investigated prototyp-ical systems in which these effects are important is thevanadium oxide spinel, with formula A V O . There hasbeen much experimental and theoretical effort to under-stand the properties of A V O [1, 2, 3, 4, 5, 6, 7, 8, 9],where A is a non-magnetic species such as Mg [1], Zn [2],or Cd [3]. As is well known, the V (3 d ) ion sits ina position of local octahedral symmetry and thereforehas a threefold degenerate orbital ground state. Fur-thermore, the V ions occupy the vertices of a tetrahe-dron and their mutual antiferromagnetic superexchangeinteractions are topologically frustrated. A common fea-ture found in these materials is a sequence of two phasetransitions [1, 2, 3]. The higher temperature transitionis a structural distortion involving a compression of theVO octahedra and a consequent partial lifting of the or-bital degeneracy. The orbital ordering is accompanied,at lower temperature, by an antiferromagnetic ordering.Various models [4, 5, 6, 7, 8, 9] have been proposed toexplain this behavior. However, up to date, there is notyet a full consensus on the precise nature of the orbitalordering.Replacing the atom at the A site by a magneticspecies changes the physics, leading to different and veryinteresting behavior. Recent attention has turned toMnV O [10, 11, 12, 13], where the A site ion, Mn ,is in a 3 d high spin configuration S =5/2 with quenchedorbital angular momentum. MnV O exhibits a phasetransition at approximately 56 K from a paramagneticcubic phase into a collinear ferrimagnetic phase, also witha cubic structure. Around 53 K there is a second tran-sition to a tetragonal structure, with the spin structurebecoming non-collinear [10]. Recently, it was found thatthe cubic to tetragonal transition could be induced bya modest magnetic field of a few Tesla [11]. Since then there have been careful x-ray scattering studies of thestructure showing that the low temperature space groupis I /a [12]. In addition, it has been suggested based onNMR and susceptibility measurements that the systemalso exhibits a re-entrant spin glass behavior [13]. In thispaper we report the results of neutron scattering mea-surements on both powder and single crystal samples ofMnV O . Neutron measurements show the existence oftwo phase transitions, and allow for a definitive deter-mination of the low temperature non-collinear ferrimag-netic structure. Inelastic neutron scattering shows thatthe cubic to tetragonal transition is associated with theopening of a gap in the magnetic excitation spectrum.These observations put tight constraints on theoreticalmodels for the spin and orbital physics of MnV O .The powder sample used in this study was prepared bysolid-state reaction from stoichiometric mixture of MnOand V O . MnV O single crystals were grown usingthe floating-zone technique. All samples were charac-terized by x-ray diffraction and magnetization measure-ments. The temperature dependence of the low field(0.1 kOe) magnetization of a MnV O single crystal un-der zero-field cooling (ZFC) and field cooling (FC) con-ditions is shown in Fig. 1(a). Qualitatively, the mag-netization curves look similar to those reported previ-ously [12, 13]. Upon decreasing temperature, the FCmagnetization goes through a maximum and shows asharp decrease before it starts to increase again. As visi-ble in Fig. 1(a), the rapid decrease in magnetization, near50 K, marks the point where the FC and ZFC curvesbegin to diverge. Below 50 K, the ZFC magnetizationshows a gradual decrease, while the FC magnetizationincreases.To monitor the changes in the crystal and magneticstructures across these transitions, several neutron scat-tering experiments were performed. Time-of-flight neu-tron diffraction measurements were carried out usingthe single crystal diffractometer (SCD) at the IPNS,
10 20 30 40 50 60 70 80 90012345 (c)(b)
T (K) M / H ( c m / m o l ) ZFCFCH= 0.1 TeslaH // [001] (a)
40 45 50 55 60 65 70 (400)
T (K)
75 K40.5 K (004) T (400)(220) T l (r.l.u.) I n t en s i t y ( a r b . un i t s ) I n t eg r a t ed I n t en s i t y ( a r b . un i t s ) (200) MnVV
Tetragonal Cubic
FIG. 1: (a) The zero-field-cooling (ZFC) and the field-cooling(FC) temperature dependence of magnetization in MnV O single crystal. (b) Temperature dependence of the (400) and(200) Bragg peaks integrated intensities showing the existenceof two magnetic transitions. The solid lines are guides to theeye. (c) Splitting of the (400) cubic peak into two tetragonal(220) T and (004) T , as the crystal structure distorts to form abody-centered tetragonal phase. Argonne, on a 0.2 g single-crystal specimen. High-resolution neutron powder diffraction measurements wereperformed on the BT1 diffractometer at NCNR, using thewavelength 1.54 ˚A. Additional elastic and inelastic mea-surements were conducted using the cold-neutrons 3-axisspectrometer TASP, at the SINQ spallation source. Forthese, we made use of a single-crystal of approximately1.3 g, aligned in the ( hhl ) horizontal scattering plane.Elastic measurements were carried out using a monochro-matic neutron beam (with wave-vector k = 1.97 ˚A − ) and20 ′ collimators in front and after the sample. For theinelastic neutron scattering (INS) measurements, TASPspectrometer was operated with a fixed final energy E f = 3.5 meV, open − ′ − ′ − ′ collimation, and a cooledBe filter after the sample.Fig. 1(b) shows the evolution with temperature of the(400) and (200) peaks integrated intensities, measuredusing the SCD. Diffraction peaks are indexed in thecubic-spinel structure. The (400) peak intensity startsto increase at approximately 60 K ( T F ) and exhibits akink at about 52 K ( T S ). As the temperature is low-ered, the intensity continues to increase and saturatesbelow 45 K. It is noteworthy that the order-parameterprofile shows a long tail which extends above 70 K. Thismay be due to the critical scattering associated with ashort-range order above T F . A very similar temperaturedependence was observed for the (220) peak, measuredusing the 3-axis spectrometer (Fig. 3(b)). In contrast, the (200) reflection, which is forbidden in the cubic symme-try ( F d m ), appears only below T S and increases as thetemperature decreases. Further examination of diffrac-tion data confirmed that the transition at T S is relatedto the modification of the crystal structure. The occur-rence of tetragonal distortion is clearly demonstrated inthe Fig. 1(c) by the splitting of the (400) Bragg peakinto two components, which in the tetragonal unit cell( a T ≈ a/ √ c T ≈ c ) can be indexed as (220) T and(004) T .The low-temperature crystal structure was determinedfrom a complete set of SCD data that mapped the en-tire reciprocal space. Mixed nuclear and magnetic reflec-tions with Q (= 4 π sin θ/λ ) ≤ − were excluded fromthe structure refinement, carried out using GSAS [16].Checking the systematic absences among high- Q reflec-tions, we confirmed the I /a space group, recently pro-posed by Suzuki et al. [12]. This space group impliesa relaxation of the symmetry constraints at the oxy-gen site (Wyckoff positions: 16 f ). Thus, the compres-sion of the VO octahedra along the c crystallographicaxis ( c T /a T ≈ .
98) is accompanied by a small distor-tion of the V-O bonds in the basal plane. Referring toFig. 2(a) which shows a view of the V-tetrahedron alongthe c axis, the V-O bonds are arranged in an antiferrodis-tortive alternating pattern with short (dashed lines) andlong (bold lines) distances. This is consistent with the so-called A -type orbital ordering with antiferro-order alongthe c axis and ferro- in the ab plane, similar to that pro-posed by Tsunetsugu and Motome [4, 5] for V-spinelswith nonmagnetic A -site cations.Between the two transition temperatures ( T F , T S ), themagnetic scattering appears only on top of the structuralreflections, validating the collinear ferrimagnetic modelproposed by Plumier and Sougi [10]. On the other hand,one observes below T S the appearance of additional mag-netic peaks: ( hk
0) with h, k = 2 n , symmetry-forbiddenin the tetragonal space-group I /a . For instance, thecubic (200) peak, indexed in the tetragonal lattice as(110) T , is purely magnetic and can be explained by anantiferromagnetic (AFM) ordering within the ab plane.Nevertheless, the c -axis components of Mn and V mo-ments remain ferrimagnetically ordered. To generate allthe spin configurations compatible with the crystal sym-metry we carried out a group theory analysis [17] usingthe programs SARA h [18] and BasIREPS [19]. There areeight irreducible representations (IR) associated with the I /a space group and k → =(000). Among these, only oneallows for a ferrimagnetic alignment of Mn and V sublat-tices. The basis vectors of this representation are listedin Table I. It shows that the Mn moments are alignedparallel to the tetragonal c -axis, while the V momentsmay have components on any of the three crystal axes.Interestingly, the model proposed by Plumier [10] withV-moments lying in ( h
00) sheets, is excluded by sym-
FIG. 2: (Color online) (a) Projection of the V tetrahedronin the ab plane. V-O bonds are arranged in an alternatingpattern giving rise to a staggered-like orbital arrangement.(b)(c) Graphical representations of the low-temperature non-collinear ferrimagnetic structure of the MnV O . The Mnmoments are aligned parallel to the c axis, while the V mo-ments are canted by approximately 65 ◦ . (d) Projection of themagnetic structure on the tetragonal basal plane. metry. The a and b -axis components are constrained toform an orthogonally stacked AFM structure as shownin Fig. 2.Full refinements of various symmetry-allowed magneticstructure models were performed using high-resolutionpowder diffraction data. The use of powder sampleavoids complications related to multiple magnetic do-mains and extinctions. Rietveld refinements were per-formed using the FULLPROF program [20]. In the pow-der diffraction investigation, the cubic phase was foundto persist in a small fraction below T S , and it has beentaken into account in the refinements.Above the structural transition, the diffraction pat-tern was fitted using a simple collinear ferrimagneticmodel, with the Mn and V moments aligned antiparallelto each other. Such a collinear order may be stabilizedby an order-by-disorder mechanism [21], as previouslysuggested in Ref. [5]. As discussed above, below T S theV-moments develop AFM components parallel to the ab plane. As the Mn moments produce a strong effectivemagnetic field for the V ions, the V moments tend toorient themselves almost perpendicular to the directionof the effective field. The magnetic structure model pre-sented in Table I gave the best fit to the diffraction pat-tern. Refinements using spherical Mn and V form TABLE I: Basis vectors (BVs) of an IR of the tetrahedralspace group I /a (with k → = (0,0,0)). BVs are defined relativeto the tetragonal axes. Magnetic moments for an atom j isgiven by m j = P i C i ψ i where C i is the mixing coefficient of BVs ψ i . ψ Mn1 (0, , ) (0 0 1)Mn2 ( , , ) (0 0 1) ψ ′ ψ ′ ψ ′ V1 (0,0, ) (0 0 -1) (1 0 0) (0 1 0)V2 ( , , ) (0 0 -1) (0 1 0) (-1 0 0)V3 (0, , ) (0 0 -1) (-1 0 0) (0 -1 0)V4 ( , , ) (0 0 -1) (0 -1 0) (1 0 0) factors, on the 5 K data, yielded the ordered moments: m Mn ≈ . µ B and m V ≈ . µ B . The V momentsare canted with respect to the c -axis by approximately65.12 ◦ . A stereographic view of the magnetic structure isillustrated in Fig. 2(b)(c). The ab -projections of V mo-ments are antiparallel within each layer and orthogonalbetween layers. According to Kugel-Khomskii’s predic-tion [22], this arrangement may favor the A -type orbitalorder. Fig. 2(d) displays a projection of the MnV O structure in the ab plane and the compatibility betweenthe magnetic and a staggered orbital ordering.The structural investigation was complemented withinelastic neutron scattering measurements performed atdifferent temperatures ranging from 1.5 K to 70 K. Thespin-wave spectrum across the Brillouin zone was mea-sured in a series of constant- Q scans. At 1.5 K, the spec-trum consists of a gapped acoustic mode (with the gap∆ ≈ . meV ) and several optical branches. The disper-sion of the low-energy mode along the c -axis is shown inthe inset of Fig. 3(a). A detailed analysis of the spec-trum will be reported elsewhere [23]. Here we will fo-cuss only on the temperature behavior of the energy gap.Fig. 3(a) shows the energy scans measured at the zonecenter (220), at various temperatures. Fits of the gapmode, indicated by solid lines in Fig. 3(a), were doneusing a cross section function: d σd Ω dE ′ ∝ A q ω q L ( ω − ω q , Γ)[ n ( ω q ) + 1] (1)where A q term describes the q-dependence of the inten-sity, L is a Lorentzian peak-shape function of width Γand [ n ( ω q ) + 1] is the Bose factor. The approximatedispersion relation near the zone center was written as: ω q = ∆ + ( v q ) , where v is the spin wave velocity deter-mined to be approximately 1.88 meV. The model crosssection was numerically convoluted with the spectrome-ter resolution function calculated in the Popovici approx-imation [24]. ( m e V )
25 K30 K35 K40 K (meV) I n t en s i t y ( c t s . / ~ s e c ) Q (2,2,0)
50 K45 K (a) [2 2 ]T=1.5 K
10 20 30 40 50 60 700.00.30.60.91.21.5 T (K) E ne r g y G ap ( m e V ) (b) )1( N TTII dN TT )1( I n t eg r a t ed I n t en s i t y ( a r b . un i t s ) FIG. 3: (a) Energy-scans measured at different temperatures,at Q = (2 2 0). Solid lines are fits to the data. The large peakcentered on 0 meV is due to incoherent scattering. Inset: Dis-persion of the low-energy spin-wave branch along the c -axis,measured at 1.5 K. (b) Variation with the temperature of theenergy-gap (filled dots) and (220) peak intensity (open dots).The gap mode extrapolates to zero at the same temperaturewhere the structural transition occurs. Power-law fit, shownby solid lines, indicate that ∆( T ) scales approximately as thesquare of staggered magnetization. The variation of the energy gap, ∆, with temperatureis shown in Fig. 3(b). It decreases with increasing tem-perature and vanishes, moving into the incoherent peak,exactly at the structural transition ( T S ). The energy gapin the spin-wave spectrum can be explained by the exis-tence of single-ion anisotropy. Such anisotropy may be aconsequence of the unquenched orbital angular momen-tum of the V ion. To quantify the temperature depen-dence of the gap, we performed a least-square fit using thepower-law ∆( T ) ∝ ( T S − T ) d . The fit yielded an exponent d ≃ I ( T ) ∝ ( T F,S − T ) β .The critical exponents reproducing the temperature de-pendence of the (220) peak are β ≃ β ≃ β = 0 .
36) or 3D Ising( β = 0 .