Magnetic Order of the Hexagonal Rare Earth Manganite Dy(0.5)Y(0.5)MnO3
Joel S. Helton, Deepak K. Singh, Harikrishnan S. Nair, Suja Elizabeth
MMagnetic order of the hexagonal rare-earth manganite Dy . Y . MnO Joel S. Helton , ∗ , Deepak K. Singh , , Harikrishnan S. Nair , and Suja Elizabeth NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Department of Materials Science and Engineering,University of Maryland, College Park, MD 20742, USA J¨ulich Centre for Neutron Science, Forschungszentrum J¨ulich,Outstation at FRM-II, D-85747 Garching, Germany and Department of Physics, Indian Institute of Science, Bangalore 560012, India (Dated: October 29, 2018)Hexagonal Dy . Y . MnO , a multiferroic rare-earth manganite with geometrically frustratedantiferromagnetism, has been investigated with single-crystal neutron diffraction measurements.Below 3.4 K magnetic order is observed on both the Mn (antiferromagnetic) and Dy (ferrimagnetic)sublattices that is identical to that of undiluted hexagonal DyMnO at low temperature. The Mnmoments undergo a spin reorientation transition between 3.4 K and 10 K, with antiferromagneticorder of the Mn sublattice persisting up to 70 K; the antiferromagnetic order in this phase is distinctfrom that observed in undiluted (h)DyMnO , yielding a qualitatively new phase diagram not seen inother hexagonal rare-earth manganites. A magnetic field applied parallel to the crystallographic c axis will drive a transition from the antiferromagnetic phase into the low-temperature ferrimagneticphase with little hysteresis. PACS numbers: 75.25.-j, 75.85.+t, 75.50.Ee, 75.47.Lx
I. INTRODUCTION
The crystalline structure of rare-earth manganites( R MnO with R = Y, Sc, or a lanthanide) is deter-mined by the ionic radius of the R cation. Materi-als with a large R ionic radius ( R = La through Tb)crystallize in an orthorhombic perovskite structure, whilematerials with a smaller R ionic radius ( R = Y, Sc,or Ho through Lu) crystallize in a hexagonal struc-ture. DyMnO typically crystallizes in the orthorhombicstructure, but with proper growth conditions hexagonal(h)DyMnO can be stabilized. The hexagonal rare-earth manganites, (h) R MnO , are paraelectric at veryhigh temperatures but display a structural transition( T C ≈ P cm space group. The (h) R MnO ma-terials feature slightly distorted triangular lattice planesof Mn ions; the antiferromagnetic nearest-neighbor ex-change interaction leads to geometrically frustrated mag-netism. Below a N´eel temperature of ≈
100 K these ma-terials are magnetically ordered, with easy-plane antifer-romagnetic order of the Mn sublattice coexisting withthe ferroelectric order. Many hexagonal rare-earth man-ganites display one or more spin reorientation transitionsof the Mn moments at lower temperatures or underan applied field; the R ions also form distorted tri-angular lattice planes and, for magnetic ions, will orderalong the c axis. Several of these materials have attractedinterest because of significant magnetoelectric ormagnetoelastic effects. Despite the structural similari-ties between the various members of the (h) R MnO fam-ily, the magnetically ordered structures often differ, withstructures that transform according to each of the fourone-dimensional irreducible representations of the pointgroup observed in at least one material. The dependence of the magnetic ordering of the Mn sublattice on therare-earth element has been attributed to the ionic ra-dius of the R cation or a biquadratic 3 d -4 f magneticcoupling. Hexagonal (h)DyMnO , with the largest rare-earthionic radius of this series, features an interesting mag-netic phase diagram. In the low-temperature phase(below ≈ irreducible rep-resentation. At a temperature of 8 K the Mn mo-ments undergo a spin reorientation transition and areordered in the Γ representation up to 68 K. X-rayresonant magnetic scattering measurements also find aweak Dy moment in this temperature range, ordered ac-cording to the Γ representation. This incompatibleorder, with different irreducible representations presenton the two sublattices, calls into question long stand-ing assumptions about the rigidity of the 3 d -4 f inter-action in (h) R MnO materials. YMnO features mag-netism only on the Mn sublattice and is known to orderin the Γ irreducible representation below T N ≈
75 K. YMnO has also been reported to feature large magne-toelastic effects and coupling between electric and mag-netic domains. Compounds where magnetic rare-earthions are partially replaced with nonmagnetic Y ions,such as Ho − x Y x MnO and Er − x Y x MnO , al-low for further examination of the role that the rare-earth ions play in determining the magnetic structure andopen up the possibility of novel phase diagrams not ob-served in undoped compounds. We report single-crystalneutron diffraction studies of hexagonal Dy . Y . MnO (DYMO) and find evidence for a spin reorientation tran-sition not seen in other hexagonal rare-earth manganitesat zero field. a r X i v : . [ c ond - m a t . s t r- e l ] A ug II. EXPERIMENT
Large, high-quality single-crystal samples ofDy . Y . MnO were prepared as previously reported. DYMO crystallizes in the hexagonal P cm spacegroup ( a = b = 6.161(1) ˚A and c = 11.446(2) ˚A. As in otherhexagonal rare-earth manganites, Mn ions ( S = 2)occupy the 6 c positions at ( x , 0, 0) with x ≈ . Amaterial with x = would feature perfect triangularlattice planes; in DYMO x = 0.3379(4) yielding aslightly distorted triangular lattice. The rare-earth R ions occupy two crystallographically distinct sites, atthe 2 a and 4 b Wyckoff positions, and also form distortedtriangular lattice planes. In DYMO the rare-earth sitesare occupied with equal probability by nonmagnetic Y ions and H / Dy ions ( gJ = 10 µ B ), as determinedby x-ray powder diffraction on crushed single crystals. Previously reported specific heat measurements foundpeaks at 3 K and 68 K; analogously with other hexag-onal rare-earth manganites such as DyMnO it wassuggested that these peaks correspond to the onset ofantiferromagnetic order of the Mn lattice, T Mn N ≈
68 K,and ferrimagnetic order of Dy moments on the rare-earthlattice, T Dy N ≈ (cid:48) -47 (cid:48) -40 (cid:48) -open collimation as well as PGfilters to reduce contamination of the beam with higher-order neutron wavelengths. The detailed temperaturedependence of four magnetic reflections (shown in Fig. 1)was measured using a large ( ≈ H L ) scattering plane at a fixed neutron energyof 30.5 meV ( λ = 1.64 ˚A). Refinement of the orderedmoments utilized diffraction measurements taken at tem-peratures of 1.6 K, 25 K, and 120 K at a fixed neutronenergy of 30.5 meV. In order to minimize absorption ofneutrons by the sample, these measurements were takenwith small single crystals: an 8-mg sample mounted inthe ( H L ) scattering plane and a 6-mg sample mountedin the ( H K
0) scattering plane. Some magnetic re-flections also featured weak nuclear contributions whichwere removed by subtracting the 120 K intensity; theDebye-Waller factor has been ignored, which is justifi-able, given that the intensities of nuclear Bragg peakswith no magnetic intensity [such as (0 0 L ) where L iseven] remained constant within the statistical uncertain-ties between 1.6 K and 120 K. The scattering intensityin absolute units, and from this the value of the orderedmoments, was determined by normalizing the intensitiesof nuclear Bragg peaks measured at 120 K to the calcu-lated nuclear intensities. The intensities of the (1 0 0)and (3 ¯1 0) reflections in a magnetic field were measuredon the 6-mg sample mounted in the ( H K
0) scatteringplane; the sample was placed inside a helium flow dewar with a minimum temperature of 4 K inserted into a 7-Tvertical field superconducting magnet. These data weretaken at a fixed neutron energy of 14.7 meV ( λ = 2.36 ˚A).All neutron diffraction data are reported in terms of theintegrated intensity, integrated over a rocking curve ( θ scan) through the peak position.The allowed magnetic structures in DYMO correspondto the six irreducible representations of the P cm spacegroup with propagation vector (cid:126)k = 0; as in other hexago-nal rare-earth manganites, only the four one-dimensionalirreducible representations (designated as Γ through Γ )are required to describe the observed structures. Foreach of these representations the Mn sublattice displaysantiferromagnetic order within the ab plane, with thethree spins around any triangle oriented 120 ◦ apart. The R sublattice is ordered along the crystallographic c axis. The rare-earth 4 b sites are antiferromagnetically or-dered for the Γ , Γ , and Γ representations; the 2 a rare-earth sites are antiferromagnetically ordered in the Γ representation and paramagnetic for the Γ and Γ rep-resentations. The 2 a and 4 b sites are each ferromagneti-cally ordered in the Γ representation, with the couplingbetween the two sites yielding either ferromagnetism orferrimagnetism. In phases where only the Mn sublatticeis magnetically ordered a hexagonal rare-earth mangan-ite with x = (featuring undistorted triangular latticeplanes) would have perfectly identical neutron scatteringstructure factors in either the Γ or Γ representations, aswell as in the Γ or Γ representations. Unambiguous dif-ferentiation between these homometric magnetic struc-tures requires complementary measurement techniquessuch as optical second harmonic spectroscopy. Thedistortion of the triangular planes leads to some vari-ation in the neutron scattering structure factors; how-ever, these results, from single-crystal diffraction mea-surements on a strongly absorbing sample, will not beable to distinguish between the Γ and Γ structures. III. RESULTSA. Zero-field magnetic order
Figure 1 displays the temperature dependence of theintegrated intensities of the (1 0 0), (1 0 1), (2 0 0), and(2 0 1) Bragg reflections measured while warming from2.1 K to 130 K. The background and any high temper-ature nuclear contributions to the intensities have beensubtracted. At 2.1 K all four reflections display mag-netic intensity, with the (1 0 1) reflection the strongest.Between 2.1 K and 3.4 K the measured intensities ofthe ( H H H H ( 1 0 0 ) ( 1 0 1 ) ( 2 0 0 ) ( 2 0 1 ) Integrated Intensity (arb. units)
T e m p e r a t u r e ( K )
Int. Intensity (arb. units)
T e m p e r a t u r e ( K )
FIG. 1: (Color online) Integrated magnetic intensities of the(1 0 0), (1 0 1), (2 0 0), and (2 0 1) Bragg reflections as a func-tion of temperature. All data were measured while warming.The inset shows a closer view of the low temperature portionof the graph. Transitions are observed at T Mn N = 70 K and T Dy N = 3.4 K; these temperatures are designated with dashedvertical lines. The red dotted line reflects a fit of the (1 0 0)intensity to an order parameter form with β = 0.25 ± order for both the Mn and Dy sublattice. In the anti-ferromagnetic phase between 10 K and 70 K the data areconsistent with Mn sublattice order in either the Γ or Γ irreducible representation.Mn order Dy orderΓ Γ Γ Γ Γ (1 0 0) 100 0 100 0 100(1 0 1) 17 100 15 100 0(2 0 0) 32 0 27 0 38(2 0 1) 1 26 1 33 0 tion becomes the strongest measured; this rapid changein intensity persists only to around 10 K. This will beshown to correspond to a spin reorientation transition ofthe Mn moments and perhaps explains the 10 K anomalyreported in the derivative of 1/ χ . Above 10 K the in-tensities of all peaks slowly decrease until reaching zeroat 70 K. The intensity can be fit to an order parameterform: I ( T ) ∝ ( | T − T N | /T N ) β . The dotted red line inFig. 1 is a fit of the (1 0 0) intensity to this form with β = 0.25 ± representation. Previous magnetiza-tion measurements on DYMO with (cid:126)H || (cid:126)c revealeda low-temperature state with a spontaneous magnetiza-tion of ≈ µ B per formula unit (measured at 2 K). Ofthe four irreducible representations present in hexagonalrare-earth manganites only the Γ structure is consistentwith either ferrimagnetism or ferromagnetism; undopedhexagonal DyMnO is ferrimagnetic at low temperaturesand is known to order in the Γ representation. Whenordering in the Γ structure the magnetic cross sectionsof the ( H H a and 4 b sites that are antiparallel butequal in magnitude, a refinement of magnetic reflec-tions measured at 1.6 K reveals ordered moments of3.7 ± µ B for the Mn ions and 3.1 ± µ B for the Dyions (1.6 ± µ B for each rare-earth site). This struc-ture is displayed in Fig. 2(a). (The crystal structuresshown in Figure 2 were produced using VESTA . ) Whenmagnetic domains are fully aligned this ordered momentwill lead to a net magnetization of 3.1 ± µ B per unitcell (or 0.52 ± µ B per formula unit) along the crys-tallographic c axis, which is consistent with the reportedbulk spontaneous magnetization. Allowing for differentordered moments on the Dy 4 b and 2 a sites did not ap-preciably improve the fit of the 1.6 K data, nor couldallowing for different moments on these sites produce acomparably good fit while yielding a net moment consis-tent with magnetization measurements. A ferromagneticground state can likewise be excluded. A ferromagneticstate with equal ordered moments on the 2 a and 4 b siteswould give no intensity for the ( H structure the intensities of these re-flections depend on the difference in moment at the rare-earth sites: I ( (cid:126)Q H ) ∝ | (cid:126)M b − (cid:126)M a | , where the orderedmoments on the 2 a and 4 b sites are (cid:126)M a and (cid:126)M b . A fer-romagnetic state with different ordered moments on the2 a and 4 b sites is consistent with the neutron diffractiondata only while yielding a net moment inconsistent withmagnetization measurements. The Mn ordered momentat 1.6 K is close to the full moment value; however, theDy ordered moment is considerably reduced from the full10 µ B value of the H / Dy ions. The low tempera-ture magnetization in undoped DyMnO would suggesta similarly reduced ordered moment for the Dy ions inthe ferrimagnetic phase. T < 3.4 K (P6 c ′ m ′ ) (a)
10 K < T < 70 K (P6 cm) (P6 ′ cm ′) (b) FIG. 2: (Color online) (a) Magnetic structure in the low-temperature ferrimagnetic phase, present below T Dy N = 3.4 K.The structure belongs to the P c (cid:48) m (cid:48) magnetic space group(Γ irreducible representation). Mn ions at z = 0 are shown inpurple, Mn ions at z = 1/2 are shown in orange, and the rare-earth ions are shown in blue. The refined ordered momentsare 3.7 ± µ B on the Mn ions and 3.1 ± µ B on theDy ions. (b) The two possible magnetic structures for theantiferromagnetic phase: P cm magnetic space group (Γ irreducible representation) on the left and P (cid:48) cm (cid:48) magneticspace group (Γ ) on the right. The Mn ordered moment is3.5 ± µ B . Any Dy ordered moment in this temperaturerange is too small to be measured by neutron diffraction. Thestructural unit cell is outlined in gray The magnetic structure in the antiferromagnetic phase(10 K < T <
70 K) is consistent with an ordered momenton only the Mn sublattice, with order according to eitherthe Γ or Γ irreducible representation. These magneticstructures are shown in Fig. 2(b). It should be notedthat neither of these possibilities are consistent with thestructure of the Mn moments in (h)DyMnO , which or-der in the Γ representation above the low-temperatureferrimagnetic phase. A refinement of magnetic reflec-tions measured at 25 K gives an ordered moment of3.5 ± µ B for the Mn sublattice. The ordered momentat 25 K is comparable in size to that determined at 1.6 K,suggesting a spin reorientation transition where Mn spinsrotate between 3.4 K and 10 K with little change inmagnitude. Element specific x-ray resonant magneticscattering measurements on hexagonal DyMnO andHoMnO have reported a weak rare-earth moment atcomparable temperatures, induced by a splitting of theground-state crystal field doublet. While DYMO mightsimilarly feature a weak Dy ordered moment in this tem-perature range, neutron scattering measurements will besensitive to only the much larger ordered moment of theMn sublattice and the refinement is not improved by al-lowing for an ordered moment on the Dy sublattice at25 K.The magnetic structure of YMnO is known to be theΓ representation. If the antiferromagnetic phase ofDYMO were likewise Γ , the spin reorientation transi-tion into the low-temperature Γ phase would differ from the spin reorientation transitions previously observed inhexagonal rare-earth manganites. A magnetic struc-ture in the Γ irreducible representation can be trans-formed into the Γ representation through a 90 ◦ coun-terclockwise rotation of all Mn moments. However, atransformation of a structure in the Γ representationas shown in Fig. 2(b) into the Γ representation wouldrequire a 180 ◦ rotation of only the Mn moments in the z = plane. In other hexagonal rare-earth mangan-ites, it has been suggested that spin reorientation tran-sitions between the four irreducible representations oc-cur via in-phase or antiphase rotations where the mo-ments in adjacent Mn layers rotate with an equal (in-phase) or opposite (antiphase) direction. For example,the Mn moments in HoMnO display an in-phase re-orientation transition (Γ to Γ ) at T ≈
40 K andan antiphase transition (Γ to Γ ) at T ≈ display an antiphaserotation (Γ to Γ ) at T ≈ , Er x Y − x MnO , and YMnO underpressure have been reported to feature broad tempera-ture ranges where the magnetic structure is not one of thefour irreducible representations, the observed structurescan still be described as an in-phase or antiphase rota-tion of all Mn moments away from one of the principalstructures. B. Field dependence of the magnetic order
Below T Dy N = 3.4 K DYMO is ferrimagnetic witha spontaneous net magnetization. Above T Dy N , M ( H )curves display symmetric magnetization steps at a criti-cal field value that increases with temperature; the sizeof these steps decreases with increasing temperature, be-coming immeasurably small around 40 K. This behav-ior is remarkably similar to that previously reported in(h)DyMnO , but the moment increase associated withthe magnetization steps in DYMO is about one half of theincrease in (h)DyMnO . Figure 3 displays the intensityof the (1 0 0) magnetic Bragg reflection as a function offield with (cid:126)H || (cid:126)c at temperatures between 4 K and 50 K,measured while increasing the field after zero field cool-ing. For each of these temperatures, we find a suddendrop in the (1 0 0) intensity at a critical field value thatincreases with temperature. As was shown in Fig. 1, theintensity of the (1 0 0) reflection will be much higher inthe antiferromagnetic phase than in the low-temperaturephase, such that this behavior is easily associated with afield-induced transition into the ferrimagnetic phase. Thedata definitively show a spin reorientation of the Mn mo-ments along with the field-induced ferrimagnetic order-ing of the Dy moments, as the intensity of this reflectionwould not drop if the Mn moments remained ordered inthe original structure. The intensity of this reflection inthe field-induced phase is weaker than in zero field at lowtemperature [the dotted horizontal line represents the ex-pected intensity of the (1 0 0) reflection at 2 K and zero T = 4 K 6 K 1 1 K 1 5 K 2 0 K 5 0 K Integrated Intensity (arb. units) m H ( T )
FIG. 3: (Color online) Integrated intensity of the (1 0 0) peakas a function of field. The data were taken while increasingfield. Lines are a guide to the eye. The dotted horizonal linerepresents the expected intensity at 2 K in zero field. field]. This likely arises from a considerably smaller Dyordered moment, consistent with the smaller magnitudeof the magnetization steps at higher temperatures in the M ( H ) curves. Interestingly, neutron diffraction is sensi-tive enough that this transition is still clearly measurablein the 50 K data, while it could not be measured above40 K in the magnetization data. The field dependence of the intensities at the (1 0 0)and (3 ¯1 0) reflections at T = 15 K is displayed in Fig. 4.In Fig. 4(a), both reflections show the expected tran-sition at µ H c ≈ displays little hysteresis while magnetiza-tion steps in ErMnO display considerable hysteresis.The (3 ¯1 0) reflection displays scattering in the low-temperature Γ phase and very little scattering in theantiferromagnetic phase, such that this change in inten-sity is likewise consistent with a field-induced transitionbetween the two. A more detailed view of the (1 0 0)intensity in the high-field region is shown in Fig. 4(b).Interestingly, the intensity of this peak rises slowly withincreasing field up to about 4 T but then decreases withincreasing field beyond 5 T. This likely reflects the evolu-tion of the system from ferrimagnetic to ferromagnetic asthe field is increased, as the fully polarized state (ferro-magnetic with an equal moment for the 4 a and 2 b sites)would display no scattering at (1 0 0). IV. SUMMARY
Below T Dy N = 3.4 K Dy . Y . MnO is magnetically or-dered in the Γ irreducible representation with antiferro-magnetic Mn order and ferrimagnetic Dy order. Between3.4 K and 10 K we observe a spin reorientation transitionof the Mn moments. Antiferromagnetic order of the Mnsites persists up to T Mn N = 70 K. The magnetic structure
051 01 52 0 (3 -1 0) Integrated Intensity (arb. units) ( b ) m H ( T ) ( a ) (1 0 0) Integrated Intensity (arb. units) ( 1 0 0 ) ( 3 - 1 0 )
F i e l dD e c r e a s i n g F i e l dI n c r e a s i n g
FIG. 4: (Color online) (a) Integrated intensities of the (1 0 0)(left scale) and (3 ¯1 0) (right scale) peaks measured at T = 15 K. Solid symbols represent measurements taken withincreasing field, and open symbols represent those taken witha decreasing field. (b) Detail of the high field region for the(1 0 0) intensity. of this phase is either Γ or Γ , inconsistent with the Γ order observed in undiluted (h)DyMnO . In the anti-ferromagnetic phase, a magnetic field applied parallel tothe c axis will drive a field-induced transition into thelow-temperature ferrimagnetic phase with little hystere-sis. Further knowledge of the different magnetic struc-tures and reorientation transitions displayed by the Mnmoments in various (h) R MnO materials should lead toimproved understanding of the unusual 3 d -4 f magneticcoupling present in these materials. While the mag-netic structure of the antiferromagnetic phase cannot bedefinitively determined from this experiment, it is clearthat Dy . Y . MnO displays a zero-field spin reorien-tation transition not previously observed in any otherhexagonal rare-earth manganite. If the magnetic struc-ture is Γ , then the Γ to Γ spin reorientation transitionwould involve only half of the Mn ions in a manner notobserved in other (h) R MnO materials. The H - T phasediagram of HoMnO features a boundary between Γ andΓ phases at µ H ≈ to Γ spin reorientation transition has not been reported. Fur-ther work will be necessary to distinguish between theΓ and Γ structures in the antiferromagnetic phase andto determine if the domain walls arising from this uniquespin reorientation will display magnetoelectric couplingas is observed in compounds such as HoMnO orYMnO . ACKNOWLEDGEMENTS
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