GdPtPb: A non collinear antiferromagnet with distorted Kagomé lattice
GGdPtPb: A non collinear antiferromagnet with distorted Kagom´e lattice
S. Manni,
1, 2
Sergey L. Bud’ko,
1, 2 and Paul C. Canfield
1, 2 Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA Ames Laboratory, Iowa State University, Ames, IA 50011, USA (Dated: October 2, 2018)In the spirit of searching for Gd-based, frustrated, rare earth magnets, we have found antifero-magnetism (AF) in GdPtPb which crystallizes in the ZrNiAl-type structure that has a distortedKagom´e lattice of Gd-triangles. Single crystals were grown and investigated using structural, mag-netic, transport and thermodynamic measurements. GdPtPb orders antiferromagnetically at 15.5 Karguably with a planar, non-collinear structure. The high temperature magnetic susceptibility datareveal an ”anti-frustration” behavior having a frustration parameter, | f | = | Θ | / T N = 0.25, whichcan be explained by mean field theory (MFT) within a two sub-lattice model. Study of the magneticphase diagram down to T = 1.8 K reveals a change of magnetic structure through a metamagnetictransition at around 20 kOe and the disappearance of the AF ordering near 140 kOe. In total, ourwork indicates that, GdPtPb can serve as an example of a planar, non collinear, AF with a distortedKagom´e magnetic sub-lattice. PACS numbers: 75.40.Cx, 75.10.Jm, 75.40.Gb, 75.50.Lk
I. INTRODUCTION
Magnetic frustration in insulators can lead to in-triguing ground states such as quantum spin liquids(QSL) or spin ices. Magnetic frustration is usuallyrealized in geometrically frustrated pyrochlore, triangu-lar, Kagom´e or hyperkagom´e spin sub-lattices with a lo-calized, often nearest neighbor, description of magneticspin exchanges. This approach brings a fundamental dif-ficulty to the description of magnetic frustration in inter-metallic systems which have longer range spin-spin inter-actions.Recently, significant attempts were made to realize andtheoretically understand magnetically frustrated groundstates in geometrically frustrated rare earth intermetal-lic compounds.
The main focus of these efforts hasbeen concentrated around either a quasi-Kagom´e lat-tice with ZrNiAl-type structure or a Shastry-Sutherlandlattice with the U Pt Si-type structure.
Due to thelong range nature of the RKKY-interaction, realizing aQSL state seems to be a difficult goal to achieve in in-termetallic compounds where, in general, a magneticallyordered ground state is achieved by the longer range mag-netic exchange and/or with the help of quantum disorderor lattice disorder. Rather intermetallic compounds of-fer a rich variety of magnetic ground states both as afunction of temperature as well as a function of appliedmagnetic field. Examples include CePdAl and YbAgGeboth with the ZrNiAl-type structure, and Yb Pt Pb withthe U Pt Si-type structure.
On the other hand thereare some promising (and debated) examples of potentialmetallic spin liquids such as CeRhSn and Pr Ir O which are paramagnetic down to lowest temperature de-spite strong AF spin correlations.We have focused our search for magnetically frustratedground states in rare earth intermetallic systems with theZrNiAl-type structure. In this structure, rare earth ionsform a distorted Kagom´e lattice in the ab -plane and are stacked along the c -axis. If the interlayer distance ofthe ab -planes is much larger than rare earth distances inthe ab -plane, the possibility of low dimensional frustratedexchange interaction arises. In the R PtPb ( R = rareearth ion) intermetallic series, CePtPb was reported to be an antiferromagnet with low T N = 0.9 K, simi-lar to YbAgGe. In many Ce and Yb-based, frustratedintermetallics magnetic exchange is governed by groundstate doublets ( J = 1/2). Often, due to crystal electricfield splitting, magnetic anisotropy influences the mag-netic exchange interaction. This can be the case for allrare earths except Gd and Eu -based ones. Hence, wewanted to explore a Gd-based, geometrically frustratedlattice where, due to absence of crystal electric field ef-fect, the whole J = 7/2 multiplet participates in mag-netic exchange interaction and the Gd has J = S =7/2 Heisenberg moment.We have grown and studied single crystals of GdPtPb,which crystallizes in the same crystal structure asCePtPb and synthesized in single crystalline form.GdPtPb orders antiferromagnetically below 15.5 K and,most interestingly, it shows ”anti-frustration” behaviorhaving a frustration parameter | f | = | Θ | /T N much lessthan one. Magnetic susceptibility suggests a possible spe-cial, non-collinear antiferromagnetic, structure. Overallwe have characterized GdPtPb structurally, magneticallyand thermodynamically and tried to relate its magnetismto its underlying, at first glance-geometrically frustrated,magnetic sub-lattice. II. EXPERIMENTAL AND STRUCTURALDETAILS
GdPtPb single crystals are grown from a Pb-rich solu-tion with an initial stoichiometry of Gd:Pt:Pb = 5:5:90.Elemental, pure ( ≥
99 %), metals were packed in 2 mlfritted Al O crucible set and then sealed in a quartz a r X i v : . [ c ond - m a t . s t r- e l ] J un FIG. 1. (a) Crystal structure of GdPtPb shown in ab - plane.It shows a distorted Kagom´e lattice of the Gd triangles. Redballs represent Gd; blue Pt and pink Pb, the size of the ballsare not according the scale of atomic radius. (b) Crystalstructure perpendicular to ab -plane. (c) Hexagonal, rod-likeGdPtPb crystals on a mm grid and growth of GdPtPb rodson a GdPb cubic crystal. ampule under partial pressure of Argon before putting infurnace. The whole assembly was heated to 1180 ◦ C andcooled down to 600 ◦ C at a 5 ◦ C/hour rate after which theremaining, Pb-rich, solution was decanted. We obtainedmillimeter size, hexagonal, rod-like crystals of GdPtPb(Fig. 1c) and some GdPb impurity phase, often as cu-bic single crystals, shown in Fig. 1(c). In general GdPtPband GdPb were not inter-grown, although when GdPb was present it often had some GdPtPb rods attached toit. In a very similar method, LaPtPb, hexagonal rod-like, crystals were grown from a solution with an initialstoichiometry of La:Pt:Pb = 10:10:80. LaPtPb crystalswere used to estimate the non-magnetic contribution tothe specific heat of the GdPtPb-system. TABLE I. Structural details of GdPtPb obtained from Ri-etveld analysis of powder x-ray diffraction data (see Fig. 2)Crystal system HexagonalSpace group P − m a 7.637(12) ˚Ac 3.9649(6) ˚A α ◦ β ◦ γ ◦ Cell volume 200.26(8) ˚A To determine the structure of GdPtPb, powder x-ray diffraction was done on crushed single crystals usinga Rigaku Miniflex diffractometer and fitted with pub-lished crystal structure of CePtPb by Rietveld refinementmethod using GSAS-EXPGUI software.
CePtPb isreported to be crystallized in hexagonal P − /m crystalstructure. Fig. 2 shows measured powder diffractiondata ( I obs ), fitting with P − m crystal structure ( I cal )and difference between measured data and fitting ( I diff ). I o b s I c a l I b k g I d if f * P b f l u x
Intensity (a.u) q ( o ) * G d P t P b (211)(210)(201) (300)(111)(101)(200) (200)(110) (600)(500)(400)(300)Intensity (counts) q ( o ) FIG. 2. Powder x-ray diffraction pattern of GdPtPb groundsingle crystals ( I obs ), Rietveld refinement of the pattern with P − /m crystal structure ( I cal ) and I diff = I obs - I cal . Insetshows θ - 2 θ scan on one GdPtPb single crystal for x-rayincidence angle θ with the plane perpendicular to rod axis.TABLE II. Atomic coordinates of the GdPtPb structure ob-tained from Rietveld analysis of the powder x-ray diffractiondata (see Fig. 2)Atom Wyck x y z Pb 3g 0.26558(30) 0.0 0.5Gd 3f 0.6066(5) 0.0 0.0Pt 2d 0.33333 0.66667 0.5Pt 1f 0.0 0.0 0.0
We have observed a single Pb-impurity peak which wasestimated to correspond to less than 5% elemental Pb(most likely residual droplets of flux on the surface ofthe crystals) in the phase. The inferred crystal structureparameters are listed in Table I. The lattice parametersreported for CePtPb are a = 7.73 ˚A and c = 4.13 ˚A andvolume is 213.4 ˚A . Comparing these values with theparameters listed in Table I, we can confirm a lathanidecontraction in GdPtPb, compared to CePtPb. The GdPtPb crystal structure is drawn from the re-fine lattice parameters (Table I) and atomic coordi-nates(Table II), shown in Fig. 1. In the ab -plane, Gdtriangles form a distorted Kagom´e network [see Fig. 1(a)]. In the ab -plane, the Gd-Gd distance is 4.07˚A. TheKagom´e network of Gd triangles are layered along c -axis. The Gd-Gd interlayer distance is 3.96 ˚A. In thisstructure, if we consider the longer range RKKY interac-tion between Gd spins on a frustrated Kagom´e lattice,we can expect an unconventional magnetically orderedground state in GdPtPb.To determine the crystallographic c -axis and the ab -plane on the hexagonal, rod-like crystals we have donea θ - 2 θ scan on one piece of single crystal. The rod-like crystal is placed on the XRD zero reflection puckin such a way that x-ray beam is incident with θ anglewith respect to the plane perpendicular to the axis ofthe rod. We obtained only ( h
00) reflections; the inferredvalue of the a lattice parameter is 7.65 ˚A, which is veryclose the value listed in Table I. This confirms that theplane perpendicular to the rod direction is ab -plane and c -axis is along the rod.Magnetic measurements were done using a QuantumDesign Magnetic Property Measurement System SQUIDmagnetometer in the 1.8-300 K temperature range and0 - 55 kOe magnetic field range. Mostly the measure-ments were done on single crystal pieces of 0.2 - 1 mgmass. Electrical resistivity was measured by a standardfour probe method on a rectangular bar like crystal (di-mensions: A ≈ , l ≈ c -axis and current was applied in this direction. For theheat capacity measurements we used five GdPtPb singlecrystals with a total mass around 2 mg and aligned themon the heat capacity puck such that the applied field wasalways within the ab -plane. Heat capacity measurementson the LaPbPt were done with similar mass of crystals.Measurements were done in a Quantum Design PhysicalProperty Measurement System by relaxation method inthe 1.8 - 60 K temperature range and 0 - 140 kOe fieldrange. III. RESULTS
Fig. 3(a) shows the temperature dependent, inversemagnetic susceptibility (1/ χ = H/M ) plot, measured ina 5 kOe field along the ab -plane ( χ ab ) and the c -axis ( χ c )and inverse of calculated average magnetic susceptibility( χ avg ) where, χ avg = (2 χ ab + χ c )/3. The inset shows anexpanded view of the low-temperature χ ( T ) data. χ ab drops to roughly one half of its maximum value at thelowest measured temperature, and χ c changes its slopeand remains almost constant with a slight low tempera-ture upturn below 5 K (see inset). The d ( χT ) /dT data(inset, Fig. 3(a)) for both field directions have a maxi-mum at T = 15.5 K (see inset). This clearly indicatesthat GdPtPb is an antiferromagnet with T N = 15.5 K.High temperature magnetic susceptibility is isotropic andfollows the Curie-Weiss (CW) behavior 1 /χ = ( T − Θ) /C where C is the Curie constant reflecting effective moment( µ eff ≈ √ C ) and Θ is the CW temperature reflectingthe average magnetic exchange interaction. The fittingis done over different temperature ranges: 60 K to 300K; 75 K to 300 K; 100 K to 300 K and 150 K to 300 K,variation of the fitted parameters are indicated withinthe parenthesis. By fitting inverse χ ab , χ c and χ avg , wehave obtained µ eff = 7.82 ( ± µ B , 7.74 ( ± µ B and 7.8 ( ± µ B respectively, very close to theoreticalvalue of Gd (7.94 µ B ) and the CW temperature (Θ) ab = -5.12 ( ±
1) K, (Θ) c = -2.78 ( ±
1) K and (Θ) avg = -4.2( ±
1) K respectively. Notably, | Θ ab | , | Θ c | << T N which is f = 0 o f = 5 5 o f = 9 0 o d i s c b a c k g r o u n d H = 5 k O e c a b c c c a v g ( b ) G d P t P b c (mol/cm3) T ( K )
G d P t P b ( a )
H = 5 k O e
Magnteization (10-3 G cm3)
T ( K ) c (cm3/mol) T ( K ) d ( c T)/dT(cm3/mol)
FIG. 3. (a)Temperature dependent inverse magnetic suscep-tibility data for H || ab ( χ ab ), H || c ( χ c ), measured at H = 5kOe and average value 1/ χ avg and fitting of the data above100 K with a Curie Weiss (CW) temperature dependence. In-set shows magnetic susceptibility and d ( χT ) /dT vs. T below30 K.(b) Temperature dependent magnetization near T N withthree different rotation angle ( φ ) in ab -plane and field along ab -plane, measured at H = 5 kOe. The disc background signalis also shown. Inset shows mounting scheme of the rotationmeasurement and definition of φ . discussed in the context of the mean field theory below.The low- T magnetic susceptibility along the easy-plane( ab -plane) extrapolates to a finite value at T = 0 K, whichhints that magnetic structure is a non-collinear AF type.We obtained M ab ( T = 1.8 K)/ M ab ( T N ) = 0.43 - 0.51in multiple measurements. To prove that it is a robusteffect, we have measured temperature dependent magne-tization ( M ) by rotating the crystal in the ab -plane andapplying field along ab -plane. For this measurement wemounted the rod-like crystal inside a teflon disc, at thecenter of the disc making the rod perpendicular to thedisc surface. Hence the ab -plane is parallel to the discplane (shown in inset of Fig. 3 (b)). For the different ro-tation angles the disc is rotated keeping it vertical in the M ( m B) F i e l d ( k O e ) G d P t P b( a ) ( b ) M ab/H (cm3/mo l ) T ( K )
2 K 5 K 9 K 1 4 K dM/dH
F i e l d ( k O e ) d ( c abT/)dT (cm3/mo l ) FIG. 4. (a)Field dependent magnetization measurement atdifferent temperature and field for H || ab and H || c and insetshows dM/dH vs. H for H || ab . (b)The temperature depen-dent M ab /H and d ( χ ab T ) /dT near T N for different appliedfield values. straw such that the applied field is always parallel to thedisc plane. The rotation angle is measured with respectto a mark on the teflon disc which has an arbitary anglewith the a -axis (inset Fig. 3 (b)) For the three rotationangles φ = 0 ( ± ◦ , 55 ( ± ◦ and 90( ± ◦ , M ab ( T = 1.8K)/ M ab ( T N ) = 0.37, 0.46 and 0.47 respectively, shownin Fig. 3 (b). Our multiple H || ab measurements lead usto conclude that (i) there is little in-plane anisotropy and(ii) χ ab ( T → χ ab ( T N ) ≈ H || ab ( M ab ) and at T= 2 K for H || c ( M c ). A sharp metamagnetic transition is evidentin M ab and dM/dH at 22 kOe, which broadens with in-creasing temperature, and vanishes above the T N . M c is proportional to field having no evident metamagnetictransition in the measured field range. Below 22 kOe, aclear anisotropy exists between M ab and M c , but abovethe metamagnetic transition M ab (cid:39) M c . We also observe
051 01 52 0
G d P t P b
0 k O e 9 0 k O e 1 0 0 k O e 1 4 0 k O e L a P b P t h e a t c a p a c i t y
Cp (J/mole K)
T ( K ) ( a )
G d P t P b ( b ) D C (J/mole K)
T ( K )
0 k O e 9 0 k O e D C/T (J/mole K2)
T ( K )
0 k O e 9 0 k O e D S (J/mole K)
FIG. 5. (a)Temperature dependent heat capacity of GdPtPbat zero field at 90 kOe, 100 kOe and 140 kOe field. LaPbPtheat capacity to estimate non-magnetic contribution of heatcapacity is also shown. (b) Temperature dependence of mag-netic heat capacity (∆ C ) for zero field and 90 kOe field, cal-culated after a power-law extrapolation of C vs. T down to( C, T ) = (0,0) and magnetic entropy for the same field val-ues, calculated by integrating ∆
C/T . Inset shows ∆
C/T vs. T for zero field, 90 kOe and 140 kOe field near the lowtemperature hump (pointed by vertical arrow) without anyextrapolation. that M ab ( T ) /H , for 30 kOe, 40 kOe and 55 kOe (shownin the Fig. 4(b)) is similar to M c ( T ) /H . All of these dataindicate a field induced change of magnetic structure.Long range AF ordering at T N = 15.5 K is furtherconfirmed by heat capacity ( C p ) data. Fig. 5(a) shows C p versus T in zero field as well as 90 kOe, 100 kOeand 140 kOe field applied along the ab -plane. A sharp, λ -like, anomaly is observed at T N in zero field. Withincreasing field the anomaly shifts to lower temperatureand at 140 kOe, no sharp anomaly is observed down to1.8 K. We have estimated the magnetic contribution ofthe heat capacity by subtracting LaPbPt heat capacity.To calculate the magnetic entropy (∆ S ) down to 0 K, I \ \ cH \ \ a b r ( mW -cm) T ( K )
0 k O e 1 0 k O e 5 0 k O e 1 0 0 k O e 1 1 0 k O e 1 2 0 k O e 1 3 0 k O e 1 4 0 k O e
G d P t P b
R R R = 2 . 7 7 r ( mW -cm) T ( K )
H = 0 O e
FIG. 6. Resistivity ( ρ ) versus T for different field along the ab -plane. Inset shows the temperature dependent electricalresistivity ( ρ ) in zero field for current along c -axis. C versus T data is extrapolated to ( C, T ) = (0,0) usinga power law fit. Then the magnetic heat capacity (∆ C )is estimated by subtracting LaPbPt heat capacity fromextrapolated C and finally, ∆ C/T is integrated over therange between 0 -50 K [shown in Fig. 5 (b)]. In appliedmagnetic field, we observe a shift of the sharp anomalyin ∆ C at T N to lower temperature as well as a shiftingof some residual entropy to higher temperature, the laterbeing evident from the tail in ∆ C above T N for 90 kOe.For zero field, we observe that just above T N , ∆ S reaches up to 77% of the theoretically expected value forGd which is Rln (2 J +1) = Rln J = 7/2. The remaining entropy is spread well above T N .This indicates that there is some amount of short rangeorder or fluctuations present above T N . ∆ S saturates toa value little more than Rln S does not satu-rate and is continuously increasing after a slope changeat T N . Only about 48% of magnetic entropy is recoverednear the magnetic ordering temperature at 90 kOe; theremaining entropy is shifted to higher temperature dueto partial polarization of the paramagnetic spins alongthe direction of the magnetic field. Below T N a broadhump is observed in ∆ C/T [see inset Fig. 5(b)], whichwill be discussed below.Electrical transport measurements on GdPtPb weredone by applying current along the c -axis and field per-pendicular to the c -axis. Temperature dependent electri-cal resistivity, in zero field, is shown in the inset of Fig 6.The room temperature resistivity ( ρ ) is ∼ µ Ω-cm andthe residual resistivity ratio [RRR = ρ (300K)/ ρ (1.8K)]is 2.8. Despite the lackluster RRR, we observe a sharpanomaly in ρ (T) at T N due to loss of spin disorderscattering. In an applied field parallel to ab -plane, theanomaly shifts to lower temperature, as shown by an ar- MR (%)
H ( k O e )
I \ \ cH \ \ a b 2 K
G d P t P b
5 K1 0 K1 5 K2 0 K
MR (%)
H ( k O e ) r ( mW -cm) FIG. 7. MR versus H (left-axis) ρ versus H (right-axis) at2K for H || ab . Inset shows magnetoresistance (MR) versus H near the metamagnetic transition at different temperature,showing the anomaly. row in the main panel of Fig 6. At higher fields theanomaly due to loss of spin disorder scattering also weak-ens and the feature changes. At a 140 kOe we do notobserve any anomaly down to 1.8 K.Magnetic field dependent electrical transport measure-ment data are shown in Fig. 7. At 2 K magnetoresistance[MR= [ ρ (H)- ρ (0 kOe)]/ ρ (0 kOe) x 100] was measured,after an initial increase, followed by a sharp drop at the20 kOe metamagnetic field, ρ only decreases by 17% upto 140 kOe ( M R = -17%). In the
M R vs. H and ρ vs. H data, measured at 2 K, we observe a sharp kinkaround 20 kOe. With increasing temperature the sharpkink in MR broadens and vanishes above T N (see inset).For T > T N , The M R is negative for all the field valuesmeasured, consistent with a suppression of spin-disorderscattering in the paramagnetic state associated with Bril-louin like polarization of the Gd moments.Using our magnetization, electrical transport and heatcapacity data, we can construct a H - T phase diagramfor the magnetically ordered state of GdPtPb for H || ab ,shown in Fig. 8. For the field parallel to ab -plane, theboundary between AF ordered phase and paramagnetic(PM) phase are determined from (1) the dρT /dT vs. T anomaly, which is a jump for 0, 10 and 50 kOe mag-netic field (shown for 0 Oe in Fig.9(a)) and a pronouncedminimum for 100, 110, 120 and 130 kOe magnetic field(shown for 100 kOe in Fig.9(b)); (2) the peak position inthe d ( χ ab T ) /dT vs. T (inset Fig. 4 ) and (3) peak in C p vs. T (Fig. 5). Up to 130 kOe we could track the tran-sition, at 140 kOe, no sharp feature we could associatewith a transition is observed down to 1.8 K in resistivityand heat capacity. These data (Fig.8) suggest either afield induced quantum critical point or a quantum phasetransition, most likely to a saturated paramagnetic be-havior, near 140 kOe. In addition to the phase boundary d r / d T v s . T a n o m a l y C v s . T p e a k d c T / d T p e a k d M / d H p e a k R - H p e a k p o s i t i o n
T (K)
H ( k O e )
A F - Ip h a s e A F - I I p h a s e
G d P t P b H | | a b
P M
FIG. 8. H - T phase diagram of GdPtPb for H || ab . T -axisrefers magnetic ordering temperature, H -axis refers to mag-netic field applied within the ab -plane. d r /dT T ( K ) d r / d T ( a ) C C d( c abT/dT) d ( c a b T / d T )
G d P t P b
0 O e ( b ) d r / d T C C T ( K )G d P t P b d r /dT FIG. 9. (a) d ( χ ab T ) /dT , C and dρ/dT versus T for 0 Oeapplied magnetic field, vertical arrow points to T N (b) C and dρ/dT versus T for 100 kOe applied magnetic field, verticalarrows point to T N of the magnetic order, a change in the magnetic structurearound 20-22 kOe is observed. The metamagnetic phaseboundary is plotted in the phase digram from the peakposition in the M R vs. H plot (see inset Fig. 7) and peakin dM/dH (inset of Fig. 4 (a)). IV. DISCUSSION AND CONCLUSION
From the analysis of the high temperature (
T > | Θ ab | (cid:39)| Θ c | << T N . Taking Θ avg ≈ -4 K, we find a frustrationparameter | f | = | Θ avg | /T N ≈ | f | >> T N due to competing magnetic exchange inter-action in a frustrated lattice. We can explain Θ << T N from a more general approach in the MFT. In the MFT,antiferromagnetism is explained by total magnetism dueto interaction between two interpenetrating spin sub-lattices (1 and 2), having spin-up and spin-down. In thefirst order MFT, the molecular field ( B ) in one sub-latticeis considered to be only proportional to the total magne-tization ( M ) in the other sub-lattice, B = −| λ | M , where | λ | is the molecular field constant. In general, the inter-action within one sub-lattice can be significantly differ-ent from the interaction between two sub-lattices. Thisleads to more general considerations where we need toconsider molecular fields due to the interaction betweentwo sub-lattices (constant given by | λ | , which is antiferro-magnetic) and within a sub-lattice (constant given by Γ).The molecular fields in two sub-lattices are then given by B = − Γ M − | λ | M and B = − Γ M − | λ | M . Nowif we consider an equal number of spins, n/
2, in the twosub-lattices, from the MFT calculations, T N = ( | λ |− Γ) C and Θ = − ( | λ | + Γ) C , where C is the Curie constant. So if Γ (cid:54) = 0 then | Θ | (cid:54) = T N . In our case, T N / Θ avg ≈ -4which would suggest that | λ | / Γ ≈ -1.67. If we considera simple two sub-lattice picture of antiferromagnetismfor GdPtPb, we can assume J and J are the nearestneighbor and the second nearest neighbor exchange in-teractions proportional to Γ and | λ | respectively withinthe ab -plane (we are assuming exchange interaction along c -axis will be similar for the two sub-lattices). So we get J /J ≈ -1.67 and they have opposite sign. Since | λ | isantiferromagnetic and J >
0, we get J < | J | > | J | , hence average ex-change interaction which is proportional to Θ avg is smalland antiferromagnetic type. Similar analysis was donein EuRh As by Singh et. al. . Hence MFT analysissuggests that for GdPtPb, the antiferromagnetic J isgreater than the ferromagnetic J . This is possible forRKKY-type exchange interaction which follows a oscil-latory decay function in space.The low- T magnetic susceptibility, below the meta-magnetic transition field (20 kOe) gives χ ab ( T → χ ab ( T N ) ≈ ab -plane. The non-collinear structure can either be intrinsic or may orig-inate from three domains of collinear spins rotated by120 ◦ to each other in the hexagonal ab -plane. To de-termine the exact spin structure and magnetic Q -vector,microscopic measurements are underway. We designatethis antiferromagnetic phase as AF-I in the phase dia-gram (see Fig. 8). Above the metamagnetic transitionfield, χ ab ( T → χ ab ( T N ) ≈ χ ab = χ c . We des-ignate this as AF-II phase (see Fig. 8).The broad hump, observed in ∆ C/T below T N [see in-set Fig. 5(b)] is also weakly visible in the ∆ C . In somecases such low- T hump in heat capacity originates frompartial disorder of the spins due to structural defects, and vanishes with the better ordering in the single crys-talline material. . We have not observed any structuraldisorder in GdPtPb. In addition to that, we observedthat the position of the that hump in ∆ C/T does notshift or significantly broaden with the increasing mag-netic field, a stark contrast to the structural disorderscenario. Hence the structural disorder is not the rea-son behind the low- T broad hump in ∆ C/T . For 140kOe magnetic field, when the antiferromagnetic orderingis suppressed below 1.8 K , the broad hump in ∆
C/T around 4 K still survives. This strongly suggests thatthis feature is not related to magnetic ordering. Such abroad hump in ∆ C below the λ -like anomaly at T N isobserved in some other Gd-based systems like GdBiPt , GdCu Si and GdFe Ge . A very similar feature isobserved in the calculated magnetic heat capacity fromthe MFT where the broad hump increases with increas-ing value of S ( J ) and at the classical limit of spin S = 10,the ∆ C does not go to zero rather saturate to a finitevalue. This indicates that this Schottky-like anomalyappears due to Zeeman-splitting of the 2 J + 1 multipletunder the internal magnetic field. This becomes experi-mentally distinguishable in case of only a Gd-based com-pound where whole 2 J +1 multiplet participates in themagnetism instead of the ground state doublet and ismost likely origin of the feature we observe in GdPtPb.In Summary, the search for Gd-based frustrated AFin the ZrNiAl-type distorted Kagom´e structure lead usto the discovery of antiferromagnet, GdPtPb, in singlecrystalline form which magnetically orders with a planarnon-collinear magnetic structure below 15.5 K and un-dergoes a field induced change in the magnetic structurearound 20 kOe.We conclude that GdPtPb can serve as an example ofmean field non-collinear AF on hexagonal lattice with adistorted Kagom´e magnetic sub-lattice.SM thanks David C. Johnston and Valentin Taufourfor very useful discussion. SM was funded by the Gordonand Betty Moore Foundations EPiQS Initiative throughGrant GBMF4411. This work was supported by theUS Department of Energy, Office of Science, Basic En-ergy Sciences, Materials Science and Engineering Divi-sion. Ames Laboratory is operated for the US Depart-ment of Energy by Iowa State University under contractNo. DE-AC02-07CH11358. L. Balents, Nature , 199 (2010). A. Kitaev, Ann. Phys. , 2 (2006). Steven T. Bramwell, Michel J. P. Gingras, Science. ,1495-1501 (2001). A. P. Ramirez, Annu. Rev. Mater. Sci. , 453 (1994). R. Ballou, J. Alloys Compounds , 510 (1998). P. Coleman, A. H. Nevidomskyy, J. Low Temp Phys ,182 (2010). Y. Tokiwa, C. Stingl, M-S. Kim, T. Takabatake, P Gegen-wart Sci. Adv. , e1500001 (2015). G. M. Schmiedeshoff, E. D. Mun, A. W. Lounsbury, S.J. Tracy, E. C. Palm, S. T. Hannahs, J.-H. Park, T. P.Murphy, S. L. Bud’ko, and P. C. Canfield, Phys. Rev. B. , 180408(R) (2011) Y. Tokiwa, M. Garst, P. Gegenwart, S. L. Bud’ko, P. C.Canfield, Phys. Rev. Lett. , 116401 (2013). A. D¨onni, G. Ehlers, H. Maletta, P. Fischer, H. Kitazawa,M. Zolliker, J. Phys. Condens. Matter , 11213 (1996). V. Fritsch, N. Bagrets, G. Goll, W. Kittler, M. J. Wolf, K.Grube, C.-L. Huang, H. v. L¨ohneysen, Phys. Rev. B ,054416 (2014). M. S. Kim, M. C. Bennett, M. C. Aronson, Phys Rev. B , 144425 (2008). M. S. Kim, M. C. Aronson, J. Phys.: Condens. Matter, , 164204 (2011). Keola Wierschem, Sai Swaroop Sunku, Tai Kong, Toshim-itsu Ito, Paul C. Canfield, Christos Panagopoulos, andPinaki Sengupta, Phys. Rev. B, , 214433 (2015). S. Nakatsuji, Y. Machida, Y. Maeno, T. Tayama, T. Sakak-ibara, J. van Duijn, L. Balicas, J. N. Millican, R. T.Macaluso, and Julia Y. Chan, Phys. Rev. Lett. , 087204(2006). R. Movshovich, J. M. Lawrence, M. F. Hundley, J.Neumeier, J. D. Thompson, A. Lacerda, Z. Fisk, Phys.Rev. B P. C. Canfield, T. Kong, U. S. Kaluarachchi and N. H. Jo,Philos. Mag. , 84 (2016). A.C Larson and Dreele R. B. Von. General Structure Anal-ysis System (GSAS). Technical report, Los Alamos Na-tional Laboratory, 2000. Brian H. Toby. EXPGUI , a graphical user interface forGSAS. J. Appl. Crystallogr.
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