Complex magnetic order in YbMn2Sb2 single crystals observed by µSR

J. Munevar,1, 2, ∗ F. R. Arantes,1 L. Mendonca-Ferreira,1 M. A. Avila,1 and R. A. Ribeiro1, 3

1CCNH, Universidade Federal do ABC (UFABC), Santo Andre, SP 09210-580, Brazil2Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

3Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA(Dated: April 27, 2020)

The crystal growth and the structural, transport and magnetic properties of the magnetically frus-trated YbMn2Sb2 single crystals are reported. The crystals show a trigonal symmetry (space groupP 3m1), where corrugated honeycomb layers of MnSb are separated by Yb atoms. No structuralphase transition was observed down to 22 K. The resistivity measurements show a predominantlyinsulating behavior. The combined resistivity, dc susceptibility and heat capacity measurementsconfirm successive transitions at 230 K, 116 K and 27 K, being the transition at TN=116 K due tothe Mn+2 lattice antiferromagnetic ordering. Muon spin rotation experiments (µSR) reveal a morecomplicated scenario, with temperature dependence of the magnetic volume fraction reflecting shortrange and long range magnetic order, and a strongly disordered magnetic ground state. The roleof spin-lattice coupling and its relationship with exchange interactions between Mn moments arediscussed as possible cause of the complex magnetic behavior observed.

I. INTRODUCTION

The family of compounds with general formulaAM2X2, where A is a divalent cation, M is a transi-tion metal and X are pnictides or chalcogenides, hasrecently gained interest due to their complex magneticproperties [1–3], and to their potential to yield new high-temperature superconductors [4–6] or thermoelectric ma-terials [7, 8]. This family of compounds can show eitherthe tetragonal ThCr2Si2 structure as in the Fe-based su-perconductors, or the trigonal CaAl2Si2 structure, wherethe MX layer presents a corrugated honeycomb lattice,known as a lattice where frustrated magnetism is com-monly observed. Fig. 1 illustrates the difference in theMnSb layer due to crystal lattice symmetry [9]. Frus-trated magnetism has been thoroughly investigated dur-ing the last decades [10], since it can come from geometricconstraints in the crystal lattice or from complex behav-ior of the competing exchange interactions between mo-ments. In the honeycomb lattice, the magnetic momentslie in the vertices of a hexagon and, in this arrangement,magnetically frustrated interactions arise from competi-tion of the exchange interactions between nearest neigh-bours (n.n) J1, next-nearest neighbours (n.n.n) J2, thethird next-nearest neighbours J3, and even exchange be-tween moments in different layers along the c axis Jc.

In the AM2X2 compounds where the transition metalis Mn, the magnetic properties and their correspondingcritical temperatures strongly depend on the crystallinestructure, since they can crystallize either in the tetrag-onal body-centered structure ThCr2Si2 or in the trigonalCaAl2Si2 structure [11]. In the first case, the magneticorder of Mn is only destroyed at several hundred Kelvin,as in YbMn2Si2 and BaMn2Bi2, with Neel temperatures(TN ) of 526 K and 390 K, respectively [12, 13]. In the

∗ Corresponding author: julian.munevar@ufabc.edu.br

latter case, compounds with trigonal structure exhibitantiferromagnetic (AFM) order of Mn moments at dis-tinctly lower temperatures (< 160 K), and in some casesa weak ferromagnetism above this transition temperaturehas been reported [1, 3]. In both structures the [M2X2]−2

lattices are separated by layers of A+2 ions; however, theMn atoms are arranged in a corrugated structure whenthe compounds display a trigonal symmetry, whereas forthe tetragonal symmetry there is a two-dimensional pla-nar lattice (see Fig. 1).

One of the compounds that has recently attracted at-tention, CaMn2Sb2, crystallizes in the trigonal structurewith TN between 85-88 K and with Mn moments alignedantiferromagnetically in the ab plane [14, 15]. Magneti-zation measurements suggest weak ferromagnetism aboveTN coming from magnetic polarons formed at crystal de-fects [1]. It is argued that the low TN for this compoundis caused by a frustrated antiferromagnetic honeycomblattice, where the magnetic order could be one of threepossible magnetic phases, namely, a Neel phase and twospiral phases [16], i.e., the magnetically ordered state isnearly degenerate. This hypothesis, however, is disputedin a recent work, which assigns the suppression of theordering temperature to a low dimensionality of the Mnnetwork that leads to a frustrated bond in one of thedirections in the ab plane [3].

The compound YbMn2Sb2 studied in this work crys-tallizes in the trigonal structure mentioned above forCaMn2Sb2. For this compound, a recent study in poly-crystalline samples claims a ferromagnetic (FM) phaseat room temperature, with a Curie temperature (TC) of338 K and a magnetic moment of about 3.5 µB/Mn [17],followed by an antiferromagnetic ordering of Mn below120 K, with no evidence of magnetic moment for Yb downto 4 K [18]. Resistivity, thermal conductivity and See-beck effect measurements confirm the antiferromagnetictransition observed in the magnetization measurements,showing also an intriguing metallic behavior and a highthermal conductivity due to lattice vibrations [19].

arX

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ysic

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These strikingly different results can be settled by theuse of single crystalline specimens of YbMn2Sb2. Thegrowth of single crystals of intermetallic YbMn2Sb2 alsoenables the study of the magnetic properties for differentcrystal orientations, and for this reason we were moti-vated to pursue the growth of intermetallic single crys-tals by the flux method [20]. To our knowledge, thereare no reports on magnetic studies on single crystallinespecimens of YbMn2Sb2 up to the present date.

a) b)

c) d)

FIG. 1. Crystal structure for (a) trigonal YbMn2Sb2 and (b)tetragonal YbMn2Si2 [9]. Views of the crystal lattice perpen-dicular to the ab plane for each structure are shown in (c)and (d). Yb atoms are represented in light blue, Mn atomsin purple and Sb/Si atoms in brown. The lines between theMn and Si/Sb atoms represent the corresponding bonds.

Magnetization, resistivity, heat capacity and muonspin rotation (µSR) experiments on YbMn2Sb2 singlecrystals can provide a unique point of view of the realiza-tion of the magnetic state of YbMn2Sb2. In particular,the advantage of using a local probe technique such asµSR is that it allows access to a fluctuation time windowthat is not accessible by standard magnetization or neu-tron scattering measurements. Its unique sensitivity tosmall internal fields can detect magnetic order from veryweak magnetic moments, allows the observation of disor-dered magnetic order, the dynamics of fluctuating fieldsand also the phase separation between magnetic and non-magnetic phases within the same sample. The combina-tion of the above mentioned techniques can extend thecomprehension of the physical properties of YbMn2Sb2,and will allow a comparison with the previously pro-posed models for the magnetic order in YbMn2Sb2 andCaMn2Sb2. We find that the magnetic order evolves froma weak ferromagnetic order to a disordered long rangeanisotropic antiferromagnetic order as temperature de-creases.

II. EXPERIMENTAL METHODS

High-quality single crystals of YbMn2Sb2 were grownusing Sn-flux technique. Amounts of Yb, Mn, Sb and Snin the ratio 1:2:2:30 were weighted on a high-precisionbalance and put into an alumina crucible. The cruciblewas inserted into a quartz tube together with quartzwool, and the tube was evacuated and sealed. The mix-ture was heated to 1423 K for 4 h and further kept atthis temperature for 24 h, and then cooled down to 823K over 120 h. The ampoule was taken to a centrifuge toremove the flux and large single crystals of YbMn2Sb2

were extracted. Hexagon-shaped black crystals of ap-proximately 2.5×2.5 mm2 were obtained, as shown inFig. 2. It is worth noticing that the crystal shape al-ready suggests a trigonal crystal lattice. To investigatethe structural properties, temperature dependent X-raydiffraction patterns from powdered samples were mea-sured in a BRUKER diffractometer with a Mo Kα X-raytube (λ = 0.709 A). The resistivity and specific heat mea-surements were performed in a Quantum Design PPMS:the DC resistivity between 2 and 300 K was performedon two different crystals of the same batch, and the spe-cific heat with the heat capacity option ranging tem-peratures from 2 to 250 K. The dc magnetic propertieswere measured with a Quantum Design MPMS3 SQUID-VSM magnetometer from 2 to 300 K. µSR spectra wereobtained using the GPS instrument at the Swiss MuonSource of the Paul Scherrer Institute, Switzerland. Zerofield (ZF), weak transverse field (wTF) and longitudinalfield (LF) spectra were obtained for temperatures from1.6 to 630 K and longitudinal fields up to 150 mT.

III. RESULTS

The temperature dependent X-ray diffraction patternsconfirm a trigonal structure belonging to the space groupP3m1 between 22 K and 300 K. The expected reflectionsfor YbMn2Sb2 and Sn (from the flux) were observed (Fig.2(a)): the Rietveld refinement of the pattern at roomtemperature results in a = 4.5278 A, and c = 7.4481 A,with the presence of about 3% of Sn. These latticeparameters are very close to those reported previously[18], and smaller than the ones reported for CaMn2Sb2

[1], due to the difference in the atomic radius betweenCa+2 and Yb+3. The Rietveld refinement confirmed thatthe crystal structure consists of Yb atoms that separatethe MnSb layers, where the Mn atoms are connectedby Sb atoms and form a corrugated honeycomb lattice.The Mn-Mn distance obtained at room temperature isdMn−Mn=3.099 A, smaller than the dMn−Mn values forCaMn2Sb2 [1].

The temperature evolution of the lattice parametersand the unit cell volume were obtained by performing aglobal fit using the GSASII software [22], taking all thepatterns from 22 to 270 K and the same phases (mainphase and Sn impurity). These results are shown in the

3

10 15 20 25 30 352 (degrees)

250

0

250

500

750

1000

1250In

tens

ity (a

.u.)

(a)

DataSnYbMn2Sb2

100 200T (K)

4.504.514.524.534.54

a (Å

)

(c)

a

100 200T (K)

7.42

7.44

c (Å

)

(d)

c

100 200T (K)

131.5

132.0

132.5

V (Å

3 )

(e)

V

(b)

FIG. 2. (a) X-ray diffraction pattern for YbMn2Sb2 at roomtemperature, showing the corresponding reflections for themain phase and Sn impurity from the flux. (b) YbMn2Sb2

single crystals. (c)-(e) Temperature dependence of lattice pa-rameters a and c, and crystal lattice volume V obtained fromthe Rietveld refinement, respectively.

Figs. 2(c)-(e). It is clearly seen that the a lattice pa-rameter has a negligible temperature variation, while thec lattice parameter shows a decrease starting below ap-proximately 250 K and becomes more pronounced near120 K. The unit cell volume also reflects a similar de-crease. The influence of these changes in the lattice pa-rameters on the magnetic properties and the temperaturedependence of dMn−Mn will be discussed later.

The temperature dependence of the resistivity ofYbMn2Sb2 is shown in the Fig. 3(a). Despite show-ing distinct resistivity values, crystals from the samebatch present insulating behavior. This was previouslyobserved in resistivity measurements on CaMn2Sb2, andit was suggested that crystal defects may be responsiblefor such behavior. However, the resistivity in CaMn2Sb2

varies over several decades [1], whereas our measurementdoes not show such a remarkable increase. By comparingour results with those reported in ref. [1], we notice thatthe effect of Yb in the transport properties resembles thehole doping induced by Na substitutions at the Ca site

in CaMn2Sb2. The insulating behavior observed for ourtwo different crystals of the same YbMn2Sb2 batch differsfrom the results reported in [19], where polycrystallineYbMn2Sb2 clearly show metallic behavior. The effect ofimpurities on the transport properties may be more sig-nificant in polycrystalline specimens [21]. Fig. 3(a) also

shows 1ρdρdT , in particular reflecting a phase transition at

116 K and a minimum at approximately 245 K.A previous neutron diffraction study on YbMn2Sb2

showed antiferromagnetic order below 120 K, with theMn magnetic moments forming an angle θ ≈ 64° withrespect to the c-axis [18]. This magnetic structure is dif-ferent from the one observed for CaMn2Sb2, where theMn magnetic moments lie in the ab plane [1, 16]. Thisdifference is not obvious, since both crystal lattices aresimilar. Also, it was previously reported that YbMn2Sb2

has a clear ferromagnetic order at room temperature [17].We will show that the magnetic order in YbMn2Sb2 ismuch more complex than previously reported.

The magnetization measurements for YbMn2Sb2 areshown in Figs. 3(b)-(d). The ZFC-FC curves measuredin the direction parallel to the crystallographic c axis ofthe crystal and under different external fields are shownin Fig. 3(b). Three transitions are clearly observed, atapproximately 30 K, 116 K and 200 K. The transition at116 K is similar to that observed in CaMn2Sb2 and, ac-cording to the neutron diffraction studies in CaMn2Sb2

and YbMn2Sb2, antiferromagnetic order is expected.The broad peak around approximately 200 K is very sen-sitive to the magnitude of the external field, as it shiftsto lower temperatures with an increasing external field.The ZFC and FC curves indicate irreversible behavior inthe whole temperature range measured, in particular atlow external fields. Finally, all the features for measure-ments at low fields are suppressed with a large externalfield, suggesting that the magnetic interactions presentare weak.

Figure 3(c) shows the ZFC-FC curves with an exter-nal field of 0.05 T both parallel and perpendicular to thecrystallographic c-axis. There is a continuous increaseof χ from room temperature up to 200 K, followed by asmall decrease, and magnetic anisotropy is reflected bythe larger χ values for H||c. The magnetic transition at116 K is noticed only as a variation in the magnetizationin the ab plane, and no remarkable difference betweenZFC and FC modes is seen. The AFM transitions aremore clearly seen when d(χeT )

dT is plotted (see Fig. 3(c),

red line), where χe = 13χ‖ + 2

3χ⊥. Below 30 K, a furthertransition is seen as an irreversible behavior between theZFC and FC measurements, possibly caused by a rear-rangement of Mn magnetic moments.

Figure 3(d) shows M × H curves with the externalfield parallel to the crystallographic c axis at differenttemperatures. This figure shows an interesting behav-ior: a decrease of the magnetization as the temperaturedecreases, possibly caused by the crossover between theweak ferromagnetic phase and the AFM phase. The Mnatoms reach a small magnetic moment of approximately

4

0 50 100 150 200 250 300T (K)

100

101

(-c

m)

(a)

1

210

8

6

4

2

0

d dT×

102

ddT × 102

0 50 100 150 200 250 300T (K)

4

6

8

10

12

103

× (e

mu/

mol

-Oe)

ZFC: open symbolsH c

(b)0.01 T0.05 T0.1 T1 T5 T

0 50 100 150 200 250 300T (K)

0

2

4

6

103

× (e

mu/

mol

-Oe)

H=0.05 T

(c)

ZFC: H cFC: H cZFC: H cFC: H c

0

2

4

6

8

10

12

103

×d(

T)dT

103 × d( T)dT

1.0 0.5 0.0 0.5 1.0H (10 kOe)

4

2

0

2

4

103 M

(B/f.

u.)

H c

(d)

50

100

150

200

250

300

Tem

pera

ture

(K)

FIG. 3. (a) Resistivity measurements performed for two single crystals of YbMn2Sb2 belonging to the same batch. 1ρdρdT

is also

shown in red. (b) ZFC-FC curves for different magnitudes of applied magnetic field measured with H ‖ c. (c) ZFC-FC curveswith an applied field of 0.05 T and measured along the axes a and emphc. Below 116 K the light blue curves (H ⊥ c) showa behavior consistent with an antiferromagnetic ordering. (d) External magnetic field dependence of the magnetization from5 K up to room temperature with H ‖ c.

10−2µB/f.u. without the observation of metamagnetictransitions (curves measured at 5 K and 100 K), and witha small but noticeable difference between different crystalorientations (not shown), indicative of a small magneticanisotropy related to the magnetic order.

The temperature dependent specific heat measurement(Fig. 4) shows two magnetic transitions at approximately235 K and 116 K, related to the weak FM and AFM tran-sitions observed from magnetization measurements, re-spectively. Interestingly, no evidence of further magnetictransitions close to 30 K is observed. The low tempera-ture fit of the specific heat (CP /T versus T 2) yielded aDebye temperature of θD = 106 K, which is significantlylower than that reported for CaMn2Sb2 [1]. In order toextract the magnetic contribution to the sample specificheat, we took the specific heat data of the non-magneticequivalent of YbMn2Sb2, i.e. YbZn2Sb2 [23], and sub-tracted it from the data obtained for YbMn2Sb2. Thespecific heat curve for YbZn2Sb2 was modelled using asum of two contributions, namely, one following the De-bye model and the other following the Einstein model:

Cp(T ) = f × 9Nk

(T

θD

)3 ∫ θDT

0

dxexx4/(ex − 1)2+

+ (1− f)× 3Nk( ε

kT

)2 e(εkT )(

e(εkT ) − 1

)2 ,where N is the Avogadro constant, k is the Boltzmann

constant, θD is the Debye temperature, TE is the Ein-stein temperature, ε = kTE and T is the temperature.The corresponding Debye and Einstein temperatures areθZnD = 131(1) K and θZnE = 235(3) K.

We separated the lattice and magnetic contributionsto the heat capacity, and integrated the magnetic heatcapacity (Cmag) in order to obtain the magnetic en-tropy (Smag, Fig. ??, red curve). Our analysis yieldsSmag =14.46 J/mol-K, which corresponds to S = 2.35 '52 (Smag = R ln (2S + 1)), meaning that the Mn momentsare in the +2 high-spin state.

The µSR experiments were conducted on a single crys-tal with its c axis parallel to the muon beam (i.e. muonmomentum), and the muon spin rotated 40 degrees rela-

5

0 50 100 150 200 250 300T (K)

0

20

40

60

80

100

120

140C p

(J/m

ol.K

)

YbZn2Sb2 fitDataYbZn2Sb2Cmag

0.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

S m (J

/mol

.K)

Smag

FIG. 4. Specific heat as a function of the temperature forYbMn2Sb2. The peak at 116 K indicates the antiferromag-netic transition. The magnetic heat capacity and the respec-tive magnetic entropy are also shown, with a line showing theapproximate value of Smag for S = 5

2.

tive to the muon beam. Muon decays were detected byfour detectors labeled as up (U), down (D), backward (B)and forward (F). Using this setup, the magnetic responserelated to the crystallographic c axis (UD), as well as tothe ab plane (BF) was observed, since each set of detec-tors reflect the projection of the muon spin polarizationinfluenced by the internal field in the corresponding di-rection.

The general fitting function for an asymmetry spec-trum of a single crystalline specimen is strongly depen-dent on the initial muon spin and the internal field direc-tions. In a simplified case, where the internal fields areassumed to be static and magnetic order is long range, itis given by

A(t) = A0

(e−λLt cos2 θ + e−

σT t

2 sin2 θ cos (ωt)), (1)

where A0 is the initial asymmetry, λL is the relaxationrate for the longitudinal component of the asymmetry, σTis the Gaussian relaxation rate for the transverse compo-nent of the asymmetry, θ is the angle between the internalfield and the muon direction, and ω = γµBµ is the muonspin angular frequency. Equation 1 was used to fit thespectrum in Fig. 5(c). A different fitting function waschosen for the spectra in Figs. 5(a)-(b) due to the ab-sence of muon spin precession, the evidently exponentialrelaxation seen, and assuming a quasistatic regime:

A0P (t) = Ase−λst +AF e

−λF t + BG. (2)

A0 is the initial asymmetry of the muon, As is theasymmetry corresponding to a component reflecting slowmuon spin relaxation λs, AF is the asymmetry corre-sponding to a component of the spectrum reflecting a fast

0 1 2 3 4 5 6

0.0

0.1

0.2

A(t)

ab plane

(a)

5 K5 K LF40 K70 K90 K115 K125 K295 K400 K613 K

0 1 2 3 4 5 6

0.0

0.1

0.2

A(t)

c axis

(b)

0.000 0.005 0.010 0.015 0.020

0.0

0.2

0.4

A(t)

(c)

ab planec axis

0 2 4 6 8t ( s)

0.2

0.0

0.2

A(t)

(d)

5 K140 K

FIG. 5. ZF-µSR spectra obtained for YbMn2Sb2 single crystalbetween 5 and 613 K, for (a) the BF detectors (muon spinprojection in the crystal ab plane) and (b) the UD detectors(muon spin projection in the crystal c axis) detectors. (c)ZF-µSR spectra at 5 K at early times (< 20 ns). (d) 5 mTweak TF-µSR spectra at 5 and 140 K.

relaxation rate λF , and BG is a temperature independentbackground contribution to the total polarization.

The fitting function for the weak TF-µSR spectra (Fig.5(d)) is:

P (t) = PTF e−λTF t cos (γµBTF t), (3)

where PTF is the muon polarization under the exter-nal weak transverse field, λTF is the corresponding re-laxation rate and BTF is the total field sensed at themuon site. All the spectra were fitted within the 0.2-10 µs time range. Global fits were performed using theMusrfit software [24], keeping λF and BG constant over5− 117 K.

Figures 5(a)-(b) show selected ZF-µSR spectra for tem-peratures from 5 K to 613 K. An initial decrease of asym-

6

metry accompanied by a temperature-dependent expo-nential damping of the asymmetry is observed for the fulltemperature range. An asymmetry decrease of approxi-mately 12 % is presumed to occur between 140 and 295K in both orientations. A further decrease of the asym-metry is observed below approximately 116 K, reflectingthe robustness of the long range antiferromagnetic tran-sition previously observed. Figure 5(c) shows early timeZF-µSR spectra for both orientations (∼20 ns) at 5 K.A clear muon spin precession was seen for the muon spinprojection on the c axis only, where it is also observedthat for both spectra the asymmetry is strongly dampedat very early times (∼ 10 ns). This could explain the ab-sence of muon spin precession for higher temperatures.

The precessing spectrum in Fig. 5(c) was fitted us-ing Eq. 1, setting λL equal to zero. The internal fieldobtained is Bint = 1.84(6) T, sin2 θ = 0.81(3) andσF = 194(50) µs−1. The muons stopping in the crys-tal are sensing a very strong and broadened field, andit can be inferred that the internal field direction withrespect to the muon spin polarization (or the crystal caxis) is θ = 64(1) degrees, which is consistent with theprevious neutron study [18].

The relaxation rates of the slowly relaxing componentλs obtained from ZF-µSR, the zero field asymmetriesof the fast component AF , and the magnetic volumefraction obtained from weak TF-µSR measurements areshown in Fig. 6(a)-(c). The behavior of λs (Fig. 6(a))shows a minor increase as it approaches to TN , as is ex-pected from the slowing down of the moment fluctua-tions. Below 116 K, λs shows different behavior for eachprojection of the muon spin explored, as follows: in the abplane is seen a considerable increase of λs is seen, reach-ing a maximum at approximately 80 K and decreasing,whereas for the c axis a modest increase is seen at TN ,followed by a further increase below approximately 70 K.Furthermore, an additional increase in λs is observed atlower temperatures with peak at approximately 27 K.

Figure 6(b) shows the ZF asymmetry obtained for thefast relaxing component in the spectra AF , for each muonspin projection. We see that prior to the onset of theAFM transition at TN , there is an asymmetry increaseof about 10 %. This asymmetry increase may be asso-ciated to regions of the crystal developing short rangemagnetic order and a very large muon relaxation rateλF . At TN we clearly see a jump in AF reflecting themagnetic transition, and below TN , we observe a furtherincrease of AF reaching a maximum at approximately 40K and stabilizing below 27 K. In order to extract the non-magnetic volume fraction of the sample, we analysed theweak TF-µSR spectra (Fig. 5(d)), and the TF asymme-try extracted is shown in Fig. 6(c). This TF asymmetryis proportional to the nonmagnetic volume fraction of thecrystal, and it starts to decrease already at high tempera-tures (∼300 K), being followed by a sharp decrease at 116K and reaching a minimum value at lower temperatures.Figure 6(c) implies that below TN the system undergoesa magnetic phase transition, which is consistent with our

0.0

0.5

1.0

1.5

2.0

S (s

1 )

(a)

ab planec axis

0.00

0.05

0.10

0.15

A F (t

)

(b)

100 101 102

T (K)

0.05

0.10

0.15

0.20

0.25

TF A

sym

met

ry

(c)

FIG. 6. (a) Muon spin relaxation rate, (b) average inter-nal field angle and (c) TF asymmetry for YbMn2Sb2 singlecrystal. The dashed lines indicate the temperatures where amagnetic transition is observed/expected.

previous results.In order to verify whether the internal fields are static

or dynamic, LF-µSR experiments were performed at 5 Kfor fields as large as 0.15 T (see Fig. 5). Our experimentsshow that the external field has a negligible effect on themuon spin depolarization. This may be caused becauseto decouple such strongly interacting spins it would benecessary to apply large fields. For instance, if we haveσF ' 200 µs−1, the LF field necessary to observe asym-metry decoupling would be around σF

γµ' 20 kG.

IV. DISCUSSION

We now discuss the different features observed in ouranalysis, namely, the transitions at ∼250 K, at TN =116 K and at ∼27 K. The magnetization measurements inFigs.3(b)-(d) at high temperatures show irreversible and

7

anisotropic behavior, suggesting that magnetic order isalready present at these temperatures. Furthermore, theFig. ?? clearly shows a peak in the specific heat indicatinga phase transition at around 225 K. A variation in themuon spin polarization between 140 and 400 K is alsoseen (Figs. 6(b) and 6(c)), reflecting the appearance ofa small magnetic volume fraction (∼10 %) within thistemperature range.

The influence of crystal defects that favor the onset ofthese observed short range correlations, possibly leadingto the previously reported polaron-mediated magnetic in-teractions can be the reason to observe such behavior [1].Any magnetically ordered state for T >120 K was ob-served by the neutron diffraction experiments reportedin Ref. [18]. µSR is a local probe technique that is moresuitable to detect magnetic volume fractions, even forsmall fields or short range order, and that can be thereason for the absence of evidence of magnetic correla-tions from neutron diffraction.

The resistivity measurements (see Fig. 3(a)) evidencean anomalous insulating behavior, with a very broad in-crease around 225 K. This behavior may be signature ofan increasing conduction electron scattering in the crys-tal. The observed behavior of the transport and magneticproperties has been previously assigned to scattering pro-cesses induced by the moments present in the sample atthese temperature ranges [1, 15, 19], probably related toparamagnon states at point defects in the crystal latticeabove TN that are predicted in the theory of classicalHeisenberg spins interacting in the honeycomb lattice[26]. This would explain the observed variation of themagnetization and resistivity between samples up to oneorder of magnitude, as it was also noted in ref. [1]. Thisphenomenon could result from the distribution of defectsin the crystalline structure varying from one sample toanother, and thus affecting the formation of magnetic po-larons and in consequence the magnetic response in thesetemperature ranges.

It was previously known from neutron diffraction re-sults that the Mn moments align antiferromagneticallybelow 120 K [18]. We observe the onset of a long rangemagnetic order at 116 K, manifested as a phase transitionin the resistivity, magnetization and specific heat mea-surements (Fig. 3 and Fig. 4), and as a clear increase inλs and the magnetic volume fraction in the µSR results(Fig. 6). The magnetization measurements show thatthe AFM order below 116 K is sensitive to the externalmagnetic field. The specific heat confirms the magnetictransition by observing a clear peak at this temperature,the spin state of Mn moments is found to be S = 5

2 .A higher TN compared to CaMn2Sb2 (TN = 85 K [15])seems plausible, since the distance between Mn atoms issmaller for YbMn2Sb2, in favor of a stronger exchangeinteraction between Mn moments.

The µSR spectra do not show any indication of muonspin precession except at 5 K, nor an internal field de-coupling due to the longitudinal field at 5 K (see Fig. 5).This points to a scenario where static order is present,

but strongly disordered. It is not a spin glass transitionbecause the phase transition also manifests in the specificheat measurement (Fig. ??). Anisotropy is also observedfrom µSR and magnetization measurements. Specificallyfor the µSR results (see Fig. 6), a larger λs is observedfor the muon spin projection on the ab plane, suggestingthat larger internal field fluctuations occur, which couldbe taken as an indication of stronger competition withinmagnetic moments between the ab plane.

A competition between magnetic ground states maybe plausible, as follows: the J1/J2-J3 phase diagram[1, 16, 26, 27] suggests a plethora of possible magneticground states, and the ratio between the correspondingexchange interactions Ji will determine the nature of themagnetic ground state. A strongly disordered groundstate could appear if the system is on the vicinity of sev-eral magnetic ground states, as it was demonstrated forCaMn2Sb2 single crystals and its proximity to a mag-netic tricritical point [1, 16]. According to our results,this may be the scenario of the magnetic ground statefor YbMn2Sb2.

We also found a temperature dependent correlation be-tween the magnetic order and the crystal lattice volume,as can be seen in Fig. 7(a), where the unit cell parame-ter c (Fig. 2(c)) follows a similar behavior compared tothe saturation magnetic moment HC , extracted from thehysteresis loops presented in Fig. 3(d). There is only anegligible variation of the above mentioned parametersdown to 225 K, followed by a decrease reaching a min-imum value at around 50 K. This spin-lattice couplingwas suggested by a previous report [19], where thermalconductivity measurements indicated spin-lattice inter-actions accounting for a maximum near 30 K. This spin-lattice coupling may affect the bulk properties, possiblydepending on the crystal size and quality, explaining whythe results can vary between samples. We also see the dis-tance between Mn atoms and the coercive field, plottedin Fig. 7(b), increasing below approximately 120 K.

The results presented in Fig. 7 suggest that the com-pression of the crystal lattice and the subsequent reduc-tion in dMn−Mn are directly related to the change in themagnetic properties, namely, the irreversible behavior re-flected by the increase in HC . One possible explanationfor this behavior may be a spin Jahn-Teller effect that hasbeen discussed previously in magnetically frustrated sys-tems [28–31], where a non-Kramers degeneracy may leadto a Jahn-Teller distortion. A deeper insight is needed inorder to clarify the mechanisms involved.

Finally, below 30 K, there is a noticeable increase ofthe magnetization irreversibility, a maximum in the muonspin relaxation rate λs and a constant value for AF .This behavior might be caused by a transition from aNeel state to another magnetic state. According to thechange in the lattice parameters and the distances be-tween Mn atoms dMn−Mn, this could be explained byassuming that a temperature dependent reduction of theunit cell dimensions would lead to an increase in Jc and areduction in J1, J2 and J3, therefore changing the ratios

8

0 50 100 150 200 250 300T (K)

200

0

200

400

600

HC (m

T)

(b)

HC

dMn Mn3.1

3.2

3.3

3.4

3.5

d Mn

Mn (

Å)

0 50 100 150 200 250 300

5.0

5.2

5.4

5.61T

×10

3 (B/M

n)(a)

Mn

c 7.41

7.42

7.43

7.44

7.45

c (Å

)

FIG. 7. (a) Saturation moment at 1 T and c lattice parame-ters obtained for YbMn2Sb2. (b) Coercive field and distancebetween nearest Mn atoms.

Jc/J1, J3/J1 and J2/J1 in favor of another ordered state,as represented in the phase diagram [16]. This changewould represent no change of entropy in the system andthus no change in the sample specific heat. However,since the present experiments do not allow extraction ofindividual exchange constants, it is necessary to seek amore suitable technique to confirm this hypothesis.

The behavior of λs could be understood within the as-sumption of a quasistatic scenario, where λs ' 2ν

3 , andν representing the fluctuation rate of the muon spin [32–34]. The fluctuation time τ = 1

ν is around 10−6 s, closeto the resolution limit of µSR, but slow enough to ob-serve static magnetic order by neutron diffraction. How-ever, looking Fig. 6(a) in detail, we see that anisotropyis reflected as a slower fluctuation time τ close to TNin the ab plane, and a similar τ at 27 K. One possibil-

ity would be the crossover from a magnetic ground statewhere magnetic interactions occur in layers, to a 3D mag-netic ground state. This hypothesis may be supported bythe spin-lattice coupling we observe in Fig. 7, but furtherexperiments are needed to confirm this.

All these observations suggest that the magnetic orderobserved in YbMn2Sb2 arises from competing exchangeinteractions between Mn moments controlled by a spin-lattice coupling. The presence of slowly fluctuating lo-cal fields also suggest that the magnetic ground state isstrongly disordered, in accordance with previous reportson other materials showing similar behavior [32–34]. Theobservation of magnetic fluctuations at high tempera-tures, reflected by irreversible magnetization curves atsuch temperature ranges and a nonzero magnetic volumefraction observed by µSR, may be consequence of thedefects that lead to the formation of magnetic polarons.Future work on this material can be directed towardspressure-dependent experiments, where the spin-latticeinteraction can be taken further to explore experimen-tally the phase diagram for a classical arrangement ofspins.

V. CONCLUSION

We have performed a detailed magnetic characteriza-tion on YbMn2Sb2 single crystals, finding a very complexmagnetic state, that has been analysed in light of ourmeasurements as well as previous reports and theoreticalmodels. This work opens a new alternative to study mag-netic frustration in general, and will be specially usefulto understand and correlate the arrangement of momentsin a crystal lattice and their magnetic interactions.

The authors thank H. Luetkens and A. Amato for theirsupport during the µSR experiments at PSI, the Mul-tiuser Central Facilities (UFABC) for the experimentalsupport, and E. Morenzoni for important discussions.The research leading to these results has received fund-ing from the European Community’s Seventh FrameworkProgramme (FP7/2007-2013) under Grant AgreementNo. 290605 (PSI-FELLOW/COFUND), and from theBrazilian funding agencies CNPq, FAPESP (Grants No.2011/19924-2 and 2014/20365-6) and CAPES. RAR wasfunded by the Gordon and Betty Moore Foundation’sEP: QS Initivative through grant No. GBMF4411.

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