PHYSICAL REVIEW B 85, 174402 (2012)

Thermodynamic studies on single-crystalline Gd2BaNiO5

E. A. Popova,1 R. Klingeler,2 N. Tristan,3 B. Buchner,3 and A. N. Vasiliev4,*

1Moscow State Institute of Electronics and Mathematics (Technical University), 109028 Moscow, Russia2Kirchhoff Institute for Physics, University of Heidelberg, INF 227 69120, Heidelberg, Germany

3Leibniz-Institute for Solid State and Materials Research IFW Dresden, 01171 Dresden, Germany4Low Temperature Physics and Superconductivity Department, Moscow State University, 119991 Moscow, Russia

(Received 22 October 2011; revised manuscript received 10 February 2012; published 2 May 2012)

We present the thermodynamic properties and the magnetic phase diagram of Gd2BaNiO5 investigated bymeans of specific heat and magnetization measurements performed along the main crystallographic axes of thesingle crystal. Our data imply antiferromagnetic ordering at TN = 55 K and a spontaneous spin-reorientationtransition at TSR = 24 K. Upon application of external magnetic fields, a spin-flop transition is observed atT < TSR in magnetic fields B ‖ b axis and at TSR < T < TN in magnetic fields B ‖ a axis. The magneticphase diagram in Gd2BaNiO5 is established from these data. Considering Gd-Gd and Gd-Ni interactions allowsestimating the magnetic contribution of the gadolinium subsystem to the magnetization and the specific heat. TheGd-Gd interaction is organized via Ni chains being therefore sensitive to the angle between Gd and Ni magneticmoments. The analysis of the experimental data shows that the behavior of the nickel subsystem differs from thatof a classical antiferromagnet.

DOI: 10.1103/PhysRevB.85.174402 PACS number(s): 75.30.Kz, 75.40.Cx, 75.10.Pq

I. INTRODUCTION

Magnetism in low-dimensional systems is a fundamentallyrelevant phenomenon where quantum effects may cause noveland intriguing ground states with unusual excitations. Afamous example is the antiferromagnetic spin chain withinteger spin, i.e., Haldane chain, where a gap in the elementaryexcitation spectrum appears.1,2 The magnetic subsystem inY2BaNiO5 excellently realizes such a one-dimensional systemwith negligible interactions between the chains of integer spinS = 1 at the Ni2+ ion sites, which are almost isotropically cou-pled by antiferromagnetic exchange interactions. Structurally,R2BaNiO5 (R = rare-earth or yttrium) contains flattenedcorner-sharing NiO6 octahedra, which form infinite chainsalong the a axis interconnected through R3+ and Ba2+ ions.3

Indeed, there is no long range magnetic order in Y2BaNiO5

down to at least 0.1 K4 and a singlet ground state is confirmedby neutron and magnetization studies, which imply a Haldanegap of about 10 meV in the magnetic excitation spectrum.5,6

In addition, the family of R2BaNiO5 allows studying theborderline between quantum and classical magnetism byintroducing magnetic rare-earth ions at the R-sites. This yieldsa subsystem of rather classical spins weakly coupled to the S =1 antiferromagnetic Haldane chains.3 Interestingly, dependingon the actual rare-earth ion, long range antiferromagnetic orderappears in the range 10 ÷ 50 K,7–10 which yields an effectivestaggered field acting on the S = 1 chains. Since there isonly weak direct coupling between the rare-earth moments,the interaction is necessarily mediated by the Ni chains. Theanisotropy of the rare-earth ions causes the orientation ofthe magnetic moments of both Ni2+ and R3+ ions. On theother hand, clear signatures of the quantum ground stateare still observed since polarized and unpolarized inelasticneutron scattering experiments on R2BaNiO5 have shown theparadoxical coexistence of Haldane-gap excitations and spinwaves, i.e., of classical and quantum spin dynamics, in theordered state.11–13

In Gd2BaNiO5, the R-sites are occupied by Gd3+-ionswith half-filled f -shells, i.e., S = 7/2. It crystallizes in

the orthorhombic space group Immm.14,15 Observation of themagnetic superstructure in the ordered state by means ofneutron diffraction has not yet been successful due to thehigh absorption cross section of natural Gd. However, infraredoptical spectroscopy16 and Mossbauer spectroscopy17 enableus to conclude that Gd2BaNiO5 orders antiferromagneticallyat TN = 53 K and undergoes a spin-reorientation transition atTSR = 24 K. The temperature dependencies of the magneticsusceptibility taken along the a and b axes, respectively,indicate a Curie-Weiss-like behavior above TN.18 However, adetailed analysis of these dependences and of the magneticphase diagram below TN is missing and, at present, thebehavior of the Ni subsystem, which is supposed to beintrinsically disordered even below TN, has not been analyzed.

In this work the thermodynamic properties of a Gd2BaNiO5

single crystal are investigated by means of detailed mag-netization and specific heat measurements performed indifferent orientations of the magnetic field with respect to thecrystallographic axes. The magnetic susceptibility and specificheat data confirm antiferromagnetic ordering and spontaneousspin reorientation found by previous optical and Mossbauerstudies.16,17 Our measurements allow us to establish theanisotropic magnetic phase diagram. In particular, a spin-floptransition is observed at T < TSR in a magnetic field B ‖ b axisand at TSR < T < TN in a magnetic field B ‖ a axis. Analyzingboth the specific heat and the magnetization data demandsconsidering both the Gd-Gd and the Gd-Ni interactions, whichallow a quantitative estimate of the respective contributionsdue to the gadolinium subsystem. Our analysis implies thatthe behavior of the nickel subsystem differs from the behaviorof the ordered spins in an antiferromagnet.

II. EXPERIMENTAL

A Gd2BaNiO5 single crystal was grown by the travelling-solvent floating-zone technique, as described in Ref. 19. Thestatic magnetization M(T ) was measured in a magnetic fieldof B = 0.05 T in the temperature range 1.8–350 K using a

174402-11098-0121/2012/85(17)/174402(7) ©2012 American Physical Society

E. A. POPOVA et al. PHYSICAL REVIEW B 85, 174402 (2012)

MPMS-XL5 SQUID magnetometer (Quantum Design). Thefield dependence of the magnetization M(B) was measuredat temperatures 4.2 ÷ 120 K in magnetic fields up to 15 Tby means of a home-built vibrating sample magnetometer(VSM).20 The field sweep rate was approximately 0.2 T /min.The specific heat was studied in the temperature range 1.8 ÷300 K in magnetic fields of 0, 1, and 2 T, respectively, orientedalong the b axis of the crystal by means of a relaxation methodin the Physical Property Measurement System (QuantumDesign).

A. Experimental results

The evolution of long range spin order in Gd2BaNiO5 andthe associated phase transitions yield pronounced anomaliesin the magnetization and specific heat data (Fig. 1). In thespecific heat in Fig. 1(b) there is a jumplike or weaklyλ-type anomaly at TN = 55 K, which signals the onset oflong range magnetic order by means of a second-order phasetransition. The sharp anomaly at TSR = 24 K implies adiscontinuous phase transition associated with spontaneousspin reorientation. Both temperatures are in good agreementwith the optical and Mossbauer spectroscopy data in Refs. 16and 17. In addition, there is a broad hump in the specificheat data at T ≈ 20 K. This feature is indicative of a Schottkyanomaly, which reveals the temperature-driven repopulation ofthe ground state of the Gd3+ ions split in the internal magneticfield in the ordered state associated with the ordered state.

CM

FIG. 1. (Color online) (a) Temperature dependences of themagnetization M measured along the different crystallographic axesin an external magnetic field of B = 0.05 T. (b) The temperaturedependence of the specific heat C(T ) measured in zero magnetic fieldin the temperature range 2–100 K. In both plots experimental dataare shown by open symbols, and solid lines display the contributionof the Gd subsystem (see the text). TN and TSR mark the onset of longrange antiferromagnetic order and the spin-reorientation transition,respectively.

Quantitatively, the specific heat jump at TN amounts to�C = 2.4 J/(mol·K). This value does not agree with thecalculated jump �C = 5S(S+1)

S2+(S+1)2 R (R is the gas constant)predicted by mean field theory for antiferromagnetic spinorder.21 To be specific, the mean field theory predicts �CNi =16.6 J/(mol·K) for the Ni2+ (S = 1) subsystem and �CGd =40.3 J/(mol·K) for the Gd3+ (S = 7/2) one. The data henceimply either strong spin disorder and/or the reduction of themagnetic moments caused by quantum spin fluctuations belowTN or the presence of significant spin correlations which yielda release of entropy already well above the Neel temperature.We suppose that both effects are relevant. There is indeedexperimental evidence for spin disorder at T < TN since spinorientation at TSR is associated with entropy changes, too,presumably mainly of magnetic nature. These discontinuousentropy changes amount to �SSR = 0.37 J/(mol·K).

In Fig. 1(a) the temperature dependencies of the mag-netization Ma(T ), Mb(T ), and Mc(T ) measured along thecrystallographic a, b, and c axes, respectively, are displayed.While above T ≈ 100 K, as shown in Fig. 2, the magnetizationmeasured in different directions is almost isotropic, thereis a significant anisotropy of the magnetic properties belowthe Neel temperature. However, the data display no clearanomaly at TN. At T < TN, the magnetization Ma measuredalong the a axis is smaller than Mb and Mc measured alongthe b and c axes, respectively. The discontinuous transitionat TSR is indicated by a pronounced jump in the magneti-zation. The data imply, upon cooling, magnetization jumpsat 0.05 T of �M(B||a) = 5.9 × 10−2 μB/f.u., �M(B||b) =−8.7 × 10−2 μB/f.u., and �M(B||c) = 2.4 × 10−2 μB/f.u.

for the different field directions. We note a small kink in χb(T)and χc(T) at T = 7 K.

In order to establish the magnetic phase diagram, thefield dependences of the magnetization Ma(B), Mb(B), andMc(B) were measured along the a, b, and c axes at varioustemperatures. These dependences taken at T = 4.2 K and T =30 K are shown in Fig. 3. Above B ∼ 5 T, all magnetizationcurves have a nonlinear character with a negative curvature,i.e., the magnetization curves are bent to the right. Ma is larger

T

B abc

BB

M

B

FIG. 2. (Color online) Temperature dependence of the magne-tization M measured along the a, b, and c axes, respectively, inan external magnetic field of B = 0.05 T. Experimental data areshown by open symbols. Solid lines show the contribution of the Gdsubsystem for the case of negligible Gd-Gd and Gd-Ni interactions.Inset: Temperature dependence of the internal magnetic field Bex

acting on the Gd3+ moments (see the text).

174402-2

THERMODYNAMIC STUDIES ON SINGLE-CRYSTALLINE . . . PHYSICAL REVIEW B 85, 174402 (2012)M

FIG. 3. (Color online) Field dependences of the magnetizationMa(B), Mb(B), and Mc(B) measured along the a, b, and c axes,respectively, at T = 4.2 K and T = 30 K. Lower inset: Ma(B) andMb(B) in small fields. Upper inset: Ma(B) at T = 30 K and Mb(B) atT = 4.2 K where the spin-flop transition is observed. Experimentaldata are shown by open symbols; solid lines show the contribution ofGd subsystem.

than Mb and Mc but there is very similar field dependence inthe high field range. In contrast, there is a strong anisotropybelow B ∼ 5 T if the field is applied along the a or b axes.This becomes visible in more detail by the magnetizationcurves M(B‖a) and M(B‖b), shown in Fig. 4. The mainfeatures in the curves are jumps in the magnetization, whichare present at temperatures below TSR = 24 K in magneticfields B ‖ b axis and at TSR < T < TN for B ‖ a axis. It isstraightforward to attribute these features with a spin-floplikefield-driven reorientation of the spins. There are clear maximain the derivatives ∂M/∂B, which enable us to identify thecorresponding critical fields BC, e.g., BC(T = 4.2 K) ‖ b =1.25 T. A tiny hysteresis indicates the first-order characterof the spin-flop transition. At intermediate fields there isa quasilinear field dependence of the magnetization whichextrapolates to M(B = 0) = 0 as expected for a spin-floptransition [cf. dashed line in Fig. 4(a)]. Upon heating the jumpin M(B‖b) reduces in size. Concomitantly, the critical fieldBC increases with increasing the temperature up to T ≈ 14 Kand then decreases and eventually vanishes at TSR. In contrast,there is no such feature in M(B‖a) for temperatures belowTSR, but it appears at TSR < T < TN. Again, the jump �M

reduces and smoothes upon heating, and the critical field BC

shifts towards higher fields with increasing the temperature upto TN. The spin-flop transition is absent above TN as well asfor magnetic fields applied along the c axis.

This behavior is summarized in the magnetic phase diagramin Fig. 5. Here, the effect of external magnetic fields applied‖b axis (full symbols) and ‖ a axis (open symbols) ismerged. Clearly, two separate regimes are visible. The phaseboundaries meet at TSR(B = 0) where the first-order spin-reorientation transition is associated with both entropy andmagnetization jumps (cf. Fig. 1). The opposite signs of themagnetization jumps �M(B‖a) and �M(B‖b) observed insmall magnetic fields already imply that the phase boundariesoriginating at TSR exhibit opposite slopes dBC/dT . For adiscontinuous phase transition, the slope of the phase boundary

MM

B

B

B

FIG. 4. (Color online) Field dependence of the magnetization(a) Mb(B) in magnetic fields up to B = 3 T ‖ b and (b) Ma(B)in magnetic fields up to B = 8 T ‖ a at different temperatures inthe antiferromagnetically ordered phase (note: TSR = 23 K). Inset:Derivatives ∂M/∂B.

is associated with the ratio of the entropy changes �S and themagnetization changes �M at the phase transition according

N

FIG. 5. Magnetic phase diagram constructed from the magneti-zation data and specific heat data. Open (filled) squares denote thespin-reorientation fields BC as extracted from M(B‖a) (M(B‖b))measurements; cycles label the antiferromagnetic ordering tempera-ture TN and the spin-reorientation temperature TSR from specific heatdata. Lines are guides to the eyes.

174402-3

E. A. POPOVA et al. PHYSICAL REVIEW B 85, 174402 (2012)

CT

CT

N

FIG. 6. (Color online) Temperature dependence of the specificheat C(T , B)/T at B = 0, B = 1 T ‖ b axis, and B = 2 T ‖ b axis.The inset highlights the antiferromagnetic transition.

to dB/dT = − �S/�M (Clausius–Clapeyron relation).22

Our experimental data presented previously hence allow usto calculate the initial slopes of the phase boundaries atTSR, i.e., dB‖b/dT = − 7.1 T/K and dB‖b/dT = 10.5 T/K.Interestingly, the strong specific heat discontinuity at the phaseboundary vanishes in external magnetic fields B‖a = 2 T(Fig. 6). In contrast, although magnetic fields B‖b suppress thephase transition, the pronounced entropy jump is preserved, asevidenced by a strong peak in the specific heat (Fig. 6). Notethat the flat slope of the phase boundary suggests negligiblemagnetization changes �M(B‖b) ∼ 0 if TSR is suppresseddown to ∼15 K and �M(B‖b) < 0 at lower temperatures.

III. DISCUSSION

Gd2BaNiO5 contains two kinds of magnetic ions, i.e.,Ni2+ (S = 1) and Gd3+ (S = 7/2, L = 0) ions, which ingeneral govern its magnetic properties. At high temperatures,however, the magnetic susceptibility is described by theGd3+-paramagnetism. The susceptibility data, above T =100 K, are well described by the Curie-Weiss law with theWeiss temperature � ≈ − 13 K and the effective magneticmoment μeff = 11.17 μB. The negative value of � pointsto predominance of antiferromagnetic exchange interactions.The value of μeff is very close to the free-ion value for theGd3+-ion of μeff = 11.22 μB (note the two gadolinium ionsper f.u. in Gd2BaNiO5). On the other hand, the theoreticaleffective moment amounts to μeff = 11.58 μB if spin S = 1of the Ni2+-ion is taken into account, which contradicts theexperimental data. This indicates that the Ni subsystem onlycontributes negligibly to the magnetic susceptibility in thistemperature range, which agrees to studies on the isostructuralcompound Y2BaNiO5 where the magnetic susceptibility isvery small and exhibits a maximum at room temperature,indicating the Haldane gap state.23 The value of this maximumis much less (by a factor of 1000) than the susceptibilityof Gd2BaNiO5. We hence may conclude that the Haldanegap state is preserved in Gd2BaNiO5 at high temperatures.

This assumption is supported by the observation of an energygap in the magnetic excitation spectrum of about 11 meV inR2BaNiO5 with R = Pr, Nd, above the magnetic orderingtemperature of these compounds.8,11

As previously mentioned, it is reported that the mag-netically ordered phases of Nd2BaNiO5 and Pr2BaNiO5

coexist with the Haldane gap state of the Ni chains.8,11 Inthis situation it is not a priori clear whether at all or towhich extent the Ni subsystem exhibits isotropic susceptibilityexponentially decreasing to zero at low temperatures typicalfor the quasi-1D S = 1 Heisenberg antiferromagnet or whetherit shows anisotropic magnetic properties similar to a classicalantiferromagnet. In order to extract this information from theexperimental data presented above, the magnetic response ofthe Gd subsystem to the total magnetization and specific heatof Gd2BaNiO5 should be estimated. It is governed by the low-lying Gd3+-crystal field levels split in the effective magneticfield resulting from both the external and internal fields.We conclude from neutron scattering experiments on othercompounds of the family R2BaNiO5,11–13 that both magneticsubsystems—the Ni and the Gd one—can be considered astwo interacting sublattices of which orientation of magneticmoments can be read from the magnetization data.

The sharp jump in the magnetization curve as well asthe linear dependence of M(B) at B > BC, which can beinterpolated to zero at B = 0 (cf. Figs. 3 and 4), are typical foran uniaxial antiferromagnet magnetized along the easy axis.The data imply that a spin-flop transitions occurs in magneticfields B ‖ b axis at T < TSR = 24 K and above this temperaturewhen B ‖ a axis. The appearance of a spin-flop transition forB ‖ b and the observation of a significant decrease of Mb(T )upon cooling below TSR strongly suggest that the magneticmoments of both the Gd3+- and the Ni2+-ions are arrangedin the bc plane at T < TSR and in small magnetic fields (seeFig. 6). Applying magnetic fields along the b axis causes aflop of the magnetic moments into the ac plane at a criticalfield BC. The closer inspection of Mb(T ) reveals a positivecurvature just below TSR. Concomitantly, the specific heatdata exhibit a Schottky-like feature, which will be discussedquantitatively below. Qualitatively, the Schottky anomaly isassociated with a temperature-driven repopulation of theground state sublevels of the Gd3+ ions, which is expectedto show up in the magnetization, too. Indeed, the positivecurvature in the magnetization data can be straightforwardlyassociated with such a Schottky-type anomaly. Note thata finite value of Mb at the lowest temperature possiblypoints to a small deviation of the nickel moments from theb axis.

The phase diagram in Fig. 5 summarizes the effect ofexternal magnetic fields and temperatures. At T < TSR andeither B ‖ b < BC or B ⊥ b, the Gd3+- and Ni2+-momentslie in the bc plane while they are arranged within the ac

plane above TSR and B ‖ a < BC or B ⊥ a. Applying amagnetic field perpendicular to the respective easy magneticaxis causes canting of the moments without anomalies in themagnetization curves M(B) in the investigated field rangeuntil eventually in very high fields the full alignment ofthe moments is expected. Applying magnetic fields alongthe easy magnetic axis—the direction of which depends ontemperature—yields a spin-flop transition which results in a

174402-4

THERMODYNAMIC STUDIES ON SINGLE-CRYSTALLINE . . . PHYSICAL REVIEW B 85, 174402 (2012)

situation with perpendicular fields and canting of spins, asmentioned before.

Upon heating, the diminishing of the difference betweentransverse and longitudinal susceptibility should cause anincrease of the spin-flop field and a decrease of the associatedmagnetization jump. This is indeed observed at very lowtemperatures as well as above TSR. At T > TSR and T <

14 K, the spin-flop field shifts gradually to higher fields withincreasing temperature. In contrast, below TSR, there is a regionof the phase diagram between T ≈ 14 K and TSR wheredBC/dT < 0. This behavior is caused by the shift of thespin-reorientational phase transition to lower temperature inapplied external magnetic fields B ‖ b. Qualitatively, magneticfields parallel to the b axis stabilize the magnetic structurewith magnetization vector aligned along the b axis and henceshift the spin-reorientational transition to lower temperatures,which causes the experimentally observed nonmonotonoustemperature dependence of BC.

In order to estimate the contribution of the Gd subsystem tothe magnetization and the specific heat below TN, one has toconsider the splitting of the Gd3+ ground state. The Gd3+ ionsoccupy a C2v symmetry position. The effective magnetic fieldBeff acting on the Gd3+-ions results from both the externalfield B and the internal field Bex, which mainly arises from theNi subsystem due to f -d interaction. In addition, the Gd-Gdinteraction has to be taken into account. Beff splits the Gd3+ground state into 2S + 1 = 8 sublevels. The energies of thesesublevels can be written as

E = ± 12n�1,2, (1)

�1,2 = g

√B2

eff1,2a + B2eff1,2b + B2

eff1,2cμB, (2)

where n = 1, 3, 5, and 7. Here, we assume g = 2 for theall components ga = gb = gc = g of the g factor ofthe Gd3+-ion. Beff1,2α (α = a, b, c) are the components ofthe effective magnetic field. The indices 1 and 2 represent theGd sublattices, named first and second sublattices, for whichthe component of the field created by the Ni subsystem Bexα isoriented along or opposite to the direction of the external fieldB, respectively. Below TN, Gd3+-ions with opposite directionsof the magnetic moments are not equivalent in the presence ofexternal magnetic field B ‖ α, and the effective fields actingon the Gd3+-ions read

Beff1α = B + κ11αMGd1α + κ12αMGd

2α + Bexα(3)

Beff2α = B + κ11αMGd2α + κ12αMGd

1α − Bexα.

Here, MGd1α and MGd

2α are the components of the magneticmoments of the first and second Gd sublattices, respectively.The parameters κ11 and κ12 determine the internal magneticfields acting on the Gd3+-ion with the magnetic moments,which are induced by Gd3+ ions with the same (κ11) andopposite (κ12) directions of their magnetic moments. Ex-panding the magnetic moments of gadolinium ions MGd

1,2α

in the effective magnetic fields [Eq. (3)] in powers of thedifferences (Beff1α − (B + Bexα)) and (Beff2α − (B − Bexα))for the first and second Gd sublattices, respectively, we obtain

the components of the magnetic moments:

MGd1α = M−

0ακ12αχ+αα + M+

0α(1 − κ11αχ−αα)

(1 − κ11αχ−αα)(1 − κ11αχ+

αα) − κ212αχ−

ααχ+αα

(4)

MGd2α = M+

0ακ12αχ−αα + M−

0α(1 − κ11αχ+αα)

(1 − κ11αχ−αα)(1 − κ11αχ+

αα) − κ212αχ−

ααχ+αα

. (5)

Here, M±0α and χ±

αα are the components of the magneticmoments and magnetic susceptibility, respectively, in theeffective field �Beff = �B + �Bex. The “ + ” sign relates to thefirst Gd sublattice, the “ − ” one to the second sublattice.M±

0α is calculated by differentiating Eq. (1) with respect tothe components of the effective magnetic field assuming theBoltzmann distribution of electrons on the energy sublevels ofGd3+ ion:

M±0α = 2

g2Beffαμ2B

�1,2

[4cth

(4�1,2

kT

)− 0.5cth

(�1,2

2kT

)],

(6)

where k is the Boltzmann constant. The factor 2 reflectsthe fact that the formula unit contains two gadolinium ions.Here, the splittings �1,2 are calculated from Eq. (2) usingappropriate values of Beff . Thereby, in the case of B ‖ a axis,the components of the effective field are Beff a = B ± Bex a;Beff b = ±Bex b; and Beff z = ±Bex c. Analogous expressionscan be derived for other directions of the external magneticfield. The components of the magnetic susceptibility arecalculated by differentiating (6) with respect to the externalmagnetic field, χ±

αα = dM±0α

dB| �Beff= �B+ �Bex

. The components of thetotal magnetization can be described as a superposition oftwo contributions, Mα = 0.5(M1α + M2α), where eachcontribution corresponds to one of the two Gd sublattices withappropriate Beff .

As mentioned previously, the Schottky anomaly observedin the specific heat C(T ) reveals the temperature-drivenrepopulation of the ground state sublevels of the Gd3+-ion.In terms of the two Gd sublattices this contribution can bewritten as

C1,2 = 2R

(�1,2

kT

)2(

1

4sh2(�1,2

2kT

) − 16

sh2( 4�1,2

kT

))

, (7)

where R is the gas constant.In accordance with Eqs. (4)–(7), the contributions of the

Gd subsystem to specific heat C(T , B = 0) and magnetizationMa(T ), Mb(T ), and Mc(T ) were calculated varying theparameters κ11, κ12, Bex(T ) as well as the angles betweenthe nickel magnetic moments and crystallographic axes. Thefitting curves thus obtained independently for T < TSR andTSR < T < TN are shown by solid lines in Fig. 1. In thefollowing the details of the fitting will be discussed.

The interactions between the Ni and the Gd subsystems aredefined by the exchange field Bex. We assume that the magneticfield Bex created by the nickel subsystem is oriented along thedirection of the nickel magnetic moment. In assumption ofthe temperature-independent angles α, β, and γ , between thedirections of the magnetic moments of the Ni2+ ions and the a,b, and c axes of the crystal, respectively, we obtain α1 = 90◦,β1 = 8.5◦, γ1 = 81.5◦ at T < TSR, and α2 = 14◦, β2 = 90◦,γ2 = 76◦ at TSR < T < TN. The value of the magnetic field Bex

174402-5

E. A. POPOVA et al. PHYSICAL REVIEW B 85, 174402 (2012)

TABLE I. The κ11 and κ12 parameters of Gd-Gd interactions in various magnetic phases of Gd2BaNiO5.

T < TSR TSR < T < TN

α a b c a b c

κ11α − 0.32 − 0.305 − 0.2 − 0.52 − 0.45 − 0.21(G2 mol/erg)κ12α − 0.4 − 0.126 − 0.4 − 0.13 − 0.3 − 0.42(G2 mol/erg)κ11α − 0.36 − 0.3 − 0.21(G2 mol/erg)flop-phaseκ12α − 0.22 − 0.3 − 0.42(G2 mol/erg)flop-phase

is proportional to the nickel magnetic moment. This notionis supported by the observation that the splitting �(T ) of theEr3+ ground doublet in the analogous compound Er2BaNiO5,measured by infrared spectroscopy,24 is proportional to themagnetic moment MNi(T ) of the nickel subsystem measuredby neutron diffraction.25 In the case of Gd2BaNiO5, notemperature dependence of the nickel magnetic moments hasbeen observed. We mention that the decrease of the magneticfield Bex at increasing temperature up to TN has been takeninto account in the form Bex(T ) = P1

P2+exp(P3(T −P4)) , similarto an expression given in Ref. 7. Here, P1, P2, P3, andP4 are fitting parameters. The fitted Bex(T ) curve shownin the inset to Fig. 2 has a kink at the temperature of thespontaneous spin-reorientational phase transition. The valueof the magnetic field Bex depends on the angle between thedirections of the magnetic moments of Gd3+ and Ni2+ ionsdue to Ising type of the interaction.26 The kink in the Bex(T )dependence at T = TSR manifests the different orientationsof the magnetic moments of the Gd3+ ions with respectto the nickel magnetic moments below and above TSR. Ifone neglects the Gd-Gd interactions, i.e., κ11 = κ12 = 0,the calculated Gd contribution to the magnetic susceptibilityconsiderably exceeds the experimental results, as shown inFig. 2 by solid lines. Therefore, the Gd-Gd interactions aremandatory to be included. The values of the fitted parametersκ11 and κ12 shown in Table I are close to κ11 = κ12 =− 0.0451 T /μB = − 0.081 G2 mol/erg estimated for poly-crystalline Er2BaNiO5.19 The difference between κ11 and κ12,as given in Table I, could be ascribed to the difference inthe exchange pathways. The values of κ11 and κ12 parameterschange at the spin reorientation and the spin-flop transitions.Tentatively, this change may be ascribed to the fact that theGd-Gd interaction is organized via Ni chains being thereforesensitive to the angle between Gd and Ni magnetic moments.

All fitted parameters κ11, κ12, Bex(T ), and angles α, β, andγ were used for calculation of the gadolinium contribution tothe magnetization M(B), represented by solid lines in Fig. 3. Inaddition, the value of Bex estimated from the fitting procedureallows us to explain the shift of the Schottky anomaly in C(T ,B) to higher temperature in a magnetic field B ‖ b = 2 T,as visible in Fig. 6. As has already been mentioned, belowTSR the magnetic moments of the Gd3+ ions lie in the bc

plane. In zero external magnetic field B = 0 the effective

magnetic fields calculated with Eq. (2) are roughly the samefor both, i.e., the first and second Gd sublattices becausethe magnetic field created by the gadolinium sublatticesBGd−Gd ≈ 0.2 T is very small compared with the magnetic fieldcreated by the nickel subsystem Bex ≈ 12 T. However, in anapplied field B = 1 T (B ‖ b axis) the gadolinium contributionto the specific heat is different for the two Gd sublattices. Forthe Gd sublattice with magnetic moment projections opposedto the external magnetic field direction, the magnetic field leadsto a decrease of the splitting of the ground state of the Gd3+ion, and the Schottky anomaly shifts to lower temperatures.For the other Gd sublattice, the splitting increases, and theSchottky anomaly appears at higher temperatures. However,the total contribution of the two Gd sublattices does not lead toa shift of the Schottky anomaly because external magnetic fieldB = 1 T is again small compared with Bex. When the systemis in the flop phase, the magnetic moments of Gd3+ ions areperpendicular to the external magnetic field direction. In thiscase, both Gd sublattices give absolutely equal contributionsto the specific heat. The magnetic field leads to an increaseof the splitting, and the Schottky anomaly shifts to highertemperatures, as it is observed in experiment (cf. Fig. 6).

The difference [Mα − MαGd](T ) of the experimental data

and the calculated Gd-contribution is mainly due to magneticsusceptibility of the Ni ions. In the temperature range TSR <

T < TN, the magnetic susceptibility along the different crystaldirections is reasonably well described by the contributionof the Gd subsystem only, while the contribution of the Nisubsystem is negligible within the limits of the experimentalerror bars (cf. Fig. 1). Below TSR, however, this differenceimplies a more complex behavior. The difference [Mα −Mα

Gd](T ) does not vanish at lowest temperatures, and it hasthe same value for different directions. Such behavior of thenickel subsystem indeed differs from that of a classical antifer-romagnet. This behavior cannot be explained by paramagneticimpurities, which should give a Curie-like contribution to themagnetization M(T ). However, the experimental data exhibitclear kinks in Ma(T ) and Mb(T ) at T = 7 K while there is noanomaly in the specific heat data indicating a phase transitionat this temperature. The magnetization M(T ) of the Haldanegap system, as known, should exhibit isotropic exponentialdecrease to zero at low temperatures. At present, however,there is no description of the temperature dependence M(T )

174402-6

THERMODYNAMIC STUDIES ON SINGLE-CRYSTALLINE . . . PHYSICAL REVIEW B 85, 174402 (2012)

for the Haldane gap system in staggered magnetic field actingfrom the R subsystem.

IV. CONCLUSIONS

The thermodynamic properties of Gd2BaNiO5 singlecrystal are investigated by specific heat and magnetiza-tion measurements. Antiferromagnetic and spontaneous spin-reorientational phase transitions take place at TN = 55 K and atTSR = 24 K, respectively. The Gd-Gd interaction is organizedvia Ni chains being therefore sensitive to the angle between Gdand Ni magnetic moments. Below TSR, the magnetic momentsof both Ni2+ and Gd3+ ions lie in the bc plane of the crystal,and they flop to the ac plane under external magnetic fieldB ‖ b axis. At TSR < T < TN, the magnetic moments flop

from the ac to the bc plane. The anisotropic magnetic phasediagram in Gd2BaNiO5 is established from the experimentaldata. Considering the Gd-Gd and the Gd-Ni interactions allowsestimating the contribution of the gadolinium subsystem to themagnetization and the specific heat and hence to discuss the Nisubsystem separately. Our analysis implies that the behaviorof the nickel subsystem indeed differs from that of a classicalantiferromagnet, and in particular our data suggest a gappedstate of the Ni subsystem at low temperatures.

ACKNOWLEDGMENTS

The authors thank Guy Dhalenne and Pauline Higel for thegrowth of Gd2BaNiO5 single crystals. R.K., N.T., and B.B.acknowledge support from the D.F.G. via KL 1824/2. A.N.V.acknowledge support from Russian Ministry of Science andEducation through State Contract 11.519.11.6012.

*Corresponding author: vasil@lt.phys.msu.ru1F. D. M. Haldane, Phys. Lett. A 93, 464 (1983); Phys. Rev. Lett.50, 1153 (1983).

2I. Affleck, J. Phys.: Condens. Matter 1, 3047 (1989).3A. Zheludev, S. Maslov, T. Yokoo, S. Raymond, S. E. Na-gler, and J. Akimitsu, J. Phys.: Condens. Matter 13, R525(2001).

4K. Kojima, A. Keren, L. P. Le, G. M. Luke, B. Nachumi, W. D. Wu,Y. J. Uemura, K. Kiyono, S. Miyasaka, H. Takagi, and S. Uchida,Phys. Rev. Lett. 74, 3471 (1995).

5R. Saez-Puche, J. M. Corondo, C. L. Otero-Dıaz, and J. M. Martın-Llorente, J. Solid State Chem. 93, 461 (1991).

6J. Darriet and L. P. Regnault, Solid State Commun. 86, 409(1993).

7E. Garcıa-Matres, J. L. Garcia-Munoz, J. L. Martınez, andJ. Rodrıguez-Carvajal, J. Magn. Magn. Mater. 149, 363(1995).

8A. Zheludev, J. M. Tranquada, T. Vogt, and D. J. Buttrey, Europhys.Lett. 35, 385 (1996).

9V. Sachan, D. J. Buttrey, J. M. Tranquada, and G. Shirane, Phys.Rev. B 49, 9658 (1994).

10E. A. Popova, D. V. Volkov, A. N. Vasiliev, A. A. Demidov,N. P. Kolmakova, I. A. Gudim, L. N. Bezmaternykh, N. Tristan,Y. Skourski, B. Buchner, C. Hess, and R. Klingeler, Phys. Rev. B75, 224413 (2007).

11A. Zheludev, J. M. Tranquada, T. Vogt, and D. J. Buttrey, Phys.Rev. B 54, 7210 (1996).

12S. Raymond, T. Yokoo, A. Zheludev, S. E. Nagler, A. Wildes, andJ. Akimitsu, Phys. Rev. Lett. 82, 2382 (1999).

13T. Yokoo, S. A. Raymond, A. Zheludev, S. Maslov, E. Ressouche,I. Zaliznyak, R. Erwin, M. Nakamura, and J. Akimitsu, Phys. Rev.B 58, 14424 (1998).

14S. Schiffler and H. Muller-Buschbaum, Z. Anorg. Allg. Chem. 532,10 (1986).

15J. Amador, E. Gutierrez Puebla, M. A. Monge, and I. Rasines, SolidState Ionics 32-33, 123 (1989).

16M. N. Popova, I. V. Paukov, Yu. A. Hadjiiskii, and B. V. Mill, Phys.Lett. A 203, 412 (1995).

17G. A. Stewart, S. J. Harker, M. Strecker, and G. Wortmann, Phys.Rev. B 61, 6220 (2000).

18A. Butera, M. T. Causa, M. Tovar, S. B. Oseroff, and S.-W. Cheong,J. Magn. Magn. Mater. 140, 1681 (1995).

19M. N. Popova, S. A. Klimin, P. Higel, and G. Dhalenne, Phys. Lett.A 354, 487 (2006).

20R. Klingeler, B. Buchner, K.-Y. Choi, V. Kataev, U. Ammerahl,A. Revcolevschi, and J. Schnack, Phys. Rev. B 73, 014426 (2006).

21A. Tari, The Specific Heat of Matter at Low Temperatures (ImperialCollege Press, London, 2003).

22A. H. Morrish, The Physical Principles of Magnetism (Wiley,New York, 1965).

23T. Yokoo, T. Sakaguchi, K. Kakurai, and J. Akimitsu, J. Phys. Soc.Jpn. 64, 3651 (1995).

24M. N. Popova, S. A. Klimin, E. P. Chukalina, B. Z. Malkin, R. Z.Levitin, B. V. Mill, and E. Antic-Fidancev, Phys. Rev. B 68, 155103(2003).

25J. A. Alonso, J. Amador, J. L. Martınez, I. Rasines, J. Rodrıguez-Carvajal, and R. Saez-Puche, Solid State Commun. 76, 467 (1990).

26T. Kennedy, J. Phys.: Condens. Matters 2, 5737 (1990).

174402-7