Heat Capacity and Magnetic Phase Diagram of the Low-Dimensional Antiferromagnet Y 2 BaCuO 5
aa r X i v : . [ c ond - m a t . s t r- e l ] J u l Heat Capacity and Magnetic Phase Diagram of theLow-Dimensional Antiferromagnet Y BaCuO W. Knafo , , , C. Meingast , A. Inaba , Th. Wolf , and H. v.L¨ohneysen , Forschungszentrum Karlsruhe, Institut f¨ur Festk¨orperphysik, D-76021 Karlsruhe,Germany Physikalisches Institut, Universit¨at Karlsruhe, D-76128 Karlsruhe, Germany Laboratoire National des Champs Magn´etiques Puls´es, 143 avenue de Rangueil,31400 Toulouse, France Research Center for Molecular Thermodynamics, Graduate School of Science,Osaka University, Toyonaka, Osaka 560-0043, JapanPACS numbers: 74.72.Bk, 75.30.Gw, 75.30.Kz, 75.50.Ee
22 October 2018Keywords: Low-dimensional antiferromagnetism; Specific heat; Phase diagram;Field-induced anisotropy; Isosbestic point; Y BaCuO ; YBa Cu O δ ; BaNi V O ;Sr CuO Cl ; Pr CuO Abstract.
A study by specific heat of a polycrystalline sample of the low-dimensional magneticsystem Y BaCuO is presented. Magnetic fields up to 14 T are applied and permit toextract the ( T , H ) phase diagram. Below µ H ∗ ≃ T N = 15 . H ∗ , T N increases linearly with H and a field-induced increaseof the entropy at T N is related to the presence of an isosbestic point at T X ≃
20 K,where all the specific heat curves cross. A comparison is made between Y BaCuO andthe quasi-two-dimensional magnetic systems BaNi V O , Sr CuO Cl , and Pr CuO ,for which very similar phase diagrams have been reported. An effective field-inducedmagnetic anisotropy is proposed to explain these phase diagrams.
1. Introduction
Because of their layered structure, the undoped high-temperature superconductingcuprates are low-dimensional magnetic systems. Indeed, Cu-O-Cu superexchange pathswithin the planes are responsible for a strong two-dimensional (2D) magnetic exchange J ≃ S = 1 / ions. In the undoped state,three-dimensional (3D) long range ordering occurs below a N´eel temperature T N ofabout several hundreds Kelvin [1, 2], due to a small additional magnetic exchange J ′ between the layers. At the magnetic quantum phase transition of some heavy-fermion eat Capacity and Magnetic Phase Diagram of Y BaCuO T C cuprates could be of primary importance to elucidate whysuperconductivity develops in these systems [5]. However, the magnetic energy scalesare rather high (several hundreds Kelvin) and their investigation is difficult to perform,due to the loss of oxygen and to the sample melting at high temperatures.A possible alternative is to study the magnetic properties of systems similar to thehigh- T C cuprates, but with much smaller magnetic energy scales. One of them is the”green phase” compound Y BaCuO , which is known as an impurity phase of the high- T C YBa Cu O δ [6] and whose green color indicates its insulating character. As in thehigh- T C cuprates, the magnetic properties of Y BaCuO are strongly low-dimensionaland originate from the S = 1 / ions. Indeed, broad anomalies in the magneticsusceptibility and in the specific heat, whose maxima were reported at T max ≃
30 K [7]and T ′ max ≃
20 K [8], respectively, are believed to be due to the low-dimensional magneticexchange of Y BaCuO . However, and contrary to the layered high T C cuprates wherethe magnetic exchange is quasi-2D, Y BaCuO has a rather complex 3D lattice structure,shown in Fig. 1, and the question whether the dominant magnetic interactions are one-dimensional (1D) or 2D is still open. Three kinds of Cu-O-O-Cu superexchange paths,either 1D or 2D were suggested [9]. It is unclear, however, which one of the threepaths is dominating. The fact that, in Y BaCuO , the superexchange paths go throughtwo oxygens, contrary to one oxygen for YBa Cu O δ , explains the smaller magneticenergy scales [9]. At lower temperatures, 3D antiferromagnetic long-range ordering setsin below the N´eel temperature T N ≃ . BaCuO under magneticfields up to 14 T, which permits to extract the ( T, H ) phase diagram of this system. Inthe discussion, we compare the phase diagram of Y BaCuO to similar phase diagramsobtained for other low-dimensional systems, and we propose to explain them using thepicture of an effective field-induced anisotropy.
2. Experimental details
The polycrystalline sample of Y BaCuO studied here was synthesized by the directmethod in air. Appropriate amounts of Y O , BaCO , and CuO were mixed intensely,then pressed into pellets, and finally reaction sintered with increasing temperature stepsbetween 750 and 960 ◦ C, without intermediate grinding. X-ray powder diffractometrydid not show any trace of impurity phases. Except for 730 ppm Sr and 222 ppm Fe,no other impurities were detected by x-ray fluorescence analysis. The specific heat wasmeasured under magnetic fields up to 14 T using a Physical Properties MeasurementSystem (PPMS) from Quantum Design, and using an adiabatic calorimeter at zero fieldup to 400 K [11]. The specific heats below 200 K obtained by both methods agree eat Capacity and Magnetic Phase Diagram of Y BaCuO Figure 1. (color online) Lattice unit cell of Y BaCuO , where the CuO pyramidsare represented in gray. well with each other. To enhance the resolution in the vicinity of the magnetic phasetransitions, the relaxation curves from the PPMS were analyzed following a proceduresimilar to the one proposed by Lashley et al. [12]. Here we will show only the PPMSdata.
3. Results
Fig. 2 (a) shows the total specific heat C p ( T ) of Y BaCuO measured at zero magneticfield, together with the phonon background C php ( T ). C php ( T ) was estimated using anappropriate scaling of the non-magnetic specific heat of YBa Cu O [13]. Fig. 2 (a)shows C p ( T ) and C php ( T ) for temperatures up to 80 K, while the Inset shows the datafor temperatures up to 300 K. These plots indicate that the specific heat of Y BaCuO is almost purely phononic above 70 K and that a magnetic signal develops belowroughly 70 K. In Fig. 2 (b), the magnetic contribution to the specific heat, calculatedusing C magp ( T ) = C p ( T ) − C php ( T ), is shown in a C magp ( T ) /T versus T plot. C magp ischaracterized by a broad anomaly, whose maximum occurs at about 20 K, and by asmall jump at T N ≃
15 K, as typically observed for low-dimensional systems [14, 15].The integration of C magp ( T ) /T up to 70 K leads to an entropy change of ∆ S mag ≃ . R ln2 ≃ .
76 J/mol K expectedfor the S = 1 / T N , which was first reported by Gros et al. [10].In the following, we will concentrate on the effects of the magnetic field on this anomaly. eat Capacity and Magnetic Phase Diagram of Y BaCuO C / T ( J / m o l K ) T (K) b) = 0 T m H m ag p T N Y BaCuO C ( J / m o l K ) Phonons a) Total p Figure 2. (color online) (a) Total and lattice specific heat of Y BaCuO , in a C p versus T plot, with T up to 80 K; data are plotted up to 300 K in the Inset. (b)Magnetic specific heat C magp of Y BaCuO , in a C magp /T versus T plot. Above 60 K, C magp is less than 2 % of the total specific heat C p . In Fig. 3 (a), the magnetic specific heat of Y BaCuO is shown for the magneticfields µ H = 0, 8, and 14 T in a C magp ( T ) /T versus T plot. The N´eel temperature T N and the size of the anomaly at the antiferromagnetic transition both increase withincreasing H . Above T N , all the curves cross at an isosbestic point [16] at T X ≃
20 K,which will be discussed in Section 4. For each magnetic field, an appropriate background(dotted lines in Fig. 3 (a)) is used to obtain the anomaly ∆ C magp ( T ) associated with the3D magnetic ordering. In Fig. 3 (b), a plot of ∆ C magp ( T ) /T obtained for various fieldsup to 14 T emphasizes the field-induced increases of T N and of the size of the anomalyat the antiferromagnetic transition. Its typical width, of about 0.8 K (full width athalf maximum), is almost unaffected by the magnetic field and could arise from sampleimperfections (strains, impurities...) or from the polycrystalline nature of the sample.In Fig. 4, the jump (∆ C magp /T ) max in the specific heat at T N and the associatedentropy change ∆ S N [17] are plotted as a function of H . Since the width of the anomalyis almost unaffected by H , similar field dependences are obtained for (∆ C magp /T ) max and eat Capacity and Magnetic Phase Diagram of Y BaCuO Y BaCuO T (K) a) m H = C / T ( J / m o l K ) m ag p T N T X D C / T ( m J / m o l K ) m ag T (K) p b) m H = 0 T
10 T12 T6 T5 T4 T3 T2 T
Figure 3. (color online) (a) Magnetic specific heat C magp of Y BaCuO , in a C magp /T versus T plot, at µ H = 0 ,
8, and 14 T. The dotted lines indicate the backgroundused to separate the anomaly at T N .(b) Anomaly ∆ C magp of Y BaCuO at T N , in a∆ C magp /T versus T plot, for magnetic fields 0 ≤ µ H ≤
14 T. ∆ S N : both are nearly constant for µ H ≤ µ H ∗ ≈ H for H ≥ H ∗ . The small value ∆ S N ( H = 0) / ∆ S mag = (4 . ± . ∗ − is aconsequence of the low-dimensional character of the magnetic exchange [14], ∆ S N beingenhanced by a factor 2.5 at µ H = 14 T.In Fig. 5, the T - H phase diagram of Y BaCuO is shown for magnetic fields up to14 T, T N being defined at the minimum of slope of ∆ C magp /T . The N´eel temperature T N is independent of H for µ H ≤ µ H ∗ ≃ T N ( H = 0) = 15 . ± . H for H ≥ H ∗ , where T N ( H ) = T N, + aH , with T N, = 15 . ± .
1K and a = 0 . ± .
02 K/T (above 10 T a slight deviation from this regime is observed).In the next Section, the field-induced increases of T N and ∆ S N will be qualitativelyexplained using the picture of a field-induced anisotropy. eat Capacity and Magnetic Phase Diagram of Y BaCuO m H (T) Y BaCuO ( D C / T ) ( m J / m o l K ) p D S / R l n2 ( % ) N ( D C / T ) p D S / R ln2 N m a x max m ag mag Figure 4. (color online) Variation with H of the jump (∆ C magp /T ) max in the specificheat at the N´eel ordering and of the associated entropy change ∆ S N .
4. Discussion BaCuO - explanation in terms of field-induced anisotropy The phase diagram of the low dimensional magnetic system Y BaCuO (Fig. 5) is verysimilar to those of the quasi-2D magnetic systems BaNi V O [15], Sr CuO Cl [19],and Pr CuO [20] (see Section 4.2), and we interpret them similarly, using a pictureintroduced 30 years ago by Villain and Loveluck for quasi-1D antiferromagnetic systems[21]. In this picture, the increase of T N ( H ) is induced by a reduction of the spinfluctuations parallel to H , due to an alignment of the antiferromagnetic fluctuations, aswell as the antiferromagnetically coupled static spins, perpendicular to H . This effectcan be described by an effective field-induced anisotropy, whose easy axis is ⊥ H [22]and which competes with the intrinsic anisotropy of the system. As long as the field-induced anisotropy is weaker than the intrinsic anisotropy, i.e., for H ≤ H ∗ , T N ( H )is unaffected by the magnetic field and the spins align along the intrinsic easy axes.For H ≥ H ∗ , the field-induced anisotropy is stronger than the intrinsic anisotropy and T N ( H ) is controlled by H , the spins being aligned along the field-induced easy axes( ⊥ H ).The crossing point of the specific-heat data of Y BaCuO at T X ≃
20 K (Fig. 3(a)), is, to our knowledge, the first isosbestic point [16] reported in the thermodynamicproperties of a low-dimensional magnetic system. This effect is the consequence of atransfer of the specific-heat weight, with respect to the conservation of the magneticentropy ∆ S mag . Indeed, our data show that the application of a magnetic field leadsto a gain of entropy at T N , i.e. below T X , which equals approximatively the loss of eat Capacity and Magnetic Phase Diagram of Y BaCuO T ( H =0) N T AF PM µ H ( T ) T (K)Y BaCuO T N ,0 N Figure 5. (color online) (
T, H ) phase diagram of Y BaCuO (polycrystal) obtained byspecific-heat measurements (AF = antiferromagnetic phase, PM = high-temperatureparamagnetic regime). entropy above T X . Consistently with the picture introduced above, we propose thatthe isosbestic point at T X is due to a field-induced transfer of the specific-heat weightfrom the large and broad low-dimensional short-range ordering anomaly to the small3D long-range ordering anomaly at T N .Little is known microscopically about the magnetic properties of Y BaCuO , i.e.,about the exact nature of the exchange interactions and of the magnetic anisotropy.The non-layered crystal structure of Y BaCuO (see Fig. 1) precludes a prediction ofthe superexchange paths, the dominant paths being probably 1D or 2D [9]. The shapesof the magnetic susceptibility [7] and of the specific heat [8] just indicate that thedominant exchange interactions have a low-dimensional character, either 1D or 2D [9].Some authors suggested a 2D character of the exchange and an XY anisotropy, fromappropriate fits of the magnetic susceptibility [7, 23] and of the ESR linewidth [24],respectively, but these results cannot be considered as definitive proofs. The nature ofthe antiferromagnetic ordering below T N is also unclear, since several structures havebeen proposed, where the spins are aligned either in the ( a , c ) plane [9, 25] or along c [26](cf. Ref. [24] for a summary of the proposed magnetic structures). Further experimentalstudies on single crystals, such as by magnetization and neutron scattering techniques,are necessary to determine unambiguously the nature of the spin anisotropy and ofthe magnetic exchange in Y BaCuO , which can not be predicted from the complexthree-dimensional structure of Y BaCuO (Fig. 1). However, we interpret the high-field increase of T N ( H ) in Y BaCuO as a consequence of a field-induced anisotropy,a picture that works for both quasi-1D systems [21] and quasi-2D systems [15], theintrinsic spin anisotropy being always ultimately of Ising-kind. A knowledge of the eat Capacity and Magnetic Phase Diagram of Y BaCuO BaCuO .An additional difficulty arises from the fact that the results presented here wereobtained on a polycrystalline sample of Y BaCuO , so that our phase diagram isequivalent to take the average of the phase diagrams of a single crystal over all possiblefield directions. In the quasi-2D magnet BaNi V O , there is hardly any modificationof the magnetic properties when H k c (hard axis) [27], which implies that a phasediagram obtained with a polycrystalline sample would be similar to the phase diagramreported for H ⊥ c [15], possibly with a slight broadening of the transition. By analogy,we believe that it is reasonable to interpret the phase diagram of a polycrystallineY BaCuO similarly to the phase diagram that would be obtained for a single crystalwith H parallel to the easy axis or to the easy plane (depending on the nature of theanisotropy).The extrapolation of the ”high-field” linear behavior of T N ( H ) to zero field leads toa temperature T N, smaller than T N ( H = 0) by ∆ = 0 . V O ,Sr CuO Cl , and Pr CuO [15] (see also Section 4.2), we speculate that, in Y BaCuO , T N, is a virtual ordering temperature, which would characterize the system in thelimit of no easy-axis anisotropy. In this picture, the increase of T N ( H = 0) by ∆ is aconsequence of the intrinsic easy-axis anisotropy. A linear extrapolation of the high-field variation of ∆ S N ( H ) also leads to ∆ S N, / ∆ S mag = (2 . ± . ∗ − at H = 0 (cf.Fig. 4). As well as T N, , we associate the extrapolated entropy change ∆ S N, / ∆ S mag with the limit of no easy-axis anisotropy. At zero magnetic field, the N´eel temperature T N ( H = 0) and the associated change of entropy ∆ S N ( H = 0) have non-zero values,probably because of the combination of the magnetic anisotropy (XY and Ising) and ofa 3D character of the magnetic exchange [28]. BaCuO and those of the quasi-2DBaNi V O , Sr CuO Cl , and Pr CuO As mentioned above, the T - H phase diagram of polycrystalline Y BaCuO , shown inFig. 5, has a striking resemblance with the phase diagrams of single crystals of thequasi-2D antiferromagnets BaNi V O [15], Sr CuO Cl [19], and Pr CuO [20], whichare shown in Fig. 6 (a), (b), and (c), respectively, for H applied within the easy plane[29]. In these insulating systems, T N ( H ) is constant for H ≤ H ∗ and increases with H for H ≥ H ∗ . A linear increase of T N ( H ) is unambiguously obtained in the high-field regimeof Y BaCuO and BaNi V O [15] and is compatible, within the experimental errors,with the phase diagrams of Sr CuO Cl [19] and Pr CuO [20]. In Table 1, T N ( H = 0), T N, , H ∗ , and a (from a fit by T N ( H ) = T N, + aH for H > H ∗ ) are given for eachof these systems. For Y BaCuO [7] and BaNi V O [30], the temperature T max ofthe maximum of the magnetic susceptibility χ ( T ), characteristic of the low-dimensionalmagnetic exchange, is also given. The investigation of the magnetic properties of thesetwo systems is rather easy, since their full magnetic entropy is contained below room eat Capacity and Magnetic Phase Diagram of Y BaCuO µ Η ( Τ ) T (K) BaNi V O H c PMAF'AF
H TT N ,0 N * a) (Knafo et al., 2007) µ Η ( Τ ) T (K) Pr CuO H c PMAF TT N ,0 N c) (Sumarlin et al., 1995) µ Η ( Τ ) T (K) Sr CuO Cl H c PMAF TT N ,0 N
2 2 b) (Suh et al., 1995) Figure 6. (color online) (
T, H ) phase diagrams of the quasi-2D magnetic systems (a)BaNi V O [15], b) Sr CuO Cl [19], and c) Pr CuO [20], with H ⊥ c . The data in(b) and (c) were scanned from Ref.[19] and [20]. temperature (see Section 3 and Ref. [15]), as illustrated by the rather small values of T N and T max , which are of the order of several tens of Kelvin. Oppositely, the magneticproperties of Sr CuO Cl and Pr CuO , as well as those of the underdoped high- T C cuprates, are more difficult to investigate, being associated with temperature scales T max > T N ≃
300 K [31]. eat Capacity and Magnetic Phase Diagram of Y BaCuO T N ( H ) with increasing magnetic field inBaNi V O , Sr CuO Cl , and Pr CuO , as well as the one observed in Y BaCuO ,using an effective field-induced anisotropy [21]. Contrary to the present work, which wasmade using a polycrystal of Y BaCuO , the studies of BaNi V O , Sr CuO Cl , andPr CuO were performed on single crystals with H ⊥ c [15, 19, 20]. While the magneticproperties of Y BaCuO cannot be easily related to its 3D and rather complex crystalstructure (Fig. 1), the quasi-2D magnetic exchange paths of BaNi V O , Sr CuO Cl ,and Pr CuO are a direct consequence of their layered crystallographic structure, andtheir intrinsic anisotropy is controlled by the symmetry of their lattice. The intrinsicin-plane anisotropy, hexagonal for BaNi V O [30] and tetragonal for Sr CuO Cl [19]and Pr CuO [20], leads to magnetic domains at zero field where the spins align (inthe easy plane) along one of three equivalent easy axes in BaNi V O and along one oftwo equivalent easy axes in Sr CuO Cl and Pr CuO [19, 20, 30]. In Ref. [19], Suhet al. proposed that the change of behavior of T N ( H ), which occurs at µ H ∗ ≃ CuO Cl , is related to a field-induced crossover from a regime controlled by theintrinsic XY anisotropy to a regime controlled by the field-induced Ising anisotropy.For Sr CuO Cl , but also for BaNi V O and Pr CuO , we propose that the change ofbehavior of T N ( H ) at H ∗ results in fact from a crossover between a regime controlledby the intrinsic Ising-like in-plane anisotropy (with two or three equivalent easy axes)to a regime controlled by the field-induced Ising anisotropy (with one easy axis) [15].Although the XY anisotropy plays an important role in both regimes above and below Table 1.
Characteristics of the magnetic properties of Y BaCuO , BaNi V O ,Sr CuO Cl , and Pr CuO . Y BaCuO BaNi V O Sr CuO Cl Pr CuO T max (K) ∗ ♮
30 150 n.d. n.d. T N ( H = 0) (K) 15.6 47.4 256.5 282.8∆ S N ( H = 0) / ∆ S mag − − n.d. n.d. H † (polycrystal) ⊥ c ⊥ c ⊥ c µ H ∗ (T) † ≃ ≃ . ≃ . ≃ T N, (K) † a (K/T) † S N, / ∆ S mag † − n.d. n.d. n.d.Symmetry orth. hex. tetr. tetr.Ref. [7] [15, 30] [19] [20] ∗ : defined as the temperature of the maximum of χ ( T ) ♮ : n.d. = non determined, hex. = hexagonal, orth. = orthorhombic, tetr. = tetragonal † : T N ( H ) = T N, + aH and ∆ S N ( H ) ≃ ∆ S N, + bH for H ≥ H ∗ eat Capacity and Magnetic Phase Diagram of Y BaCuO H ∗ , we believe that the crossover at H ∗ is not directly related to the XY anisotropy,as proposed in Ref. [19], but is due to the small residual Ising-like anisotropy, whichultimately determines the easy axis within the XY plane.We furthermore speculate that, for Sr CuO Cl and Pr CuO , as well as forBaNi V O [15], T N, corresponds to a ”virtual” N´eel temperature which would beachieved in a limit with no in-plane anisotropy, being controlled by the combinationof the 2D exchange, the XY anisotropy, and the interlayer 3D exchange. Thus, T N, would give an upper limit of the Berezinskii-Kosterlitz-Thouless temperature T BKT ,characteristic of a pure 2D XY magnetic system [28]. Moreover, T N, and T BKT wouldbe equal if the interlayer exchange would be negligible. This would also apply forY BaCuO if one could prove, e.g., by neutron scattering, that it is quasi-2D (thus notquasi-1D). Since a strictly low-dimensional (1D or 2D) Heisenberg system corresponds toa limit with no transition [28], thus with ∆ S N →
0, the fact that ∆ S N ( H = 0) / ∆ S mag is six times smaller in BaNi V O than in Y BaCuO (Table 1) indicates a strongerlow-dimensional character in BaNi V O than in Y BaCuO . The non-zero values of T N, and ∆ S N, in Y BaCuO are the consequence of the XY anisotropy and/or of the3D exchange, in addition to the low-dimensional exchange (1D or 2D) [28].In Ref. [14] Bloembergen compared the specific-heat data of several quasi-2Dmagnetic systems. He discussed how the residual 3D intralayer exchange, as well asXY and in-plane anisotropies, stabilize long-range ordering in these systems, leading toan increase of T N and of the size of the associated specific-heat anomaly. Our data,but also our interpretation, are very similar to the ones of Bloembergen [14] (cf. theheat-capacity data from Fig. 3 of the present article and from Fig. 2 and 3 of Ref.[14]). As an important new feature, our work shows that a magnetic field can be usedto continuously tune the magnetic anisotropy of low-dimensional systems.In Fig. 7, we present a tentative extension to very high magnetic fields of the phasediagrams of Y BaCuO , BaNi V O , Sr CuO Cl , and Pr CuO . In these systems, thelow-dimensional (1D or 2D) exchange J is the dominant magnetic energy scale, anda ferromagnetic polarized regime, where the spins are aligned parallel to the magneticfield, has to be reached at magnetic fields H > H J , with H J ∝ J . This implies that thephase line T N ( H ), which first increases linearly, as reported here, will reach a maximumbefore decreasing down to zero at H J , the spins being in a canted antiferromagnetic statefor H ∗ < H < H J . As evidenced by the broad maxima observed in the heat capacityand magnetic susceptibility measurements, a crossover occurs at zero-field at T J ∝ J ,which corresponds to the onset of low-dimensional short-range ordering and consists oflow-dimensional antiferromagnetic fluctuations. The application of a magnetic field isexpected to decrease T J , and we speculate that T J ( H ) will merge at very high fields withthe transition line T N ( H ) of the canted ordered state, since T N ( H ) will cancel out at H J ∝ J ∝ T J ( H = 0). Finally, a crossover characteristic of the field-induced polarizedstate is expected to occur at T H ∝ H . Pulsed magnetic fields should be used to extendthe phase diagram presented in Fig. 5 up to much higher fields, in order to try to reachits polarized state and to check the validity of the tentative phase diagram of Fig. 7. eat Capacity and Magnetic Phase Diagram of Y BaCuO H J α N T ( H =0) PM H TT N ,0 * H PPMAF N T ( H ) = N ,0 T + aH AF' SRAF T J J T H H J α α Figure 7. (color online) Phase diagram expected at high enough magneticfields for Y BaCuO , BaNi V O , Sr CuO Cl , and Pr CuO (AF = low-fieldantiferromagnetic phase, AF’ = field-induced canted phase, PPM = high-field polarizedparamagnetic phase, PM = high-temperature paramagnetic regime, and SRAF = low-dimensional short-range antiferromagnetic regime). This should enable one to extract the different magnetic energy scales and lead to abetter understanding of the magnetic properties of Y BaCuO .
5. Conclusion
The T - H phase diagram of the low-dimensional magnetic system Y BaCuO determinedby heat-capacity measurements has revealed striking resemblances with the phasediagrams of the quasi-2D magnetic systems BaNi V O , Sr CuO Cl , and Pr CuO .Although we do not know the nature of the exchange (quasi-1D or quasi-2D) and ofthe magnetic anisotropy in Y BaCuO , we interprete the increase of T N ( H ) as resultingfrom a field-induced anisotropy. In this scenario, at the lowest energy or correspondingfield scales, the Ising-like anisotropy is important. Further, our work permitted todemonstrate that external magnetic fields can be used to continuously tune an effectivespin anisotropy. We observed a field-induced transfer of magnetic entropy from thelow-dimensional high-temperature broad signal to the anomaly associated with the 3Dordering at T N , which is related to the presence of an isosbestic point at T X ≃
20 K.The comparison of the magnetic properties of Y BaCuO , BaNi V O , Sr CuO Cl ,and Pr CuO should be useful to refine theoretical models. New theoreticaldevelopments are needed to understand these properties on a more quantitativelevel, notably the linear increase of T N with H at moderate magnetic fields. Thetheories, which already consider the XY anisotropy and the different kinds of exchangeinteractions (see for example Ref. [32]), should be extended to include an Ising-likeanisotropy term, which ultimately determines the direction of the ordered spins and eat Capacity and Magnetic Phase Diagram of Y BaCuO BaCuO and BaNi V O can be accessed rather easily and their studymay yield significant clues for understanding the magnetic properties of the high- T C cuprates.In the future, single crystals of Y BaCuO should be studied to determine thenature of the anisotropy and of the magnetic exchange (e.g., from susceptibility andneutron scattering measurements). Pulsed magnetic fields could also be used to extendthe phase diagram of Y BaCuO to higher fields. Finally, it would be interesting totry to decrease by doping the strength of the exchange interactions, in order to enterinto a paramagnetic conducting phase and to study the properties of the related metal-insulator crossover. Acknowledgments
We would like to thank K.-P. Bohnen and R. Heid for providing us the ab-initiocalculations of the phonon contribution to the specific heat of YBa Cu O . This workwas supported by the Helmholtz-Gemeinschaft through the Virtual Institute of Researchon Quantum Phase Transitions and Project VH-NG-016. References [1] M.J. Jurgens, P. Burlet, C. Vettier, L.P. Regnault, J.Y. Henry, J. Rossat-Mignod, H. Noel, M.Potel, P. Gougeon, and J.C. Levet, Physica B , 846 (1989).[2] T. Nakano, M. Oda, C. Manabe, M. Momono, Y. Miura, and M. Ido, Phys. Rev. B , 16000(1994).[3] P. Thalmeier, G. Zwicknagl, O. Stockert, G. Sparn, and F. Steglich, Frontiers in superconductingmaterials , Chapter 3 (Springer, Berlin, 2005).[4] J. Flouquet, G. Knebel, D. Braithwaite, D. Aoki, J.P. Brison, F. Hardy, A. Huxley, S. Raymond,B. Salce, and I. Sheikin, C.R. Physique , 22 (2006).[5] J.G. Storey, J.L. Tallon, and G.V.M. Williams, to be published (cond-mat.supra-con/0707.2239).[6] W.Y. Liang and J.W. Loram, Physica C , 230 (2004).[7] E.W Ong, B.L. Ramakrishna, and Z. Iqbal, Solid. State Commun. , 171 (1988).[8] G.F. Goya, R.C. Mercader, L.B. Steren, R.D. S´anchez, M.T. Causa, and M. Tovar, J. Phys.:Condens. Matter , 4529 (1996).[9] C. Meyer, F. Hartmann-Boutron, Y. Gros, P. Strobel, J.L. Tholence, and M. Pernet, Solid. StateCommun. , 1339 (1990).[10] Y. Gros, F. Hartmann-Boutron, J. Odin, A. Berton, P. Strobel, and C. Meyer, J. Magn. Magn.Mater. , 621 (1992).[11] T. Matsuo, K. Kohno, A. Inaba, T. Mochida, A. Izuoka, T. Sugawara, J. Chem. Phys. , 9809(1998).[12] J.C. Lashley, M.F. Hundley, A. Migliori, J.L. Sarrao, P.G. Pagliuso, T.W. Darling, M. Jaime, J.C.Cooley, W.L. Hults, L. Morales, D.J. Thoma, J.L. Smith, J. Boerio-Goates, B.F. Woodfield,G.R. Stewart, R.A. Fisher, and N.E. Phillips, Cryogenics , 369 (2003).[13] The phonon contribution to the specific heat of YBa Cu O , noted C ph, p ( T ), was calculatedby K.-P. Bohnen and R. Heid from the density of states determined within density functionaltheory [K.-P. Bohnen, R. Heid, and M. Krauss, Europhys. Lett. , 104 (2003)]. Knowing thatthere are 9 and 13 atoms per Y BaCuO and YBa Cu O formulas, respectively, we estimated eat Capacity and Magnetic Phase Diagram of Y BaCuO the phonon background of Y BaCuO by C php ( T ) = 9 / ∗ C ph, p (1 . ∗ T ). The factor 1.08was ajusted so that C p ( T ) ≃ C php ( T ) above 100 K, where the signal is assumed to be only ofphononic origin.[14] P. Bloembergen, Physica , 51 (1977).[15] W. Knafo, C. Meingast, K. Grube, S. Drobnik, P. Popovich, P. Schweiss, P. Adelmann, Th. Wolf,and H. v. L¨ohneysen, Phys. Rev. Lett. , 137206 (2007).[16] D. Vollhardt, Phys. Rev. Lett. , 1307 (1997).[17] For each magnetic field, (∆ C magp /T ) max corresponds to the maximal value of ∆ C magp ( T ) /T and∆ S N is obtained by integration of ∆ C magp ( T ) (Fig. 3 (b)).[18] The shape of the antiferromagnetic anomaly (Fig. 3 (b)) is characteristic of a second-order phasetransition broadened by some sample inhomogeneities. While a pure, thus non broadened, secondorder transition leads to a step-like anomaly at T N in the specific heat, the present case consistsin a broad transition where T N can be defined at the minimum of slope of C p ( T ).[19] B.J. Suh, F. Borsa, L.L. Miller, M. Corti, D.C. Johnston, and D.R. Torgeson, Phys. Rev. Lett. , 2212 (1995).[20] I.W. Sumarlin et al., Phys. Rev. B , 5824 (1995).[21] J. Villain and J. M. Loveluck, J. Phys. (Paris) , L77 (1977).[22] H.J.M De Groot and L.J. De Jongh, Magnetic properties of layered transition metal compounds edited by L.J. DeJongh (Kluwer Academic Publishers, Dordrecht/Boston/London, 1990), pp.379-404.[23] L.A. Baum, A.E. Goeta, R.C. Mercader, and A.L. Thompson, Solid. State Commun. , 387(2004).[24] H. Ohta, S. Kimura, and M. Motokawa, J. Phys. Soc. Jpn. , 3934 (1995).[25] T. Chattopadhyay, P.J. Brown, U. K¨obler, and M. Wilhelm, Europhys. Lett. , 685 (1989).[26] I.V. Golosovsky, P. B¨oni, and P. Fischer, Solid. State Commun. , 1035 (1993).[27] W. Knafo, C. Meingast, K. Grube, S. Drobnik, P. Popovich, P. Schweiss, P. Adelmann, Th. Wolf,and H. v. L¨ohneysen, J. Magn. Magn. Mater. , 1248 (2007).[28] Only 3D systems and 2D Ising systems exhibit long-range magnetic ordering at a non-zerotemperature [L.J. De Jongh, Magnetic properties of layered transition metal compounds editedby L.J. DeJongh (Kluwer Academic Publishers, Dordrecht/Boston/London, 1990), pp. 1-47]. Ifa magnetic system is purely 1D, or purely 2D Heisenberg or XY, no long-range ordering can beattained at non-zero temperature. Pure 2D XY systems correspond to a particular case, wherea topological short-range ordering can theoretically occur at aBerezinskii-Kosterlitz-Thouless temperature T BKT > ,493 (1971), J.M. Kosterlitz and D.J. Thouless, J. Phys. C , 1181 (1973)]. A magnetic entropyassociated to a transition can thus be only obtained if the system is 3D Ising, 3D XY, 3DHeisenberg, 2D Ising, or 2D XY.[29] While the phase diagram of Y BaCuO was obtained here from the specific heat, those ofBaNi V O , Sr CuO Cl , and Pr CuO were obtained from specific heat and thermal expansion[15], magnetization and NMR [19], and neutron scattering [20], respectively.[30] N. Rogado, Q. Huang, J. W. Lynn, A. P. Ramirez, D. Huse, and R. J. Cava, Phys. Rev. B ,144443 (2002).[31] To our knowledge, the magnetic susceptibility of these systems has never been measured aboveroom temperature. We note that for the quasi-2D La CuO , which belongs to the same family asSr CuO Cl and Pr CuO , a maximum of χ ( T ) occurs at about 1000 K and antiferromagneticordering is established below T N ≃
300 K [D.C. Johnston, S.K. Sinha, A.J. Jacobson, and J.M.Newsam, Physica , 572 (1988)].[32] A. Cuccoli, T. Roscilde, V. Tognetti, R. Vaia, and P. Verrucchi, Phys. Rev. B67