Magnetic-field-induced transition from metastable spin glass to possible antiferromagnetic-ferromagnetic phase separation in C d 0.5 C u 0.5 C r 2 O 4
Li-qin Yan, Wen Yin, Ferran Maciá, Jun-rong Zhang, Lun-hua He, Fang-wei Wang
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J a n Magnetic-field-induced transition from metastable spin glass to possibleantiferromagnetic-ferromagnetic phase separation in Cd . Cu . Cr O Li-qin Yan, ∗ Wen Yin, Ferran Maci´a, Jun-rong Zhang, Lun-hua He, and Fang-wei Wang National Laboratory for Condensed Matter Physics,Institute of Physics, Chinese Academy of Sciences, Beijing 100080,China Departament de Fsica Fonamental, Facultat de Fsica, Universitat de Barcelona,Avda. Diagonal 647, Planta 4, Edifici nou, 08028 Barcelona, Spain (Dated: November 13, 2018)Using ac susceptibility, dc magnetization and heat capacity measurements, we have investigatedthe magnetic properties of Cd . Cu . Cr O . Cd . Cu . Cr O has an extraordinary magneticphase including a metastable spin-glass(SG) phase at zero field, a possible phase separation scenarioof AFM/FM above ∼ . T field, and at intermediate fields, an apparent pseudo reentrant spin-glass(RSG) plateau is observed. These phenomena are closely correlated with the pinning effect of the Cu sublattice on the frustrated lattice. PACS numbers: 75.50.Lk, 75.30.Kz, 75.50.Ee
I. INTRODUCTION
The notion of a geometrically frustratedantiferromagnet has attracted considerable inter-est over the past more than one decade. In its simplestform, a lattice geometry results in frustration of theantiferromagnetic (AFM) exchange interaction. Suchmaterials are characterized by the absence of longrange order at temperatures well below the Curie-Weiss temperature (Θ CW ), and have very unusual lowtemperature properties . An interest-ing feature of the system is the release of magneticfrustration. Normally, the magnetic frustration canbe eliminated or removed by spin-Peierls transitionat T N arising from the spin-lattice coupling or anapplied high magnetic field at low temperature . Theoretically, the vast degeneracy of their classicalground states makes them be highly susceptible even tosmall perturbations. A separate phase transition into anAFM state is expected .Experiments have shown thatby means of replacing the nonmagnetic-site partiallyby magnetic ions, a local preferential direction will beimposed in frustrated lattice, removing somehow thestrong intrinsic magnetic frustration and presentinga geometric spin-glass(SG) state . Note that thepresence of the disorder coming from either the sitedisorder or the competing interaction between AFM andferromagnetism (FM), often generates a conventionalSG state. In systems which possess disorder and highlygeometric frustration often display some unconventionalSG behavior, usually named as geometrical SG. If so,then a subtle balance between them, i.e., disorder andgeometric frustration, will bring about an unusual SGstate. The views on the nature of the freezing of thisSG, whether it is a phase transition or a non equilibriumphenomenon, are still controversial. And it is unclearhow it will evolve under a small perturbation providedthat it is a nonequilibrium SG. Understanding thenature of such a SG state is regarded as an important physics issue from theoretical and experimental pointsof view . CdCr O is a classical frustrated antiferromagnet, inwhich the magnetic Cr ions are on three dimensionalcorner-sharing tetrahedral sublattices, which results ingeometrical frustration of the AFM nearest neighborexchange interactions ( T N , 7.8 K) . It undergoesa first-order three-dimensional spin-Peierls transition at T N from a cubic paramagnetic to a tetragonal Nel state ;Low-temperature neutron powder diffraction showed thepresence of spiral AFM spin structure and muon-spin-relaxation measurements (mSR) indicated that substan-tial magnetic frustration still remains at the millikelvintemperatures . In this paper, we report on the SG stateof a high-quality polycrystalline Cd . Cu . Cr O withmagnetic ions Cu half doped revealed by ac suscepti-bility, dc magnetization and heat capacity measurements.We demonstrate for the first time that the ground-state iswell characterized in a metastable SG state at zero fieldand a possible magnetic phase separation of AFM/FMunder a magnetic field as the ground-state degeneracy isbroken. II. EXPERIMENT
The preparation, crystal structure and the primarymagnetic property of Cd . Cu . Cr O in present studyhave been well described and characterized by previ-ous experimental measurements . All magnetizationand heat capacity measurements were performed using aPhysical Property Measurement System (Quantum De-sign). Data were collected upon warming after coolingthe samples at zero field. Specific-heat measurementswere done in a thermal relaxation method. III. RESULTSA. Structure and fundamental magnetic property
The crystal structure of Cd . Cu . Cr O has a cu-bic spinel space group F d m , which consists of two ba-sic units, Cd/CuO tetrahedron and CrO octahedron.There are at least two main kinds of magnetic interac-tions in Cd . Cu . Cr O , the nearest-neighbor Cr-Crinteraction and the next nearest-neighbor Cu-Cr inter-action, according with reentrant SG (RSG) characterwhere only the first and second nearest-neighbor inter-actions are important in RSG materials . The Cu-Crand Cd-Cr bonds are not uniformly distributed due toA-site random distribution. Clearly, upon substitutionof Cd by magnetic Cu ions, the competition betweenthe Cu-Cr and Cr-Cr interactions causes spin arrange-ments transfer from AFM to ferrimagnetic and the ge-ometrical frustration turns to be suppressed . Thusthe Cu magnetic sublattice is extracted with ferro-magnetic coupling, similar to that of tetrahedral spinel CuCr O , where the magnetic moment of the Cu sublat-tice is ferromagnetic coupling, antiparallel to the resul-tant Cr sublattice one . Previous ZFC magnetic studyat 0.1T indicated that Cd . Cu . Cr O experiences aparamagnetism(PM)-ferrimagnetism(FI)-SG (RSG) liketransition ( T c , 20K; T g , 8K). At the same time, its indexof frustration ( f = | Θ cw /T N | ) varies from 10 to 1, whichmight be attributed to the interaction between Cu sublattice and Cr sublattice, namely, the pinning ef-fect of sublattice Cu on magnetic frustration (or spiralAFM configuration) excites a local preferential direction,similar to Mn-rich Y M nO and SrCr Ga − x F e x O series . B. Metastable spin glass
Figure 1 shows the temperature dependence of ac sus-ceptibility data in a frequency range of 33 ω/ π Hz under ac field of 1Oe for Cd . Cu . Cr O . Thecurves display a maximum at a temperature T f , whichshifts with (increasing) frequency upwards for χ ′ ( ω, T )and downwards for χ ” ( ω, T ). This is a distinct featureof a SG state . The value of the frequency sensitivityof T f ( ω ),∆ T f ( ω ) / [ T f ( ω )∆ log ω ], has been a criterionfor the presence of a canonical SG from SG like . It isabout 0.013 for χ ′ ( ω, T ), lower than those reported forother typical insulating SG systems, indicating an uncon-ventional SG transition. However, it is about 0.025 for χ ” ( ω, T ), close to that of conventional SG. . We knowthe out-of-phase χ ” , is the magnetic energy loss, some-times reflecting certain information that is drown or notobvious in the in-phase χ ′ ( ω, T ). The different extractedparameters for χ ′ ( ω, T ) and χ ” ( ω, T ) appear to reflectthat this unusual SG in Cd . Cu . Cr O is made bymore than one component. The divergence of the maxi- -3.5 -3.0 -2.5 -12-10-8-6 0 20 400369 L n τ Ln[(T f -T SG )/T SG ] x=0.5 χ '' ( e m u / m o l ) χ ' ( e m u / m o l ) Temperature(K) T f2 T f1 T(K) M ( e m u / g ) FIG. 1: (Color online) χ ′ ( ω ) and χ ” ( ω ) vs T for ω/ π =33,333,777,3333,7777,9999 Hz[top to bottom for χ ′ and bot-tom to top for χ ” ]. The left inset displays the measured freez-ing temperatures T f ( ω, T ), T f ( ω, T ) and the best fitted lineby Eq.(1) for χ ′ and χ ” . The right inset shows the tempera-ture dependence of ZFC (closed circles) and FC (open circles)magnetization for Cd . Cu . Cr O compound under variousmagnetic fields of 0.01, 0.05, 0.1, 0.5 T. The arrow indicatesthe direction of increasing field. mum relaxation time τ max , occurring at the peak temper-ature, can be investigated by using conventional criticalslowing down: ττ = ξ − zν = (cid:18)(cid:18)(cid:18) T f ( ω ) − T SG T SG (cid:19)(cid:19)(cid:19) − zν (1)here, T SG is the SG phase transition temperature and T f and T f , defined as the maxima of the in-phase and out-of-phase ac susceptibility, respectively, are the frequency-dependent freezing temperatures at which the maximumrelaxation time of the system corresponds to the mea-sured frequency. The left inset of Fig.1 presents a bestfit to the data. When τ is 10 − s typically taken inthe SG system, T SG and zν for χ ′ ( ω, T ) are 15.90 K and zν = 6.08, respectively, whereas, for χ ” ( ω, T ), a goodscaling yields T SG = 13.15 K and zν = 7.80. z and ν are critical dynamics exponents. Although the T SG and zν values of χ ′ ( ω, T ) and χ ” ( ω, T ) are slightly different,their magnitudes of zµ are within the conventional SGphase transition .It is reminiscent that the appearance of RSG-likeplateau in M-T curve of our previous study may beinduced by an applied dc magnetic field since no RSGplateau is observed in the in-phase χ ′ ( ω, T ) as well as out-of-phase χ ” ( ω, T ). This assumption is further confirmedby the temperature dependence of the zero-field-cooled(ZFC) and field-cooled (FC) magnetizations curves from2 to 300 K in various fields of 0.01-0.5 T (see the right in-set of Fig. 1). The cusp of ZFC magnetization at 0.01 Tcoincides well with the cusp seen in the lowest frequencyac susceptibility measurement (33Hz). The FC and ZFCmagnetization curves separate at around 17 K and 0.01T, then the cusp temperature decreases monotonicallywith increasing applied field, together with a formationof a pseudo RSG plateau (see the ZFC curves at 0.05and 0.1 T). Clearly, applying magnetic field in the SGstate produces a reduction in this SG phase and an in-crease of magnetic ordered phase. This transition canbe considered as a metastable SG to magnetic orderingtransition up to 0.5 T and the superposition of ZFC andFC is observed. C. Magnetic-field-induced possible AFM/FMphase separation behavior
1. Magnetic field dependence of ac susceptibility
Figure 2 shows the ac susceptibility χ ′ ( ω, T ) and χ ” ( ω, T ) for 333Hz, in different superposed dc fields andac field of 1Oe. Both χ ′ ( ω, T ) and χ ” ( ω, T ) are sup-pressed drastically at the dc fields. An applied fieldrounds the peak off and broadens it to a plateau state,then enters it into a double peak structure for χ ′ ( ω, T )(see the left inset of Fig. 2). Obviously, applying adc field, the SG phase is suppressed and ordered mag-netic clusters are induced. Whereas χ ” ( ω, T ) is differentfrom the double peak structure of χ ′ ( ω, T ), the peaks aresmeared out in amplitude and shift downwards (see theright inset of Fig.2), showing a characteristic feature of aconventional SG . With increasing magnetic field, thetwo maxima in χ ′ ( ω, T ) shift toward opposite directions,implying a possible magnetic phase separation system.Normally, the transition on the high temperature side isascribed to a formation of field-induced grown size FMclusters embedded in a SG matrix while the transi-tion on the low temperature side is a conventional SGtransition. The formation of FM clusters in a SG matrixshould arise from the field-induced stepwise connection ofsmall short-range-ordered clusters along the local prefer-ential direction of magnetic ordering. Once it is a trueSG transition on the low temperature side, the dc fielddependence of the freezing temperature T f ( H ) should bescaled by the equation T f ( H ) = 1 − bH δ (2)with δ = 2 / .Figure 2(b) plots the experimental values of T f ( H ) for χ ′ ( ω, T ), T f ( H ) for χ ” ( ω, T ), and the fitted curves toEq.(2).The fitted values of the exponent δ are 0.186 for χ ′ ( ω, T ) and 0.023 for χ ” ( ω, T ), which is far lower thanthe typical SG value 2/3. It thus turns out that the phasetransition on low temperature side is not a conventionalSG transition. It is speculated that this transition shouldbe dominated by the geometrical SG, which is closelyrelated to AFM transition in the frustrated lattice. T f ( K ) µ H(T) T f1 T f2 (b) x=0.5 H Oe50002000100050035020020 0 χ ' ( e m u / m o l ) T(K) χ '' ( e m u / m o l ) T(K) χ ' ( e m u / m o l ) Temperature(K) (a)
FIG. 2: (a) Temperature dependence of in − phase ac suscep-tibility measured at a frequency of 333 Hz under differentapplied dc fields. The right inset presents the correspondingout − of − phase ac susceptibility. The left inset shows a mag-nification of the in − phase ac susceptibility for dc fields µ H = 0.1, 0.2, 0.5 T. (b) The experimental T f ( H ) values and thefitted data to Eq.(2).
2. Magnetization curve at 2K
According to the above ZFC and FC measurements,the superposition of ZFC and FC curves takes place at µ H > . T , implying that a completed SG-magneticordering transition can be achieved. If dc field leadsto a complete transition of SG-ferro(-ferri)magnetic or-dering, the magnetic moment should be saturated inhigh field. However, it is not the case. The insetof Fig. 3(a) presents the original magnetization curveat 2 K. It is obviously hard to saturate and the fullsaturation state is not achieved even under a field of13 T, indicating an existence of intrinsic AFM order.The absences of saturation at 13 T and S-type fea-ture can be correlated with the AFM/FM phase sepa-ration scenario. The magnetic contribution from ferro(-ferri)magnetic and AFM parts is fitted by a linear leastsquare method, which leads to M ferro = 0 . µ B /f.u. derived from the ferro(-ferri)magnetic lattice part. Thisabsolute value of M ferro is larger than the expected sat-uration moment µ s ∼ . µ B /f.u. for the parallel Cu ratio at 13 T and 2 K, implying an additive magnetic con-tribution ∼ . µ B /f.u. parallel to Cu magnetic mo-ment. This additive magnetic moment should originatefrom the local preferential direction in the Cr tetrahedronamong the field-induced FM clusters. We have herebyconcluded that the magnetic field induces the transitionof metastable SG into not only FM clusters but also AFMphase. This transition exhibits a possible phase separa-tion of AFM/FM corresponding to the transition at the“double peak structures” in the ac susceptibility mea-surement under dc fields.
3. Magnetic entropy changes from isothermalmagnetization measurements
In order to get an insight into this scenario we carriedout the measurements of the isothermal magnetizationcurves in the temperature range of 5 −
50 K and mag-netic fields up to 5.0 T (see Fig. 3(a)). The temperaturestep of 3 K was chosen. The behavior of the isothermsdiffers from the typical SG and ferromagnetic behaviors.As the temperature is decreased the M vs H curve bendsmore, but neither sign of saturation nor S-type behavioris present. Fig. 3(b) shows the Arrot plots obtained fromthe magnetization isotherms. A considerable curvatureabove 17 K is observed as a sign of disordered system .There is a positive small intercept at 5-14 K and lowfields, suggesting that the system exhibits rather a weakmagnetization than a conventional SG. The data takenat high fields can be fitted by straight lines. Extrapolat-ing these lines at temperatures between 5 and 14 K, apositive intercept with the M axis is reached, indicat-ing a field-induced magnetic order alignment. Magneticentropy change versus temperature is shown in Fig. 3(c).Two peaks can be observed at ∼
11 and ∼ K at µ H = 0 . | ∆ S M | around T AF M is one of the features of first order phase transitions. Onthe other hand, the | ∆ S M | peak on the high temperaturerange is broadened and high fields shifts the Curie tem-perature several degrees from around 21 K to 24 K, im-plying now a continuous second ordering FM transition,in agreement with the above result from ac susceptibilityunder dc field. Consequently, we conclude that the lowtemperature transition ( ∼ K ) is the metastable SG-AFM ordering while the high temperature one ( ∼ K )is the metastable SG-FM clusters.
4. Heat capacity measurement
To further confirm the scenario discussed above, themeasurements of the heat capacity have been performedunder the fields of µ H = 0 T, and 0.5 T (see Fig. 4) .One advantage of this insulating system is the lack ofan electronic contribution to the specific heat.The de- -2 -1 0 1 2 3 4 5 605101520
2K AFMFM M ( e m u / g ) µ H(T) M ( µ Β / f . u . ) µ Η(Τ) (a) M ( e m u / g ) µ H/M(T.g/emu)
5K 50K(b) - ∆ S ( J / k g . K ) Temperature(K) (C)
FIG. 3: (Color online) (a) Magnetic field dependence of themagnetization of Cd . Cu . Cr O at various temperaturesof 5 −
50 K. The inset presents the magnetization curve at 2 Kand AFM/FM moment contributions fitted by a linear leastsquare method. (b) The corresponding Arrott plot. (c) Tem-perature dependence of the entropy changes for the magneticfield difference from 0 to 0.1, 0.2, 0.5, 1, 2, 3, 4, 5 T. The linesare only guides for eyes. pendence of C on temperature nearly accords with the C m ∼ T law at zero field and low temperatures (thebottom inset of Fig.4), which is similar to geometri-cally frustrated SG systems, such as the spinel lattice and kagome lattice . Furthermore, a character of con-ventional SG state is observed through a broad max-imum of C/T at about 25 K instead of an anomalyat the freezing temperature 17 K at zero field. Thesetwo features indicate an unusual metastable SG state in Cd . Cu . Cr O . No distinct two peaks are observedin the specific heat curve under a field of 0.5 T. Onlya knee development is found at ∼
25 K. However, themagnetic entropy change ∆ S heat at µ H = 0 . C p / T ( J / K g . K ) Temperature(K) C ( J / K g . K ) T (K ) - ∆ S ( J / K g . K ) T(K)
FIG. 4: (Color online) Temperature dependence of the heatcapacity of Cd . Cu . Cr O measured under the fields of µ H = 0 T, and 0.5 T. For clarify, the data for µ H = 0is shifted up 0 . J/Kg.K . The top inset plots the entropychange from heat capacity measurements with the magneticfield changes from 0 to 0.5 T. The bottom inset depicts thetemperature dependence of C deviated from the C m ∼ T law in zero field. Fig.4) exhibits the corresponding double peak structureto ∆ S mag , further confirming the possible landscape ofAFM/FM phase separation under an external magneticfield. IV. DISCUSSION
Combining our results with the introduction men-tioned before, it is already clear that for A-site Cu half doped CdCr O , a metastable SG at zero dc field isemergent. The formation of the metastable SG groundstate in Cd . Cu . Cr O is closely pertinent to the mag-netic interaction between Cu sublattice and Cr sublat-tice. Half number of Cd atoms substituted by Cu in-troduces a magnetic moment that increases not only themagnetic interaction between Cu sublattice and Cr sub-lattice but also the probability of the local CrO octahe-dron distortion. The large ionic radii difference between Cu ions(0 .
72 ˚ A ) and Cd ions (0 .
97 ˚ A ) results in AO tetrahedron distortion or a local crystal distortion, whichfavors the off − center of Cr ions via oxygen atom dis-placement. Thus the geometrical frustration tends torelease due to the variation of local Cr − Cr bond length. This is a benefit for the pinning effect of Cu sublatticeon Cr sublattice. The Cu − Cr interaction would imposea “preferential direction” for the orientation of the spinsand therefore, two SG components, namely, conventionalSG, which arises from site disorder or magnetic interac-tions competition, and geometrical SG, which is from thesubstantial geometrical magnetic frustration, would ap-pear. A subtle balance between them would produce ametastable SG state.Applying a magnetic field this balance is destroyed anda transition from metastable SG to possible AFM/FMphase separation is induced. This phenomenon is alsoclosely correlated with the pinning effect of the Cu sub-lattice on a frustrated lattice. The magnetic frustrationarises from the Cr ions, arranged in a corner − sharingtetrahedral lattice (pyrochlore lattice) while the Cu sublattice, interacting ferromagnetically, would pin itssurrounding magnetic frustration to a preferential direc-tion somehow, exhibiting a metastable SG state. Undera magnetic field the pinning effect will be enhanced andthe disorder will become weaker, i.e., the balance betweenthe geometrical SG and conventional SG will be broken,exhibiting AFM/FM phase separation. V. CONCLUSIONS
As a whole, our experimental results provide a mag-netic landscape of Cu ions half doped CdCr O . Cu intermediate substitution for Cd ions suppressesthe magnetic frustration by imposing a local preferentialdirection in Cr tetrahedron. The subtle balance state be-tween the pinning interaction and substantial frustrationmanifests a metastable SG behavior. An applied mag-netic field induces a transition from this SG phase to apossible AFM/FM phase separation state. This newly Cu doped CdCr O material will enable the in-depthstudy on the rich physical properties of magnetic frustra-tion compounds. Acknowledgments
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