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Itinerant Electron Metamagnetism M Itinerant electron metamagnetism M. Shimizu To cite this version: M. Shimizu. Itinerant electron metamagnetism. Journal de Physique, 1982, 43 (1), pp.155-163. 10.1051/jphys:01982004301015500. jpa-00209372 HAL Id: jpa-00209372 https://hal.archives-ouvertes.fr/jpa-00209372 Submitted on 1 Jan 1982 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. J. Physique 43 (1982) 155-163 JANVIER 1982, 155 Classification Physics Abstracts 75. lOL - 75.20E - 75.30C Itinerant electron metamagnetism M. Shimizu (*) Laboratoire Louis-Néel, C.N.R.S.,166X, 38042 Grenoble Cedex, France (Reçu le 10 aout 1981, accepté le 17 septembre 1981) Résumé. 2014 Les conditions rigoureuses pour les transitions métamagnétiques entre l’état paramagnétique et l’état ferromagnétique ou entre l’état ferromagnétique faible et l’état ferromagnétique normal sont déduites. Les expressions de ces conditions et celles des champs critiques sont obtenues dans un modèle simple pour un système d’électrons itinérants, et également pour un système plus complexe de moments magnétiques locaux et d’électrons itinérants. Les résultats sont appliqués à TiBe2, YCo2, Pd, à certains composés entre les métaux de terres rares et de transition, à Co(S, Se)2, etc. Ils permettent d’expliquer que TiBe2 et, sans doute, YCo2 et Pd ne présentent pas la transition métamagnétique, en accord avec les résultats expérimentaux. Abstract. 2014 Rigorous conditions for the metamagnetic transitions between the paramagnetic and ferromagnetic states and between the weak ferromagnetic and normal ferromagnetic states are derived. The expressions for the conditions and the critical field are derived in the simple model for an itinerant electron system and for a combined system of localized magnetic moments and itinerant electrons. The results are applied to TiBe2, YCo2, Pd, com- pounds of rare earth metals and transition metals, Co(S, Se)2, etc. It is explained that TiBe2 and perhaps YCo2 and Pd will not show the metamagnetic transition in consistent with the experimental results. 1. Introduction. - The metamagnetic transition up to 190 kOe [6] and 213 kOe [7]. In the cases of (MT) from the paramagnetic state to the ferromagnetic YCo2 and TiBe2 the highest fields used in experiment state by applying the magnetic field was first discussed are much higher than the values predicted by Wohl- by Wohlfarth and Rhodes [1] for the itinerant electron farth [2]. Cyrot and Lavagna [8] have also predicted model. They showed that the paramagnetic metals MT for YC02 at about 1 000 k0e, using their calculat- or alloys will show MT, if there is a maximum in the ed density of states. In our estimation from their temperature variation of the paramagnetic suscepti- calculated density of states, MT seems to be impossible bility as in Pd, or as a more strict condition, if the in YCo2. Recently, Jarlborg and Freeman [9] have coefficient a3 in the expansion of the magnetic energy E also predicted MT in Pd at 3 220 k0e from the cal- given by culation of its electronic structure under the magnetic field In this paper it is shown that the condition for MT, a3 > 0 is not complete and the previous estimations where H is the as a applied magnetic field, power of Hc are not reliable. We should include the higher series of the is defin- magnetization M, negative. They order terms at least up to the M6 term in the expan- ed the critical field for MT from the He paramagnetic sion of the magnetic (free) energy E in order to dis- state to the state the inflection ferromagnetic by point cuss MT, as shown below. It is possible that even if in the of E M as a function of H. plot against a3 0 the second minimum corresponding to the Recently, using the same definition of Hc as before, ferromagnetic state in addition to’ the first minimum Wohlfarth the [2] has predicted value of H,, for Pd, corresponding to the induced paramagnetic state and as 1 170 and 58 YC02 TiBe2 100, k0e, respecti- in the plot of E against NI does not appear even at MT has so far never vely. However, experimentally very high field when the contribution from the higher been observed for Pd to 325 k0e up [3], for YC02 order terms to E is large. The condition for MT is to 150 k0e and 380 k0e and for up [4] [5] TiBe2 more strict than a3 0. It is well-known that in the case a3 0 the paramagnetic susceptibility x increa- ses with increasing H. Therefore, the increase of x with increasing H, as observed in Pd [3], YC02 [4, 5] Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01982004301015500 156 and TiBe2 [6, 7], does not necessarily mean the occur- magnetic interaction with higher powers of M than rence of MT, although it is one of the necessary M2, the temperature dependence of the molecular conditions. field coefficient, the complicated magnetic structures, On the one hand, there are many intermetallic the distribution of the magnetic moments, etc. In the compounds of rare earth metals and transition metals, case of Co(SxSe1-.J2 compounds the distribution of e.g. RCo2 [10, 1], where R means the rare earth metals cobalt atoms with and without magnetic moment and is Dy, Ho or Er, (Ho, Y)Co2 [12], etc., which has been ascertained in experiment [16] and MT has show MT from the paramagnetic state to the ferro- been discussed in terms of the distribution of the two magnetic state and also many compounds, e.g. kinds of Co atoms with and without magnetic moment ThCo5 [13], Y2Ni16 [14], Co(S, Se)2 [15,16], (Co, Ni)S2 [24, 25]. [17], etc. show MT from the weak ferromagnetic state In section 2, general conditions for MT based on the to the ferromagnetic state with a larger magnetization. thermodynamics are shown without regard to any On the other hand, there are many alloys and rare specific model for MT. In section 3, MT between MT earth compounds which also show from the anti- a simple paramagnetic state and a ferromagnetic ferromagnetic state to the ferrimagnetic or ferro- state is discussed in the simplest model, that is, the magnetic state or from the ferrimagnetic state to the least number of terms in the expansion of the free ferromagnetic state and which show the dependence energy in a power series of M2 and the analytical on H of M very similar to the one of MT that can be expressions of the conditions for MT and of the criti- explained by the model of narrow domain wall [18]. cal fields which show a hysteresis are obtained. In In this paper we will discuss only the former case and section 4, MT between a weak ferromagnetic and will no discuss the latter case, There are review articles normal ferromagnetic states is discussed in terms of for the magnetic properties of intermetallic compounds the least number of terms in the expansion of the of rare earth metals and transition metals [10, 19-21]. free energy and the conditions for this kind of MT and Especially, in some of RC02 compounds, ErCo2, the critical fields are obtained. In section 5, from the HoCo2 and DyCo2 the first-order transition was experimental results of the field dependence of M observed [10, 11, 22] and MT was observed only in a for TiBe2, YC02 and Pd the values of the coefficients very narrow temperature range, 5 - 10 K [10, 11 ]. in the expansion of the free energy with respect to M The first-order transition, which corresponds to the are estimated and the conditions for MT are examined. case He = 0 in MT, in these compounds was quali- It is concluded that TiBe2 will not show MT and for tatively explained by the combined model of the Pd and YC02 it is very difficult to predict whether localized magnetic moment on R atoms and itinerant they show MT or not from our present knowledge electrons on Co atoms or the so-called s-d model [4], for the dependence on H of M. Even if it exists it where the expansion of free energy with respect to M occurs at very high fields higher than 325 kOe for Pd only due to the itinerant electrons was taken into and 380 kOe for YC02- In section 6, the reason for the account. Recently, it has been pointed out that the occurrence of the variety of MT in various rare earth expansion of the magnetic free energy with respect compounds and the character of MT are discussed and to the total magnetization given by the sum of the some conclusions are given. - magnetization due to the localized moments and that due to the itinerant electrons is very important to 2. General conditions for the metamagnetic transi- discuss the first-order transition and to derive this tion. - The magnetic free energy f can be given as a transition temperature [23]. This expansion of the function of the temperature T, the volume V, the free energy with respect to the total magnetization concentration c, if necessary, and the magnetization M is also very important to discuss MT in various kinds of a metal, alloy or compound.
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