Anomalous magnetic thermodynamics in uncompensated collinear antiferromagnets

Monte Carlo simulations show that the net magnetization of collinear antiferromagnets (AFM) with uncompensated surfaces exhibits a unique thermodynamic behavior, with a temperature dependence unlike that of ferromagnets or of the Néel vector. The magnetization of AFM is not equal to that of its surface, even though it results from surface effects. This phenomenon appears in thin AFM films but is valid even in the limit of semi-infinite systems. The net magnetization of AFM therefore corresponds to a distinct topological thermodynamic state due to the free surface. Copyright c © EPLA, 2014 Introduction. – Since their discovery [1,2], antiferromagnets have attracted immense attention due to their unique magnetization properties. Like ferromagnets (FM), antiferromagnets (AFM) exhibit a spontaneous long-range ordering of the atomic spins below the Néel temperature (TN), but unlike FM, the spins order antiparallel, and cancel each other out, and the net magnetization of a perfect AFM is zero. If, however, there are defects, such as vacancies, grain boundaries, or surfaces, AFM can have a small uncompensated magnetization. As a specific manifestation of this effect, when an AFM film has an odd number of atomic planes along the Néel vector, i.e., the axis of antiparallel alignment, the spins are not fully compensated and the AFM will exhibit a non-zero net magnetization because of the uncompensated surface [1]. In this paper we will show, using Monte Carlo simulations (MC), that the magnetization of AFM as a function of temperature shows a behavior which is strongly different from that of the Néel vector, that of a ferromagnet, or even that of the surface, despite the fact that the AFM magnetization only exists because of the uncompensated surface. Numerical methods, such as Monte Carlo simulations, allow a unique and straight-forward approach to model magnetic systems. The thermodynamic behavior, in particular the critical region of phase transitions, of FM thin films has been studied extensively (see for example refs. [3–6]). Pioneering works of Binder, Hohenberg, and Landau showed how the modification of exchange interactions at surfaces can strongly affect the magnetic ordering in systems with free surfaces [7–13]. When the pairwise exchange interaction between spins on the surface is the same as that between spins in the core of the film, the system undergoes an ordinary phase transition [14,15] at the critical temperature and the magnetization on the surface is weaker because spins at the surface have fewer neighbors. When, however, the exchange at the surface is stronger, possibly due to the reduction of the crystal field [16] or the enhanced of single-site spinorbit coupling [17], the thermodynamic behavior changes drastically [18]. When the surface exchange is strong enough to overcompensate for the missing neighbors, then the system undergoes an extraordinary phase transition [14,15], where the surface orders at a higher temperature and has a magnetization which is stronger than in the core of the film. The properties of the surface are therefore crucial for the thermodynamic behavior of low-dimensional systems. For example, EuTe(111) films exhibit strongly reduced magnetization near the surface of the film [19], whereas the magnetization of NiO(111) and NiO(100) films is stronger at the surfaces, and the surface order persists even above the TN of bulk NiO [17,20]. Moreover, KMnF3(110) [21] and MnO(001) [22,23] surfaces exhibit ordering at temperatures that are twice as high as the TN of the bulk counterparts. Monte Carlo simulations used to calculate spin-spin correlation functions showed this is possible