A Unified Model For Exchange Bias And Exchange Spring

Many advanced magnetic devices rely on exchange bias and exchange spring,which get a lot of attentions in the theoretical and experimental studies.When the ferromagnet/antiferromagnet system is cooled below the antiferromagnetic Neel temperature,the hysteresis loop of the system is no longer centrosymmetric about the applied field.This phenomenon is called exchange bias.Since the exchange bias phenomenon was discovered,it has been extensively studied and discussed.But,due to the complexity of the interface structure,exchange bias can't be thoroughly analyzed and understood.On the other hand,the magnetic behavior displays the spring-like characteristic with the applied field,that is,exchange spring,which usually occurs in soft/hard heterostructures,producing a giant energy product.The ferromagnet/antiferromagnet system and the soft/hard heterostructure have many similar features.However,exchange bias and exchange spring are investigated separately.This paper,for the first time,proposed a unified model for exchange bias and exchange spring,which takes the domain wall into account and can calculate hysteresis loop,exchange bias field and coercivity,consistent with the related experiments.Numerical and analytical results show that the inverse relationship between exchange bias field and ferromagnetic thickness will be broken.More importantly,a simple method is proposed to calculate the magnetic phase diagrams for the soft/hard and ferromagnet/antiferromagnet film systems.The magnetic phase diagram of the ferromagnet/antiferromagnet bilayers includes two bias phases(reversible exchange bias and irreversible exchange bias)and three non-bias phases(rigid composite magnet,decoupled magnet and exchange spring).With the increases of the interface exchange coupling,two bias phases will shrink in the magnetic phase diagram until they disappear,while the exchange spring region expands.On the other hand,theoretical calculations indicate that the ferromagnet/antiferromagnet systems are similar to the soft/hard heterostructures,which can achieve a giant energy product.