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Thermal magnetic noise in magnetoresistive read heads was studied extensively in recent years. It is believed that thermal magnetic noise is becoming the dominant noise source in read heads for hard-disk drive applications. Most previous work concentrated on magnetic white noise from free layers. This work shows that magnetic noise from a synthetic antiferromagnet can be comparable to that from a free layer in tunneling read heads for current and future hard-disk drives. An analytical model is established for thermal magnetic noise based on the single domain particle assumption. The model agrees well with results from a full micromagnetic model. This indicates that magnetic thermal fluctuations in current tunneling heads are close to being coherent.