I have a data frame with 2 columns. I have ordered them using order() function

data<-data[order(data$Mortality),]
head(data)

                       Hospital.Name     Mortality
 FORT DUNCAN MEDICAL CENTER                      8.1
 TOMBALL REGIONAL MEDICAL CENTER                 8.5
 DETAR HOSPITAL NAVARRO                          8.7
 CYPRESS FAIRBANKS MEDICAL CENTER                8.7
 MISSION REGIONAL MEDICAL CENTER                 8.8
 METHODIST HOSPITAL,THE                          8.8

3rd and 4th positions are ties (Mortality = 8.7 for both). I want to break the tie with alphabetical order in data$Hospital.Name so that "CYPRESS FAIRBANKS" is 3rd and "DETAR HOSPITAL" as 4th.

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